Patent Publication Number: US-6712700-B1

Title: Stereo model displaying method and apparatus in video game, game apparatus, and computer-readable recording medium stored with stereo model displaying program for video game

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method and an apparatus of displaying a stereo model in a video game, a game apparatus and a computer-readable recording medium stored with a program of displaying a stereo model for a video game, for drawing a stereo model constituted by a plurality of polygons in a virtual three-dimensional space. Here, a stereo model designates 3D object constituted by a plurality of polygons. 
     2. Related Art 
     In recent years, by progress of display-related art, particularly computer graphics (CG) art, there have been produced more than before, games of three-dimensional images expressed more photorealistically. However, on the other hand, a new look has been taken at a game by images which are expressed non-photorealistically, that is, in a hand-writing tone and demand therefor is enhancing. As an example of such a non-photorealistic image, there is an image which is referred to as cel animation tone since the image resembles an image of cel animation produced by cel pictures. 
     Conventionally, in order to express a non-photorealistic game image in the cel animation tone, it is necessary to produce a character or a background image by handwriting, particularly, when a direction of displaying the character is changed in a game, an image in correspondence with each display direction is prepared by handwriting. In this way, a character image in cel animation tone is produced by manual labor and accordingly, only character images from limited directions have been prepared. 
     SUMMARY OF THE INVENTION 
     It is an object of the invention to provide a method and an apparatus of displaying a stereo model in a video game capable of displaying a character in a cel animation tone in an arbitrary direction in real time, a game apparatus and a computer-readable record medium stored with a stereo model display program for a video game. 
     In order to achieve the above-described object, according to a first aspect of the invention, there is provided a method of displaying a stereo model in a video game which is a method of displaying a stereo model in a video game for drawing the stereo model constituted by a plurality of polygons in a virtual three-dimensional space, the method comprising: 
     a first step of determining a direction of displaying the stereo model in response to an operation input; 
     a second step of arranging the stereo model and a contour drawing model having a shape of including the stereo model and constituted by a plurality of polygons in conformity with the direction determined at the first step such that a positional relationship in which the contour drawing model includes the stereo model is constituted; and 
     a third step of drawing the stereo model by reducing a gray scale number of a brightness previously given to the stereo model and drawing only the polygon of the contour drawing model in which a surface of the polygon is directed in a direction reverse to the direction determined at the first step. In this case, “a direction of displaying the stereo model” is, for example, a direction from the stereo model to a view point. Further, “surface” mentioned above, is a face of the stereo model directed to an outer side. By executing such a method, the stereo model in a cel animation tone is drawn. 
     According to the invention, the direction of displaying the stereo model is determined in response to the operation input and the stereo model is drawn in the cel animation tone in accordance with the determined direction. Thereby, even in the direction of displaying the stereo model is changed by the operation input, the stereo model from the changed direction can be drawn in the cel animation tone in real time. 
     According to the method of displaying a stereo model in a video game, the third step may be constituted by a step of drawing the stereo model by reducing the gray scale number of the brightness previously given to the stereo model and drawing only the polygon of the contour drawing model in which the surface of the polygon is directed in the direction reverse to the direction determined at the first step by using a predetermined color. 
     According to the method of displaying a stereo model in a video game, the first step may be constituted by a step of moving the stereo model and determining the direction of displaying the stereo model in response to the operation input. 
     According to the method of displaying a stereo model in a video game, the first step may be constituted by a step of switching a view point and determining the direction of displaying the stereo model in response to the operation input. 
     According to the method of displaying a stereo model in a video game, the stereo model may be a character. 
     Further, according to a second aspect of the invention, there is provided a computer-readable record medium which is a computer-readable record medium stored with a stereo model display program for a video game for drawing a stereo model constituted by a plurality of polygons in a virtual three-dimensional space: 
     wherein the stereo model display program makes the computer execute: 
     a first step of determining a direction of displaying the stereo model in response to an operation input; 
     a second step of arranging the stereo model and a contour drawing model having a shape of including the stereo model and constituted by a plurality of polygons in conformity with the direction determined at the first step such that a positional relationship in which the contour drawing model includes the stereo model is constituted; and 
     a third step of drawing the stereo model by reducing a gray scale number of a brightness previously given to the stereo model and drawing only the polygon of the contour drawing model in which a surface of the polygon is directed in a direction reverse to the direction determined at the first step. 
     According to the program, the third step may be constituted by a step of drawing the stereo model by reducing the gray scale number of the brightness previously given to the stereo model and drawing only the polygon of the contour drawing model in which the surface of the polygon is directed in the direction reverse to the direction determined at the first step by using a predetermined color. 
     According to the program, the first step may be constituted by a step of moving the stereo model and determining the direction of displaying the stereo model in response to the operation input. 
     According to the program, the first step may be constituted by a step of switching a view point and determining the direction of displaying the stereo model in response to the operation input. 
     According to the program, the stereo model may be a character. 
     Further, the program according to the second aspect of the invention is stored in a record medium of, for example, CD-ROM, floppy disk, memory cartridge, memory, hard disk or the like or a storing apparatus. By making a computer read the program stored in a record medium or a storing apparatus in this way, an apparatus of displaying a stereo model and a game apparatus, mentioned below, can be realized. Further, the program can be easily distributed and sold independent from an apparatus as a software product by a record medium. Further, by executing the program by using a hardware such as a computer, the graphics technology of the invention can easily be executed by the hardware. 
     Further, according to a third aspect of the invention, there is provided an apparatus of displaying a stereo model in a video game which is an apparatus of displaying a stereo model in a video game for drawing a stereo model constituted by a plurality of polygons in a virtual three-dimensional space, wherein the apparatus executes: 
     determining a direction of displaying the stereo model in response to an operation input; 
     arranging the stereo model and a contour drawing model having a shape of including the stereo model and constituted by a plurality of polygons in conformity with the determined direction such that a positional relationship in which the contour drawing model includes the stereo model is constituted; and 
     drawing the stereo model by reducing a gray scale number of a brightness previously given to the stereo model and drawing only the polygon of the contour drawing mode in which a surface of the polygon is directed in a direction reverse to the determined direction. 
     By making a computer execute the respective steps by the method of displaying a stereo model according to a first mode of the invention, an effect similar to that in the method of displaying a stereo model, mentioned above, can be achieved. 
     Therefore, by executing the described processing steps by using a hardware of a computer or the like, the stereo model display technology of the invention can easily be executed by the hardware. 
     Further, according to a fourth aspect of the invention, there is provided a game apparatus which is a game apparatus for drawing a stereo model constituted by a plurality of polygons in a virtual three-dimensional space, the apparatus comprising: 
     a computer; 
     a computer-readable record medium stored with a program which the computer is made to execute; 
     wherein the program makes the computer execute: 
     a determining processing of determining a direction of displaying the stereo model in response to an operation input; 
     an arranging processing of arranging the stereo model and a contour drawing model having a shape of including the stereo model and constituted by a plurality of polygons in conformity with the direction determined by the determining processing such that a positional relationship in which the contour drawing model includes the stereo model is constituted; and 
     a drawing processing of drawing the stereo model by reducing a gray scale number of a brightness previously given to the stereo model and drawing only the polygon of the contour drawing model in which a surface of the polygon is directed to a direction reverse to the direction determined by the determining processing. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a functional block diagram of a cel animation tone coloring processing; 
     FIG. 2 is a diagram showing an example of a brightness range table; 
     FIG. 3 is a diagram showing an example of a brightness range table; 
     FIG. 4 is a flowchart showing a total processing according to the invention; 
     FIG. 5 is a flowchart showing a game image drawing processing in a cel animation tone coloring processing; 
     FIG. 6 is a schematic diagram showing a data structure of character data in a cell animation tone coloring processing; 
     FIG. 7 is a view showing an example of a display screen of a game; 
     FIG. 8 is a view showing an example of a display screen of a game, showing an example of a display screen displayed after FIG. 7 by an operation input; 
     FIG. 9 is a flowchart showing a cel animation tone coloring processing and a stereo model drawing processing according to Embodiments 1 and 2; 
     FIGS. 10A,  10 B and  10 C are schematic diagrams showing a data structure of a polygon model in which FIG. 10A shows a data structure of a total of a stereo model, FIG. 10B shows a data structure of a triangular polygon before perspective view conversion and FIG. 10C shows a data structure of apex data table; 
     FIG. 11 shows a data structure of a triangular polygon after perspective view conversion in correspondence with FIG. 10B; 
     FIGS. 12A,  12 B,  12 C,  12 D,  12 E and  12 F show an example of an image for explaining respective stages of processing when a triangular polygon is drawn by an algorism of a cel animation tone coloring processing in which FIGS. 12A and 12B show areas drawn when the threshold of 0.75 is set, FIGS. 12C and 12D show ranges drawn when a threshold of 0.5 is set in the case in which a Z buffer is not used in a cel animation coloring processing and FIGS. 12E and 12F show ranges drawn when a threshold of 0.5 is set in the case in which the Z buffer is used in the cel animation tone coloring processing; 
     FIG. 13 shows an example of an image when a triangular polygon is drawn by an algorism of a cel animation tone coloring processing; 
     FIG. 14 shows an example of an image when a triangular polygon is drawn by conventional technology; 
     FIG. 15 is a flowchart showing a cel animation tone coloring processing and a stereo model drawing processing (part 2) according to Embodiments 1 and 2; 
     FIG. 16 is a schematic diagram of a data structure of a triangular polygon used in a cel animation tone coloring processing and Embodiments 1 and 2 in correspondence with FIG. 10B; 
     FIG. 17 is a functional block diagram of a first contour drawing processing; 
     FIG. 18 is a schematic view for explaining a positional relationship among a camera, a stereo model and a contour drawing model in the first contour drawing processing in which directions in which surfaces of the stereo model and the contour drawing model are directed are shown by arrow marks; 
     FIG. 19 is a schematic view showing an example of data stored in CD-ROM  131 ; 
     FIG. 20 is a flowchart showing the first and a second contour drawing processing and a game image drawing processing of Embodiments 1 and 2; 
     FIG. 21 is a schematic diagram showing a data structure of character data in the first and the second contour drawing processings and Embodiments 1 and 2; 
     FIG. 22 is a flowchart showing a contour drawing model drawing processing in the first contour drawing processing and Embodiment 1; 
     FIG. 23 shows an example of a texture for carrying out blurred expression; 
     FIG. 24 is a flowchart of a contour drawing model drawing processing of the first contour drawing processing and Embodiment 1; 
     FIG. 25 is a schematic view for explaining head and tail determination of a triangular polygon; 
     FIG. 26 is a schematic view for explaining a method of determining head and tail; 
     FIG. 27 is a schematic view for explaining head and tail determination of a triangular polygon in the first contour drawing processing; 
     FIG. 28 is a flowchart of a stereo model drawing processing in the first and the second contour drawing processings; 
     FIG. 29 is a functional block diagram of the second contour drawing processing; 
     FIG. 30 is a schematic view for explaining a positional relationship among a camera, a stereo model and a contour drawing model in the second contour drawing processing in which directions in which surfaces of the stereo model and the contour drawing model are directed are shown by arrow marks; 
     FIG. 31 is a flowchart of a contour drawing model acquiring processing in the second contour drawing processing and Embodiment 2; 
     FIG. 32 is a flowchart of a contour drawing model drawing processing in the second contour drawing processing and Embodiment 2; 
     FIG. 33 is a schematic view for explaining head and tail determination of a triangular polygon in the second contour drawing processing; 
     FIG. 34 is a block diagram showing an example of a game machine for household use executing a program according to the invention; 
     FIG. 35 is a block diagram showing an example of a graphics processing unit in FIG. 34; 
     FIG. 36 is a functional block diagram of Embodiment 1; 
     FIG. 37 shows a display example of only a self character shown in FIG. 7 in a state directed to the right direction of a display screen  120 ; 
     FIG. 38 shows a display example in which the self character is in the midst of changing a direction by moving the rightfoot rearwardly to direct in the left direction of the display screen  120 ; 
     FIG. 39 shows a display example in a state in which the self character is directed to the left direction of the display screen by moving the leftfoot from a state shown by FIG. 38; 
     FIG. 40 shows a display example of a state in which a camera is moved upwardly in response to operation of an operation button by a player from the state of FIG. 37; 
     FIG. 41 shows a display example of a state in which the player further operates the operation button to thereby move the camera further upwardly from the state of FIG. 40; 
     FIG. 42 is a functional block diagram of Embodiment 2; 
     FIG. 43 shows a display example of an image rendered by using conventional technology; 
     FIG. 44 shows a display example of an image rendered by using a cel animation tone coloring processing; 
     FIG. 45 is a table showing an example of a brightness range table used in rendering in FIG.  44  and FIG. 47; 
     FIG. 46 shows a display example of an image rendered by using the first and the second contour drawing processings; and 
     FIG. 47 shows a display example of an image rendered by using Embodiments 1 and 2. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT(S) 
     An explanation will be given of an embodiment of the invention in reference to the attached drawings as follows. 
     First, an explanation will be given of an outline of an embodiment of the invention. A game apparatus according to the embodiment of the invention includes means for determining a direction of displaying a stereo model, arranging means for arranging the stereo model and a contour drawing model and drawing means for drawing the two models. 
     The means for determining a direction of displaying a stereo model, determines a direction of displaying a stereo model by moving the stereo model constituting, for example, a character of a game in accordance with, for example, operation of a player. The arranging means arranges the stereo model and the contour drawing model in a shape capable of including the stereo model in accordance with the direction determined by an operation input, for example, in the same direction and at the same position. Thereby, there is constituted a positional relationship in which the contour drawing model includes the stereo model. 
     The drawing means carries out coloring in a cel animation tone to the stereo model by drawing a picture by reducing a gray scale number of brightness. Meanwhile, with regard to the contour drawing model, among polygons constituting the contour drawing model, only a polygon an outer side of which is directed in a reverse direction relative to a view point, is drawn by, for example, black. When a hidden face erasing processing is carried out in the drawing processing, only a portion of the contour drawing model which is extruded from the stereo model in view from the view point, is drawn and accordingly, as a result, a contour drawing processing is carried out. 
     Thereby, the stereo model drawn in a self animation tone can be displayed in real time. Prior to the explanation of the embodiment according to the invention, in the following, firstly, a detailed explanation will be given of a cel animation tone coloring processing and two kinds of contour drawing processings necessary for the invention. 
     (1) Cel Animation Tone Coloring Processing 
     According to a cel animation tone coloring processing, coloring in a cel animation tone is carried out to a stereo model expressing a character or the like of a game. That is, the stereo model is colored by a gray scale number lower than a gray scale number of brightness provided when a photorealistic game image is formed. 
     An explanation will be given of an outline of the cel animation tone coloring processing in reference to a functional block diagram of FIG. 1. A game machine according to the cel animation tone coloring processing includes an operation input unit  300 , a game progressing unit  310  including a character action determining unit  313 , a game situation setting unit  315  including a character direction setting unit  317  and a view axis direction setting unit  318 , a stereo model drawing unit  320  and an image display control unit  340 . Further, the stereo model drawing unit  320  includes an apex conversion and light source calculating unit  322 , a brightness calculating unit  324 , a drawing color supplying unit  326 , a brightness range table  328 , a brightness range setting unit  332  and a pixel processing unit  334 . The pixel processing unit  334  includes a brightness comparing unit  336 . 
     The operation input unit  300  outputs operation information of a button, a lever or the like of the operation input unit  300  operated by a player of a game to the game progressing unit  310 . 
     The game progressing unit  310  determines, based on information from the operation input unit  300 , content of progressing the game such as action of a character, a change in a view point position, a change in a direction of a view axis, or movement of a position of a light source, a change in a direction of light ray and gives instruction to the game progress situation setting unit  315 . The character action determining unit  313  in the game processing unit  310  is provided with a function of particularly determining the action of the character based on the information from the operation input unit  300 . 
     The game progress situation setting unit  315  calculates and sets a position, a direction and a shape of the character, the position of the view point or the direction of the view axis, the position of the light source, the direction of the light ray, and an increase or a decrease in a physical strength in accordance with the action of the character, in accordance with the content of progressing the game instructed by the game processing unit  310 . The character direction setting unit  317  in the game progress situation setting unit  315  is provided with a function of particularly determining a direction of the character relative to the view point in accordance with the content of progressing the game instructed by the game progressing unit  310 . Meanwhile, the view axis direction setting unit  318  in the game progress situation setting unit  315  is provided with a function of particularly setting the direction of the view axis in accordance with the content of progressing the game instructed by the game progressing unit  310 . 
     Further, the physical strength of the character is a capacity value provided to the character and when the character is attacked in a battle against an enemy character, the value is reduced by a value calculated based on attack force of the enemy character and defence force of the character. Further, when the character rests at a predetermined rest site in the world of the game, the physical strength of the character increases to a value of maximum physical strength of the character. 
     An arranging matrix setting unit  319  carries out processing of determining an arranging matrix of a stereo model for expressing a character in accordance with position coordinates and a direction of the character and a position of a view point which are set by the game progress situation setting unit  315 . The arranging matrix is a matrix for carrying out parallel movement, rotation and perspective view conversion of a stereo model. 
     The stereo model drawing unit  320  executes a processing of providing a stereo model with coloring in a cel animation tone by a function included therein. 
     The apex conversion and light source calculating unit  322  of the stereo model drawing unit  320  executes apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) with regard to respective apexes of triangular polygons constituting a stereo model arranged in a virtual three-dimensional space and carries out light source calculation with regard to the respective apexes of the triangular polygons subjected to apex conversion. Here, there is used the arranging matrix of a stereo model set by the arranging matrix setting unit  319 . 
     Further, the apex conversion and the light source calculating unit  322  of the stereo model drawing unit  320  also carries out head and tail determination of the respective triangular polygons of the stereo model. Only a surface directing head to a view point constitutes an object of drawing. A detailed description will be given of the head and tail determination in (2) contour drawing processing. 
     The brightness calculating unit  324  of the stereo model drawing unit  320  calculates a brightness from color at respective apexes of the triangular polygons calculated by the apex conversion and light source calculating unit  322 . Normally, the apex conversion and the light source calculating unit  322  calculates color in an RGB system and accordingly, the brightness calculating unit  324  calculates a brightness Y by subjecting RGB to YIQ conversion. The brightness at the respective apex of the triangular polygon is outputted to the pixel processing unit  394 . 
     The brightness range table  328  is, for example, a table as shown in FIG.  2 . That is, this is a table paired with a threshold and a reference brightness which are set here to three stages (levels) such that threshold value 0.75 versus reference brightness 0.75, threshold value 0.5 versus reference brightness 0.50 and threshold 0.00 versus reference brightness 0.25. Further, here, the brightness is provided with a real number value from 0 to 1. In place of the threshold value, a range may be designated by an upper limit and a lower limit (for example, refer to FIG.  3 ). 
     By referring to the brightness range table  328 , the drawing color supplying unit  326  calculates color for drawing in correspondence with the respective threshold. The drawing color in correspondence with the respective threshold is calculated by the reference brightness in correspondence with the threshold and information of color previous set to the respective triangular polygon. The calculated drawing color is outputted to the pixel processing unit  334  by the drawing color supplying unit  326 . 
     Further, the drawing color supplying unit  326  may calculate the drawing color in execution or may previously calculate the drawing color and store the data. For example, when the brightness range table as shown by, for example, FIG. 2, it is necessary to previously store three drawing color data for respective polygon. 
     The brightness range setting unit  332  selects one threshold of the brightness range table  328  and sets the threshold to the pixel processing unit  334 . When the brightness range table  328  as shown by FIG. 2 is used as it is, the brightness range setting unit  332  sets the threshold value one by one in turn from upper columns. When the range by the upper limit and the lower limit is designated in place of the threshold value, the threshold can be selected and set at random. 
     The pixel processing unit  334  interpolates brightnesses at respective apexes of a triangular polygon outputted from the brightness calculating unit  324  and calculates brightnesses at respective pixels at inside of the polygon (brightness distribution in polygon). The system of interpolation may be of algorism of Coulaw shading or an algorism of Fon shading. 
     Further, the brightness comparing unit  336  compares the brightness at the respective pixel with the threshold value set by the brightness range setting unit  332  and when the brightness at the pixel is equal to or larger than the threshold, the drawing color based on the reference brightness in correspondence with the threshold is drawn as color of the pixel. When the brightness at the pixel is less that the threshold, color of the pixel is not drawn at this stage. When the brightness range setting unit  332  sets all of thresholds in the brightness range table  328  and processes all of pixels in a polygon, inside of the polygon is painted to classify in three stages. 
     Further, when the brightness range table  430  as shown by FIG. 2 is used as it is, hidden face erasure by the Z buffer method is further utilized. Because, for example, according to FIG. 2, brightness equal to or larger than 0.75 is also equal to or larger than 0.5 or equal to or larger than 0.0 and therefore, the upper limit of the brightness range is set such that the drawing color is prevented from being painted overlappingly. When brightness of a certain pixel is equal to or larger than 0.75, the drawing color in correspondence with the threshold 0.75 is drawn as color of the pixel and the Z value of the pixel is stored to the Z buffer. 
     When the threshold becomes 0.5, the Z value of the pixel is read from the Z buffer and compared with the Z value of the pixel intended to write, however, the two values are naturally the same and accordingly, the drawing color in correspondence with the threshold 0.5 is not drawn with regard to the pixel. The same goes with the threshold 0.0. 
     Further, brightness at the apex of a polygon or at a pixel at inside of the polygon is dealt with as an attribute value of color (RGB) referred to as a normally used as transparency. Normally, the a value is defined by a range of 0-255 and the a value multiplied by 255 is actually used. Therefore, the threshold values (upper limit and lower limit value) of the brightness range table  430  may be values in the range of 0-255. 
     Finally, the image display control unit  340  designates a drawing area for displaying an image on a display screen drawn by the pixel processing unit  334 . The drawing area is normally divided in two, one is used for display and other is used for writing. Further, when writing to a writing area is finished, the writing area is used to switch as a displaying area, further, the displaying area is used to switch as the writing area. The image display control unit  340  controls the switching operation. 
     Next, an explanation will be given of a processing flow with regard to a cel animation tone coloring processing. 
     (Total Processing Flow) 
     FIG. 4 shows a processing flow of a total of a cel animation tone coloring processing. When a game is started, initial setting is carried out (Step S 2 ). In the processing of the initial setting, there is included a processing of acquiring data of a stereo model for expressing a character to be drawn. Next, operation of button, lever or the like of the operation input unit  300  is carried out by a player of the game (step S 3 ). Further, based on information of the operation input at step S 3 , for example, there is carried out a game progress processing for determining content of progressing the game such that the character moves to the left or the character attacks, a change in a view point position, a change in a direction of a view axis, a movement of a light source position, a change in a direction of light ray or the like (step S 4 ). 
     Thereafter, in accordance with content of progressing the game determined at step S 4 , there is carried out a game progress situation setting processing for setting a position, a direction and a shape of the character, the position of the view point, the direction of the view axis, the position of the light source or the direction of the light ray, further, an increase or a decrease of physical strength in accordance with the action of the character (step S 5 ). Next, there is carried out a game image drawing processing for drawing a game image in accordance with a game progress situation (step S 6 ). A detailed description will be given later of the game image drawing processing. 
     Further, there is carried out a game image displaying processing for displaying the game image drawn by the game image drawing processing at step S 6  (step S 7 ). Normally, the drawing area is divided in two areas of a writing area and a displaying area and in this case, by the game image drawing processing executed at step S 6 , there is carried out a processing of switching the writing area written with data to the displaying area and switching the displaying area to a successive writing area. 
     Next, it is determined whether the game is over (step S 8 ). In the game progress situation setting processing executed in accordance with the operation input at step S 3  (step S 5 ), when the physical strength of a self character operated by the player of the game is reduced and set to 0, the condition of game over is satisfied. At step S 8 , the physical strength of the self character operated by player of the game is inspected and it is determined whether the game is over. Further, when the physical strength of the self character is not 0, the operation returns to step S 3  and awaits for successive operation input. Meanwhile, in the case of game over, the game is finished. Further, even in the case of finishing the game, a result thereof is displayed on a display screen at step S 7 , the player can grasp a final situation of the game from the display screen. 
     FIG. 5 shows a processing flow expressing an outline of the game image drawing processing at step S 6  (FIG.  4 ). First, there is carried out a background model drawing processing for drawing a background model for expressing a background portion in a game image (step S 11 ). The drawing processing is the same as a conventional drawing processing and therefore, a detailed description thereof will not be given here. Further, following steps S 13  through S 15  are repeated until drawing all of characters (steps S 12 ). 
     A first one of the repeated steps is a step of executing a deforming processing for deforming one unprocessed character (step S 13 ). In accordance with the operation input executed at the step S 3  of FIG. 4, motion of the unprocessed character is determined by the game progress processing at step S 4 . Further, there is executed a processing of deforming a stereo model for expressing the unprocessed character, which is set by the game progress situation setting processing at step S 6  which is executed further in accordance therewith. 
     A second one of the repeated steps is a step of setting an arranging matrix of the unprocessed character (step S 14 ). The arranging matrix is a matrix for parallel movement, rotation and perspective view conversion of a stereo model for expressing the unprocessed character and is formed based on position coordinates and a direction of the character set by the game progress situation setting processing at step S 5  and a position of a viewpoint. Further, a third one of the repeated steps is a step of executing a stereo model drawing processing for drawing a stereo model for expressing the unprocessed character (step S 15 ). A detailed description will be given later of the stereo model drawing processing. 
     After all of characters have been drawn, there is executed a window drawing processing for drawing a window for displaying capacitances or the like of the characters to a user (step S 16 ). The window drawing processing is the same as the conventional drawing process and therefore, a detailed description thereof will not be given here. 
     Next, although an explanation will be given of a simple example with regard to progress of a game story in accordance with the operation input of the player of the game (FIG.  7  and FIG.  8 ), prior thereto, an explanation will be given of data of characters used in the cel animation tone coloring processing. The character data includes a numerical value of maximum physical strength  10  (for example, 300), a numerical value of current physical strength  12  (for example, 300) a numerical value of attack force  14  (for example, 123), a numerical value of defence force  16  (for example, 51), coordinates (x, y, z) of a reference position  18  (for example, (15.0, 0.0, 3.2)), rotational angles around X, Y, Z axes constituting a direction  20  of character (for example, (0, −90, 0)), pointer  22  for motion data and pointer  24  for model data of the stereo model. 
     FIG. 7 shows an example of a display screen  120  for displaying an image of a game for progressing a story for making a self character fight against an enemy character in a virtual three-dimensional space by operating a self character C 101  by the player of the game. In this case, there is displayed an image from a right front direction of the self character C 101 . That is, a direction of displaying the self character is the right front direction and as the direction  20  of the character, rotational angles around X, Y, Z axes in correspondence therewith are stored. On the left side of the display screen, there emerge an enemy character  1  (C 111 ) and an enemy character  2  (C 113 ). 
     Here, a position of a view point is determined by the game progress situation setting processing (step S 5 ) in accordance with a positional relationship between the self character and the enemy character and the direction of the self character. Further, with regard to the respective characters there are formed an image colored in a cel animation tone from the position of the view point and is displayed on the display screen. 
     A window W 105  is displayed with status of the self character C 101  and a window W 115  is displayed with statuses of the enemy characters C 111  and C 113 . In FIG. 6, there are displayed physical strength (numeral value of physical strength  12  of FIG. 6) and maximum physical strength (numerical value of maximum physical strength  10  of FIG.  6 ). 
     The self character attacks the enemy character in accordance with the operation input of the player from the operation input unit  300 . Meanwhile, the enemy character attacks the self character in accordance with a predetermined algorism. When the respective character is attacked in a battle, the physical strength of the attacked character is reduced by a value calculated based on attack force of attacking character (numerical value of attack force  14  of FIG. 6) and defence force (numerical value of defence force  16  of FIG. 6) of attacked character. 
     When the physical strength of the enemy character becomes equal to or smaller than 0, the enemy character is erased from the game screen and the story of the game is progressed. Meanwhile, when the physical strength of the self character becomes equal to or smaller than 0, it is determined at step S 8  (FIG. 4) that the game is over and the game is finished. Further, when the respective character rests at a predetermined rest site installed in the game, the physical strength of the respective character reduced by the battle can be recovered to a value of the maximum physical strength of the respective character (maximum physical strength  10  of FIG.  6 ). 
     FIG. 8 shows the display screen  120  when the player of the game operates the operation input unit  300  to thereby move the self character C 101  in the left direction of the display screen from a state of the display screen shown in FIG.  7 . 
     In response to the operation input, action of the character of “moving in the left direction of the display screen” is determined by the game progress processing (step S 4  of FIG.  4 ). In accordance with the action of the character, a direction, a position and a shape of the character is determined by the game progress situation setting processing (step S 5  of FIG.  4 ). According to the example of FIG. 8, the direction of the character is determined in the left direction relative to the display screen and the position of the character is moved similarly in the left direction relative to the display screen. Further, the shape of the character is set with a shape for expressing running motion. 
     Further, when a reference position of the character (coordinates of reference position  18  of FIG. 6) is set to, for example, the foot of the character and the direction of the character is changed, respective rotational angles passing through the reference position of the character and around axes in parallel with respective axes of X, Y and Z (direction  20  of FIG. 6) are changed. The movement is carried out by changing the coordinates of the reference position of the character (coordinates of reference position  18  of FIG. 6) in a virtual three-dimensional space. Further, deformation to a running shape is carried out by setting data of running motion to motion of the character (motion data of FIG.  6 ). Actually, the pointer  22  of motion data of FIG. 6 is set with a pointer to data of running motion. 
     In this way, even when the game progress situation of direction or position of the character is changed, the character is drawn as the image in a cel animation tone. 
     (Stereo Model Drawing Processing) 
     FIG. 9 shows a flow of a processing of drawing a stereo model in a cel animation tone coloring processing. First, initial setting is carried out (step S 603 ). In the initial setting, there is acquired a brightness range table in correspondence with the stereo model (for example, FIG. 2 or FIG.  3 ). Next, there are carried out apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) and light source calculation with respect to one apex (step S 605 ). 
     The apex conversion is carried out by using the arranging matrix set at step S 14  of FIG.  5 . Here, the perspective view conversion converts coordinate values of the respective apex of a polygon in the world coordinate system into the screen coordinate system. Further, the light source calculation calculates shadow (brightness) produced by virtual light ray emitted from a light source. 
     Further, there are two methods in the light source calculation of the stereo model processing in the cel animation tone coloring processing, that is, (A) a method in consideration of material defined in a polygon and (B) a method not in consideration of color for material. In the case of (A), calculation is carried out by the following equation. 
     
