Abstract:
An image processing apparatus includes a command analyzing unit obtaining color information of each endpoint of an object by analyzing a drawing command, a draw processing unit obtaining the color information of successive scanned points inside the object through incremental interpolation of the color information, thereby successively producing the color information for an entirety of the object, and an image processing unit processing the color information outputted by the draw processing unit.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to an image processing apparatus, an image processing method, and an image processing program. 
   2. Description of the Related Art 
   In recent years, owing that the functions for color DTP and word processors have been improved, not only text but complicated objects have also become easy to create. The gradation function is one of such functions often used for improving the appearance of documents. One conventional method known for creating drawing data is to create a gradation pattern beforehand, and then masking objects in correspondence with the gradation. 
   However, with a gradient fill shown in  FIG. 30 , creating a gradation pattern beforehand may be difficult, in a case where drawing is performed by defining three different colors on each end point of a triangle, and interpolating the inside thereof. 
   As for another method, in a case where the direction for gradation (halftoning) is horizontal, objects divided into different shades can be overlapped onto each other. This may also be performed for the vertical direction. 
   Nevertheless, using software, for example, to compensate the inside of the three end points in a manner shown in  FIG. 30  requires large amounts of processing. 
   In order to solve the aforementioned problem, Japanese Patent No. 2897765 discloses a method of drawing a gradation object directly instead of drawing a gradation object through reception of PDL commands, and thus referring to a gradation adjustment table for adjusting the difference between density obtained by computation and gradation during printing. 
   Further, a CRT display providing high gradient can, in general, express color gradation easily, while a printer providing low gradient, on the other hand, has difficulty in outputting color gradation, especially neutral colors (colors with slight gradation). In order to overcome such difficulty, Japanese Laid-Open Patent Application No. 9-190538 discloses a method where drawing is performed by dividing a gradating portion into plural objects having a width of 2 pixels or more. 
   Japanese Laid-Open Patent Application No. 2001-101431 discloses a square-shaped gradient fill in which horizontal lines that have same shade are obtained, in a case where shades are different in a vertical direction, by copying a previously drawn line, so as to increase processing speed. 
   In the field of 3D graphics, RGB colors are distributed to the endpoints of a triangular polygon, and compensated according to a plane equation. Japanese Laid-Open Patent Application No. 11-15997 discloses a mapping process by distributing addresses of a mapping pattern to each end point of a polygon and interpolating the inside of the polygon. 
   Conventionally, forming a gradation pattern beforehand and masking an object according to the gradation pattern is known as a method for generating drawing data. This method, however, requires large memory space for purposes of, for example, forming large gradation patterns, or performing a masking operation. 
   Furthermore, it may be difficult to form a gradation pattern beforehand by employing a method of defining different colors to three endpoints of a triangle and interpolating the inside of the triangle (See gradient fill of  FIG. 30 ). 
   Furthermore, gradation (halftoning) for a single direction (horizontally or vertically) can be performed by dividing gradation into objects having different shades and overlapping the objects on top of each other (e.g.  FIG. 31 ). In this case, however, drawing process is conducted redundantly for many portions; therefore, much memory access is required. 
   In the aforementioned Japanese Patent No. 2897765, shades are created by performing linear conversion from the left side of an object to the right side of the object and interpolating in a horizontal direction; nevertheless, the manner of how shades are interpolated is not clearly described. Furthermore, in the case where interpolation is performed in accordance with the left and right sides of the object, the value of interpolation may change drastically when there is a change in one of the sides (as the object shown in  FIG. 32 ); this causes a border to be noticeable at the line of the change and deteriorate image quality. 
   Meanwhile, in a case where a object that is targeted for drawing is rotated, for example, when intensifying the paper employed for printing or when changing the direction of the paper, the aforementioned method may cause gradation of the rotated object to be different compared to that of the object before the rotation, and thereby deteriorate image quality (This is due to the fact that the difference in gradation is not obtained by using a plane equation in accordance with all of the endpoints of the object. Therefore, the aforementioned method may lack precision in forming gradation. Further, the trapezoid employed as an example in the conventional method cannot form a plane and is unable to create gradation suitably unless it is divided into triangles). Furthermore, a gradation adjustment table is required to be provided in the RAM inside the hardware of LSI for increasing processing speed, to thereby increase the size of hardware of the LSI and its cost. 
   In the aforementioned Japanese Patent Laid-Open Application No. 09-190538 where gradation portion is divided into a plurality of objects in sizes of no less than 2 pixels, calculation may be simple when gradation is either in a horizontal direction or a vertical direction (although it is still necessary to perform much calculation for obtaining the slope of the sides of the respective divided objects); however, employing the aforementioned method in obtaining a gradation, for example, shown in  FIG. 30 , shall require too much calculation. 
   The aforementioned Japanese Patent Laid-Open Application No. 2001-101431 is effective only when gradation is in a single horizontal direction, and it cannot be applied to a gradient fill where three endpoints of a triangle (e.g.  FIG. 30 ) are respectively defined with different colors. 
   SUMMARY OF THE INVENTION 
   It is a general object of the present invention to provide an image processing apparatus, an image processing method, and an image processing program, that substantially obviate one or more of the problems caused by the limitations and disadvantages(of the related art. 
   More specifically, it is an object of the present invention to provide an image processing apparatus, an image processing method, and an image processing program to require no large memory space such as space for expanding a large gradation pattern or space for conducting a masking process to drawing data. 
   It is also an object of the present invention to provide an image processing apparatus, an image processing method, and an image processing program that suitably output neutral colors (colors with slight gradation) even with a low gradient printer by employing a color information interpolating unit which controls changes in color by obtaining changes of resolution (mesh) with reference to prescribed smallest (minimum) color lengths in a vertical and horizontal direction of a square surrounding an object (Thereby, while the sides of the object is computed with an ordinary resolution, resolution can be changed for the object having its inside filled). 
   It is also an object of the present invention to provide an image processing apparatus, an image processing method, and an image processing program that increase processing speed of a (gradient fill) drawing process by operating a setup unit, a start point computation unit, a horizontal color information interpolating unit, a color conversion unit, and a halftone unit, in parallel. 
   Features and advantages of the present invention will be set forth in the description which follows, and in part will become apparent from the description and the accompanying drawings, or may be learned by practice of the invention according to the teachings provided in the description. Objects as well as other features and advantages of the present invention will be realized and attained by an image processing apparatus, an image processing method, and an image processing program particularly pointed out in the specification in such full, clear, concise, and exact terms as to enable a person having ordinary skill in the art to practice the invention. 
   To achieve these and other advantages and in accordance with the purpose of the invention, as embodied and broadly described herein, the invention provides an image processing apparatus including: a command analyzing unit obtaining color information of each endpoint of an object by analyzing a drawing command; a draw processing unit obtaining the color information of successive scanned points inside the object through incremental interpolation of the color information, thereby successively producing the color information for an entirety of the object; and an image processing unit processing the color information outputted by the draw processing unit, wherein the draw processing unit further includes a color information interpolating unit controlling change of color by interpolating color in horizontal and vertical directions in accordance with a mesh, which is shaped as a square surrounding the object and is divided into minimal color lengths in vertical and horizontal directions. 
