a mode of implementing the present invention is described below with reference to the drawings . fig1 shows an external view of this picture generating device . in this figure , symbol 1 indicates the main body of a game machine . this game machine main body 1 has the shape of a box and is provided at its front face with a display 1a . a speaker mounting aperture ( not shown ) is provided laterally of display 1a , and a speaker 14 is arranged within this aperture . an operating panel 2 is provided on the front face below display 1a , and a gun unit 11 is arranged on this operating panel 2 . gun unit 11 is equipped with a trigger and this gun unit 11 is operated by a player . a game processing board is provided within game machine main body 1 . display 1a , gun unit 11 of operating panel 2 , and the speaker are connected to the game processing board 10 . by this means , a player is able to enjoy a gun - shooting game using display 1a and gun unit 11 of operating panel 2 . fig2 is a block diagram of a game processing device according to this embodiment . in outline , this game device comprises display 1a , gun unit 11 , game processing board 10 , output device 12 , and speaker 14 . game processing board 10 comprises : counter 100 , cpu ( central processing unit ) 101 , rom 102 , ram 103 , sound device 104 , input / output interface 106 , scroll data calculating device 107 , co - processor ( auxiliary computational processing device ) 108 , topographic data rom 109 , geometrizer 110 , shape data rom 111 , drawing device 112 , texture data rom 113 , texture map ram 114 , frame buffer 115 , picture synthesizing device 116 , and d / a converter 117 . cpu 101 is connected through a bus line to rom 102 that stores a prescribed program and image processing program etc ., ram 103 that stores data , sound device 104 , input / output interface 106 , scroll data calculating device 107 , co - processor 108 , and geometrizer 110 . ram 103 functions as a buffer through which there are performed writing of various commands to the geometrizer ( such as object display ), and writing necessary data for the various calculations . input / output interface 106 is connected to trigger 11a and 11b and position sensor 11c of gun unit 11 ; by means of this interface , operating signals of trigger 11a and 11b and position sensor 11c of gun unit 11 are input to the cpu 101 as digital quantities . also , output device 12 is connected to input / output interface 106 and output device 12 is actuated in response to drive control instructions from cpu 101 and operating chamber 2 is moved in response to the content of the game . sound device 104 is connected to speaker 14 through power amplifier 105 ; after power amplification , the audio signal generated by sound device 104 is supplied to speaker 14 . in this embodiment , under the control of the program incorporated in rom 102 , cpu 101 reads the operating signal from operating device 11 and graphic data from graphic data rom 109 , or motion data (&# 34 ; enemy characters etc .&# 34 ; and three - dimensional data such as &# 34 ; topography , space , and background of various structures etc .&# 34 ;) from motion data rom 111 , and performs at least behaviour calculation ( simulation ) and calculation of special effects . behaviour calculation means simulation of the motion of enemies in virtual space . in this process , after co - ordinate values have been determined in three - dimensional space , a conversion matrix for converting these co - ordinate values to the visual - field co - ordinate system , and shape data ( polygon data ) are specified in geometrizer 110 . graphics data rom 109 is connected to co - processor 108 so that predetermined graphics data are transferred to co - processor 108 ( and cpu 101 ). co - processor 108 is provided in order to undertake , chiefly , calculation of floating - point decimals . as a result , various decisions are executed by co - processor 108 and the results of these decisions are transferred to cpu 101 : the calculation load on the cpu is thereby lightened . geometrizer 110 is connected to motion data rom 111 and drawing device 112 . as already mentioned , shape data consisting of a plurality of polygons ( three - dimensional data such as characters , topography and background constituted by the vertices of these polygons ) are stored beforehand in motion data rom 111 and these shape data are transferred to geometrizer 110 . geometrizer 110 transparently converts shape data specified by a conversion matrix sent from cpu 101 and thereby obtains data that have been converted to the visual - field co - ordinate system from the co - ordinate system in three - dimensional virtual space . drawing device 112 affixes textures on to the shape data of the visual field co - ordinate system obtained by the conversion and outputs the result to frame buffer 115 . in order to perform this affixing of texture , drawing device 112 is connected to texture data