JP2003030685A - Image processor and image processing method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To smoothly perform the movement of a character to a ball. SOLUTION: An image processor is provided with a virtual area generation means generating a collision area 43 for collision judgment at a position a prescribed distance away from the image of the ball and a judgment means judging at which position on the collision area 43 the character, a fielder for instance, is present. Corresponding to the relative position to the collision area 43 of the character, an image change means smoothly changes a character posture from a standby state to a ball catching state. Also, the processing for not displaying a plurality of polygons in contact with each other is accurately performed.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image processing apparatus and an image processing method, and more particularly to an image processing apparatus capable of smoothly moving a character with respect to a ball in a video game or the like simulating a ball game such as baseball or soccer. And an image processing method.

[0002]

2. Description of the Related Art With the progress of computer technology, video game machines (image processing devices) using computer graphics technology have come into wide use. Above all, the popularity of video game machines imitating ball games such as baseball and soccer has been strong, and many video game machines of this type have been devised.

However, conventional video game machines
I had many problems as follows.

First, it was difficult to smoothly display the fielder's ball catching motion.

In the conventional video game machine, generally, a display for displaying a batter, a fielder, etc., an operation stick for operating the batter, a fielder, etc. on the screen, and a desired image is displayed on the screen according to the operation of the operation stick. And an image processing circuit for performing the same. In such a video game machine, a plane image called a sprite is prepared for each motion posture of each fielder, and the sprite according to the progress of the game is displayed on the screen. In addition, a virtual area for collision determination called a collision area is provided near the fielder, and when the ball enters the collision area, the fielder catches the ball.

For example, when the player operates the stick, the fielder on the screen follows the ball according to the stick operation. At this time, the collision area also moves with the fielder. When the fielder catches up with the ball and enters the collision area near the fielder, the fielder performs a ball catching operation. That is, the video game machine judges that the ball on the screen has reached the vicinity of the fielder, and displays the sprite indicating the catching motion. Therefore, the fielder does not start the catching motion unless the ball enters the collision area on the screen.

However, the time from the ball entering the collision area to the fielder catching the ball is extremely short, and the fielder must be allowed to perform the ball catching operation in an extremely short time after the ball enters the collision area. Therefore, the fielder's ball-catching motion becomes awkward and it is difficult to provide a realistic game. As a method of solving such a problem, a method of enlarging the collision area in the vicinity of the fielder can be considered. That is, a method of increasing the time from when the ball enters the collision area to when the fielder catches the ball can be considered. However, if the collision area is increased, the fielder will start catching the ball far away from the fielder, and the fielder will catch the ball even if it cannot be caught. Inconvenience newly occurs.

Secondly, many calculations are required for the collision determination process between the hit ball and the fence, which hinders high-speed processing.

In the video game machine, when a hit ball flies over an outfielder, a collision judgment between the hit ball and the fence is made. For example, when the fence is displayed with a plurality of polygons (polygons), it has been determined whether the coordinates of the ball are on the polygons. When it is determined that the ball has collided with the polygon forming the fence, the ball is rebounded from the fence.

That is, in the conventional baseball game,
The collision determination between the ball and the fence is performed depending on whether or not the coordinate value of the ball is located on the polygon forming the fence. However, since the coordinate values of the ball and polygon are expressed by three-dimensional data,
A lot of arithmetic processing has to be spent in order to determine the positional relationship between the two. Therefore, there is a problem such as a decrease in processing speed of the entire game.

Third, like a uniform number and uniform,
It was difficult to accurately perform hidden surface processing on polygons that are in close contact with each other.

In a video game such as baseball or soccer, it is desirable to give each player a different jersey number in order to increase the realism of the game. However,,
If different images are prepared for each player's uniform, the display data will be enormous. For this reason,
The uniform image and the uniform image are prepared separately, and the uniform image is superimposed on the uniform image.

However, when the uniform number and the uniform are displayed by polygons, the following problems occur. When the polygons overlap each other, a process (a hidden surface process) of not displaying the overlapped portion of the polygons on the far side of the screen is performed. As a method of such hidden surface processing, a method (Z sort method) has been devised in which the priority order of each polygon is determined by the size of the coordinate (z coordinate value) in the depth direction of the polygon and the polygons are displayed according to the priority order. ing. That is, in the Z sort method, the representative point is determined for each polygon, and the priority order of the polygons is determined according to the magnitude of the z coordinate value between the representative points.

As described above, in the Z sort method, one representative point must be determined for each polygon. The representative point can be determined by setting the frontmost vertex of the polygon vertices as the representative point, the polygon innermost vertex as the representative point, or the polygon vertices. There is a method of using the center of gravity as the representative point. However, whichever method is used, when two polygons are in close contact with each other like a uniform number and a uniform (two z coordinate values are close to each other), the priority order of the polygons is accurately determined. Difficult to do. That is, the hidden number may be hidden and displayed under the uniform, and the hidden surface may be erroneously processed.

As a method of avoiding such a problem, a method of giving the uniform number a higher priority than that of the uniform so that the uniform number is always superimposed on the uniform is conceivable.
However, this method may cause a new problem that the uniform number is displayed when the fielder faces the front (when the back is not displayed). Therefore, conventionally,
It was extremely difficult to accurately perform the hidden surface treatment of polygons that are in close contact with each other.

The present invention has been made in view of the above problems, and a first object of the present invention is to provide an image processing apparatus and an image processing method capable of smoothly performing a ball catching operation. It is in.

It is a second object of the present invention to provide an image processing apparatus and an image processing method capable of executing collision determination between a hit ball and a fence by a simple calculation.

A third object of the present invention is to provide an image processing apparatus and an image processing method capable of accurately performing hidden surface processing on polygons that are in close contact with each other such as a uniform number and a uniform.