   The present invention also provides an image processing method comprising the steps of: a) obtaining color information of each endpoint of an object by analyzing a drawing command; b) obtaining the color information of successive scanned points inside the object through incremental interpolation of the color information, thereby successively producing the color information for an entirety of the object; and c) processing the color information outputted in step b), wherein step b) further includes a step of: controlling change of color by interpolating color in horizontal and vertical directions in accordance with a mesh, which is shaped as a square surrounding the object and is divided into minimal color lengths in vertical and horizontal directions. 
   The present invention also provides an image processing program including the functions of: a) obtaining color information of each endpoint of an object by analyzing a drawing command; b) obtaining the color information of successive scanned points inside the object through incremental interpolation of the color information, thereby successively producing the color information for an entirety of the object; and c) processing the color information outputted in function b), wherein function b) further includes a function of: controlling change of color by interpolating color in horizontal and vertical directions in accordance with a mesh, which is shaped as a square surrounding the object and is divided into minimal color lengths in vertical and horizontal directions. 
   Other objects and further features of the present invention will be apparent from the following detailed description when read in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a diagram for describing a mechanism of an image forming apparatus according to an embodiment of the present invention; 
       FIG. 2  is a block diagram showing an electric component control unit of an image forming apparatus according to an embodiment of the present invention; 
       FIG. 3  is a diagram showing a flow of the procedures performed according to an embodiment of the present invention; 
       FIG. 4  is a block diagram showing a data processing concept according to an embodiment of the present invention; 
       FIG. 5  is a diagram showing a concept of a procedure for drawing an object in a band memory area according to an embodiment of the present invention; 
       FIG. 6  is a diagram showing a format of a main memory according to an embodiment of the present invention; 
       FIG. 7  is a diagram showing a flow of draw processing according to an embodiment of the present invention; 
       FIG. 8  is a block diagram of the drawing unit shown in  FIG. 2 ; 
       FIG. 9  is a flow chart showing a process performed with a drawing unit according to an embodiment of the present invention; 
       FIG. 10  is a block diagram showing a structure of a draw processing unit shown in  FIG. 8 ; 
       FIG. 11  is a flow chart showing a process performed with a draw processing unit according to an embodiment of the present invention; 
       FIG. 12  is a block diagram showing a structure of a triangle setup unit shown in  FIG. 10 ; 
       FIG. 13  is a block diagram showing a structure of a generation unit  1201  shown in  FIG. 12  that generates difference R for a horizontal direction; 
       FIG. 14  is a block diagram showing a structure of a generation unit  1202  shown in  FIG. 12  that generates difference R for a vertical direction; 
       FIG. 15  is a block diagram showing a structure of a horizontal RGB DDA unit  1006  shown in  FIG. 10 ; 
       FIG. 16  is a block diagram showing a structure of an initial point generation unit  1003  shown in  FIG. 10 ; 
       FIG. 17  is a block diagram showing a structure of a horizontal XDDA unit  1005  shown in  FIG. 10 ; 
       FIG. 18  is a block diagram showing a structure of a memory address generation unit  1008  shown in  FIG. 10 ; 
       FIG. 19  is a block diagram showing a structure of an RGB interpolating unit  1004  shown in  FIG. 10 ; 
       FIG. 20  is a block diagram showing a structure of an image processing unit  206  shown in  FIG. 2 ; 
       FIG. 21  is a flowchart showing a process performed by an image processing unit according to an embodiment of the present invention; 
       FIG. 22  is a block diagram showing a structure of a color conversion processing unit  2001  shown in  FIG. 20 ; 
       FIG. 23  is a flowchart showing a process performed by a color conversion processing unit according to an embodiment of the present invention; 
       FIG. 24  is block diagram showing a structure of a halftone unit  2002  shown in  FIG. 20 ; 
       FIG. 25  is a flowchart showing a process performed by a halftone unit according to an embodiment of the present invention; 
       FIG. 26  is a block diagram showing a structure of a fixed length data generation unit  2408  shown in  FIG. 24 ; 
       FIG. 27  is a diagram showing a relation between coordinates of a triangle on a plane, color information, and difference; 
       FIG. 28  is a diagram showing a relation between a triangle, minimum color length (DDX, DDY), and maximum and minimum values of X and Y; 
       FIG. 29  is a diagram showing a process of interpolating the sides of a triangle from initial point (X 0 , Y 0 ), and drawing the triangle according to an embodiment of the present invention; 
       FIG. 30  is a diagram showing an example of a triangle gradient fill; 
       FIG. 31  is a diagram showing an example of forming a gradation from plural gradation patterns; and 
       FIG. 32  is a diagram showing a result of gradient fill in a case where interpolation is performed according to the left and right sides of a triangle. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   In the following, embodiments of the present invention will be described with reference to the accompanying drawings. 
   [Structure of Image Forming Apparatus] 
     FIG. 1  is a diagram showing a structure of an image forming apparatus according to an embodiment of the present invention. The image forming apparatus is a color printer of a four drum tandem type which forms images in four colors (Y, M, C, K) with separate image forming units  1 Y,  1 M,  1 C,  1 K, and combines the four color images. 
   Each of the image forming units  1 Y,  1 M,  1 C, and  1 K has, for example, OPC (Organic Photoconductor) drums  2 Y,  2 M,  2 C,  2 K with a small diameter (functioning as image bearing members); charge rollers  3 Y,  3 M,  3 C,  3 K (functioning as charging units) disposed at an upstream side surrounding the OPC drums  2 Y,  2 M,  2 C,  2 K; development units  4 Y,  4 M,  4 C,  4 K forming toner images for each of the colors Y, M, C, K by developing each of the electrostatic latent images on the OPC drums  2 Y,  2 M,  2 C,  2 K with a developer; cleaning units  5 Y,  5 M,  5 C,  5 K; and discharge units  6 Y,  6 M,  6 C,  6 K. 
   Toner bottles  7 Y,  7 M,  7 C,  7 K supplying Y toner, M toner, C toner, and K toner to each of the developing units  4 Y,  4 M,  4 C, and  4 K are disposed at the side of each of the developing units  4 Y,  4 M,  4 C, and  4 K. Further, each of the image forming units  1 Y,  1 M,  1 C,  1 K includes independent optic writing units  8 Y,  8 M,  8 C, and  8 K. The optic writing units  8 Y,  8 M,  8 C, and  8 K including, optic components, for example, a laser diode (LD) light source  9 Y,  9 M,  9 C,  9 K (serving as a light source), collimator lens  10 Y,  10 M,  10 C,  10 K, and fθ lens  11 Y,  11 M,  11 C,  11 K, and a deflection scan unit such as polygon mirrors  12 Y,  12 M,  12 C,  12 K, or reflection mirrors  13 Y,  13 M,  13 C,  13 K,  14 Y,  14 M,  14 C,  14 K. 
