Patent Publication Number: US-8982286-B2

Title: Projection apparatus, projection method and computer-readable storage medium for correcting a projection state being projected onto curved surface

Description:
BACKGROUND 
     1. Technical Field 
     The present invention relates to a projection apparatus, a projection state adjustment method, and a projection state adjustment program. 
     2. Related Art 
     Generally, a projector as an image projection apparatus is known, in which an image based on image data output from a personal computer, for example, is projected onto a projection target such as a screen. 
     Such a projector is sometimes used to project an image onto the curved surface of a circular cylinder, for example. 
     For example, in the case where an image with no distortion is appropriately projected onto a circular cylinder, it is necessary to apply geometric correction to a projected image. 
     Functions for use in such geometric correction are different depending on the positional relationship between the projector and the circular cylinder, such as the orientation of the projector relative to the circular cylinder, a distance from the projector to the circular cylinder, and the diameter of the circular cylinder. 
     Thus, it is necessary to provide the settings of geometric correction depending on the positional relationship between the projector and the circular cylinder, for example. 
     Some methods are known as a setting method for such geometric correction. 
     For example, a first method is a method in which a projector is used to project a grid pattern onto a circular cylinder, and a user adjusts the positions of intersection points of grids to sequentially change the set values of geometric correction. 
     A second method is a method in which a distance and a direction from a projector to a circular cylinder, the range of a screen on the circular cylinder, the angle of view of the projector, the position of an optical axis, and so on are found, and correction values necessary for geometric correction are calculated from the values. 
     For a third method, a technique is disclosed in JP-A-2004-320662, for example, in which typical geometric correction methods not directly involved in a circular cylinder are combined to adjust images. 
     As for the foregoing setting methods for geometric correction, according to the first method, for example, the user can intuitively perform manipulations. 
     However, it is necessary to adjust a large number of positions of intersection points, and it takes a lot of time and effort. 
     For example, in the second method, it is necessary to accurately determine the positional relationship between the projector and the circular cylinder, for example, which is usually difficult to determine, and it is difficult to implement the second method. 
     For example, according to the third method, the user can relatively easily perform manipulations because the amount of manipulations is small. 
     However, it is difficult for the user to intuitively grasp which geometric correction methods to combine. 
     Moreover, the first method and the third method provide approximate settings, and the methods do not always provide mathematically accurate correction. 
     SUMMARY 
     Therefore, it is an object of the present invention to provide a projection apparatus, a projection state adjustment method, and a projection state adjustment program that can accurately adjust the projection of an image onto a circular cylinder surface with easy manipulations by intuition. 
     In order to achieve the above object, a projection apparatus according to an aspect of the present invention includes: 
     a projection unit configured to project an image onto a target area on a curved surface formed of generatrices of a circular cylinder; 
     an image conversion unit configured to apply geometric transformation to a projected image projected by the projection unit; 
     a parameter acquiring unit configured to acquire a parameter expressing a positional relationship between the projection unit and the curved surface; and 
     a transform function determination unit configured to determine a transform function for use in the geometric transformation based on the parameter, 
     wherein the target area is an area surrounded by:
         a first line and a second line which are parallel to an axis of the circular cylinder;   a third line that is an intersection line of a first plane perpendicular to the axis with the curved surface; and   a fourth line that is an intersection line of a second plane parallel to the first plane with the curved surface, and       

     when an image area is such an area that the image applied the geometric transformation is projected onto the curved surface, the parameter includes:
         a four-corner parameter to match four corners of the image area and four corners of the target area;   a first middle point parameter to match a first middle point that is a middle point of a top side of the image area and a middle point of the third line of the target area;   a second middle point parameter to match a second middle point that is a middle point of a bottom side of the image area and a middle point of the fourth line of the target area; and   a second reference line parameter to, when a line connecting the first middle point to the second middle point of the image area is a first reference line, adjust a position of a second reference line provided between a left side of the image area and the first reference line, or between a right side of the image area and the first reference line.       

     In order to achieve the above object, a projection apparatus according to an aspect of the present invention includes: 
     a projection unit configured to project an image onto a target area on a curved surface formed of generatrices of a circular cylinder; 
     an image conversion unit configured to apply geometric transformation to a projected image projected by the projection unit; 
     a parameter acquiring unit configured to acquire a parameter expressing a positional relationship between the projection unit and the curved surface; and 
     a transform function determination unit configured to determine a transform function for use in the geometric transformation based on the parameter, 
     wherein the target area is an area surrounded by:
         a first line and a second line which are parallel to an axis of the circular cylinder;   a third line that is an intersection line of a first plane perpendicular to the axis with the curved surface; and   a fourth line that is an intersection line of a second plane parallel to the first plane with the curved surface, and       

     the geometric transformation includes:
         rotation projection transformation between a plane and a plane; and   circular cylinder geometric transformation between the target area and a plane parallel to a third plane passing between the first line and the second line.       

     In order to achieve the above object, a projection state adjustment method according to an aspect of the present invention includes the steps of: 
     projecting an image onto a target area on a curved surface formed of generatrices of a circular cylinder from a projection unit; 
     applying geometric transformation to a projected image projected from the projection unit; 
     acquiring a parameter expressing a positional relationship between the projection unit and the curved surface; and 
     determining a transform function for use in the geometric transformation based on the parameter, 
     wherein the target area is an area surrounded by:
         a first line and a second line which are parallel to an axis of the circular cylinder;   a third line that is an intersection line of a first plane perpendicular to the axis with the curved surface; and   a fourth line that is an intersection line of a second plane parallel to the first plane with the curved surface, and       

     when an image area is such an area that the image applied the geometric transformation is projected onto the curved surface, the parameter includes:
         a four-corner parameter to match four corners of the image area and four corners of the target area;   a first middle point parameter to match a first middle point that is a middle point of a top side of the image area and a middle point of the third line of the target area;   a second middle point parameter to match a second middle point that is a middle point of a bottom side of the image area and a middle point of the fourth line of the target area; and   a second reference line parameter to, when a line connecting the first middle point to the second middle point of the image area is a first reference line, adjust a position of a second reference line provided between a left side of the image area and the first reference line, or between a right side of the image area and the first reference line.       

     In order to achieve the above object, a projection state adjustment method according to an aspect of the present invention includes the steps of: 
     projecting an image onto a target area on a curved surface formed of generatrices of a circular cylinder from a projection unit; 
     applying geometric transformation to a projected image projected from the projection unit; 
     acquiring a parameter expressing a positional relationship between the projection unit and the curved surface; and 
     determining a transform function for use in the geometric transformation based on the parameter, 
     wherein the target area is an area surrounded by:
         a first line and a second line which are parallel to an axis of the circular cylinder;   a third line that is an intersection line of a first plane perpendicular to the axis with the curved surface; and   a fourth line that is an intersection line of a second plane parallel to the first plane with the curved surface, and       

     the geometric transformation includes:
         rotation projection transformation between a plane and a plane; and   circular cylinder geometric transformation between the target area and a plane parallel to a third plane passing between the first line and the second line.       