rom 113 and texture map ram 114 and is also connected to frame buffer 115 . &# 34 ; polygon data &# 34 ; consists of data groups representing the relative or absolute co - ordinates of the vertices of polygons ( multi - angle shapes : chiefly triangles or rectangles ) consisting of a set of a plurality of vertices . graphics data rom 109 stores the data of polygons that are set up comparatively roughly , sufficiently for a prescribed decision to be executed . in contrast , motion data rom 111 stores polygon data whereby shapes constituting enemies or a screen of background etc . are set more precisely . scroll data calculating device 107 calculates scroll screen data ( stored in rom 102 ) such as text ; such data processed by this calculating device 107 and frame buffer 115 arrive at display 1a through screen synthesizing device 116 and d / a converter 117 . the polygon screens ( simulation results ) of for example enemies and topography ( background ) that are temporarily stored in frame buffer 115 , and the scroll screen of necessary textual information are thereby synthesized with the designated priority to generate the final frame picture data . this picture data is converted to an analog signal by d / a converter 117 and sent to display 1a , so that the game picture is displayed in real time . the operation of a game machine according to this embodiment will now be described . fig3 shows the main routine of game processing according to this embodiment . execution of this main routine is repeated for each frame ( 1 / 60 sec ). in this main routine , cpu 101 executes the game program stored in rom 102 ( step s1 ). next , a decision is made as to whether game processing has been completed ( step s2 ). if game processing has been completed ( step s2 : yes ), game processing is executed . also , if game processing has not been completed ( step s2 : no ), a decision is made as to whether trigger 11a or 11b has been pulled so that explosion image processing should be executed ( step s3 ). if explosion image processing is not being executed ( step s3 : no ), control returns to game processing . and if explosion image processing is being executed ( step s3 : yes ), control passes to explosion image processing ( step s4 ). this explosion image processing in step s4 forms : ( 1 ) a &# 34 ; mushroom cloud &# 34 ; image ; ( 2 ) &# 34 ; pillar of fire &# 34 ; (&# 34 ; pillar of water &# 34 ;, &# 34 ; pillar of earth &# 34 ;) image , ( 3 ) ( provisional name ) &# 34 ; spiky fireball &# 34 ; image or ( 4 ) a &# 34 ; smoke &# 34 ; image . these images are selected as follows . for example , when the image viewpoint is changed by operating gun unit 11 , a target ( enemy ) appears , so the player matches up the gun sights on this enemy and pulls trigger i1a or 11b etc . a shell or missile is then fired . when this shell or missile is fired , the position of arrival of the shell or missile ( determined by a collision evaluation between the shell or missile and the background ) is specified , using the data of position sensor 11c of trigger angle and direction and the data of trigger 11a or 11b . a &# 34 ; mushroom cloud &# 34 ;, &# 34 ; pillar of fire &# 34 ;, &# 34 ; water pillar &# 34 ;, &# 34 ; pillar of earth &# 34 ;, &# 34 ; spiky fireball &# 34 ; or &# 34 ; smoke &# 34 ; image is selected using the information of the background at this position of arrival and the information of trigger l1a or 11b . the selected explosion image is then formed at the position of arrival of the shell / missile . next , image processing of a &# 34 ; mushroom cloud &# 34 ; processed in step s4 will be described with reference to fig4 to fig1 . first of all , the object data of a mushroom cloud will be described with reference to fig4 to fig7 . fig4 shows the basic image data of a mushroom cloud . the object data k of a mushroom cloud as shown in fig4 b is constituted by stacking up in the y axis direction in xyz orthogonal co - ordinates the results of mapping ( affixing ) a texture to for example prismatic mesh polygons ( or semi - transparent polygons ) p1 to p9 as shown in fig4 a . symbol f represents a planar polygon . these prismatic mesh polygons p1 to p9 are respectively constituted by for example octagonal pillar shapes as shown in fig4 c . the object data k of this mushroom cloud is constituted by arranging unit image data k1 , k2 in exactly the same place . this unit image data k1 , as shown in fig5 a , is constituted by mapping texture t1 for three - dimensional representation after stacking mesh polygons p1 to p9 . this unit image data k1 can also be represented as shown in fig6 a . unit image data k2 is constituted by mapping textures t21 to t28 in slice fashion after stacking mesh polygons p1 to p9 as shown in fig5 b . this unit image data k2 can be represented as shown in fig6 b . fig7 shows the expanding portion of unit image data k1 , k2 of fig6 . fig7 a is the expanding portion k1b of unit image data kl ; in this