Patent Publication Number: US-2015078660-A1

Title: Management Method of Color Data of Chromatic Image

Description:
TECHNICAL FIELD 
     The invention relates to the input and output processing technology of chromatic images, and in particular to the technology for achieving color consistency between input and output chromatic images. 
     BACKGROUND ART 
     Along with the development of the computer science and the color input and output technology, the chromatic image, as an information carrier, has been more and more widely applied in multiple fields such as printing, screenage, advertising, film and television, electronic commerce, and digital entertainment, and the people also have higher and higher demands for the color reproduction quality. But due to the impacts of the factors such as the imaging mechanism, the color space, the element performance, the consumptive material characteristic, and the machining accuracy, the difference between the chromatic characteristics of the input and output devices is very significant, which makes it possible that a color deviation occurs when a cross-medium or cross-platform display of the chromatic image is performed. 
     For example, cameras of different brands produced by different manufacturers are used to shoot the same scene at the same time and at the same place. Due to the element performances and the consumptive material characteristics of the camera devices themselves, a color deviation occurs when the images of the pictures taken by the two cameras are displayed on the computer. That is to say, if the picture of the same scene is taken by different cameras, different color effects may be displayed on the computer. 
     Another example is that if the same picture stored in the computer is printed using printers of different brands produced by different manufacturers, different printing effects may occur, and two printed images with a color deviation are presented. 
     In order to remove the color deviation phenomenon caused by the device to achieve the object “what you see is what you get”, ICC (International Color Consortium) introduces a color space model (CIELab color space model) independent of the device to uniformly describe the chromatic characteristics of the device, performs a nonlinear correction by means of a gamut mapping and a relationship between the input and the output of the device, establishes a color mapping relationship with the relevant color space (RGB, CMY, etc.) of the device, and achieves an accurate conversion of color information from the input device to the color space independent of the device and then to the color space of the output device. 
     But the CIELab color space model adopted in the prior art is a color space model based on an opponent color space model, and the basis of dependency thereof is that red and green serve as the a axis of CIELab, yellow and blue serve as the b axis of CIELab, black and white serve as the L axis of CIELab, and the three axes a, b, L are perpendicular to one another. This basis of construction of the model just decides that CIELab has an nonuniformity, i.e., the perpendicular setting of the red and green axes to the yellow and blue axes makes the red-yellow hue difference, the yellow-green hue difference and the green-blue hue difference be forcibly set to 90 degrees. As we all know, according to the Munsell color space model recognized as the most uniform one, the hue difference among red (5R), green (10G) and blue (10B) is substantially 120°, and yellow (10YR) is between red (5R) and green (10G) and the difference among the three colors is 60°, so the construction of the CIELab color space model has a comparatively large nonuniformity, so that the color of the converted chromatic image based on the CIELab color space model also has a comparatively large nonuniformity. 
     The CIELAB color space and the color space and color appearance space JCh based on CIELAB all have the following defects: 
     1. The color adaptation and transformation are inaccurate;
 
2. The hue is nonuniform, in particular in the blue area, the Iso-hue plane is a complicated curved surface, and the curved surface equations at different hues are different; and the hue of HGlCl takes on a distribution similar to the Munsell hue ring, which is a recognized uniform hue distribution, and the Iso-hue plane is an absolute plane;
 
3. The luminance and chrominance are not independent.
 
     The HSaIn color space and the color appearance space based on HSaIn have the following advantages of overcoming the defects of the CIEALB color space: 
     1. The Iso-hue plane is a plane passing through the HSaIn gray axis, and the hue angle is unique in the system of polar coordinates, so that it becomes possible that the color gamut transformation undergoes a one-dimensional change within the Iso-hue plane, and the color gamut mapping takes on a simple and accurate one-dimensional change;
 
2. The luminance In, the chromatic vector  , and the gray Gl are all orthogonal to the hue, so that the one-dimensional color gamut mapping is simple and feasible.
 
     In addition, when converting the chromatic image of the input device into a chromatic image based on a CIELab color space model, the calculating method is complicated, which renders the low conversion efficiency. The conversion of the chromatic image based on the CIEXYZ color space model of the input device into a chromatic image based on the CIELab color space model can be specifically performed according to the following formulae: 
     
       
         
           
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     In the above formulae, X 0 , Y 0  and Z 0  are respectively the color deviation data of the input device, and X, Y and Z are the color data of the chromatic image based on the CIEXYZ color space model of the input device; L, a and b are the data of the pixels of the converted chromatic image based on the CIELab color space model. 
     It can be seen from the above formulae that there are several calculations of extracting a cube root, and on the contrary, there will be several calculations of obtaining a third power in the calculating process of the chromatic image based on the CIEXYZ color space model; further, it will be more complicated if the calculation for conversion is directly performed at the CIELab color space model and at the RGB color space model in the physical space by stepping over the CIEXYZ color space model. Thus, the method of the prior art is comparatively complicated in the calculating and is low in the conversion efficiency. 
     Further, the conversion formulae of CIELab and XYZ in the above formulae are results concluded by means of a test fitting, and thus will bring calculation errors in the image input, processing and output with high accuracies, which renders the low accuracy of the chromatic color data obtained by calculation comparatively. 
     To sum up, the method of adopting the CIELab color space model to remove such color deviation phenomenon caused by the device in the prior art will make the color of the converted chromatic image based on the CIELab color space model also have a comparatively large nonuniformity; further, the calculating method is comparatively complicated, which renders the low conversion efficiency, the low conversion speed, and the low accuracy of the result obtained by calculation. 
     SUMMARY OF THE INVENTION 
     The embodiments of the invention provide a management method of color data of a chromatic image, which has a better uniformity and is simple in calculation. 
     According to one aspect of the invention, a method of managing color data based on color data in an HSaIn format in an HSaIn color space is provided, the method comprising: acquiring color data in an XYZ format at an input device side; converting the acquired color data in the XYZ format at the input device side into color data in an HSaIn format. 
     According to another aspect of the invention, a method of managing color data based on color data in an HSaIn format in an HSaIn color space is provided, the method comprising: acquiring color data in an HSaIn format; converting the color data in the HSaIn format into color data in an XYZ format at an output device side. 
     In the above two methods provided by the invention, the HSaIn color space is a color space based on a CIEXYZ Cartesian color space, of a color appearance attribute, and described by a cylindrical coordinate system, and is composed of a chromatic plane and a gray axis passing through the origin of the chromatic plane and perpendicular to the chromatic plane; 
     wherein the chromatic plane is a plane of the CIEXYZ Cartesian color space X+Y+Z=K, where K is a real constant; an XYZ axis of the CIEXYZ Cartesian color space performs a projection along a direction of a straight line X=Y=Z on a plane X+Y+Z=K to obtain three projection axes that are 120° with respect to one another within the chromatic plane, and unit vectors in the directions of the projection axes are  ,   and  ;
 
wherein the gray axis is a number axis composed of the straight line X=Y=Z of the CIEXYZ Cartesian color space, a numerical value on the number axis represents a gray Gl value in the HSaIn color space, a length of a chromatic vector parallel to the chromatic plane represents a chromatic Cl value in the HSaIn color space, and a polar angle of the chromatic vector represents a hue angle H in the HSaIn color space;
 
wherein the color data in the HSaIn format is in a format of the color data in the HSaIn color space, and comprises a hue H, a saturation Sa, and an intensity In in the HSaIn color space.
 
     According to another aspect of the invention, a method of managing color data based on color data in an HSaIn format in an HSaIn color appearance color space is further provided, the method comprising: acquiring color data in an XYZ format in a CIEXYZ color space at an input device side; converting the acquired color data in the XYZ format into color data in an XYZ format in a CIEXYZ color appearance color space; converting the color data in the XYZ format in the CIEXYZ color appearance color space into color data in an HSaIn format in an HSaIn color appearance color space at the input device side. 
     According to a further aspect of the invention, a method of managing color data based on color data in an HSaIn format in an HSaIn color appearance color space is provided, the method comprising: acquiring color data in an HSaIn format in an HSaIn color appearance color space at an output device side; converting the color data in the HSaIn format in the HSaIn color appearance color space into color data in an XYZ format in a CIEXYZ color appearance color space at the output device side; converting the color data in the XYZ format in the CIEXYZ color appearance color space into color image data in an XYZ format at the output device side. 
     In the above two methods provided by the invention, the HSaIn color appearance color space is a color space based on a CIEXYZ Cartesian color appearance color space, of a color appearance attribute, and described by a cylindrical coordinate system, and is composed of a chromatic plane and a gray axis passing through the origin of the chromatic plane and perpendicular to the chromatic plane; 
     wherein the chromatic plane is a plane of the CIEXYZ Cartesian color appearance color space X+Y+Z=K, where K is a real constant; an XYZ axis of the CIEXYZ Cartesian color appearance color space performs a projection along a direction of a straight line X=Y=Z on a plane X+Y+Z=K to obtain three projection axes that are 120° with respect to one another within the chromatic plane, and unit vectors in the directions of the projection axes are  ,   and  ;
 
wherein the gray axis is a number axis composed of the straight line X=Y=Z of the CIEXYZ Cartesian color appearance color space, a numerical value on the number axis represents a gray Gl value in the HSaIn color appearance color space, a length of a chromatic vector parallel to the chromatic plane represents a chromatic Cl value in the HSaIn color appearance color space, and a polar angle of the chromatic vector represents a hue angle H in the HSaIn color appearance color space;
 
wherein the color data in the HSaIn format is in a format of the color data in the HSaIn color appearance color space, and comprises a hue H, a saturation Sa, and an intensity In in the HSaIn color space.
 
     According to another aspect of the invention, a method of managing color data between a color space of a device and a CIEXYZ Cartesian color space is provided, the method comprising: 
     acquiring color data of a chromatic image of a chromatic scene from an input device; converting the acquired color data into color data in an XYZ format at an input device side according to color characteristic data of the input device. 
     According to a further aspect of the invention, a method of managing color data between a CIEXYZ Cartesian color space and a color space of a device is provided, the method comprising: acquiring color data in an XYZ format; converting the acquired color data in the XYZ format into color data in an image format in a color space of an output device according to color characteristic data of the output device. 
     According to a further aspect of the invention, a method of performing a mapping based on color data in an HSaIn format between a color gamut of an input device and a color gamut of an output device is further provided, the method comprising: 
     acquiring the color data in the HSaIn format at the input device side;
 
mapping the color data in the HSaIn format at the input device side according to a mapping relationship between the color gamut of the input device and the color gamut of the output device to obtain the color data in the HSaIn format at the output device side, which comprises:
 
determining an intensity mapping relationship In LUT  and a saturation mapping relationship Sa LUT  under an Iso-hue plane according to the gamuts of the input device and the output device, a color distribution range of an image and a color representation intention;
 
performing a color data mapping of the image from the input device side to the output device side according to the intensity mapping relationship In LUT  and the saturation mapping relationship Sa LUT  to obtain the color data in the HSaIn format at the output device side.
 
     Since the embodiments of the invention convert the chromatic image acquired from the input device into one in an XYZ format and then into one in an HSaIn format, in the case that the accuracies of the color characteristic data of the input and output devices are ensured, such conversion is a completely analyzing method, and removes the impacts of the input device on the chromatic image with a high accuracy in the conversion. Thus, the acquired chromatic image will not be influenced by the color attribute of the input device itself; further, the analytical matrix operation adopted in the calculating process for the conversion in the HSaIn format is easily achieved, which greatly simplifies the calculating process for the conversion, improves the conversion accuracy and efficiency, and accelerates the conversion speed. 
     Since the embodiments of the invention achieve the conversion from the chromatic color data independent of the device into chromatic color data dependent on a specific output device in the process of converting an HSaIn format into an XYZ format and then into an output format that can be identified and processed by the output device, the output chromatic image will be not influenced by the color characteristics of the output device itself; further, the analytical matrix operation adopted in the calculating process for the conversion of the color data from the HSaIn format into one in an output format is easily achieved, which greatly simplifies the calculating process for the conversion, improves the conversion accuracy and efficiency, and accelerates the conversion speed. Further, the conversion formulae for the conversion into color data in an HSaIn format provided in the embodiments of the invention are theoretical formulae and will not have accumulative errors in the multiple calculations, so the color data obtained by these calculations with the conversion formulae will provide higher accuracies of the color data than the conversion formulae in the prior art. 
     Especially, with respect to a color space of a new device that may appear in the future, the conversion between the color space of this new device and the HSaIn color space, and the conversion between the color space of this new device and the CIEXYZ color space can both undergo the processing of the data image according to the principle in the invention, and only the conversion angles of the color characteristics are different. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of the chromatic plane of an embodiment of the invention; 
         FIG. 2  shows a flow chart of the method of managing color data based on color data in an HSaIn format in an HSaIn color space provided by an embodiment of the invention; 
         FIG. 3  shows a flow chart of the method of managing color data based on color data in an HSaIn format in an HSaIn color appearance color space of another embodiment of the invention; 
         FIG. 4  shows a flow chart of the method of managing color data based on a CIEXYZ color space of another embodiment of the invention; 
         FIG. 5  is a schematic diagram of the deviation angles between the color characteristic data of the input device and  ,   and   of an embodiment of the invention; 
         FIG. 6  is a schematic diagram of the relationship among the HSaIn color space, the chromatic plane, the HSaIn format and the XYZ format in the invention; 
         FIGS. 7-9  are schematic diagrams of the color gamut mapping within the chromatic plane; 
         FIG. 10  is a schematic diagram of performing a mapping along the iso-Sa line under the Iso-hue plane in the HSaIn space according to the agreed In LUT ; 
         FIG. 11  is a schematic diagram of performing a mapping along the incremental Sa line under the Iso-hue plane in the HSaIn space according to the agreed intensity In LUT ; 
         FIG. 12  is a schematic diagram of the curve of the intensity In mapping In LUT ; 
         FIG. 13  is a schematic diagram of the curve of the saturation Sa mapping Sa LUT ; 
     
    
    
     DETAILED DESCRIPTION 
     In order to make objects, technical solutions and advantages of the invention clearer, the invention is further described in detail below by referring to the figures and listing preferred embodiments. But it should be noted that many details are only listed in the Description for making the readers thoroughly understand one or more aspects of the invention, and these aspects of the invention can be also achieved even without these specific details. 
     The invention puts forward an HSaIn color space model of color data in an HSaIn format. The HSaIn color space is a color space based on a CIEXYZ Cartesian color space, of a color appearance attribute, and described by a cylindrical coordinate system, and is composed of a chromatic plane and a gray axis passing through the origin of the chromatic plane and perpendicular to the chromatic plane; 
     wherein the chromatic plane is a plane of the CIEXYZ Cartesian color space X+Y+Z=K, where K is a real constant; an XYZ axis of the CIEXYZ Cartesian color space performs a projection along a direction of a straight line X=Y=Z on a plane X+Y+Z=K to obtain three projection axes that are 120° with respect to one another within the chromatic plane, and unit vectors in the directions of the projection axes are  ,   and  ;
 
wherein the gray axis is a number axis composed of the straight line X=Y=Z of the CIEXYZ Cartesian color space, a numerical value on the number axis represents a gray Gl value in the HSaIn color space, a length of a chromatic vector   parallel to the chromatic plane represents a chromatic Cl value in the HSaIn color space, and a polar angle of the chromatic vector represents a hue angle H in the HSaIn color space;
 
the HSaIn color space is an equivalent form of the HGlCl color space, and  FIG. 6  is a color space where the HSaIn color space is composed of a gray Gl axis and a chromatic plane, wherein the color data in the HSaIn format is in a format of the color data in the HSaIn color space, and comprises a hue H, a saturation Sa, and an intensity In in the HSaIn color space.
 
     As shown in  FIGS. 1 and 6 ,  FIG. 1  is the chromatic plane in the HSaIn space, and is a medium plane for the conversion between the CIEXYZ color space and the HSaIn color space, which medium plane is also the plane of the CIEXYZ space X+Y+Z=K (K is a real constant). The three unit vectors  ,  ,   within the chromatic plane are unit vectors of three vector axes that are 120° with respect to one another obtained by three coordinate axes XYZ perpendicular to one another in the CIEXYZ space performing a projection along a direction of a straight line X=Y=Z on a plane X+Y+Z=K. After a normalized corresponding processing of the unit coordinates and the unit vectors  ,  ,   in the CIEXYZ color space one color C (X, Y, Z) in the CIEXYZ color space just corresponds to the data C( ,  ,  ) within the chromatic plane, wherein X, Y and Z are respectively the modules of  ,   and   and the polar angles of  ,   and   are respectively 0°, 120° and 240°. 
     The data format in the CIEXYZ color space is an XYZ data format, and is described by the tristimulus values X, Y, Z, which respectively represent numerical values on the X, Y and Z coordinate axes in the CIEXYZ color space. 
     The hue H in the HSaIn color space can be acquired by the following formula: 
     
       
         
           
             
               
                 
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     The saturation Sa and the intensity In in the HSaIn color space can be acquired by the following formulae: 
     
       
         
           
             
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                             v 
                           
                         
                         + 
                         
                           Z 
                            
                           
                             k 
                             v 
                           
                         
                       
                        
                     
                     m 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 Gl 
                 + 
                 Cl 
               
             
             , 
             
               
 
             
              
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, p and m are nonzero real numbers, In≧Gl≧0, A≧0, B≧0 or 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     r 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     
                       K 
                       M 
                     
                      
                     
                       [ 
                       
                         
                           X 
                           p 
                         
                         + 
                         
                           Y 
                           p 
                         
                         + 
                         
                           Z 
                           p 
                         
                       
                       ] 
                     
                   
                   
                     1 
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               
 
             
              
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m &gt;0, p, q and r are nonzero real numbers, In≧Gl≧0, A≧0, B≧0 or 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     r 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 
                   
                     
                       K 
                       M 
                     
                      
                     
                       [ 
                       
                         
                           
                             ( 
                             
                               X 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                         + 
                         
                           
                             ( 
                             
                               Y 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                         + 
                         
                           
                             ( 
                             
                               Z 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                       
                       ] 
                     
                   
                   
                     1 
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 Cl 
                 + 
                 Gl 
               
             
             , 
             
               
 
             
              
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m &gt;0, p, q and r are nonzero real numbers, In≧Gl≧0, A≧0, B≧0 wherein X, Y and Z are color data in the XYZ format, i.e., the color data in the CIEXYZ Cartesian color space, and respectively represent numerical values on the X, Y and Z coordinate axes in the CIEXYZ Cartesian color space. In the process of converting the data in the CIEXYZ format into data in an HSaIn format, parameters, e.g., K M , K m , p, q, r, m, A, B, etc., in each acquiring manner can be selected within their defined ranges and are feasible in the implementation, but the preferred selection is that K M =K m =1, p=q=r=m−1, and A=B=0. 
     The color characteristic data of the device will be involved in the following embodiments, and are the hue deviations brought by the process accuracy problems of the color materials of the respective channels of the device and the like, and after the hue characteristics and the intensity data of these channels are characterized, these color data are represented as chromatic vectors within the chromatic plane, and the hue deviation angles between these chromatic vectors and the adjacent vectors  ,  ,   are represented as α, β and γ, i.e., the color characteristic data. 
       FIG. 2  shows a flow chart of the method of managing color data based on color data in an HSaIn format in an HSaIn color space provided by an embodiment of the invention. 
     As shown in  FIG. 2 , firstly, color data in an XYZ format at an input device side is acquired. There are several manners of acquiring the color data in the XYZ format at the input device side, which will be described in detail below. In the step  220 , the acquired color data in the XYZ format at the input device side is converted into color data in an HSaIn format. 
     In this embodiment, the acquiring color data in an XYZ format at in input device side can comprise: acquiring color data of a chromatic image of a chromatic scene from the input device; converting the acquired color data into color data in an XYZ format at the input device side according to color characteristic data of the input device (the step  2201 ). Another manner of acquiring color data in an XYZ format at an input side is to directly select color data in an XYZ format in a CIEXYZ color space at the input device side. 
     The input device can be a camera, a pickup camera, a video camera and the like, or the input device can be also a scanner and the like. A chromatic image stored in a digital format is acquired from the input device. Generally, the color data of the acquired chromatic image is stored in a manner of a pixel dot matrix. In the invention, color data in a UVW format of the device includes but is not limited to color data in an RGB format of the device and color data in a CMYe format of the device. With respect to the input device, the color data thereof is generally in an RGB format, and with respect to the output device such as a printer, the format of the color data of the chromatic image is generally CMYe. 
     The color data acquired from the input device can be in a three-channel format UVW or in a multichannel format. 
     If the color data is in the UVW format, in the step  2201 , the color data in the UVW format acquired from the input device is converted into color data based on a CIEXYZ color space at the input device side. 
     Specifically, the color data of the chromatic image in the UVW format acquired from the input device is converted into color data of a chromatic image in an XYZ format according to color characteristic data of the input device. That is, the impacts of the input device on the chromatic image are removed in the conversion process according to color characteristic data of the input device. 
     The color data in the UVW format acquired from the input device is converted into color data in an XYZ format at the input device side according to color characteristic data α 1 , β 1 , γ 1  of the input device and based on the following formulae 3-10, wherein the UVW format is a format represented by intensity numerical values after characterization of light intensity values perceived by a color sensor of the device at three different spectral sections: 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           X 
                         