       
         as mentioned on Appendix-1  Equation (1) 
       
     
     where “n” of Pn 0 , Pn 1 , Pn 2 , Nnx, Nny, Nnz, Pnr, Png, Pnb, Cnr, Cng, Cnb designate an n-th apex. Notation Nnx designates x component of a normal line at the n-th apex, notation Nny designates y component of the normal line at the n-th apex and notation Nnz designates z component of the normal line at the n-th apex. Notation LightMatrix designates a matrix produced by normalized light source vectors. In the following, there is shown a case of capable of defining up to three parallel light sources thereby. Further, notation LColorMatrix includes, as its components, colors of light ray emitted from light sources and in the following, there is shown a case capable of defining up to three light sources. Notation M signifies color of material of polygon and notations rgb designates its components. An output in the case of (A) is defined by notations Cnr, Cng, Cnb. 
     
       
         as mentioned on Appendix-1  Equation (2), (3) 
       
     
     where notations L 0x , L 0y  and L 0z  designate components of normalized light source vector 0, notations L 1x , L 1y  and L 1z  designate components of normalized light source vector 1, notations L 2x , L 2y  and L 2z  designate components of normalized light source vector 2. Further, components of color of light ray of the light source vector 0 are designated by notations LC 0r , LC 0g  and LC 0b , components of color of light ray of the light source vector 1 are designated by notations LC 1r , LC 1g  and LC 1b  and components of color of light ray of the light ray vector 2 are designated by notations LC 2r , LC 2g  and LC 2b . Further, the respective component of color is provided with a value between 0.0 through 1.0. For example, when only the light source 0 is present and white color is used by an angle of 45 degree relative of X, Y and X axes, the following matrices are constituted. 
     
       
         as mentioned on Appendix-1  Equation (4), (5) 
       
     
     Further, in the case of (B), calculation is carried out by the following equation. 
      as mentioned on Appendix-1  Equation (6) 
     Results of the two calculation equations are naturally different from each other and the calculation result of (A) is correct. However, an amount of calculation of (B) is smaller than that in (A) and accordingly, the processing can be accelerated. Further, quality of image is not normally changed. 
     Next, it is determined whether a polygon (face) including the apex is a head face (step S 607 ). The determination is carried out in the case of a triangular polygon by in which direction a triangular polygon constituted by the apex and two apexes processed therebefore is directed. An explanation will be given of a further detailed head and tail determining method in (2) contour drawing processing. Further, with regard to initial two apexes, processings other than those in steps S 605  and S 609  are not carried out. Further, although in the stereo model drawing processing, the head and tail determination is carried out at this stage, it is also possible to carry out the head and tail determination prior to the stage. 
     When the polygon (face) including the apex is a tail face, the operation returns to step S 605 . When the polygon (face) including the apex is the head face, there is calculated a brightness at the apex where the apex conversion and light source calculation are carried out (step S 609 ). In the calculation of the brightness, the YIQ conversion is carried out. When the color at the apex is calculated by the method of (A), mentioned above, calculation is carried out by the following equation. 
     
       
         as mentioned on Appendix-1  Equation (7) 
       
     
     When color of apex is calculated by the method of (B), mentioned above, calculation is carried out by the following equation. 
     
       
         as mentioned on Appendix- 1   Equation (8) 
       
     
     Further, a matrix inputted with numerical values shows a first row of 3′3 matrix for conversion from RGB to YIQ. By way of precaution, the 3′3 matrix (conversion matrix) is shown below. 
     
       
         as mentioned on Appendix-1  Equation (9) 
       
     
     FIGS. 10A,  10 B and  10 C show a data structure of a stereo model before subjected to perspective view conversion. Front address of model data of the stereo model is stored in the pointer  24  to the model data of the stereo model shown in FIG.  6 . FIG. 10A shows a data structure of the stereo model and there are a total of N pieces of triangular polygons. As shown by FIG. 10B, the respective triangular polygon is provided with color for material (YIQ) and three of apex data indexes (IDX). Although in this case, the color of the material is provided by the YIQ system, the color may be provided by the RGB system. By using the apex data IDX, information with regard to the apex can be provided from the apex data table shown by FIG.  10 C. 
     The apex data table is stored with three-dimensional coordinates (P nx , P ny , P nz ,) and normal line vectors (Nnx, Nny, Nnz) (“n” designates apex number). When the perspective view conversion is carried out, the data structure of the triangular polygon is changed. The data structure in correspondence with FIG. 10B is shown by FIG.  11 . At respective apex, there are stored coordinate values (x, y, z) in the screen coordinate system, color (r, g, b) at the apex and a value. An area stored with the α value is stored with the brightness calculated at step S 609 . Further, although a detailed explanation will be given below, when a triangular shape drawing processing unit  205  carries out a processing, three apex common colors (r, g, b) are stored with drawing colors in correspondence with the brightness range. Further, although the brightness falls in a range of 0.0 through 1.0, the α value is an integer from 0 through 255 and accordingly, the α value multiplied by the brightness by 255 is used. 
     Referring back to FIG. 9, an explanation will be given of the processing flow. After step S 609 , there is calculated drawing color of polygon including apex subjected to apex conversion and light source calculation (step S 611 ). The drawing color of the polygon is calculated from the reference brightness in correspondence with the respective brightness range stored in the brightness range table and the color of the polygon. For example, when the color of the polygon is held as color of the YIQ system, In YIQ, only IQ is used, and calculation is carried out by the following equation by using the respective reference brightness Tn. 
     
       
         as mentioned on Appendix-1  Equation (10) 
       
     
     When there are three of the reference brightnesses Tn (T 1 , T 2 , T 3 ), three of the drawing colors are calculated. Further, when the color of the polygon is not held as color of the YIQ system but held as color of the RGB system, there is carried out a calculation of converting from RGB to YIQ by the conversion matrix, shown above. Further, although results of calculation are different from each other, when it is necessary to calculate the drawing colors at high speed, the following calculation is carried out. 
     
       
         as mentioned on Appendix-1  Equation (11) 
       