     In order to achieve the above object, a non-transitory computer-readable storage medium according to an aspect of the present invention stores a projection state adjustment program that causes a computer to: 
     project an image onto a target area on a curved surface formed of generatrices of a circular cylinder from a projection unit; 
     apply geometric transformation to a projected image projected from the projection unit; 
     acquire a parameter expressing a positional relationship between the projection unit and the curved surface; and 
     determine a transform function for use in the geometric transformation based on the parameter, 
     wherein the target area is an area surrounded by:
         a first line and a second line which are parallel to an axis of the circular cylinder;   a third line that is an intersection line of a first plane perpendicular to the axis with the curved surface; and   a fourth line that is an intersection line of a second plane parallel to the first plane with the curved surface, and       

     when an image area such an area that the image applied the geometric transformation is projected onto the curved surface, the parameter includes:
         a four-corner parameter to match four corners of the image area and four corners of the target area;   a first middle point parameter to match a first middle point that is a middle point of a top side of the image area and a middle point of the third line of the target area;   a second middle point parameter to match a second middle point that is a middle point of a bottom side of the image area and a middle point of the fourth line of the target area; and   a second reference line parameter to, when a line connecting the first middle point to the second middle point of the image area is a first reference line, adjust a position of a second reference line provided between a left side of the image area and the first reference line, or between a right side of the image area and the first reference line.       

     In order to achieve the above object, a non-transitory computer-readable storage medium according to an aspect of the present invention stores a projection state adjustment program that causes a computer to: 
     project an image onto a target area on a curved surface formed of generatrices of a circular cylinder from a projection unit; 
     apply geometric transformation to a projected image projected from the projection unit; 
     acquire a parameter expressing a positional relationship between the projection unit and the curved surface; and 
     determine a transform function for use in the geometric transformation based on the parameter, 
     wherein the target area is an area surrounded by:
         a first line and a second line which are parallel to an axis of the circular cylinder;   a third line that is an intersection line of a first plane perpendicular to the axis with the curved surface; and   a fourth line that is an intersection line of a second plane parallel to the first plane with the curved surface, and       

     the geometric transformation includes:
         rotation projection transformation between a plane and a plane; and   circular cylinder geometric transformation between the target area and a plane parallel to a third plane passing between the first line and the second line.       

    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram of an exemplary configuration of a projector according to an embodiment of the present invention; 
         FIG. 2  is a diagram illustrating projection of an image onto a circular cylinder using a projector; 
         FIG. 3  is a diagram illustrating the degree of freedom of the positional relationship between the projector and the circular cylinder; 
         FIG. 4  is a diagram illustrating the degree of freedom of the positional relationship between the projector and the circular cylinder; 
         FIG. 5  is a diagram illustrating the degree of freedom of the positional relationship between the projector and the circular cylinder; 
         FIG. 6  is a diagram illustrating an exemplary adjustment chart according to an embodiment; 
         FIG. 7  is a diagram illustrating an exemplary adjustment chart according to an embodiment; 
         FIG. 8  is a diagram illustrating an exemplary adjustment chart according to an embodiment; 
         FIG. 9  is a diagram illustrating an exemplary adjustment chart according to an embodiment; 
         FIG. 10  is a flowchart of an exemplary projection state adjustment process according to an embodiment; 
         FIG. 11  is a flowchart of an exemplary first adjustment chart process according to an embodiment; 
         FIG. 12  is a flowchart of an exemplary adjustment process according to an embodiment; 
         FIG. 13  is a diagram of an exemplary projection state of an adjustment chart onto the circular cylinder before the projection state adjustment process; 
         FIG. 14  is a diagram of an exemplary projection state of an adjustment chart onto the circular cylinder after the first adjustment chart process; 
         FIG. 15  is a flowchart of an exemplary second adjustment chart process according to an embodiment; 
         FIG. 16  is a diagram of an exemplary projection state of an adjustment chart onto the circular cylinder after the second adjustment chart process; 
         FIG. 17  is a flowchart of an exemplary third adjustment chart process according to an embodiment; 
         FIG. 18  is a diagram of an exemplary projection state of an adjustment chart onto the circular cylinder after the third adjustment chart process; 
         FIG. 19  is a flowchart of an exemplary fourth adjustment chart process according to an embodiment; 
         FIG. 20  is a diagram of an exemplary projection state of an adjustment chart onto the circular cylinder after the fourth adjustment chart process; 
         FIGS. 21A to 21D  are diagrams illustrating a first transformation and a second transformation in the projection state adjustment process according to an embodiment; 
         FIG. 22  is a diagram illustrating projection of an image onto a circular cylinder using the projector according to an embodiment; 
         FIG. 23  is a diagram illustrating projection of an image onto a circular cylinder according to an exemplary modification of an embodiment; 
         FIG. 24  is a diagram illustrating projection of an image onto a curved surface according to an exemplary modification of an embodiment; 
         FIG. 25  is a diagram illustrating an adjustment chart according to an embodiment; and 
         FIG. 26  is a diagram illustrating an adjustment chart according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     An embodiment of the present invention will be described with reference to the drawings. A projection apparatus according to the embodiment uses a digital light processing (DLP) (registered trademark) method using a micromirror display device. 
       FIG. 1  is a diagram of the schematic configuration of a projector  1  as the projection apparatus according to the embodiment. 
     The projector  1  according to the embodiment can appropriately project an image with no distortion onto a circular cylinder. 
     Thus, the projector  1  performs geometric transformation on a projected image. 
     The projector  1  is configured to acquire parameters necessary for geometric transformation from a user, as described later. 
     The projector  1  includes an input/output connector unit  11 , an input/output interface (I/F)  12 , an image conversion unit  13 , a projection processing unit  14 , a micromirror element  15 , a light source unit  16 , a mirror  18 , a projection lens  20 , a CPU  25 , a main memory  26 , a program memory  27 , an operation unit  28 , a posture sensor  29 , an audio processing unit  30 , a speaker  32 , a projection adjustment unit  40 , and a system bus SB. 
     The input/output connector unit  11  is provided with a terminal such as a pin jack (RCA) type video input terminal or a D-sub  15  type RGB input terminal, for example, to which analog image signals are input. 
     The input image signals are input to the image conversion unit  13  through the input/output I/F  12  and the system bus SB. 
     The input analog image signals in various standards are converted into digital image signals at the input/output I/F  12 . 
     It is noted that the input/output connector unit  11  may be configured to include an HDMI (registered trademark) terminal, for example, and to receive digital image signals as well as analog image signals. 
     Moreover, the input/output connector unit  11  receives analog or digital audio signals. 
     The input audio signals are input to the audio processing unit  30  through the input/output I/F  12  and the system bus SB. 
     Furthermore, the input/output connector unit  11  may be provided with an RS232C terminal or a USB terminal, for example. 
     The image conversion unit  13  is also called a scaler. 
     The image conversion unit  13  converts the input image data to adjust resolution, a grayscale level, and the like and generates image data in a predetermined format appropriate for projection. 
     The image conversion unit  13  transmits the converted image data to the projection processing unit  14 . 
     The image conversion unit  13  transmits, to the projection processing unit  14 , image data on which symbols representing various operating states for an on-screen display (OSD) have been superimposed, as processed image data, when necessary. 
     Moreover, the image conversion unit  13  performs geometric transformation on a projected image to project, onto a projection target such as a screen, an image in an appropriate shape in accordance with a projection state. 