   The image forming units  1 Y,  1 M,  1 C,  1 K are disposed vertically, and a transfer belt unit  15  is disposed on its right side in a manner contacting the OPC drums  2 Y,  2 M,  2 C,  2 K. In the transfer belt unit  15 , a transfer belt  16  is stretched by rollers  17 – 20  and rotated by a driving source (not shown). A sheet feeding tray containing transfer sheet (transfer medium) is disposed at a lower portion of the image forming apparatus. A fixing unit  22 , a sheet eject roller  23 , and a sheet eject tray  24  are disposed at an upper portion of the image forming apparatus. 
   In a procedure of forming an image in each of the image forming units  1 Y,  1 M,  1 C, and  1 K, the OPC drums  2 Y,  2 M,  2 C, and  2 K are rotated by a driving source (not shown), are uniformly charged by the charge rollers  3 Y,  3 M,  3 C,  3 K, and are subjected to optic writing by the optic write units  8 Y,  8 M,  8 C,  8 K in accordance with image data for each color, to thereby form electro latent images on the respective OPC drums  2 Y,  2 M,  2 C, and  2 K. 
   The electro latent images on the respective OPC drums  2 Y,  2 M,  2 C, and  2 K are developed into respective toner images corresponding to Y, M, C, K by the developing units  4 Y,  4 M,  4 C,  4 K. The transfer sheet is, meanwhile, supplied from the sheet feeding tray  21  in a horizontal direction by a sheet feeding roller  25 , and is conveyed to the image forming units  1 Y,  1 M,  1 C, and  1 K in a vertical direction by a conveying unit. The transfer belt  16 ,absorbing the transfer sheet with static electricity, conveys the transfer sheet. The transfer sheet conveyed on the transfer belt  16  is applied with transfer bias by a transfer bias supply unit (not shown) for allowing the respective Y, M, C, K toner images on the OPC drums  2 Y,  2 M,  2 C,  2 K to be sequentially transferred thereon in an overlapped manner, thereby resulting to the formation of a full color image on the transfer sheet. The transfer sheet has the full color image fixed thereon by a fixing unit  22 , and is ejected from the sheet eject tray  24  by a sheet eject roller  23 . 
   The aforementioned procedure is controlled by a control unit  26 . 
   [Structure of Control Unit] 
     FIG. 2  is a block diagram of the control unit  26  shown in  FIG. 1 . 
   Numeral  201  is a CPU which performs the overall controls for the color printer. Numeral  202  is a CPU interface that is connected to a memory arbiter (memory controller)  203  for serving as an interface between the CPU  201  and the memory controller  203 . The memory arbiter  203  controls a main memory  224 , and controls the transfer between the main memory  224  and, for example, the CPU  201 , a local bus interface  204 , decoding units  209  to  212 , a draw processing unit  205 , an image processing unit  206 , and a encoding unit  207 . 
   The local bus interface  204  serves as an interface for a ROM  218  and/or a panel controller  217  with respect to, for example, the main memory  224 . 
   The draw processing unit  205  receives a drawing command from the CPU  201 , and successively transfers memory addresses and color information (e.g. RGB, gradation) in a horizontal direction to the image processing unit  206 . 
   The image processing unit  206  receives the memory addresses and the color information (RGB) from the draw processing unit  205 , conducts image processing, and performs drawing with respect to band memory spaces in the main memory  224 . 
   The encoding unit  207  encodes the band data in the main memory  224  and transfers the encoded data to the main memory  224 . 
   Numeral  208  is a communication controller which is connected to a network for receiving various data and commands therefrom, and also to various controllers via the memory arbiter  203 . 
   The decoding units  209  through  212  receive encoded data, encoded by encoding unit  207 , corresponding to each C, M, Y, K, then decode the encoded data, and then transfer the decoded data to respective engine controllers  213  through  216  corresponding to C, M, Y, K. 
   Numeral  218  is a ROM which stores, for example, font information (e.g. letters), and programs of the CPU  201 . 
   Numeral  217  is a panel controller which controls a panel  219 . 
   The panel  219  informs operations of a user to, for example, a copy unit. 
   The respective engine controllers  213  through  216  receives images from the decoding parts  209  through  212  and transfers the images to respective printer engines  220 ,  221 ,  222 , and  223  corresponding to C, M, Y, K. The main memory  224  stores, for example, code data of the encoding unit  209 , programs of the CPU  201 , font data, and other various data. 
   [Operation] 
     FIG. 3  shows an overall operation flow of an image processing apparatus according to an embodiment of the present invention. 
   In step S 301 , the CPU  201  shown in  FIG. 2  generates a drawing command and transfers the drawing command to the draw processing unit  205 . 
   In step S 302 , the draw processing unit  205  shown in  FIG. 2  successively obtains, addresses of a horizontal direction of the band memory space and color information (RGB) values, in a vertical direction of an object, and then transfers the obtained addresses and color information (RGB) values to the image processing unit  206  shown in  FIG. 2 . 
   In step S 303 , the image processing unit  206  shown in  FIG. 2  conducts image processing and draws to the CMYK binary band memory spaces shown in  FIG. 5 . 
     FIG. 4  is a conceptual diagram showing the processes of an image processing apparatus according to an embodiment of the present invention. 
   Numeral  401  is a CPU which transfers a drawing command to a drawing unit  402 , and performs a drawing process on halftoned band memory (main memory)  404  corresponding to C, M, Y, K. 
   The drawing unit  402  receives the drawing command from the CPU  401 , analyzes the command, scans a graphic object successively in a horizontal direction for obtaining addresses in the band memory  404  and color information (RGB), and transfers the obtained addresses and color information (RGB) to the image processing unit  403 . 
   The image processing unit  403  receives respective origin addresses and the thresholds of the C, M, Y, K band memories  404  from the CPU  401 , receives the addresses and color information (RGB) from the draw processing unit  402 , and performs a color conversion process (conversion into CMYK value). After the color conversion process (conversion to CMYK value), the image processing unit  403  generates halftoned band data to the respective band memory  404  corresponding to C, M, Y, K. 
   The band memory (main memory)  404  serves to store, for example, page code data corresponding to C, M, Y, K and halftoned band data. 
   Numeral  405  is an encoding unit which encodes halftoned band data corresponding to C, M, Y, K and transfers the data to respective page code memory spaces corresponding to C, M, Y, K in the main memory  404 . 
   Numerals  406  through  409  are decoding units which synchronize with respective printer engines  414  through  417  corresponding to C, M, Y, K; read and decode necessary codes of C, M, Y, K from the main memory  404 ; and transfer the decoded codes to respective engine controllers  410  through  413  corresponding to C, M, Y, K. 
   The C, M, Y, K engine controllers  410  through  413  receive codes from the decoding units  406  through  409  and control the respective printer engines  414  through  417 . 