[0019]

The invention according to claim 1 is
In order to achieve the above-mentioned first object, when it is determined that the first image and the second image collide, in the image processing device that changes the shape of the second image, from the first image, A virtual region generating unit that generates a virtual region at a position separated by a distance that allows the first image to move within a predetermined time;
And a determining unit that determines whether the second image is located in the virtual region, and an image changing unit that changes the shape of the second image when it is determined that the second image is located in the virtual region. The image processing device.

According to a second aspect of the present invention, there is provided the first object, including position determining means for determining the moving speed and position of the first image, and the virtual area generating means, The image processing apparatus according to claim 1, wherein the shape of the virtual area is changed based on the determination result by the position determination means.

The invention according to claim 3 is to achieve the first object, wherein the virtual area generating means is to achieve the first object. The image processing apparatus according to claim 2, wherein the area of the virtual region is reduced as the speed of one image decreases.

The invention according to claim 4 is to achieve the first object, wherein the virtual area is the first area.
The image processing apparatus according to any one of claims 1 to 3, wherein the image processing apparatus has a shape extending in a direction perpendicular to a moving direction of an image.

The invention according to claim 5 is to achieve the first object, wherein the image changing means has a second image having a shape corresponding to the position of the first image on the virtual region. The image processing apparatus according to claim 1, which generates

The invention according to claim 6 is to achieve the first object, wherein the image changing means has a second shape having a shape corresponding to a height of the first image with respect to a reference plane image. The image processing apparatus according to claim 1, which generates an image.

The invention according to claim 7 is to achieve the first object, wherein the first image represents a baseball and the second image represents a baseball fielder. The image processing device according to any one of claims 1 to 6, wherein the image changing unit gradually changes the posture of the fielder in accordance with the catching operation.

The invention according to claim 8 is for achieving the third object, and is a coordinate conversion means for projecting a plurality of polygons represented by a three-dimensional coordinate system onto a two-dimensional coordinate system. The hidden surface processing for determining the display order of the plurality of polygons projected on the two-dimensional coordinate system based on the magnitude of the coordinate value in the depth direction with respect to the display screen, and preferentially displaying the polygons according to this display order. In the image processing device including means, the hidden surface processing means sets the display order of a polygon group consisting of a plurality of polygons whose description order is predetermined to the coordinate value in the depth direction of one polygon forming the polygon group. Based on
Only when it is determined to display the polygon group, the image processing apparatus preferentially displays each polygon forming the polygon group based on the description order.

The invention according to claim 9 is to achieve the third object, wherein the hidden surface processing means is based on the coordinate value in the depth direction of the polygon having the highest description order. 9. The image processing apparatus according to claim 8, wherein the display order of is determined.

The invention according to claim 10 is to achieve the third object, wherein the one polygon represents a uniform number and the other polygon represents a uniform. It is a processing device.

The invention as set forth in claim 11 is for achieving the second object, in the image processing device for judging the collision between the curved surface image having the radius R from the center point and the first image. Calculate the distance r from the center point to the first image,
The image processing apparatus determines that the first image collides with the curved surface image when the distance r reaches the distance R.

The invention according to claim 12 is to achieve the second object, wherein the curved surface image represents a baseball fence and the first image represents a ball.
The image processing device according to item 1.

The invention as set forth in claim 13 is for achieving the above-mentioned first object and comprises the first image and the second image.
In the image processing method of changing the shape of the second image when it is determined that the images collide with each other, at a position away from the first image by a distance that allows the first image to move within a predetermined time,
A virtual region is generated, it is determined whether the second image is located in the virtual region, and if it is determined that the second image is located in the virtual region, an image processing method that changes the shape of the second image is performed. is there.

According to a fourteenth aspect of the present invention, which is to achieve the first object, the moving speed and position of the first image are determined, and the virtual area of the virtual region is determined based on the moving speed and position. The image processing method according to claim 11, wherein the shape is changed.

The invention as set forth in claim 15 is for achieving the third object, wherein a plurality of polygons represented by a dimensional coordinate system are projected onto a two-dimensional coordinate system to form a two-dimensional coordinate system. The display order of the plurality of projected polygons is determined based on the size of the coordinate value in the depth direction with respect to the display screen, and in the image processing method that preferentially displays polygons according to this display order, the description order is Only when it is determined that the display order of a predetermined polygon group including a plurality of polygons is to be displayed based on the coordinate values in the depth direction of one of the polygons that make up the polygon group, This is an image processing method for preferentially displaying each polygon forming a group based on the above described order of description.

The invention as set forth in claim 16 is for achieving the second object, and in the image processing method for determining the collision between the curved surface image having the radius R from the center point and the first image, Calculate the distance r from the center point to the first image,
When the distance r reaches the distance R, the image processing method determines that the first image has collided with the curved surface image.

[0035]

According to the first aspect of the invention, the virtual area generation means generates the virtual area at a position separated from the first image by a distance that allows the first image to move within a predetermined time. That is, the virtual area is generated at a position separated by a predetermined distance with respect to the moving direction of the first image. Then, the determining unit determines whether or not the second image is located in the virtual region, and when it is determined that the second image is located in the virtual region, the image changing unit changes the shape of the second image. .

For example, when the second image representing the fielder enters the virtual area, the posture of the fielder gradually changes from the standby posture to the catching posture. After this, when the first image representing the ball reaches the fielder, the posture of the fielder is the posture at the time of catching the ball. According to the present invention, the virtual area for collision determination is the first
Since it is located away from the image, it is possible to lengthen the time from when the second image enters the virtual area to when the first image and the second image collide. Therefore, when the present invention is applied to a baseball game, it is possible to secure a sufficient time for changing the posture of the fielder at the time of catching a ball, and to realize a smooth ball catching operation.

According to the second aspect of the invention, the position judging means judges the moving speed and the position of the first image, and the virtual area generating means changes the shape of the virtual area based on the judgment result by the position judging means. For example, in the third aspect of the present invention, when the speed of the first image is low, the virtual area generation means reduces the area of the virtual area. When the speed of the ball (first image) is slow, it is possible to avoid the inconvenience that the fielder (second image) starts the catching operation at a position away from the ball. That is, it is possible to solve the problem that a fielder jumps at a ball that is about to stop and catches the ball.