                       
                       
                         
                           Y 
                         
                       
                       
                         
                           Z 
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         α 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         β 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         γ 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   U 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   V 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   W 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 3, α 1 &gt;0, β 1 &gt;0, γ 1 &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           X 
                         
                       
                       
                         
                           Y 
                         
                       
                       
                         
                           Z 
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         α 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         β 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         γ 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   U 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   V 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   W 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     4 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 4, α 1 &gt;0, β 1 &gt;0, γ 1 &lt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           X 
                         
                       
                       
                         
                           Y 
                         
                       
                       
                         
                           Z 
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         α 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         β 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         γ 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   U 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   V 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   W 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     5 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 5, α 1 &gt;0, β 1 &lt;0, γ 1 &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           X 
                         
                       
                       
                         
                           Y 
                         
                       
                       
                         
                           Z 
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         α 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         β 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         γ 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   U 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   V 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   W 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     6 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 6, α 1 &gt;0, β 1 &lt;0, γ 1 &lt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           X 
                         
                       
                       
                         
                           Y 
                         
                       
                       
                         
                           Z 
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         α 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         β 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         γ 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   U 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   V 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   W 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     7 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 7, α 1 &lt;0, β 1 &gt;0, γ 1 &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           X 
                         
                       
                       
                         
                           Y 
                         
                       
                       
                         
                           Z 
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         α 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         β 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         γ 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   U 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   V 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   W 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     8 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 8, α 1 &lt;0, β 1 &gt;0, γ 1 &lt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           X 
                         
                       
                       
                         
                           Y 
                         
                       
                       
                         
                           Z 
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         α 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         β 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         γ 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   U 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   V 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   W 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     9 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 9, α 1 &lt;0, β 1 &lt;0, γ 1 &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           X 
                         
                       
                       
                         
                           Y 
                         
                       
                       
                         
                           Z 
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         α 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         β 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         γ 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   U 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   V 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   W 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     10 
                   
                   ) 
                 
               
             
           
         
       
     
     in the formula 10, α 1 &lt;0, β 1 &lt;0, γ 1 &lt;0;
 
wherein the values of U 1 , V 1  and W 1  in the above formulae 3-10 are the characterized color data in the UVW format of the input device; α 1  is a hue deviation angle between  , and  ; β 1  is a hue deviation angle between  ; and  ; γ 1  is a hue deviation angle between  , and  ;  ,   and   are characterized UVW channel color data of the input device to represent chromatic vectors within the chromatic plane. The color characteristic data of the input device is obtained from the input device beforehand, e.g., the color deviation characteristic of the input device is acquired when installing the drive program of the input device, and the color characteristic data of the input device can be specifically stored in a profile header file. Wherein the schematic diagram of the deviation angles between the color characteristic data of the input device and  ,  ,   is as shown in  FIG. 5 .
 
     It can be seen from the above formulae 3-10 that the matrix that convers the chromatic image from the UVW format into the XYZ format further includes the deviation angles obtained according to the color characteristic data of the input device, so that the impacts of the input device on the chromatic image are removed by means of the deviation angles in the process of converting the color data in the UVW format into the color data in the XYZ format. 
     If the color data is in the multichannel format, in the step  2201 , the color data in the multichannel format acquired from the input device is converted into color data based on a CIEXYZ color space at the input device side. 
     Specifically, color data of respective channels are obtained to represent chromatic vectors within the chromatic plane according to color characteristic data of the input device, i.e., characterized hue deviation angles of the respective channels, in combination with values of the color data of the respective channels; wherein the characterized hue deviation angles are respectively hue deviation angles of characterized hue angles of the respective channels of the device relative to adjacent polar angles  ,  ,   within the chromatic plane; 
     the chromatic vectors of the respective channels of the device within the chromatic plane are decomposed into ones in the directions  ,  ,   according to a vector decomposition rule and a linear addition is performed in the directions  ,  ,   respectively to thereby obtain data to serve as the color data in the XYZ format. 
     After the chromatic image which is not influenced by the color attribute of the input device itself is acquired, the chromatic image which is not influenced by the color attribute of the output device itself can be output through the output device for an output display or an output printing, projection and the like. The output device can specifically include a display, a printer, a printing machine, a projector and the like. The so-called chromatic image in an output format refers to a chromatic image in a storage format that can be identified and processed by the output device. For example, if the output device is a display, the output format of the chromatic image thereof is generally an RGB format; if the output device is a printer, the output format of the chromatic image thereof is generally a CMYe format. The specific method of converting the color data of the chromatic image in the HSaIn format into color data of a chromatic image in an output format, and removing impacts of the color attribute of the output device itself on the output chromatic image in the conversion process will be introduced in detail below. 
     Next, in the step  222 , the color data in the HSaIn format in the HSaIn color space at the input device side is mapped according to a mapping relationship between a color gamut of the input device and a color gamut of the output device to obtain the color data in the HSaIn format in the HSaIn color space at the output device side. Specifically,  FIG. 7 ,  FIG. 8  and  FIG. 9  show a color gamut comparing relationship between the input device and the output device, a white field position within the chromatic plane, and a color distribution range of an image;  FIG. 10  and  FIG. 11  show an intensity mapping relationship and a saturation mapping relationship under an Iso-hue plane in the HSaIn color space under the determination of the color representation intention;  FIG. 12  and  FIG. 13  show an intensity mapping relationship In LUT  and a saturation mapping relationship Sa LUT  corresponding to the input and output gamuts, and the mapping of all color data of the image from the input device side to the output device side is performed according to In LUT  and Sa LUT  to obtain the color data in the HSaIn format in the HSaIn color appearance color space at the output device side. 
     Within the chromatic plane, a pure chromatic vector of each channel of each device is represented according to the intensity numerical value of the channel and the characterized hue value of the spectrum of the channel, all possible intensity numerical values of all the channels are traversed, and the set of all the chromatic vectors obtained by these traversed intensity data undergoing a pure chromatic vector addition within the chromatic plane according to a vector addition rule is just the color gamut represented by this device within the chromatic plane. The white field position in the color gamut is a position where the chromatic vector obtained after the addition of the pure chromatic vectors corresponding to the XYZ values of the white field self-defined by the respective devices within the chromatic plane is located. If the XYZ values of the white field are equal, the white field position is on the origin of the polar coordinate. The color distribution range of the image is a set of the positions of the superimposed chromatic vectors obtained by the XYZ value data of all the pixels of this image by means of the vector addition rule within the chromatic plane, and the distribution formed by this set is just the color distribution range of this image within the chromatic plane. The color representation intention is preset one of the color management strategies of the color gamut mapping, and is generally divided into a perceptual color representation intention, a saturated color representation intention, a relative chrominance color representation intention and an absolute color representation intention according to the textbook, and more color representation intentions can be further defined according to specific requirements for the color management, and no unnecessary details are given herein. 
       FIG. 7 ,  FIG. 8  and  FIG. 9  show schematic examples of the gamuts of the input and output devices within the chromatic plane, the white field position and the distribution range of the image, and one input image distribution under the perceptual color representation intention from the state that the output color gamut cannot be completely covered to the state that the output gamut is completely covered. 
       FIG. 10  and  FIG. 11  are schematic diagrams of the color gamut mapping. Performing the color gamut mapping in the HSaIn color space is divided into performing an intensity In preferential mapping and performing a saturation Sa preferential mapping under the iso-H. The In preferential mapping is to map In according to LUT on the premise that the Sa mapping relationship is preset; the Sa preferential mapping is to map Sa according to LUT on the premise that the In mapping relationship is preset. 
       FIG. 10  shows that in process of performing the color gamut mapping in the HSaIn color space, on the premise of the iso-hue H, the transverse axis is the Cl chromatic vector under the hue H, the longitudinal axis is the Gl gray, on the premise of the iso-Sa, the schematic diagram of performing the intensity mapping with In LUT  as shown in  FIG. 12  is performed, and the output intensities of all the color data under the iso-H and the iso-Sa are obtained finally to thereby obtain the color data H, Sa, In at the output device side. 
       FIG. 11  shows that in the process of performing the color gamut mapping in the HSaIn color space, on the premise of the iso-hue H, the transverse axis is the Cl chromatic vector under the hue H, the longitudinal axis is the Gl gray, on the premise that the preset incremental Sa line is performed according to the color representation intention, the schematic diagram of performing the intensity mapping with In LUT  as shown in  FIG. 12  is performed, and the output intensities of all the color data under the iso-H and the incremental Sa are obtained finally to thereby obtain the color data H, Sa, In at the output device side. 
     Similarly, there is a further intensity mapping performed on the premise of a preset Sa curve of another rule according to the color representation intention to obtain the color data H, Sa, In at the output device side, and no unnecessary details are given herein. 
     Similarly, there is a further method of further performing a saturation Sa mapping after presetting the intensity In mapping according to the color representation intention on the premise of the iso-hue H to obtain the color data H, Sa, In at the output device side, and no unnecessary details are given herein. 
       FIG. 12  and  FIG. 13  are respectively a schematic diagram of the intensity In mapping LUT and a schematic diagram of the saturation Sa mapping LUT. 
     In the stem  224 , the color data in the HSaIn format at the output device side is converted into color data in an XYZ format. Specifically, if the saturation Sa and the intensity In in the color data in the HSaIn format at the input device side are acquired according to the formulae below, 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     
                       K 
                       m 
                     
                      
                     
                       [ 
                       
                         Min 
                          
                         
                           ( 
                           
                             X 
                             , 
                             Y 
                             , 
                             Z 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                   p 
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     
                       K 
                       M 
                     
                      
                     
                       [ 
                       
                         Max 
                          
                         
                           ( 
                           
                             X 
                             , 
                             Y 
                             , 
                             Z 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                   q 
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               
 
             
              
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, In≧Gl≧0, A≧0, B≧0, p and q are nonzero real numbers the color data in the XYZ format at the output device side is acquired according to the following formulae: 
     
       
         
           
               
             
               { 
               
                 
                   
                     
                       
                         
                           H 
                           ′ 
                         
                         = 
                         
                           H 
                           
                             60 
                              
                             ° 
                           
                         
                       
                       , 
                       
                         h 
                         = 
                         
                           [ 
                           
                             H 
                             ′ 
                           
                           ] 
                         
                       
                       , 
                       
                         
                           [ 
                           • 
                           ] 
                         
                          
                         
                             
                         
                          
                         is 
                          
                         
                             
                         
                          
                         a 
                          
                         
                             
                         
                          
                         round 
                          
                         
                             
                         
                          
                         symbol 
                          
                         
                             
                         
                          
                         with 
                          
                         
                             
                         
                          
                         respect 
                          
                         
                             
                         
                          
                         to 
                          
                         
                             
                         
                          
                         • 
                       
                       , 
                       
                         H 
                         ∈ 
                         
                           [ 
                           
                             
                               0 
                                
                               ° 
                             
                             , 
                             
                               360 
                                
                               ° 
                             
                           
                           ) 
                         
                       
                       , 
                       
                         h 
                         = 
                         0 
                       
                       , 
                       1 
                       , 
                       2 
                       , 
                       3 
                       , 
                       4 
                       , 
                       5 
                     
                   
                   
                     
                         
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             ( 
                             
                               
                                 In 
                                 - 
                                 B 
                               
                               
                                 K 
                                 M 
                               
                             
                             ) 
                           
                           
                             1 
                             q 
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 H 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       120 
                                        
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       In 
                                        
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           Sa 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     A 
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       H 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   H 
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       120 
                                        
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ) 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       0 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       120 
                                        
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                               
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 H 
                               
                             
                           
                           + 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       In 
                                        
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           Sa 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     A 
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   H 
                                 
                                 - 
                                 
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       H 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 H 
                               
                             
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             ( 
                             
                               
                                 In 
                                 - 
                                 B 
                               
                               
                                 K 
                                 M 
                               
                             
                             ) 
                           
                           
                             1 
                             q 
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ) 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       1 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ) 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             ( 
                             
                               
                                 In 
                                 - 
                                 B 
                               
                               
                                 K 
                                 M 
                               
                             
                             ) 
                           
                           
                             1 
                             q 
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       120 
                                        
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       240 
                                        
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       In 
                                        
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           Sa 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     A 
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         240 
                                          
                                         ° 
                                       
                                       - 
                                       H 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     ( 
                                     
                                       H 
                                       - 
                                       
                                         120 
                                          
                                         ° 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       240 
                                        
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       2 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ) 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       240 
                                        
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       120 
                                        
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       In 
                                        
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           Sa 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     A 
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       H 
                                       - 
                                       
                                         120 
                                          
                                         ° 
                                       
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         240 
                                          
                                         ° 
                                       
                                       - 
                                       H 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       120 
                                        
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             ( 
                             
                               
                                 In 
                                 - 
                                 B 
                               
                               
                                 K 
                                 M 
                               
                             
                             ) 
                           
                           
                             1 
                             q 
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       3 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       240 
                                        
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       In 
                                        
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           Sa 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     A 
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       H 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     ( 
                                     
                                       H 
                                       - 
                                       
                                         240 
                                          
                                         ° 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ) 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             ( 
                             
                               
                                 In 
                                 - 
                                 B 
                               
                               
                                 K 
                                 M 
                               
                             
                             ) 
                           
                           
                             1 
                             q 
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       4 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             ( 
                             
                               
                                 In 
                                 - 
                                 B 
                               
                               
                                 K 
                                 M 
                               
                             
                             ) 
                           
                           
                             1 
                             q 
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ) 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                               
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       240 
                                        
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       In 
                                        
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           Sa 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     A 
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       H 
                                       - 
                                       
                                         240 
                                          
                                         ° 
                                       
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     ( 
                                     
                                       - 
                                       H 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       - 
                                       H 
                                     
                                     - 
                                     
                                       240 
                                        
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       5 
                     
                   
                 
               
             
           
         
       
     
     or if the saturation Sa and the intensity In in the color data in the HSaIn format at the input device side are acquired according to the formulae below, 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     
                       K 
                       m 
                     
                      
                     
                       [ 
                       
                         Min 
                          
                         
                           ( 
                           
                             X 
                             , 
                             Y 
                             , 
                             Z 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                   p 
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     1 
                     3 
                   
                    
                   
                     
                       
                         K 
                         M 
                       
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               
 
             
              
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m , In≧Gl≧0, A≧0, B≧0, p and q are nonzero real numbers the color data in the XYZ format at the output device side is acquired according to the following formulae: 
     
       
         
           
             
               when 
                
               
                   
               
                
               0 
                
               ° 
             
             ≤ 
             H 
             &lt; 
             
               120 
                
               ° 
             
           
         
       
       
         
           
             X 
             = 
             
               
                 
                   
                     [ 
                     
                       
                         
                           3 
                            
                           
                               
                           
                            
                           In 
                         
                         - 
                         B 
                       
                       
                         K 
                         M 
                       
                     
                     ] 
                   
                   
                     1 
                     q 
                   
                 
                  
                 
                   
                     sin 
                      
                     
                       ( 
                       
                         
                           120 
                            
                           ° 
                         
                         - 
                         H 
                       
                       ) 
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         H 
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             120 
                              
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
               - 
               
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                  
                 
                   
                     
                       2 
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             
                               120 
                                
                               ° 
                             
                             - 
                             H 
                           
                           ) 
                         
                       
                     
                     - 
                     
                       sin 
                        
                       
                         ( 
                         H 
                         ) 
                       
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         H 
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             120 
                              
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             Y 
             = 
             
               
                 
                   
                     [ 
                     
                       
                         
                           3 
                            
                           
                               
                           
                            
                           In 
                         
                         - 
                         B 
                       
                       
                         K 
                         M 
                       
                     
                     ] 
                   
                   
                     1 
                     q 
                   
                 
                  
                 
                   
                     sin 
                      
                     
                       ( 
                       H 
                       ) 
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         H 
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             120 
                              
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
               - 
               
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                  
                 
                   
                     
                       2 
                        
                       
                         sin 
                          
                         
                           ( 
                           H 
                           ) 
                         
                       
                     
                     - 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             120 
                              
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         H 
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             120 
                              
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             Z 
             = 
             
               
                 [ 
                 
                   
                     
                       In 
                        
                       
                         ( 
                         
                           1 
                           - 
                           Sa 
                         
                         ) 
                       
                     
                     - 
                     A 
                   
                   
                     K 
                     m 
                   
                 
                 ] 
               
               
                 1 
                 p 
               
             
           
         
       
       
         
           
             
               when 
                
               
                   
               
                
               120 
                
               ° 
             
             ≤ 
             H 
             &lt; 
             
               240 
                
               ° 
             
           
         
       
       
         
           
             
               X 
               = 
               
                 
                   [ 
                   
                     
                       
                         In 
                          
                         
                           ( 
                           
                             1 
                             - 
                             Sa 
                           
                           ) 
                         
                       
                       - 
                       A 
                     
                     
                       K 
                       m 
                     
                   
                   ] 
                 
                 
                   1 
                   p 
                 
               
             
             , 
             
               
 
             
              
             
               Y 
               = 
               
                 
                   
                     
                       [ 
                       
                         
                           
                             3 
                              
                             
                                 
                             
                              
                             In 
                           
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ] 
                     
                     
                       1 
                       q 
                     
                   
                    
                   
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             240 
                              
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                     
                       
                         sin 
                          
                         
                           ( 
                           
                             H 
                             - 
                             
                               120 
                                
                               ° 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         sin 
                          
                         
                           ( 
                           
                             
                               240 
                                
                               ° 
                             
                             - 
                             H 
                           
                           ) 
                         
                       
                     
                   
                 
                 - 
                 
                   
                     
                       [ 
                       
                         
                           
                             In 
                              
                             
                               ( 
                               
                                 1 
                                 - 
                                 Sa 
                               
                               ) 
                             
                           
                           - 
                           A 
                         
                         
                           K 
                           m 
                         
                       
                       ] 
                     
                     
                       1 
                       p 
                     
                   
                    
                   
                     
                       
                         2 
                          
                         
                           sin 
                            
                           
                             ( 
                             
                               
                                 240 
                                  
                                 ° 
                               
                               - 
                               H 
                             
                             ) 
                           
                         
                       
                       - 
                       
                         sin 
                          
                         
                           ( 
                           
                             H 
                             - 
                             
                               120 
                                
                               ° 
                             
                           
                           ) 
                         
                       
                     
                     
                       
                         sin 
                          
                         
                           ( 
                           
                             H 
                             - 
                             
                               120 
                                
                               ° 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         sin 
                          
                         
                           ( 
                           
                             
                               240 
                                
                               ° 
                             
                             - 
                             H 
                           
                           ) 
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             Z 
             = 
             
               
                 
                   
                     [ 
                     
                       
                         
                           3 
                            
                           
                               
                           
                            
                           In 
                         
                         - 
                         B 
                       
                       
                         K 
                         M 
                       
                     
                     ] 
                   
                   
                     1 
                     q 
                   
                 
                  
                 
                   
                     sin 
                      
                     
                       ( 
                       
                         H 
                         - 
                         
                           120 
                            
                           ° 
                         
                       
                       ) 
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             120 
                              
                             ° 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             240 
                              
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
               - 
               
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                  
                 
                   
                     
                       2 
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             H 
                             - 
                             
                               120 
                                
                               ° 
                             
                           
                           ) 
                         
                       
                     
                     - 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             240 
                              
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             120 
                              
                             ° 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             240 
                              
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               when 
                
               
                   
               
                
               240 
                
               ° 
             
             ≤ 
             H 
             &lt; 
             
               360 
                
               ° 
             
           
         
       
       
         
           
             X 
             = 
             
               
                 
                   
                     [ 
                     
                       
                         
                           3 
                            
                           
                               
                           
                            
                           In 
                         
                         - 
                         B 
                       
                       
                         K 
                         M 
                       
                     
                     ] 
                   
                   
                     1 
                     q 
                   
                 
                  
                 
                   
                     sin 
                      
                     
                       ( 
                       
                         H 
                         - 
                         
                           240 
                            
                           ° 
                         
                       
                       ) 
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             240 
                              
                             ° 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
               - 
               
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                  
                 
                   
                     
                       2 
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             H 
                             - 
                             
                               240 
                                
                               ° 
                             
                           
                           ) 
                         