expanding portion k1b , texture t1b appearing in three - dimensional shape is affixed to mesh polygons p1 to p5 . fig7 b is the expanding portion k2b of unit image data k2 . this expanding portion k2b is the result of affixing for example textures t21b , t22b in slice fashion . in image data kb obtained by arranging these at the same location in xyz orthogonal co - ordinates , as shown in fig7 c , in places where the texture of expanding portion k2b is not mapped ( between textures t21b , t22b etc . ), an image solely of expanding portion k1b appears , whereas , in places where textures t21b , t22b of expanding portion k2b are mapped , an image of expanding portions k1b , k2b appears . thus , by for example rotating textures t21 to t28 of unit image data k2 , without losing the three - dimensional effect , an image can be obtained in which flames appear to move : thus a complex image can be obtained . next , the image processing operation of an object constituted as above will be described with reference to fig8 to fig1 . fig9 a is a view of object data k seen from the xy plane . object data k , as shown in fig9 a , consists of object portion ( hereinbelow referred to as &# 34 ; image element &# 34 ;) a to image element e , and image element f . image element a consists of an element a1 obtained by mapping a texture for three - dimensional representation to a prismatic mesh polygon , and an element a2 obtained by mapping a slice - shape texture to a prismatic mesh polygon . it should be noted that the height of the prism of image element a is extremely small . the same applies to image element b to image element e . first of all , when trigger 11b of gun unit 11 for missile firing is pulled , a missile is fired . cpu 101 then finds the location where the missile lands from an evaluation of collision with the background , using for this purpose the relationship of the direction of gun unit 11 and the gun sights . then , when the missile reaches the point of arrival , first of all , the object data k of the mushroom cloud is fetched from rom 102 , so that an explosion image is displayed at this position ( steps s400 , s401 ). next , flag f1 is set ( step s402 ). the image of the mushroom cloud object is thereby displayed at the position of this point of arrival . as shown in fig9 a , this mushroom cloud image is arranged in a condition with the image element a to image element f compressed in the y axis direction in the xyz orthogonal co - ordinate system . cpu 101 then multiplies image element a in fig9 a by the prescribed operator q1 ( step s403 ). it also multiplies image element b in fig9 b by the prescribed operator q2 , image element c by the prescribed operator q3 , . . . , and image element e by the prescribed operator q5 , respectively ( step s404 ). also , it multiplies image element f in fig9 a by the prescribed operator q6 . as a rule , operators q1 to q6 may be assumed to act in the direction such that image element a to image element f are each expanded in the prescribed co - ordinate system every time this routine is executed . by this means , as shown in fig9 b , image element a constitutes image data such that , whilst it rises in the direction of the y axis , it is displaced in the direction in which the area of the image element a spreads out in the xz plane , while a hole appears at its centre . also , image element b constitutes data whereby , whilst rising in the y axis direction , movement takes place such that the volume of image element b expands in the xyz orthogonal co - ordinate system . also , image elements c , d , e constitute data elongating in the y axis direction . next , a decision is made as to whether image element b has reached the prescribed value ( step s406 ). this step serves to execute processing whereby all the various image elements are erased when image element b has reached a prescribed value . usually , the prescribed value is not reached immediately ( step s406 : no ), so , next , a decision is made as to whether the prescribed area of image element e has reached 0 ( step s408 ). this step consists in decision processing such as to effect erasure of the image elements from image element e upwards . since the prescribed area of image element e will not have become 0 immediately ( step s407 : no ), this decision is followed by a decision as to whether the prescribed area of image element d has not become 0 ( step s408 ). this step also constitutes decision processing in order to arrange for the image elements to disappear upwards from image element c . since this will not of course become zero immediately ( step s408 : no ), the next step is to decide whether the prescribed area of image element c will not have become zero ( step s409 ). after this , this process is skipped . then , when this routine ( step s401 to s409 ) has been executed a prescribed number of times , if image element b has reached the prescribed value ( step s406 : yes ), it is ascertained