     FIG. 5  is a conceptual diagram of a process performed according to an embodiment of the present invention. The CPU  201  shown in  FIG. 2  receives a drawing command, transfers the drawing command to the draw processing unit  205 . The draw processing unit  205  performs a drawing process and transfers processed results to the image processing unit  206  shown in  FIG. 2 . The image processing unit  206  draws an object to a halftoned band memory corresponding to C, M, Y, K in the main memory  224  shown in  FIG. 2 . 
   [Main Memory Format] 
     FIG. 6  shows a format of a main memory according to an embodiment of the present invention. 
   With reference to  FIG. 6 , the C, M, Y, K binary band memory spaces are spaces which store image processed (processed into, for example, binary value, quaternary value, or hexadecimal value) band information corresponding to C, M, Y, K. 
   The cyan binary band memory space is a space storing halftoned encoded data of a cyan band that amount to plural pages. 
   The magenta binary band memory space is a space storing halftoned encoded data of a magenta band that amount to plural pages. 
   The yellow binary band memory space is a space storing halftoned encoded data of a yellow band that amount to plural pages. 
   The black binary band memory space is a space storing halftoned encoded data of a black band that amount to plural pages. 
   The program space is a space storing various programs of a CPU. 
   [Drawing Process] 
     FIG. 7  shows a flow of a drawing process according to an embodiment of the present invention. 
   The CPU  201  transfers a drawing command to the draw processing unit  205  ({circle around (1)}). 
   The draw processing unit  205  analyzes the drawing command and transfers color information of an object and a memory address thereof to the image processing unit  206  ({circle around (2)}). 
   The image processing unit  206  performs image processing to the color information from the draw processing unit  205 , and provides the image processed data to the C, M, Y, K binary band memory spaces of the main memory ({circle around (3)}). 
   [Drawing Unit] 
     FIG. 8  is a block diagram of the draw processing unit  205  shown in  FIG. 2 . 
   Numeral  801  is a memory arbiter interface serving as an interface with respect to the memory arbiter  203  shown in  FIG. 2 . The memory arbiter interface  801  receives a drawing command from the CPU  201  shown in  FIG. 2  and transfers the drawing command to a draw processing unit  802 . In  FIG. 8 , the memory arbiter  203  receives a request signal requesting access to the main memory  224 . The memory arbiter  203  returns an acknowledge signal for informing that preparation is made for accessing to the main memory  224 . 
   The draw processing unit  802  receives the drawing command from the CPU  201  shown in  FIG. 2 , analyzes the drawing command, and obtains the differential coefficients, for a horizontal direction (dRX, dGX, dBX) and a vertical direction (dRY, dGY, dBY), from a plane equation in accordance with color information of each endpoint of a triangle object, to thereby successively obtain the memory addresses and color information (RGB) in a horizontal direction, from a vertical direction, and transfer the obtained memory addresses for each pixel to the image processing unit  206  shown in  FIG. 2  in accordance with bandwidth of band data and logical addresses (X 0 , Y 0 , X 1 , Y 1 , X 2 , Y 2 ) of each endpoint of a graphic shape. 
   In the block diagram of  FIG. 8 , numeral  803  is a parameter storage unit for temporarily storing parameters of the draw processing unit  802 . Numeral  804  is a controller for entirely controlling the draw processing unit  205 . 
     FIG. 9  shows a processing flow of the drawing processing unit according to an embodiment of the present invention. 
   Step S 901 : Set bandwidth of respective C, M, Y, K band memory spaces in a main memory to a parameter storage unit. 
   Step S 902 : Set a color conversion table for a color conversion unit. 
   Step S 903 : Set threshold size of dither for a halftone unit. 
   Step S 904 : Set values of DDX and DDY for an RGB interpolating unit. 
   Step S 905 : Read drawing command. 
   Step S 906 : Conduct drawing process. 
   Step S 907 : Conduct color conversion. 
   Step S 908 : Conduct halftone process (halftoning). 
   Step S 909 : Withdraw from loop after all drawing commands are conducted. 
   [Draw Processing Unit] 
     FIG. 10  is a block diagram of the draw processing unit  802  shown in  FIG. 8 . 
   Numeral  1001  is a command analyzing unit which analyzes a drawing command from the CPU  201  shown in  FIG. 2 , obtains coordinates (X 0 , Y 0 , X 1 , Y 1 , X 2 , Y 2 ) and color information (R 0 , G 0 , B 0 , R 1 , G 1 , B 1 , R 2 , G 2 , B 2 ) for each endpoint of a triangle, and transfers the coordinates and the color information to, for example, a triangle setup unit  1002 , a start point generation unit  1003 , and an RGB interpolating unit  1004 . 
   The triangle setup unit  1002  obtains differential coefficients for a horizontal direction (dRX, dGX, dBX) and a vertical direction (dRY, dGY, dBY) from a plane equation of a triangle in accordance with the coordinates and color information of each endpoint obtained from the command analyzing unit  1001 , and transfers the obtained differential coefficients to the start point generation unit  1003  and the RGB interpolating unit  1004 . 
   Obtaining the differential coefficients for the horizontal and vertical directions from the plane equation of a triangle is described with reference to  FIG. 27  and Equation 1 given below. 
                   ⅆ   R       ⅆ   X       =           (     R2   -   R0     )     ⁢     (     X1   -   X0     )       +       (     R1   -   R0     )     ⁢     (     X2   -   X0     )               (     Y2   -   Y0     )     ⁢     (     X1   -   X0     )       +       (     Y1   -   Y0     )     ⁢     (     X2   -   X0     )             ⁢     
     ⁢         ⅆ   R       ⅆ   Y       =           (     R2   -   R0     )     ⁢     (     Y1   -   Y0     )       +       (     R1   -   R0     )     ⁢     (     Y2   -   Y0     )               (     Y2   -   Y0     )     ⁢     (     X1   -   X0     )       +       (     Y1   -   Y0     )     ⁢     (     X2   -   X0     )             ⁢     
     ⁢         ⅆ   G       ⅆ   X       =           (     G2   -   G0     )     ⁢     (     X1   -   X0     )       +       (     G1   -   G0     )     ⁢     (     X2   -   X0     )               (     Y2   -   Y0     )     ⁢     (     X1   -   X0     )       +       (     Y1   -   Y0     )     ⁢     (     X2   -   X0     )             ⁢     
     ⁢         ⅆ   G       ⅆ   Y       =           (     G2   -   G0     )     ⁢     (     Y1   -   Y0     )       +       (     G1   -   G0     )     ⁢     (     Y2   -   Y0     )               (     Y2   -   Y0     )     ⁢     (     X1   -   X0     )       +       (     Y1   -   Y0     )     ⁢     (     X2   -   X0     )             ⁢     
     ⁢         ⅆ   B       ⅆ   X       =           (     B2   -   B0     )     ⁢     (     X1   -   X0     )       +       (     B1   -   B0     )     ⁢     (     X2   -   X0     )               (     Y2   -   Y0     )     ⁢     (     X1   -   X0     )       +       (     Y1   -   Y0     )     ⁢     (     X2   -   X0     )             ⁢     
     ⁢         ⅆ   B       ⅆ   Y       =           (     B2   -   B0     )     ⁢     (     Y1   -   Y0     )       +       (     B1   -   B0     )     ⁢     (     Y2   -   Y0     )               (     Y2   -   Y0     )     ⁢     (     X1   -   X0     )       +       (     Y1   -   Y0     )     ⁢     (     X2   -   X0     )                     Equation   ⁢           ⁢   1             
 
   The start point generation unit  1003  determines a left side of the triangle (in a case where the triangle is a counterclockwise triangle as shown in  FIG. 29 ) in accordance with the coordinates of each endpoint of the triangle (X 0 , Y 0 , X 1 , Y 1 , X 2 , Y 2 ) received from the command analyzing unit  1001 , successively obtains the values of start point X and R,G,B values in a horizontal direction from a vertical direction of the left side, and transfers the obtained values to a horizontal X DDA unit  1005  and a horizontal RGB DDA unit  1006 . 