                       
                     
                     - 
                     
                       sin 
                        
                       
                         ( 
                         
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             240 
                              
                             ° 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             Y 
             = 
             
               
                 [ 
                 
                   
                     
                       In 
                        
                       
                         ( 
                         
                           1 
                           - 
                           Sa 
                         
                         ) 
                       
                     
                     - 
                     A 
                   
                   
                     K 
                     m 
                   
                 
                 ] 
               
               
                 1 
                 p 
               
             
           
         
       
       
         
           
             Z 
             = 
             
               
                 
                   
                     [ 
                     
                       
                         
                           3 
                            
                           
                               
                           
                            
                           In 
                         
                         - 
                         B 
                       
                       
                         K 
                         M 
                       
                     
                     ] 
                   
                   
                     1 
                     q 
                   
                 
                  
                 
                   
                     sin 
                      
                     
                       ( 
                       
                         - 
                         H 
                       
                       ) 
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             240 
                              
                             ° 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
               - 
               
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                  
                 
                   
                     
                       2 
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             - 
                             H 
                           
                           ) 
                         
                       
                     
                     - 
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             240 
                              
                             ° 
                           
                         
                         ) 
                       
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             240 
                              
                             ° 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
             
           
         
       
     
     or if the saturation Sa and the intensity In in the color data in the HSaIn format at the input device side are acquired according to the formulae below, 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     p 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     1 
                     2 
                   
                    
                   
                     
                       
                         K 
                         M 
                       
                        
                       
                         [ 
                         
                           
                             Max 
                              
                             
                               ( 
                               
                                 X 
                                 , 
                                 Y 
                                 , 
                                 Z 
                               
                               ) 
                             
                           
                           + 
                           
                             Min 
                              
                             
                               ( 
                               
                                 X 
                                 , 
                                 Y 
                                 , 
                                 Z 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               
 
             
              
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m , In≧Gl≧0, A≧0, B≧0, p and q are nonzero real numbers the color data in the XYZ format at the output device side is acquired according to the following formulae: 
     
       
         
           
             { 
             
               
                 
                   
                       
                      
                     
                       
                         
                           H 
                           ′ 
                         
                         = 
                         
                           H 
                           
                             60 
                              
                             ° 
                           
                         
                       
                       , 
                       
                         h 
                         = 
                         
                           [ 
                           
                             H 
                             ′ 
                           
                           ] 
                         
                       
                       , 
                       
                         
                           [ 
                           • 
                           ] 
                         
                          
                         
                             
                         
                          
                         is 
                          
                         
                             
                         
                          
                         a 
                          
                         
                             
                         
                          
                         round 
                          
                         
                             
                         
                          
                         symbol 
                          
                         
                             
                         
                          
                         with 
                          
                         
                             
                         
                          
                         respect 
                          
                         
                             
                         
                          
                         to 
                          
                         
                             
                         
                          
                         • 
                       
                       , 
                       
                         H 
                         ∈ 
                         
                           [ 
                           
                             0 
                             , 
                             
                               360 
                                
                               ° 
                             
                           
                           ) 
                         
                       
                       , 
                       
                         h 
                         = 
                         0 
                       
                       , 
                       1 
                       , 
                       2 
                       , 
                       3 
                       , 
                       4 
                       , 
                       5 
                     
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                       
                      
                     
                       
                         X 
                         = 
                         
                           
                             
                               [ 
                               
                                 2 
                                  
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                               
                               ] 
                             
                             
                               1 
                               q 
                             
                           
                           - 
                           
                             
                               [ 
                               
                                 
                                   
                                     In 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         Sa 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   A 
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               1 
                               p 
                             
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             
                               
                                 [ 
                                 
                                   2 
                                    
                                   
                                     
                                       In 
                                       - 
                                       B 
                                     
                                     
                                       K 
                                       M 
                                     
                                   
                                 
                                 ] 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 H 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       120 
                                        
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 [ 
                                 
                                   
                                     
                                       In 
                                        
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           Sa 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     A 
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ] 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   
                                     
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             
                                               120 
                                                
                                               ° 
                                             
                                             - 
                                             H 
                                           
                                           ) 
                                         
                                       
                                       - 
                                     
                                   
                                 
                                 
                                   
                                     
                                       2 
                                        
                                       
                                           
                                       
                                        
                                       sin 
                                        
                                       
                                           
                                       
                                        
                                       H 
                                     
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       120 
                                        
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             [ 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ] 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                     
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       X 
                       = 
                       
                         
                           
                             
                               [ 
                               
                                 2 
                                  
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                               
                               ] 
                             
                             
                               1 
                               q 
                             
                           
                            
                           
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   
                                     120 
                                      
                                     ° 
                                   
                                   - 
                                   H 
                                 
                                 ) 
                               
                             
                             
                               sin 
                                
                               
                                   
                               
                                
                               H 
                             
                           
                         
                         + 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     In 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         Sa 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   A 
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               1 
                               p 
                             
                           
                            
                           
                             
                               
                                 
                                   
                                     
                                       sin 
                                        
                                       
                                           
                                       
                                        
                                       H 
                                     
                                     - 
                                   
                                 
                               
                               
                                 
                                   
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           
                                             120 
                                              
                                             ° 
                                           
                                           - 
                                           H 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             
                               sin 
                                
                               
                                   
                               
                                
                               H 
                             
                           
                         
                       
                     
                     , 
                     
                       Y 
                       = 
                       
                         
                           
                             [ 
                             
                               2 
                                
                               
                                 
                                   In 
                                   - 
                                   B 
                                 
                                 
                                   K 
                                   M 
                                 
                               
                             
                             ] 
                           
                           
                             1 
                             q 
                           
                         
                         - 
                         
                           
                             [ 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ] 
                           
                           
                             1 
                             p 
                           
                         
                       
                     
                     , 
                     
                       Z 
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 In 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     Sa 
                                   
                                   ) 
                                 
                               
                               - 
                               A 
                             
                             
                               K 
                               m 
                             
                           
                           ] 
                         
                         
                           1 
                           p 
                         
                       
                     
                     , 
                   
                 
                 
                   
                       
                      
                     
                       h 
                       = 
                       0 
                     
                   
                 
               
               
                 
                   
                     
                       X 
                       = 
                       
                         
                           
                             
                               [ 
                               
                                 2 
                                  
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                               
                               ] 
                             
                             
                               1 
                               q 
                             
                           
                            
                           
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   
                                     120 
                                      
                                     ° 
                                   
                                   - 
                                   H 
                                 
                                 ) 
                               
                             
                             
                               sin 
                                
                               
                                   
                               
                                
                               H 
                             
                           
                         
                         + 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     In 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         Sa 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   A 
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               1 
                               p 
                             
                           
                            
                           
                             
                               
                                 
                                   
                                     
                                       sin 
                                        
                                       
                                           
                                       
                                        
                                       H 
                                     
                                     - 
                                   
                                 
                               
                               
                                 
                                   
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           
                                             120 
                                              
                                             ° 
                                           
                                           - 
                                           H 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             
                               sin 
                                
                               
                                   
                               
                                
                               H 
                             
                           
                         
                       
                     
                     , 
                     
                       Y 
                       = 
                       
                         
                           
                             [ 
                             
                               2 
                                
                               
                                 
                                   In 
                                   - 
                                   B 
                                 
                                 
                                   K 
                                   M 
                                 
                               
                             
                             ] 
                           
                           
                             1 
                             q 
                           
                         
                         - 
                         
                           
                             [ 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ] 
                           
                           
                             1 
                             p 
                           
                         
                       
                     
                     , 
                     
                       Z 
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 In 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     Sa 
                                   
                                   ) 
                                 
                               
                               - 
                               A 
                             
                             
                               K 
                               m 
                             
                           
                           ] 
                         
                         
                           1 
                           p 
                         
                       
                     
                     , 
                   
                 
                 
                   
                     h 
                     = 
                     1 
                   
                 
               
               
                 
                   
                     
                       X 
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 In 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     Sa 
                                   
                                   ) 
                                 
                               
                               - 
                               A 
                             
                             
                               K 
                               m 
                             
                           
                           ] 
                         
                         
                           1 
                           p 
                         
                       
                     
                     , 
                     
                       Y 
                       = 
                       
                         
                           
                             [ 
                             
                               2 
                                
                               
                                 
                                   In 
                                   - 
                                   B 
                                 
                                 
                                   K 
                                   M 
                                 
                               
                             
                             ] 
                           
                           
                             1 
                             q 
                           
                         
                         - 
                         
                           
                             [ 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ] 
                           
                           
                             1 
                             p 
                           
                         
                       
                     
                     , 
                     
                       Z 
                       = 
                       
                         
                           
                             
                               [ 
                               
                                 2 
                                  
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                               
                               ] 
                             
                             
                               1 
                               q 
                             
                           
                            
                           
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   H 
                                   - 
                                   
                                     120 
                                      
                                     ° 
                                   
                                 
                                 ) 
                               
                             
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   
                                     240 
                                      
                                     ° 
                                   
                                   - 
                                   H 
                                 
                                 ) 
                               
                             
                           
                         
                         + 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     In 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         Sa 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   A 
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               1 
                               p 
                             
                           
                            
                           
                             
                               
                                 
                                   
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           
                                             240 
                                              
                                             ° 
                                           
                                           - 
                                           H 
                                         
                                         ) 
                                       
                                     
                                     - 
                                   
                                 
                               
                               
                                 
                                   
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           H 
                                           - 
                                           
                                             120 
                                              
                                             ° 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   
                                     240 
                                      
                                     ° 
                                   
                                   - 
                                   H 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     , 
                   
                 
                 
                   
                     h 
                     = 
                     2 
                   
                 
               
               
                 
                   
                     
                       X 
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 In 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     Sa 
                                   
                                   ) 
                                 
                               
                               - 
                               A 
                             
                             
                               K 
                               m 
                             
                           
                           ] 
                         
                         
                           1 
                           p 
                         
                       
                     
                     , 
                     
                       Y 
                       = 
                       
                         
                           
                             
                               [ 
                               
                                 2 
                                  
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                               
                               ] 
                             
                             
                               1 
                               q 
                             
                           
                            
                           
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   
                                     240 
                                      
                                     ° 
                                   
                                   - 
                                   H 
                                 
                                 ) 
                               
                             
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   H 
                                   - 
                                   
                                     120 
                                      
                                     ° 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         + 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     In 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         Sa 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   A 
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               1 
                               p 
                             
                           
                            
                           
                             
                               
                                 
                                   
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           H 
                                           - 
                                           
                                             120 
                                              
                                             ° 
                                           
                                         
                                         ) 
                                       
                                     
                                     - 
                                   
                                 
                               
                               
                                 
                                   
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           
                                             240 
                                              
                                             ° 
                                           
                                           - 
                                           H 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   H 
                                   - 
                                   
                                     120 
                                      
                                     ° 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     , 
                     
                       Z 
                       = 
                       
                         
                           
                             [ 
                             
                               2 
                                
                               
                                 
                                   In 
                                   - 
                                   B 
                                 
                                 
                                   K 
                                   M 
                                 
                               
                             
                             ] 
                           
                           
                             1 
                             q 
                           
                         
                         - 
                         
                           
                             [ 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ] 
                           
                           
                             1 
                             p 
                           
                         
                       
                     
                   
                 
                 
                   
                     h 
                     = 
                     3 
                   
                 
               
               
                 
                   
                     
                       X 
                       = 
                       
                         
                           
                             
                               [ 
                               
                                 2 
                                  
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                               
                               ] 
                             
                             
                               1 
                               q 
                             
                           
                            
                           
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   
                                     240 
                                      
                                     ° 
                                   
                                   - 
                                   H 
                                 
                                 ) 
                               
                             
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   - 
                                   H 
                                 
                                 ) 
                               
                             
                           
                         
                         + 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     In 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         Sa 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   A 
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               1 
                               p 
                             
                           
                            
                           
                             
                               
                                 
                                   
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           - 
                                           H 
                                         
                                         ) 
                                       
                                     
                                     - 
                                   
                                 
                               
                               
                                 
                                   
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           H 
                                           - 
                                           
                                             240 
                                              
                                             ° 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   - 
                                   H 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     , 
                     
                       Y 
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 In 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     Sa 
                                   
                                   ) 
                                 
                               
                               - 
                               A 
                             
                             
                               K 
                               m 
                             
                           
                           ] 
                         
                         
                           1 
                           p 
                         
                       
                     
                     , 
                     
                       Z 
                       = 
                       
                         
                           
                             [ 
                             
                               2 
                                
                               
                                 
                                   In 
                                   - 
                                   B 
                                 
                                 
                                   K 
                                   M 
                                 
                               
                             
                             ] 
                           
                           
                             1 
                             q 
                           
                         
                         - 
                         
                           
                             [ 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ] 
                           
                           
                             1 
                             p 
                           
                         
                       
                     
                     , 
                   
                 
                 
                   
                     h 
                     = 
                     4 
                   
                 
               
               
                 
                   
                     
                       X 
                       = 
                       
                         
                           
                             [ 
                             
                               2 
                                
                               
                                 
                                   In 
                                   - 
                                   B 
                                 
                                 
                                   K 
                                   M 
                                 
                               
                             
                             ] 
                           
                           
                             1 
                             q 
                           
                         
                         - 
                         
                           
                             [ 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ] 
                           
                           
                             1 
                             p 
                           
                         
                       
                     
                     , 
                     
                       Y 
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 In 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     Sa 
                                   
                                   ) 
                                 
                               
                               - 
                               A 
                             
                             
                               K 
                               m 
                             
                           
                           ] 
                         
                         
                           1 
                           p 
                         
                       
                     
                     , 
                     
                       Z 
                       = 
                       
                         
                           
                             
                               [ 
                               
                                 2 
                                  
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                               
                               ] 
                             
                             
                               1 
                               q 
                             
                           
                            
                           
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   - 
                                   H 
                                 
                                 ) 
                               
                             
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   H 
                                   - 
                                   
                                     240 
                                      
                                     ° 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         + 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     In 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         Sa 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   A 
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               1 
                               p 
                             
                           
                            
                           
                             
                               
                                 
                                   
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           H 
                                           - 
                                           
                                             240 
                                              
                                             ° 
                                           
                                         
                                         ) 
                                       
                                     
                                     - 
                                   
                                 
                               
                               
                                 
                                   
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           - 
                                           H 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   H 
                                   - 
                                   
                                     240 
                                      
                                     ° 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     h 
                     = 
                     5 
                   
                 
               
             
               
           
         
       
     
     or if the saturation Sa and the intensity In in the color data in the HSaIn format at the input device side are acquired according to the formulae below, 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     p 
                   
                 
                 + 
                 A 
               
             
             , 
             
               Cl 
               = 
               
                 
                   
                     K 
                     M 
                   
                    
                   
                     
                        
                       
                         
                           X 
                            
                           
                             i 
                             V 
                           
                         
                         + 
                         
                           Y 
                            
                           
                             j 
                             V 
                           
                         
                         + 
                         
                           Z 
                            
                           
                             k 
                             V 
                           
                         
                       
                        
                     
                     m 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               m 
                
               
                   
               
                
               is 
                
               
                   
               
                
               real 
                
               
                   
               
                
               number 
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 Gl 
                 + 
                 Cl 
               
             
             , 
             
               
 
             
              
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, p and in are nonzero real numbers, In≧Gl≧0, A≧0, B≧0 the color data in the XYZ format at the output device side is acquired according to the following formulae: 
     
       
         
           
             
               h 
               = 
               
                 [ 
                 
                   H 
                   
                     120 
                      
                     ° 
                   
                 
                 ] 
               
             
             , 
             
               
 
             
              
             
               
                 [ 
                 • 
                 ] 
               
                
               
                   
               
                
               is 
                
               
                   
               
                
               a 
                
               
                   
               
                
               round 
                
               
                   
               
                
               symbol 
                
               
                   
               
                
               with 
                
               
                   
               
                
               respect 
                
               
                   
               
                
               to 
                
               
                   
               
                
               • 
             
             , 
             
               
 
             
              
             
               H 
               ∈ 
               
                 [ 
                 
                   
                     0 
                      
                     ° 
                   
                   , 
                   
                     360 
                      
                     ° 
                   
                 
                 ) 
               
             
             , 
             
               
 
             
              
             
               h 
               = 
               0 
             
             , 
             1 
             , 
             2 
           
         
       
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               0 
             
             , 
             
               
 
             
              
             
               X 
               = 
               
                 
                   
                     
                       ( 
                       
                         
                           SaIn 
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ) 
                     
                     
                       1 
                       m 
                     
                   
                    
                   
                     [ 
                     
                       
                         cos 
                          
                         
                           ( 
                           H 
                           ) 
                         
                       
                       + 
                       
                         
                           
                             3 
                           
                           3 
                         
                          
                         
                           sin 
                            
                           
                             ( 
                             H 
                             ) 
                           
                         
                       
                     
                     ] 
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                            
                           In 
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
               
             
             , 
             
               
 
             
              
             
               Y 
               = 
               
                 
                   
                     
                       2 
                        
                       
                         3 
                       
                     
                     3 
                   
                    
                   
                     sin 
                      
                     
                       ( 
                       H 
                       ) 
                     
                   
                    
                   
                     
                       ( 
                       
                         
                           SaIn 
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ) 
                     
                     
                       1 
                       m 
                     
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                            
                           In 
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
               
             
             , 
             
               
 
             
              
             
               Z 
               = 
               
                 
                   [ 
                   
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             Sa 
                           
                           ) 
                         
                          
                         In 
                       
                       - 
                       A 
                     
                     
                       K 
                       m 
                     
                   
                   ] 
                 
                 
                   1 
                   p 
                 
               
             
             , 
             
               
 
             
              
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               1 
             
             , 
             
               
 
             
              
             
               X 
               = 
               
                 
                   [ 
                   
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             Sa 
                           
                           ) 
                         
                          
                         In 
                       
                       - 
                       A 
                     
                     
                       K 
                       m 
                     
                   
                   ] 
                 
                 
                   1 
                   p 
                 
               
             
             , 
             
               
 
             
              
             
               Y 
               = 
               
                 
                   
                     [ 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                            
                           In 
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                 - 
                 
                   
                     
                       ( 
                       
                         
                           SaIn 
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ) 
                     
                     
                       1 
                       m 
                     
                   
                    
                   
                     [ 
                     
                       
                         cos 
                          
                         
                           ( 
                           H 
                           ) 
                         
                       
                       + 
                       
                         
                           
                             3 
                           
                           3 
                         
                          
                         
                           sin 
                            
                           
                             ( 
                             H 
                             ) 
                           
                         
                       
                     
                     ] 
                   
                 
               
             
             , 
             
               
 
             
              
             
               Z 
               = 
               
                 
                   
                     [ 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                            
                           In 
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                 - 
                 
                   
                     
                       ( 
                       
                         
                           SaIn 
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ) 
                     
                     
                       1 
                       m 
                     
                   
                    
                   
                     [ 
                     
                       
                         cos 
                          
                         
                           ( 
                           H 
                           ) 
                         
                       
                       + 
                       
                         
                           
                             3 
                           
                           3 
                         
                          
                         
                           sin 
                            
                           
                             ( 
                             H 
                             ) 
                           
                         
                       
                     
                     ] 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               2 
             
             , 
             
               
 
             
              
             
               X 
               = 
               
                 
                   
                     
                       ( 
                       
                         
                           SaIn 
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ) 
                     
                     
                       1 
                       m 
                     
                   
                    
                   
                     [ 
                     
                       
                         cos 
                          
                         
                           ( 
                           H 
                           ) 
                         
                       
                       + 
                       
                         
                           
                             3 
                           
                           3 
                         
                          
                         
                           sin 
                            
                           
                             ( 
                             H 
                             ) 
                           
                         
                       
                     
                     ] 
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                            
                           In 
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
               
             
             , 
             
               
 
             
              
             
               Y 
               = 
               
                 
                   [ 
                   
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             Sa 
                           
                           ) 
                         
                          
                         In 
                       
                       - 
                       A 
                     
                     
                       K 
                       m 
                     
                   
                   ] 
                 
                 
                   1 
                   p 
                 
               
             
             , 
             
               
 
             
              
             
               Z 
               = 
               
                 
                   
                     [ 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                            
                           In 
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                 - 
                 
                   
                     
                       2 
                        
                       
                         3 
                       
                     
                     3 
                   
                    
                   
                     sin 
                      
                     
                       ( 
                       H 
                       ) 
                     
                   
                    
                   
                     
                       ( 
                       
                         
                           SaIn 
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ) 
                     
                     
                       1 
                       m 
                     
                   
                 
               
             
           
         
       
     
     or if the saturation Sa and the intensity In in the color data in the HSaIn format at the input device side are acquired according to the formulae below, 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     r 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     
                       K 
                       M 
                     