According to the fourth aspect of the invention, the virtual area has a shape extending in a direction perpendicular to the moving direction of the first image. Therefore, the fielder (second image)
Ball that flew from the position of the fielder to the left and right (first image)
Can catch.

In the fifth aspect of the invention, the image changing means generates a second image having a shape corresponding to the position of the first image on the virtual area. For example, when the fielder (second image) is located in the center of the virtual area, the ball (first image) flies in front of the fielder, so that the fielder who catches the ball in a forward posture is displayed. On the other hand, when the fielder is located at the end of the virtual area, the ball flies to the side of the fielder, so that the fielder who catches the ball in a sideways posture is displayed. In this way, by changing the posture of the fielder according to the position of the fielder in the virtual area, it is possible to reproduce a ball-catching motion close to the real thing.

In the invention described in claim 6, the image changing means generates a second image having a shape corresponding to the height of the first image with respect to the reference plane image. For example, the ball (first
When the position of (image) is higher than the ground (reference plane image), the fielder who catches the fly is displayed, and when the position of the ball is low, the fielder who catches Goro is displayed. As described above, by changing the catching attitude of the fielder according to the height of the ball, it is possible to reproduce the catching attitude of the fielder close to the real thing.

In the invention according to claim 7, the first image represents a baseball, the second image represents a baseball fielder, and the image changing means gradually changes the posture of the fielder according to the catching motion. To do. This makes it possible to realize a smooth ball catching operation.

In the invention described in claim 8, the coordinate conversion means projects a plurality of polygons represented by a three-dimensional coordinate system onto a two-dimensional coordinate system. Then, the hidden surface processing means determines the display order of the plurality of polygons projected on the two-dimensional coordinate system,
The determination is made based on the size of the coordinate value in the depth direction on the display screen, and the polygons are preferentially displayed according to this display order. Further, the hidden surface processing means determines the display order of the polygon group including a plurality of polygons whose description order is predetermined, based on the coordinate value in the depth direction of one polygon forming the polygon group. Then, the hidden surface processing means preferentially displays each polygon forming the polygon group based on the description order only when it is determined to display the polygon group.

That is, in the same polygon group, the coordinate values of the polygons in the depth direction are not compared (for example, Z sort), and the polygons are displayed according to a predetermined description order. Therefore, even when two polygons are in close contact with each other, it is possible to accurately perform the hidden surface processing. For example, the polygon representing the uniform and the polygon representing the uniform number can be accurately displayed as shown in the invention of claim 10.

In the ninth aspect of the invention, the hidden surface processing means determines the display order of the polygon group based on the coordinate values in the depth direction of the polygon having the highest description order.
Therefore, according to the present invention, the display order of polygon groups can be determined in the same manner as other polygons. Therefore, for example, the conventional hidden surface processing using the Z sort method and the hidden surface processing according to the present invention can be performed. It is possible to ensure compatibility.

In the eleventh aspect of the present invention, assuming a curved surface image having a radius R from the center point, the first calculates the distance r from the gift to the center point. Then, the image processing apparatus uses the distance r
When reaches the distance R, it is determined that the first image collides with the curved surface image. For example, in the invention of claim 11, when the curved surface image represents a baseball fence and the first image represents a ball, by comparing the distance R and the distance r, the ball and the fence can be easily separated. Collision determination can be performed.

In the thirteenth aspect of the present invention, a virtual area is generated at a position away from the first image by a distance that allows the first image to move within a predetermined time. Then, in the virtual area, the second
It is determined whether or not the image is located, and when it is determined that the second image is located in the virtual area, the shape of the second image is changed. For example, according to the present invention, since the virtual area for collision determination is located away from the first image, the time from when the second image enters the virtual area until when the first image and the second image collide is reduced. Can be long. Therefore, when the present invention is applied to a baseball game, it is possible to secure a sufficient time for changing the posture of a fielder when catching a ball.
It is possible to realize a smooth ball catching operation.

In the fourteenth aspect of the present invention, the moving speed and position of the first image are determined, and the shape of the virtual area is changed based on this moving speed and position.

According to the fifteenth aspect of the present invention, the display order of the plurality of polygons projected on the two-dimensional coordinate system is determined based on the size of the coordinate value in the depth direction with respect to the display screen, and the display order is determined. The polygon is displayed preferentially according to. Further, the display order of a polygon group including a plurality of polygons whose description order is predetermined is determined based on the coordinate values of one polygon forming the polygon group in the depth direction. Then, only when it is decided to display the polygon group, each polygon forming the polygon group is preferentially displayed based on the description order.

That is, in the same polygon group, the comparison of the coordinate values of the respective polygons in the depth direction (for example, Z sort) is not performed, and the polygons are displayed according to a predetermined description order. Therefore, even when two polygons are in close contact with each other, it is possible to accurately perform the hidden surface processing.

In the sixteenth aspect of the present invention, assuming a curved surface image having a radius R from the center point, the first calculates the distance r from the gift to the center point. Then, when the distance r reaches the distance R, it is determined that the first image has collided with the curved surface image.
For example, when the curved surface image represents a baseball fence and the first image represents a ball, the collision determination between the ball and the fence can be easily performed by comparing the distance R and the distance r. .

[0051]

EXAMPLES (First Example) I. Example Configuration FIG. 1 is an external view of a video game machine using the image processing apparatus according to the first embodiment of the present invention. In this figure, the main body 1 of the video game machine has a substantially box shape, and a board for game processing and the like are provided therein. Further, two connectors 2a are provided on the front surface of the video game machine main body 1, and these connectors 2a are provided with a PAD for game operation.
2b is connected via a cable 2c. When two players enjoy a baseball game etc., two PAD2
b is used.