   The RGB interpolating unit  1004  forms a mesh by dividing a square surrounding the triangle (See  FIG. 28 ) into units of minimum color length DDY in a vertical direction and minimum color length DDX in a horizontal direction in accordance with the coordinates of each of the endpoints of the triangle (X 0 , Y 0 , X 1 , Y 1 , X 2 , Y 2 ) received from the command analyzing unit  1001 . Based on the mesh, the RGB interpolating unit  1004  sends a Y direction update signal to the start point generation unit  1003  when the values of horizontal start point X and Y output from the start point generation unit  1003 , crosses over the mesh (border) in a vertical direction, to thereby update the RGB values for a horizontal direction that are transferred from the start point generation unit  1003  to the horizontal XDDA unit  1005  and the horizontal RGB DDA unit  1006 . 
   Further, the RGB interpolating unit  1004  overlooks the X value of each horizontal pixel of the horizontal XDDA unit  1005  and sends an X direction update signal to an RGB switching unit  1007  when the X value crosses over the mesh (border) in a horizontal direction, to thereby render the RGB switching unit  1007  to update the RGB value that is output from the horizontal RGB DDA  1006 . 
   Although a typical computation is employed to compute resolution for the sides of the object, resolution can be modified for the object having an inside thereof filled. 
   The horizontal XDDA unit  1005  receives horizontal start point X value, Y value from the start point generation unit  1003 , scans the triangle in a horizontal direction, successively obtains the X values of each pixel by DDA (Digitial Differential Analysis), and transfers the obtained X values to the RGB interpolating unit  1004  and the memory address generation unit  1008 . 
   The horizontal RGB DDA unit  1006  receives differential coefficients dRX, dGX, dBX from the triangle setup unit  1002  and the RGB horizontal start point values from the start point generation unit  1003 , and interpolates the RGB of each pixel in the horizontal direction by DDA. The horizontal RGB DDA unit  1006 , then, transfers the interpolated RGB values to the RGB switching unit  1007 . 
   The RGB switching unit  1007  updates the interpolated RGB values received from the horizontal RGB DDA unit  1006  according to the X direction update signals from the RGB interpolating unit  1004 . 
   The memory address generation unit  1008  converts the logical coordinates (addresses) of the band memory from the horizontal XDDA (X, Y) into physical coordinates (addresses) of the band memory in accordance with the bandwidth of the band memory, and transfers the converted coordinates to the image processing unit interface  1009 . 
   The image processing unit interface  1009  transfers the addresses from the memory address generation unit  1008  and the RGB values from the RGB switching unit  1007  to the image processing unit  206  shown in  FIG. 2 . 
   Numeral  1010  is a controller which entirely controls the draw processing unit  205  shown in  FIG. 2 . 
   [Draw Processing Flow] 
     FIG. 11  shows a processing flow of a draw processing unit according to an embodiment of the present invention. 
   Step S 1101 : A command analyzing unit analyzes a drawing command, and obtains endpoints of a triangle (X 0 , Y 0 , X 1 , Y 1 , X 2 , Y 2 ) and color information of the endpoints (R 0 , G 0 , B 0 , R 1 , G 1 , B 1 , R 2 , G 2 , B 2 ). 
   Step S 1102 : A triangle setup unit obtains differential coefficients for a horizontal direction dRX, dGX, dBX and differential coefficients for a vertical direction dRY, dGY, dBY. 
   Step S 1103 : Set initial value (Initialize). 
   Step S 1104 : A start point generation unit obtains a left side in accordance with vectors of the sides of the triangle, and acquires the values of start points in a horizontal direction (XYRGB) of a vertical direction IY of the left side. 
   Step S 1105 : An RGB interpolating unit determines whether the values of the start points crosses over boundaries of the square, which surrounds the triangle and is divided into prescribed units of minimum color length in a vertical direction DDY. 
   Step S 1106 : Update RGB start point value in horizontal direction of IY. 
   Step S 1107 : A horizontal XDDA unit obtains an X value in a horizontal direction. 
   Step S 1108 : A horizontal RGB DDA unit obtains an RGB value in a horizontal direction. 
   Step S 1109 : The RGB interpolating unit determines whether the values of the start points cross over boundaries of the square, surrounds the triangle and is divided into prescribed units of minimum color length in a horizontal direction DDX. 
   Step S 1110 : Update RGB value in a horizontal direction of IY. 
   Step S 1111 : Determine whether all pixels are processed in a horizontal direction. 
   Step S 1112 : Add 1 to the value of IY. 
   Step S 1113 : Determine whether all pixels are processed in a vertical direction. 
   [Triangle Setup Unit] 
     FIG. 12  is a block diagram of the triangle setup unit  1002  shown in  FIG. 10 . 
   Numeral  1201  is an R horizontal differential coefficient generation unit that generates the value of a differential coefficient (R) for a horizontal direction dRX from a plane equation of a triangle. 
   Numeral  1202  is an R vertical differential coefficient generation unit that generates the value of a differential coefficient (R) for a vertical direction dRY from a plane equation of a triangle. 
   Numeral  1203  is a G horizontal differential coefficient generation unit that generates the value of a differential coefficient (G) for a horizontal direction dGX from a plane equation of a triangle. 
   Numeral  1204  is a G vertical differential coefficient generation unit that generates the value of a differential coefficient (G) for a vertical direction dGY from a plane equation of a triangle. 
   Numeral  1205  is a B horizontal differential coefficient generation unit that generates the value of a differential coefficient (B) for a horizontal direction dBX from a plane equation of a triangle. 
   Numeral  1206  is a B vertical differential coefficient generation unit that generates the value of a differential coefficient (B) for a vertical direction dBY from a plane equation of a triangle. 