     
     Notation M designates color of material of polygon. Although in the above-described two Equations, the calculation results are different from each other and the image quality differs slightly, a second one of the equations can provide a substantially similar image at high speed. 
     Next, one of the brightness range in the brightness range table is selected (step S 613 ). Further, although in the mode of the animation tone coloring processing, there is used the brightness range table shown in FIG. 2, the brightness range table as shown in FIG. 3 can also be used. FIG. 3 shows an example of the table designated with the brightness range by the upper limit and the lower limit. That is, the reference brightness 0.75 is set to the upper limit 1.00 and the lower limit 0.75 of the brightness range, the reference brightness 0.50 is set to the upper limit 0.74 and the lower limit 0.50 of the brightness range and the reference brightness 0.25 is set to the upper limit 0.49 and the lower limit 0.00 of the brightness range. When such a brightness range table is used, the brightness range including the upper limit and the lower limit can be selected and set at random. However, FIG. 3 shows a case of a computer which is effective down to a second order of decimal. When comparison between the brightness of the respective pixel and the two brightness values of the upper limit and the lower limit cannot be carried out simply in the brightness comparing process explained below, the brightness range is selected, for example, in turn from upper columns of FIG.  3 . Further, in this case, the processing is carried out by only the lower limit value. 
     Thereafter, the brightness at the apex of the polygon is interpolated and the brightness in the respective pixel at inside of the polygon (brightness distribution in polygon) is calculated. Although color of the apex is interpolated, since the three apexes are provided with the same drawing color and accordingly, the result remains the same even after the interpolation. Further, when the brightness at the pixel falls in the selected brightness range, the pixel is drawn by the drawing color in correspondence with the selected brightness range (step S 615 ). The steps S 613  and S 615  are repeated until the processing is carried out with regard to all of the brightness ranges (step S 617 ). 
     The processing of comparing the brightness can be carried out also by using the Z buffer. Although the Z buffer is used for hidden face erasure, in the cel animation tone coloring processing, by also using the Z buffer, an effect similar to that in the case of comparing to the upper limit value of the brightness can be achieved. 
     For example, in the case of the brightness range table as shown in FIG. 2, the threshold value 0.75 is selected. By interpolating the brightness and the coordinates (including Z value) of the respective apex of the polygon, the brightness and coordinates (including Z value) of the respective pixel are calculated. Further, when the color is set to the drawing color in correspondence with the threshold 0.75 for three apexes, the color of the respective pixel becomes the drawing color even after the interpolation. 
     The pixel processing unit  334  compares the brightness of the pixel with the threshold 0.75 and compares the Z value of the pixel calculated by the interpolation and the Z value of the pixel stored in the Z buffer. When the Z value of the pixel the brightness of which is equal to or larger than the threshold 0.75 and calculated by the interpolation, is smaller than the Z value of the pixel stored in the Z buffer, the pixel processing unit  334  draws the color of the pixel by the drawing color in correspondence with the threshold 0.75. 
     When drawing of the polygon is carried out firstly and brightness is equal to or larger than 0.75, the drawing color is written. FIGS. 12A and 12B show two examples of a triangular polygon  1011  and a triangular polygon  1012 . Brightnesses of apexes P 11 , P 12  and P 13  of the triangular polygon  1011  are respectively set to 0.0, 1.0 and 1.0. Further, brightnesses of apexes P 21 , P 22  and P 23  of the triangular polygon  1012  are respectively set to 0.0, 0.5 and 1.0. When the above-described processing is executed, painted portions in the respective triangular polygons are colored by the drawing color. 
     Next, the threshold value 0.5 is selected. The pixel processing unit  334  calculates the brightness and the coordinates (including Z value) of the respective pixel at inside of the polygon. The pixel processing unit  334  compares the brightness of the pixel with the threshold 0.5 and compares the Z value of the pixel calculated by calculation with the Z value of the pixel stored in the Z buffer. When the brightness of the pixel is equal to or larger than the threshold 0.5 and the Z value of the pixel calculated by calculation is smaller than the Z value of the pixel stored in the Z buffer, the pixel processing unit  334  draws the color of the pixel by the drawing color in correspondence with the threshold 0.5. 
     When the Z buffer is not used, as shown by FIGS. 12C and 12D, areas of the brightness 1.0 through 0.5 are colored by the drawing color in correspondence with the threshold 0.5. With regard to areas having the brightness equal to or larger than 0.75, the Z value stored in the Z buffer is the same as the Z value calculated by calculation and accordingly, the areas having the brightness equal to or larger than 0.75 are not drawn by the drawing color in correspondence with the threshold 0.5. That is, as shown by FIGS. 12E and 12F, the areas having the brightness of 0.5 through 0.74 and the areas having the brightness equal to or larger than 0.75 are colored by different drawing colors. 
     FIGS. 13A and 13B show a result of carrying out the processing similarly with respect to the threshold 0.0 in the example of FIG.  2 . Brightnesses of apexes P 11 , P 12  and P 13 ( a ) of the triangular polygon in FIG. 13A are respectively set to 0.0, 1.0 and 1.0. Further, brightnesses of apexes P 21 , P 22 , P 23  of the triangular polygon  1012  in FIG. 13B are respectively set to 0.0, 0.5 and 1.0. Numerals surrounded by dotted lines, that is, 0.5 and 0.75 indicate thresholds of brightnesses. In this way, the respective triangular polygons are divided into three areas and colored with drawing colors. 
     FIGS. 14A and 14B show a result of Coulaw shading. Brightnesses of apexes P 31 , P 32  and P 33  of a triangular polygon  1021  in FIG. 14A are respectively set to 0.0, 1.0 and 1.0. Further, brightnesses of apexes P 41 , P 42  and P 43  of a triangular polygon  1022  in FIG. 14B are respectively set to 0.0, 0.5 and 1.0. That is, the brightnesses of the respective apexes are the same as those of the triangular polygons  1011  and  1012  shown by FIGS. 13A and 13B. However, although according to the Coulaw shading, the brightness is smoothly changed by interpolation, in FIGS. 13A and 13B, the brightness is changed only at a boundary of partitioned areas. That is, it is known that there are present three of areas where the brightness stays to be flat to thereby constitute the cel animation tone. 
     Further, there also is the case in which the smallest lower limit value of the brightness range table is not 0.0. In order to eliminate a portion which is not colored at all in the polygon, in repeating step S 617  of FIG. 9, step S 615  is executed by setting the lower limit value to 0.0 at final repetition. 
     Steps S 605  through S 617 , mentioned above, are repeated until all of apexes of the stereo model have been processed, as a result, the processings are repeated until all of the polygons have been processed (step S 619 ). 
     It is preferable to form the above-described brightness range table which is optimum for the respective stereo model. However, it is also preferable to classify the stereo model into a number of categories and prepare brightness range tables for respective categories. It is conceivable to set a number of brightness ranges included in a brightness range table to 2 or 3 in conformity with actual cel animation. However, according to the above-described processing, only a number of times of repetition at step S 617  is increased and accordingly, the number can easily be set to a number of 2 or more. However, since the number of times of repetition is increased, when the number is increased, the processing is retarded. 
     When the above-described processing is executed, all of the polygons of the stereo model expressing a character of a game or the like are painted to classify by brightnesses at predetermined stages and an image colored in the cel animation tone can be provided with respect to the stereo model. In accordance with operation input, the image colored in the cel animation tone is successively formed and accordingly, it is not necessary to prepare previously a hand-written game image and a game smoothly following the operation input can be produced. 
     (Stereo Model Drawing Processing (Part 2)) 
     FIG. 15 shows a flow of a second stereo model drawing processing. A main difference between FIG.  15  and FIG. 9 resides in that step S 611  of FIG. 9 is replaced by step S 641  of FIG.  15 . That is, in FIG. 9, although in FIG. 9, the drawing color is calculated at respective time, according to the stereo model drawing processing (part 2), the drawing color is previously calculated and stored and therefore, it is necessary to carry out a processing of reading drawing color of polygon at step S 641 . Further, step S 641  may be carried out before steps S 635  and S 639  or may be carried out after step S 643  so far as step S 641  is carried out in parallel with these steps. The drawing color is previously calculated and stored and accordingly, the drawing color may be read until the drawing color is actually used. 
     For example, when the brightness range table as shown by FIG. 2 is used, three drawing color data are previously stored for respective polygon. As shown by FIG. 16, with regard to respective polygon, there are stored drawing colors (r, g, b) in correspondence with a first brightness range, drawing colors in correspondence with a second brightness range (r, g, b) and drawing colors in correspondence with a third brightness range (r, g, b), apex data IDX of apex 0 constituting the polygon, apex data IDX of apex 1 thereof and apex data IDX of apex 2 in place of FIG. 10B, described above. These data are prepared by a number of polygons of a stereo model. 
     In FIG. 15, first, initial setting is carried out (step S 633 ). In the initial setting, there is acquired a brightness range table (for example, FIG. 2 or FIG. 3) in correspondence with a stereo model. Further, data of the stereo model is acquired. Next, there is carried out apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) and light source calculation with respect to one apex (step S 635 ). Enlargement, contraction, rotation, parallel movement and perspective view conversion are carried out by using the arranging matrix set at step S 14  of FIG.  5 . 
     Further, the two methods of light source calculation described in the first stereo model drawing processing are adaptable as they are even in the stereo model drawing processing (part 2). 
     Next, it is determined whether a polygon (face) including the apex is a head face (step S 637 ). The determination is carried out in the case of a triangular polygon by to which direction the triangular polygon constituted by two apexes processed before the apex is directed. A detailed description will be given of a method of head and tail determination in (2) contour drawing processing. Further, with respect to the initial two apexes, processings other than those at steps S 635  and S 639  are not carried out. Further, according to the stereo model drawing processing (part 2), the head and tail determination is carried out at the stage, however, the head and tail determination can be carried out prior to the stage. 
     When the polygon (face) including the apex is a tail face, the operation returns to step S 635 . When the polygon (face) including the apex is a head face, there is calculated a brightness at the apex subjected to the apex conversion and the light source calculation (step S 639 ). In calculation of the brightness, the YIQ conversion is carried out. 
     Further, drawing color of the polygon including the apex subjected to the apex conversion and the light source calculation is read (step S 641 ). Data of the read drawing color is previously calculated and a calculation method in previously calculating the data may be either of the two methods explained in the first stereo model drawing processing or may be other method. Further, the drawing colors may be defined one by one. According to the stereo model drawing processing (part 2), the drawing color is previously prepared and therefore, the execution speed is accelerated, however, drawing color cannot simply be changed to color other than the prepared drawing colors. In contrast thereto, when the drawing color is calculated in execution by using the reference brightness defined in the brightness range table as in the first stereo model drawing processing, the drawing color can pertinently be changed by only changing the brightness range table or the reference brightness. 
     Next, one of brightness ranges of the brightness range table is selected (step S 643 ). Further, although according to the embodiment, the brightness range table shown in FIG. 2 is used, the brightness range table as shown by FIG. 3 can also be used. When such a brightness range table is used, the brightness range including the upper limit and the lower limit can be selected and set at random. When the comparison between the brightness of the respective pixel and the two brightness values of the upper limit and the lower limit cannot simply be carried out in the brightness comparing processing explained below, the brightness ranges are selected, for example, in turn from upper columns of FIG.  3 . Further, in this case, the processing is carried out only by the lower limit value. 
     Thereafter, the brightness of the apex of the polygon is interpolated and the brightness at the respective pixel at inside of the polygon (brightness distribution in polygon) is calculated. Although color of the apex is interpolated, all of the three apexes are provided with the same drawing color and therefore, the result remains the same even after the interpolation. Further, when the brightness at the pixel falls in the selected brightness range, the pixel is drawn by the drawing color in correspondence with the selected brightness range (step S 645 ). The steps S 643  and S 645  are repeated until the processing is carried out with respect to all of the brightness ranges (step S 647 ). 
     The processing of comparing the brightness can be carried out by also using the Z buffer. Although the Z buffer is used in hidden face erasure, in the cel animation coloring processing, an effect similar to that in the case of comparing with the upper limit value of the brightness is achieved by also using the Z buffer. 
     Further, there is a case in which the value of the smallest lower limit value of the brightness range table is not 0.0. In order to eliminate a portion which is not colored at all in the polygon, in repeating S 647  of FIG. 15, step S 645  is carried out by setting the lower limit value to 0.0 at final repetition. 
     As described above, step S 635  through S 647  are repeated until the processing has been carried out with respect to all of the apexes of the stereo model and as a result, the steps are repeated until the processing has been carried out with respect to all of the polygons (step S 649 ). 
     When the above-described processing is carried out, all of polygons of the stereo model for expressing a character of a game or the like are painted to classify by brightnesses at predetermined stages and with regard to the stereo model, there can be provided an image colored in the cel animation tone. Particularly, the stereo model drawing processing (part  2 ) is further accelerated than the first stereo model drawing processing. The image colored in the cel animation tone is successively formed in accordance with the operation input and therefore, it is not necessary to previously prepare a hand-written game image and a game smoothly following the operation input can be produced. 
     (2) Contour Drawing Processing 
     According to the contour drawing processing, a contour line is attached to a stereo model for expressing a character of a game or the like. 
     An explanation will be given of an outline of the contour drawing processing in reference to a functional block diagram of FIG. 17. A game apparatus according to the contour drawing processing includes an operation input unit  410 , a game progressing unit  430  including a character action determining unit  435 , a game progress situation setting unit  440  including a character direction setting unit  443  and a view axis direction setting unit  447 , an arranging matrix setting unit  360 , a stereo model processing unit  400 , a contour drawing model acquiring unit  350 , a contour drawing model processing unit  370  for receiving the arranging matrix from the arranging matrix setting unit  360 , a blurred expression texture mapping unit  380 , a pixel processing unit  390  receiving data from the blurred expression texture mapping unit  380  and the stereo model processing unit  400  and including a hidden face erasure processing unit  395  and an image display control unit  420 . 
     The operation input unit  410  outputs operation information of button or lever of the operation input unit  410  operated by a player of a game to the game progressing unit  430 . 
     The game progressing unit  430  determines content of progressing the game such as action of a character, a change in a view point position, a change in a direction of a view axis, or movement of a position of a light source, a change in a direction of light ray based on information from the operation input unit  410  and provides instruction to the game progress situation setting unit  440 . The character action determining unit  435  in the game progressing unit  430  is provided with particularly a function of determining the action of the character based on information from the operation input unit  410 . 
     The game progress situation setting unit  440  calculates and sets a position, a direction and a shape of the character, the position of the view point, the direction of the view axis, the position of the light source, the direction of the light ray, further, an increase or a decrease of physical strength in accordance with action of the character in accordance with the content of progressing the game instructed to the game progressing unit  430 . The character direction setting unit  443  in the game progress situation setting unit  440  is provided with a function of particularly determining a direction with respect to the view point of the character in accordance with the content of progressing the game instructed to the game progressing unit  430 . Meanwhile, the view axis direction setting unit  447  in the game progress situation setting unit  440  is provided with a function of particularly setting the direction of the view axis in accordance with the content of progressing the game instructed to the game progressing unit  430 . 
     The arranging matrix setting unit  360  carried out a processing of determining the arranging matrix of the stereo model expressing the character in accordance with the position coordinates and the direction of the character set by the game progress situation setting unit  440  and the position of the view point. The arranging matrix is a matrix for carrying out parallel movement, rotation and perspective view conversion of the stereo model. 
     Although a detailed description will be given later, when a contour drawing model relatively larger than the stereo model is acquired and a reference position of the contour drawing model is disposed at a position in correspondence with the reference position of the stereo model, the arranging matrix determined by the arranging matrix setting unit  360 , can be used commonly by the stereo model processing unit  400  and the contour drawing model processing unit  370 . When the arranging matrix can commonly be used, one storing area for the arranging matrix can be prepared for respective character and accordingly, the common use is efficient. 
     However, there also is a case in which the arranging matrix is not commonly used or cannot be used commonly. In that case, an arranging matrix for the stereo model and an arranging matrix for the contour drawing model are formed and stored in respective storing areas. Further, when the arranging matrix cannot be used commonly as mentioned later, there also is the case in which one storing area of the arranging matrix is prepared, immediately before using the arranging matrix at the stereo model processing unit  400  and the contour drawing model processing unit  370 , the arranging matrix of the stereo model is set to include contraction conversion and the arranging matrix of the contour drawing model is set to include enlargement conversion. 
     The contour drawing model acquiring unit  350  forms a contour drawing model in correspondence with, for example, a stereo model constituted by triangular polygons. Further, when the contour drawing model is previously formed, the contour drawing model acquiring unit  350  reads a contour drawing model constituted by the triangular polygons previously formed. Further, the respective polygon of the acquired contour drawing model is provided with head and tail reverse to that of a corresponding polygon of the stereo model. Further, the contour drawing model becomes larger than the stereo model. Further, color in drawing the contour drawing model is previously set. Further, although the contour drawing model is obliged to finally become large relative to the corresponding stereo model, there is a case in which the size of the contour drawing model at this stage is the same as that of the stereo model. When the contour drawing model having the size the same as that of the stereo model is acquired by the contour drawing model acquiring unit  350 , a processing of enlarging the contour drawing model is carried out immediately before drawing the contour drawing model. Further, in this case, the stereo model and the contour drawing model cannot share the arranging matrix. 
     Color of the contour drawing model acquired by the contour drawing model acquiring unit  350  may be color the same as that of the corresponding stereo model. In this case, before drawing the acquired contour drawing model, the color of the contour drawing model is changed to other color. 
     The reference position of the contour drawing model is normally defined to dispose at the reference position of the corresponding stereo model or at a vicinity thereof. When the reference position of the stereo model and the reference position of the contour drawing model are significantly different from each other, the arranging matrix cannot be commonly used. For example, FIG. 18 shows a case in which the size of a contour drawing model  510  is larger than the size of a stereo model  500 . In FIG. 18, arrow mark directions of respective faces indicate head faces. According to the stereo model  500 , outer sides of respective faces in a hexagonal shape constitute head faces and according to the contour drawing model  510  and inner sides of respective faces in the hexagonal shape constitute head faces. 
     A stereo model reference position  520  constituting the reference position of the stereo model  500  and a contour drawing model reference position  530  constituting the reference position of the contour drawing model  510  are both defined at centers of the respective models. Further, the contour drawing model  110  is defined to be larger than the stereo model  500  centering on the contour drawing model reference position  530 . 
     The contour drawing model processing unit  370  carries out coordinates conversion of respective apexes of the contour drawing model by using the arranging matrix set by the matrix setting unit  360  for arranging the contour drawing model. Further, the contour drawing model processing unit  370  determines whether the respective faces of the contour drawing model (for example, respective polygons) direct surfaces or direct rear faces to a view point set in a virtual space. Further, the contour drawing model processing unit  370  does not carry out calculation of brightness of light reflected at the faces of the contour drawing model. When a contour drawing model having a size the same as that of the stereo model is acquired at the contour drawing model acquiring unit  350 , the contour drawing model processing unit  370  executes apex conversion for enlarging the size of the contour drawing model. In this case, also in the enlarged case, the relationship between the stereo model and the contour drawing model is as shown by FIG.  18 . The designated state shows a state of the contour drawing model in a virtual three-dimensional space. The state of the contour drawing model is defined by information in correspondence with the contour drawing model. Information of the state is information indicating a position, a direction, a size and the like in the virtual space. 
     Further, the head and tail determination of a face is carried out for determining a polygon directing a surface thereof to a camera  550 . Only a polygon directing the surface to the camera  550  constitutes a display object. In the example of FIG. 18, faces  511  and  512  of the contour drawing model  510  proximate to the camera  550  are out of the drawing object. In this way, a face thereof disposed on an outer side of the stereo model  500  and proximate to the camera  550  is out of the drawing object and accordingly, the stereo model  500  can normally be drawn. Meanwhile, only faces  513 ,  514 ,  515  and  516  of the contour drawing model  510  rearward from the stereo model  500  constitute the drawing object. Further, when a direction from the stereo model  500  to the camera  550  is made positive, it is known that a face of the contour drawing model  510  constituting the drawing object is a face an outer side (not in direction of surface) is directed in a negative direction. However, since hidden face erasure is carried out at the hidden face erasure processing unit  395  of the pixel processing unit  390 , even when a face constitutes the drawing object, all of the face is not necessarily drawn. 
     The blurred expression texture mapping unit  380  executes a processing of mapping blurred expression texture to the contour drawing model such that a contour line drawn as a result becomes a blurred line. The blurred expression texture is a texture having a pattern including a change in brightness or transparency and an example thereof will be shown later. Further, it is not necessary needed that the contour line is blurred and accordingly, the processing of the blurred expression texture mapping unit  380  is selectively executed. 
     The stereo model processing unit  400  carries out a processing of the stereo model. That is, the stereo model processing unit  400  carries out apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) with regard to the respective apexes of the stereo model. Further, the stereo model processing unit  400  calculates brightness of light reflected by the surface of the stereo model. Further, the stereo model processing unit  400  carries out head and tail determination of respective faces of the stereo model (for example, respective polygons). Further, when the sizes of the stereo model and the contour drawing model are the same, there may be carried out also a processing of contracting the size of the stereo model by the stereo model processing unit  400 . By contracting the size of the stereo model, relatively, the size of the contour drawing model becomes larger than the size of the stereo model. 
     Also in the case of carrying out the contraction processing by the stereo model processing unit  400 , the relationship between the stereo model  500  and the contour drawing model  510  is as shown by FIG.  8 . Further, the head and tail determination of a face is the same as that in the contour drawing model processing unit  370  and among faces of the stereo model, a face in which a direction thereof the same as a view line direction of the camera constitutes a direction of a head face thereof, is excluded from the drawing object. According to the example of FIG. 18, faces  503 ,  504 ,  505  and  506  on a rear side in view from the camera are excluded from the drawing object. 
     The pixel processing unit  390  carries out a processing of drawing the respective pixel. For example, the pixel processing unit  390  calculates color of respective pixel in a face from color of an apex of the face by interpolation and determines and draws color of the respective pixel while executing a hidden face erasure processing using the Z buffer by the hidden face erasure processing unit  395 . The pixel processing unit  390  carries out the processing with respect to faces constituting the drawing object in the contour drawing model processing unit  370  and the stereo model processing unit  400 . 
     For example, in the case of FIG. 18, two faces  501  and  502  of the stereo model  500  most proximate to the camera  550  are drawn and the four faces  513 ,  514  and  515  and  516  of the contour drawing model remote from the camera  550  are drawn. The four faces of the contour drawing model  510  are extruded to the left and to the right from the stereo model  500  in view from the camera  550  and accordingly, only extruded portions thereof are drawn without being subjected to hidden face erasure. The excluded portions constitute the contour line. Further, the pixel processing unit  390  determines color in consideration of color of material of the contour drawing model. Further, there also is a case in which the color of the contour line (color for black or dark contour line) is made to constitute color of the contour drawing model by totally disregarding the color of the material. 
     Finally, the image display control unit  420  designates a drawing area written with data for displaying on the display screen. The drawing area is normally classified in two, one is used for display and other is used for writing. Further, when writing to the writing area has been finished, the writing area is used to switch to the display area and the display area is used to switch to the writing area. The image display control unit  420  controls the switching operation. 
     (Premise) 
     FIG. 19 schematically shows an example of data written to CD-ROM  131 . According to the contour drawing processing, there is a case in which data of the contour drawing model is previously formed and stored to CD-ROM  131  and the data is read from CD-ROM  131  in executing a game. 
     A program area  132  is stored with a program for executing the invention in a computer. A detailed description will be given later of content of the program. 
     A system data area  133  is stored with various data processed by the program stored in the program area  132 , mentioned above. The image data area  134  is stored with data including stereo model data  137  and contour drawing model data  135 . However, when the contour drawing model is formed in the contour drawing model acquiring processing, mentioned later, there is no need of storing the contour drawing model data  135 . Further, data of texture for expressing blur or the like is also stored to the image data area  134 . 
     The contour drawing model data  135  is previously formed from the stereo model data  137  and is provided with the following characteristic. 
     That is, the size of the contour drawing model is defined to be larger than the stereo model. For example, according to the contour drawing model, apexes thereof are moved in normal line directions of respective apexes of a corresponding stereo model by a length of 2 percent of a total length of the stereo model and is defined to enlarge by about 2 percent as a whole. When the enlargement rate is larger, the contour line is drawn further boldly and when the enlargement rate is smaller and the contour drawing model is enlarged only slightly, the contour line is drawn further finely. Further, when the contour drawing model is defined to enlarge not uniformly but partially, only the contour line of the enlarged portion is boldly drawn. Adjustment of the size is normally carried out by a producer of the stereo model and accordingly, a contour line reflected with the intention of the producer can be drawn. 
     Further, color for material of the respective polygon of the contour drawing model is set to color chroma of which is the same as that of the stereo model and brightness of which is reduced. Further, there also is the case in which all of respective polygons are set to single color of black or the like. Further, there also is the case in which there is carried out setting for mapping blurred expression texture. The color for material is adjusted by a producer and accordingly, the contour line can be drawn by color intended by the producer. 
     Further, head and tail of the respective polygon of the contour drawing model are reverted. Specifically, one location of an order defining apexes of the respective triangle constituting the contour drawing model is switched. 
     Further, the size of the contour drawing model may be defined to be a size the same as the size of the corresponding stereo model. In this case, after acquiring the contour drawing model by the contour drawing model acquiring processing, mentioned later, the contour drawing model is enlarged during a time period until setting the arranging matrix of the contour arranging model by the contour drawing model arranging processing, mentioned later. Or, in setting the arranging matrix of the contour drawing model by the contour drawing model arranging processing, the arranging matrix may be determined such that the arranging matrix includes enlargement conversion. Conversely, when the stereo model is arranged, the arranging matrix of the stereo model may be determined such that the arranging matrix of the stereo model includes contraction conversion. 
     Further, color of material of the respective polygon of the contour drawing model may be the same as color of material of the respective polygon of the corresponding stereo model. In this case, in a processing of drawing the contour drawing model, mentioned later, for example, the contour drawing model is drawn by color defined separately such as black or the like. 
     A sound data area  136  is stored with data for outputting sound. Further, the sound processing is not directly related to the invention and accordingly, it is not necessary to store data to the sound data area. 
     Next, an explanation will be given of a processing flow of the contour drawing processing. 
     (Total Processing Flow) 
     The processing flow at a level shown by FIG. 4 remains the same also in the contour drawing processing. When the game is started, initial setting is carried out (step S 2 ). The processing of the initial setting includes the processing of acquiring data of a stereo model expressing a character to be drawn. Further, the contour drawing processing also includes a processing of acquiring data of a contour drawing model. Next, operation of button, lever or the like of the operation input unit  410  is carried out by a player of the game (step S 3 ). Further, there is carried out the game progress processing for determining content of progressing the game such as, for example, action of the character in which the character moves to the left or the character attacks, a change in a view point position, a change in a direction of a view axis, or movement of a light source position, a change in a direction of light ray or the like based on information of the operation input at step S 3  (step S 4 ). 
     Thereafter, there is carried out the game progress situation setting processing for setting a game progress situation such as a position, a direction and a shape of the character, the position of the view point or the direction of the view axis, the position of the light source or the direction of light ray, further, an increase or a decrease in physical strength in accordance with action of the character and the like in accordance with the content of progressing the game determined at step S 4  (step S 5 ). Next, there is carried out the game image drawing processing for drawing an image of the game in accordance with the game progress situation (step S 6 ). A detailed description will later be given of the game image drawing processing. 
     Further, there is carried out the game image display processing for displaying the game image shown by the game image drawing processing at step S 6  (step S 7 ). 
     Next, it is determined whether the game is over (step S 8 ). In the game progress situation setting processing (step S 5 ) carried out in accordance with the operation input at the step S 3 , when physical strength of a self character operated by the player of the game is reduced and set to 0, the condition of game over is satisfied. At step S 8 , the physical strength of the self character operated by the player of the game is inspected and it is determined whether the game is over. When the physical strength of the self character is not 0, the operation returns to step S 3  and awaits for successive operation input. Meanwhile, when the game is over, the game is finished. Further, even after the game is over, at step S 7 , the result is displayed on a display screen and accordingly, the player can grasp a final situation from the display screen. 