     Specifically, in the embodiment, the image conversion unit  13  performs geometric transformation to appropriately project an image onto a circular cylinder. 
     The light source unit  16  emits light of a plurality of colors including the primary colors of red (R), green (G), and blue (B). 
     The light source unit  16  is configured to sequentially emit the plurality of colors divided in time. 
     The light emitted from the light source unit  16  is totally reflected by the mirror  18  and enters the micromirror element  15 . 
     The micromirror element  15  includes a plurality of micromirrors arranged in an array. 
     The micromirrors operate on/off at high speeds, and reflect the light emitted from the light source unit  16  in a direction of the projection lens  20 , or divert the light in a direction away from the projection lens  20 . 
     A necessary number of the micromirrors for, for example, WXGA (Wide eXtended Graphic Array) (1280 pixels wide×800 pixels high) is arranged in the micromirror element  15 . 
     With the reflection from the micromirrors, the micromirror element  15  forms an image in, for example, the WXGA resolution. 
     In this manner, the micromirror element  15  functions as a spatial optical modulator. 
     The projection processing unit  14  drives the micromirror element  15  to display an image represented by the image data transmitted from the image conversion unit  13  in accordance with the image data. 
     In other words, the projection processing unit  14  operates on/off of the micromirrors of the micromirror element  15 . 
     The projection processing unit  14  drives the micromirror element  15  in time division at high speeds. 
     The number of divisions of a unit time is obtained by multiplying a frame rate in accordance with a predetermined format [frames/second], the number of divided color components, and the number of display grayscale levels. 
     Moreover, the projection processing unit  14  also controls the operation of the light source unit  16  in synchronization with the operation of the micromirror element  15 . 
     In other words, the projection processing unit  14  divides each frame in time, and controls the operation of the light source unit  16  to sequentially emit the light of all the color components in each frame. 
     The projection lens  20  adjusts the light guided from the micromirror element  15  to light to be projected onto a projection target (not illustrated) such as a screen or a circular cylinder. 
     Therefore, an optical image formed by the reflected light from the micromirror element  15  is projected and displayed on the projection target such as a screen or a circular cylinder via the projection lens  20 . 
     The projection lens  20  includes a zoom mechanism and has a function of changing the size of an image to be projected. 
     Moreover, the projection lens  20  includes a focus adjustment mechanism for adjusting the focus state of a projected image. 
     In this manner, the projection processing unit  14 , the micromirror element  15 , the light source unit  16 , the projection lens  20 , and the like function as a projection unit  22  that projects an image. 
     The audio processing unit  30  includes a sound generator such as a PCM sound source. 
     The audio processing unit  30  drives the speaker  32  to amplify and release sounds based on analog audio data input from the input/output connector unit  11  or based on an analog signal obtained by converting digital audio data given upon projection operation. 
     Moreover, the audio processing unit  30  generates a beep sound and the like when necessary. 
     The speaker  32  is a general speaker that emits the sound based on the signal input from the audio processing unit  30 . 
     The CPU  25  controls the operation of the image conversion unit  13 , the projection processing unit  14 , the audio processing unit  30 , and the projection adjustment unit  40  described below. 
     The CPU  25  is connected to the main memory  26  and the program memory  27 . 
     The main memory  26  includes, for example, an SRAM. 
     The main memory  26  functions as working memory of the CPU  25 . 
     The program memory  27  includes an electrically rewritable nonvolatile memory. 
     The program memory  27  stores an operating program, various fixed-format data, and the like that are executed by the CPU  25 . 
     Moreover, the CPU  25  is connected to the operation unit  28 . 
     The operation unit  28  includes a key operation unit provided to a main body of the projector  1 , and an infrared light receiving unit that receives infrared light from a remote control (not illustrated) dedicated to the projector  1 . 
     The operation unit  28  includes an arrow key and an OK button. 
     The operation unit  28  outputs, to the CPU  25 , a key operation signal based on a key operated by a user with the key operation unit of the main body or the remote control. 
     The CPU  25  uses the program and data stored in the main memory  26  and the program memory  27  to control the operation of the units of the projector  1  in accordance with the user&#39;s instruction from the operation unit  28 . 
     The posture sensor  29  includes a three-axis accelerometer, for example. 
     The accelerometer detects the angle of posture of the projector  1  in the gravity direction, that is, the angles of pitch and roll. 
     The posture sensor  29  outputs the detected result to the projection adjustment unit  40 . 
     However, the posture sensor  29  is not a necessary component, as described later. 
     The projection adjustment unit  40  determines a transform function for image geometric transformation used for appropriately projecting an image onto a circular cylinder, for example. 
     The projection adjustment unit  40  includes a chart generation unit  41 , a parameter acquiring unit  42 , a parameter storage unit  43 , a transform function determination unit  44 , a transform function storage unit  45 , and a transform function reading unit  46 . 
     The chart generation unit  41  generates a projection state adjustment chart, described later. 
     The adjustment chart is generated by reading a grid pattern and markers or the like to display parameters to be presently adjusted, for example, which are recorded on the program memory  27 . 
     The parameter acquiring unit  42  acquires 12 conversion parameters, described later, based on the input from the user, for example. 
     The parameter storage unit  43  stores the conversion parameters acquired by the parameter acquiring unit  42 . 
     The transform function determination unit  44  calculates a transform function for use in geometric transformation of an image based on the conversion parameters acquired by the parameter acquiring unit  42 . 
     The transform function storage unit  45  stores the transform function calculated by the transform function determination unit  44 . 
     The transform function reading unit  46  reads the transform function stored on the transform function storage unit  45 , and outputs the transform function to the image conversion unit  13 , for example. 
     The image conversion unit  13  performs the geometric transformation of an image based on the transform function. 
     The operation of the projector  1  according to the embodiment will be described. 
     Let us consider the case where the projector  1  projects an image onto a curved surface formed of generatrices of a right circular cylinder. 
     First, the relationship among the projector  1 , a circular cylinder  200 , a projection area  100 , and a target area  210  onto which an image is projected, will be described with reference to  FIG. 2 . 
     Suppose that a range in which light emitted from the projection lens  20  of the projector  1  is projected onto a projection target is referred to as the projection area  100 . 
     On the surface of the circular cylinder  200 , the area onto which an image is desired to be projected is referred to as the target area  210 . 
     In the embodiment, the projector  1  operates to project an image onto the circular cylinder  200  as if a sheet with a rectangular image depicted thereon is attached to the circular cylinder  200 . 
     The target area  210  is the area corresponding to the sheet, onto which an image is finally projected. 
     Here, a left side  212  and a right side  214  of the target area  210  are set parallel to a center axis  202  of the circular cylinder  200 . 
     A top side  216  and a bottom side  218  of the target area  210  are disposed on a plane perpendicular to the center axis  202  of the circular cylinder  200 . 
     On the projection area  100 , suppose that an area including an image corrected by geometric transformation is referred to as an image area  101 . 
     That is, the projector  1  according to the embodiment operates to match the image area  101  and the target area  210 . 
     Here, the projector  1  performs geometric transformation to project a desired image onto the circular cylinder  200  as if a sheet with this image depicted thereon is attached to the circular cylinder  200 . 