   [Horizontal Differential Coefficient Generation Unit] 
     FIG. 13  is a block diagram showing the R horizontal differential coefficient generation unit  1201  shown in  FIG. 12 . The block diagram expresses the equation of dR/dX in Equation 1 in the form of hardware. 
   [Vertical Differential Coefficient Generation Unit] 
     FIG. 14  is a block diagram showing the R vertical differential coefficient generation unit  1202  shown in  FIG. 12 . The block diagram expresses the equation of dR/dY in Equation 1 in the form of hardware. 
   [Horizontal RGB DDA Unit] 
     FIG. 15  is a block diagram showing the horizontal RGB DDA unit  1006  shown in  FIG. 10 . 
   Numerals  1501  through  1503  are registers which store start point values of RGB values in a horizontal direction from the start point generation unit  1003  shown in  FIG. 10 . 
   Numerals  1504  to  1506  are registers which store differential coefficients of RGB values in a horizontal direction from the triangle setup unit  1002  shown in  FIG. 10 . 
   Numerals  1507  through  1509  are adders which conduct addition for performing respective DDA processing for R, G, and B. 
   Numerals  1510  through  1512  are frame memory address multiplexers (MUX) which transfer the start point values of RGB  1501  through  1503  to the registers  1513  through  1515  as initial values in the respective DDA processing for R, G, and B, and then transfers the output of the adders  1507  through  1509  during the DDA processing to the registers  1513  through  1515 . 
   The registers  1513  through  1515  store process results of the respective DDA processing for R, G, and B. 
   [Start Point Generation Unit] 
     FIG. 16  shows a block diagram of the start point generation unit  1003  shown in  FIG. 10 . 
   Numeral  1601  is a left side searching unit which determines a left side by referring to the vectors of endpoints of the sides of a triangle, transfers a start point (X, Y) and an end point (X, Y) to a X differential coefficient computing unit  1602 , and transfers values of X, Y to the registers  1603  and  1604 . 
   The process is continued until there are no more left sides remaining. 
   The X differential coefficient computation unit  1602  receives the start point (X, Y) and the terminating point (X, Y) from the left side searching unit  1601 , obtains the differential coefficient in the vertical direction (terminating point X−start point X)/(terminating point Y−start point Y), and transfers the obtained differential coefficient to the register  1605 . 
   The register  1603  stores the value of the start point X from the left side searching unit  1601 . 
   The register  1604  stores the value of the start point Y from the left side searching unit  1601 . 
   The register  1605  stores the value of the differential coefficient X from the X differential coefficient computing unit  1602 . 
   The adder  1606  performs the adding process of the DDA for X in a vertical direction. 
   The adder  1607  performs the adding process of the DDA for Y in a horizontal direction. 
   Numeral  1608  is a frame memory address multiplier (MUX) which transfers the start point values X of the register  1603  to a register  1610  as initial values in the DDA processing for X in a vertical direction, and then, during the DDA processing, transfers the output of the adders  1606  to the register  1610 . 
   Numeral  1609  is an MUX (frame memory address multiplexer) which transfers the start point values of Y of the register  1604  to the register  1611  as initial values in the DDA processing for Y in a vertical direction, and then, during the DDA processing, transfers the output of the adders  1606  to the register  1611 . 
   The register  1610  stores process results of the DDA processing of X in the vertical direction. 
   The register  1611  stores process results of the DDA processing of Y in the vertical direction. 
   Numeral  1612  is a subtractor which subtracts the value of the start point X from the process results of the DDA processing of X in a vertical direction  1610 , obtains X differential coefficient from the start point of the left side that is being subjected to processing, and transfers the obtained X differential coefficient to the multipliers of the RGB interpolating units  1615 ,  1617 , and  1619 . 
   Numerals  1614  through  1622  are RGB interpolating units which perform plane interpolation in accordance with the differential coefficients in the X, Y directions obtained in  1612  and  1613 , and the differential coefficients obtained by the triangle setup unit  1002  in  FIG. 10 . The RGB interpolating units  1614  through  1622 , thereby, obtain an RGB start point of the left side for the horizontal direction. 
   Numeral  1614  is a multiplier which multiplies the differential coefficient value for the horizontal direction dRX obtained from the triangle setup unit  1002  shown in  FIG. 10  and the differential coefficient value for the vertical direction X obtained from the subtractor  1612 , and transfers the multiplication result to the adder  1620 . 
   Numeral  1615  is a multiplier which multiplies the differential coefficient value for the horizontal direction dRY obtained from the triangle setup unit  1002  shown in  FIG. 10  and the differential coefficient value for the vertical direction Y obtained from the subtractor  1613 , and transfers the multiplication result to the adder  1620 . 
   Numeral  1616  is a multiplier which multiplies the differential coefficient value for the horizontal direction dGX obtained from the triangle setup unit  1002  shown in  FIG. 10  and the differential coefficient value for the vertical direction X obtained from the subtractor  1612 , and transfers the multiplication result to the adder  1621 . 
   Numeral  1617  is a multiplier which multiplies the differential coefficient value for the horizontal direction dGY obtained from the triangle setup unit  1002  shown in  FIG. 10  and the differential coefficient value for the vertical direction Y obtained from the subtractor  1613 , and transfers the multiplication result to the adder  1621 . 
   Numeral  1618  is a multiplier which multiplies the differential coefficient value for the horizontal direction dBX obtained from the triangle setup unit  1002  shown in  FIG. 10  and the differential coefficient value for the vertical direction X obtained from the subtractor  1612 , and transfers the multiplication result to the adder  1622 . 
   Numeral  1619  is a multiplier which multiplies the differential coefficient value for the horizontal direction dBY obtained from the triangle setup unit  1002  shown in  FIG. 10  and the differential coefficient value for the vertical direction Y obtained from the subtractor  1613 , and transfers the multiplication result to the adder  1622 . 
   The adder  1620  adds the multiplication results in  1614  and  1615   
   The adder  1621  adds the multiplication results in  1616  and  1617 . 
   The adder  1622  adds the multiplication results in  1618  and  1619 . 
   Numeral  1623  is a register which stores the value of the processed results for a vertical direction according to XDDA. 
   Numeral  1624  is a register which stores the value of the processed results for a vertical direction according to YDDA. 
   Numeral  1625  is a register which updates the resultant R value from interpolating RGB of the left side for the vertical direction when the Y direction update signal from the RGB interpolating unit  1004  shown in  FIG. 10  is in an “ON” state. 
   Numeral  1626  is a register which updates the resultant G value from interpolating RGB of the left side for the vertical direction when the Y direction update signal from the RGB interpolating unit  1004  shown in  FIG. 10  is in an “ON” state. 
   Numeral  1627  is a register which updates the resultant B value from interpolating RGB of the left side for the vertical direction when the Y direction update signal from the RGB interpolating unit  1004  shown in  FIG. 10  is in an “ON” state. 
   [Horizontal XDDA Unit] 
     FIG. 17  is a block diagram showing a horizontal XDDA unit  1005  shown in  FIG. 10 . 