A ROM is provided on the upper part of the video game machine body 1.
Cartridge I / F1a for connecting cartridge, CD-
A CD-ROM drive 1b for reading ROM is provided. Although not shown, a video output terminal and an audio output terminal are provided on the back surface of the video game machine body 1. This video output terminal is cable 4a
Is connected to the video input terminal of the TV receiver 5 via an audio output terminal, and the audio output terminal is connected via a cable 4b to a T
It is connected to the audio input terminal of the V receiver 5. In such a video game machine, the user can
By operating the, the game can be played while watching the screen displayed on the TV receiver 5.

FIG. 2 is a block diagram showing an outline of the TV game machine according to this embodiment. This image processing apparatus includes a CPU block 10 that controls the entire apparatus, a video block 11 that controls display of a game screen, a sound block 12 that produces sound effects, a subsystem 13 that reads a CD-ROM, and the like. Has been done.

The CPU block 10 is an SCU (System C
ontrol Unit) 100, main CPU 101, RAM 1
02, ROM 103, cartridge I / F 1a, sub C
The PU 104 and the CPU bus 103 are included. The main CPU 101 controls the entire apparatus. The main CPU 101 has a DSP (Di
(Gital Signal Processor) has the same calculation function, and can execute application software at high speed. RAM
Reference numeral 102 is used as a work area of the main CPU 101. An initial program for initialization processing and the like are written in the ROM 103. SCU
100 controls the buses 105, 106, and 107 so that the main CPU 101, VDPs 120 and 130,
Data is smoothly input and output between the DSP 140, the CPU 141, and the like. In addition, the SCU 100 has a DMA controller inside and can transfer sprite data during a game to the VRAM in the video block 11. As a result, application software such as a game can be executed at high speed. The cartridge I / F 1a is for inputting application software supplied in the form of a ROM cartridge.

The sub CPU 104 is an SMPC (System M
This is called an anager & Peripheral Control) and has a function of collecting peripheral data from the PAD 2b via the connector 2a in response to a request from the main CPU 101. Main CPU 101 is sub CPU 1
Based on the peripheral data received from 04, processing such as moving outfielders in the game screen is performed. Any peripherals such as PAD, joystick, keyboard, etc. can be connected to the connector 2a. The sub CPU 104 has a function of automatically recognizing the type of peripheral connected to the connector 2a (terminal on the main body side) and collecting peripheral data and the like according to a communication method corresponding to the type of peripheral.

The video block 11 is a VDP for drawing a character or the like composed of polygon data of a video game.
A (Video Display Processor) 120, a VDP 130 that performs drawing of a background screen, synthesis of polygon image data and a background image, clipping processing, and the like. VD
P120 is VRAM 121 and frame buffer 12
2, 123 are connected. The drawing data of the polygon representing the character of the video game machine is the main CPU 101.
From the SCU100 to the VDP120, VR
Written to AM121. The drawing data written in the VRAM 121 is, for example, 16 or 8 bits / pixe.
Frame buffer 122 or 12 for drawing in l format
3 is drawn. The drawn data in the frame buffer 122 or 123 is sent to the VDP 130. Information for controlling drawing is sent from the main CPU 101 to the SCU 100.
To the VDP 120 via. And VDP1
20 executes the drawing process according to this instruction.

The VDP 130 is connected to the VRAM 131, and the image data output from the VDP 130 is stored in the memory 1
It is configured to be output to the encoder 160 via 32. The encoder 160 generates a video signal by adding a synchronization signal or the like to this image data and outputs it to the TV receiver 5. As a result, the screen of the baseball game is displayed on the TV receiver 5.

The sound block 12 is composed of a DSP 140 that synthesizes voice according to the PCM system or the FM system, and a CPU 141 that controls the DSP 140 and the like. The audio data generated by the DSP 140 is converted into a 2-channel signal by the D / A converter 170 and then output to the speaker 5b.

The subsystem 13 includes a CD-ROM drive 1b, a CD I / F 180, a CPU 181, and an MPEG.
It is composed of AUDIO 182, MPEG VIDEO 183 and the like. This subsystem 13 is a CD-R
It has the functions of reading application software supplied in the form of OM and playing moving images. CD-R
The OM drive 1b reads data from a CD-ROM. The CPU 181 is a CD-ROM drive 1
The control of b, the error correction of the read data, and the like are performed. The data read from the CD-ROM is supplied to the main CPU 101 via the CD I / F 180, the bus 106, and the SCU 100, and is used as application software. In addition, MPEG AUDI
The O182 and MPEG VIDEO 183 are devices for restoring data compressed according to the MPEG standard (Motion Picture Expert Groug). These MPEG
By reproducing the MPEG compressed data written in the CD-ROM using the AUDIO 182 and the MPEG VIDEO 183, it becomes possible to reproduce the moving image.

Next, the configuration of the image processing apparatus according to this embodiment will be described. FIG. 3 shows the main CPU 101 and the RAM 1.
2 is a functional block diagram of an image processing apparatus configured by 02, a ROM 103, and the like. In this figure, the virtual area generation means 31 has a function of generating a collision area (virtual area) at a front position in the moving direction of the ball (first image). The position determination means 34 determines the speed and height (position) of the ball, and gives the determination result to the virtual area generation means 31. The determination unit 32 is configured to determine the positional relationship between the collision area and the fielder, and give the determination result to the image changing unit 33. The image changing unit 33 changes the posture of the fielder (second image) based on the determination result (positional relationship between the collision area and the fielder) by the determination unit 32. That is, when a fielder enters the collision area, the fielder catches a ball.

FIG. 4 shows an example of a baseball game screen displayed by the video game machine according to this embodiment. This baseball game can be executed by one or two people. That is, when there are two players, the two players perform defense and attack alternately, and when there is only one player, the players are computers (video game machines).
Alternately defend and attack with your opponent. On the display 5, a scene according to the progress of the game is displayed as three-dimensional graphics. In pitching, the scene seen from behind the batter is displayed, but immediately after the hit, the scene centered on the fielder is displayed as shown in the figure.