     With this geometric transformation, a desired image is included in the image area  101 , and the image area  101  matched with the target area  210 . 
     First, the degree of freedom of the projection state will be described with reference to  FIGS. 3 to 5 . 
     As depicted in  FIG. 3 , a coordinate system is defined as follows, with the position of the projection lens  20  of the projector  1  being the origin point. 
     That is, the projection direction of the projector  1  is defined as a z-axis. 
     The right direction of the projector  1  is defined as an x-axis, and the upper direction is defined as a y-axis on a plane perpendicular to the z-axis when the projector  1  is oriented in the z-axis direction. 
       FIG. 3  is a diagram of the positional relationship among the projector  1 , the circular cylinder  200 , and the target area  210 . 
     As described above, the left side  212  and the right side  214  of the target area  210  are parallel to each other, and the left side  212  and the right side  214  are also parallel to the center axis  202  of the circular cylinder  200 . 
     Moreover, suppose that a plane passing through a top end  212 - 1  of the left side  212  and perpendicular to the center axis  202  of the circular cylinder  200  is a first plane  221 . The first plane  221  passes through a top end  214 - 1  of the right side  214 . 
     Furthermore, in the intersection line of the circular cylinder  200  with the first plane  221 , a portion sandwiched between the left side  212  and the right side  214  is matched with the top side  216  of the target area  210 . 
     Suppose that a plane passing through a lower end  212 - 2  of the left side  212  and perpendicular to the center axis  202  of the circular cylinder  200  is a second plane  222 . The second plane  222  passes through a lower end  214 - 2  of the right side  214 . 
     In addition, in the intersection line of the circular cylinder  200  with the second plane  222 , a portion sandwiched between the left side  212  and the right side  214  is matched with the bottom side  218  of the target area  210 . 
     Suppose that the intersection point of the center axis  202  of the circular cylinder  200  with the first plane  221  is a first center O1, and the intersection point of the center axis  202  of the circular cylinder  200  with the second plane  222  is a second center O2. 
     The degree of freedom of the circular cylinder  200  relative to the projector  1  can be expressed by six degrees of freedom in total, i.e., coordinates O1 (x1, y1, z1) of the first center O1 and coordinates O2 (x2, y2, z2) of the second center O2. 
     It is noted that since the change in a radius R of the circular cylinder is the same as expansion or contraction of the entire coordinate system including the projector  1  and the circular cylinder  200 , the radius R of the circular cylinder is set to one, and is not included in the degree of freedom. 
       FIG. 4  is a diagram of the first plane  221 . 
     As depicted in  FIG. 4 , a rotation angle to the top end  214 - 1  of the right side  214  from a given reference line  226  is set to θ1, and a rotation angle to the top end  212 - 1  of the left side  212  from the reference line  226  is set to θ2. 
     As described above, the left side  212  and the right side  214  on the circular cylinder  200  can be expressed by two degrees of freedom. 
     Here, suppose that an angle expressing a portion onto which an image expressed by (θ2−θ1) is projected is referred to as a projection angle θ. 
       FIG. 5  is a diagram of a projection range on a plane where the z coordinate of an image that the projector  1  projects is one. 
     The projection range is expressed in a rectangle, so that the projection range can be expressed by four degrees of freedom in total, i.e., upper left coordinates D1 (x3, y3, 1) and lower right coordinates D2 (x4, y4, 1), for example. 
     As described above, in the case where an image is projected onto the circular cylinder  200  as if a sheet with a rectangular image depicted thereon is attached to the circular cylinder  200 , and the right and left sides of this image are adjusted to be parallel to the center axis  202  of the circular cylinder  200 , the degree of freedom of the projection state is 12 degrees in total. 
     In the projection state adjustment operation in which the projection of an image onto the circular cylinder  200  is adjusted as described above, the projector  1  according to the embodiment provides the projection state adjustment operation in which the user can intuitively adjust projection with a fewer number of manipulations and can accurately adjust the projection state. 
     As described above, since the degrees of freedom of projection onto the circular cylinder are 12 degrees, it is necessary to acquire 12 parameters in adjusting the projection state in order to accurately adjust the projection state. 
     Exemplary parameters for use in adjusting the projection state of the projector  1  according to the embodiment and exemplary adjustment charts for use in adjusting the projection state will be described with reference to  FIGS. 6 to 9 . 
     Adjustment charts for use in adjusting the projection state according to the embodiment are those as depicted in  FIGS. 6 to 9 . 
     All of these adjustment charts include the outer frame of the image area  101  expressing an image on the projection area  100 . 
     Moreover, for easy understanding, the adjustment charts include grid lines provided within the outer frame. 
     The grid lines are provided in such a way that intervals are provided equally on an image to be projected. 
     In the embodiment, adjustment markers, described later, included in the adjustment charts are adjusted so as to be matched with the corresponding locations on the target area  210 , which is the area onto which the image described with reference to  FIG. 2  is projected, and thus the projection state is adjusted. 
       FIG. 6  is a diagram of a first adjustment chart  110 . 
     The first adjustment chart  110  includes a first corner marker  112  expressing the upper left corner of the image area  101 , a second corner marker  114  expressing the lower left corner of the image area  101 , a third corner marker  116  expressing the lower right corner of the image area  101 , and a fourth corner marker  118  expressing the upper right corner of the image area  101 . 
     The projector  1  performs geometric transformation on the first adjustment chart  110  in such a way that the first corner marker  112 , the second corner marker  114 , the third corner marker  116 , and the fourth corner marker  118  are each moved to the top, bottom, left, and right in response to user manipulations. 
     Since the first corner marker  112 , the second corner marker  114 , the third corner marker  116 , and the fourth corner marker  118  each have two degrees of freedom, the first adjustment chart  110  has eight degrees of freedom in total. 
     That is, eight degrees of freedom out of the forgoing 12 degrees of freedom are defined using the first adjustment chart  110 . 
       FIG. 7  is a diagram of a second adjustment chart  120 . 
     The second adjustment chart  120  includes a median marker  122  expressing a line connecting the middle point of the projected image on the top side of the image area  101  to the middle point of the projected image on the bottom side of the image area  101 . 
     The projector  1  performs geometric transformation on the second adjustment chart  120  in such a way that the median marker  122  is moved to the left and right in response to user manipulations. 
     Since the median marker  122  has one degree of freedom, the second adjustment chart  120  has one degree of freedom. 
     That is, one degree of freedom out of the foregoing 12 degrees of freedom is defined using the second adjustment chart  120 . 
       FIG. 8  is a diagram of a third adjustment chart  130 . 
     The third adjustment chart  130  includes a top side marker  132  expressing the middle point of the projected image on the top side of the image area  101  and a bottom side marker  134  expressing the middle point of the projected image on the bottom side of the image area  101 . 
     The projector  1  performs geometric transformation on the third adjustment chart  130  in such a way that the top side marker  132  and the bottom side marker  134  are moved vertically in response to user manipulations. 
     Since the top side marker  132  and the bottom side marker  134  each have one degree of freedom, the third adjustment chart  130  has two degrees of freedom in total. 
     That is, two degrees of freedom out of the foregoing 12 degrees of freedom are defined using the third adjustment chart  130 . 