     FIG. 20 shows a processing flow expressing an outline of the game image drawing processing at step S 6  (FIG.  4 ). First, there is carried out a background model drawing processing for drawing a background model for expressing a background portion in the game image (step S 22 ). The drawing processing is the same as the conventional drawing processing and therefore, a detailed description will not be given thereof here. Further, there are repeated steps S 24  through S 27  shown below until all characters are drawn (step S 23 ). 
     A first one of the repeated steps is a step of executing a deforming processing for deforming an unprocessed character (step S 24 ). Motion of the unprocessed character is determined by the game progress processing at step S 4  in accordance with the operation input executed at step S 3  of FIG.  4 . Further, there is executed a processing of deforming a stereo model for expressing the unprocessed character set by the game progress situation setting processing at step S 5  executed in accordance therewith. Further, according to the contour drawing processing, a processing for deforming a contour drawing model is also executed in accordance with the processing of deforming the stereo model. 
     A second one of the repeated steps is a step of setting an arranging matrix for the unprocessed character (step S 25 ). The arranging matrix is a matrix for parallel movement, rotation and perspective view conversion of the stereo model for expressing the unprocessed character and is formed based on position coordinates and a direction of the character and a position of a view point set by the game progress situation setting processing at step S 5 . As described above, when the contour drawing model is already defined to be large relative to the stereo model and the reference position of the contour drawing model is the same as the reference position of the stereo model, the arranging matrix of the stereo model can also be used for the contour drawing model. When the condition is not satisfied, arranging matrices may be set to respectives of the stereo model and the contour drawing model. Further, there also is a case in which in the contour drawing model drawing processing, described later, an arranging matrix including enlargement conversion is set for the contour drawing model. Further, there also is a case in which in the stereo model drawing processing, an arranging matrix including contraction conversion is set for the stereo model. 
     Further, a third one of the repeated steps is a step of executing the contour drawing model drawing processing for drawing the contour drawing model (step S 26 ). A detailed description will be given later of the contour drawing model drawing processing. 
     A fourth one of the repeated steps is a step of executing the stereo model drawing processing for drawing the stereo model for expressing the unprocessed character (step S 27 ). A detailed description will be later of the stereo model drawing processing. 
     After all the characters have been drawn, there is executed a window drawing processing for drawing a window for expressing a capability of a character or the like to a user (step S 28 ). The window drawing processing is the same as the conventional drawing processing and accordingly, a detailed description will not be given here. Further, when the drawing processing is carried out successively for the respective characters in this way, one arranging matrix (two when arranging matrix cannot be used commonly) may be prepared to all the characters and therefore, the operation is efficient. 
     Next, although an explanation will be given of a simple example with regard to progress of a game story in accordance with the operation input of the player of the game (FIG.  7  and FIG.  8 ), prior thereto, an explanation will be given of data of characters used in the contour drawing processing in reference to FIG.  21 . The character data includes a numerical value of maximum physical strength  10  (for example, 300), a numerical value of current physical strength  12  (for example, 300), a numerical value of attack force  14  (for example, 123), a numerical value of defence force  16  (for example, 51), coordinates (x, y, z) of reference position  18  (for example, (15.0, 0.0, 3.2)), rotational angles around X, Y, Z axes constituting direction of character  20  (for example, (0, −90, 0)), pointer  22  to motion data, pointer  24  to model data of the stereo model and pointer  26  to model data of the contour drawing model. 
     FIG. 7 shows the display screen  120  for displaying the image of the game for progressing the story while making the self character fight against enemy character in the virtual three-dimensional space by operating the self character C 101  by the player of the game. In this case, there is displayed the image of the self character C 101  from the right front direction. There emerge the enemy character  1  (C 111 ) and the enemy character  2  (C 113 ) on the left side of the display screen. 
     In this case, the position of the view point is determined by the game progress situation setting processing (step S 5 ) in accordance with the positional relationship between the self character and the enemy character and the direction of the self character. Further, there is formed a non-photorealistic image attaching the contour line to the character is formed from the position of the view point of the respective character and is displayed on the display screen. 
     The self character attacks the enemy character in accordance with the operation input of the player from the operation input unit  410 . Meanwhile, the enemy character attacks the self character in accordance with the predetermined algorism. 
     FIG. 8 shows the display screen when the self character C 101  is moved in the left direction of the display screen by operating the operation input unit  410  by the player of the game from the state of the display screen shown in FIG.  7 . 
     The action of the character of “move in the left direction of the display screen” is determined by the game progress processing (step S 4  of FIG. 4) in response to the operation input. In accordance with the action of the character, the direction, the position and the shape of the character are determined by the game progress situation setting processing (step S 5  of FIG.  4 ). According to the example of FIG. 8, the direction of the character is determined to the left direction relative to the display screen and the position of the character is similarly moved in the left direction relative to the display screen. Further, the shape of the character is set with a shape for expressing running operation. 
     In this way, even when the game progress situation such as the direction, the position or the like of the character is changed, the contour line is drawn to the character. (Contour drawing model acquiring processing) 
     FIG. 22 shows the processing of acquiring the contour drawing model included in the initial setting (step S 2 ) of FIG.  4 . Here, at first, it is determined whether the contour drawing model is to be formed (step S 203 ). Because there are present a case of previously preparing the contour drawing model and a case of forming the contour drawing model at this stage. The determination is executed by determining whether the contour drawing model in correspondence with the stereo model is stored in CD-ROM  131 . When it is determined that the contour drawing model is stored therein, it is determined that the contour drawing model is not formed and when it is determined that the contour drawing model is not stored therein, it is determined that the contour drawing model is formed. 
     When it is determined that the contour drawing model is not formed, data of the contour drawing model stored in CD-ROM  131  is read (step S 207 ). According to the respective polygon of the contour drawing model, as explained above in reference to FIG. 18, head and tail thereof is reverted to that of the polygon in correspondence with the stereo model. Further, the size of the read contour drawing model is defined to be larger than the corresponding stereo model. Further, color of the contour drawing model is defined by color darker than that of the corresponding stereo model. 
     When it is determined that the contour drawing model is formed, a processing of forming the contour drawing model is carried out (step S 205 ). Similar to step S 207 , also in the case of forming the contour drawing model at this stage, according to the respective polygon of the contour drawing model, as explained above in reference to FIG. 13, head and tail thereof is reverted to that of the corresponding polygon of the stereo model. 
     The size of the contour drawing model is formed to be larger than that of the corresponding stereo model. For example, there is formed the contour drawing model which is enlarged by moving apexes thereof in normal line directions of respective apexes of the stereo model. When the contour drawing model is larger than the stereo model, the contour line is drawn further boldly and when the contour drawing model is only slightly larger than the stereo model, the contour line is drawn further finely. 
     Further, there may be formed the contour drawing model which is enlarged by moving faces thereof in normal line directions of respective faces of the stereo model. Further, there may be formed the contour drawing model which is enlarged by moving respective apexes of the stereo model centering on the reference position normally defined in the stereo model. 
     Further, at this time point, the size of the contour drawing model may be formed by a size the same as a size of the corresponding stereo model. In this case, the contour drawing model is enlarged during a time period after acquiring the contour drawing model by the contour drawing model, until the arranging matrix of the contour drawing model is set by the contour drawing model arranging processing, mentioned later. Or, in setting the arranging matrix of the contour drawing model in the contour drawing model arranging processing, the arranging matrix may be determined to include enlargement conversion of the arranging matrix. Conversely, in arranging the stereo model, the arranging matrix of the stereo model may be determined such that the arranging matrix of the stereo model includes contraction conversion. 
     Meanwhile, color of material of the respective polygon of the contour drawing model is formed by color darker than color for material of the respective polygon of the corresponding stereo model. Further, at this time point, the color of the formed contour drawing model may not be defined. Or, color of material of the respective polygon of the contour drawing model may be the same as the color of material of the respective polygon of the corresponding stereo model. In this case, in the processing of drawing the contour drawing model, the color of the contour drawing model is not considered and the contour drawing model is drawn by separately defined color such as black or the like or color of texture expressing blur. 
     Next, it is determined whether texture expressing blur is mapped in the contour drawing model (step S 209 ). When the contour drawing model is formed at step S 205 , based on data of the corresponding stereo model, the determination is executed. Meanwhile, when the contour drawing model is read at step S 207 , the determination is executed based on data of the read contour drawing model. When it is determined that texture expressing blur is mapped, at step S 211 , texture expressing blur is mapped in the contour drawing model. That is, texture coordinates (U, V) are set to the respective apexes of the polygon. 
     Further, as described above, texture expressing blur is provided with a pattern including a change in brightness or transparency. FIG. 23 shows an example of a texture including a change in brightness. This is a texture having a pattern in which white hatched lines are finely drawn in a black matrix. Brightness of the black portion is low, brightness at the white portion is high and therefore, the texture shown by FIG. 23 includes a change in the brightness. 
     According to the invention, the contour line is drawn by cutting out portions of the contour drawing model as lines. That is, when the contour drawing model mapped with texture is drawn as the contour line, a line in correspondence with a line cut out from the contour drawing model as the contour line, is cut out from the texture and is drawn. At this occasion, when the line is cut out from the texture substantially in the vertical direction or substantially in the horizontal direction, any line also includes a change in brightness. By drawing such a line as a contour line, the contour line including the change in the brightness is drawn. That is, blur of the contour line is expressed and the contour line in further hand-writing tone is drawn. 
     In the case of the texture shown in FIG. 23, even when a line is cut out in any direction, the line includes the change in the brightness. However, depending on a direction of cutting out the line, there also is a case in which the brightness hardly changes. It can be adjusted which portion of the contour drawing model is drawn as the contour line in which direction and accordingly, according to the texture expressing blur, the pattern is adjusted mainly in accordance with the direction of cutting out the contour drawing model. 
     Further, when the contour line is drawn by the contour drawing model mapped with texture having a pattern including a pattern including a change in transparency, the contour line includes a change in transparency. At a portion having high transparency, in accordance with a rate thereof, color proximate to color of a background is drawn and at a portion having low transparency, color proximate to color of the texture, for example, black or the like is drawn. Thereby, a contour line including a change in light and shade is drawn and blur of the contour line is expressed. 
     When it is determined that the texture expressing blur is not mapped and when the processing of mapping the texture has been finished, the contour drawing model acquiring processing is finished. 
     (Contour Drawing Model Arranging Processing) 
     At step S 25  of FIG. 20, the arranging matrix of the stereo model expressing the unprocessed character and the contour drawing model is set and there is carried out the processing of arranging the contour drawing model by the arranging matrix. Normally, the reference position of the contour drawing model is provided at a position in correspondence with the reference position of the stereo model. Further, the arranging matrix of the contour drawing model is set such that the reference position of the contour drawing model is arranged at the reference position of the stereo model or at a vicinity thereof. 
     Here, there is set the arranging matrix including rotation conversion in which when the direction of the stereo model is changed, also the contour drawing model corresponds thereto. When the shape of the stereo model is changed, the deformation processing is carried out such that the contour drawing model corresponds thereto. 
     At this stage, when the size of the contour drawing model is the same as that of the stereo model, the contour drawing model is enlarged. Specifically, the arranging matrix of the contour drawing model is set such that respective apexes of the contour drawing model are subjected to enlargement conversion in accordance with a predetermined enlargement rate centering on the reference position of the contour drawing model. Or, conversely, the stereo model may be contracted. That is, in this case, the arranging matrix of the stereo model is set such that respective apexes of the stereo model are subjected to contraction conversion in accordance with a predetermined contraction rate centering on the reference position of the stereo model. 
     Thereby, finally, the relatively large contour drawing model is arranged to include the stereo model. Depending on a relationship between arrangement positions, directions, shapes and the like of the two models, there can also occur a case in which the contour drawing model does not include completely the stereo model. However, also in this case, the contour line is drawn at a portion including thereof. 
     Further, it is not necessarily needed to set the arranging matrix at this stage and respective elements necessary for apex conversion such as arrangement coordinates, a direction and an enlargement and contraction rate and the like may be fixed. Also in this case, actual apex conversion is carried out at a stage of a processing of drawing the respective model. 
     (Contour Drawing Model Drawing Processing) 
     In FIG. 24 showing a flow of a processing of drawing a contour drawing model, processings explained below are repeatedly carried out until all of apexes of the contour drawing model have been processed (step S 503 ). A first processing of the processings repeatedly carried out, is an apex conversion (enlargement, contraction, notation, parallel movement, perspective view conversion) processing for one apex (step S 505 ). Here, the arranging matrix calculated at step S 25  (FIG. 20) is used in the apex conversion. Further, with regard to initial two apexes, steps other than steps S 505 , S 509  and S 511  are not executed. 
     Here, caution is required in that light source calculation is not executed with regard to the contour drawing model. The reason is that a contour line is drawn regardless of a position of a light source or the like and it is useless to carry out the light source calculation. For example, there is a case in which color of material of a contour drawing model is disregarded. When the size of a contour drawing model is the same as that of a stereo model, there is a case in which in accordance with an arranging matrix set in an arranging processing, a contour drawing model is subjected to enlargement conversion at this stage. 
     Further, there is carried out a processing of determining whether a polygon (face) including the apex is a head face (step S 507 ). According to the determination, in the case of a triangular polygon, it is determined to which direction the triangular polygon constituted by two apexes processed prior to the apex is directed. FIG. 25 shows an example of a triangular polygon constituting a stereo model for explaining a head and tail determining method. According to the example, in the drawing, an apex number of an upper apex is 0, an apex number of an apex on a lower left side is 1 and an apex number of an apex on a lower right side is 2. That is, the apex numbers are provided in the counterclockwise direction from the upper apex. 
     According to the contour drawing processing, a face in which the apex numbers of the respective apexes of a triangular polygon seem to be provided in the counterclockwise direction, is defined as a head face (so-to-speak right hand system). Therefore, in the case of the triangular polygon, a face on this side of paper face constitutes a head face. When there is a normal line vector in the direction of the head face, by a sign of inner product of the normal vector and a view line vector, head and tail of the triangular polygon can be determined. That is, when the sign of the inner product is negative, with regard to a view point position, the triangular polygon directs a head face and when the sign of the inner product is positive, with regard to the view point position, the triangular polygon directs a tail face. 
     Actually, as shown by FIG. 26, there is calculated outer product a′b of a vector “a” from the apex 0 to the apex 1 projected to the screen and a vector “b” from the apex 0 to the apex 2 projected to the screen and it is determined whether the face is the head face by a direction of a vector “n” constituting a result of the outer product. The vector “n” is in parallel with z axis and it is determined whether the face is the head face by inspecting a sign of z component of the vector “n”. That is, when the sign is positive, the face is head and when the sign is negative, the face is tail. On the left side of FIG. 26, the numbers of the apexes of the triangle constitute the counterclockwise direction, and the vector “n” as the result of the outer product is directed in the positive direction of z axis and accordingly, the face is head. Meanwhile, on the right side of FIG. 26, the numbers of the apexes of the triangle constitute the clockwise direction, the vector “n” as the result of the outer product is directed in the negative direction of z axis and accordingly, the face is tail. 
     In the case of the contour drawing model in the contour drawing processing, head and tail of a face of the contour drawing model is reverse to that of a corresponding polygon of the stereo model. FIG. 27 shows a polygon which corresponds to the polygon of FIG.  25  and head and tail of which is reverted. Respective apexes of a triangular polygon shown in FIG. 27 are provided with apex numbers of 0, 1, 2 in an order of upper middle, lower right and lower left. That is, apex numbers are attached to a corresponding triangular polygon in an order reverse to that of FIG.  27 . That is, in FIG. 27, it is determined that this side of paper face is a tail face. Further, according to the contour drawing processing, the head and tail determination is carried out at this stage, however, it is also possible that the head and tail determination is carried out prior to the stage. 
     When the polygon (face) including the apex is the tail face, the operation returns to step S 503 . When the polygon (face) including the apex is the head face, it is determined whether texture expressing blur is mapped (step S 509 ). 
     This signifies texture mapping with regard to the polygon. When the texture expressing blur is mapped, texture coordinates of texture for expressing blur are calculated (step S 511 ). When texture mapping is carried out, apexes of the polygon have already been designated with texture coordinates (U, V), however, when the polygon is arranged obliquely to the screen, the texture may be displayed to distort on the screen. In order to avoid the distortion, there is carried out a texture perspective processing. According to the texture perspective processing, for example, by using Q=1/w (“w” designates a depth from the screen), new texture coordinates (S, V) are calculated. Notations S and V can be calculated by putting, for example, S=U′Q, T=V′Q. Calculated (S, V) are set as texture coordinates in correspondence with apexes of the polygon. When the texture expressing blur is not mapped, the operation proceeds to step S 513 . 
     Further, for example, the pixel processing unit  390  shown in FIG. 17 is driven (step S 513 ). As described above, the pixel processing unit  390  forms data at the respective pixels at inside of the triangular polygon by interpolating data of the respective apexes of the triangular polygon. Data of the respective apexes are color of material, screen coordinate values, and texture coordinate values when step S 511  is executed. Data at the respective pixel are color of material and pixel color when step S 511  is executed. 
     However, it is also possible to set color of the contour line at the respective pixel by disregarding color of material at the time point. Further, it is also possible to set color of the respective apex in consideration of color of material. The pixel processing unit  390  draws a display image by further using data at the respective pixels at inside of the formed triangular polygon. At this occasion, hidden face erasure is carried out using the Z buffer. 
     Although there is shown an example of using the Z buffer for the hidden face erasure, with regard to a simple model as shown by FIG. 18, there may be executed a hidden face erasure processing such as the Z sort method in which the Z buffer is not used. However, in the case of a further complicated model, for example, in the case inwhich the hand of a person is arranged in front of the body, when the hidden face erasure using the Z buffer is not carried out, it is difficult to accurately draw the contour line. 
     (Stereo Model Drawing Processing) 
     FIG. 28 shows a flow of a processing of drawing a stereo model common to the contour drawing processing and (3) contour drawing processing (part 2), shown below. Here, following processings are repeatedly carried out until all of apexes of a stereo model have been processed (step S 533 ). A first one of repeated processings is apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) and light source calculation with regard to one apex (step S 555 ). Further, with regard to initial two apexes, processings other than steps S 555  and S 559  are not carried out. 
     In the apex conversion, there is used the arranging matrix set at step S 25  (FIG.  20 ). However, in the case in which the size of the contour drawing model is the same as that of the stereo model, there also is a case in which the contour drawing model is relatively enlarged by contracting the size of the stereo model. In this case, there is executed contraction conversion at step S 555 . Further, the stereo model can simply be contracted by moving respective apexes thereof toward center of the stereo model along normal lines thereof. 
     Next, it is determined whether a polygon (face) including the apex is a head face (step S 557 ). According to the determination, in the case of a triangular polygon, it is determined by to which direction a triangular polygon constituted by two apexes processed prior to the apex is directed. According to the determination, there can be used the method explained in the processing of drawing the contour drawing model. Further, although according to the contour drawing processing, head and tail determination is carried out at this stage, the head and tail determination can be carried out prior to the stage. 
     When the polygon (face) including the apex is a tail face, the operation returns to the step S 553 . When the polygon (face) including the apex is the head face, there is carried out a processing of calculating texture coordinates of the apex (step S 559 ). When the texture mapping processing is carried out, the apexes of the polygon are already designated with texture coordinates (U, V), as the texture perspective processing, in this case, by using Q=1/w (w designates depth from screen), there is carried out the calculation of S=U′Q, T=V′Q. However, it is arbitrary whether the texture mapping is executed. 
     Further, the pixel processing unit  390  shown in, for example, FIG. 17 is driven (step S 561 ). As mentioned above, the pixel processing unit  390  forms data at respective pixel at inside of the triangular polygon by interpolating data of the respective apex of the triangular polygon. Data of the respective apex are color of material, screen coordinate values and texture coordinate values. Further, data at respective pixel are color of material and texture color. Further, the pixel processing unit  390  draws a display image by using data at respective pixels at inside of the formed triangular polygon. At this occasion, the hidden face erasure is carried out by using the Z buffer. 
     When the above-described processings are executed, the stereo model for expressing a character of a game or the like is rendered as in a normal case, according to the contour drawing model introduced by the contour drawing processing, a portion of a face thereof rearward from the stereo model which is not hidden by the stereo model, is drawn and accordingly, the portion is rendered as a contour line. According to the contour drawing processing, only by introducing the contour drawing model, a processing substantially similar to that in a normal stereo model is executed to thereby enable to simply draw the contour line. In this way, according to the contour drawing processing, a game image attached with a contour line in accordance with operation input can be formed in real time. 
     (3) Contour Drawing Processing (Part 2) 
     Also in the second contour drawing processing, a contour line is attached to a stereo model for expressing a character of a game or the like. 
     An explanation will be given of an outline of the second contour drawing processing in reference to a functional block diagram of FIG. 29. A game apparatus according to the second contour drawing processing includes an operation input unit  700 , a game progressing unit  770  including a character action determining unit  775 , a game progress situation setting unit  780  including a character direction setting unit  783  and a view axis direction setting unit  787 , an arranging matrix setting unit  720 , a stereo model processing unit  740 , a contour drawing model acquiring unit  710 , a contour drawing model processing unit  730  receiving an arranging matrix from the arranging matrix setting unit  720  and including a reversed head and tail determining unit  735 , a blur expression texture mapping unit  750 , a pixel processing unit  760  receiving data from the blur expression texture mapping unit  750  and the stereo model processing unit  740  and including hidden face erasure processing unit  765  and an image display control unit  790 . 
     The operation input unit  700  outputs operation information of button, lever or the like of the operation input unit  700  operated by a player of a game to the game progressing unit  770 . 
     The game progressing unit  770  determines content of progressing the game such as action of a character, a change in a view point position, a change in a direction of a view axis, or movement of a position of a light source, a change in a direction of light ray or the like based on the information from the operation input unit  700  and gives instruction to the game progress situation setting unit  780 . The character action determining unit  775  in the game processing unit  770  is provided with a function of particularly determining action of a character based on the information from the operation input unit  700 . 
     The game progress situation setting unit  780  calculates and sets a position, a direction and a shape of the character, the position of the view point or the direction of the view axis, the position of the light source, the direction of the light ray and an increase or a decrease of physical strength in accordance with the action of the character or the like in accordance with the content of progressing the game instructed by the game progressing unit  770 . The character direction setting unit  783  in the game progress situation setting unit  780  is provided with a function of particularly determining a direction with regard to a view point of the character in accordance with the content of progressing the game instructed by the game progressing unit  770 . Meanwhile, the view axis direction setting unit  787  in the game progress situation setting unit  780  is provided with a function of particularly setting the direction of the view axis in accordance with the content of progressing the game instructed by the game progressing unit  770 . 
     The arranging matrix setting unit  720  carries out a processing of determining an arranging matrix of a stereo model for expressing the character in accordance with position coordinates and a direction of the character and the position of the view point set by the game progress situation setting unit  780 . The arranging matrix is a matrix for executing parallel movement, rotation and perspective view conversion of the stereo model. 
     When a contour drawing model which is large relative to the stereo model is acquired and a reference position of the contour drawing model is present at a position in correspondence with a reference position of the stereo model, the arranging matrix determined by the arranging matrix setting unit  720  can commonly be used by the stereo model processing unit  740  and the contour drawing model processing unit  730 . When the arranging matrix can commonly be used, one storing area for the arranging matrix may be prepared for respective character and therefore, the operation is efficient. 
     However, there also is a case in which the arranging matrix is not commonly used or cannot be commonly used. In that case, an arranging matrix of the stereo model and an arranging matrix of the contour drawing model are formed and respectively stored to storing areas. Further, when the arranging matrix cannot commonly be used as described later, there also is a case in which one storing area of an arranging matrix is prepared, immediately before the arranging matrix is used by the stereo model processing unit  740  and the contour drawing model processing unit  730 , a setting operation is carried out such that an arranging matrix of the stereo model includes contraction conversion or an arranging matrix of the contour drawing model includes enlargement conversion. 
     The contour drawing model acquiring unit  710  forms a contour drawing model in correspondence with a stereo model constituted by, for example, a triangular polygon. Further, when the contour drawing model has previously been formed, the contour drawing model acquiring unit  710  reads a contour drawing model which is previously formed and is constituted by a triangular polygon. According to the second contour drawing processing, different from the previously-described contour drawing processing (hereinafter, may be referred to as first contour drawing processing), head and tail of respective polygon of the acquired contour drawing model is the same as that of a polygon in correspondence with the stereo model. Further, the contour drawing model is larger than the stereo model and is defined by predetermined coloring for a contour line. Further, although the contour drawing model must finally be large relative to the stereo model, there is a case in which a size of an object for drawing a contour at this stage is the same as that of a stereo model. In this case, the contour drawing model is processed to draw to be large relative to the stereo model before the contour drawing model and the stereo model are drawn. 
     Further, there also is a case in which color of the contour drawing model succeeds color of material of a corresponding stereo model as it is. In this case, color for drawing is separately designated. The reference position of the contour drawing model is normally defined to dispose at the reference position of the corresponding stereo model or at a vicinity thereof. For example, FIG. 30 shows a case in which a contour drawing model  610  is defined to be larger than a stereo model  600 . According to FIG. 30, arrow mark directions of respective faces thereof designate head faces. Outer sides of respective faces in a hexagonal shape of both of the stereo model  600  and the contour drawing model  610 , constitute head faces. 
     Both of a stereo model reference position  620  constituting the reference position of the stereo model  600  and a contour drawing model reference position  630  constituting the reference position of the contour drawing model  610  are defined at centers of the respective models. Further, the contour drawing model  610  is defined to be larger than the stereo model  600  centering on the contour drawing model reference position  630 . 
     The contour drawing model processing unit  730  executes apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) with regard to respective apexes of the contour drawing model by using the arranging matrix by the arranging matrix setting unit  720  and executes head and tail determination of the respective polygon of the contour drawing model. However, different from the above-described contour drawing processing, the head and tail determination is carried out by the reversed head and tail determining unit  735 . Further, in this case, light source calculation is not executed. For example, in the case in which the contour drawing model having a size the same as that of the stereo model is acquired at the contour drawing model acquiring unit  710 , the contour drawing model processing unit  730  executes apex conversion for enlarging the contour line drawing model. Also in the case of enlarging the contour line drawing model at this stage, the relationship between the stereo model and the contour drawing model is as shown by FIG.  30 . 
     Further, in the case of the contour drawing model of the second contour drawing processing, a determination reference in determining a surface and a rear face with regard to respective faces of the contour drawing model is reversed. For example, consider a case in which as shown by FIG. 25, when a surface of a polygon is viewed from a camera, apex numbers are attached to apexes of respective polygon such that apex numbers of the respective apexes constitute the counterclockwise direction. In this case, according to a head and tail determination with regard to a model other than the contour drawing model, when the polygon is viewed from the camera, in the case in which the order of the apex numbers are distributed in the counterclockwise direction, it is determined that the polygon directs the surface to the camera. Meanwhile, according to the head and tail determination with regard to the contour drawing model, when the polygon is viewed from the camera, in the case in which the order of the apex numbers are distributed in the clockwise direction, it is determined that the polygon directs the surface to the camera. In the example of FIG. 30, only faces  613 ,  614 ,  615  and  616  directing arrow marks in directions the same camera  650  as the direction of a view line  640  constitute drawing objects. Although these faces are normally out of drawing objects since the faces are tail faces, according to the second contour drawing processing, these faces are dealt with as the drawing objects. Thereby, faces  611  and  612  disposed on outer sides of the stereo model  600  and proximate to a camera  650  are out of drawing objects and accordingly, the stereo model  600  is normally drawn. Further, when a direction from the stereo model  600  of the camera  650  is made positive, it is known that with regard to a face of the contour drawing model constituting a drawing object, an outer side thereof (direction of head face) is a face directed in a negative direction. Further, hidden face erasure is carried out by the hidden face erasure processing unit  765  of the pixel processing unit  760  and accordingly, even when faces constitute drawing objects, all of the faces are not drawn. 