The fielders J and K can be moved by operating the PAD 2b. That is, if the player is a PA
When the D2b is operated, the main CPU 101 causes the ball 42
Of the fielders J and K located in the flight direction, the fielder J located on the infield side is moved first. When the fielder J misses the ball, the main CPU 101 causes the PAD2
Then, the outfielder K on the outfield side is moved according to the operation of b. In this way, it is possible to move a plurality of fielders by a simple operation.

At the same time when the batter 41 hits the ball, the main CPU 101 calculates the speed and direction of the ball 42,
An expected drop point 44 of the ball 42 is calculated from these calculation results. The expected drop point 44 is actually displayed on the screen. If the fielder J or K is moved to the vicinity of the expected drop point 44 before the ball 42 falls,
Fielder J or K can catch a fly.

A virtual collision area 43 is located on the ground (reference plane image) in the flight direction (forward) of the ball 42. This collision area 43
It is used when determining the collision between the ball 42 and the fielder, and is not actually displayed. When the fielder J or K moves into the collision area 43, the fielder J or K can catch the ball 42. On the other hand, as long as the fielder J or K is located outside the collision area 43, the fielder J or K does not catch the ball.

This collision area will be described in detail with reference to FIGS. FIG. 5: is a figure for demonstrating each positional relationship of a collision area, a ball, and a fielder. As shown in this figure, the collision area 43
Is located on the ground, which is separated from the ball 42 by a predetermined distance. That is, the collision area 43
Follows the flight of the ball 42 and moves on the ground in front of the ball 43. Collision area 43 and ball 42
The distance between and corresponds to the distance traveled by the ball 42 during a time of 12 interrupts.

In this embodiment, since an interrupt occurs every frame (vertical blanking cycle period 1/60 msec × 2 = 33.3 msec), 12 interrupt times are about 0.4 sec. . Further, since the postures of the fielders J and K change every interrupt (one frame), the fielder can perform the movement for 12 frames in the time of 12 interrupts. For example, as shown in FIG. 6, after the fielder J who has entered the collision area 43 starts catching the ball and finishes catching the ball, the fielder J turns his body toward the ball for 12 frames. The operation of can be performed.
Therefore, the fielder's ball catching operation can be displayed smoothly.

FIG. 7 is a diagram for explaining the collision area 43 and the catching posture. As shown in this figure, the collision area 43 includes areas A, B ₁ , B ₂ , and C.
₁ and C ₂ , each area A, B ₁ , B ₂ ,
Field catching postures 71 to 75 are associated with C ₁ and C ₂ . For example, when the fielder enters the area A, the ball comes to the front of the fielder, and the attitude of the fielder when catching the ball becomes a catching attitude 73. If the fielder enters area C ₁ , the ball is to the left of the fielder (the ball is in area A).
Therefore, the fielder's catching attitude becomes like catching attitude 71. In addition, the catching postures 71 to 75 shown in FIG.
In the case where the height of the ball is low, the catching posture is selected according to the height of the ball.

FIG. 8 is a top view of the collision area. As described above, the collision area 43 is composed of the areas A, B ₁ , B ₂ , C ₁ and C ₂ . The most central area A is located below the flight path of the ball and has a circular shape. Outside the area A, fan-shaped areas B ₁ , B ₂ , C ₁ and C ₂ are sequentially provided. Areas B ₁ , B ₂ , C ₁ and C ₂ disappear in order as the speed of the ball decreases. For example, when the ball bounces to the ground and the speed of the ball decreases, the areas C ₁ and C ₂ first disappear.

Further, when the speed of the ball decreases, the areas B ₁ and B ₂ disappear and only the area A remains. In real-life baseball, it is usually impossible for a fielder to jump on the ball (see catching postures 71 and 75 in FIG. 7) when the ball is about to stop. Therefore, by appropriately changing the size of the collision area 43 according to the speed of the ball, it is possible to make the action of the fielder on the screen closer to the action of the actual fielder.

[0070] In addition, it varies with the area B _1, B ₂ of the effective angle theta _b, area C _1, the effective angle of C ₂ theta _c likewise speed of the ball or the like. For example, when the speed of the ball is high, it is necessary to quickly move the fielder to the passing position of the ball. At this time, when the area of the collision area 43 is small, it becomes extremely difficult to catch the ball. Therefore, in such a case, the effective angle θ _b ,
By increasing θ _c and widening the area of the collision area 43, it is possible to reduce the difficulty of catching a ball at a high speed.

FIG. 9 shows how the shape of the collision area 43 changes with the movement of the ball. After the ball is hit, the collision area 43 passes through the positions (a) to (d) in order until it stops. The position (a) shows the position of the collision area immediately after the impact. As described above, when the ball is at a high speed, the effective angles θ _b and θ _c are increased in order to reduce the difficulty of catching the ball. Then, when the speed of the ball decreases, the effective angles θ _b and θ _c decrease, and the area of the collision area 43 decreases (position (b)).

Further, when the ball reaches the position (c) while reducing its velocity, the areas C ₁ and C ₂ of the collision area 43 disappear. Immediately before the ball stops (position (d)), areas B ₁ and B _{2 of the} collision area 43 are
Disappears. Since this collision area 43 is only the circular area A, the fielder can catch the ball from all directions. In this way, by changing the shape of the collision area 43 in accordance with the speed of the ball, it is possible to reproduce a real fielder's catching motion.

FIG. 10 is a diagram showing the fielder's catching posture according to the position of the fielder on the collision area and the height of the ball. In this figure, the vertical axis shows the height of the ball,
The horizontal axis represents the position of the fielder on the collision area.
Ball catching attitudes 111 to 113 represent fielders who catch balls while jumping, and ball catching attitudes 114 represent fielders who catch a fly. Further, the catching postures 115 to 119 represent the fielders who catch the ball at the chest height of the fielder, and the catching postures 120 to 1
Reference numeral 24 represents a fielder who catches Goro. Also, catching posture 1
25 represents a fielder who catches a ball while jumping to the front. Among these catching attitudes, catching attitudes 115 and 11
9, 120 and 124 are for catching a ball while moving.