                      
                     
                       [ 
                       
                         
                           X 
                           p 
                         
                         + 
                         
                           Y 
                           p 
                         
                         + 
                         
                           Z 
                           p 
                         
                       
                       ] 
                     
                   
                   
                     1 
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               
 
             
              
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m &gt;0, p, q and r are nonzero real numbers, In≧Gl≧0, A≧0, B≧0
 
the color data in the XYZ format at the output device side is acquired according to the following formulae:
 
     
       
         
           
             
               h 
               = 
               
                 [ 
                 
                   H 
                   
                     120 
                      
                     ° 
                   
                 
                 ] 
               
             
             , 
             
               
 
             
              
             
               
                 [ 
                 • 
                 ] 
               
                
               
                   
               
                
               is 
                
               
                   
               
                
               a 
                
               
                   
               
                
               round 
                
               
                   
               
                
               symbol 
                
               
                   
               
                
               with 
                
               
                   
               
                
               respect 
                
               
                   
               
                
               to 
                
               
                   
               
                
               • 
             
             , 
             
               
 
             
              
             
               H 
               ∈ 
               
                 [ 
                 
                   
                     0 
                      
                     ° 
                   
                   , 
                   
                     360 
                      
                     ° 
                   
                 
                 ) 
               
             
             , 
             
               
 
             
              
             
               h 
               = 
               0 
             
             , 
             1 
             , 
             2 
           
         
       
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               0 
             
             , 
             
               
 
             
              
             
               
                 then 
                  
                 
                     
                 
                  
                 Z 
               
               = 
               
                 
                   
                     
                       
                         [ 
                         
                           
                             
                               In 
                                
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   Sa 
                                 
                                 ) 
                               
                             
                             - 
                             A 
                           
                           
                             K 
                             m 
                           
                         
                         ] 
                       
                       
                         1 
                         r 
                       
                     
                      
                     
                       
 
                     
                     [ 
                     
                       
                         
                           
                             sin 
                              
                             
                               ( 
                               
                                 
                                   120 
                                    
                                   ° 
                                 
                                 - 
                                 H 
                               
                               ) 
                             
                           
                           
                             sin 
                              
                             
                                 
                             
                              
                             H 
                           
                         
                          
                         Y 
                       
                       + 
                       
                         
                           
                             
                               
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 H 
                               
                               - 
                               
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       120 
                                        
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                             
                               sin 
                                
                               
                                   
                               
                                
                               H 
                             
                           
                            
                           
                             [ 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ] 
                           
                         
                         
                           1 
                           r 
                         
                       
                     
                     ] 
                   
                   + 
                   
                     Y 
                     p 
                   
                 
                 = 
                 
                   
                     
                       ( 
                       
                         
                           In 
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ) 
                     
                     q 
                   
                   - 
                   
                     
                       [ 
                       
                         
                           
                             In 
                              
                             
                               ( 
                               
                                 1 
                                 - 
                                 Sa 
                               
                               ) 
                             
                           
                           - 
                           A 
                         
                         
                           K 
                           m 
                         
                       
                       ] 
                     
                     
                       p 
                       r 
                     
                   
                 
               
             
           
         
       
       
         
           
             X 
             = 
             
               
                 
                   
                     sin 
                      
                     
                       ( 
                       
                         
                           120 
                            
                           ° 
                         
                         - 
                         H 
                       
                       ) 
                     
                   
                   
                     sin 
                      
                     
                         
                     
                      
                     H 
                   
                 
                  
                 Y 
               
               + 
               
                 
                   
                     
                       
                         sin 
                          
                         
                             
                         
                          
                         H 
                       
                       - 
                       
                         sin 
                          
                         
                             
                         
                          
                         
                           ( 
                           
                             
                               120 
                                
                               ° 
                             
                             - 
                             H 
                           
                           ) 
                         
                       
                     
                     
                       sin 
                        
                       
                           
                       
                        
                       H 
                     
                   
                    
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                 
                 
                   1 
                   r 
                 
               
             
           
         
       
     
     the values of X and Y represented by In, Sa, H, p, q and r are obtained according to the specitic values of p, q and r, X&gt;Y≧0,Y≦Z≧0, Z is a value satisfying the actual physical condition 
     
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               1 
             
             , 
             
               
 
             
              
             
               
                 then 
                  
                 
                     
                 
                  
                 X 
               
               = 
               
                 
                   
                     
                       
                         [ 
                         
                           
                             
                               In 
                                
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   Sa 
                                 
                                 ) 
                               
                             
                             - 
                             A 
                           
                           
                             K 
                             m 
                           
                         
                         ] 
                       
                       
                         1 
                         r 
                       
                     
                      
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         H 
                                         - 
                                         
                                           120 
                                            
                                           ° 
                                         
                                       
                                       ) 
                                     
                                   
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         
                                           240 
                                            
                                           ° 
                                         
                                         - 
                                         H 
                                       
                                       ) 
                                     
                                   
                                 
                                  
                                 Y 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           
                                             240 
                                              
                                             ° 
                                           
                                           - 
                                           H 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           H 
                                           - 
                                           
                                             120 
                                              
                                             ° 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         
                                           240 
                                            
                                           ° 
                                         
                                         - 
                                         H 
                                       
                                       ) 
                                     
                                   
                                 
                                  
                                 
                                   [ 
                                   
                                     
                                       
                                         In 
                                          
                                         
                                           ( 
                                           
                                             1 
                                             - 
                                             Sa 
                                           
                                           ) 
                                         
                                       
                                       - 
                                       A 
                                     
                                     
                                       K 
                                       m 
                                     
                                   
                                   ] 
                                 
                               
                               
                                 1 
                                 r 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                   p 
                 
                 + 
                 
                     
                   
                     
                       Y 
                       p 
                     
                     = 
                     
                       
                         
                           
                             ( 
                             
                               
                                 In 
                                 - 
                                 B 
                               
                               
                                 K 
                                 M 
                               
                             
                             ) 
                           
                           q 
                         
                         - 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     In 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         Sa 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   A 
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               p 
                               r 
                             
                           
                            
                           
                             
 
                           
                            
                           Z 
                         
                       
                       = 
                       
                         
                           
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   H 
                                   - 
                                   
                                     120 
                                      
                                     ° 
                                   
                                 
                                 ) 
                               
                             
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   
                                     240 
                                      
                                     ° 
                                   
                                   - 
                                   H 
                                 
                                 ) 
                               
                             
                           
                            
                           Y 
                         
                         + 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         240 
                                          
                                         ° 
                                       
                                       - 
                                       H 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       H 
                                       - 
                                       
                                         120 
                                          
                                         ° 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       240 
                                        
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                              
                             
                               [ 
                               
                                 
                                   
                                     In 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         Sa 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   A 
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                           
                           
                             1 
                             r 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     the values of X and Y represented by In, Sa, H, p, q and r are obtained according to the specific values of p, q and r, X&gt;Y≧0,Y≦Z≧0, Z is a value satis 1 ing the actual physical condition 
     
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               2 
             
             , 
             
               
 
             
              
             
               
                 then 
                  
                 
                     
                 
                  
                 Y 
               
               = 
               
                 
                   
                     
                       
                         [ 
                         
                           
                             
                               In 
                                
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   Sa 
                                 
                                 ) 
                               
                             
                             - 
                             A 
                           
                           
                             K 
                             m 
                           
                         
                         ] 
                       
                       
                         1 
                         r 
                       
                     
                      
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         - 
                                         H 
                                       
                                       ) 
                                     
                                   
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         H 
                                         - 
                                         
                                           240 
                                            
                                           ° 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                  
                                 X 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           H 
                                           - 
                                           
                                             240 
                                              
                                             ° 
                                           
                                         
                                         ) 
                                       
                                     
                                     - 
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           - 
                                           H 
                                         
                                         ) 
                                       
                                     
                                   
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         H 
                                         - 
                                         
                                           240 
                                            
                                           ° 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                  
                                 
                                   [ 
                                   
                                     
                                       
                                         In 
                                          
                                         
                                           ( 
                                           
                                             1 
                                             - 
                                             Sa 
                                           
                                           ) 
                                         
                                       
                                       - 
                                       A 
                                     
                                     
                                       K 
                                       m 
                                     
                                   
                                   ] 
                                 
                               
                               
                                 1 
                                 r 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                   p 
                 
                 + 
                 
                     
                   
                     
                       X 
                       p 
                     
                     = 
                     
                       
                         
                           
                             ( 
                             
                               
                                 In 
                                 - 
                                 B 
                               
                               
                                 K 
                                 M 
                               
                             
                             ) 
                           
                           q 
                         
                         - 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     In 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         Sa 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   A 
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               p 
                               r 
                             
                           
                            
                           
                             
 
                           
                            
                           Z 
                         
                       
                       = 
                       
                         
                           
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   - 
                                   H 
                                 
                                 ) 
                               
                             
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   H 
                                   - 
                                   
                                     240 
                                      
                                     ° 
                                   
                                 
                                 ) 
                               
                             
                           
                            
                           X 
                         
                         + 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       H 
                                       - 
                                       
                                         240 
                                          
                                         ° 
                                       
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       H 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       240 
                                        
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                              
                             
                               [ 
                               
                                 
                                   
                                     In 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         Sa 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   A 
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                           
                           
                             1 
                             r 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     the values of X and Y represented by In, Sa, H, p, q and r are obtained according to the specific values of p, q and r, X&gt;Y≧0,Y≦Z≧0, Z is a value satis 1 ing the actual physical condition
 
or if the saturation Sa and the intensity In in the color data in the HSaIn format at the input device side are acquired according to the formulae below,
 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     r 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 
                   
                     
                       K 
                       M 
                     
                      
                     
                       [ 
                       
                         
                           
                             ( 
                             
                               X 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                         + 
                         
                           
                             ( 
                             
                               Y 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                         + 
                         
                           
                             ( 
                             
                               Z 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                       
                       ] 
                     
                   
                   
                     1 
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 Cl 
                 + 
                 Gl 
               
             
             , 
             
               
 
             
              
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, p, q and r are nonzero real numbers, In≧Gl≧0, A≧0, B≧0 the color data in the XYZ format at the output device side is acquired according to the following formulae: 
     
       
         
           
             
               h 
               = 
               
                 [ 
                 
                   H 
                   
                     120 
                      
                     ° 
                   
                 
                 ] 
               
             
             , 
             
               
 
             
              
             
               
                 [ 
                 • 
                 ] 
               
                
               
                   
               
                
               is 
                
               
                   
               
                
               a 
                
               
                   
               
                
               round 
                
               
                   
               
                
               symbol 
                
               
                   
               
                
               with 
                
               
                   
               
                
               respect 
                
               
                   
               
                
               to 
                
               
                   
               
                
               • 
             
             , 
             
               
 
             
              
             
               H 
               ∈ 
               
                 [ 
                 
                   
                     0 
                      
                     ° 
                   
                   , 
                   
                     360 
                      
                     ° 
                   
                 
                 ) 
               
             
             , 
             
               
 
             
              
             
               h 
               = 
               0 
             
             , 
             1 
             , 
             2 
           
         
       
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               0 
             
             , 
             
               
 
             
              
             
               X 
               = 
               
                 
                   
                     
                       
                         ( 
                         
                           
                             InSa 
                             - 
                             B 
                           
                           
                             K 
                             m 
                           
                         
                         ) 
                       
                       
                         q 
                         p 
                       
                     
                      
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             120 
                              
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                   
                     
                       [ 
                       
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               
                                 120 
                                  
                                 ° 
                               
                               - 
                               H 
                             
                             ) 
                           
                         
                         + 
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             H 
                             ) 
                           
                         
                       
                       ] 
                     
                     
                       1 
                       p 
                     
                   
                 
                 + 
                 
                   [ 
                   
                     
                       
                         In 
                          
                         
                           ( 
                           
                             1 
                             - 
                             Sa 
                           
                           ) 
                         
                       
                       - 
                       A 
                     
                     
                       K 
                       m 
                     
                   
                   ] 
                 
               
             
             , 
             
               
 
             
              
             
               Y 
               = 
               
                 
                   
                     
                       
                         ( 
                         
                           
                             InSa 
                             - 
                             B 
                           
                           
                             K 
                             m 
                           
                         
                         ) 
                       
                       
                         q 
                         p 
                       
                     
                      
                     
                       sin 
                        
                       
                         ( 
                         H 
                         ) 
                       
                     
                   
                   
                     
                       [ 
                       
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             H 
                             ) 
                           
                         
                         + 
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               
                                 120 
                                  
                                 ° 
                               
                               - 
                               H 
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     
                       1 
                       p 
                     
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     r 
                   
                 
               
             
             , 
             
               
 
             
              
             
               Z 
               = 
               
                 
                   [ 
                   
                     
                       
                         In 
                          
                         
                           ( 
                           
                             1 
                             - 
                             Sa 
                           
                           ) 
                         
                       
                       - 
                       A 
                     
                     
                       K 
                       m 
                     
                   
                   ] 
                 
                 
                   1 
                   r 
                 
               
             
           
         
       
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               1 
             
             , 
             
               
 
             
              
             
               X 
               = 
               
                 
                   [ 
                   
                     
                       
                         In 
                          
                         
                           ( 
                           
                             1 
                             - 
                             Sa 
                           
                           ) 
                         
                       
                       - 
                       A 
                     
                     
                       K 
                       m 
                     
                   
                   ] 
                 
                 
                   1 
                   r 
                 
               
             
             , 
             
               
 
             
              
             
               Y 
               = 
               
                 
                   
                     
                       
                         ( 
                         
                           
                             InSa 
                             - 
                             B 
                           
                           
                             K 
                             m 
                           
                         
                         ) 
                       
                       
                         q 
                         p 
                       
                     
                      
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             240 
                              
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                   
                     
                       [ 
                       
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               H 
                               - 
                               
                                 120 
                                  
                                 ° 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               
                                 240 
                                  
                                 ° 
                               
                               - 
                               H 
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     
                       1 
                       p 
                     
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     r 
                   
                 
               
             
             , 
             
               
 
             
              
             
               Z 
               = 
               
                 
                   
                     
                       
                         ( 
                         
                           
                             InSa 
                             - 
                             B 
                           
                           
                             K 
                             m 
                           
                         
                         ) 
                       
                       
                         q 
                         p 
                       
                     
                      
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             120 
                              
                             ° 
                           
                         
                         ) 
                       
                     
                   
                   
                     
                       [ 
                       
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               H 
                               - 
                               
                                 120 
                                  
                                 ° 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               
                                 240 
                                  
                                 ° 
                               
                               - 
                               H 
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     
                       1 
                       p 
                     
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     r 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               2 
             
             , 
             
               
 
             
              
             
               X 
               = 
               
                 
                   
                     
                       
                         ( 
                         
                           
                             InSa 
                             - 
                             B 
                           
                           
                             K 
                             m 
                           
                         
                         ) 
                       
                       
                         q 
                         p 
                       
                     
                      
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             240 
                              
                             ° 
                           
                         
                         ) 
                       
                     
                   
                   
                     
                       [ 
                       
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               - 
                               H 
                             
                             ) 
                           
                         
                         + 
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               H 
                               - 
                               
                                 240 
                                  
                                 ° 
                               
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     
                       1 
                       p 
                     
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     r 
                   
                 
               
             
             , 
             
               
 
             
              
             
               Y 
               = 
               
                 
                   [ 
                   
                     
                       
                         In 
                          
                         
                           ( 
                           
                             1 
                             - 
                             Sa 
                           
                           ) 
                         
                       
                       - 
                       A 
                     
                     
                       K 
                       m 
                     
                   
                   ] 
                 
                 
                   1 
                   r 
                 
               
             
             , 
             
               
 
             
              
             
               Z 
               = 
               
                 
                   
                     
                       
                         ( 
                         
                           
                             InSa 
                             - 
                             B 
                           
                           
                             K 
                             m 
                           
                         
                         ) 
                       
                       
                         q 
                         p 
                       
                     
                      
                     
                       sin 
                        
                       
                         ( 
                         
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                   
                     
                       [ 
                       
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               H 
                               - 
                               
                                 240 
                                  
                                 ° 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               - 
                               H 
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     
                       1 
                       p 
                     
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     r 
                   
                 
               
             
           
         
       
     
     The parameters, e.g., K M , K m , p, q, r, m, A, B, etc., in the respective converting manners from the data in the HGlCl format to the data in the CIEXYZ format should be selected by referring to the converting manners from the data in the CIEXYZ format to the data in the HGlCl format within the defined range of each parameter, and the parameters are preferably selected as follows: K M =K m =1, p=q=r=m−1, and A=B=0. 
     In the embodiment, the step  2241  can be further included after converting the color data in the HSaIn format at the output device side into color data in an XYZ format. In the step  2241 , the color data in the XYZ format at the output device side is converted into color data of the output device. 
     If the color data at the output device side is in a UVW format, the color data in the XYZ format at the output device side is converted into color data in a UVW format according to the following formulae 21-28: 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             U 
                             2 
                           
                         
                       
                       
                         
                           
                             V 
                             2 
                           
                         
                       
                       
                         
                           
                             W 
                             2 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         α 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       2 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       2 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         β 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       2 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         γ 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               X 
                             
                           
                           
                             
                               Y 
                             
                           
                           
                             
                               Z 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     21 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 21, α 2 &gt;0, β 2 &gt;0, γ 2 &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             U 
                             2 
                           
                         
                       
                       
                         
                           
                             V 
                             2 
                           
                         
                       
                       
                         
                           
                             W 
                             2 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         α 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       2 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         β 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       2 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         γ 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               X 
                             
                           
                           
                             
                               Y 
                             
                           
                           
                             
                               Z 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     22 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 22, α 2 &gt;0, β 2 &gt;0, γ 2 &lt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             U 
                             2 
                           
                         
                       
                       
                         
                           
                             V 
                             2 
                           
                         
                       
                       
                         
                           
                             W 
                             2 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         α 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       2 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       2 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         β 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         γ 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               X 
                             
                           
                           
                             
                               Y 
                             
                           
                           
                             
                               Z 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     23 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 23, α 2 &gt;0, β 2 &lt;0, γ 2 &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             U 
                             2 
                           
                         
                       
                       
                         
                           
                             V 
                             2 
                           
                         
                       
                       
                         
                           
                             W 
                             2 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         α 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       2 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         β 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         γ 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               X 
                             
                           
                           
                             
                               Y 
                             
                           
                           
                             
                               Z 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     24 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 24, α 2 &gt;0, β 2 &lt;0, γ 2 &lt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             U 
                             2 
                           
                         
                       
                       
                         
                           
                             V 
                             2 
                           
                         
                       
                       
                         
                           
                             W 
                             2 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         α 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       2 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         β 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       2 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         γ 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               X 
                             
                           
                           
                             
                               Y 
                             
                           
                           
                             
                               Z 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     25 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 25, α 2 &lt;0, β 2 &gt;0, γ 2 &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             U 
                             2 
                           
                         
                       
                       
                         
                           
                             V 
                             2 
                           
                         
                       
                       
                         
                           
                             W 
                             2 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         α 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         β 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       2 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         γ 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               X 
                             
                           
                           
                             
                               Y 
                             
                           
                           
                             
                               Z 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     26 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 26, α 2 &lt;0, β 2 &gt;0, γ 2 &lt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             U 
                             2 
                           
                         
                       
                       
                         
                           
                             V 
                             2 
                           
                         
                       
                       
                         
                           
                             W 
                             2 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         α 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       2 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         β 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         γ 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               X 
                             
                           
                           
                             
                               Y 
                             
                           
                           
                             
                               Z 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     27 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 27, α 2 &gt;0, β 2 &lt;0, γ 2 &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             U 
                             2 
                           
                         
                       
                       
                         
                           
                             V 
                             2 
                           
                         
                       
                       
                         
                           
                             W 
                             2 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         α 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         β 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         γ 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               X 
                             
                           
                           
                             
                               Y 
                             
                           
                           