     The blur expression texture mapping unit  750  executes a processing for mapping blurred expression texture for the contour drawing model such that a contour drawing which is drawn as a result constitutes a blurred line. Further, it is not necessary needed that a contour line is blurred, the processing of the blur expression texture mapping unit  750  is selectively executed. 
     The stereo model processing unit  740  carries out a processing of the stereo model. That is, the stereo model processing unit  740  executes apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) and light source calculation to respective apexes of the stereo model by using the arranging matrix by the arranging matrix setting unit  720  and carries out head and tail determination of respective polygon of the stereo model. When a size of the contour drawing model after having been processed by the contour drawing model processing until  740  is the same as that of the stereo model, the stereo model processing unit  740  executes apex conversion for contracting the size of the stereo model such that the stereo model becomes small relative to the contour drawing model. In this case, also in the case of contracting the size, the relationship between the stereo model and the contour drawing model is as shown by FIG.  30 . 
     Further, head and tail determination of face is carried out similar to normal determination, that is, contrary to the case of the contour drawing model, among faces of the stereo model  600 , faces thereof directing arrow marks in directions the same as the direction of the view line  640  of the camera  650  are excluded from drawing objects. In the example of FIG. 30, faces  603 ,  604 ,  605  and  606  on a rear side in view from the camera  650  are excluded from drawing objects. In this case, there also is carried out a processing for texture mapping of the stereo model as necessary. 
     The pixel processing unit  760  carries out a processing of drawing respective pixels. For example, the pixel processing unit  760  calculates color of the respective pixels at inside of the polygon by interpolating color of apex of the polygon and determines color of the respective pixel while executing hidden face erasure processing using the Z buffer method. The pixel processing unit  760  executes the processing with regard to faces constituting drawing objects at the contour drawing model processing unit  720  and the stereo model processing unit  740 . 
     For example, in the case of FIG. 30, faces  601  and  602  of the stereo model  600  the most proximate to the camera  650  are drawn and the four faces  613 ,  614 ,  615  and  616  of the contour drawing model remote from the camera  650  are drawn. The four face of the contour drawing model  610  are extruded to the left and to the right from the stereo model  600  in view from the camera  650  and accordingly, only extruded portions are drawn without being subjected to hidden face erasure. The extruded portions constitute contour lines. Further, the pixel processing unit  760  determines color in consideration of color of material of the contour drawing model. Further, there also is a case in which the color of the material is totally disregarded and color of the contour line (black or dark color for contour line) constitutes color of the contour drawing model. 
     Finally, the image display control unit  790  designates a drawing area for displaying an image on the display screen written with data by the pixel processing unit  760 . The drawing area is normally classified in two, one of them is used for display and other thereof is used for writing. Further, when writing to the writing area has been finished, the writing area is used to switch to the display area and the display area is used to switch to the writing area. The image display control unit  790  controls the switching operation. 
     (Premise) 
     Also in the second contour drawing processing, there is a case in which data of a contour drawing model is previously formed and stored to CD-ROM  131  and in executing a game, the data is read from CD-ROM  131 . The example of data written to CD-ROM  131  shown by FIG. 19 stays the same also in the second contour drawing processing at a level shown by FIG.  19 . 
     The program area  132  is stored with a program for executing the invention by a computer. A detailed description will be given later of content of the program. 
     The system data area  133  is stored with various data to be processed by the program stored to the program area  132 , mentioned above. The data area  134  is stored with data including the stereo model data  137  and the contour drawing model data  135 . However, when a contour drawing model is formed by a contour drawing model acquiring processing, mentioned later, it is not necessary to store the contour drawing model data  135 . Further, data of texture for expressing blur or the like is also stored to the image data area  134 . 
     The contour drawing model data  135  is previously formed from the stereo model data  137  and is provided with following characteristic. 
     That is, the size of a contour drawing model is defined to be larger than that of a stereo model. For example, according to the contour drawing model, apexes thereof are moved in normal line directions of corresponding respective apexes of the stereo model by a length of 2 percent of a total length of the stereo model and is defined to enlarge by about 2 percent as a whole. When the enlargement rate is larger, the contour line is drawn further boldly and when the enlargement rate is smaller and the contour drawing model is enlarged slightly, the contour line is drawn further finely. Further, when the contour drawing model is defined to enlarge not uniformly but partially, only the contour line at the further enlarged portion is drawn boldly. Adjustment of the size is normally carried out by a producer and accordingly, the contour line reflecting intention of the producer can be drawn. 
     Color of material of respective polygon of the contour drawing model is set to color having chroma the same as that of the stereo model and brightness lower than that of the stereo model. Further, there also is the case in which all of respective polygons are set to single color such as black. Further, there also is the case in which a setting is carried out for mapping texture for expressing blur. Color of material is adjusted by the producer and therefore, the contour line can be drawn by color intended by the producer. Further, head and tail of respective polygon of the contour drawing model in the second contour drawing processing is not reverted. This is a point different from the above-described contour drawing processing. 
     Further, the size of the contour drawing model may be defined to be a size the same as that of the corresponding stereo model. In this case, after acquiring the contour drawing model acquiring processing, mentioned later, the contour drawing model is enlarged during a time period until an arranging matrix of the contour drawing model is set by a contour drawing model arranging processing, mentioned later. Or, the arranging matrix may be determined such that when the arranging matrix of the contour drawing model is set by the contour drawing model arranging processing, the arranging matrix includes enlargement conversion. Conversely, the arranging matrix of the stereo model may be determined such that when the stereo model is arranged, the arranging matrix of the stereo model includes contraction conversion. 
     Further, color of material of respective polygon of the contour drawing model may be the same as color of material of respective polygon of the corresponding stereo model. In this case, in the processing of drawing the contour drawing model, mentioned later, for example, the contour drawing model is drawn by separately defined color such as black. 
     The sound data  136  is stored with data for outputting sound. Further, the sound processing is not directly related to the invention and accordingly, it is not necessary to store data to the sound data area  136 . 
     Next, an explanation will be given of a processing flow of the second contour drawing processing. 
     (Total Processing Flow) 
     The processing flow at the level shown by FIG. 4 stays the same with that in the second contour drawing processing. When a game is started, initial setting is carried out (step S 2 ). In a processing of the initial setting, there is included a processing of acquiring data of a stereo model for expressing a character to be drawn. Further, there also is included a processing of acquiring data of a contour drawing model. Next, there is carried out operation of button, lever or the like of the operation input portion  700  by a player of the game (step S 3 ). Further, based on information of the operation input at step S 3 , there is carried out a game progress processing for determining content of progressing the game such as action of a character in which, for example, the character moves to the left or the character attacks or the like, a change in a view point position, a change in a direction of a view axis, or movement of a light source position, a change in a direction of light ray or the like (step S 4 ). 
     Thereafter, in accordance with the content of progressing the game determined at step S 4 , there is carried out a game progress situation setting processing for setting a position, a direction and a shape of the character, the position of the view point or the direction of the view axis, the position of the light source or the direction of the light ray, further, an increase or a decrease of physical strength in accordance with action of the character and the like (step S 5 ). Next, there is carried out a game image drawing processing for drawing a game image in accordance with the game progress situation (step S 6 ). A detailed description will be given later of the game image drawing processing. 
     Further, there is carried out a game image display processing for displaying the game image drawn by the game image drawing processing at step S 6  (step S 7 ). 
     Next, it is determined whether the game is over (step S 8 ). At the game progress situation setting processing executed in accordance with the operation input at step S 3  (step S 5 ), when physical strength of a self character operated by the player of the game is reduced and set to 0, a condition of game over is satisfied. At step S 8 , the physical strength of the self character operated by the player of the game is inspected and it is determined whether the game is over. When the physical strength of the self character is not 0, the operation returns to step S 3  and awaits for successive operation input. Meanwhile, when the game is over, the game is finished. Further, even after the game is over, a result thereof is displayed on the display screen at step S 7  and accordingly, the player can grasp the final situation of the game from the display screen. 
     Further, the processing flow expressing the outline of the game image drawing processing (step S 6  (FIG.  4 )) shown by FIG. 20 stays the same as that of the second contour drawing processing at the level shown by FIG.  20 . There is carried out a background model drawing processing for drawing a background model for expressing a background portion in the game image (step S 22 ). The drawing processing is the same as the conventional drawing processing and accordingly, a detailed description will not be given here. Further, the following steps S 24  through S 27  are repeated until all of characters have been drawn (step S 23 ). 
     A first one of the repeated steps is a step of executing a deformation processing for deforming an unprocessed character (step S 24 ). Motion of the unprocessed character is determined by the game progress processing at step S 4  in accordance with the operation input executed at step S 3  of FIG.  4 . Further, there is executed a processing of deforming the stereo model for expressing the unprocessed character set by the game progress situation setting processing at step S 6  executed further in accordance therewith. Further, in the second contour drawing processing, in accordance with the processing of deforming the stereo model, a processing of deforming the contour drawing model is also executed. 
     A second one of the repeated steps is a step of setting an arranging matrix of the unprocessed character (step S 25 ). The arranging matrix is a matrix for parallel movement, rotation and perspective view conversion of the stereo model expressing the unprocessed character and is formed based on position coordinates and a direction of the character and the position of the view point set by the game progress situation setting processing at step S 5 . As described above, when the contour drawing mode is already defined to be large relative to the stereo model and the reference position of the contour drawing model is the same as the reference position of the stereo model, the arranging matrix of the stereo model can also be used for the contour drawing model. When the condition is not satisfied, arranging matrices may be set to respectives of the stereo model and the contour drawing model. Further, there also is the case in which an arranging matrix including enlargement conversion is set to the contour drawing model in the contour drawing model drawing processing, mentioned later, further, there also is the case in which an arranging matrix including contraction conversion is set to the stereo model in the stereo model drawing processing. 
     Further, a third one of the repeated steps is a step of executing a contour drawing model drawing processing for drawing the contour drawing model (step S 26 ). A detailed description will be given later of the contour drawing model drawing processing. 
     A fourth one of the repeated steps is a step of executing a stereo model drawing processing for drawing the stereo model for expressing the unprocessed character (step S 27 ). A detailed description will be given later of the stereo model drawing processing. 
     After all of the characters have been drawn, there is carried out a window drawing processing for drawing a window for displaying capability of the character or the like to a user (step S 28 ). The window drawing processing is the same as conventional drawing processing and accordingly, a detailed description will not be given here. 
     The structure of the character data explained in reference to FIG. 21 stays the same as that of the first contour drawing processing and includes a numerical value of maximum physical strength  10 , a numerical value of current physical strength  12 , a numerical value of attack force  14 , a numerical value of defence force  16 , coordinates (x, y, z) of the reference position  18 , rotational angles around X, Y, Z axes constituting direction  20  of the character, pointer  22  to motion data, pointer  24  to model data of the stereo model and point  26  to model data of the contour drawing model. The model data of the contour drawing model differs from that of the first contour drawing processing as explained in the second contour drawing processing (premise). 
     Next, an explanation will be given of a simple example with regard to progress of a game story in accordance with operation input of the player of the game (FIG.  7  and FIG.  8 ). 
     FIG. 7 shows the example of the display screen  120  for displaying an image of a game for progressing the story by making the character fight against enemy character in a virtual three-dimensional space by operating the self character C 101  by the player of the game. In this case, the image of the self character C 101  from the right front direction is displayed. On the left side of the screen, the enemy character  1  (C 111 ) and the enemy character  2  (C 113 ) emerge. 
     At this occasion, the position of the view point is determined by the game progress situation setting processing (step S 5 ) in accordance with the positional relationship between the self character and the enemy character and the direction of the self character. Further, with regard to the respective characters, from the position of the view point, non-photorealistic images attached with contour lines are formed to the characters and displayed on the display screen  120 . 
     In accordance with the operation input of the player from the operation input unit  700  (FIG.  29 ), the self character attacks the enemy character. Meanwhile, the enemy character attacks the self character in accordance with the predetermined algorism. 
     FIG. 8 shows the display screen  120  when the player of the game moves the self character C 101  in the left direction of the display screen by operating the operation input unit  700 . 
     Action of the character of (move in the left direction of the display screen) is determined by the game progress processing (step S 4  of FIG. 4) in response to the operation input. In accordance with the action of the character, the direction, the position and the shape of the character are determined by the game progress situation setting processing (step S 5  of FIG.  4 ). In the example of FIG. 8, the direction of the character is determined to the left direction relative to the display screen and the position of the character is moved similarly in the left direction relative to the display screen. Further, the shape of the character is set with a shape for expressing running motion. 
     In this way, even when the game progress situation of the direction, the position or the like of the character is changed, the contour line is drawn to the character. 
     (Contour Drawing Model Acquiring Processing) 
     The processing of acquiring the contour drawing model included in the initial set (step S 2 ) of FIG. 4 is shown in FIG.  31 . Here, firstly, it is determined whether the contour drawing model is to be formed (step S 223 ). The reason is that there are present a case of previously preparing the contour drawing model and a case of forming the contour drawing model at this stage. The determination is executed by determining whether the contour drawing model in correspondence with the stereo model is stored to CD-ROM  131 . When it is determined that the contour drawing model is stored thereto, it is determined that the contour drawing model is not formed and when it is determined that the contour drawing model is not stored thereto, it is determined that the contour drawing model is formed. 
     When it is determined that the contour drawing model is not formed, data of the contour drawing model stored to CD-ROM  131  is read (step S 277 ). According to respective polygon of the contour drawing model, as explained above in reference to FIG. 30, different from the first contour drawing processing, head and tail thereof is the same as that of the corresponding polygon of the stereo model. Further, the size of the read contour drawing model is defined to be larger than that of the stereo model. Further, color of the contour drawing model is defined by color darker than that of the corresponding stereo model. 
     When it is determined that the contour drawing model is formed, there is carried out a processing of forming the contour drawing model (step S 225 ). Similar to step S 227 , also when the contour drawing model is formed at this stage, according to the respective polygon of the contour drawing model, head and tail thereof is made to be the same as that of the corresponding polygon of the stereo model (refer to FIG.  30 ). 
     The size of the contour drawing model is formed to be larger than that of the corresponding stereo model. For example, there is formed, for example, the contour drawing model apexes of which are moved to enlarge in normal line directions of respective apexes of the stereo model. When the contour drawing model is larger than the stereo model, the contour line is drawn further boldly and when the contour drawing model is slightly larger than the stereo model, the contour line is drawn further finely. 
     Further, there may be formed the contour drawing model which is enlarged by moving faces of the stereo model in normal line directions of the respective faces. Further, there may be formed the contour drawing model which is enlarged by moving respective apexes of the stereo model centering on the reference position normally defined in the stereo model. 
     Further, at this time point, the size of the contour drawing model may be formed by a size the same as a size of the corresponding stereo model. In this case, after acquiring the contour drawing model by the contour drawing model acquiring processing, the contour drawing model is enlarged during a time period until the arranging matrix of the contour drawing model is set by the contour drawing model arranging processing, mentioned later. Or, when the arranging matrix of the contour drawing model is set by the contour drawing model arranging processing, the arranging matrix may be determined to include enlargement conversion thereof. Conversely, when the stereo model is arranged, the arranging matrix of the stereo model may be determined such that the arranging matrix of the stereo model includes contraction conversion. 
     Meanwhile, color of material of respective polygon of the contour drawing model is formed by color which is darker than color of material of the respective polygon of the corresponding stereo model. Further, at this time point, color of the formed contour drawing model may not be defined. Or, color of material of the respective polygon of the contour drawing model may be the same as color of material of the respective polygon of the corresponding stereo model. In this case, in the processing of drawing the contour drawing model, color of the contour drawing model is not considered and the contour drawing model is drawn by color separately defined such as black or a color of texture for expressing blur. 
     Next, it is determined whether texture for expressing blur is mapped to the contour drawing model (step S 299 ). When the contour drawing model is formed at step S 225 , the determination is executed based on data of the corresponding stereo model. Meanwhile, when the contour drawing model is read at the step S 227 , the determination is executed based on data of the read contour drawing model. When it is determined that the texture for expressing blur is mapped, texture expressing blur is mapped to the contour drawing model at step S 231 . That is, respective apexes of the polygon are set with texture coordinates (U, V). 
     Further, as described above, the texture for expressing blur is texture having a pattern including a change in brightness or transparency and is a texture shown by, for example, FIG.  23 . When it is determined that the texture for expressing blur is not mapped and when the processing of mapping the texture has been finished, the contour drawing model acquiring processing is finished. 
     (Contour Drawing Model Arranging Processing) 
     The arranging matrix of the stereo model and the contour drawing model for expressing the unprocessed character is set at step S 25  of FIG.  20  and the processing of arranging the contour drawing model is carried out by the arranging matrix. Normally, the reference position of the contour drawing model is provided at a position in correspondence with the reference position of the stereo model. Further, the arranging matrix of the contour drawing model is set such that the reference position of the contour drawing model is arranged at the position of arranging the reference position of the respective model or at a vicinity thereof. 
     In this case, when the direction of the stereo model is changed, there is set the arranging matrix including rotation conversion such that the contour drawing model corresponds thereto. When the shape of the stereo model is changed, the deformation processing is carried out such that the contour drawing model corresponds thereto. 
     When the contour drawing model is provided with the size the same as that of corresponding stereo model at this stage, the contour drawing model is enlarged. Specifically, the arranging matrix of the contour drawing model is set such that respective apexes of the contour drawing model are subjected to enlargement conversion in accordance with a predetermined enlargement rate. Or, conversely, the stereo model may be contracted. That is, in this case, the arranging matrix of the stereo model is set such that respective apexes of the stereo model are subjected to contraction conversion in accordance with a predetermined contraction rate centering on the reference position of the stereo model. 
     Thereby, finally, the relatively large contour drawing model is arranged to include the stereo model. There can also be a case in which the contour drawing model does not completely include the stereo model by relationships of arrangement positions, directions, shapes or the like of the two models. However, even in such a case, the contour line is drawn with regard to included portions. 
     Further, it is not necessarily needed that the arranging matrix is set at this stage but respective elements necessary for apex conversion of arranged coordinates, directions, enlargement and contraction rate or the like may be fixed. Also in this case, actual apex conversion is carried out at a stage of a processing of drawing the respective models. 
     (Contour Drawing Model Drawing Processing) 
     In FIG. 32 expressing a drawing processing flow of the contour drawing model, processings explained below are repeated until all of apexes of the contour drawing model have been processed (step S 523 ). A first one of the repeated processing is apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) with regard to one apex (step S 525 ). Further, with regard to initial two apexes, steps other than S 525 , S 529  and S 531  are not executed. 
     Caution is required here that light source calculation is not executed with regard to the contour drawing model. The reason is that the contour line is not related to a position of a light source and it is useless to carry out light source calculation (depending on cases, there is a case in which color of material of the contour drawing model is finally disregarded). When the size of the contour drawing model is the same as that of the stereo model, there also is a case in which the contour drawing model is subjected to enlargement conversion at this stage in accordance with the arranging matrix set by the arranging processing. 
     Further, a polygon (face) including the apex is subjected to a determining processing of whether the face is a tail face by normal determination reference (step S 527 ). Although normally, only a head face constitutes a drawing object, in the case of the contour drawing model of the second contour drawing processing, the tail face constitutes the drawing object by normal determination reference. In the case of a triangular polygon, the determination of the step is carried out by to which direction a triangular polygon constituted by two apexes processed prior to the apex is directed. 
     As shown by FIG. 25, for example, by the normal determination reference, this side of paper face is defined as head face when respective apexes of a triangular polygon attached with apex numbers in the counterclockwise direction (so-to-speak right hand system). According to the second contour drawing processing, the reference of head and tail determination is reversed and it is determined that this side of paper face is head face when the apex numbers are attached in the clockwise direction. Only a face which is determined as head face by the reverted head and tail determination reference constitutes the drawing object. The reason is that as a result, the head face in the determination reference of second contour drawing processing, is determined as tail face by the normal determination reference. 
     FIG. 33 shows an example of a triangular polygon constituting a determination object. Respective apexes of the triangular polygon shown in FIG. 33 are provided with apex numbers of 0, 1, 2 in an order of upper side, lower left side and lower right side in the drawing. Although in the example of FIG. 33, this side of paper face constitutes head face by the way of attaching the apex numbers, according to the reverted determination reference, this side of paper face constitutes tail face. In the case of tail face by the reverted determination reference, the face is normally head face and accordingly, the face is out of the drawing object. Further, although according to the second contour drawing processing, at this stage, the head and tail determination is carried out, it is also possible to carry out the head and tail determination prior to the stage. 
     When the polygon (face) including the apex is the head face under the normal determination reference, the operation returns to step S 523 . When the polygon (face) including the apex is the tail face under the normal determination reference, there is carried out a processing of determining whether texture expressing blur is mapped (step S 529 ). This signifies texture mapping with regard to the polygon. When the texture expressing the blur is mapped, there is executed a processing of calculating texture coordinates of the texture for expressing the blur (step S 531 ). As texture perspective processing, in this case, by using Q=1/w (“w” designates a depth from the screen), there is carried out calculation of S=U′Q, T=V′Q. When the texture for expressing the blur is not mapped, the operation proceeds to step S 533 . 
     Further, the pixel processing unit  760  shown, for example, by FIG. 31 is driven (step S 533 ). As described above, according to the pixel processing unit  760 , data of respective apexes of a triangular polygon are interpolated and data of respective pixels at inside of the triangular polygon are formed. Data of respective apex are color of material, screen coordinate values and texture coordinate values when step S 531  is executed. Further, data at respective pixel are color of material and pixel color when step S 531  is executed. However, at this time point, it is also possible to set color of the contour line at respective apex by disregarding color of material. Further, it is also possible to set color of respective apex in consideration of color of material. The pixel processing unit  760  draws a display image by using data at respective pixels at inside of the formed triangular polygon. At this occasion, hidden face erasure is carried out by using the Z buffer. 
     (Stereo Model Drawing Processing) 
     The processing of drawing the stereo model is not changed from that of the first contour drawing processing (FIG.  28 ). That is, following processings are repeatedly executed until all of apexes of the stereo model have been processed (step S 553 ). A first one of the repeated processings is apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) and light source calculation with regard to one apex (step S 555 ). When the size of the contour drawing model is the same as the size of the stereo model, there also is a case in which the contour drawing model is relatively enlarged by contracting the stereo model. In this case, contraction conversion is executed at step S 555 . 
     Next, there is executed a processing of determining whether the polygon (face) including the apex is a head face (step S 557 ). According to the determination, it is determined in the case of a triangular polygon by to which direction a triangular polygon constituted by two apexes processed before the apex is directed. When the polygon (face) including the apex is a tail face, the operation returns to step S 553 . When the polygon (face) including the apex is the head face, there is executed a processing of calculating texture coordinates of the apex (step S 559 ). Further, the pixel processing unit  760  shown by, for example, FIG. 31 is driven (step S 561 ). 
     As described above, data at respective pixels at inside of the triangular polygon are formed by interpolating data of the respective apexes of the triangular polygon by the pixel processing unit  760 . Data of the respective apex are color of material, screen coordinate values and texture coordinate values. Data at the respective pixel are color of material and pixel color. Further, the pixel processing unit  760  draws a display image by using data at respective pixels at inside of the formed triangular polygon. At this occasion, hidden face erasure is carried out by using the Z buffer. 
     When the above-described processing is carried out, the stereo model for expressing a character of a game or the like is rendered as in a normal case and according to the contour drawing model introduced by the second contour drawing processing, a portion at inside of a face rearward from the stereo model which is not hidden by the stereo model is drawn and therefore, the portion is rendered as the contour line. According to the second contour drawing processing, the contour line can further simply be drawn by executing a processing substantially similar to that of a normal stereo model only by introducing the contour drawing model and reversing the head and tail determination of the contour drawing model. In this way, according to the second contour drawing processing, a game image attached with a contour line in accordance with operation input can be formed in real time. 
     1. Hardware Constitution 
     Next, FIG. 34 shows an example of a household game machine  1000  for executing a computer program when the invention is implemented by a computer program. The household game machine  1000  includes a household game main body  101  and the household game machine main body  101  includes an operation processing unit  103  connected to an inner bus  119 , a memory  105 , a sound processing unit  109 , a graphics processing unit  111 , a CD-ROM drive  113 , a communication interface  115  and an interface unit  117 . 
     The sound processing unit  109  and the graphics processing unit  111  of the household game machine main body  101  are connected to an output apparatus  121  having a display screen  120 . Further, the CD-ROM drive  113  can be mounted with CD-ROM  131 . The communication interface  115  is connected to a network  151  via a communication medium  141 . The interface unit  117  is connected with a key pad  161  having operation buttons  166 LL,  166 LR,  166 LU,  166 LD,  166 RL,  166 RR,  166 RU and  166 RD and a memory card  171 . 
     The operation processing unit  103  includes CPU, ROM and the like, executes a program stored to CD-ROM  131  and controls the household game machine  1000 . The memory  105  is a work area of the operation processing unit  103 . The memory card  171  is a memory area for holding data referred by a program. When a program executed by the operation processing unit  103  instructs to make sound output, the sound processing unit  109  interprets the instruction and outputs a sound signal to the output apparatus  121 . 
     The graphics processing unit  111  outputs a signal for displaying to the display screen  120  of the output apparatus  121  in accordance with drawing instruction outputted from the operation processing unit  103 . The CD-ROm drive  113  reads programs and data in CD-ROM  131 . The communication interface  115  is connected to the network  151  via the communication medium  141  and communication with other computer is carried out. The interface unit  117  outputs an input from the key pad  161  to the memory  105  and the operation processing unit  103  interprets thereof and executes operation processing. 
     Programs and data according to the invention are initially stored in, for example, CD-ROM  131 . The programs and data are read by the CD-ROM drive  113  in execution and is loaded to the memory  105 . The operation processing unit  103  processes the programs and data according to the invention which are loaded to the memory  105  and outputs drawing instruction to the graphics processing unit  115 . Further, intermediary data is stored to the memory  105 . The graphics processing unit  111  carries out processing in accordance with the drawing instruction from the operation processing unit  103  and outputs a signal for displaying on the display screen  120  of the output apparatus  121 . 
     Next, a detailed explanation will be given of an example of the graphics processing unit  111  shown in FIG. 34 in reference to FIG.  35 . The graphics processing unit  111  includes a bus control unit  201  for exchanging with the inner bus  119 , a geometry calculation unit  207  and a triangle drawing processing unit  205  for exchanging data with the bus control unit  201 , a pixel color processing unit  209  for receiving data from the triangle drawing processing unit  205  and executing a processing, a Z buffer  211  for storing a Z value of respective pixel and used by the pixel color processing unit  209  and a frame buffer  213  for storing data for display screen from the pixel color processing unit  209 . Further, a display signal from the frame buffer  213  is outputted to the output apparatus  121 . 