Further, the catching posture is selected according to the position of the fielder on the collision area. For example, the fielder is area A
When the ball is located at the position (1) and the ball is at a high position (fly), the catching posture 114 with the grab raised is displayed. Further, when the fielder is located in the area C ₁ and the ball is located at the chest level of the fielder, the catching posture 115 with the glove extended to the left is displayed. in this way,
By changing the catching posture of the fielder according to the position of the fielder on the collision area and the height of the ball, a realistic baseball game can be provided.

II. Operation Next, the operation of the image position determination device according to the present embodiment will be described with reference to the flowcharts shown in FIGS.

FIG. 11 is a flowchart showing the operation of the video game machine using image processing. This flowchart is executed for each interrupt (one frame) on condition that the ball is hit by the batter. First, the position determination means 34 determines the moving direction, angle, and speed of the ball immediately after hitting (S1). Then, the virtual area generation means 31 determines, based on the speed of the ball,
The shape (size, effective angle) of the collision area 43 is determined. For example, immediately after hitting, when the speed of the ball is high, effectively the angle theta _b of areas B _1, B ₂ of the collision area 43, the area C _1, C ₂ the effective angle theta _c increases (FIG. 8, FIG. 9). The collision area 43 thus determined is located on the ground, which is separated from the ball by a predetermined distance in the forward direction. The distance between the collision area 43 and the ball is 4 at the time of 12 interrupts.
It corresponds to the distance that 2 goes. The collision area 43
Is not actually displayed on the screen.

The virtual area generating means 31 associates the fielder's ball catching posture with the areas A, B ₁ , B ₂ , C ₁ , C ₂ of the collision area 43 (S2). For example, as shown in FIG. 10, a catching posture for catching a ball in front of a fielder is associated with the area A, and the areas B ₁ , B ₂ , C ₁ , and C ₂ are respectively associated with the catching posture. Is associated with a catching attitude of catching a ball on the side of a fielder.

Subsequently, the judging means 32 selects a fielder who is likely to catch the ball (at a position close to the ball) from all the fielders, and the distance between the fielder and the center position of the collision area 43. D is calculated (S3). For example, in FIG. 1, when the fielder J is selected, the distance D between the fielder J and the center position of the collision area 43 is calculated. If the distance D is larger than the maximum radius of the collision area 43, that is, if the fielder J is located outside the collision area 43 (YES in S4).
Then, the determination means 32 executes the process of S10.

In S10, the judgment means 32 determines that the fielder J
Other than that, it is judged whether there is a fielder who may catch the ball. When there is a fielder K other than the fielder J who may catch the ball (NO in S10), the processing target is transferred to the fielder K (S9). Then, with respect to the fielder K, the processes of S3 and S4 described above are executed. As a result, if it is determined that the distance D between the fielder K and the center position of the collision area 43 is larger than the maximum size of the collision area 43, S10 is further executed. S
In the case where the determination means 32 determines that there is no fielder who may catch the ball other than the fielders J and K in 10 (YES in S10), the processing of this flowchart is ended, and it is illustrated. No return to the main flow chart.

After that, an interrupt occurs for each frame, and the above-mentioned flowchart of FIG. 10 is repeatedly executed. The ball moves and the speed and height of the ball also change when a predetermined time has elapsed after the ball was hit. The ball position determination means 34 determines the moving direction, angle, and speed of the ball at this time (S1), and the virtual area generation means 31 determines the shape (size, effective angle) of the collision area 43 based on the speed of the ball. Will be decided again. For example, when the speed of the ball becomes slow, the effective angle θ _b and the effective angle θ _c of the collision area 43 become small.

It is assumed that the player operates the PAD 2b and the player J enters the collision area 43. Then, the determination result of step S4 is NO, and the processing of S5 and thereafter is executed. The determining means 32 determines whether or not the distance D is smaller than the radius Ar of the area A, that is, the fielder J is in the area A.
It is determined whether or not it is located inside (S5). If the result of the determination is NO, the determining means 32 determines whether or not the distance D is smaller than the radius Br of the areas B ₁ and B ₂ (S).
6). Further, when the result of the determination is NO, it is determined whether the distance D is smaller than the radius Cr of the areas C ₁ and C ₂ (S7). That is, the determination means 32 uses S5 to S
At 7, it is determined in which area of the collision area 43 the fielder J is located.

For example, when the determination means 32 determines that the fielder J is located in the area B ₁ (YES in S6), S
8 subroutine is executed.

FIG. 12 shows the subroutine of S8. In step S81, the image changing unit 33 calculates the angle formed by the center point of the collision area 43 and the fielder J.
Then, the image changing unit 33 determines whether or not the catching attitude corresponding to the calculated angle is defined (S8).
2). When the catching attitude is not defined (N in S82)
O), after the process is transferred to the next fielder (S86),
Returning to the main flowchart of FIG. For example, fielder J
In the case of entering the left side of the collision area 43 (the area B ₁ side), the catching posture 115 in FIG. 10 is defined (YES in S82), and therefore the processes of S83 and subsequent steps are executed.

The image changing means 33 determines the correct catching posture based on the information of the PAD (or stick) 2b, the orientation of the fielder, the height of the ball, etc. (S83). And
When the catching attitude determined in this way does not exist (NO in S84), the process is performed to the next fielder, for example, fielder K.
(S86), the process returns to the main flowchart of FIG. On the other hand, when the catching attitude determined in S83 exists (YES in S84), the attitude of the fielder J on the screen is changed to the catching attitude (S85), and the process is performed after returning to the main flowchart of FIG. To finish. In this way, after the fielder to catch the ball is determined, the subroutine of FIG. 12 is not executed, and the posture changing process (not shown) is executed for each interrupt. By this posture changing process, the posture of the fielder J gradually changes for each frame.
Then, 12 interrupts after the fielder J starts the catching motion, the ball enters the glove of the fielder J.