whether or not flag f2 is set ( step s410 ). cpu 101 is enabled to perform calculation such that the width of image elements a , f is decreased ( step s411 ), by applying operators q1 , q6 . next , cpu 101 applies operators such that the width of image element e in the y axis direction becomes smaller with a prescribed value and such that image element d decreases with a value smaller than that by which image element e is decreased , by applying operators q5 , q4 . flag f2 is also set ( step s411 ). steps s407 to s409 are then executed . thus , every time this routine ( steps s401 to s406 , s410 , s407 to s409 ) is executed , in steps s403 , s404 and s405 , by the action of operators q1 , q6 , widths w1 and w2 of image elements a , f are reduced as shown in fig1 a , and image element e is decreased in the y axis direction , while image element d is decreased but by less than image element e . then , when the prescribed area of image element e has become 0 ( step s407 : yes ), it is ascertained whether flag f3 has been set ( step s413 ). flag f3 has not been set ( step s413 : no ), so cpu 101 applies operators such that the width in the y axis direction of image element d becomes smaller by a prescribed value and image element c decreases with a value that is smaller than the value with which image element e decreases , by operating with operators q4 and q3 , and sets flag f3 ( step s411 ). by this means , the mushroom cloud object is displayed as an image in which image element e has disappeared , while image element d has become smaller . processing then proceeds through steps s408 and s409 . thus , every time this routine ( steps s401 to s406 , s410 , s407 , s413 , s408 and s409 ) is executed , in steps s403 , s404 and s405 , by the action of operators q1 , q6 , width w1 , w2 of image elements a , f are decreased as shown in fig1 a , and image element d is decreased in the y axis direction , while image element c is decreased by a value smaller than that of image element d . thus , when image element d becomes 0 ( step s408 : yes ), image element d disappears more rapidly , and setting of operator q3 in the direction in which image element c disappears , and setting of flag f4 are performed ( steps s415 , s416 ). next , in the condition in which image elements a , c to e and f have been erased ( step s409 ), a process to erase image element b is commenced ( step s417 ). at this step 417 , as shown in fig1 b , only image element b is being displayed . cpu 101 therefore subdivides image element b into image elements b1 to b5 and performs erasure from image element b5 in sequence to b1 ( step s417 ). thus , since the image is changed by applying operators to object data k , a large amount of explosion data , such as was required conventionally , is not needed . also , a complex image can be obtained since two textures are superimposed . next , image processing of a &# 34 ; pillar of fire &# 34 ; processed in step s4 will be described with reference to fig1 to fig1 . first of all , the object data of the pillar of fire will be described with reference to fig1 and fig1 . in fig1 , the object data k00 of the pillar of fire is constituted of image elements a0 , b0 , c0 . image element a0 consists in for example an octagonal polygon as shown in fig4 c arranged in an xyz orthogonal co - ordinate system and with a cylindrical texture mapped on to it . likewise , image element b0 consists in for example an octagonal polygon p as shown in fig4 c , polygon p , which is larger than image element a , being arranged concentrically with image element a in an xyz orthogonal co - ordinate system and having mapped on to it a cylindrical texture . likewise , image element c0 is for example an octagonal polygon p as shown in fig4 c , polygon p , which is larger than image element b , being arranged concentrically with image element a in the xyz orthogonal co - ordinate system , and having mapped on to it a cylindrical texture . a texture t10 with a spiky top as shown for example in fig1 a is mapped on to these image elements a0 , b0 . also , a cloud - like texture t20 as shown for example in fig1 b is mapped on to image element c0 . thus , in fact , the pillar of fire object data k00 will be displayed in a condition as shown in fig1 a in which the upper side of image element a0 is indented , the upper side of image element b0 is indented , while image element c0 is displayed as a circular cloud . next , the image processing of the pillar of fire object will be described with reference to fig1 to fig1 . fig1 is a flow chart of image processing of this pillar of fire object . fig1 is a diagram showing how the appearance of the pillar of fire object changes . first of all it is ascertained whether or not flag f10 is set ( step s500 ). this is in order to prevent the reading operation being performed again after the pillar of fire object data k00 has been read . if reading of the object data k00 has not been completed ( step