     The bus control unit  201  of the graphics processing unit  111  receives drawing instruction outputted from the operation processing unit  103  via the inner bus  119  and outputs the drawing instruction to the geometry calculation unit  207  or the triangle drawing processing unit  205  in the graphics processing unit  111 . Depending on cases, the bus control unit  201  also carries out a processing for outputting an output of the geometry calculation unit  207  or the triangle drawing processing unit  205  to the memory  105  via the inner bus  119 . The geometry calculation unit  207  executes geometrical operation of coordinate transformation, light source calculation, rotation, contraction, enlargement or the like. The geometry calculation unit  207  outputs a result of geometrical operation to the triangle drawing processing unit  205 . 
     The triangle drawing processing unit  205  interpolates data of respective apexes of a triangular polygon and forms data at the respective points at inside of the triangular polygon. The pixel color processing unit  209  writes a display image to the frame buffer  213  by using data at respective points at inside of the triangular polygon formed by the triangle drawing processing unit  205 . At this occasion, hidden face erasure is carried out by using the Z buffer  211 . According to the invention, particularly, the triangle drawing processing unit  205  forms an a value expressing transparency with regard to the respective point at inside of the triangular polygon and therefore, the pixel color processing unit  209  executes also a processing of storing color at the point to a predetermined position of the frame buffer  213  only when the α value falls in a constant range. 
     For example, when the operation processing unit  103  outputs drawing instruction for carrying out perspective view conversion and light source calculation to the graphics processing unit  111  with information with regard to a position and color of respective apex of the triangular polygon in the world coordinate system and light source as data, following processing are executed in the graphic processing unit  111 . 
     The bus control unit  201  received with the drawing instruction, outputs the instruction to the geometry calculation unit  207 . The geometry calculation unit  207  executes perspective view conversion and light source calculation and calculates a coordinate value (including Z value) in the screen coordinate system and color of the respective apex of the triangular polygon. The geometry calculation unit  207  outputs a result of the calculation to the triangle drawing processing unit  205 . The triangle drawing processing unit  205  calculates the coordinate value (including Z value) at the respective pixel at inside of the triangular polygon by using the coordinate value (including Z value) and color at the respective apex of the triangular polygon. Further, the triangle drawing processing unit  205  outputs the coordinate value (including Z value) and color at the respective pixel to the pixel color processing unit  209 . 
     The pixel color processing unit  209  reads current Z value of the pixel from the Z buffer  211  and compares the current Z value with the Z value outputted from the triangle drawing processing unit  205 . When the outputted Z value is smaller than the current Z value, the pixel processing unit  209  stores the outputted Z value at a store position in the Z buffer  211  in correspondence with the pixel and stores color of the pixel at a store position in the frame buffer  213  in correspondence with the coordinate value of the pixel. 
     Respective embodiments shown below are executed by the household game machine  1000  shown by FIG.  34 . 
     2. Embodiment 1 
     Embodiment 1 is a combination of the cel animation tone coloring processing and the first contour drawing processing. That is, as an example of a game image in the cel animation tone, a stereo model for expressing a character of a game or the like is attached with a contour line and colored in the cel animation tone. 
     As shown by FIG. 36, a game apparatus according to Embodiment 1 includes an operation input unit  840 , a game progressing unit  810  including a character action determining unit  815 , a game progress situation setting unit  880  including a character direction setting unit  883  and a view axis direction setting unit  887 , an arranging matrix setting unit  850 , a stereo model processing unit  860  including an apex conversion and light source calculating unit  862 , a brightness calculating unit  864 , a drawing color supplying unit  866 , a brightness range table  865  and a brightness setting unit  868 , a contour drawing model acquiring unit  800 , a contour drawing model processing unit  820  receiving an arranging matrix from the arranging matrix setting unit  850 , a blur expression texture mapping unit  830 , a pixel processing unit  870  receiving data from the stereo model processing unit  860  and the blur expression texture mapping unit  830  and including a hidden face erasure processing unit  873  and a brightness comparing unit  877  and an image display control unit  890 . 
     The operation input unit  840  is realized by, for example, the key pad  161  and the interface unit  117  of FIG.  34 . The operation input unit  840  outputs operation information of button, lever or the like of the operation input unit  840  operated by a player of a game to the game progressing unit  810 . 
     The game progressing unit  810  determines content of progressing the game such as action of a character, a change in a view point position, a change in a direction of a view axis, or movement of a position of a light source, a change in a direction of light ray or the like based on the information from the operation input unit  840  and gives instruction to the game progress situation setting unit. The character action determining unit  815  at inside of the game progressing unit  810  is provided with a function of particularly determining the action of the character based on the information from the operation input unit  840 . 
     The game progress situation setting unit  880  calculates and sets a position, a direction and a shape of the character and the position of the view point or the direction of the view axis, the position of the light source, the direction of the light ray and an increase or a decrease of physical strength in accordance with the action of the character or the like in accordance with the content of progressing the game instructed by the game progressing unit  810 . The character direction setting unit  883  at inside of the game progress situation setting unit  880  is provided with a function of particularly determining the direction with respect to the view point of the character in accordance with the content of progressing the game instructed by the game progressing unit  810 . Meanwhile, the view axis direction setting unit  887  at inside of the game progress situation setting unit  880  is provided with a function of particularly setting the direction of the view axis in accordance with the content of progressing the game instructed by the game progressing unit  810 . 
     The arranging matrix setting unit  850  executes a processing of determining an arranging matrix of a stereo model for expressing a character in accordance with position coordinates and a direction of the character and the position of the view point set by the game progress situation setting unit  880 . The arranging matrix is a matrix for executing parallel movement, rotation and perspective view conversion of the stereo model. 
     When a contour drawing model which is large relative to the stereo model is acquired and a reference position of the contour drawing model is present at a position in correspondence with a reference position of the stereo model, the arranging matrix determined by the arranging matrix setting unit  850  can commonly be used by the stereo model processing unit  860  and the contour drawing model processing unit  820 . When the arranging matrix can commonly be used, one store area for the arranging matrix may ba prepared for the respective character and accordingly, the operation is efficient. 
     However, there also is a case in which the arranging matrix is not commonly used or cannot commonly be used. In that case, an arranging matrix of the stereo model and an arranging matrix of the contour drawing model are formed and respectively stored to store areas. Further, when the arranging matrix cannot commonly be used as mentioned later, there also is the case in which one store area of an arranging matrix is prepared, immediately before using the arranging matrix in the stereo model processing unit  860  and the contour drawing model processing unit  820 , a setting operation is carried out such that the arranging matrix of the stereo model includes contraction conversion or the arranging matrix of the contour drawing model includes enlargement conversion. 
     The contour drawing model acquiring unit  800  forms the contour drawing model in correspondence with the stereo model constituted by, for example, a triangular polygon. When the contour drawing model is previously formed, the contour drawing model acquiring unit  800  reads the contour drawing model which is previously formed and constituted by the triangular polygon. Further, according to respective polygon of the acquired contour model drawing model, head and tail thereof is reverse to that of corresponding polygon of the stereo model. Further, the contour drawing model is larger than the stereo model and is defined by predetermined coloring for a contour line. Further, although the contour drawing model must be large relative to the corresponding stereo model, there also is a case in which a size of the contour drawing model at this stage is the same as that of the stereo model. In this case, the contour drawing model is processed to be drawn to be large relative to the stereo model until the contour drawing model and the stereo model are drawn. Further, there also is a case in which color of the contour drawing model succeeds color of material of the corresponding stereo model as it is. In this case, color for drawing is separately designated. 
     The contour drawing model processing unit  820  executes apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) with regard to the respective apex of the contour drawing model by using the arranging matrix by the arranging matrix setting unit  850  and executes head and tail determination of the respective polygon of the contour drawing model. In the apex conversion, there is used the arranging matrix, mentioned above. Further, in this case, light source calculation is not executed. When the contour drawing model acquiring unit  100  acquires the contour drawing model having a size the same as that of the stereo model, the contour drawing model processing unit  820  executes apex conversion for enlarging the size of the contour line drawing model. 
     The blur expression texture mapping unit  830  executes a processing for mapping blur expression texture in the contour drawing model such that a drawn contour line becomes a blurred line as a result. The blur expression texture is a texture having a pattern including a change in brightness or transparency (refer to FIG.  23 ). Further, it is not necessarily needed that the contour line is blurred and accordingly, the processing of the blur expression texture mapping unit  830  is selectively executed. 
     The stereo model processing unit  860  executes a processing for providing coloring in the cel animation tone to the stereo model as an example of non-photorealistic rendering in cooperation with the pixel processing unit  870 . 
     The apex conversion and light source calculating unit  862  of the stereo model processing unit  860  executes apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) with regard to respective apex of the triangular polygon constituting the stereo model arranged in a virtual three-dimensional space by using the arranging matrix by the arranging matrix setting unit  850  and executes light source calculation with regard to the respective apex of the triangular polygon subjected to apex conversion. 
     Further, the apex conversion and the light source calculating unit  862  of the stereo model processing unit  860  also carries out head and tail determination of the respective triangular polygon of the stereo model. Only a face directing a head face to the view point constitutes a drawing object. 
     The brightness calculating unit  864  of the stereo model processing unit  860  calculates brightness from color of the respective apex of the triangular polygon calculated by the apex conversion and the light source calculating unit  862 . Normally, the apex conversion and the light source calculating unit  862  calculates color in the RGB system and therefore, the brightness calculating unit  864  calculates brightness Y by converting RGB into YIQ. The brightness of the respective apex of the triangular polygon is outputted to the pixel processing unit  870 . 
     The brightness range table  865  is a table shown by, for example, FIG.  2  and is held in, for example, the memory  105 . That is, the table paired with a threshold and reference brightness are set to three stages (levels) in this case such that a threshold 0.75 versus reference brightness 0.75, a threshold 0.5 versus reference brightness 0.50 and a threshold 0.00 versus reference brightness 0.25. Further, in this case, the brightness is provided with a real number value from 0 to 1. A range by an upper limit and a lower limit may be designated in place of the threshold (for example, refer to FIG. 3 ). 
     In reference to the brightness range table  865 , the drawing color supplying unit  866  calculates drawing color in correspondence with the threshold. The drawing color in correspondence with the respective threshold is calculated by the reference brightness in correspondence with the threshold and information of color previously set to the respective triangular polygon of the stereo model. The drawing color supplying unit  866  outputs the calculated drawing color to the pixel processing unit  870 . 
     Further, the drawing color supplying unit  866  may calculate the drawing color in execution, or may calculate drawing color previously and store the data. For example, when the brightness range table as shown by, for example, FIG. 2 is used, it is necessary to store three drawing color data of the respective polygon. For example, refer to FIG.  16 . 
     The brightness range setting unit  868  selects one threshold of the brightness range table  865  and sets the threshold to the pixel processing unit  870 . When the brightness range table  865  as shown by FIG. 2 is used as it is, the brightness range setting unit  868  sets the threshold one by one in turn from upper columns. When the range by the upper limit and the lower limit is designated in place of the threshold, the threshold can be selected and set at random. 
     When the triangular polygon constituting the drawing object of the contour drawing model is processed, the pixel processing unit  870  determines color of the respective pixel in the triangular polygon constituting the drawing object of the contour drawing model while executing the hidden face erasure processing by using the hidden face erasure processing unit  873  and outputs the color to the frame buffer  213 . 
     Meanwhile, when the triangular polygon constituting the drawing object of the stereo model is processed, the pixel processing unit  870  firstly interpolates brightness at the respective apex of the triangular polygon outputted from the brightness calculating unit  864  and calculates brightness (brightness distribution in polygon) of the respective pixel at inside of the polygon. The calculation is carried out by, for example, the triangle processing unit  205  of FIG.  35 . 
     Further, the brightness comparing unit  877  compares the brightness at the respective pixel with the threshold set by the brightness range setting unit  868 . When the brightness at the pixel is equal to or larger than the threshold, the pixel processing unit  870  stores the pixel to the frame buffer  213  by drawing color based on the reference brightness in correspondence with the threshold. In the case of the drawing processing, the hidden face erasure processing is executed by using the hidden face erasure processing unit  873 . When the brightness of the pixel is less than the threshold, the pixel is not stored to the frame buffer  213  at the stage. The drawing processing including the comparing processing is carried out by, for example, the pixel color processing unit  209  of FIG.  35 . When the brightness range setting unit  868  sets all the thresholds of the brightness range table  865  to the pixel processing unit  870  and the pixel processing unit  870  executes a drawing processing with regard to all the pixels in the triangular polygon in correspondence therewith, inside of the polygon is painted to classify in three stages according to the example of FIG.  2 . The processing is carried out with regard to all the triangular polygons of the stereo model. 
     According to the invention, there is a case in which hidden face erasure by the Z buffer  211  is utilized. Because, for example, when the stereo model is formed in a shape of a human being and the arm is disposed in front of the body, there is a case in which it is difficult to draw an accurate contour line when the Z buffer method is not used in view of a positional relationship between a face of the contour drawing object and a face of the stereo model. 
     In addition thereto, when the brightness range table  865  as shown by FIG. 2 is used as it is in the stereo model acquiring unit  860  and the pixel processing unit  870 , the hidden face erasure by the Z buffer  211  is utilized. For example, in accordance with FIG. 2, the brightness which is equal to or larger than 0.75 is also equal to or larger than 0.5 and also equal to or larger than 0.0 and accordingly, it is necessary to set an upper limit value of the brightness range such that the drawing color is not painted overlappingly. When the brightness of a certain pixel is equal to or larger than 0.75, the pixel is drawn by drawing color in correspondence with the threshold 0.75 and the Z value of the pixel is stored to the Z buffer  211 . 
     When the threshold becomes 0.5, the Z value of the pixel is read from the Z buffer  211  and is compared with the Z value of the same pixel to be written, however, naturally, these are the same and accordingly, the drawing color in correspondence with the threshold 0.5 is not written to the frame buffer  213  with regard to the pixel. The same goes with the threshold 0.0. 
     Further, the brightness at the apex of the polygon and the pixel at inside of the polygon, is normally dealt with as an attribute value of color (RGB) referred to as a used as transparency. Normally, the a value is defined in a range of 0-255 and accordingly, there is used an actual a value multiplied by brightness by 255. Therefore, the threshold (upper limit and lower limit values) of the brightness range table  865  may be a value in a range of 0-255. 
     Finally, the image display control unit  890  designates an area of the frame buffer to which the pixel processing unit  870  writes data for displaying on the display screen. The frame buffer is normally provided with two areas, one is used for display and other is used for writing. Further, when writing to the writing area has been finished, the writing area is used to switch to the display area and the display area is used to switch to the writing area. The image display control unit  890  controls the switching operation. 
     (Premise) 
     Also in Embodiment 1, there is a case in which data of the contour drawing model is previously formed and stored to CD-ROM  131  and the data is read from CD-ROM  131  in executing game. The example of data written to CD-ROM  131  shown by. FIG. 19 is the same as in Embodiment 1 at the level shown by FIG.  19 . 
     The program area  132  is stored with a program for executing the invention by the household game machine  1000 . A detailed description will be given of data of the content of the program. 
     The system data area  133  is stored with various data processed by the program stored to the program area  132 , mentioned above. The image data area  134  is stored with data including the stereo model data  137  and the contour drawing model data  135 . However, when the contour drawing model is formed in a contour drawing model acquiring processing, mentioned later, it is not necessary to store the contour drawing model data  135 . Further, data of texture for expressing blur or the like is also stored to the image data area  134 . 
     The contour drawing model data  135  is previously formed from the stereo model data  137  and is provided with following characteristic. 
     That is, the size of the contour drawing model is defined to be larger than that of the stereo model. Further, color of material of the respective polygon of the contour drawing mode is set to color having chroma the same as that of the stereo model and brightness lower than that of the stereo model. Further, there also is the case in which all of respective polygons are set to single color such as black. Further, there also is a case in which a setting for mapping texture for blur expression is carried out. Further, head and tail of the respective polygon of the contour drawing model is reversed. Specifically, the order by which apexes of the respective triangle constituting the contour drawing model is defined, is switched at one location. 
     Further, the size of the contour drawing model may be defined by a size the same as a size of the corresponding stereo model. In this case, after acquiring the contour drawing mode by a contour drawing model acquiring processing, mentioned later, the contour drawing model is enlarged during a time period until the arranging matrix of the contour drawing model is set by a contour drawing model arranging processing, mentioned later. Or, when the arranging matrix of the contour drawing model is set by the contour drawing model arranging processing, the arranging matrix may be determined such that the arranging matrix includes enlargement conversion. Conversely, in arranging the stereo model, the arranging matrix of the stereo model may be determined such that the arranging matrix of the stereo model includes contraction conversion. 
     Further, color of material of respective polygon of the contour drawing model may be the same as color of material of respective polygon of corresponding stereo model. In this case, in a processing of drawing the contour drawing model, mentioned later, for example, the contour drawing model is drawn by separately defined color such as black. 
     The sound data area  136  is stored with data for outputting sound from the sound output apparatus  125  by the sound processing unit  109  shown by FIG.  34 . 
     Next, an explanation will be given of a processing flow with regard to Embodiment 1. The following processing is the processing which the operation processing unit  103  (FIG. 34) executes by controlling other elements in the household game machine main body  101 . 
     (Total Processing Flow) 
     The processing flow at the level shown by FIG. 4 stays the same also in Embodiment 1. When a game is started, initial setting is carried out (step S 2 ). The processing of the initial setting includes a processing of acquiring data of the stereo model expressing a character to be drawn. Further, Embodiment 1 also includes a processing of acquiring data of the contour drawing model. Next, there is carried out operation of button, lever or the like the key pad  161  by a player of the game (step S 3 ). Further, there is carried out a game progress processing of determining content of progressing the game such as action of the character in which the character moves to the left or the character attacks or the like, a change in a view point position, a change in a direction of a view axis, or movement of a light source position, a change in a direction of light ray or the like based on information of the operation input at step S 3  (step S 4 ). 
     Thereafter, in accordance with the content of progressing the game determined at step S 4 , there is carried out a game progress situation setting processing for setting a game progress situation such as a position, a direction and a shape of the character, the position of the view point or the direction of the view axis, the position of the light source or the direction of the light ray and an increase or a decrease in physical strength in accordance with action of the character (step S 5 ). Next, there is carried out a game image drawing processing for writing a game image in accordance with the game progress situation to the frame buffer  213  (step S 6 ). A detailed description will be given later of the game image drawing processing. 
     Further, there is carried out a game image displaying processing for displaying the game image written to the frame buffer  213  by the game image drawing processing at step S 6  (step S 7 ). Normally, the frame buffer  213  is divided in two areas of a writing area and a display area and in this case, there is carried out a processing in which the writing area written with data by the game image drawing processing executed at step S 6  is switched to the display area and the display area is switched to successive writing area. 
     Next, it is determined whether the game is over (step S 8 ). In the game progress situation setting processing executed in accordance with the operation input at step S 3  (step S 5 ), when physical strength of a self character operated by a player of the game is reduced and set to 0, the condition of game over is satisfied. At step S 8 , the physical strength of the self character operated by the player of the game is inspected and it is determined whether the game is over. When the physical strength of the self character is not 0, the operation returns to step S 3  and awaits for successive operation input. Meanwhile, when the game is over, the game is finished. Further, even when the game is over, since a result thereof is displayed on the display screen  120  at step S 7 , the player can grasp a final situation of the game from the display screen  120 . 
     The processing flow showing an outline of the game image drawing processing (step S 6  (FIG.  4 )) shown in FIG. 20 stays the same also in Embodiment 1 at the level shown by FIG.  20 . At first, there is carried out the background model drawing processing for drawing a background model for expressing a background portion in the game image (step S 22 ). The drawing processing is the same as the conventional drawing processing and accordingly, a detailed description will not be given here. Further, the following steps S 24  through S 27  are repeated until all characters are drawn (step S 23 ). 
     A first one of the repeated steps is a step of executing a deformation processing for deforming one unprocessed character (step S 24 ). Motion of the unprocessed character in accordance with the operation input executed at step S 3  of FIG. 4 is determined in the game progress processing at step S 4 . Further, there is executed the deformation processing of the stereo model for expressing the unprocessed character which is set in the game progress situation setting processing at step S 6  executed in accordance therewith. Further, in Embodiment 1, there is also executed a deformation processing of the contour drawing model in accordance with the deformation processing of the stereo model. 
     A second one of the repeated steps is a step of setting an arranging matrix of the unprocessed character (step S 25 ). The arranging matrix is a matrix for parallel movement, rotation and perspective view conversion of the stereo model for expressing the unprocessed character and is formed based on position coordinates and a direction of the character and the position of the view point set by the game progress situation setting processing at step S 5 . As described above, when the contour drawing model is already defined to be large relative to the stereo model and the reference position of the contour drawing model is the same as the reference position of the stereo model, the arranging matrix of the stereo model can be used also in the contour drawing model. When the condition is not satisfied, arranging matrices may be set to respectives of the stereo model and contour drawing model. Further, there also is the case in which there is set an arranging matrix including enlargement conversion with regard to the contour drawing model in the contour drawing model drawing processing, mentioned later. Further, there also is the case in which an arranging matrix including contraction conversion is set to the stereo model in the stereo model drawing processing. 
     Further, a third one of the repeated steps is a step of executing the contour drawing model drawing processing for drawing the contour drawing model (step S 26 ). A description will be given later of the contour drawing model drawing processing. 
     A fourth one of the repeated steps is a step of executing the stereo model drawing processing for drawing the stereo model for expressing the unprocessed character (step S 17 ). A description will be given later of the stereo model drawing processing. 
     After all the characters have been drawn, there is executed the window drawing processing for drawing a window for displaying capability of the character or the like to a user (step S 28 ). The window drawing processing is also the same as the conventional drawing processing and therefore, a detailed description will not be given there. 
     The structure of the character data explained in reference to FIG. 21 stays the same as in the first contour drawing processing and includes a numerical value of maximum physical strength  10 , a numerical value of current physical strength  12 , a numerical value of attack force  14 , a numerical value of defence force  16 , coordinates (x, y, z) of reference position  18 , rotational angles around X, Y and Z axes constituting direction  20  of character, pointer  22  to motion data, pointer  24  to model data of the stereo model and pointer  26  to model data of the contour drawing model. The character data is held, for example, in the memory  105 . Further, for example, when the model data of the stereo model is stored to CD-ROM  131 , the pointer  24  to the model data of the stereo model is a front address of the model data when the model data is read from CD-ROM  131  to the memory  105 . Similarly, for example, when the model data  135  (FIG. 19) of the contour drawing model is stored to CD-ROM  131 , the pointer  26  to the model data of the contour drawing model is a front address of the model data when the model data is read from CD-ROM  131  to the memory  105 . Further, there is a case in which the model data of the contour drawing model is formed in execution and in that case, the front address of the memory  105  stored with the model data of the formed contour drawing model becomes the pointer  26 . 
     Next, an explanation will given of a simple example (FIG.  7  and FIG. 8) with regard to progress of a game story in accordance with the operation input of the player of the game. 
     FIG. 7 shows the example of the display screen  120  displaying an image of the game for progressing a story while making the self character fight against the enemy character in a virtual three-dimensional space by operating the self character C 101  by the player of the game. In this case, there is displayed the image of the self character C 101  from the right front side. On the left side of the display screen, the enemy character  1  (C 111 ) and the enemy character  2  (C 113 ) emerge. 
     In this case, the position of the view point is determined by the game progress situation setting processing (step S 5 ) in accordance with the positional relationship between the self character and the enemy character and the direction of the self character. Further, with regard to the respective characters, from the position of the view point, there are formed non-photorealistic images attached with contour lines and colored in the cel animation tone and the images are displayed on the display screen. 
     In accordance with the operation input of the player from the key pad  161 , the self character attacks the enemy character. Meanwhile, the enemy character attacks the self character in accordance with a predetermined algorism. 
     FIG. 8 shows the display screen  120  when the self character C 101  is moved in the left direction of the display screen by depressing the operation button  161 LL of the key pad  161  by the player of the game. 
     In accordance with the operation input, action of the character of “move in the left direction of the display screen” is determined by the game progress processing (step S 4  of FIG.  4 ). In accordance with the action of the character, the direction, the position and the shape of the character is determined by the game progress situation setting processing (step S 5  of FIG.  4 ). According to the example of FIG. 8, the direction of the character is determined to the left direction relative to the display screen and the position of the character is moved similarly in the left direction relative to the display screen. Further, the shape of the character is set with a shape for expressing running motion. 
     In this way, even when the game progress situation of the direction, the position or the like of the character is changed, the character is drawn as an image in the cel animation tone drawn with the contour line. 
     (Contour Drawing Model Acquiring Processing) 
     The processing of acquiring the contour drawing model shown by FIG. 22 stays the same also in Embodiment 1. Here, firstly, it is determined whether the contour drawing model is to be formed (step S 203 ). Because there are present a case in which the contour drawing model is previously prepared and a case in which the contour drawing model is formed at this stage. The determination is executed by determining, for example, whether the contour drawing model in correspondence with the stereo model is stored to CD-ROM  131 . 
     When it is determined that the contour drawing model is not formed, data of the contour drawing model stored to CD-ROM  131  is read (step S 207 ). According to the respective polygon of the contour drawing model, head and tail thereof is reversed to that of the corresponding polygon of the stereo model. Further, the size of the read contour drawing model is defined to be larger than that of the corresponding stereo model. Further, the color of the contour drawing model is defined by color darker than that of the corresponding stereo model. 
     When it is determined that the contour drawing model is formed, there is carried out the processing of forming the contour drawing model (step S 205 ). Similar to step S 207 , also when the contour drawing model is formed at this stage, according to the respective polygon of the contour drawing model, head and tail thereof is reverse to that of the corresponding polygon of the stereo model. 
     The size of the contour drawing model is formed to be larger than that of the corresponding stereo model. For example, there is formed the contour drawing model which is enlarged by moving apexes thereof in normal line directions of respective apexes of the stereo model. When the contour drawing model is larger than the stereo model, the contour line is drawn further boldly and when the contour drawing model is slightly larger than the stereo model, the contour line is drawn further finely. 
     Further, there may be formed the contour drawing model which is enlarged by moving faces thereof in normal line directions of respective faces of the stereo model. Further, there may be formed the contour drawing model which is enlarged by moving respective apexes of the stereo model centering on the reference position normally defined in the stereo model. 
     Further, at this time point, the contour drawing model may be formed such that the size of the contour drawing model is the same as the size of the corresponding stereo model. In this case, after acquiring the contour drawing model by the contour drawing model acquiring processing, the contour drawing model is enlarged during a time period until the arranging matrix of the contour drawing model is set by the contour drawing model arranging processing, mentioned later. Or, when the arranging matrix of the contour drawing model is set by the contour drawing model arranging processing, the arranging matrix may be determined such that the arranging matrix includes enlargement conversion. Conversely, when the stereo model is arranged, the arranging matrix of the stereo model may be determined such that the arranging matrix of the stereo model includes contraction conversion. 
     Meanwhile, color of material of the respective polygon of the contour drawing model is formed by color darker than color of material of the respective polygon of the corresponding stereo model. Further, at this time point, the color of the formed contour drawing model may not be defined. Or, color of material of the respective polygon of the contour drawing model may be the same as color of material of the respective polygon of the corresponding stereo model. In this case, in the processing of drawing the contour drawing model, color of the contour drawing model is not considered, for example, the contour drawing model is drawn by separately defined color of black or the like or color of texture for expressing blur. 