Therefore, according to the present embodiment, since the fielder can perform the action of 12 interrupts (12 frames) after the fielder enters the collision area 43, the ball-catching action close to the real thing is reproduced. It becomes possible. Further, by changing the ball catching posture according to the position of the fielder on the collision area 43, it is possible to realize a realistic ball catching operation.

(Second Embodiment) A video game machine according to the second embodiment is a video game machine according to the above-mentioned first embodiment to which a function for displaying a uniform number is added. Hereinafter, this function will be described with reference to FIGS. 13 and 14.

FIG. 14 is a diagram for explaining the data structure of a polygon representing the upper body of the player. In this figure, the uniforms are four polygon groups 14A, 14
B, 14C, 14D. Each polygon group is composed of a polygon representing a part of the uniform and a polygon representing a part of the uniform number. That is, the polygon 14A is composed of a polygon 1401 representing a part of a uniform divided into four parts, and a polygon 1411 representing a part of a uniform number divided into four parts. Similarly, the polygon group 14B is composed of polygons 1402 and 1412, and the polygon group 14C is composed of polygons 1403 and 1413. The polygon group 14D is composed of polygons 1404 and 1414.

Polygon groups 14A, 14B, 14
The polygon description order (priority order) is set for each of C and 14D. For example, in the polygon group 14A, the uniform polygon 140
The description rank is set in the order of 1 and the polygon number 1411 of the uniform number. Also, polygon groups 14A, 14B, 1
The polygon having the highest description rank in each of 4C and 14D is selected as a polygon representing each polygon group. That is, the polygons 1401, 1402, 1403, and 1404 that display uniforms are selected as the polygons representing the polygon groups 14A, 14B, 14C, and 14D, respectively.

The procedure for displaying the polygon data thus configured will be described with reference to FIG. (A) in the figure
As shown in FIG.
1 to 1404, polygons 1411 to 141 representing uniform numbers
4 is represented by coordinates in a three-dimensional coordinate system.
The main CPU 101 (FIG. 2) performs coordinate conversion on this three-dimensional coordinate system to generate the two-dimensional coordinate system shown in FIG. Coordinate conversion is performed by polygons 1401 to 140.
This is performed by projecting the coordinates of the vertices of 4, 1411 to 1414 onto a two-dimensional coordinate system.

Then, the main CPU 101 causes the polygons 1401, 1402, 1403, 14 representing each of the polygon groups 14A, 14B, 14C, 14D.
04 and other polygons (polygons representing fielder's chest, arms, etc.) are determined. For example, when the fielder faces the front (the chest faces the screen), the back is located behind the chest. That is, the polygons 1401, 1402, 1403, 140 representing the polygon groups 14A, 14B, 14C, 14D, respectively.
The Z coordinate value of 4 is larger than the Z coordinate value of the polygon representing the chest. Therefore, in this case, polygon group 1
The entire 4A, 14B, 14C, 14D disappears (the back is hidden behind the chest).

On the other hand, when the fielder is facing backward with respect to the screen, the polygon groups 14A, 14B, 14C,
Polygons 1401 and 140 representing each of 14D
The Z coordinate values of 2, 1403, and 1404 are smaller than the Z coordinate value of the polygon representing the chest. In this case, the polygon groups 14A, 14B, 14C, 14D are displayed with priority over the chest polygons. Polygon group 14A, 14
In each of B, 14C and 14D, polygons are displayed according to a predetermined description order. For example,
In the polygon group 14A, the polygon 14 representing the uniform number is superimposed on the polygon 1401 representing the uniform.
11 is overwritten. That is, in the same polygon group, the Z coordinate values of the polygons are not compared (Z sort), and the polygons are displayed according to a predetermined description order.

As described above, in the same polygon group, the Z coordinate values of the polygons are not compared with each other, and the polygons are displayed according to a predetermined description order. Therefore, even when two polygons are in close contact with each other, such as a uniform and a polygon, it is possible to perform an accurate hidden surface treatment. For example, the polygon representing the uniform and the polygon representing the uniform number can be accurately displayed as shown in the invention of claim 10. Further, since the display order of the polygon group is determined based on the Z coordinate value of the polygon having the highest description order, compatibility between the hidden surface processing and the Z sort method according to this embodiment can be ensured. .

The present embodiment is not limited to displaying the uniform number on the uniform, but can be applied to the number on the competition vehicle.

(Third Embodiment) The video game machine according to the present embodiment is the video game machine according to the above-mentioned first embodiment to which the following functions are added. A video game machine according to a third embodiment of the present invention will be described with reference to FIG.

FIG. 15 is an external view of the stadium 1500 on the screen. A virtual center point 1502 is set behind the second base, and an arc having a radius R and an angle θ with respect to the center point 1502 is displayed as an outfield fence 1501. Further, in this figure, reference numeral 1503 indicates a ball hit by a batter. Main C
The PU 101 calculates the distance r from the center point 1502 to the ball 1503, and determines whether the angle φ in the figure is within the range of the angle θ. In addition to these two conditions, if the condition that the height of the ball 1503 is less than or equal to the height of the outfield fence 1501 is satisfied, the main CPU
101 determines that the ball 1503 has collided with the outfield fence 1501. Then, the main CPU 101 performs a process of bouncing the ball 1503 from the outfield fence 1501, and the bouncing ball is displayed on the display 5.

According to this embodiment, it is possible to determine the collision between the ball and the outfield fence only by calculating the distance r and the like, and there is no need to perform the complicated collision determination processing between polygons. Therefore, it is possible to easily determine the collision between the ball and the outfield fence.

(Other Embodiments) The present invention is not limited to the above embodiments, but can be modified and implemented without departing from the spirit of the present invention. For example, the present invention may be applied to not only baseball games but also soccer games, tennis games, and the like.

[0098]

As described above, according to the present invention, the following effects can be obtained.