       FIG. 9  is a diagram of a fourth adjustment chart  140 . 
     The fourth adjustment chart  140  includes a one-fourth line marker  142  that is a line between the left side of the image area and the median indicated by the foregoing median marker  122 , and a three-fourths line marker  144  that is a line between the right side of the image area and the foregoing median. 
     The projector  1  performs geometric transformation on the fourth adjustment chart  140  in such a way that the one-fourth line marker  142  and the three-fourths line marker  144  are moved to the left and right in response to user manipulations. 
     Here, the one-fourth line marker  142  and the three-fourths line marker  144  are configured to move symmetrically (to change the width) with the foregoing median being the center axis. 
     That is, since the one-fourth line marker  142  and the three-fourths line marker  144  have one degree of freedom, the fourth adjustment chart  140  has one degree of freedom. 
     That is, one degree of freedom out of the foregoing 12 degrees of freedom is defined using the fourth adjustment chart  140 . 
     As described above, in the embodiment, the first adjustment chart  110 , the second adjustment chart  120 , the third adjustment chart  130 , and the fourth adjustment chart  140  define the 12 degrees of freedom. 
     As a result, the projector  1  can calculate a transform function for geometric transformation necessary to accurately match the image area  101  and the target area  210  using parameters input with the adjustment charts. 
     As described above, for example, the median marker  122  functions as a first reference line. 
     For example, the one-fourth line marker  142  and the three-fourths line marker  144  function as second reference lines. 
     Next, a projection state adjustment process in the projector  1  according to the embodiment will be described with reference to a flowchart depicted in  FIG. 10 . 
     The projection state adjustment process is started by a user&#39;s instruction when the projector  1  is oriented toward the circular cylinder  200 , for example. 
     In Step S 101 , the projection adjustment unit  40  performs a first adjustment chart process of adjusting the positions of four corners of the image area. 
     The first adjustment chart process will be described with reference to a flowchart depicted in  FIG. 11 . 
     In Step S 201 , the projection adjustment unit  40  projects the first adjustment chart  110 . 
     That is, the projection adjustment unit  40  generates the first adjustment chart  110 , and causes the projection processing unit  14  to project the first adjustment chart  110 . 
     In Step S 202 , the projection adjustment unit  40  highlights the first corner marker  112  at the upper left on the first adjustment chart  110 . 
     That is, the projection adjustment unit  40  generates the first adjustment chart  110  on which the first corner marker  112  is highlighted more than the other corner markers by changing the color or size of the first corner marker  112 , for example, and outputs the first adjustment chart  110  to the image conversion unit  13 . 
     The image conversion unit  13  applies image conversion to the first adjustment chart  110 , and outputs the converted first adjustment chart  110  to the projection processing unit  14 . 
     The projection processing unit  14  projects the first adjustment chart  110 , which has undergone the image conversion and has been input from the image conversion unit  13 . 
     In Step S 203 , the projection adjustment unit  40  performs an adjustment process on the first corner marker  112 . 
     The adjustment process will be described with reference to  FIG. 12 . 
     In Step S 301 , the projection adjustment unit  40  projects the adjustment chart. 
     In the adjustment process on the first corner marker  112 , the projection adjustment unit  40  projects the first adjustment chart  110  on which the first corner marker  112  is highlighted. 
     In the projection, the user performs adjustment manipulations using the arrow key, for example. 
     For example, in the adjustment process on the first corner marker  112 , the user inputs an instruction to move the first corner marker  112  to the top, bottom, left, and right using the arrow key in such a way that the position of the first corner marker  112  is matched with the top end  212 - 1  of the left side  212  of the target area  210 . 
     In Step S 302 , the projection adjustment unit  40  determines whether the user has performed adjustment manipulations. 
     When the projection adjustment unit  40  determines that adjustment manipulations have been made, the process goes to Step S 303 . 
     In Step S 303 , the projection adjustment unit  40  causes the image conversion unit  13  to apply image conversion. 
     In the image conversion, the projection adjustment unit  40  determines conversion parameters based on user adjustment manipulations, and calculates a transform function for geometric transformation on the projected image based on the conversion parameters. 
     The projection adjustment unit  40  outputs the calculated transform function to the image conversion unit  13 . 
     The image conversion unit  13  performs arithmetic operations on geometric transformation for the projected image based on the transform function acquired from the projection adjustment unit  40 . 
     After that, the process returns to Step S 301 . 
     For example, in the adjustment process on the first corner marker  112 , the projection adjustment unit  40  determines conversion parameters for moving the projection position of the first corner marker  112  in the direction corresponding to the pressed arrow key. 
     The projection adjustment unit  40  calculates a transform function to deform the first adjustment chart  110  based on the present transform function and the determined conversion parameters. 
     The user manipulates the arrow key in such a way that the position of the first corner marker  112  is matched with the top end  212 - 1  of the left side  212  of the target area  210  while seeing the first adjustment chart  110  projected onto the circular cylinder  200 . 
     The projection adjustment unit  40  outputs the calculated transform function to the image conversion unit  13 . 
     The image conversion unit  13  performs arithmetic operations on geometric transformation for the first adjustment chart  110  based on the transform function acquired from the projection adjustment unit  40 . 
     In Step S 301 , the first adjustment chart  110  subjected to geometric transformation is projected. 
     In Step S 302 , when the projection adjustment unit  40  determines that adjustment manipulations have not been made, the process goes to Step S 304 . 
     In Step S 304 , the projection adjustment unit  40  determines whether the user has input OK indicating the completion of the adjustment process. 
     When the projection adjustment unit  40  determines that the user has not input OK, the process returns to Step S 301 , and the present projection is maintained. 
     On the other hand, when the projection adjustment unit  40  determines that the user has input OK, the process goes to Step S 305 . 
     For example, in the adjustment process on the first corner marker  112 , when the position of the first corner marker  112  is matched with the top end  212 - 1  of the left side  212  of the target area  210 , the user presses the OK button. 
     As described above, the conversion parameters on geometric transformation for the adjustment chart are sequentially acquired in response to user adjustment manipulations until the user presses the OK button, and a transform function is calculated from the conversion parameters. 
     Moreover, geometric transformation is applied to the adjustment chart using the calculated transform function, and the adjustment chart subjected to the geometric transformation is projected. 
     In Step S 305 , the projection adjustment unit  40  stores the conversion parameters on the geometric transformation process in the previous Step S 303  in the parameter storage unit  43 , and records the transform function in the transform function storage unit  45 . 
     After the recording, the adjustment process is ended, and the process returns to the first adjustment chart process. 
     Referring again to  FIG. 11 , the description is continued on the first adjustment chart process. 
     After the adjustment process in Step S 203 , the process goes to Step S 204 . 
     In Step S 204 , the projection adjustment unit  40  ends highlighting the first corner marker  112 , and highlights the second corner marker  114  at the lower left. 
     That is, the projection adjustment unit  40  generates the first adjustment chart  110  on which the second corner marker  114  is highlighted, and outputs the first adjustment chart  110  to the projection processing unit  14  through the image conversion unit  13  for projecting the first adjustment chart  110 . 
     In Step S 205 , the projection adjustment unit  40  performs an adjustment process on the second corner marker  114 . 
     The adjustment process is similar to the case of the first corner marker  112 . 