     Next, it is determined whether texture for expressing blur is mapped in the contour drawing model (step S 209 ). When the contour drawing model is formed at step S 205 , the determination is executed based on data of the corresponding stereo model. Meanwhile, when the contour drawing model is read at step S 207 , the determination is executed based on data of the read contour drawing model. When it is determined that texture for expressing blur is mapped, texture for expressing blur is mapped in the contour drawing model at step S 211 . That is, texture coordinates (U, V) are set at respective apex of the polygon. 
     Further, as described above, texture for expressing blur is provided with a pattern including a change in brightness or transparency. An example shown in FIG. 23 of texture including a change in brightness is provided with a pattern in which white hatched lines are finely drawn in a black matrix. Brightness at the black portion is low, brightness at the white portion is high and accordingly, the texture shown by FIG. 23 includes the change in brightness. Thereby, blur of the contour line is expressed and the contour line further in the hand writing tone is drawn. 
     When it is determined that texture for expressing blur is not mapped and when the processing of mapping the texture has been finished, the operation processing unit  103  finishes the contour drawing model acquiring processing. 
     (Contour drawing model arranging processing) 
     At step S 25  of FIG. 20, the arranging matrix for the stereo model and the contour drawing model for expressing the unprocessed character is set and there is carried out the processing of arranging the contour drawing model by the arranging matrix. The reference position of the contour drawing model is provided at a position in correspondence with the reference position of the stereo model. Further, the arranging matrix of the contour drawing model is set such that the reference position of the contour drawing model is arranged at the reference position of the stereo model or a vicinity thereof. 
     At this occasion, when the direction of the stereo model is changed, the contour drawing model is set with the arranging matrix including rotation conversion in correspondence therewith. When the shape of the stereo model is changed, a deformation processing carried out such that the contour drawing model corresponds therewith. 
     When the contour drawing model is provided with a size the same as that of the stereo model at this stage, the contour drawing model is enlarged. Specifically, the arranging matrix of the contour drawing model is set such that respective apexes of the contour drawing model are subjected to enlargement conversion in accordance with a predetermined enlargement rate centering on the reference position of the contour drawing model. Or, conversely, the stereo model may be contracted. That is, in this case, the arranging matrix of the stereo model is set such that respective apexes of the stereo model are subjected to contraction conversion in accordance with a predetermined contraction rate centering on the reference position of the stereo model. 
     Thereby, finally, the relatively large contour drawing model is arranged to include the stereo model. There can occur also a case in which the contour drawing model does not completely include the stereo model depending on a relationship of arranging positions, directions, shapes or the like of the two models. However, also in such a case, the contour line is drawn with regard to included portions. 
     Further, at this stage, it is not necessarily needed to set the arranging matrix but respective elements necessary for apex conversion of arranged coordinates and direction and enlargement or contraction rate or the like may be fixed. Also in this case, actual apex conversion is executed at the stage of the processing of drawing the respective models. 
     (Contour Drawing Model Drawing Processing) 
     The drawing processing flow of the contour drawing model shown by FIG. 24 can also be used in Embodiment 1. In FIG. 24, processings explained below are repeatedly carried out until all of apexes of the contour drawing model have been processed (step S 503 ). A first one of the repeatedly executed processings is apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) processing with respect to one apex (step S 505 ). Here, the arranging matrix calculated at step S 25  (FIG. 20) is used in the apex conversion. Further, with regard to initial two apexes, steps other than steps S 505 , S 509  and S 511  are not executed. 
     For example, the processing is executed by the geometry calculation unit  207  instructed by the operation processing unit  103 . In this case, the geometry calculation unit  207  does not execute light source calculation with regard to the contour drawing model. When the size of the contour drawing model is the same as that of the stereo model, there also is the case in which in accordance with the arranging matrix set by the arranging processing, at this stage, the contour drawing model is subjected to enlargement conversion. 
     Further, there is carried out the processing of determining whether the polygon (face) including the apex is a head face (step S 507 ). With regard to the head and tail determination, a description has been given in the first contour drawing processing and therefore, an explanation thereof will be omitted. Further, it is also possible to carry out the head and tail determination prior to the stage. 
     Further, when the polygon (face) including the apex is the tail face, the operation returns to step S 503 . When the polygon (face) including the apex is the head face, it is determined whether texture expressing blur is mapped (step S 509 ). 
     This signifies texture mapping with regard to the polygon. When texture expressing blur is mapped, there is calculated texture coordinates of texture for expressing blur with respect to the apex (step S 511 ). When the texture mapping is carried out, the apex of the polygon is already designated with texture coordinates (U, V), however, when the polygon is arranged obliquely to the screen, there is a case in which the texture is displayed to distort on the screen. 
     In order to avoid the distortion, there is carried out texture perspective processing. According to the texture perspective processing, for example, by using Q=1/w (“w” designates a depth from the screen) new texture coordinates (S, V) are calculated. Notations S and V can be calculated by, for example, setting S=U′Q, T=V′Q. The calculated (S, V) are set as texture coordinates in correspondence with apex of the polygon. When texture for expressing blur is not mapped, the operation proceeds to step S 513 . 
     Further, for example, the triangle drawing processing unit  205  and the pixel color processing unit  209  (FIG. 35) included in the pixel processing unit  870  are driven (step S 513 ). As described above, the triangle drawing processing unit  205  interpolates data of respective apex of the triangular polygon and forms data at the respective pixel at inside of the triangular polygon. Data of the respective apex are color of material, screen coordinate values, and texture coordinate values when step S 511  is carried out. Data at the respective pixel are color of material and pixel color when step S 511  is executed. 
     However, it is also possible to set color of the contour line at respective apex by disregarding color of material. Further, it is also possible to set color of the respective apex in consideration of color of material. In either of th cases, color of the contour line is set to color darker than color for drawing the stereo model by the stereo model drawing processing, mentioned later. Further, when the brightness range table as shown by FIG. 2 is used by the stereo model drawing processing, the color of the contour line is set by color darker than color calculated based on the lowest reference brightness 0.25. The pixel color processing unit  209  writes the display image to the frame buffer  213  by using data at the respective pixel of the triangular polygon formed by the triangle drawing processing unit  205 . At this occasion, the hidden face erasure is carried out by using the Z buffer  211 . 
     Although there is shown the example of using the Z buffer  211  in the hidden face erasure, there may be executed a hidden face erasure processing such as the Z sort method in which the Z buffer  211  is not used with regard to a simple model as shown by FIGS. 13A and 13B. However, in the case of a further complicated model in which, for example, the hand of a person is arranged in front of the body or the like, when the hidden face erasure using the Z buffer  211  is not carried out, it is difficult to accurately draw the contour line. 
     (Stereo Model Drawing Processing) 
     The flow of the processing of drawing the stereo model shown in FIG. 9 can also be used in Embodiment 1. First, initial setting is executed (step S 603 ). In the initial setting, a brightness range table in correspondence with the stereo model (for example, FIG. 2 or FIG. 3) is acquired. Next, there is carried out apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) and light source calculation with regard to one apex (step S 605 ). The step is executed by, for example, the geometry calculation unit  207  by instruction from the operation processing unit  103 . Data of the stereo model is stored to, for example, CD-ROM  131  and data previously read by the memory  105  is used. 
     Apex conversion is executed by using the arranging matrix set at step S 25  of FIG.  20 . However, when the contour drawing model is provided with a size the same as that of the stereo model, there also is a case in which the contour drawing model is relatively enlarged by contracting the size of the stereo model. In this case, at step S 605 , contraction conversion is executed. Further, the stereo model can simply be contracted by moving apexes thereof toward center of the stereo model along normal lines thereof. 
     Further, according to light source calculation in the stereo model drawing processing described above in reference to FIG. 9, there are two methods, that is, (A) a method in consideration of color of material defined at the polygon and (B) a method not in consideration of the color of the material and both of them can be used also in Embodiment 1. However, an explanation thereof will be omitted here. 
     Next, it is determined whether the polygon including the apex directs its surface to a camera (step S 607 ). The determination is executed in the case of triangular polygon by to which direction the triangular polygon constituted by the apex and two apexes processed therebefore is directed. In the determination, there can be used the method explained in the processing of drawing the contour drawing model. Further, although according to the stereo model drawing processing, head and tail determination is carried out at this stage, it is also possible to carry out the head and tail determination prior to the stage. 
     When the polygon (face) including apex is tail face, the operation returns to step S 605 . When the polygon (face) including the apex is head face, there is calculated brightness at the apex subjected to apex conversion and light source calculation (step S 609 ). In calculating the brightness, the YIQ conversion is executed. 
     After step S 609 , there is calculated drawing color of the polygon including the apex subjected to apex conversion and light source calculation (step S 611 ). The drawing color of the polygon is calculated from the reference brightness in correspondence with the brightness range stored to the brightness range table and the color of the polygon. 
     When there are three of the reference brightness (Tn) (T 1 , T 2 , T 3 ) three of the drawing color are calculated. Further, when the color of the polygon is not held as color of the YIQ system, that is, when the color of the polygon is held as color of the RGB system, there is executed a calculation of converting from RGB to YIQ by the conversion matrix, shown above. 
     Next, one of the brightness ranges of the brightness range table is selected (step S 613 ). Further, although in Embodiment 1, there is used the brightness range table shown by FIG. 2 is used, the brightness range table as shown by FIG. 3 can also be used. The table is held in, for example, the memory  105 . When such a brightness range table is used, the brightness range including the upper limit and the lower limit can be selected and set at random. When a comparison between the brightness of the respective pixel and the two brightness values of the upper limit and the lower limit cannot simply be carried out in the brightness comparison processing, explained below, the brightness range is selected in turn from upper columns of FIG.  3 . Further, in this case, the processing is carried out only by the lower limit value. 
     Thereafter, the brightness at the apex of the polygon is interpolated, and the brightness (brightness distribution in polygon) at the respective pixel at inside of the polygon is calculated. Although color of the apex is also interpolated, all of the three apexes are provided with the same drawing color and therefore, the result remains the same even after the interpolation. Further, when the brightness at the pixel falls in a selected brightness range, the pixel is drawn by the drawing color in correspondence with the selected brightness range (step S 615 ). The interpolation processing of the brightness and the drawing processing of the respective pixel are executed by, for example, instruction from the calculation processing unit  103  by the triangle drawing processing unit  205  in FIG.  35 . The comparing processing of whether the brightness at the respective pixel falls in the selected brightness range, is executed, for example, by the pixel color processing unit  209 . The steps S 613  and S 615  are repeated until the processing has been carried out with respect to all of the brightness ranges (step S 617 ). 
     For example, when the pixel color processing unit  209  cannot deal with the two brightness values of the upper limit and the lower limit, by also using the Z buffer  211 , the same effect can be achieved. Although the Z buffer  211  is used for hidden face erasure, according to Embodiment 1, by also using the Z buffer  211 , an effect similar to that in the case of comparing with the upper limit value of the brightness is achieved. The processing using the Z buffer is carried out by the pixel color processing unit  209  by, for example, instruction from the calculation processing unit  103 . 
     The above steps S 605  through S 617  are repeated until the processing is carried out with respect to all the apexes of the stereo model and, as a result, are repeated until the processing is carried out with respect to all of the polygons (step S 619 ). 
     (Stereo Model Drawing Processing (Part 2)) 
     The flow of the second stereo model processing shown by FIG. 15 can also be used in Embodiment 1. In FIG. 15, firstly, initial setting is carried out (step S 633 ). According to the initial setting, there is acquired the brightness range table in correspondence with the stereo model (for example, FIG. 2 or FIG.  3 ). Further, the drawing color of the stereo model stored to CD-ROM  131  is read by the memory  105 . Next, there is carried out apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) and light source calculation with regard to one apex (step S 635 ). The step is executed by the geometry calculation unit  207  by instruction from the operation processing unit  103 . Data of the stereo model is stored to, for example, CD-ROM  131  and data previously read by the memory  105  is used. 
     Enlargement, contraction, rotation, parallel movement or perspective conversion is carried out by using the arranging matrix set at step S 25  of FIG.  20 . The step is executed by the geometry calculation unit  207  by instruction from, for example, the calculation processing unit  103 . However, when the contour drawing model is provided with a size the same as that of the stereo model, there is a case in which the contour drawing model is relatively enlarged by contracting the stereo model. In this case, at step S 635 , contraction conversion is executed. Further, the size can simply be contracted by moving respective apexes toward the center of the stereo model along normal lines thereof. 
     Further, the two methods of light calculation described in another stereo model drawing processing are applicable as they are also in the stereo model drawing processing (part 2). 
     Next, it is determined whether the polygon (face) including the apex is head face (step S 637 ). The determination is executed in the case of a triangular polygon by to which direction the triangular polygon constituted by two apexes processed prior to the apex is directed. In the determination, there can be used the method explained in the processing of drawing the contour drawing model. Further, although according to the stereo model drawing processing (part 2), at this stage, head and tail determination is carried out, it is also possible to carry out the head and tail determination prior to the stage. 
     When the polygon (face) including the apex is the tail face, the operation returns to step S 635 . When the polygon (face) including the apex is the head face, there is calculated brightness at the apex subjected to apex conversion and light source calculation (step S 639 ). In calculating the brightness, the YIQ conversion is executed. 
     Further, drawing color of the polygon including the apex subjected to apex conversion and light source calculation is read from the memory  105  (step S 641 ). Although data of the read drawing color is previously calculated, the calculation method in previously calculating the data may be either of the two methods explained in another stereo model drawing processing or may be other method. Further, the drawing color may be defined one by one. 
     Next, one of the brightness ranges of the bright range table is selected (step S 643 ). Further, although according to the embodiment, the brightness range table shown by FIG. 2 is used, the brightness range table as shown by FIG. 3 can also be used. When such a brightness range table is used, the brightness range including the upper limit and the lower limit can be selected and set at random. When the comparison between the brightness of the respective pixel and the two brightness values of the upper limit and the lower limit cannot be simply carried out in the brightness comparing processing, explained below, the brightness range is selected, for example, in turn from upper columns of FIG.  3 . Further, in this case, the processing is carried out only by the upper limit value. 
     Thereafter, the brightness at the apex of the polygon is interpolated and the brightness at the respective pixel at inside of the polygon (brightness distribution in the polygon) is calculated. Although color of the apex is also interpolated, all of the three apexes are provided with the same drawing color and accordingly, even when the color of the apex is interpolated, the result remains the same. Further, when the brightness of the pixel falls in the selected brightness range, drawing is carried out by the drawing color in correspondence with the selected brightness range (step S 645 ). The processing of interpolating the brightness is carried out by, for example, the triangle drawing processing unit  205  in FIG.  35 . The comparison processing of whether the brightness at the respective pixel falls in the selected brightness range, is executed by, for example, the pixel color processing unit  209 . The steps S 643  and S 645  are repeated until the processing is carried out with regard to all of the presence ranges (step S 647 ). 
     For example, when the pixel color processing unit  209  cannot deal with the two brightness values of the upper limit and the lower limit, by also using the Z buffer  211 , the same effect can be achieved. Although the Z buffer  211  is used in hidden face erasure, according to the embodiment, by also using the Z buffer  211 , an effect similar to that in the case of comparing with the upper limit value of the brightness is achieved. 
     Further, there also is the case in which a value of the smallest lower value of the brightness range table is not 0.0. In order to eliminate a portion which is not colored at all in the polygon, in repeating step S 647  of FIG. 15, step S 645  is executed by setting the lower limit value to 0.0 at a final repetition. 
     As described above, steps S 635  through S 647  are repeated until the processing is carried out with respect to all the apexes of the stereo model and, as a result, repeated until the processing is carried out with respect to all the polygons (step S 649 ). 
     When the above-described processing is executed, all of the polygons of the stereo model are painted to classify by predetermined stages of brightness and with regard to the stereo model, the image in the cel animation tone can be provided. Further, according to the contour drawing model introduced in Embodiment 1, a portion of a face rearward from the stereo model which is not hidden by the stereo model, is drawn and accordingly, the portion is rendered as the contour line. According to Embodiment 1, in drawing the contour line, the contour line can simply be drawn by executing the processing substantially to a normal rendering processing by only introducing the contour drawing model. 
     In FIG. 37, there is shown an example of the display screen  120  when only self character is drawn in the game image drawing processing of Embodiment 1. In FIG. 37, there is drawn the self character in a state in which the self character is directed to the right direction of the display screen. 
     When the player depresses the operation button  166 LL from the state in which the self character is directed to the right direction of the display screen, in response thereto, it is determined that the self character moves in the left direction of the display screen and there is carried out a processing in which the self character is directed gradually in the left direction and moves in the left direction. 
     FIG. 38 shows an example of the display screen  120  in which the self character is in the midst of changing the direction by drawing the rightfoot rearwardly to be directed to the left direction of the display screen from the state shown by FIG.  37 . According to the example, the self character rotates by way of the direction directed to the front side of the display screen and accordingly, according to the display screen shown by FIG. 38, there is shown a state in which the character is directed to the front side of the display screen. 
     FIG. 39 shows an example of the display screen  120  in a state in which the self character is directed to the left direction of the display screen by moving the leftfoot from the state shown by FIG.  38 . In this way, even when the self character moves in accordance with the operation input, the game image in the cel animation tone can be provided in real time. 
     Meanwhile, FIG. 40 shows an example of the display screen  120  in a state in which a camera is moved upwardly in response to operation of the operation button  166 RU by the player from the state of FIG.  37 . The image of the self character from above is displayed. 
     FIG. 41 shows an example of display screen  120  in a state in which the camera is moved further upwardly by further operating the operation button  166 RU by the player from the state of FIG.  40 . Further, since a distance between the self character and the camera is increased, the self character is displayed comparatively smaller than in FIG.  37  and FIG.  40 . In this way, when the camera is moved in response to the operation input, that is, even when the view point is switched, the game image in the cel animation tone can be provided in real time. 
     In this way, by using the CG technology, the game image in the self animation tone attached with the contour line in accordance with the operation input can be provided in real time. 
     3. Embodiment 2 
     In Embodiment 2, the cel animation tone coloring processing and the second contour drawing processing are combined. That is, the stereo model for expressing a character of a game or the like is attached with a contour line and colored in the cel animation tone. 
     As shown by FIG. 42, a game apparatus according to Embodiment 2, includes an operation input unit  940 , a game progressing unit  910  including a character action determining unit  915 , a game progress situation setting unit  980  including a character direction setting unit  983  and a view axis direction setting unit  987 , an arranging matrix setting unit  950 , a stereo model processing unit  960  including an apex conversion and light source calculating unit  962 , a brightness calculating unit  964 , a drawing color supplying unit  966 , a brightness range table  965  and a brightness setting unit  968 , a contour drawing model acquiring unit  900 , a contour drawing model processing unit  920  receiving an arranging matrix from the arranging matrix setting unit  950  and including a reversed head and tail determining unit  925 , a blur expression texture mapping unit  930 , a pixel processing unit  970  receiving data from the stereo model processing unit  960  and the blur expression texture mapping unit  930  and including a hidden face erasure processing unit  973  and a brightness comparing unit  977  and an image display control unit  990 . 
     The operation input unit  940  is realized by, for example, the key pad  161  and the interface unit  117  of FIG.  34 . The operation input unit  940  outputs operation information of button, lever or the like of the operation input unit  940  operated by a player of a game to the game progressing unit  910 . 
     The game progressing unit  910  determines content of progressing the game such as action of a character, a change in a view point position, a change in a direction of a view axis, or movement in a position of a light source, a change in a direction of light ray or the like based on information from the operation input unit  940  and gives instruction to the game progress situation setting unit. The character action determining unit  915  in the game progressing unit  910  is provided with a function of particularly determining the action of the character based on the information from the operation input unit  940 . 
     The game progress situation determining unit  980  calculates and sets a position, a direction and a shape of the character, the position of the view point or the direction of the view axis, the position of the light source, the direction of the light ray and an increase or a decrease of physical strength in accordance with the action of the character in accordance with the content of progressing the game instructed by the game progressing unit  910 . The character direction setting unit  983  in the game progress situation setting unit  980  is provided with a function of particularly determining a direction with respect to the view point of the character in accordance with the content of progressing the game instructed by the game progressing unit  910 . Meanwhile, the view axis direction setting unit  987  in the game progress situation setting unit  980  is provided with a function of particularly setting the direction of the view axis in accordance with the content of progressing the game instructed by the game progressing unit  910 . 
     The arranging matrix setting unit  950  executes a processing of determining the arranging matrix of the stereo model for expressing the character in accordance with position coordinates and a direction of the character and the position of the view point set by the game progress situation setting unit  980 . The arranging matrix is a matrix for executing parallel movement, rotation and perspective view conversion of the stereo model. 
     When the contour drawing model which is large relative to the stereo model is acquired and the reference position of the contour drawing model is present at the position in correspondence with the reference position of the stereo model, the arranging matrix determined by the arranging matrix setting unit  950  can commonly be used by the stereo model processing unit  960  and the contour drawing model processing unit  920 . When the arranging matrix can be used commonly, one store area for the arranging matrix may be prepared for the respective character and accordingly, the operation is efficient. 
     However, there also is the case in which the arranging matrix is not commonly used or cannot be commonly used. In that case, an arranging matrix of the stereo model and an arranging matrix of the contour drawing model are formed and are stored respectively in store areas. Further, when the arranging matrix cannot be commonly used, there also is a case in which one store area of the arranging matrix is prepared, immediately before the arranging matrix is used by the stereo model processing unit  960  and the contour drawing model processing unit  920 , a setting is carried such that the arranging matrix of the stereo model includes contraction conversion or the arranging matrix of the contour drawing model includes enlargement conversion. 
     The contour drawing model acquiring unit  900  forms the contour drawing model in correspondence with, for example, the stereo model constituted by a triangular polygon. Further, when the contour drawing model has previously been formed, the contour drawing model acquiring unit  900  reads the contour drawing model which is previously formed and constituted by the triangular polygon. According to the respective polygon of the acquired contour drawing model, head and tail thereof is the same as that of the corresponding polygon of the stereo model. Further, the contour drawing model is larger than the stereo model and is defined by predetermined coloring for a contour line. Further, although the contour drawing model must finally be large relative to the corresponding stereo model, there is a case in which the size of the contour drawing object at this stage is the same as the stereo model. In this case, the contour drawing model is processed to be drawn to be large relative to the stereo model until the contour drawing model and the stereo model are drawn. 
     Further, there also is the case in which color of the contour drawing model succeeds color of material of the corresponding stereo model as it is. In this case, color for drawing is separately designated. The reference position of the contour drawing model is normally defined to dispose at the difference position of the stereo model or a vicinity thereof. 
     The contour drawing model processing unit  930  executes apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) by using the arranging matrix by the arranging matrix setting unit  950  with regard to respective apex of the contour drawing model and executes head and tail determination of the respective polygon of the contour drawing model. The above-described arranging matrix is used in the apex conversion. The head and tail determination is carried out by the reversed head and tail determining unit  925 . Further, in this case, light source calculation is not executed. When the contour drawing model having a size the same as that of the stereo model is acquired by the contour drawing model acquiring unit  900 , the contour drawing model processing unit  920  executes apex conversion for enlarging the contour line drawing model. 
     The blur expression texture mapping unit  930  executes a processing for mapping blur expression texture in the contour drawing model such that the contour line drawn as a result constitutes a blurred line. The blur expression texture is the texture having a pattern including a change in brightness or transparency (refer to FIG.  23 ). Further, it is not necessarily needed that the contour line is blurred and accordingly, the blur expression texture mapping unit  930  is selectively operated. 
     The stereo model processing unit  960  executes a processing of providing the stereo model with coloring in a cel animation tone as an example of non-photorealistic rendering in cooperation with the pixel processing unit  970 . 
     The apex conversion and light source calculating unit  962  of the stereo model processing unit  960  executes apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) by using the arranging matrix by the arranging matrix setting unit  950  with regard to the respective apex of the triangular polygon constituting the stereo model arranged in a virtual three-dimensional space and carries out light source calculation with regard to the respective apex of the triangular polygon subjected to the apex conversion. 
     Further, the apex conversion and light source calculating unit  962  of the stereo model processing unit  960  also executes head and tail determination of the respective triangular polygon of the stereo model. Only a face directing head face to the visual point constitutes a drawing object. 
     The brightness calculating unit  964  of the stereo model processing unit  960  calculates brightness from color at respective apex of the triangular polygon calculated by the apex conversion and light source calculating unit  962 . The apex conversion and light source calculating unit  962  normally calculates color in the RGB system and accordingly, the brightness calculating unit  964  calculates brightness Y by converting RGB into YIQ. The brightness at the respective apex of the triangular polygon is outputted to the pixel processing unit  970 . 
     The brightness range table  965  is a table as shown by, for example, FIG.  2 . That is, this is a table paired with threshold and reference brightness and in this case, there are set three stages (levels) such that threshold 0.75 versus reference brightness 0.75, threshold 0.5 versus reference brightness 0.50 and threshold 0.00 versus reference brightness 0.25. Further, in this case, the brightness is provided with a real number value from 0 to 1. A range by an upper limit and a lower limit may be designated in place of the threshold (for example, refer to FIG.  3 ). 
     The drawing color supplying unit  966  calculates drawing color in correspondence with the respective threshold in reference to the brightness range table  965 . The drawing color in correspondence with the respective threshold is calculated by reference brightness in correspondence with threshold and information of color previously set to respective triangular polygon of the stereo model. The drawing color supplying unit  966  outputs the calculated drawing color to the pixel processing unit  970 . 
     Further, the drawing color supplying unit  966  may calculate the drawing color in execution or may previously calculate the drawing color and store the data. For example, when the brightness range table as shown by FIG. 2 is used, it is necessary to store three drawing color data for respective polygon. For example, refer to FIG.  16 . 
     The brightness range setting unit  968  selects one threshold of the brightness range table  965  and sets the threshold to the pixel processing unit  970 . When the brightness range table  965  as shown by FIG. 2 is used as it is, the brightness range setting unit  968  sets brightness one by one in turn from upper columns. When the range by the upper limit and the lower limit is set in place of the threshold, the brightness can be selected and set at random. 
     When the triangular polygon constituting the drawing object of the contour drawing model is processed, the pixel processing unit  970  determines color of respective pixel in the triangular polygon constituting the drawing object of the contour drawing model while executing hidden face erasure processing by using the hidden face erasure processing unit  973  and writes the color to the frame buffer  213 . 
     Meanwhile, when the triangular polygon constituting the drawing object of the stereo model is processed, firstly, the pixel processing unit  970  interpolates brightness at respective apex of the triangular polygon outputted from the brightness calculating unit  964  and calculates brightness in the respective pixel at inside of polygon (brightness distribution in polygon). 
     Further, the brightness comparing unit  977  compares brightness at the respective pixel with the threshold set by the brightness range setting unit  968 . When the brightness at the pixel is equal to or larger than the threshold, the pixel processing unit  970  draws the pixel by drawing color based on the reference brightness in correspondence with the threshold. In the drawing processing, the hidden face erasure processing is also executed by using the hidden face erasure processing unit  973 . When the brightness at the pixel is less than the threshold, the pixel is not drawn at this stage. When the brightness range setting unit  968  sets all of thresholds of the brightness range table  965  to the pixel processing unit  970  and in correspondence therewith, the pixel processing unit  970  executes drawing processing with regard to all of pixels in the triangular polygon, the inside of the triangular polygon is painted to classify in three stages according to example of FIG.  2 . The processing is executed to all of triangular polygons of the stereo model. 
     According to the invention, there is a case in which hidden face erasure by the Z buffer  211  is utilized in the hidden face erasure processing. For example, when the stereo model is formed in a shape of a human being and the arm is disposed in front of the body or the like, there is a case in which it is difficult to draw an accurate contour line when the Z buffer method is not used in view of a positional relationship between faces of the contour drawing object and the stereo model. 