   Numeral  1701  is a register which stores start point value X for a horizontal direction generated from the generation unit  1003  shown in  FIG. 10 . 
   Numeral  1702  is a register which stores start point value Y for a horizontal direction generated from the generation unit  1003  shown in  FIG. 10 . 
   Numeral  1703  is an adder which conducts addition for performing a DDA process for X. 
   Numeral  1704  is an MUX which transfers the start point value X stored in the register  1701  to a register  1705  as an initial value in the DDA process for X, and then, during the DDA process, transfers the output of the adder  1703  to the register  1705 . 
   The register  1705  stores process results of the DDA process for X. 
   [Memory Address Generation Unit] 
     FIG. 18  is a block diagram of the memory address generation unit  1008  shown in  FIG. 10 . 
   Numeral  1801  is a register which stores X value output from the horizontal X DDA unit  1005  shown in  FIG. 10 . 
   Numeral  1802  is a register which stores Y value output from the horizontal X DDA unit  1005  shown in  FIG. 10 . 
   Numeral  1803  is a multiplier which multiplies the X value of the register  1801  and bandwidth. 
   Numeral  1804  is an adder which adds the output from the multiplier  1803  to the Y value of the register  1802 , thereby obtaining a memory address (physical address). 
   Numeral  1805  is a register which stores the obtained memory address (physical address). 
   [RGB Interpolating Unit] 
     FIG. 19  is a block diagram of the RGB interpolating unit  1004  shown in  FIG. 10 . 
   Numeral  1901  is a minimum X value generation unit which receives X coordinates of each of the endpoints of the triangle from the command analyzing unit  1001  shown in  FIG. 10 , obtains a minimum X value, and transfers the obtained minimum X value to the subtractor  1903 . 
   Numeral  1902  is a minimum Y value generation unit which receives Y coordinates of each of the endpoints of the triangle from the command analyzing unit  1001  shown in  FIG. 10 , obtains a minimum Y value, and transfers the obtained minimum Y value to the subtractor  1904 . 
   The subtractor  1903  receives the horizontal-compensated X value from the horizontal X DDA unit  1005  shown in  FIG. 10 , and the minimum X value from the minimum X value generation unit  1901  so as to obtain the difference with respect to the minimum X value for a horizontal direction of the square surrounding the triangle (as shown in  FIG. 28 ). 
   The subtractor  1904  receives the Y value from the horizontal X DDA unit  1005  shown in  FIG. 10 , and the minimum Y value from the minimum Y value generation unit  1902  so as to obtain the difference with respect to the minimum Y value for a vertical direction of the square surrounding the triangle (as shown in  FIG. 28 ). 
   Numeral  1905  is a divider which receives the smallest unit of color in a horizontal direction DDX (see  FIG. 28 ) from the parameter storage unit  803  shown in  FIG. 8 , divides the difference from the subtractor  1903  with DDX, and transfers the result of the division to a 0 decimal point determining unit  1907 . 
   Numeral  1906  is a divider which receives the smallest unit of color in a vertical direction DDY (see  FIG. 28 ) from the parameter storage unit  803  shown in  FIG. 8 , divides the difference from the subtractor  1904  with DDY, and transfers the result of the division to a 0 decimal point determining unit  1908 . 
   The 0 decimal point determining unit  1907  receives the division result from the divider  1905 , confirms that there is no remainder from the division, and determines whether the mesh shown in  FIG. 28  is being crossed over in a horizontal direction. 
   The 0 decimal point determining unit  1908  receives the division result from the divider  1906 , confirms that there is no remainder from the division, and determines whether the mesh shown in  FIG. 28  is being crossed over in a vertical direction. 
   Numeral  1909  is an OR circuit which receives a horizontal drawing signal from the controller  1010  shown in  FIG. 10  and unconditionally generates an X direction update signal when the horizontal drawing signal signifies “START”. 
   Numeral  1910  is a register storing the X direction update signal from the OR circuit  1909 . 
   Numeral  1911  is a register storing the Y direction update signal from the 0 decimal point determining unit  1908 . 
   [Image Processing Unit] 
     FIG. 20  is a block diagram of the image processing unit  206  shown in  FIG. 2 . 
   Numeral  2001  is a color conversion unit which receives color information for each pixel and band address from the drawing unit  205  shown in  FIG. 2 , generates CMYK data by performing color conversion, and transfers the generated CMYK data and the band address to a halftone unit  2002 . 
   The halftone unit  2002  receives the CMYK data and the band address from the color conversion unit  2001 , performs a halftone process thereto, and transfers the result of the halftone process to a memory arbiter interface  2005 . 
   Numeral  2003  is a parameter storage unit which temporarily stores parameters of the color conversion unit  2001  and the halftone unit  2002 . 
   Numeral  2004  is a write address generation unit which generates addresses of the CMYK binary band memory spaces (shown in  FIG. 5 ) in the main memory  224  (shown in  FIG. 2 ). 
   The memory arbiter  2005  serves as an interface with respect to the memory arbiter  203  (shown in  FIG. 2 ), and writes halftoned data to the main memory  224  (shown in  FIG. 2 ) in accordance with the addresses from the write address generation unit  2004 . 
   Numeral  2006  is a controller which entirely controls the image processing unit  206 . 
   [Process Flow of Image Processing Unit] 
     FIG. 21  shows a process flow of an image processing unit according to an embodiment of the present invention. 
   Step S 2101 : Set color conversion table for color conversion unit. 
   Step S 2102 : Set respective start point addresses of CMYK band memory space of the main memory to the parameter storage unit. 
   Step S 2103 : Set threshold size of halftone unit. 
   Step S 2104 : Set threshold of halftone unit. 
   Step S 2105 : Receive color information and memory address from the drawing unit. 
   Step S 2106 : Conduct color conversion. 
   Step S 2107 : Conduct halftone process (halftoning). 
   Step S 2108 : Withdraw from loop after all pixels are processed. 
   [Color Conversion Unit] 
     FIG. 22  is a block diagram of the color conversion unit  2001  shown in  FIG. 20 . 
   Numeral  2201  is a grid point selection unit which receives image data (RGB) from the drawing unit  205  shown in  FIG. 2 , divides the respective R, G, B components into N BIT upper image data and 8-N BIT lower image data, changes the N BIT upper image data into HR, HG, HB and the 8-N BIT lower image data into DR, DG, DB, obtains TYPE by determining which of the six tetrahedrons of a cube (formed of 8 grid points) should HR, HG, HB, DR, DG, DB belong to, and transfers HR, HG, HB, TYPE to a grid point address generation unit  2204  and DR, DG, DB to a grid point interpolating unit  2202 . 
   The grid point interpolating unit  2202  obtains C, M, Y, K data by interpolating in accordance with four interpolated CMYK grid points of a tetrahedron from a data extracting unit  2205  and DR, DG, DB of the grid point selection unit  2201 . 