     That is, the user manipulates the arrow key in such a way that the second corner marker  114  is matched with the lower end  212 - 2  of the left side  212  of the target area  210 . 
     The projection adjustment unit  40  calculates a transform function for geometric transformation to deform the first adjustment chart  110  in such a way that the projection position of the second corner marker  114  is moved to the top, bottom, left, and right in response to pressing of the arrow key. 
     The image conversion unit  13  performs geometric transformation on the first adjustment chart  110  based on the calculated transform function. 
     When the position of the second corner marker  114  is matched with the lower end  212 - 2  of the left side  212  of the target area  210 , the user presses the OK button. 
     The conversion parameters and the transform function at this time are recorded, and then the adjustment process is ended. 
     In Step S 206 , the projection adjustment unit  40  ends highlighting the second corner marker  114 , and highlights the third corner marker  116  at the lower right. 
     In Step S 207 , the projection adjustment unit  40  performs an adjustment process on the third corner marker  116 . 
     The adjustment process is similar to the case of the first corner marker  112 . 
     That is, the user manipulates the arrow key in such a way that the third corner marker  116  is matched with the lower end  214 - 2  of the right side  214  of the target area  210 . 
     The projection adjustment unit  40  calculates a transform function for geometric transformation to deform the first adjustment chart  110  in such a way that the projection position of the third corner marker  116  is moved to the top, bottom, left, and right in response to pressing of the arrow key. 
     The image conversion unit  13  performs geometric transformation on the first adjustment chart  110  based on the calculated transform function. 
     When the position of the third corner marker  116  is matched with the lower end  214 - 2  of the right side  214  of the target area  210 , the user presses the OK button. 
     The conversion parameters and the transform function at this time are recorded, and then the adjustment process is ended. 
     In Step S 208 , the projection adjustment unit  40  ends highlighting the third corner marker  116 , and highlights the fourth corner marker  118  at the upper right. 
     In Step S 209 , the projection adjustment unit  40  performs an adjustment process on the fourth corner marker  118 . 
     The adjustment process is similar to the case of the first corner marker  112 . 
     That is, the user manipulates the arrow key in such a way that the fourth corner marker  118  is matched with the top end  214 - 1  of the right side  214  of the target area  210 . 
     The projection adjustment unit  40  calculates a transform function for geometric transformation to deform the first adjustment chart  110  in such a way that the projection position of the fourth corner marker  118  is moved to the top, bottom, left, and right in response to pressing of the arrow key. 
     The image conversion unit  13  performs geometric transformation on the first adjustment chart  110  based on the calculated transform function. 
     When the position of the fourth corner marker  118  is matched with the top end  214 - 1  of the right side  214  of the target area  210 , the user presses the OK button. 
     The conversion parameters and the transform function at this time are recorded, and then the adjustment process is ended. 
     As described above, the first adjustment chart process is ended, and the process returns to the projection state adjustment process. 
     For example, suppose that the first adjustment chart  110  is first projected as depicted in  FIG. 13 . 
     Here, on the chart depicted in  FIG. 13 , for simplicity, the number of grids within the outer frame is half the number of grids on the chart depicted in  FIG. 6  vertically and horizontally. 
     Moreover, the markers are not displayed on the chart. 
     In  FIG. 13 , broken lines indicate the target area  210 . 
     These also apply in  FIGS. 14 ,  16 ,  18 , and  20  below. 
     According to the first adjustment chart process described above, the first adjustment chart  110  projected as depicted in  FIG. 13  is turned into the state in which the positions of four corners are matched with the positions of four corners of the target area  210  as depicted in  FIG. 14 . 
     Referring again to  FIG. 10 , the description is continued. 
     After the first adjustment chart process, in Step S 102 , the projection adjustment unit  40  performs a second adjustment chart process. 
     An exemplary second adjustment chart process will be described with reference to  FIG. 15 . 
     Although the second adjustment chart process is different in the adjustment chart and the markers for use, the second adjustment chart process is basically similar to the first adjustment chart process. 
     In Step S 401 , the projection adjustment unit  40  projects the second adjustment chart  120  including the median marker  122 . 
     In Step S 402 , the projection adjustment unit  40  performs an adjustment process on the median marker  122 . 
     The user manipulates the left and right keys of the arrow key in such a way that the median marker  122  is positioned in the middle between the left side  212  and the right side  214  of the target area  210 . 
     The projection adjustment unit  40  calculates a transform function for geometric transformation to deform the second adjustment chart  120  in such a way that the projection position of the median marker  122  is moved to the left and right in response to pressing of the left and right keys. 
     The image conversion unit  13  performs geometric transformation on the second adjustment chart  120  based on the calculated transform function. 
     When the position of the median marker  122  is positioned in the middle between the left side  212  and the right side  214 , the user presses the OK button. 
     The conversion parameters and the transform function at this time are recorded, and then the adjustment process is ended. 
     For example, according to the second adjustment chart process, the adjustment chart projected as depicted in  FIG. 14  is turned as depicted in  FIG. 16 . 
     That is, the center in the lateral direction of the second adjustment chart  120 , which is the projected image, is matched with the center of the target area  210  in the lateral direction. 
     Referring again to  FIG. 10 , the description is continued. 
     After the second adjustment chart process, in Step S 103 , the projection adjustment unit  40  performs a third adjustment chart process. 
     An exemplary third adjustment chart process will be described with reference to  FIG. 17 . 
     Although the third adjustment chart process is different in the adjustment chart and the markers for use, the third adjustment chart process is basically similar to the first adjustment chart process. 
     In Step S 501 , the projection adjustment unit  40  projects the third adjustment chart  130 . 
     In Step S 502 , the projection adjustment unit  40  highlights the top side marker  132  on the third adjustment chart  130 . 
     In Step S 503 , the projection adjustment unit  40  performs an adjustment process on the top side marker  132 . 
     The user manipulates the up and down keys of the arrow key in such a way that the top side marker  132  is at the same height as the middle point of the top side  216  of the target area  210 , that is, the top side marker  132  is matched with the middle point of the top side  216 . 
     The projection adjustment unit  40  calculates a transform function for geometric transformation to deform the third adjustment chart  130  in such a way that the projection position of the top side marker  132  is moved vertically in response to pressing of the up and down keys. 
     The image conversion unit  13  performs geometric transformation on the third adjustment chart  130  based on the calculated transform function. 
     When the position of the top side marker  132  is at the same height as the middle point of the top side  216  of the target area  210 , the user presses the OK button. 
     The conversion parameters and the transform function at this time are recorded, and then the adjustment process is ended. 
     In Step S 504 , the projection adjustment unit  40  highlights the bottom side marker  134  on the third adjustment chart  130 . 
     In Step S 505 , the projection adjustment unit  40  performs an adjustment process on the bottom side marker  134 . 
     The user manipulates the up and down keys of the arrow key in such a way that the bottom side marker  134  is at the same height as the bottom side  218  of the target area  210 , that is, the bottom side marker  134  is matched with the middle point of the bottom side  218 . 
     The projection adjustment unit  40  calculates a transform function for geometric transformation to deform the third adjustment chart  130  in such a way that the projection position of the bottom side marker  134  is moved vertically in response to pressing of the up and down keys. 