                             
                               Z 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     28 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 28, α 2 &lt;0, β 2 &lt;0, γ 2 &lt;0; 
     wherein in the formulae 21-28, α 2  is a hue deviation angle between   and  ; β 2  is a hue deviation angle between   and  ; γ 2  is a hue deviation angle between   and  , the values of U 2 , V 2  and W 2  are the color data in the UVW format of the output device obtained after the conversion; the values of X, Y and Z in the formulae 21-28 are the color data in the XYZ format;  ,   and   are UVW channel color data of the output device to represent chromatic vectors within the chromatic plane. 
     If the color data of the output device is in a multichannel format, the color data C 1 , C 2  . . . . , C n  in the multichannel format is obtained according to characterized hue data α 1 , α 2 , . . . , α n  of the respective channels C 1 , C 2 , . . . , C n  in the color space of the multichannel device and a conversion relationship from predefined  ,   and   of the output device to chromatic vectors  ,  , L,   within the chromatic plane. 
     After the chromatic color data of the output device is obtained, it will be converted into a chromatic image of the output device to be sent to the output device for an image output. The output device, after receiving the chromatic image in the output format that can be identified and processed thereby, performs an image output, e.g., displaying, printing, projecting and the like. 
     Since the output device has undergone the corresponding processing of removing the color attribute of the output device itself before receiving the chromatic image of the output device and outputting the received chromatic image, when the same chromatic image based on the HSaIn color space model is output through the output devices of different color attributes, almost consistent images will be output. For example, when the printing is performed through the printers of different color attributes, almost consistent chromatic images will be printed to hereby achieve the object “what you see is what you get”. 
     In the embodiment, the management method of obtaining color data in an HSaIn format from color data in an XYZ format at the input device side and the management method of obtaining color data in an XYZ format at the output device side from color data in an HSaIn format at the output device side can be independent of each other. 
       FIG. 3  shows a flow chart of the method of managing color data based on color data in an HSaIn format in an HSaIn color appearance color space of another embodiment of the invention. 
     The HSaIn color appearance color space describing the color data in the HSaIn format in the embodiment shown in  FIG. 3  of the invention and the HSaIn color space describing the color data in the HSaIn format in the embodiment shown in  FIG. 2  are essentially the same. That is to say, the HSaIn color appearance color space is a color space based on a CIEXYZ Cartesian color appearance color space, of a color appearance attribute, and described by a cylindrical coordinate system, and is composed of a chromatic plane and a gray axis passing through the origin of the chromatic plane and perpendicular to the chromatic plane; 
     wherein the chromatic plane is a plane of the CIEXYZ Cartesian color appearance color space X+Y+Z=K, where K is a real constant; an XYZ axis of the CIEXYZ Cartesian color appearance color space performs a projection along a direction of a straight line X=Y=Z on a plane X+Y+Z=K to obtain three projection axes that are 120° with respect to one another within the chromatic plane, and unit vectors in the directions of the projection axes are  ,   and  ;
 
wherein the color data in the HSaIn format comprises a hue H, a saturation Sa, and an intensity In in the HSaIn color appearance color space; the hue H is described by a polar angle within the chromatic plane in the HSaIn color appearance color space, Sa is described by a proportion of the chromaticness to the intensity Cl/In, and m is described by the sum of the gray and the chromaticness Gl+Cl, Gl=min(X, Y, Z), and is described by the gray axis data of HSaIn,
 
     
       
         
           
             
               Cl 
               = 
               
                 
                    
                   
                     
                       X 
                        
                       
                         i 
                         V 
                       
                     
                     + 
                     
                       Y 
                        
                       
                         j 
                         V 
                       
                     
                     + 
                     
                       Z 
                        
                       
                         k 
                         V 
                       
                     
                   
                    
                 
                 m 
               
             
             , 
           
         
       
     
     m is a real number and is described by the m th  power of the module of the chromatic vector parallel to the chromatic plane in the HSaIn space. 
     As shown in  FIG. 3 , color data in an XYZ format in a CIEXYZ color space at the input device side is acquired. There are several manners of acquiring the color data in the XYZ format in the CIEXYZ color space at the input device side. The context has given detailed descriptions of the embodiment shown in  FIG. 2 , and no unnecessary details are given herein. In the step  320 , the acquired color data in the XYZ format at the input device side is converted into color data in an XYZ format in a CIEXYZ color appearance color space. In the step  3202 , the color data in the XYZ format in the CIEXYZ color appearance color space is converted into color data in an HSaIn format in an HSaIn color appearance color space at the input device side. 
     Specially, the converting the acquired color data in the XYZ format into color data in an XYZ format in a CIEXYZ color appearance color space (the step  320 ) comprises: converting the color data in the XYZ format into color appearance color data R a ′, G a ′, B a ′ in an RGB format at the input device side under a predefined observation condition according to a technical standard CIECAM02; obtaining three color characteristic data R a ′, G a ′, B a ′, i.e., hue deviation angles α a , β a  and γ a  within the chromatic plane, using characteristic hue values of cone response chromatograms of R a ′, G a ′ and B a ′; performing a conversion into color data X a , Y a , Z a  in an XYZ format in a CIEXYZ color appearance color space according to R a ′, G a ′ and B a ′ and the hue deviation angles α a , β a  and γ a . 
     Specifically, the performing a conversion into color data X a , Y a , Z a  in an XYZ format in a CIEXYZ color appearance color space according to R a ′, G a ′ and B a ′ and the hue deviation angles α a , β a  and γ a  comprises: 
     converting R a ′, G a ′ and B a ′ into color data in an XYZ format in the CIEXYZ color appearance color space according to the following formulae 60-67: 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             a 
                           
                         
                       
                       
                         
                           
                             Y 
                             a 
                           
                         
                       
                       
                         
                           
                             Z 
                             a 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                         [ 
                         
                           
                             
                               
                                 R 
                                 a 
                                 ′ 
                               
                             
                           
                           
                             
                               
                                 G 
                                 a 
                                 ′ 
                               
                             
                           
                           
                             
                               
                                 B 
                                 a 
                                 ′ 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     60 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 60, α a &gt;0, β a &gt;0, γ a &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             a 
                           
                         
                       
                       
                         
                           
                             Y 
                             a 
                           
                         
                       
                       
                         
                           
                             Z 
                             a 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       + 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   R 
                                   a 
                                   ′ 
                                 
                               
                             
                             
                               
                                 
                                   G 
                                   a 
                                   ′ 
                                 
                               
                             
                             
                               
                                 
                                   B 
                                   a 
                                   ′ 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     61 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 61, α a &gt;0, β a &gt;0, γ a &lt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             a 
                           
                         
                       
                       
                         
                           
                             Y 
                             a 
                           
                         
                       
                       
                         
                           
                             Z 
                             a 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       + 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   R 
                                   a 
                                   ′ 
                                 
                               
                             
                             
                               
                                 
                                   G 
                                   a 
                                   ′ 
                                 
                               
                             
                             
                               
                                 
                                   B 
                                   a 
                                   ′ 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     62 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 62, α a &gt;0, β a &lt;0, γ a &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             a 
                           
                         
                       
                       
                         
                           
                             Y 
                             a 
                           
                         
                       
                       
                         
                           
                             Z 
                             a 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       + 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       + 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   R 
                                   a 
                                   ′ 
                                 
                               
                             
                             
                               
                                 
                                   G 
                                   a 
                                   ′ 
                                 
                               
                             
                             
                               
                                 
                                   B 
                                   a 
                                   ′ 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     63 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 63, α a &gt;0, β a &lt;0, γ a &lt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             a 
                           
                         
                       
                       
                         
                           
                             Y 
                             a 
                           
                         
                       
                       
                         
                           
                             Z 
                             a 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       + 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   R 
                                   a 
                                   ′ 
                                 
                               
                             
                             
                               
                                 
                                   G 
                                   a 
                                   ′ 
                                 
                               
                             
                             
                               
                                 
                                   B 
                                   a 
                                   ′ 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     64 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 64, α a &lt;0, β a &gt;0, γ a &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             a 
                           
                         
                       
                       
                         
                           
                             Y 
                             a 
                           
                         
                       
                       
                         
                           
                             Z 
                             a 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       + 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       + 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                         [ 
                         
                           
                             
                               
                                 R 
                                 a 
                                 ′ 
                               
                             
                           
                           
                             
                               
                                 G 
                                 a 
                                 ′ 
                               
                             
                           
                           
                             
                               
                                 B 
                                 a 
                                 ′ 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     65 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 65, α a &lt;0. β a &gt;0, γ a &lt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             a 
                           
                         
                       
                       
                         
                           
                             Y 
                             a 
                           
                         
                       
                       
                         
                           
                             Z 
                             a 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       + 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       + 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                         [ 
                         
                           
                             
                               
                                 R 
                                 a 
                                 ′ 
                               
                             
                           
                           
                             
                               
                                 G 
                                 a 
                                 ′ 
                               
                             
                           
                           
                             
                               
                                 B 
                                 a 
                                 ′ 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     66 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 66, α a &lt;0, β a &lt;0, γ a &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             a 
                           
                         
                       
                       
                         
                           
                             Y 
                             a 
                           
                         
                       
                       
                         
                           
                             Z 
                             a 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       + 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       + 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       + 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       × 
                       
                         [ 
                         
                           
                             
                               
                                 R 
                                 a 
                                 ′ 
                               
                             
                           
                           
                             
                               
                                 G 
                                 a 
                                 ′ 
                               
                             
                           
                           
                             
                               
                                 B 
                                 a 
                                 ′ 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     67 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 67, α a &lt;0, β a &lt;0, γ a &lt;0;
 
wherein the values of R a ′, G a ′ and B a ′ in the above formulae 60-67 are the color data in the RGB format; the values of X a , Y a  and Z a  in the formulae 60-67 are the converted color data in the CIEXYZ color appearance color space; α a  is a hue deviation angle between   and  ; β a  is a hue deviation angle between   and  ; γ a  is a hue deviation angle between   and  ; R a ′, G a ′ and B a ′ are modules of the chromatic vectors  ,  ,   within the chromatic plane.
 
     Specially, the converting the color data in the XYZ format in the CIEXYZ color appearance color space into color data in an HSaIn format in an HSaIn color appearance color space at the input device side (the step  3202 ) comprises: 
     acquiring the hue H in the color data in the HSaIn format at the input device side according to the following formula: 
     
       
         
           
             
               
                 
                   H 
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               arccos 
                               ( 
                               
                                 
                                   
                                     2 
                                      
                                     
                                       X 
                                       a 
                                     
                                   
                                   - 
                                   
                                     Y 
                                     a 
                                   
                                   - 
                                   
                                     Z 
                                     a 
                                   
                                 
                                 
                                   2 
                                    
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 ( 
                                                 
                                                   
                                                     X 
                                                     a 
                                                   
                                                   - 
                                                   
                                                     Y 
                                                     z 
                                                   
                                                 
                                                 ) 
                                               
                                               2 
                                             
                                             + 
                                             
                                               
                                                 ( 
                                                 
                                                   
                                                     Y 
                                                     a 
                                                   
                                                   - 
                                                   
                                                     Z 
                                                     a 
                                                   
                                                 
                                                 ) 
                                               
                                               2 
                                             
                                             + 
                                           
                                         
                                       
                                       
                                         
                                           
                                             
                                               ( 
                                               
                                                 
                                                   X 
                                                   a 
                                                 
                                                 - 
                                                 
                                                   Y 
                                                   a 
                                                 
                                               
                                               ) 
                                             
                                              
                                             
                                               ( 
                                               
                                                 
                                                   Y 
                                                   a 
                                                 
                                                 - 
                                                 
                                                   Z 
                                                   a 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                             , 
                           
                         
                         
                           
                             
                               Y 
                               a 
                             
                             ≥ 
                             
                               Z 
                               a 
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 2 
                                  
                                 π 
                               
                               - 
                               
                                 arccos 
                                 ( 
                                 
                                   
                                     
                                       2 
                                        
                                       
                                         X 
                                         a 
                                       
                                     
                                     - 
                                     
                                       Y 
                                       a 
                                     
                                     - 
                                     
                                       Z 
                                       a 
                                     
                                   
                                   
                                     2 
                                      
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   ( 
                                                   
                                                     
                                                       X 
                                                       a 
                                                     
                                                     - 
                                                     
                                                       Y 
                                                       z 
                                                     
                                                   
                                                   ) 
                                                 
                                                 2 
                                               
                                               + 
                                               
                                                 
                                                   ( 
                                                   
                                                     
                                                       Y 
                                                       a 
                                                     
                                                     - 
                                                     
                                                       Z 
                                                       a 
                                                     
                                                   
                                                   ) 
                                                 
                                                 2 
                                               
                                               + 
                                             
                                           
                                         
                                         
                                           
                                             
                                               
                                                 ( 
                                                 
                                                   
                                                     X 
                                                     a 
                                                   
                                                   - 
                                                   
                                                     Y 
                                                     a 
                                                   
                                                 
                                                 ) 
                                               
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     Y 
                                                     a 
                                                   
                                                   - 
                                                   
                                                     Z 
                                                     a 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                             , 
                           
                         
                         
                           
                             
                               Y 
                               a 
                             
                             &lt; 
                             
                               Z 
                               a 
                             
                           
                         
                       
                       
                         
                           
                             undefined 
                             , 
                           
                         
                         
                           
                             
                               X 
                               a 
                             
                             = 
                             
                               
                                 Y 
                                 a 
                               
                               = 
                               
                                 Z 
                                 a 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     wherein the tristimulus values X a , Y a , Z a  are the color data in the XYZ format, i.e., the color data in the CIEXYZ Cartesian color appearance color space, and respectively represent numerical values on the X, Y and Z coordinate axes in the CIEXYZ Cartesian color space. 
     The saturation Sa and the intensity In in the color data in the HSaIn format at the input device side are acquired according to the following formulae and based on the color data in the XYZ format in the CIEXYZ color appearance color space: 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     
                       K 
                       m 
                     
                      
                     
                       [ 
                       
                         Min 
                          
                         
                           ( 
                           
                             X 
                             , 
                             Y 
                             , 
                             Z 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                   p 
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     
                       K 
                       M 
                     
                      
                     
                       [ 
                       
                         Max 
                          
                         
                           ( 
                           
                             X 
                             , 
                             Y 
                             , 
                             Z 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                   q 
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, In≧Gl≧0, A≧0, B≧0, p and q are nonzero real numbers or 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     
                       K 
                       m 
                     
                      
                     
                       [ 
                       
                         Min 
                          
                         
                           ( 
                           
                             X 
                             , 
                             Y 
                             , 
                             Z 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                   p 
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     1 
                     3 
                   
                    
                   
                     
                       
                         K 
                         M 
                       
                        
                       
                         ( 
                         
                           X 
                           + 
                           Y 
                           + 
                           Z 
                         
                         ) 
                       
                     
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m , In≧Gl≧0, A≧0, B≧0, p and q are nonzero real numbers or 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     p 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     1 
                     2 
                   
                    
                   
                     
                       
                         K 
                         M 
                       
                        
                       
                         [ 
                         
                           
                             Max 
                              
                             
                               ( 
                               
                                 X 
                                 , 
                                 Y 
                                 , 
                                 Z 
                               
                               ) 
                             
                           
                           + 
                           
                             Min 
                              
                             
                               ( 
                               
                                 X 
                                 , 
                                 Y 
                                 , 
                                 Z 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m , In≧Gl≧0, A≧0, B≧0, p and q are nonzero real numbers or 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     p 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 
                   
                     K 
                     M 
                   
                    
                   
                     
                        
                       
                         
                           X 
                            
                           
                             i 
                             V 
                           
                         
                         + 
                         
                           Y 
                            
                           
                             j 
                             V 
                           
                         
                         + 
                         
                           Z 
                            
                           
                             k 
                             V 
                           
                         
                       
                        
                     
                     m 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 Gl 
                 + 
                 Cl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, p and m are nonzero real numbers, In≧Gl≧0, A≧0, B≧0 or 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     r 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     
                       K 
                       M 
                     
                      
                     
                       [ 
                       
                         
                           X 
                           P 
                         
                         + 
                         
                           Y 
                           P 
                         
                         + 
                         
                           Z 
                           P 
                         
                       
                       ] 
                     
                   
                   
                     1 
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m &gt;0, p, q and r are nonzero real numbers, In≧Gl≧0, A≧0, B≧0 or 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     r 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 
                   
                     
                       K 
                       m 
                     
                      
                     
                       [ 
                       
                         
                           
                             ( 
                             
                               X 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                         + 
                         
                           
                             ( 
                             
                               Y 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                         + 
                         
                           
                             ( 
                             
                               Z 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                       
                       ] 
                     
                   
                   
                     1 
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 Cl 
                 + 
                 Gl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m &gt;0, p, q and r are nonzero real numbers, In≧Gl≧0, A≧0, B≧0 
     In the process of converting the data in the CIEXYZ format into data in an HSaIn format, parameters, e.g., K M , K m , p, q, r, m, A, B, etc., in each acquiring manner can be selected within their defined ranges and are feasible in the implementation, but the preferred selection is that K M =K m =1, p=q=r=m−1, and A=B=0. 
     After the chromatic image independent of the impacts of the color characteristic of the device itself is acquired, the chromatic image independent of the impacts of the color characteristic of the device itself can be output through the output device for an output display or an output printing, projection and the like. The output device can specifically include a display, a printer, a printing machine, a projector and the like. The so-called chromatic image in an output format refers to a chromatic image in a storage format that can be identified and processed by the output device. For example, if the output device is a display, the output format of the chromatic image thereof is generally an RGB format; if the output device is a printer, the output format of the chromatic image thereof is generally a CMYe format. The specific method of converting the color data of the chromatic image in the HSaIn format into color data of a chromatic image in an output format, and removing the impacts of the color attribute of the output device itself on the output chromatic image in the conversion process will be introduced in detail below. 
     The embodiment shown in  FIG. 3  further comprises the step  322 , in which the color data in the HSaIn format in the HSaIn color appearance color space at the input device side is mapped according to a mapping relationship between a color gamut of the input device and a color gamut of the output device to obtain the color data in the HSaIn format in the HSaIn color appearance color space at the output device side. Specifically,  FIG. 7 ,  FIG. 8  and  FIG. 9  show a color gamut comparing relationship between the input device and the output device, a white field position within the chromatic plane, and a color distribution range of an image;  FIG. 10  and  FIG. 11  show an intensity mapping relationship and a saturation mapping relationship under an Iso-hue plane in the HSaIn color appearance color space under the determination of the color representation intention;  FIG. 12  and  FIG. 13  show an intensity mapping relationship In LUT  and a saturation mapping relationship Sa LUT  corresponding to the input and output gamuts, and the mapping of all color data of the image from the input device side to the output device side is performed according to In LUT  and Sa LUT  to obtain the color data in the HSaIn format in the HSaIn color appearance color space at the output device side. 
     Within the chromatic plane, a pure chromatic vector of each channel of each device is represented according to the intensity numerical value of the channel and the characterized hue value of the spectrum of the channel, all possible intensity numerical values of all the channels are traversed, and the set of all the chromatic vectors obtained by these traversed intensity data undergoing a pure chromatic vector addition within the chromatic plane according to a vector addition rule is just the color gamut represented by this device within the chromatic plane. The white field position in the color gamut is a position where the chromatic vector obtained after the addition of the pure chromatic vectors corresponding to the XYZ values of the white field self-defined by the respective devices within the chromatic plane is located. If the XYZ values of the white field are equal, the white field position is on the origin of the polar coordinate. The color distribution range of the image is a set of the positions of the superimposed chromatic vectors obtained by the XYZ value data of all the pixels of this image by means of the vector addition rule within the chromatic plane, and the distribution formed by this set is just the color distribution range of this image within the chromatic plane. The color representation intention is preset one of the color management strategies of the color gamut mapping, and is generally divided into a perceptual color representation intention, a saturated color representation intention, a relative chrominance color representation intention and an absolute color representation intention according to the textbook, and more color representation intentions can be further defined according to specific requirements for the color management, and no unnecessary details are given herein. 
       FIG. 7 ,  FIG. 8  and  FIG. 9  show schematic examples of the gamuts of the input and output devices within the chromatic plane, the white field position and the distribution range of the image, and one input image distribution under the perceptual color representation intention from the state that the output color gamut cannot be completely covered to the state that the output gamut is completely covered. 
       FIG. 10  and  FIG. 11  are schematic diagrams of the color gamut mapping. Performing the color gamut mapping in the HSaIn color appearance color space is divided into performing an intensity In preferential mapping and performing a saturation Sa preferential mapping under the iso-H. The In preferential mapping is to map In according to LUT on the premise that the Sa mapping relationship is preset; the Sa preferential mapping is to map Sa according to LUT on the premise that the In mapping relationship is preset. 
       FIG. 10  shows that in process of performing the color gamut mapping in the HSaIn color appearance color space, on the premise of the iso-hue H, the transverse axis is the Cl chromatic vector under the hue H, the longitudinal axis is the Gl gray, on the premise of the iso-Sa, the schematic diagram of performing the intensity mapping with In LUT  as shown in  FIG. 12  is performed, and the output intensities of all the color data under the iso-H and the iso-Sa are obtained finally to thereby obtain the color data H, Sa, In at the output device side. 
       FIG. 11  shows that in the process of performing the color gamut mapping in the HSaIn color appearance color space, on the premise of the iso-hue H, the transverse axis is the Cl chromatic vector under the hue H, the longitudinal axis is the Gl gray, on the premise that the preset incremental Sa line is performed according to the color representation intention, the schematic diagram of performing the intensity mapping with In LUT  as shown in  FIG. 12  is performed, and the output intensities of all the color data under the iso-H and the incremental Sa are obtained finally to thereby obtain the color data H, Sa, In at the output device side. 
     Similarly, there is a further intensity mapping performed on the premise of a preset Sa curve of another rule according to the color representation intention to obtain the color data H, Sa, In at the output device side, and no unnecessary details are given herein. 
     Similarly, there is a further method of further performing a saturation Sa mapping after presetting the intensity In mapping according to the color representation intention on the premise of the iso-hue H to obtain the color data H, Sa, In at the output device side, and no unnecessary details are given herein. 
       FIG. 12  and  FIG. 13  are respectively a schematic diagram of the intensity In mapping LUT and a schematic diagram of the saturation Sa mapping LUT. 
     The embodiment shown in  FIG. 3  can further comprise the step  3242 . In the step  3242 , the color data in the HSaIn format in the HSaIn color appearance color space at the output device side is converted into color data in an XYZ format in a CIEXYZ color appearance color space. Specifically, the saturation Sa and the intensity In in the color data in the HSaIn format in the HSaIn color appearance color space at the input device side are acquired according to the following formulae: 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     
                       K 
                       m 
                     