s501 : no ), first of all , the object data k00 of the pillar of fire stored in rom 102 is read ( step s501 ), and flag f10 is set ( step s502 ). this object data k00 is stored in a prescribed area of ram 103 . next , cpu 101 ascertains whether or not flag f11 has been set ( step s503 ). this decision regarding flag f11 is a decision process provided for the purpose of changing over from expansion to contraction . if , at this point , flag f11 has not been set ( step s503 : no ), cpu 101 executes expansion processing in the y direction on image elements a0 , b0 in ram 103 ( step s504 ). likewise , cpu 101 performs expansion processing ( step s505 ) on image element c0 in ram 103 in the yz plane direction . next , cpu 101 ascertains whether for example image element a0 has reached a prescribed value ( step s506 ). the purpose of this step is so that the pillar of fire does not get bigger than a certain amount . as long as image element a0 has not reached its maximum ( step s506 : no ), every time this routine ( step s500 , s503 to s506 ) is executed , image elements a0 , b0 in object data k00 are subjected to expansion processing in the y direction in the xyz orthogonal co - ordinate system as shown in fig1 b , and image element c0 is subjected to expansion processing in the xz plane direction . next , when image element a0 reaches its maximum ( step s506 : yes ), flag f11 is set ( step s507 ), and return is executed . after this , since flag f10 is set ( step s500 : yes ) and flag f11 is set ( step s503 : yes ), cpu 101 goes to step s510 . in this step , image elements a0 , b0 are subjected to contraction processing in the y axis direction and expansion processing in the xz plane direction ( step s510 ). likewise , cpu 101 further performs expansion processing in the xy plane direction on image element c0 , and processing such as to make the thickness w3 of image element c0 approach 0 ( step s511 ). in this way , as shown in fig1 c , pillar of fire object data k00 is displayed as an image in which image elements a0 , b0 successively shrink in the y axis direction , and expand in the direction of the xz plane . also , image element c0 is displayed as an image in which , as it expands further in the direction of the xz plane , its thickness w3 is successively diminished . next , when image elements a0 , b0 have reached their fixed size or more in the xz plane , and thickness w3 of image element c0 has become 0 ( step s511 : yes ), processing is executed to make flags f10 and f11 0 ( step s513 ). the pillar of fire process is thereby terminated . since object data k00 is used in this way to produce an image which is changed by expansion and contraction with time in the xyz orthogonal co - ordinate system , a large amount of explosion data such as was required conventionally is not needed . a pillar of water and pillar of earth may be produced by altering the textures applied to image elements a0 and b0 to pillar of water texture or pillar of earth texture . first of all , the object data of the &# 34 ; spiky fireball &# 34 ; will be described with reference to fig1 . object data k10 of the &# 34 ; spiky fireball &# 34 ; is constituted by image elements a1 , b1 to a8 , b8 which are arranged radially in the xyz orthogonal co - odinate system . image elements a1 , b1 are arranged in the same location and image element a1 is shorter than image element b1 . the same applies regarding image elements a2 , b2 , to a8 , b8 . this object data k10 is stored in rom 102 . it should be noted that , although in fig1 ( a ), image elements a1 , b1 , to a8 , b8 are arranged in radia1 fashion in the xyz orthogonal co - ordinate system , since it is not possible to state the position of the image elements precisely , they are displayed as totality image elements a00 , b00 . also , fig1 b represents the condition in which object data k10 is seen from the xy plane , but in this figure also the image elements are displayed as a00 , b00 , except that their radia1 arrangement is shown more clearly . fig1 c is a view of object data k10 seen from the xz plane . next , the image processing of the &# 34 ; spiky fireball &# 34 ; object will be described with reference to fig1 to fig1 . fig1 is a flow chart of image processing of this &# 34 ; spiky fireball &# 34 ; object . fig1 and fig1 are diagrams showing how this &# 34 ; spiky fireball &# 34 ; object changes . first of all , it is ascertained whether or not flag f10 has been set ( step s600 ). the purpose of this is to ensure that the operation of reading of the object data k10 of the &# 34 ; spiky fireball &# 34 ; is not repeated after it has been read . if reading of object data k10 has not been completed ( step s600 : no ), first of all , the object data k10 of the &# 34 ; spiky fireball &# 34 ; stored in rom 102 is read ( step 601 ), and flag f10 is set ( step s602 ). this object data k10 is stored in a prescribed area of ram 103 . next , cpu 101 ascertains whether or not flag