     The image conversion unit  13  performs geometric transformation on the third adjustment chart  130  based on the calculated transform function. 
     When the position of the bottom side marker  134  is at the same height as the middle point of the bottom side  218  of the target area  210 , the user presses the OK button. 
     The conversion parameters and the transform function at this time are recorded, and then the adjustment process is ended. 
     As described above, the third adjustment chart process is ended, and the process returns to the projection state adjustment process. 
     For example, according to the third adjustment chart process, the adjustment chart projected as in  FIG. 16  is turned as depicted in  FIG. 18 . 
     It is noted that the order of performing the second adjustment chart process and the third adjustment chart process can be changed. 
     Moreover, the user may finely adjust the adjustment chart while repeating the second adjustment chart process and the third adjustment chart process. 
     Adjustment using the second adjustment chart process and the third adjustment chart process is performed to match four corners of the target area  210  and four corners of the image area  101 , which are on the outer frame of the adjustment chart. 
     Additionally, the middle point (the top side marker  132 ) of the top side of the image area  101  is matched with the middle point of the top side  216  of the target area  210 , and the middle point (the bottom side marker  134 ) of the bottom side of the image area  101  is matched with the middle point of the bottom side  218  of the target area  210 . 
     It is noted that in some cases, the top side of the image area  101  is not completely matched with the top side  216  of the target area  210  and the bottom side of the image area  101  is not completely matched with the bottom side  218  of the target area  210  even though the second adjustment chart process and the third adjustment chart process are performed. 
     Referring again to  FIG. 10 , the description is continued. 
     After the third adjustment chart process, in Step S 104 , the projection adjustment unit  40  performs a fourth adjustment chart process. 
     An exemplary fourth adjustment chart process will be described with reference to  FIG. 19 . 
     Although the fourth adjustment chart process is different in the adjustment chart and the markers for use, the fourth adjustment chart process is basically similar to the first adjustment chart process. 
     In Step S 601 , the projection adjustment unit  40  projects the fourth adjustment chart  140  including the one-fourth line marker  142  and the three-fourths line marker  144 . 
     In Step S 602 , the projection adjustment unit  40  performs an adjustment process on the one-fourth line marker  142  and the three-fourths line marker  144 . 
     The user manipulates the left and right keys of the arrow key in such a way that the one-fourth line marker  142  is positioned in the middle between the left side  212  of the target area  210  and the median adjusted in the third adjustment chart process and the three-fourths line marker  144  is positioned in the middle between the right side  214  of the target area  210  and the median. 
     The projection adjustment unit  40  calculates a transform function for geometric transformation to deform the fourth adjustment chart  140  in such a way that the projection positions of the one-fourth line marker  142  and the three-fourths line marker  144  are moved to the left and right in response to pressing of the left and right keys. 
     The image conversion unit  13  performs geometric transformation on the fourth adjustment chart  140  based on the calculated transform function. 
     Here, the one-fourth line marker  142  and the three-fourths line marker  144  are moved together symmetrically with respect to the median. 
     When the positions of the one-fourth line marker  142  and the three-fourths line marker  144  are at desired positions, the user presses the OK button. 
     The conversion parameters and the transform function at this time are recorded, and then the adjustment process is ended. 
     For example, according to the foregoing fourth adjustment chart process, the adjustment chart projected as in  FIG. 18  is turned as depicted in  FIG. 20 . 
     That is, the image area  101 , which is the outer frame of the fourth adjustment chart  140  and the projected image, is completely matched with the outer frame of the target area  210 , and images to be projected at even intervals, for example, in the image area are projected at even intervals. 
     That is, the images are projected as if a sheet with a rectangular image depicted thereon is attached to the circular cylinder. 
     Referring again to  FIG. 10 , the description is continued. 
     After the fourth adjustment chart process, in Step S 105 , the projection adjustment unit  40  outputs a transform function finally calculated based on 12 conversion parameters obtained as a result of the first to fourth adjustment chart processes. 
     The transform function is used for geometric transformation at the image conversion unit  13  in image projection until the transform function is canceled. 
     The transform function is stored in the transform function storage unit  45  in association with the adjustment date and the setting name. 
     As described above, the projection state adjustment process is ended. 
     The transform function recorded in the transform function storage unit  45  is read by the transform function reading unit  46  any time and output to the image conversion unit  13  for use in image conversion at the image conversion unit  13 . 
     Therefore, for example, the positional relationship between the projector  1  frequently used and the circular cylinder  200  is adjusted once for the projection state. When the transform function is once found, the projection state adjustment process may not be performed for second time and later. 
     At this time, the transform function reading unit  46  reads the transform function stored in the transform function storage unit  45 , and the projector  1  can immediately project images correctly onto a desired area. 
     Next, geometric transformation performed in the adjustment process will be described with reference to  FIGS. 21A to 21D . 
     It can be considered that geometric transformation performed in the embodiment is divided into two image conversion processes. 
     As depicted in  FIG. 21A , let us consider geometric transformation in the case where the projector  1  projects an image onto the target area  210  on the circular cylinder  200 . 
     As indicated by a two-dot chain line in  FIG. 21A , suppose that a plane passing through the right side and the left side of the target area  210  is referred to as a cut plane  250 . 
     Moreover, suppose that a plane perpendicular to the projection direction of the projector  1  is referred to as a projection plane  170 . 
     Generally, as depicted in  FIG. 21A , the cut plane  250  and the projection plane  170  are not parallel to each other. 
     On the other hand, as depicted in  FIG. 21B , in the case where the cut plane  250  and the projection plane  170  are parallel to each other, geometric transformation from the projection plane  170  to the target area  210  is relatively easily performed. 
     Therefore, in the embodiment, in the case where the cut plane  250  and the projection plane  170  are not parallel to each other, let us consider an intermediate plane  180  parallel to the cut plane  250 , as depicted in  FIG. 21C . 
     Geometric transformation from the intermediate plane  180  to the target area  210  is a first transformation. 
     For example, suppose that four variables for the center (Ox, Oy, Oz) of the circular cylinder  200  and the projection angle θ expressing the width of the target area are variables expressing the circular cylinder  200 . The variables can be determined from the move parameter of the median marker  122  in the lateral direction, the move parameter of the top side marker  132  in the vertical direction, the move parameter of the bottom side marker  134  in the vertical direction, and a half value of the value of the projection angle θ expressing the width of the target area indicated by the one-fourth line marker  142  and the three-fourths line marker  144 . 
     Moreover, as depicted in  FIG. 21D , conversion from the projection plane  170  to the intermediate plane  180  is a second transformation. 
     This second transformation is rotation projection transformation from a plane to a plane generally known. 
     The transformation formula of the rotation projection transformation can be determined from the coordinates of four corners of the image area  101  determined using the first adjustment chart  110 . 
     In the embodiment, geometric transformation from the projection plane  170  to the target area  210  as depicted in  FIG. 22  is performed by two transformations, i.e., the first transformation and the second transformation described above. 
     Here, the parameters of the first transformation can be obtained by the second adjustment chart process using the second adjustment chart  120 , the third adjustment chart process using the third adjustment chart  130 , and the fourth adjustment chart process using the fourth adjustment chart  140 . 