                      
                     
                       [ 
                       
                         Min 
                          
                         
                           ( 
                           
                             X 
                             , 
                             Y 
                             , 
                             Z 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                   p 
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     
                       K 
                       M 
                     
                      
                     
                       [ 
                       
                         Max 
                          
                         
                           ( 
                           
                             X 
                             , 
                             Y 
                             , 
                             Z 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                   q 
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, In≧Gl≧0, A≧0, B≧0, p and q are nonzero real numbers or 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     
                       K 
                       m 
                     
                      
                     
                       [ 
                       
                         Min 
                          
                         
                           ( 
                           
                             X 
                             , 
                             Y 
                             , 
                             Z 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                   p 
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     1 
                     3 
                   
                    
                   
                     
                       
                         K 
                         M 
                       
                        
                       
                         ( 
                         
                           X 
                           + 
                           Y 
                           + 
                           Z 
                         
                         ) 
                       
                     
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m , In≧Gl≧0, A≧0, B≧0, p and q are nonzero real numbers or 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     p 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     1 
                     2 
                   
                    
                   
                     
                       
                         K 
                         M 
                       
                        
                       
                         [ 
                         
                           
                             Max 
                              
                             
                               ( 
                               
                                 X 
                                 , 
                                 Y 
                                 , 
                                 Z 
                               
                               ) 
                             
                           
                           + 
                           
                             Min 
                              
                             
                               ( 
                               
                                 X 
                                 , 
                                 Y 
                                 , 
                                 Z 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m , In≧Gl≧0, A≧0, B≧0, p and q are nonzero real numbers or 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     M 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     p 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 
                   
                     K 
                     M 
                   
                    
                   
                     K 
                     M 
                   
                    
                   
                     
                        
                       
                         
                           X 
                            
                           
                             i 
                             V 
                           
                         
                         + 
                         
                           Y 
                            
                           
                             j 
                             V 
                           
                         
                         + 
                         
                           Z 
                            
                           
                             k 
                             V 
                           
                         
                       
                        
                     
                     m 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 Gl 
                 + 
                 Cl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, p and m are nonzero real numbers, In≧Gl≧0, A≧0, B≧0 or 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     r 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     
                       K 
                       M 
                     
                      
                     
                       [ 
                       
                         
                           X 
                           p 
                         
                         + 
                         
                           Y 
                           p 
                         
                         + 
                         
                           Z 
                           p 
                         
                       
                       ] 
                     
                   
                   
                     1 
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m &gt;0, p, q and r are nonzero real numbers, In≧Gl≧0, A≧0, B≧0 or 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     r 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 
                   
                     
                       K 
                       M 
                     
                      
                     
                       [ 
                       
                         
                           
                             ( 
                             
                               X 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                         + 
                         
                           
                             ( 
                             
                               Y 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                         + 
                         
                           
                             ( 
                             
                               Z 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                       
                       ] 
                     
                   
                   
                     1 
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 Cl 
                 + 
                 Gl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m &gt;0, p, q and r are nonzero real numbers, In≧Gl≧0, A≧0, B≧0 
     The color data in the XYZ format in the CIEXYZ color appearance color space at the output device side is obtained based on the following formulae: 
     if the saturation Sa and the intensity In in the color data in the HSaIn format at the input device side are acquired according to the formulae below, 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     
                       K 
                       m 
                     
                      
                     
                       [ 
                       
                         Min 
                          
                         
                           ( 
                           
                             X 
                             , 
                             Y 
                             , 
                             Z 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                   p 
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     
                       K 
                       M 
                     
                      
                     
                       [ 
                       
                         Max 
                          
                         
                           ( 
                           
                             X 
                             , 
                             Y 
                             , 
                             Z 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                   q 
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, In≧Gl≧0, A≧0, B≧0, p and q are nonzero real numbers the color data in the XYZ format at the output device side is acquired according to the following formulae: 
     
       
         
           
               
             
               { 
               
                 
                   
                     
                       
                         
                           H 
                           ′ 
                         
                         = 
                         
                           H 
                           
                             60 
                             ° 
                           
                         
                       
                       , 
                       
                         h 
                         = 
                         
                           [ 
                           
                             H 
                             ′ 
                           
                           ] 
                         
                       
                       , 
                       
                         
                           [ 
                           · 
                           ] 
                         
                          
                         
                             
                         
                          
                         is 
                          
                         
                             
                         
                          
                         a 
                          
                         
                             
                         
                          
                         round 
                          
                         
                             
                         
                          
                         symbol 
                          
                         
                             
                         
                          
                         with 
                          
                         
                             
                         
                          
                         respect 
                          
                         
                             
                         
                          
                         
                           to 
                            
                           
                               
                           
                           · 
                         
                       
                       , 
                       
                         H 
                         ∈ 
                         
                           [ 
                           
                             
                               0 
                               ° 
                             
                             , 
                             
                               360 
                               ° 
                             
                           
                           ) 
                         
                       
                       , 
                       
                         h 
                         = 
                         0 
                       
                       , 
                       1 
                       , 
                       2 
                       , 
                       3 
                       , 
                       4 
                       , 
                       5 
                     
                   
                   
                     
                         
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             ( 
                             
                               
                                 In 
                                 - 
                                 B 
                               
                               
                                 K 
                                 M 
                               
                             
                             ) 
                           
                           
                             1 
                             q 
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 H 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       120 
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       In 
                                        
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           Sa 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     A 
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       H 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   H 
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       120 
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ) 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       0 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     In 
                                     - 
                                     
                                         
                                     
                                      
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       120 
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                               
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 H 
                               
                             
                           
                           + 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       In 
                                        
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           Sa 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     A 
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   H 
                                 
                                 - 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       H 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 H 
                               
                             
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             ( 
                             
                               
                                 In 
                                 - 
                                 B 
                               
                               
                                 K 
                                 M 
                               
                             
                             ) 
                           
                           
                             1 
                             q 
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ) 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       1 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ) 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             ( 
                             
                               
                                 In 
                                 - 
                                 B 
                               
                               
                                 K 
                                 M 
                               
                             
                             ) 
                           
                           
                             1 
                             q 
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       120 
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       240 
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       In 
                                        
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           Sa 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     A 
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         240 
                                         ° 
                                       
                                       - 
                                       H 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       H 
                                       - 
                                       
                                         120 
                                         ° 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       240 
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       h 
                       = 
                       2 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ) 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       240 
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       120 
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       In 
                                        
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           Sa 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     A 
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       H 
                                       - 
                                       
                                         120 
                                         ° 
                                       
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         240 
                                         ° 
                                       
                                       - 
                                       H 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       120 
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             ( 
                             
                               
                                 In 
                                 - 
                                 B 
                               
                               
                                 K 
                                 M 
                               
                             
                             ) 
                           
                           
                             1 
                             q 
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       3 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       240 
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       In 
                                        
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           Sa 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     A 
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       H 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       H 
                                       - 
                                       
                                         240 
                                         ° 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ) 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           ( 
                           
                             
                               In 
                               - 
                               B 
                             
                             
                               K 
                               M 
                             
                           
                           ) 
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       4 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             ( 
                             
                               
                                 In 
                                 - 
                                 B 
                               
                               
                                 K 
                                 M 
                               
                             
                             ) 
                           
                           
                             1 
                             q 
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ) 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     In 
                                     - 
                                     B 
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       240 
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       ln 
                                        
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           Sa 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     A 
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 sin 
                                 ( 
                                 
                                   H 
                                   - 
                                   
                                     240 
                                     ° 
                                   
                                   - 
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         - 
                                         H 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       240 
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       5 
                     
                   
                 
               
             
           
         
       
     
     or if the saturation Sa and the intensity In in the color data in the HSaIn format at the input device side are acquired according to the formulae below, 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     
                       K 
                       m 
                     
                      
                     
                       [ 
                       
                         Min 
                          
                         
                           ( 
                           
                             X 
                             , 
                             Y 
                             , 
                             Z 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                   p 
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     1 
                     3 
                   
                    
                   
                     
                       
                         K 
                         M 
                       
                        
                       
                         ( 
                         
                           X 
                           + 
                           Y 
                           + 
                           Z 
                         
                         ) 
                       
                     
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m , In≧Gl≧0, A≧0, B≧0, p and q are nonzero real numbers the color data in the XYZ format at the output device side is acquired according to the following formulae: 
     
       
         
           
             
               when 
                
               
                   
               
                
               
                 0 
                 ° 
               
             
             ≤ 
             H 
             &lt; 
             
               120 
               ° 
             
           
         
       
       
         
           
             X 
             = 
             
               
                 
                   
                     [ 
                     
                       
                         
                           3 
                            
                           In 
                         
                         - 
                         B 
                       
                       
                         K 
                         M 
                       
                     
                     ] 
                   
                   
                     1 
                     q 
                   
                 
                  
                 
                   
                     sin 
                      
                     
                       ( 
                       
                         
                           120 
                           ° 
                         
                         - 
                         H 
                       
                       ) 
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         H 
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             120 
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
               - 
               
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                  
                 
                   
                     
                       2 
                        
                       
                           
                       
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             
                               120 
                               ° 
                             
                             - 
                             H 
                           
                           ) 
                         
                       
                     
                     - 
                     
                       sin 
                        
                       
                         ( 
                         H 
                         ) 
                       
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         H 
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             120 
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             Y 
             = 
             
               
                 
                   
                     [ 
                     
                       
                         
                           3 
                            
                           In 
                         
                         - 
                         B 
                       
                       
                         K 
                         M 
                       
                     
                     ] 
                   
                   
                     1 
                     q 
                   
                 
                  
                 
                   
                     sin 
                      
                     
                       ( 
                       H 
                       ) 
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         H 
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             120 
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
               - 
               
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                  
                 
                   
                     
                       2 
                        
                       
                           
                       
                        
                       
                         sin 
                          
                         
                           ( 
                           H 
                           ) 
                         
                       
                     
                     - 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             120 
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         H 
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             120 
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             Z 
             = 
             
               
                 [ 
                 
                   
                     
                       In 
                        
                       
                         ( 
                         
                           1 
                           - 
                           Sa 
                         
                         ) 
                       
                     
                     - 
                     A 
                   
                   
                     K 
                     m 
                   
                 
                 ] 
               
               
                 1 
                 p 
               
             
           
         
       
       
         
           
             
               when 
                
               
                   
               
                
               
                 120 
                 ° 
               
             
             ≤ 
             H 
             &lt; 
             
               240 
               ° 
             
           
         
       
       
         
           
             
               X 
               = 
               
                 
                   [ 
                   
                     
                       
                         In 
                          
                         
                           ( 
                           
                             1 
                             - 
                             Sa 
                           
                           ) 
                         
                       
                       - 
                       A 
                     
                     
                       K 
                       m 
                     
                   
                   ] 
                 
                 
                   1 
                   p 
                 
               
             
             , 
             
               
 
             
              
             
               Y 
               = 
               
                 
                   
                     
                       [ 
                       
                         
                           
                             3 
                              
                             In 
                           
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ] 
                     
                     
                       1 
                       q 
                     
                   
                    
                   
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             240 
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                     
                       
                         sin 
                          
                         
                           ( 
                           
                             H 
                             - 
                             
                               120 
                               ° 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         sin 
                          
                         
                           ( 
                           
                             
                               240 
                               ° 
                             
                             - 
                             H 
                           
                           ) 
                         
                       
                     
                   
                 
                 - 
                 
                   
                     
                       [ 
                       
                         
                           
                             In 
                              
                             
                               ( 
                               
                                 1 
                                 - 
                                 Sa 
                               
                               ) 
                             
                           
                           - 
                           A 
                         
                         
                           K 
                           m 
                         
                       
                       ] 
                     
                     
                       1 
                       p 
                     
                   
                    
                   
                     
                       
                         2 
                          
                         
                           sin 
                            
                           
                             ( 
                             
                               
                                 240 
                                 ° 
                               
                               - 
                               H 
                             
                             ) 
                           
                         
                       
                       - 
                       
                         sin 
                          
                         
                           ( 
                           
                             H 
                             - 
                             
                               120 
                               ° 
                             
                           
                           ) 
                         
                       
                     
                     
                       
                         sin 
                          
                         
                           ( 
                           
                             H 
                             - 
                             
                               120 
                               ° 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         sin 
                          
                         
                           ( 
                           
                             
                               240 
                               ° 
                             
                             - 
                             H 
                           
                           ) 
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             Z 
             = 
             
               
                 
                   
                     [ 
                     
                       
                         
                           3 
                            
                           In 
                         
                         - 
                         B 
                       
                       
                         K 
                         M 
                       
                     
                     ] 
                   
                   
                     1 
                     q 
                   
                 
                  
                 
                   
                     sin 
                      
                     
                       ( 
                       
                         H 
                         - 
                         
                           120 
                           ° 
                         
                       
                       ) 
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             120 
                             ° 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             240 
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
               - 
               
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                  
                 
                   
                     
                       2 
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             H 
                             - 
                             
                               120 
                               ° 
                             
                           
                           ) 
                         
                       
                     
                     - 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             240 
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             120 
                             ° 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             240 
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               when 
                
               
                   
               
                
               
                 240 
                 ° 
               
             
             ≤ 
             H 
             &lt; 
             
               360 
               ° 
             
           
         
       
       
         
           
             X 
             = 
             
               
                 
                   
                     [ 
                     
                       
                         
                           3 
                            
                           In 
                         
                         - 
                         B 
                       
                       
                         K 
                         M 
                       
                     
                     ] 
                   
                   
                     1 
                     q 
                   
                 
                  
                 
                   
                     sin 
                      
                     
                       ( 
                       
                         H 
                         - 
                         
                           240 
                           ° 
                         
                       
                       ) 
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             120 
                             ° 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
               - 
               
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                  
                 
                   
                     
                       2 
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             H 
                             - 
                             
                               240 
                               ° 
                             
                           
                           ) 
                         
                       
                     
                     - 
                     
                       sin 
                        
                       
                         ( 
                         
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             240 
                             ° 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             Y 
             = 
             
               
                 [ 
                 
                   
                     
                       In 
                        
                       
                         ( 
                         
                           1 
                           - 
                           Sa 
                         
                         ) 
                       
                     
                     - 
                     A 
                   
                   
                     K 
                     m 
                   
                 
                 ] 
               
               
                 1 
                 p 
               
             
           
         
       
       
         
           
             Z 
             = 
             
               
                 
                   
                     [ 
                     
                       
                         
                           3 
                            
                           In 
                         
                         - 
                         B 
                       
                       
                         K 
                         M 
                       
                     
                     ] 
                   
                   
                     1 
                     q 
                   
                 
                  
                 
                   
                     sin 
                      
                     
                       ( 
                       
                         - 
                         H 
                       
                       ) 
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             240 
                             ° 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
               - 
               
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                  
                 
                   
                     
                       2 
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             - 
                             H 
                           
                           ) 
                         
                       
                     
                     - 
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             240 
                             ° 
                           
                         
                         ) 
                       
                     
                   
                   
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             240 
                             ° 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       sin 
                        
                       
                         ( 
                         
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                 
               
             
           
         
       
     
     or if the saturation Sa and the intensity In in the color data in the HSaIn format at the input device side are acquired according to the formulae below, 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     p 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     1 
                     2 
                   
                    
                   
                     
                       
                         K 
                         M 
                       
                        
                       
                         [ 
                         
                           
                             Max 
                              
                             
                               ( 
                               
                                 X 
                                 , 
                                 Y 
                                 , 
                                 Z 
                               
                               ) 
                             
                           
                           + 
                           
                             Min 
                              
                             
                               ( 
                               
                                 X 
                                 , 
                                 Y 
                                 , 
                                 Z 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                     p 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m , In≧Gl≧0, A≧0, B≧0, p and q are nonzero real numbers the color data in the XYZ format at the output device side is acquired according to the following formulae: 
     
       
         
           
               
             
               { 
               
                 
                   
                     
                       
                         
                           
                             H 
                             ′ 
                           
                           = 
                           
                             H 
                             
                               60 
                               ° 
                             
                           
                         
                         , 
                         
                           h 
                           = 
                           
                             [ 
                             
                               H 
                               ′ 
                             
                             ] 
                           
                         
                         , 
                         
                           
                             [ 
                             · 
                             ] 
                           
                            
                           
                               
                           
                            
                           is 
                            
                           
                               
                           
                            
                           a 
                            
                           
                               
                           
                            
                           round 
                            
                           
                               
                           
                            
                           symbol 
                            
                           
                               
                           
                            
                           with 
                            
                           
                               
                           
                            
                           respect 
                            
                           
                               
                           
                            
                           
                             to 
                              
                             
                                 
                             
                             · 
                           
                         
                         , 
                         
                           H 
                           ∈ 
                           
                             [ 
                             
                               
                                 0 
                                 ° 
                               
                               , 
                               
                                 360 
                                 ° 
                               
                             
                             ) 
                           
                         
                         , 
                         
                           h 
                           = 
                           0 
                         
                         , 
                         1 
                         , 
                         2 
                         , 
                         3 
                         , 
                         4 
                         , 
                         5 
                       
                        
                       
                           
                       
                     
                   
                   
                     
                         
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             
                               [ 
                               
                                 2 
                                  
                                 
                                   
                                     
                                       
                                         
                                           In 
                                           - 
                                         
                                       
                                     
                                     
                                       
                                         B 
                                       
                                     
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                               
                               ] 
                             
                             
                               1 
                               q 
                             
                           
                           - 
                           
                             
                               [ 
                               
                                 
                                   
                                     
                                       
                                         
                                           In 
                                            
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               Sa 
                                             
                                             ) 
                                           
                                         
                                         - 
                                       
                                     
                                   
                                   
                                     
                                       A 
                                     
                                   
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               1 
                               p 
                             
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             
                               
                                 [ 
                                 
                                   2 
                                    
                                   
                                     
                                       
                                         
                                           
                                             In 
                                             - 
                                           
                                         
                                       
                                       
                                         
                                           B 
                                         
                                       
                                     
                                     
                                       K 
                                       M 
                                     
                                   
                                 
                                 ] 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 H 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       120 
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         
                                           
                                             In 
                                              
                                             
                                               ( 
                                               
                                                 1 
                                                 - 
                                                 Sa 
                                               
                                               ) 
                                             
                                           
                                           - 
                                         
                                       
                                     
                                     
                                       
                                         A 
                                       
                                     
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ] 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   
                                     
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             
                                               120 
                                               ° 
                                             
                                             - 
                                             H 
                                           
                                           ) 
                                         
                                       
                                       - 
                                     
                                   
                                 
                                 
                                   
                                     
                                       2 
                                        
                                       sin 
                                        
                                       
                                           
                                       
                                        
                                       H 
                                     
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       120 
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           In 
                                            
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               Sa 
                                             
                                             ) 
                                           
                                         
                                         - 
                                       
                                     
                                   
                                   
                                     
                                       A 
                                     
                                   
                                 
                                  
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ] 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       0 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             
                               
                                 [ 
                                 
                                   2 
                                    
                                   
                                     
                                       
                                         
                                           
                                             In 
                                             - 
                                           
                                         
                                       
                                       
                                         
                                           B 
                                         
                                       
                                     
                                     
                                       K 
                                       M 
                                     
                                   
                                 
                                 ] 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       120 
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                               
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 H 
                               
                             
                           
                           + 
                           
                             
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         
                                           
                                             In 
                                              
                                             
                                               ( 
                                               
                                                 1 
                                                 - 
                                                 Sa 
                                               
                                               ) 
                                             