     In addition thereto, when the brightness range table  965  as shown by FIG. 2 is used as it is by the stereo model processing unit  960  and the pixel processing unit  970 , hidden face erasure by the Z buffer  211  is utilized. For example, in accordance with FIG. 2, brightness equal to or larger than 0.75 is also equal to or larger than 0.5 and equal to or larger than 0.0 and accordingly, it is necessary to set an upper limit value of the brightness range such that the drawing color is not painted overlappingly. When brightness of a certain pixel is equal to or larger than 0.75, the pixel is drawn by drawing color in correspondence with threshold 0.75 and the Z value of the pixel is stored to the Z buffer  211 . 
     When the threshold becomes 0.5, the Z value of the pixel is read from the Z buffer  211  and compared with the Z value of the same pixel to be written, however, naturally, these are the same and accordingly, drawing color in correspondence with the threshold 0.5 is not written to the frame buffer  213  with regard to the pixel. The same goes with the threshold 0.0. 
     Further, the brightness at apex of the polygon and pixel at inside of polygon is dealt with as an attribute value of color (RGB) referred to as a normally used as transparency. Normally, the a value is defined by a range of 0-255 and accordingly, the actual a value multiplied by brightness by 255 is used. Therefore, the threshold (upper limit and lower limit value) of the brightness range table  375  may be a value in a range of 0-255. 
     Finally, the image display control unit  420  designates an area of the frame buffer which is written with data by the pixel processing unit  390  for displaying on the display screen. The frame buffer is normally provided with two areas, one is used for display and other is used for writing. Further, when writing to the writing area has been finished, the writing area is used to switch to the display area and the display area is used to switch to the writing area. The image display control unit  420  controls the switching operation. 
     (Premise) 
     Also in Embodiment 2, there is a case in which data of the contour drawing model is previously formed and stored to CD-ROM  131  and the data is read from CD-ROM  131  in executing a game. The example of data written to CD-ROM  131  shown in FIG. 19 stays the same also in Embodiment 2 at the level shown by FIG.  19 . 
     The program area  132  is stored with a program for executing the invention by the household game machine  1000 . A description will be given later of content of the program. 
     The system data area  133  is stored with various data processed by the program stored in the program area  132 , mentioned above. The image data area  134  is stored with data including the stereo model data  137  and the contour drawing model data  135 . However, when the contour drawing model is formed in a contour drawing model acquiring processing, mentioned later, it is not necessary to store the contour drawing model data  135 . Further, data of texture for expressing blur or the like is also stored in the image data area  134 . 
     The contour drawing model data  135  is previously formed by the stereo model data  137  and is provided with following characteristic. 
     That is, the size of the contour drawing model is defined to be larger than that of the stereo model. For example, according to the contour drawing model, apexes thereof are moved in normal line directions of the respective apexes of the corresponding stereo model by a length of 2 percent of a total length of the stereo model and the contour drawing model is defined to enlarge by about 2 percent as a whole. When the enlargement rate is larger, a contour line is drawn further boldly and when the enlargement rate is smaller and the contour drawing model is slightly enlarged, the contour line is drawn further finely. Further, when the contour drawing model is defined to enlarge further not uniformly but partially, only the contour line at the further enlarged portion is drawn boldly. Adjustment of the size is carried out normally by a producer of the stereo model and accordingly, the contour line reflecting the intention of the producer can be drawn. 
     Further, color of material of respective polygon of the contour drawing model is set to color having chroma the same as that of the stereo model and brightness lower than that of the stereo model. Further, there also is the case in which all of respective polygons are set to single color of black or the like. Further, there also is the case in which setting is carried out to map blurred expression texture. Color of material is adjusted by the producer and therefore, the contour line is drawn by color intended by the producer. Further, head and tail of respective polygon of the contour drawing model in Embodiment 2 is not reversed. This is the point different from Embodiment 1. 
     Further, the size of the contour drawing model may be defined to be the same as the size of the corresponding stereo model. In this case, after acquiring the contour drawing model by a contour drawing model acquiring processing, mentioned later, the contour drawing model is enlarged during a time period until an arranging matrix of the contour drawing model is set by a contour drawing model arranging processing, mentioned later. Or, in setting the arranging matrix of the contour drawing model by the contour drawing model arranging processing, the arranging matrix may be determined such that the arranging matrix includes enlargement conversion. Conversely, when the stereo model is arranged, the arranging matrix of the stereo model may be determined such that the arranging matrix of the stereo model includes contraction conversion. 
     Further, color of material of respective polygon of the contour drawing model may be the same as color of material of respective polygon of the corresponding stereo model. In this case, in the drawing processing of the contour drawing model, mentioned later, for example, the contour drawing model is drawn by separately defined color such as black or the like. 
     The sound data area  136  is stored with data for outputting sound from the sound output apparatus  125  by the sound processing unit  109  shown by FIG.  34 . Further, the sound processing is not directly related to the invention and therefore, it is not necessary to store data in the sound data area  136 . 
     Next, an explanation will be given of a processing flow with regard to Embodiment 2. The following processing is a processing which the operation processing unit  103  (FIG. 34) executes by controlling other element in the household game machine main body  101 . 
     (Total Processing Flow) 
     The processing flow at the level shown by FIG. 4 stays the same also in Embodiment 2. When the game is started, initial setting is carried out (step S 2 ). The initial setting processing includes a processing of acquiring data of the stereo model for expressing a character to be drawn. Further, Embodiment 2 includes also a processing of acquiring data of the contour drawing model. Next, operation of button, lever or the like of the key pad  161  is carried out by a player of the game (step S 3 ). Further, there is carried out a game progress processing for determining content of progressing the game such as action of a character in which, for example, the character moves to the left or the character attacks or the like, a change in a view point position, a change in a direction of a view axis, or movement of a light source position, a change in a direction of light ray or the like based on information of the operation input at step S 3  (step S 4 ). 
     Thereafter, in accordance with the content of progressing the game determined at step S 4 , there is carried out a game progress situation setting processing for setting a game progress situation such as a position, a direction and a shape of the character, the position of the view point or the direction of the view axis, the position of the light source or the direction of the light ray and an increase or a decrease of physical strength in accordance with action of the character in accordance with the content of progressing the game determined at step S 4  (step S 5 ). Next, there is carried out a game image drawing processing for writing a game image in accordance with the game progress situation to the frame buffer  213  (step S 6 ). A description will be given later of the game image drawing processing. 
     Further, there is carried out a game image display processing for displaying the game image written to the frame buffer  213  by the game image drawing processing at step S 6  (step S 7 ). Normally, the frame buffer  213  is divided in two areas of a writing area and a display area and in this case, there is executed a processing in which the writing area written with data by the game image drawing processing executed at step S 6  is switched to the display area and the display area is switched to successive writing area. 
     Next, it is determined whether the game is over (step S 8 ). When in the game progress situation setting processing (step S 5 ) executed in accordance with the operation input at step S 3 , physical strength of a self character operated by the player of the game is reduced and set to 0, the condition of game over is satisfied. At step S 8 , the physical strength of the self character operated by the player of the game is inspected and it is determined whether the game is over. When the physical strength of the self character is not 0, the operation returns to step S 3  and awaits for successive operation input. Meanwhile, when the game is over, the game is finished. Further, even when the game is over, a result thereof is displayed on the display screen  120  at step S 7  and accordingly, the player can grasp a final situation of the game from the display screen  120 . 
     Further, the processing flow expressing an outline of the game image drawing processing (step S 6  (FIG.  4 )) shown in FIG. 20, stays the same also in Embodiment 2 at the level shown in FIG.  20 . There is executed the background model drawing processing for drawing a background model for expressing a background portion in the game image (step S 22 ). The drawing processing is the same as the conventional drawing processing and accordingly, a detailed description will not be given here. Further, following steps S 24  through S 27  are repeated until all of characters are drawn (step S 23 ). 
     A first one of the repeated steps is the step of executing a deformation processing for deforming one unprocessed character (step S 24 ). Motion of the unprocessed character is determined by the game progress processing at step S 4  in accordance with the operation input executed at the step S 3  of FIG.  4 . Further, there is executed a processing of deforming the stereo model for expressing the unprocessed character, which is set by the game progress situation setting processing at step S 6  executed further in accordance therewith. Further, in Embodiment 2, a processing of deforming the contour drawing model is also executed in accordance with the processing of deforming the stereo model. 
     A second one of the repeated steps is a step for setting an arranging matrix of the unprocessed character (step S 25 ). The arranging matrix is a matrix for parallel movement, rotation and perspective view conversion of the stereo model for expressing the unprocessed character and is formed by position coordinates and a direction of the character and the position of the view point set by the game progress situation setting processing at step S 5 . As described above, when the contour drawing model is already defined to be large relative to the stereo model and the reference position of the contour drawing model is the same as the reference position of the stereo model, the arranging matrix of the stereo model can be used also for the contour drawing model. When the condition is not satisfied, arranging matrices may be set to respectives of the stereo model and the contour drawing model. Further, there also is a case in which an arranging matrix including enlargement conversion is set to the contour drawing model by a contour drawing model drawing processing, mentioned later. Further, there also is a case in which an arranging matrix including contraction conversion is set to the stereo model in the stereo model drawing processing. 
     Further, a third one of the repeated steps is a step of executing the contour drawing model drawing processing for drawing the contour drawing model (step S 26 ). With regard to the contour drawing model drawing processing, a detailed description has been given of the second contour drawing processing and therefore, a simple explanation will be given as follows. 
     A fourth step of the repeated steps is a step of executing the stereo model drawing processing for drawing the stereo model for expressing the unprocessed character (step S 27 ). Also with regard to the stereo model drawing processing, a detailed description has been given in Embodiment 1 and accordingly, a simple explanation will be given as follows. 
     After all of characters have been drawn, there is executed a window drawing processing for drawing a window for displaying capability of the character or the like to a user (step S 28 ). Also the window drawing processing is the same as the conventional drawing processing and therefore, a detailed description will not be given here. 
     A structure of the character data explained in reference to FIG. 21 is the same as that in the second contour drawing processing and includes a numerical value of maximum physical strength  10 , a numerical value of current physical strength  12 , a numerical value of attack force  14 , a numerical value of defence force  16 , coordinates (x, y, z) of the reference position  18 , rotational angles around X, Y and Z axes constituting direction  20  of the character, pointer  22  to motion data, pointer  24  to model data of the stereo model and pointer  26  to model data of the contour drawing model. 
     Next, an explanation will be given of a simple example (FIG.  7  and FIG. 8) with regard to a progress of a game story in accordance with the operation input of the player of the game. 
     FIG. 7 shows the example of the display screen  120  for displaying the image of the game for progressing the story while making the self character fight against enemy character in a virtual three-dimensional space by operating the self character C 101  by the player of the game. In this case, the image of the character C 101  from the front right side is displayed. On the left side of the display screen, the enemy character  1  (C 111 ) and the enemy character  2  (C 113 ) emerge. 
     Here, the position of the view point is determined by the game progress situation setting processing (step S 5 ) in accordance with the positional relationship between the self character and the enemy character and the direction of the self character. Further, with regard to the respective character, a non-photorealistic image is formed from the position of the view point and is displayed on the display screen  120 . 
     The self character attacks the enemy character in accordance with the operation input of the player from the key pad  161 . Meanwhile, the enemy character attacks the self character in accordance with a predetermined algorism. 
     FIG. 8 shows the display screen  120  when the self character C 101  is moved in the left direction of the display screen by operating the input apparatus  161  by the player of the game from the state of the display screen shown in FIG.  7 . 
     Action of the character of “move in the left direction of the display screen” in response to the operation input is determined by the game progress processing (step S 4  of FIG.  4 ). In accordance with action of the character, the direction, the position and the shape of the character are determined by the game progress situation setting processing (step S 5  of FIG.  4 ). According to the example of FIG. 8, the direction of the character is set to the left direction relative to the display screen and the position of the character is moved similarly in the left direction relative to the display screen. Further, the shape of the character is set with the shape for expressing running motion. 
     In this way, even when the game progress situation of the direction or the position of the character or the like is changed, the character is drawn as the image in the cel animation tone along with the contour line. 
     (Contour Drawing Model Acquiring Processing) 
     The processing of acquiring the contour drawing model included in the initial setting (step S 2 ) of FIG.  4  and shown by FIG. 31 is used also in Embodiment 2. In this case, firstly, it is determined whether the contour drawing model is to be formed (step S 223 ). When it is determined that the contour drawing model is not formed, data of the contour drawing model stored in CD-ROM  131  is read (step S 277 ). 
     When it is determined that the contour drawing model is formed, there is executed the processing of forming the contour drawing model (step S 225 ). When the contour drawing model is formed at this stage, according to respective polygon of the contour drawing model, head and tail thereof is made the same as that of the corresponding polygon of the stereo model (refer to FIG.  30 ). The size of the contour drawing model is formed to be larger than that of the corresponding stereo model. Meanwhile, color of material of respective polygon of the contour drawing model is formed by color darker than color of material of respective polygon of the corresponding stereo model. 
     Next, it is determined whether texture for expressing blur is mapped to the contour drawing model (step S 299 ). When it is determined that texture for expressing blue is not mapped and when the processing of mapping texture has been finished, the operation processing unit  103  finishes the drawing model acquiring processing. 
     (Contour Drawing Model Arranging Processing) 
     At step S 25  of FIG. 20, the arranging matrix of the stereo model and the contour drawing model for expressing the unprocessed character is set and the processing for arranging the contour drawing model is carried out by the arranging matrix. Normally, the reference position of the contour drawing model is set at a position in correspondence with the reference position of the stereo model. Further, the arranging matrix of the contour drawing model is set such that the reference position of the contour drawing model is arranged at the position arranged with the reference position of the stereo model or at a vicinity thereof. 
     In this case, when the direction of the stereo model is changed, the arranging matrix including rotation conversion is set such that also the contour drawing model corresponds thereto. When the shape of the stereo model is changed, the deformation processing is carried out such that the contour drawing model corresponds thereto. 
     Thereby, finally, the relatively large contour drawing model is arranged to include the stereo model. 
     (Contour Drawing Model Drawing Processing) 
     The drawing processing flow of the contour drawing model shown in FIG. 32 is used also in Embodiment 2. In this case, processings explained below are repeated until all of apexes of the contour drawing model are processed (step S 523 ). A first one of the repeated processings is apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) with respect to one apex (step S 525 ). Caution is required here to that light source calculation is not executed to the contour drawing model. 
     Further, there is executed the determination processing of whether polygon (face) including the apex is a tail face under normal determination reference (step S 527 ). Although normally, only a head face constitutes a drawing object, in the case of the contour drawing model of Embodiment 2, the tail face constitutes the drawing object under the normal determination reference. 
     When polygon (face) including the apex is the head face under normal determination reference , the operation returns to step S 523 . When the polygon (face) including the apex is the tail face under normal determination reference, there is executed the determination processing of whether texture expressing blur is mapped (step S 529 ). The step signifies texture mapping of the polygon. When texture expressing blur is mapped, there is executed the processing of calculating texture coordinates of texture for expressing blur (step S 531 ). When texture for expressing blur is not mapped, the operation proceeds to step S 533 . 
     Further, for example, the triangle drawing processing unit  205  and the pixel color processing unit  209  (FIG. 35) included in the pixel processing unit  970  are driven (step S 533 ). As described above, the triangle drawing processing unit  205  forms data at respective pixel at inside of the triangular polygon by interpolating data of respective apex of the triangular polygon. Data of the respective apex are color of material, screen coordinate values and texture coordinate values when step S 531  is executed. Further, data at respective pixel are color of material and pixel color when step S 531  is executed. The pixel color processing unit  209  writes a display image to the frame buffer  213  by using data at respective pixel at inside of the triangular polygon formed by the triangle drawing processing unit  205 . At this occasion, hidden face erasure is carried out by using the Z buffer  211 . 
     (Stereo Model Drawing Processing) 
     The flow of the processing of drawing the stereo model shown in FIG. 9 can be used also in Embodiment 2. First, initial setting is carried out (step S 603 ). In the initial setting, there is acquired the brightness range table (for example, FIG. 2 or FIG. 3) in correspondence with the stereo model. Next, there is carried out apex conversion (enlargement, contraction, rotation, parallel movement, perspective view conversion) and light source calculation with regard to one apex (step S 605 ). 
     Next, it is determined whether polygon (face) including the apex is the head face (step S 607 ). When the polygon (face) including the apex is the tail face, the operation returns to step S 605 . When the polygon (face) including the apex is the head face, there is calculated brightness at the apex where apex conversion and light source calculation are carried out (step S 609 ). 
     After step S 609 , there is calculated drawing color of polygon including the apex subjected to apex conversion and light source calculation (step S 611 ). The drawing color of polygon is calculated from reference brightness in correspondence with the respective brightness range stored in the brightness range table and color of the polygon. 
     Next, one of the brightness ranges of the brightness range table is selected (step S 613 ). Further, brightness at respective pixel at inside of the polygon (brightness distribution in polygon) is calculated by interpolating brightness at the apex of the polygon. Although color of the apex is also interpolated, since the three apexes are provided with the same drawing color and accordingly, the result remains the same even after the interpolation. Further, when the brightness at the pixel falls in the selected brightness range, the pixel is drawn by drawing color in correspondence with the selected brightness range (step S 615 ). The steps S 613  and S 615  are repeated until the processing is carried out with respect to all of the brightness ranges (step S 617 ). 
     For example, when the pixel color processing unit  209  cannot deal with two brightness values of an upper limit and a lower limit, the same effect can be achieved by also using the Z buffer  211 . Although the Z buffer  211  is used in hidden face erasure, in Embodiment 2, by also using the Z buffer  211 , an effect similar to that in the case of comparing with the upper limit value of the brightness is achieved. 
     The above steps S 605  through S 617  are repeated until the processing is carried out with respect to all of apexes of the stereo model and, as a result, repeated until the processing is carried out with respect to all of polygons (step S 619 ). 
     (Stereo Model Drawing Processing (Part 2)) 
     The flow of the second stereo model drawing processing shown in FIG. 15 can be used also in Embodiment 2. In FIG. 15, firstly, initial setting is carried out (step S 633 ). In the initial setting, there is acquired the brightness range table (for example, FIG. 2 or FIG. 3) in correspondence with the stereo model. Further, color data for drawing the stereo model is acquired. Next, there is carried out apex conversions (enlargement, contraction, rotation, parallel movement, perspective view conversion) and light source calculation are carried out with respect to one apex (step S 635 ). 
     Next, it is determined whether polygon (face) including the apex is a head face (step S 637 ). When the polygon (face) including the apex is a tail face, the operation returns to step S 635 . When the polygon (face) including the apex is the head face, there is calculated the brightness at the apex subjected to apex conversion and the light source calculation (step S 639 ). 
     Further, drawing color of the polygon including the apex subjected to apex conversion and the light source calculation is read from the memory  105  (step S 641 ). Next, one of the brightness ranges of the brightness range table is selected (step S 643 ). Thereafter, the brightness at respective pixel at inside of the polygon (brightness distribution in polygon) is calculated by interpolating the brightness at the apex of the polygon. Although color of the apex is also interpolated, since the three apexes are provided with the same drawing color and accordingly, the result remains the same even by the interpolation. Further, when the brightness at the pixel falls in a selected brightness range, drawing is carried out by drawing color in correspondence with the selected brightness range (step S 645 ). The steps S 643  and S 645  are repeated until the processing is carried out with respect to all of the brightness ranges (step S 647 ). 
     For example, when the pixel color processing unit  209  cannot deal with two brightness values of the upper limit and the lower limit, by also using the Z buffer  211 , the same effect can be achieved. Although the Z buffer  211  is used in hidden face erasure, according to the embodiment, by also using the Z buffer  211 , an effect similar to that in the case of comparing with the upper limit value is achieved. 
     The above steps S 635  through S 647  are related until the processing is carried out with respect to all apexes of the stereo model and, as a result, repeated until processing is carried out with respect to all of polygons (step S 649 ). 
     When the above-described processing are carried out, all of polygons of the stereo model are painted to classify by brightnesses at predetermined stages and with regard to the stereo model, an image in the cel animation tone can be provided. Further, according to the contour drawing model introduced in Embodiment 2, a portion of a face rearward from the stereo model which is not hidden by the stereo model is drawn and accordingly, the portion is rendered as the contour line. According to Embodiment 2, in drawing the contour line, the contour line can simply be drawn by executing the processings substantially similar to a normal rendering processing by only introducing the contour drawing model. 
     Also in Embodiment 2, there are can provided the display screen  120  substantially equivalent to that shown by FIG. 37, FIG. 38, FIG. 39, FIG.  40  and FIG.  41 . In FIG. 37, there is drawn the self character in the state in which the self character is directed to the right direction of the display screen  120 . 
     When the player depresses the operation button  166 LL from the state in which the self character is directed to the right direction of the display screen, in response thereto, it is determined that the character moves in the left direction of the display screen in accordance with the determination. The self character transits to FIG. 39 in the state in which the self character is directed in the left direction of the display screen by way of FIG. 38 in the state in which the self character is directed to the front side relative to the display screen. Even when the self character is operated in accordance with the operation input, there can be provided the game image in the cel animation tone in real time. 
     Meanwhile, FIG. 40 shows an example of the display screen  120  in the state in which the camera is moved upwardly in response to operation of the operation button  166 RU by the player from the state of FIG.  37 . The image from above the self character is displayed. 
     FIG. 41 shows an example of the display screen  120  in the state in which the camera is moved further upwardly by operating further the operation button  166 RU by the player from the state of FIG.  40 . There is displayed the image further upward from the self character. In this way, even when the camera is moved in response to the operation input, that is, even when the view point is switched, there can be provided the game image in the cel animation tone in real time. 
     Thereby, there can be provided the game image in the cel animation tone attached with the contour line in accordance with the operation input in real time by using the CG technology. 
     4. Other Embodiments 
     (1) The algorism for drawing the contour line is not limited to the above-described but drawing can be carried out by other algorism. 
     (2) The algorism for coloring the stereo model in the cel animation tone is not limited to the above-described but drawing can be carried out by other algorism. 
     (3) Although according to the initial stereo model drawing processing of Embodiments 1 and 2, in FIG. 9 expressing the stereo model drawing processing, after steps S 605  through S 609 , the processing of calculating the drawing color of the polygon is executed as step S 611 , no problem is paused when the drawing color of the polygon has been calculated until the drawing color is used at step S 615 . Therefore, step S 615  may be carried out prior to step S 609  or S 605 , may be carried out in parallel with steps S 609  and S 605  or may be carried out after step S 613  or may be carried out in parallel with step S 613 . 
     (4) At step S 609  in FIG. 9 expressing the initial stereo model drawing processing of Embodiments 1 and 2, the brightness Y of the apex of the polygon after light source calculation is calculated by the YIQ conversion. Y and Q as a result of the YIQ conversion is not used and therefore, the operation is carried out at high speed when these are not calculated, however, when a routine or the like for carrying out the YIQ conversion is already present, Y and Q may be calculated by using the routine. 
     (5) At step S 615  in FIG. 9 expressing the initial stereo model drawing processing of Embodiments 1 and 2, data of pixel at inside of polygon is formed by interpolating data of the apex of the polygon. When the processing is once carried out, the processing remains unchanged even when a different brightness range is selected and set by the repetition at step S 617  and accordingly, the result may be held and used. 
     (6) At step S 605  in FIG. 9 showing the initial stereo model drawing processing of Embodiments 1 and 2, perspective view conversion is carried out and light source calculation is carried out, however, the perspective view conversion may be carried out until step S 615 . However, when the perspective view conversion is carried out outside of a loop by step S 617 , the perspective view conversion may not be carried out at a number of times. Therefore, an amount of calculation can be reduced by executing the perspective view conversion at timing of step S 605 . 
     (7) Although in FIG.  18  and FIG. 30, the face of the contour drawing model and the face of the stereo model are brought into one-to-one correspondence, a number of the faces of the contour drawing model can also be reduced. Because when the number of the faces is reduced, the processing is accelerated. However, in the faces of the contour drawing model, there are present faces in correspondence with the stereo model. 
     (8) Change of Used Hardware 
     Although according to the above-described embodiments, there is disclosed the embodiment in which portions of processings of the stereo model and the contour line drawing model drawing processings are executed by the graphics processing unit  111 , a total of the stereo model and the contour drawing model drawing processings may be carried out by the graphics processing unit  111  or may be executed by the operation processing unit  103 . 
     Further, FIG. 34 shows only an example and can be changed variously. It is arbitrary whether the communication interface  115  is provided. It is not necessary to provide the sound processing unit  109  since the invention is not directly related to the sound processing. Further, a storing apparatus of a hard disk HDD or the like may separately be held. 
     Further, CD-ROM is an example of a record medium and there may be used other record medium such as an inner memory of ROM, CD-ROM, DVD-ROM, memory cartridge, floppy disk, magnetic disk DVD-RAM or the like. In that case, it is necessary to constitute the CD-ROM drive  113  by a drive which can be read by a corresponding medium. 
     Further, although the above-described is the case in which the invention is mounted by a computer program, the invention can be mounted by a combination of a computer program and an exclusive apparatus such as an electronic circuit or the like only by an exclusive apparatus such as an electronic circuit or the like. In that case, the apparatus may be constituted for respective functions represented by respective steps of the above-described processing flows or it is also conceivable to constitute the apparatus for respective portions of these or combinations of these. 
     As mentioned above, although a specific explanation has been given of the invention based on the embodiments, the invention is not limited to the above-described embodiments but can pertinently be changed within a range not deviated from the gist. For example, although in the above-described embodiments, a description has been given of the case in which the invention is realized with the household game machine as a platform, the invention may be realized with a computer arcaid game machine or the like as a platform. Depending on cases, it is also conceivable to realize the invention with a portable information terminal, a car navigation system or the like as a platform. 
     Further, programs or data for realizing the invention are not limited to a mode provided to a computer or a game machine by a record medium such as attachable and detachable CD-ROM or the like. That is, programs or data for realizing the invention may be in a mode in which by the communication interface  115  shown in FIG. 34, the programs or data are recorded to a memory of other apparatus side on the network  151  connected via the communication network  141  and the programs or data are successively stored to the memory  105  and used as necessary via the communication network  141 . 
     (Display Example) 
     FIG. 49 shows a display example of an image when the invention is not used, that is, when color of respective pixel in polygon is interpolated by color of apex of polygon. Further, FIG. 43, FIG. 44, FIG.  46  and FIG. 47 show an example of a display screen in which only the self character of FIG. 7 is displayed to enlarge. For example, there is known a behavior in which the brightness is naturally changed from a vicinity of the ear of the face of the character at a central portion of the image to the right side of the face of the character. Meanwhile, FIG. 44 shows an example of a display example of an image when there is used a brightness range table defining two of the brightness ranges (thresholds) and the image is drawn by an algorism of a coloring processing in the cel animation tone. FIG. 45 shows the brightness range table used in FIG.  44 . In this case, there are set two stages of threshold value and reference brightness such that threshold 0.3125 versus reference brightness 0.75 and threshold 0 versus reference brightness 0.60. Different from FIG. 43, it is known that FIG. 44 is painted to classify by two stages of the brightness from a vicinity of the ear of the face of the character at the central portion of the image to the right side of the face of the character. 
     Further, FIG. 46 shows a display example when the image is drawn by the algorism of the first and the second contour drawing processing. In FIG. 46, there is known a behavior in which the brightness is naturally changed, for example, from a vicinity of the ear of the face of the character at a central portion of the image to the right side of the face of the character. Further, it is known that a contour line of the hair, the body, a bag or the like is also drawn. 
     FIG. 47 shows a display example of the image when the image is drawn by the algorism of Embodiments 1 and 2. The brightness range table of FIG. 45 is used similar to FIG.  44 . In FIG. 47, it is known that the image is painted to classify by two stages of the brightness from a vicinity of the ear of the face of the character at a central portion of the image to the right side of the face of a person. Further, it is known that a contour line of the hair, body, a bag or the like is also drawn. 
     By using the algorism of the invention, as a non-realistic image, there can be provided a game image attached with a contour line, an image in the cel animation tone, and an image in the cel animation tone drawn with a contour line in real time in accordance with operation input.