f21 is set ( step s603 ). this checking of flag f21 is a decision process to effect changeover from expansion to contraction . since at this point flag f21 is not set ( step s603 : no ), cpu 101 executes expansion processing in the radial direction with respect to the xyz orthogonal co - ordinate system on each of the image elements a1 to a8 in ram 103 ( step s604 ). next cpu 101 ascertains whether for example image element a0 has reached its prescribed value ( for example its maximum value ) ( step s505 ). this step is to prevent image elements a1 to a8 getting larger than a fixed amount . as long as image element a0 has not reached its maximum ( step s605 : no ), every time this routine ( step s600 , s603 to s605 ) is executed , image elements a1 to a8 in object data k00 are subjected to expansion processing in the radial direction in the xyz orthogonal co - ordinate system . also , every time this processing routine is executed , the colour of image elements a1 to a8 is changed from yellow to red . fig1 a shows how image element a1 expands ( only image element a1 is shown ). next , when image element a1 has reached its maximum ( step s605 : yes ), flag f21 is set ( step s606 ), and return is commenced . after this , since flag f20 is set ( step s600 : yes ), and flag f21 is set ( step s603 : yes ), cpu 101 goes to step s610 . in this step , processing is performed to shrink image elements a1 to a8 in the radial direction in the xyz co - ordinate direction , and processing is performed to expand image elements b1 to b8 in radial fashion in the xyz coordinate direction ( step s610 ). also , in this processing step , the colour of image elements b1 to b8 is changed from red to black . a check is then made to establish for example whether the area of image element a1 has become 0 or not ( step s611 ). if it is found that the area of image element a1 has not reached 0 ( step s611 : no ), return is executed . thus , every time this routine ( step s600 , s603 , s610 , s611 ) is executed , image elements a1 to a8 shrink and , in substitution for image elements a1 to a8 , image elements b1 to b8 expand . fig1 b shows this process for image elements a1 , b1 . after this , when the area of image element a1 has become 0 ( in other words , when image elements a1 to a8 have become 0 : step s611 : yes ), image processing is executed ( step s612 ) such that image elements b1 to b8 descend following a parabola whilst rotating about the y axis . as a result , as shown in fig1 c , image element b1 is displayed in a condition descending on a parabola whilst rotating about the y axis . at the same time , regarding image elements b1 to b8 , as shown in fig1 , of the object data k10 of the &# 34 ; spiky fireball &# 34 ;, in the xyz orthogonal co - ordinate system , image elements a1 to a8 expand in the radial direction with passage of time , and , when these image elements a1 to a8 have reached a fixed size , image elements a1 to a8 shrink , while image elements b1 to b8 expand to replace them . these image elements a1 to a8 change from yellow to red with passage of time after being first displayed . image elements b1 to b8 also change with passage of time after being first displayed , from red to black . after this , when the area of image elements a1 to a8 has reached 0 , image elements b1 to b8 descend along parabolic trajectories whilst rotating about the y axis . in this way , the image elements a1 to a8 , b1 to b8 of object data k10 are made to expand and shrink , so it is not necessary to have image data that changes in a series , as conventionally ; the amount of image data can therefore be reduced and , since two textures can be superimposed , complicated images can be obtained . first of all , the object data of smoke will be described with reference to fig1 . as shown in fig1 a , object data k50 is formed by respectively mapping textures t51 and t52 providing a smoke shape on to planar mesh polygons p51 and p52 , with image elements a51 , a52 partially overlapping . of this object data k50 , at least image element a52 is then subjected to animation processing . in this way , an image showing a lot of changes can be obtained by performing animation on at least one texture t52 , of the smoke object , whose form is made to show a series of changes in the prescribed time .
an object is to provide an image processing device that is capable of reproducing effectively objects or characters in a condition showing considerable variation , such as explosions or smoke . this image processing device is constituted of an output device and processing devices constituted of rom that stores data constituting an object whose mode is anticipated to show a series of changes in prescribed time , the object being constituted of a plurality of portions , and that execute image processing whereby animation is effected in respect of each portion , the processing results from these processing devices being displayed on an output device .