                                           
                                           - 
                                         
                                       
                                     
                                     
                                       
                                         A 
                                       
                                     
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ] 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   
                                     
                                       
                                         sin 
                                          
                                         
                                             
                                         
                                          
                                         H 
                                       
                                       - 
                                     
                                   
                                 
                                 
                                   
                                     
                                       2 
                                        
                                       
                                           
                                       
                                        
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             
                                               120 
                                               ° 
                                             
                                             - 
                                             H 
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 H 
                               
                             
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             
                               [ 
                               
                                 2 
                                  
                                 
                                   
                                     
                                       
                                         
                                           In 
                                           - 
                                         
                                       
                                     
                                     
                                       
                                         B 
                                       
                                     
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                               
                               ] 
                             
                             
                               1 
                               q 
                             
                           
                           - 
                           
                             
                               [ 
                               
                                 
                                   
                                     
                                       
                                         
                                           In 
                                            
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               Sa 
                                             
                                             ) 
                                           
                                         
                                         - 
                                       
                                     
                                   
                                   
                                     
                                       A 
                                     
                                   
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               1 
                               p 
                             
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       
                                         In 
                                          
                                         
                                           ( 
                                           
                                             1 
                                             - 
                                             Sa 
                                           
                                           ) 
                                         
                                       
                                       - 
                                     
                                   
                                 
                                 
                                   
                                     A 
                                   
                                 
                               
                               
                                 K 
                                 m 
                               
                             
                             ] 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       1 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       
                                         In 
                                          
                                         
                                           ( 
                                           
                                             1 
                                             - 
                                             Sa 
                                           
                                           ) 
                                         
                                       
                                       - 
                                     
                                   
                                 
                                 
                                   
                                     A 
                                   
                                 
                               
                               
                                 K 
                                 m 
                               
                             
                             ] 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             
                               [ 
                               
                                 2 
                                  
                                 
                                   
                                     
                                       
                                         
                                           In 
                                           - 
                                         
                                       
                                     
                                     
                                       
                                         B 
                                       
                                     
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                               
                               ] 
                             
                             
                               1 
                               q 
                             
                           
                           - 
                           
                             
                               [ 
                               
                                 
                                   
                                     
                                       
                                         
                                           In 
                                            
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               Sa 
                                             
                                             ) 
                                           
                                         
                                         - 
                                       
                                     
                                   
                                   
                                     
                                       A 
                                     
                                   
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               1 
                               p 
                             
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             
                               
                                 [ 
                                 
                                   2 
                                    
                                   
                                     
                                       
                                         
                                           
                                             In 
                                             - 
                                           
                                         
                                       
                                       
                                         
                                           B 
                                         
                                       
                                     
                                     
                                       K 
                                       M 
                                     
                                   
                                 
                                 ] 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       120 
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       240 
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         
                                           
                                             In 
                                              
                                             
                                               ( 
                                               
                                                 1 
                                                 - 
                                                 Sa 
                                               
                                               ) 
                                             
                                           
                                           - 
                                         
                                       
                                     
                                     
                                       
                                         A 
                                       
                                     
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ] 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   
                                     
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             
                                               240 
                                               ° 
                                             
                                             - 
                                             H 
                                           
                                           ) 
                                         
                                       
                                       - 
                                     
                                   
                                 
                                 
                                   
                                     
                                       2 
                                        
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             H 
                                             - 
                                             
                                               120 
                                               ° 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       240 
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       2 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       
                                         In 
                                          
                                         
                                           ( 
                                           
                                             1 
                                             - 
                                             Sa 
                                           
                                           ) 
                                         
                                       
                                       - 
                                     
                                   
                                 
                                 
                                   
                                     A 
                                   
                                 
                               
                               
                                 K 
                                 m 
                               
                             
                             ] 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             
                               
                                 [ 
                                 
                                   2 
                                    
                                   
                                     
                                       
                                         
                                           
                                             In 
                                             - 
                                           
                                         
                                       
                                       
                                         
                                           B 
                                         
                                       
                                     
                                     
                                       K 
                                       M 
                                     
                                   
                                 
                                 ] 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       240 
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       120 
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         
                                           
                                             In 
                                              
                                             
                                               ( 
                                               
                                                 1 
                                                 - 
                                                 Sa 
                                               
                                               ) 
                                             
                                           
                                           - 
                                         
                                       
                                     
                                     
                                       
                                         A 
                                       
                                     
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ] 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   
                                     
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             H 
                                             - 
                                             
                                               120 
                                               ° 
                                             
                                           
                                           ) 
                                         
                                       
                                       - 
                                     
                                   
                                 
                                 
                                   
                                     
                                       2 
                                        
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             
                                               240 
                                               ° 
                                             
                                             - 
                                             H 
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       120 
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             
                               [ 
                               
                                 2 
                                  
                                 
                                   
                                     
                                       
                                         
                                           In 
                                           - 
                                         
                                       
                                     
                                     
                                       
                                         B 
                                       
                                     
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                               
                               ] 
                             
                             
                               1 
                               q 
                             
                           
                           - 
                           
                             
                               [ 
                               
                                 
                                   
                                     
                                       
                                         
                                           In 
                                            
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               Sa 
                                             
                                             ) 
                                           
                                         
                                         - 
                                       
                                     
                                   
                                   
                                     
                                       A 
                                     
                                   
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               1 
                               p 
                             
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       3 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             
                               
                                 [ 
                                 
                                   2 
                                    
                                   
                                     
                                       
                                         
                                           
                                             In 
                                             - 
                                           
                                         
                                       
                                       
                                         
                                           B 
                                         
                                       
                                     
                                     
                                       K 
                                       M 
                                     
                                   
                                 
                                 ] 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       240 
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         
                                           
                                             In 
                                              
                                             
                                               ( 
                                               
                                                 1 
                                                 - 
                                                 Sa 
                                               
                                               ) 
                                             
                                           
                                           - 
                                         
                                       
                                     
                                     
                                       
                                         A 
                                       
                                     
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ] 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   
                                     
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             - 
                                             H 
                                           
                                           ) 
                                         
                                       
                                       - 
                                     
                                   
                                 
                                 
                                   
                                     
                                       2 
                                        
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             H 
                                             - 
                                             
                                               240 
                                               ° 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       
                                         In 
                                          
                                         
                                           ( 
                                           
                                             1 
                                             - 
                                             Sa 
                                           
                                           ) 
                                         
                                       
                                       - 
                                     
                                   
                                 
                                 
                                   
                                     A 
                                   
                                 
                               
                               
                                 K 
                                 m 
                               
                             
                             ] 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             
                               [ 
                               
                                 2 
                                  
                                 
                                   
                                     
                                       
                                         
                                           In 
                                           - 
                                         
                                       
                                     
                                     
                                       
                                         B 
                                       
                                     
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                               
                               ] 
                             
                             
                               1 
                               q 
                             
                           
                           - 
                           
                             
                               [ 
                               
                                 
                                   
                                     
                                       
                                         
                                           In 
                                            
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               Sa 
                                             
                                             ) 
                                           
                                         
                                         - 
                                       
                                     
                                   
                                   
                                     
                                       A 
                                     
                                   
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               1 
                               p 
                             
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       4 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         = 
                         
                           
                             
                               [ 
                               
                                 2 
                                  
                                 
                                   
                                     
                                       
                                         
                                           In 
                                           - 
                                         
                                       
                                     
                                     
                                       
                                         B 
                                       
                                     
                                   
                                   
                                     K 
                                     M 
                                   
                                 
                               
                               ] 
                             
                             
                               1 
                               q 
                             
                           
                           - 
                           
                             
                               [ 
                               
                                 
                                   
                                     
                                       
                                         
                                           In 
                                            
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               Sa 
                                             
                                             ) 
                                           
                                         
                                         - 
                                       
                                     
                                   
                                   
                                     
                                       A 
                                     
                                   
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               1 
                               p 
                             
                           
                         
                       
                       , 
                       
                         Y 
                         = 
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       
                                         In 
                                          
                                         
                                           ( 
                                           
                                             1 
                                             - 
                                             Sa 
                                           
                                           ) 
                                         
                                       
                                       - 
                                     
                                   
                                 
                                 
                                   
                                     A 
                                   
                                 
                               
                               
                                 K 
                                 m 
                               
                             
                             ] 
                           
                           
                             1 
                             p 
                           
                         
                       
                       , 
                       
                         Z 
                         = 
                         
                           
                             
                               
                                 [ 
                                 
                                   2 
                                    
                                   
                                     
                                       
                                         
                                           
                                             In 
                                             - 
                                           
                                         
                                       
                                       
                                         
                                           B 
                                         
                                       
                                     
                                     
                                       K 
                                       M 
                                     
                                   
                                 
                                 ] 
                               
                               
                                 1 
                                 q 
                               
                             
                              
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       240 
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         
                                           
                                             In 
                                              
                                             
                                               ( 
                                               
                                                 1 
                                                 - 
                                                 Sa 
                                               
                                               ) 
                                             
                                           
                                           - 
                                         
                                       
                                     
                                     
                                       
                                         A 
                                       
                                     
                                   
                                   
                                     K 
                                     m 
                                   
                                 
                                 ] 
                               
                               
                                 1 
                                 p 
                               
                             
                              
                             
                               
                                 
                                   
                                     
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             H 
                                             - 
                                             
                                               240 
                                               ° 
                                             
                                           
                                           ) 
                                         
                                       
                                       - 
                                     
                                   
                                 
                                 
                                   
                                     
                                       2 
                                        
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             - 
                                             H 
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       240 
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       , 
                     
                   
                   
                     
                       h 
                       = 
                       5 
                     
                   
                 
               
             
           
         
       
     
     or if the saturation Sa and the intensity In in the color data in the HSaIn format at the input device side are acquired according to the formulae below, 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     p 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 
                   
                     K 
                     M 
                   
                    
                   
                     
                        
                       
                         
                           X 
                            
                           
                             i 
                             V 
                           
                         
                         + 
                         
                           Y 
                            
                           
                             j 
                             V 
                           
                         
                         + 
                         
                           Z 
                            
                           
                             k 
                             V 
                           
                         
                       
                        
                     
                     m 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 Gl 
                 + 
                 Cl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, p and m are nonzero real numbers, In≧Gl≧0, A≧0, B≧0 the color data in the XYZ format at the output device side is acquired according to the following formulae: 
     
       
         
           
             
               h 
               = 
               
                 [ 
                 
                   H 
                   
                     120 
                     ° 
                   
                 
                 ] 
               
             
             , 
             
               
                 [ 
                 · 
                 ] 
               
                
               
                   
               
                
               is 
                
               
                   
               
                
               a 
                
               
                   
               
                
               round 
                
               
                   
               
                
               symbol 
                
               
                   
               
                
               with 
                
               
                   
               
                
               respect 
                
               
                   
               
                
               
                 to 
                  
                 
                     
                 
                 · 
               
             
             , 
             
               
 
             
              
             
               H 
               ∈ 
               
                 [ 
                 
                   
                     0 
                     ° 
                   
                   , 
                   
                     360 
                     ° 
                   
                 
                 ) 
               
             
             , 
             
               h 
               = 
               0 
             
             , 
             1 
             , 
             2 
           
         
       
       
         
           
             
               X 
               = 
               
                 
                   
                     
                       ( 
                       
                         
                           Saln 
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ) 
                     
                     
                       1 
                       m 
                     
                   
                    
                   
                     [ 
                     
                       
                         cos 
                          
                         
                           ( 
                           H 
                           ) 
                         
                       
                       + 
                       
                         
                           
                             3 
                           
                           3 
                         
                          
                         
                           sin 
                            
                           
                             ( 
                             H 
                             ) 
                           
                         
                       
                     
                     ] 
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                            
                           In 
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
               
             
             , 
             
               Y 
               = 
               
                 
                   
                     
                       2 
                        
                       
                         3 
                       
                     
                     3 
                   
                    
                   
                     sin 
                      
                     
                       ( 
                       H 
                       ) 
                     
                   
                    
                   
                     
                       ( 
                       
                         
                           Saln 
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ) 
                     
                     
                       1 
                       m 
                     
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                            
                           In 
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
               
             
             , 
             
               Z 
               = 
               
                 
                   [ 
                   
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             Sa 
                           
                           ) 
                         
                          
                         In 
                       
                       - 
                       A 
                     
                     
                       K 
                       m 
                     
                   
                   ] 
                 
                 
                   1 
                   p 
                 
               
             
           
         
       
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               1 
             
             , 
             
               
 
             
              
             
               X 
               = 
               
                 
                   [ 
                   
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             Sa 
                           
                           ) 
                         
                          
                         In 
                       
                       - 
                       A 
                     
                     
                       K 
                       m 
                     
                   
                   ] 
                 
                 
                   1 
                   p 
                 
               
             
             , 
             
               Y 
               = 
               
                 
                   
                     [ 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                            
                           In 
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                 - 
                 
                   
                     
                       ( 
                       
                         
                           Saln 
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ) 
                     
                     
                       1 
                       m 
                     
                   
                    
                   
                     [ 
                     
                       
                         cos 
                          
                         
                           ( 
                           H 
                           ) 
                         
                       
                       - 
                       
                         
                           
                             3 
                           
                           3 
                         
                          
                         
                           sin 
                            
                           
                             ( 
                             H 
                             ) 
                           
                         
                       
                     
                     ] 
                   
                 
               
             
             , 
             
               Z 
               = 
               
                 
                   
                     [ 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                            
                           In 
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                 - 
                 
                   
                     
                       ( 
                       
                         
                           Saln 
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ) 
                     
                     
                       1 
                       m 
                     
                   
                    
                   
                     [ 
                     
                       
                         cos 
                          
                         
                           ( 
                           H 
                           ) 
                         
                       
                       + 
                       
                         
                           
                             3 
                           
                           3 
                         
                          
                         
                           sin 
                            
                           
                             ( 
                             H 
                             ) 
                           
                         
                       
                     
                     ] 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               2 
             
             , 
             
               
 
             
              
             
               X 
               = 
               
                 
                   
                     
                       ( 
                       
                         
                           Saln 
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ) 
                     
                     
                       1 
                       m 
                     
                   
                    
                   
                     [ 
                     
                       
                         cos 
                          
                         
                           ( 
                           H 
                           ) 
                         
                       
                       - 
                       
                         
                           
                             3 
                           
                           3 
                         
                          
                         
                           sin 
                            
                           
                             ( 
                             H 
                             ) 
                           
                         
                       
                     
                     ] 
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                            
                           In 
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
               
             
             , 
             
               Y 
               = 
               
                 
                   [ 
                   
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             Sa 
                           
                           ) 
                         
                          
                         In 
                       
                       - 
                       A 
                     
                     
                       K 
                       m 
                     
                   
                   ] 
                 
                 
                   1 
                   p 
                 
               
             
             , 
             
               Z 
               = 
               
                 
                   
                     [ 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                            
                           In 
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     p 
                   
                 
                 - 
                 
                   
                     
                       2 
                        
                       
                         3 
                       
                     
                     3 
                   
                    
                   
                     sin 
                      
                     
                       ( 
                       H 
                       ) 
                     
                   
                    
                   
                     
                       ( 
                       
                         
                           Saln 
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ) 
                     
                     
                       1 
                       m 
                     
                   
                 
               
             
           
         
       
     
     or if the saturation Sa and the intensity In in the color data in the HSaIn format at the input device side are acquired according to the formulae below, 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     r 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 
                   
                     
                       K 
                       M 
                     
                      
                     
                       [ 
                       
                         
                           X 
                           p 
                         
                         + 
                         
                           Y 
                           p 
                         
                         + 
                         
                           Z 
                           p 
                         
                       
                       ] 
                     
                   
                   
                     1 
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 In 
                 - 
                 Gl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, K M &gt;K m &gt;0, p, q and r are nonzero real numbers, In≧Gl≧0, A≧0, B≧0
 
the color data in the XYZ format at the output device side is acquired according to the following formulae:
 
     
       
         
           
             
               h 
               = 
               
                 [ 
                 
                   H 
                   
                     120 
                     ° 
                   
                 
                 ] 
               
             
             , 
             
               
                 [ 
                 · 
                 ] 
               
                
               
                   
               
                
               is 
                
               
                   
               
                
               a 
                
               
                   
               
                
               round 
                
               
                   
               
                
               symbol 
                
               
                   
               
                
               with 
                
               
                   
               
                
               respect 
                
               
                   
               
                
               
                 to 
                  
                 
                     
                 
                 · 
               
             
             , 
             
               
 
             
              
             
               H 
               ∈ 
               
                 [ 
                 
                   
                     0 
                     ° 
                   
                   , 
                   
                     360 
                     ° 
                   
                 
                 ) 
               
             
             , 
             
               h 
               = 
               0 
             
             , 
             1 
             , 
             2 
           
         
       
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               0 
             
             , 
             
               
 
             
              
             
               
                 then 
                  
                 
                     
                 
                  
                 Z 
               
               = 
               
                 
                   
                     
                       
                         [ 
                         
                           
                             
                               In 
                                
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   Sa 
                                 
                                 ) 
                               
                             
                             - 
                             A 
                           
                           
                             K 
                             m 
                           
                         
                         ] 
                       
                       
                         1 
                         r 
                       
                     
                      
                     
                       
 
                     
                     [ 
                     
                       
                         
                           
                             sin 
                              
                             
                               ( 
                               
                                 
                                   120 
                                   ° 
                                 
                                 - 
                                 H 
                               
                               ) 
                             
                           
                           
                             sin 
                              
                             
                                 
                             
                              
                             H 
                           
                         
                          
                         Y 
                       
                       + 
                       
                         
                           
                             
                               
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 H 
                               
                               - 
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       120 
                                       ° 
                                     
                                     - 
                                     H 
                                   
                                   ) 
                                 
                               
                             
                             
                               sin 
                                
                               
                                   
                               
                                
                               H 
                             
                           
                            
                           
                             [ 
                             
                               
                                 
                                   In 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       Sa 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 A 
                               
                               
                                 K 
                                 m 
                               
                             
                             ] 
                           
                         
                         
                           1 
                           r 
                         
                       
                     
                     ] 
                   
                   + 
                   
                     Y 
                     p 
                   
                 
                 = 
                 
                   
                     
                       ( 
                       
                         
                           In 
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ) 
                     
                     q 
                   
                   - 
                   
                     
                       [ 
                       
                         
                           
                             In 
                              
                             
                               ( 
                               
                                 1 
                                 - 
                                 Sa 
                               
                               ) 
                             
                           
                           - 
                           A 
                         
                         
                           K 
                           m 
                         
                       
                       ] 
                     
                     
                       p 
                       r 
                     
                   
                 
               
             
           
         
       
       
         
           
             X 
             = 
             
               
                 
                   
                     sin 
                      
                     
                       ( 
                       
                         
                           120 
                           ° 
                         
                         - 
                         H 
                       
                       ) 
                     
                   
                   
                     sin 
                      
                     
                         
                     
                      
                     H 
                   
                 
                  
                 Y 
               
               + 
               
                 
                   
                     
                       
                         sin 
                          
                         
                             
                         
                          
                         H 
                       
                       - 
                       
                         sin 
                          
                         
                           ( 
                           
                             
                               120 
                               ° 
                             
                             - 
                             H 
                           
                           ) 
                         
                       
                     
                     
                       sin 
                        
                       
                           
                       
                        
                       H 
                     
                   
                    
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                 
                 
                   1 
                   r 
                 
               
             
           
         
       
     
     the values of X and Y represented by In, Sa, H, p, q and r, are obtained according to the specitic values of p, q and r, X&gt;Y≧0,Y≦Z≧0, Z is a value satisfying the actual physical condition 
     
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               1 
             
             , 
             
               
 
             
              
             
               
                 then 
                  
                 
                     
                 
                  
                 X 
               
               = 
               
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 In 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     Sa 
                                   
                                   ) 
                                 
                               
                               - 
                               A 
                             
                             
                               K 
                               m 
                             
                           
                           ] 
                         
                         
                           1 
                           r 
                         
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 
                                   
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           H 
                                           - 
                                           
                                             120 
                                              
                                             ° 
                                           
                                         
                                         ) 
                                       
                                     
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           
                                             240 
                                              
                                             ° 
                                           
                                           - 
                                           H 
                                         
                                         ) 
                                       
                                     
                                   
                                    
                                   Y 
                                 
                                 + 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             
                                               240 
                                                
                                               ° 
                                             
                                             - 
                                             H 
                                           
                                           ) 
                                         
                                       
                                       - 
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             H 
                                             - 
                                             
                                               120 
                                                
                                               ° 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           
                                             240 
                                              
                                             ° 
                                           
                                           - 
                                           H 
                                         
                                         ) 
                                       
                                     
                                   
                                    
                                   