   Numeral  2203  is a color conversion table memory which stores grid point information in a format shown in  FIG. 24 , receives grid point address from the grid point address generation unit  2204 , and transfers the grid point information to the data extracting unit  2205 . 
   The grid point address generation unit  2204  obtains the grid point addresses of the color conversion table  2203  in accordance with HR, HG, HB, DR, DG, DB and TYPE from the grid point selection unit  2201 . 
   The data extracting unit  2205  extracting four parameters from the grid point data of the color conversion table memory  2203  for interpolating with the grid point interpolating unit  2202 . 
   [Process Flow of Color Conversion Unit] 
     FIG. 23  shows a process flow of the color conversion unit according to an embodiment of the present invention. 
   Step S 2301 : Convert N BIT upper image (RGB) data included the image (RGB) data input to the grid point selection unit  2201  (shown in  FIG. 22 ) into HR, HG, HB, and convert (8-N) lower image (RGB) data included in the image (RGB) data input to the grid point selection unit  2201  (shown in  FIG. 22 ) into DR, DG, DB. 
   Step S 2302 : Obtain TYPE from HR, HG, HB obtained from the grid point selection unit  2201  (shown in  FIG. 22 ). 
   Step S 2303 : Obtain grid point address from the grid point address generation unit  2204  (shown in  FIG. 22 ). 
   Step S 2304 : Read grid point data from the color conversion table memory  2203  (shown in  FIG. 23 ). 
   Step S 2305 : Obtain C, M, Y, K data by interpolating grid point data with the grid point interpolating unit  2202  (shown in  FIG. 22 ). 
   [Halftone Unit] 
     FIG. 24  is a block diagram of the halftone unit  2002  shown in  FIG. 20 . 
   Numeral  2401  is an address generation unit which receives a threshold size and generates an address of a threshold matrix storage unit  2402 . 
   The threshold matrix storage unit  2402  stores respective threshold matrixes. 
   Numeral  2403  is a data distribution unit which receives threshold values of C, M, Y, K from the threshold matrix storage unit  2402 , and distributes the respective threshold values to comparing units  2404  through  2407 . 
   The comparing unit  2404  receives and compares C threshold data from the data distribution unit  2403  and the C pixel data from the color conversion unit  2001  (shown in  FIG. 20 ), to thereby generate C halftoned data. 
   The comparing unit  2405  receives and compares M threshold data from the data distribution unit  2403  and the M pixel data from the color conversion unit  2001  (shown in  FIG. 20 ), to thereby generate M halftoned data. 
   The comparing unit  2406  receives and compares Y threshold data from the data distribution unit  2403  and the Y pixel data from the color conversion unit  2001  (shown in  FIG. 20 ), to thereby generate Y halftoned data. 
   The comparing unit  2407  receives and compares K threshold data from the data distribution unit  2403  and the K pixel data from the color conversion unit  2001  (shown in  FIG. 20 ), to thereby generate K halftoned data. 
   Numeral  2408  is a C fixed length data generation unit which successively receives C halftoned data from the comparing unit  2404  and converts the halftoned data to fixed length data. 
   Numeral  2409  is an M fixed length data generation unit which successively receives M halftoned data from the comparing unit  2405  and converts the halftoned data to fixed length data. 
   Numeral  2410  is a Y fixed length data generation unit which successively receives Y halftoned data from the comparing unit  2406  and converts the halftoned data to fixed length data. 
   Numeral  2411  is a K fixed length data generation unit which successively receives K halftoned data from the comparing unit  2407  and converts the halftoned data to fixed length data. 
   Numeral  2412  is a C FIFO which receives and temporarily stores data from the C fixed length data generation unit  2408 . 
   Numeral  2413  is an M FIFO which receives and temporarily stores data from the M fixed length data generation unit  2409 . 
   Numeral  2414  is a Y FIFO which receives and temporarily stores data from the Y fixed length data generation unit  2410 . 
   Numeral  2415  is a K FIFO which receives and temporarily stores data from the K fixed length data generation unit  2411 . 
   Numeral  2416  is an MUX which receives data from respective FIFO, successively selects and transfers the data to the memory arbiter interface  2005  (shown in  FIG. 20 ). 
   Numeral  2418  is a CMYK address generation unit which adds the respective C, M, Y, K start point addresses to the physical addresses (head addresses) from the color conversion unit  2001  (shown in  FIG. 20 ), to thereby obtain respective C, M, Y, K head addresses and transfer the obtained addresses to an MUX  2419 . 
   The MUX  2419  selects head addresses of the halftoned image data, which are to be written to the main memory, from the respective C, M, Y, K head addresses, and transfers the selected addresses to the write address generation unit  2004  (shown in  FIG. 20 ). 
   [Process Flow of Halftone Unit] 
     FIG. 25  shows a processing flow of the halftone unit according to an embodiment of the present invention. 
   Step S 2501 : Compare CMYK threshold data with CMYK pixel data and binarize. 
   Step S 2502 : Add binarized CMYK data to fixed length data. 
   Step S 2503 : Determine whether data is expanded to fixed length data. 
   Step S 2504 : Write CMYK fixed length data to FIFO. 
   Step S 2505 : Count up dither address in horizontal direction. 
   Step S 2506 : Determine whether dither address in the horizontal direction exceeds the size of the horizontal direction. 
   Step S 2507 : Clear dither address in the horizontal direction. 
   Step S 2508 : Determine whether halftoning (halftone process) for all pixels of horizontal line is completed. 
   Step S 2509 : Count up dither address in the vertical direction. 
   Step S 2510 : Determine whether halftoning (halftone process) for all pixels of all lines is completed. 
     FIG. 26  is a block diagram of the fixed length data generation unit  2408  shown in  FIG. 24 . 
   Numeral  2601  is a shifter which receives binary data from the comparing unit  2404  (shown in  FIG. 24 ) and shifts the binary data to an extent of a value obtained from a register  2606  (shown in  FIG. 26 ), and transfers the shifted binary data to an OR unit  2602 . 
   The OR unit  2602  performs OR processing to the shifted binary data from the shifter  2601 , and transfers the OR processed data to a register  2604 . 
   Numeral  2603  is a register which stores binary data that has been OR processed and added in the OR unit  2602 . 
   The register  2604  stores data that has reached a fixed length. 
   Numeral  2605  is an adder which adds “1” whenever receiving binary data from the comparing unit  2404  (shown in  FIG. 24 ). 
   The register  2606  stores shift value. 
   Although the aforementioned example describes a case where each endpoint of a gradient fill is interpolated with RGB color, the present invention may also be applied to a case of CMY, CMYK or Lab. 
   Furthermore, the present invention may be applied to a case of black and white where a single vector of gradation may be employed instead of three vectors as in the case of RGB. 
   Further, the present invention is not limited to these embodiments, but various variations and modifications may be made without departing from the scope of the present invention. 
   The present application is based on Japanese Priority Application No. 2003-017901 filed on Jan. 27, 2003, with the Japanese Patent Office, the entire contents of which are hereby incorporated by reference.