     Furthermore, the parameters of the second transformation can be obtained by the first adjustment chart process using the first adjustment chart  110 . 
     As described above, for example, the cut plane  250  corresponds to a third plane, and the first transformation corresponds to circular cylinder geometric transformation between the target area and the plane parallel to the third plane. 
     According to the projection state adjustment process of the embodiment, 12 variables can be found by mathematically completely solving the 12 variables based on inputs made by adjustment manipulations using the first to fourth adjustment charts, so that the transformation formula of accurate geometric transformation necessary for projection can be determined. 
     Moreover, 12 parameters input to solve the 12 variables include the positions of four corners of the image area  101 , the positions of the top side and the bottom side in the vertical direction, the position of the median in the lateral direction, and the interval between the one-fourth line and the three-fourths line. 
     These parameters can be grasped by the user much more intuitively than the case where the user directly inputs the positional relationship between the projector  1  and the circular cylinder  200 , the projection angle θ expressing the target area, and so on, for example. 
     Therefore, according to the embodiment, the user can intuitively perform manipulations in adjusting the projection state. 
     Moreover, the fact that the adjustment chart is updated in real time in response to the user input also facilitates manipulates by intuition. 
     Furthermore, since it is only necessary to input a minimum necessary amount of parameters, i.e., the 12 parameters, the number of manipulations for adjustment is small for the user. 
     According to the embodiment, therefore, the user can intuitively, easily, and accurately adjust the projection state. 
     In addition, geometric transformation is determined in such a way that the transformation process is separated into the first transformation and the second transformation as in the embodiment, so that the amount of arithmetic operations is reduced. 
     This is effective for high-speed processing. In the embodiment, the combination of the first adjustment chart  110  corresponding to the first transformation and the second adjustment chart  120 , the third adjustment chart  130 , and the fourth adjustment chart  140  corresponding to the second transformation is used to easily separate geometric transformation into the first transformation and the second transformation. 
     It is noted that in the embodiment, for example, the first to fourth adjustment chart processes are performed sequentially. However, the first to fourth adjustment chart processes may be appropriately returned or skipped depending on the user&#39;s instruction. 
     Moreover, the order of procedures in each process, such as the first adjustment chart process, can be similarly changed. 
     In the embodiment, the description has been made in which the user inputs all of unknown 12 parameters. 
     However, the projection adjustment unit  40  can acquire values related to a part of parameters even though the user does not always input these parameters. 
     For example, the projection adjustment unit  40  can acquire the angle of view of the projection lens  20  from a sensor provided on the projection lens  20  or from a control unit controlling the projection lens  20 . 
     Furthermore, the projection adjustment unit  40  can acquire the posture of the projector  1 , for example, from the foregoing posture sensor  29 . 
     The projection adjustment unit  40  may acquire the diameter of the circular cylinder  200  input to the operation unit  28  by the user or acquire the positional relationship between the optical axis of the projector  1  and the circular cylinder  200 . 
     Even though some of the 12 parameters are not input, all the 12 degrees of freedom are calculated and an accurate transform function can be acquired, as long as the values of the parameters are acquired. 
     That is, user manipulations necessary for adjustment can be reduced. 
     As described above, for example, the portion where the angle of view of the projection lens  20  is acquired and the posture sensor  29  function as a condition acquiring unit to acquire the positional relationship between the projection unit and the target area, but the portion and the posture sensor  29  are not necessarily included in the configuration. 
     For example, arithmetic operations for bilaterally symmetrical parameters can be reduced in the conversion parameters acquired using the first to fourth adjustment charts, as long as it is apparent that the projector  1  is disposed directly opposite to the circular cylinder  200 . 
     In this case, for example, the corner markers on the first adjustment chart may be moved in bilateral symmetry, and adjustment to be made by the third adjustment chart becomes unnecessary. 
     Moreover, adjustment to be made by the fourth adjustment chart becomes unnecessary as long as the projection angle θ is apparent. 
     In the embodiment, an example has been described in which an image is projected onto the right circular cylinder. However, the case where an image is projected onto an oblique circular cylinder is also similar to the description above, as long as the left and right sides of the target area are parallel to the axis of the oblique circular cylinder. 
     Furthermore, in the embodiment, the conditions are given that the right and left sides of the target area  210  are parallel to the axis of the circular cylinder  200 . However, for example, as depicted in  FIG. 23 , the target area  210  may be rotated with respect to the axis of the circular cylinder. 
     In this case, there are 13 conversion parameters. 
     In this case, for example, a chart can be used, as a fifth adjustment chart, to adjust this rotation angle. 
     Although the number of conversion parameters is increased, a variety of projection is made possible. 
     In addition, in the embodiment, an example has been described in which an image is projected onto the protruding curved surface of a circular cylinder. 
     However, as depicted in  FIG. 24 , also the case where an image is projected onto a recessed curved surface  300  forming a part of a circumferential surface can be operated similarly to the foregoing embodiment, not limited to the protruding curved surface. 
     In the projection, it is not necessary to change the settings of the projector  1 . 
     That is, the user can adjust the projection state by completely the same manipulates without regard to whether the cylinder is circular or recessed. 
     Moreover, in the embodiment, an example has been shown in which an image is projected onto a curved surface. However, the projection adjustment unit  40  can also be used for adjusting the projection state in the case where an image is projected onto a plane (which corresponds to a circular cylinder surface with an infinite radius). 
     In this case, the first adjustment chart process alone may be performed in which the first adjustment chart  110  is used to match four corners of the image area and four corners of the target area, and it is not necessary to perform the second to fourth adjustment chart processes. 
     That is, the second transformation alone may be performed between the foregoing first transformation and second transformation. 
     In adjustment using the adjustment chart, a position guide mark may be displayed near the center of the adjustment chart in such a way that the user can clearly recognize which point the user is currently adjusting or the user can recognize the direction of a peripheral part of the adjustment chart even in the case where the peripheral part is out of the circular cylinder and not projected. 
     For example, as depicted in  FIG. 25 , when the first corner marker  112  on the first adjustment chart  110  is being adjusted, the first adjustment chart  110  may include the position guide mark  113  near the center of the first adjustment chart  110 . 
     Similarly, for example, as depicted in  FIG. 26 , when the top side marker  132  on the third adjustment chart  130  is being adjusted, the third adjustment chart  130  may include a position guide mark  133  near the center of the third adjustment chart  130 . 
     Moreover, intervals to update the values of the parameters by user manipulations may be linearly changed in response to the number of pressing the arrow key or the time to press the arrow key, for example, or may be changed in a different way. 
     For example, intervals can be changed for a shorter time or a longer time according to parameter values or user&#39;s instructions. 
     The present invention is not limited to the embodiments as they are, and can be embodied in the implementation stage by deforming the components within a range that does not depart from its spirit. 
     Moreover, various embodiments of the invention can be formed by an appropriate combination of a plurality of the components disclosed in the embodiments. 
     For example, even if some components are deleted from all the components illustrated in the embodiments, if the problem stated in the related art, the problem being attempted to be solved by the embodiments of the invention, can be solved and, if the effects of the embodiments of the invention can be obtained, the configuration where the components have been deleted can be extracted as an embodiment of the invention. 
     Furthermore, the components over the different embodiments may be combined as appropriate.