                                     [ 
                                     
                                       
                                         
                                           In 
                                            
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               Sa 
                                             
                                             ) 
                                           
                                         
                                         - 
                                         A 
                                       
                                       
                                         K 
                                         m 
                                       
                                     
                                     ] 
                                   
                                 
                                 
                                   1 
                                   r 
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                     p 
                   
                   + 
                   
                     Y 
                     p 
                   
                 
                 = 
                 
                   
                     
                       ( 
                       
                         
                           In 
                           - 
                           B 
                         
                         
                           K 
                           M 
                         
                       
                       ) 
                     
                     q 
                   
                   - 
                   
                     
                       [ 
                       
                         
                           
                             In 
                              
                             
                               ( 
                               
                                 1 
                                 - 
                                 Sa 
                               
                               ) 
                             
                           
                           - 
                           A 
                         
                         
                           K 
                           m 
                         
                       
                       ] 
                     
                     
                       p 
                       r 
                     
                   
                 
               
             
           
         
       
       
         
           
             Z 
             = 
             
               
                 
                   
                     sin 
                      
                     
                       ( 
                       
                         H 
                         - 
                         
                           120 
                            
                           ° 
                         
                       
                       ) 
                     
                   
                   
                     sin 
                      
                     
                       ( 
                       
                         
                           240 
                            
                           ° 
                         
                         - 
                         H 
                       
                       ) 
                     
                   
                 
                  
                 Y 
               
               + 
               
                 
                   
                     
                       
                         sin 
                          
                         
                           ( 
                           
                             
                               240 
                                
                               ° 
                             
                             - 
                             H 
                           
                           ) 
                         
                       
                       - 
                       
                         sin 
                          
                         
                           ( 
                           
                             H 
                             - 
                             
                               120 
                                
                               ° 
                             
                           
                           ) 
                         
                       
                     
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             240 
                              
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                    
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                 
                 
                   1 
                   r 
                 
               
             
           
         
       
     
     the values of X and Y represented by In, Sa, H, p, q and r, are obtained according to the specific values of p, q and r, X&gt;Y≧0,Y≦Z≧0, Z is a value satisfying the actual physical condition 
     
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               2 
             
             , 
             
               
 
             
              
             
               
                 then 
                  
                 
                     
                 
                  
                 Y 
               
               = 
               
                 
                   
                     
                       
                         [ 
                         
                           
                             
                               In 
                                
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   Sa 
                                 
                                 ) 
                               
                             
                             - 
                             A 
                           
                           
                             K 
                             m 
                           
                         
                         ] 
                       
                       
                         1 
                         r 
                       
                     
                      
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         - 
                                         H 
                                       
                                       ) 
                                     
                                   
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         H 
                                         - 
                                         
                                           240 
                                            
                                           ° 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                  
                                 X 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           H 
                                           - 
                                           
                                             240 
                                              
                                             ° 
                                           
                                         
                                         ) 
                                       
                                     
                                     - 
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           - 
                                           H 
                                         
                                         ) 
                                       
                                     
                                   
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         H 
                                         - 
                                         
                                           240 
                                            
                                           ° 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                  
                                 
                                   [ 
                                   
                                     
                                       
                                         In 
                                          
                                         
                                           ( 
                                           
                                             1 
                                             - 
                                             Sa 
                                           
                                           ) 
                                         
                                       
                                       - 
                                       A 
                                     
                                     
                                       K 
                                       m 
                                     
                                   
                                   ] 
                                 
                               
                               
                                 1 
                                 r 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                   p 
                 
                 + 
                 
                     
                   
                     
                       X 
                       p 
                     
                     = 
                     
                       
                         
                           
                             ( 
                             
                               
                                 In 
                                 - 
                                 B 
                               
                               
                                 K 
                                 M 
                               
                             
                             ) 
                           
                           q 
                         
                         - 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     In 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         Sa 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   A 
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                             
                               p 
                               r 
                             
                           
                            
                           
                             
 
                           
                            
                           Z 
                         
                       
                       = 
                       
                         
                           
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   - 
                                   H 
                                 
                                 ) 
                               
                             
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   H 
                                   - 
                                   
                                     240 
                                      
                                     ° 
                                   
                                 
                                 ) 
                               
                             
                           
                            
                           X 
                         
                         + 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       H 
                                       - 
                                       
                                         240 
                                          
                                         ° 
                                       
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       H 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     - 
                                     
                                       240 
                                        
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                              
                             
                               [ 
                               
                                 
                                   
                                     In 
                                      
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         Sa 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   A 
                                 
                                 
                                   K 
                                   m 
                                 
                               
                               ] 
                             
                           
                           
                             1 
                             r 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     the values of X and Y represented by In, Sa, H, p, q and r are obtained according to the specific values of p, q and r, X&gt;Y≧0, Y&gt;Z≧0, Z is a value satisfying the actual physical condition
 
or if the saturation Sa and the intensity In in the color data in the HSaIn format at the input device side are acquired according to the formulae below,
 
     
       
         
           
             
               Gl 
               = 
               
                 
                   
                     K 
                     m 
                   
                    
                   
                     
                       Min 
                        
                       
                         ( 
                         
                           X 
                           , 
                           Y 
                           , 
                           Z 
                         
                         ) 
                       
                     
                     r 
                   
                 
                 + 
                 A 
               
             
             , 
             
               
 
             
              
             
               Cl 
               = 
               
                 
                   
                     
                       K 
                       m 
                     
                      
                     
                       [ 
                       
                         
                           
                             ( 
                             
                               X 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                         + 
                         
                           
                             ( 
                             
                               Y 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                         + 
                         
                           
                             ( 
                             
                               Z 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                         + 
                         
                           
                             ( 
                             
                               Z 
                               - 
                               Gl 
                             
                             ) 
                           
                           p 
                         
                       
                       ] 
                     
                   
                   
                     1 
                     q 
                   
                 
                 + 
                 B 
               
             
             , 
             
               
 
             
              
             
               In 
               = 
               
                 Cl 
                 + 
                 Gl 
               
             
             , 
             
               Sa 
               = 
               
                 Cl 
                 In 
               
             
           
         
       
     
     K m  and K M  are positive real numbers, p, q and r are nonzero real numbers, In≧Gl≧0, A≧0, B≧0
 
the color data in the XYZ format at the output device side is acquired according to the following formulae:
 
     
       
         
           
             
               h 
               = 
               
                 [ 
                 
                   H 
                   
                     120 
                     ° 
                   
                 
                 ] 
               
             
             , 
             
               
                 [ 
                 · 
                 ] 
               
                
               
                   
               
                
               is 
                
               
                   
               
                
               a 
                
               
                   
               
                
               round 
                
               
                   
               
                
               symbol 
                
               
                   
               
                
               with 
                
               
                   
               
                
               respect 
                
               
                   
               
                
               
                 to 
                  
                 
                     
                 
                 · 
               
             
             , 
             
               
 
             
              
             
               H 
               ∈ 
               
                 [ 
                 
                   
                     0 
                     ° 
                   
                   , 
                   
                     360 
                     ° 
                   
                 
                 ) 
               
             
             , 
             
               h 
               = 
               0 
             
             , 
             1 
             , 
             2 
           
         
       
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               0 
             
             , 
             
               
 
             
              
             
               X 
               = 
               
                 
                   
                     
                       
                         ( 
                         
                           
                             InSa 
                             - 
                             B 
                           
                           
                             K 
                             M 
                           
                         
                         ) 
                       
                       
                         q 
                         p 
                       
                     
                      
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             120 
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                   
                     
                       [ 
                       
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               
                                 120 
                                 ° 
                               
                               - 
                               H 
                             
                             ) 
                           
                         
                         + 
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             H 
                             ) 
                           
                         
                       
                       ] 
                     
                     
                       1 
                       p 
                     
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     r 
                   
                 
               
             
             , 
             
               Y 
               = 
               
                 
                   
                     
                       
                         ( 
                         
                           
                             InSa 
                             - 
                             B 
                           
                           
                             K 
                             M 
                           
                         
                         ) 
                       
                       
                         q 
                         p 
                       
                     
                      
                     
                       sin 
                        
                       
                         ( 
                         H 
                         ) 
                       
                     
                   
                   
                     
                       [ 
                       
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             H 
                             ) 
                           
                         
                         + 
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               
                                 120 
                                 ° 
                               
                               - 
                               H 
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     
                       1 
                       p 
                     
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     r 
                   
                 
               
             
             , 
             
               Z 
               = 
               
                 
                   [ 
                   
                     
                       
                         In 
                          
                         
                           ( 
                           
                             1 
                             - 
                             Sa 
                           
                           ) 
                         
                       
                       - 
                       A 
                     
                     
                       K 
                       m 
                     
                   
                   ] 
                 
                 
                   1 
                   r 
                 
               
             
           
         
       
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               1 
             
             , 
             
               
 
             
              
             
               X 
               = 
               
                 
                   [ 
                   
                     
                       
                         In 
                          
                         
                           ( 
                           
                             1 
                             - 
                             Sa 
                           
                           ) 
                         
                       
                       - 
                       A 
                     
                     
                       K 
                       m 
                     
                   
                   ] 
                 
                 
                   1 
                   r 
                 
               
             
             , 
             
               Y 
               = 
               
                 
                   
                     
                       
                         ( 
                         
                           
                             InSa 
                             - 
                             B 
                           
                           
                             K 
                             M 
                           
                         
                         ) 
                       
                       
                         q 
                         p 
                       
                     
                      
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             240 
                             ° 
                           
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                   
                     
                       [ 
                       
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               H 
                               - 
                               
                                 120 
                                 ° 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               
                                 240 
                                 ° 
                               
                               - 
                               H 
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     
                       1 
                       p 
                     
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     r 
                   
                 
               
             
             , 
             
               Z 
               = 
               
                 
                   
                     
                       
                         ( 
                         
                           
                             InSa 
                             - 
                             B 
                           
                           
                             K 
                             M 
                           
                         
                         ) 
                       
                       
                         q 
                         p 
                       
                     
                      
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             120 
                             ° 
                           
                         
                         ) 
                       
                     
                   
                   
                     
                       [ 
                       
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               H 
                               - 
                               
                                 120 
                                 ° 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               
                                 240 
                                 ° 
                               
                               - 
                               H 
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     
                       1 
                       p 
                     
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     r 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 if 
                  
                 
                     
                 
                  
                 h 
               
               = 
               2 
             
             , 
             
               
 
             
              
             
               X 
               = 
               
                 
                   
                     
                       
                         ( 
                         
                           
                             InSa 
                             - 
                             B 
                           
                           
                             K 
                             M 
                           
                         
                         ) 
                       
                       
                         q 
                         p 
                       
                     
                      
                     
                       sin 
                        
                       
                         ( 
                         
                           H 
                           - 
                           
                             240 
                             ° 
                           
                         
                         ) 
                       
                     
                   
                   
                     
                       [ 
                       
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               - 
                               H 
                             
                             ) 
                           
                         
                         + 
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               H 
                               - 
                               
                                 240 
                                 ° 
                               
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     
                       1 
                       p 
                     
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     r 
                   
                 
               
             
             , 
             
               Y 
               = 
               
                 
                   [ 
                   
                     
                       
                         In 
                          
                         
                           ( 
                           
                             1 
                             - 
                             Sa 
                           
                           ) 
                         
                       
                       - 
                       A 
                     
                     
                       K 
                       m 
                     
                   
                   ] 
                 
                 
                   1 
                   r 
                 
               
             
             , 
             
               Z 
               = 
               
                 
                   
                     
                       
                         ( 
                         
                           
                             InSa 
                             - 
                             B 
                           
                           
                             K 
                             M 
                           
                         
                         ) 
                       
                       
                         q 
                         p 
                       
                     
                      
                     
                       sin 
                        
                       
                         ( 
                         
                           - 
                           H 
                         
                         ) 
                       
                     
                   
                   
                     
                       [ 
                       
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               H 
                               - 
                               
                                 240 
                                 ° 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             sin 
                             p 
                           
                            
                           
                             ( 
                             
                               - 
                               H 
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     
                       1 
                       p 
                     
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           In 
                            
                           
                             ( 
                             
                               1 
                               - 
                               Sa 
                             
                             ) 
                           
                         
                         - 
                         A 
                       
                       
                         K 
                         m 
                       
                     
                     ] 
                   
                   
                     1 
                     r 
                   
                 
               
             
           
         
       
     
     The parameters, e.g., K M , K m , p, q, r, m, A, B, etc., in the respective converting manners from the data in the HGlCl format to the data in the CIEXYZ format should be selected by referring to the converting manners from the data in the CIEXYZ format to the data in the HGlCl format within the defined range of each parameter, and the parameters are preferably selected as follows: K M =K m =1, p=q=r=m−1, and A=B=0. 
     In the step  324 , the color data in the XYZ format in the CIEXYZ color appearance color space at the output device side is converted into color data in an image format in a color space of the output device. Specifically, the hue deviation angles α a , β a , γ a  of R a ′, G a ′ and B a ′ relative to  ,   and   respectively are acquired using spectrum characteristic data of R a ′, G a ′ and B a ′, and color appearance color data X a , Y a , Z a  is converted into color appearance color data R a ′, G a ′, B a ′ according to the following formulae 71-78: 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             R 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             G 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             B 
                             a 
                             ′` 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               
                                 X 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Z 
                                 a 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     71 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 71, α a &gt;0, β a &gt;0, γ a &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             R 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             G 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             B 
                             a 
                             ′` 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ° 
                                       
                                       + 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               
                                 X 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Z 
                                 a 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     72 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 72, α a &gt;0, β a &gt;0, γ a &lt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             R 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             G 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             B 
                             a 
                             ′ 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ∘ 
                                       
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ∘ 
                                       
                                       + 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ∘ 
                                       
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               
                                 X 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Z 
                                 a 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     73 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 73, α a &gt;0, β a &lt;0, γ a &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             R 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             G 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             B 
                             a 
                             ′ 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ∘ 
                                       
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ∘ 
                                       
                                       + 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ∘ 
                                       
                                       + 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               
                                 X 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Z 
                                 a 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     74 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 74, α a &gt;0, β a &lt;0, γ a &lt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             R 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             G 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             B 
                             a 
                             ′ 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ∘ 
                                       
                                       + 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ∘ 
                                       
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ∘ 
                                       
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               
                                 X 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Z 
                                 a 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     75 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 75, α a &lt;0, β a &gt;0, γ a &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             R 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             G 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             B 
                             a 
                             ′ 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ∘ 
                                       
                                       + 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ∘ 
                                       
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       β 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                         ∘ 
                                       
                                       + 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                       ∘ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               
                                 X 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Z 
                                 a 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     76 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 76, α a &lt;0, β a &gt;0, γ a &lt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             R 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             G 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             B 
                             a 
                             ′ 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       γ 
                                       a 
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               
                                 X 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Z 
                                 a 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     77 
                   
                   ) 
                 
               
             
           
         
       
     
     in Formula 77, α a &gt;0, β a &lt;0, γ a &gt;0; 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             R 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             G 
                             a 
                             ′ 
                           
                         
                       
                       
                         
                           
                             B 
                             a 
                             ′ 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         β 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       
                                         α 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         120 
                                          
                                         ° 
                                       
                                       + 
                                       
                                         γ 
                                         a 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       60 
                                        
                                       ° 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     × 
                     
                         
                       
                         [ 
                         
                           
                             
                               
                                 X 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 a 
                               
                             
                           
                           
                             
                               
                                 Z 
                                 a 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     78 
                   
                   ) 
                 
               
             
           
         
       
         
         
           
             in Formula 78, α a &lt;0, β a &lt;0, γ a &lt;0; 
             wherein in Formulae 71-78, α a  is a hue deviation angle between   and  ; β a  is a hue deviation angle between   and  ; γ a  is a hue deviation angle between   and  , the values of R a ′, G a ′ and B a ′ are color appearance color data in combination with an observation condition obtained after the conversion; the values of X a , Y a  and Z a  in the formulae 71-78 are the color data in the XYZ format in the CIEXYZ color appearance color space;  ,   and   are the color appearance color data in combination with the observation condition to represent chromatic vectors within the chromatic plane. 
           
         
       
    
     The color data of the cone response R a ′, G a ′, B a  is converted into color data in an XYZ format at the output device side according to a technical standard CIECAM02. 
     In the embodiment shown in  FIG. 3 , the management method of obtaining color data in an HSaIn format in an HSaIn color appearance color space from color data in an XYZ format at the input device side and the management method of obtaining color data in an XYZ format at the output device side from color data in an HSaIn format in an HSaIn color appearance color space at the output device side can be independent of each other. 
     Further, the embodiment shown in  FIG. 3  can include the step  3241 . In the step  3241 , the color data in the XYZ format at the output device side is converted into color data of the output device. The conversion of the color data in the XYZ format at the output device side into color data of the output device has been described in detail above, and no unnecessary details are further given herein. 
     After the chromatic color data of the output device is obtained, it will be converted into a chromatic image of the output device to be sent to the output device for an image output. The output device, after receiving the chromatic image in the output format that can be identified and processed thereby, performs an image output, e.g., displaying, printing, projecting and the like. 
     Since the output device has undergone the corresponding processing of removing the color attribute of the output device itself before receiving the chromatic image of the output device and outputting the received chromatic image, when the same chromatic image based on the HSaIn color space model is output through the output devices of different color attributes, almost consistent images will be output. For example, when the printing is performed through the printers of different color attributes, almost consistent chromatic images will be printed to hereby achieve the object “what you see is what you get”. 
       FIG. 4  shows a flow chart of the method of managing color data based on a CIEXYZ color space of another embodiment of the invention. 
     As shown in  FIG. 4 , firstly, color data of a chromatic scene is acquired from the input device. The input device can be a camera, a pickup camera, a video camera and the like, or the input device can be also a scanner and the like. A chromatic image stored in a digital format is acquired from the input device. Generally, the color data of the acquired chromatic image is stored in a manner of a pixel dot matrix. 
     The color data acquired from the input device can be in a three-channel format UVW or in a multichannel format. 
     In the step  410 , the color data acquired from the input device is converted into color data based on a CIEXYZ color space at the input device side. The specific process of converting the color data in the UVW format acquired from the input device into color data based on a CIEXYZ color space at the input device side in the step  410  is the same as that in the step  2201  in the embodiment shown in  FIG. 2 , and no unnecessary details are further given herein. 
     In the step  422 , the image data in the XYZ format at the input device side is mapped to color data in an XYZ format at the output device side. The mapping of the image data in the XYZ format at the input device side to color data in an XYZ format at the output device side belongs to the prior art, and no unnecessary details are further given herein. 
     In the step  412 , the acquired color data in the XYZ format at the output device side is converted into color data in a color space of the device. The conversion of the acquired color data in the XYZ format at the output device side into color data in a color space of the device in the step  412  is the same as that in the step  2241  in the embodiment shown in  FIG. 2 , and no unnecessary details are further given herein. 
     In the embodiment shown in  FIG. 4 , the management method of obtaining color data in an XYZ format at the input side from color data of the input device and the management method of obtaining color data of the output device from color data in an XYZ format at the output side can be independent of each other. 
     It can be seen from the management methods of the color data provided by the above respective embodiments that in the process of managing the color data between a color space dependent of the device and a color space independent of the device in the invention, the impacts of the input device on the chromatic image are removed according to color characteristic data of the device, and the calculations for the conversion are all matrix operations that are easily achieved, which greatly simplifies the calculating process for the conversion, improves the conversion accuracy and efficiency, and accelerates the conversion speed. Especially, the conversion formulae for the conversion into color data in an HSaIn format provided in the embodiments of the invention are theoretical formulae and will not have accumulative errors in the multiple calculations, so the color data obtained by these calculations with the conversion formulae will provide higher accuracies of the color data than the conversion formulae in the prior art. 
     It can be further seen from the management methods of the color data provided by the above respective embodiments that since the method of performing the color gamut mapping in the HSaIn color space is performed under the Iso-hue plane, the three-dimensional conversion is simplified as the one-dimensional repeated conversion, which improves the conversion efficiency and improves the conversion accuracy. 
     The chromatic image independent of the impacts of the color attribute of the input device itself can be acquired by the above method. That is to say, by the above method, the acquired pictures of the same scene taken by cameras of different brands will have a comparatively good consistency. 
     The formulae, especially the formulae containing trigonometric functions, involved in the above respective embodiments can further derive formulae in other forms, the essential meanings of which do not change, by means of mathematical operations, and since the derived formulae are essentially the same as those in the invention, they shall be deemed as ones within the scope of protection of the invention. 
     The above contents are only preferred implementation modes of the invention. It should be noted that those skilled in the art can further make some improvements and decorations in the case of not breaking away from the technical principle of the invention, and these improvements and decorations should also be deemed as ones within the scope of protection of the invention.