First, it becomes possible to display a smooth ball catching operation. In the present invention, a collision area (virtual area) is generated at a position separated from the ball (first image) by a predetermined distance. Then, the determination means determines whether or not the fielder (second image) is located in the collision area,
When it is determined that the fielder is located in the virtual area, the image changing unit changes the posture (shape) of the fielder. For example, when the fielder enters the collision area, the posture of the fielder gradually changes from the standby state to the ball catching state. After that, when the ball reaches the fielder, the posture of the fielder is in the state of catching the ball. According to the present invention, since the collision determination collision area is located away from the ball, it is possible to lengthen the time from when the fielder enters the collision area until the ball reaches the fielder. Therefore, it is possible to secure a sufficient time (time for changing the posture of the fielder) from the start of the fielder's ball catching operation to the completion of the ball catching operation, and a smooth ball catching operation can be realized. Becomes

Further, the fielder's catching posture is changed according to the position of the fielder on the collision area. For example,
When the fielder is located in the center of the collision area, the fielder shows the action of catching the ball in the forward direction, and when the fielder is at the end of the collision area, the action of the fielder in the sideways direction is displayed. be able to. This makes it possible to display a realistic catching motion.

Further, the velocity and position (height) of the ball
By changing the shape of the collision area in accordance with the above, it is possible to reproduce the ball catching operation close to the real thing. For example, when the position of the ball is higher than the ground (reference plane image), the fielder who catches the fly is displayed, and when the position of the ball is low, the fielder who catches the ground ball is displayed.

Secondly, it becomes possible to judge the collision between the hit ball and the fence by a simple calculation. In the present invention, a fence (curved surface image) having a radius R from the center point is assumed, and the distance r from the ball to the center point is appropriately calculated. Then, when the distance r reaches the distance R, it is possible to easily perform the collision determination process by determining that the ball has collided with the fence.

Thirdly, it becomes possible to accurately perform the hidden surface processing of polygons that are in close contact with each other. According to the present invention, in the same polygon group, the Z coordinate values of the polygons are not compared with each other, and the polygons are displayed according to a predetermined description order. Therefore, even when two polygons are in close contact with each other, such as a uniform and a polygon, it is possible to perform an accurate hidden surface treatment. Also, the display order of polygon groups is
Similar to the display order of other polygons, it is determined by an algorithm such as the Z sort method, so that compatibility between the hidden surface processing according to the present invention and the conventional hidden surface processing (for example, the Z sort method) can be ensured. It will be possible.

[Brief description of drawings]

FIG. 1 is an external view of a video game machine according to a first embodiment of the present invention.

FIG. 2 is a schematic configuration diagram of a video game machine according to the first embodiment of the present invention.

FIG. 3 is a functional block diagram of the image processing apparatus according to the first embodiment of the present invention.

FIG. 4 is a diagram showing a screen of a baseball game according to the first embodiment of the present invention.

FIG. 5 is a collision area according to the first embodiment of the present invention,
It is a figure showing a ball and a fielder's physical relationship.

FIG. 6 is a diagram showing a state in which a fielder has entered the collision area according to the first embodiment of the present invention.

FIG. 7 is a diagram showing a correspondence between each area of the collision areas and the catching attitude according to the first embodiment of the present invention.

FIG. 8 is a diagram for explaining details of a collision area according to the first embodiment of the present invention.

FIG. 9 is a diagram for explaining changes in the shape of the collision area according to the first embodiment of the present invention.

FIG. 10 is a diagram for explaining a ball catching posture of a fielder according to the first embodiment of the present invention.

FIG. 11 is a flowchart showing the operation of the video game machine according to the first embodiment of the present invention.

FIG. 12 is a flowchart showing the operation of the video game machine according to the first embodiment of the present invention.

FIG. 13 is a view for explaining the video game machine according to the second embodiment of the present invention.

FIG. 14 is a flowchart showing the operation of the video game machine according to the second embodiment of the present invention.

FIG. 15 is a diagram for explaining a video game machine according to a third embodiment of the present invention.

[Explanation of symbols]

31 virtual area generation means 32 determination means 33 image change means 34 position determination means 42 ball (first image) 43 collision area (virtual area) 71-75, 111-125, J, K fielder (second image) 101 main CPU (Coordinate conversion means, hidden surface processing means) 14A, 14B, 14C, 14D Polygon group 1501 Outfield fence (curved surface image)

─────────────────────────────────────────────────── ───

[Procedure amendment]

[Submission date] June 12, 2002 (2002.6.1)
2)

[Procedure Amendment 1]

[Document name to be amended] Statement

[Name of item to be amended] Claims

[Correction method] Change

[Correction content]

[Claims]

1. An image processing apparatus that determines a collision between a curved surface image having a radius R from a center point and a first image, calculates a distance r from the center point to the first image, and the distance r reaches the distance R. If so, the image processing apparatus that determines that the first image has collided with the curved image.

2. The curved surface image represents a baseball fence,
The first image is an image processing apparatus according to claim 1, wherein represents a ball.

4. An image processing method for determining a collision between a curved surface image having a radius R from a center point and a first image, wherein a distance r from the center point to the first image is calculated, and the distance r reaches the distance R. If so, an image processing method for determining that the first image has collided with the curved image.

   ─────────────────────────────────────────────────── ─── Continued front page    F-term (reference) 2C001 AA04 AA05 BA02 BA05 BA06                       BC05 BC08 CA01 CB01 CB04                       CB06 CC02                 5B050 AA10 BA07 BA08 BA09 BA12                       CA07 EA04 EA07 EA13 EA24                       EA29 FA02                 5B080 AA13 CA01 GA02

Claims (16)

[Claims] 1. In an image processing apparatus that changes the shape of a second image when it is determined that the first image and the second image collide with each other, the first image moves within a predetermined time from the first image. It is determined that the virtual area generation unit that generates the virtual area is located at a position that is distant by the obtained distance, the determination unit that determines whether the second image is located in the virtual area, and the second image is located in the virtual area. In this case, the image processing apparatus includes an image changing unit that changes the shape of the second image. 2. The position determining means for determining the moving speed and the position of the first image, wherein the virtual area generating means changes the shape of the virtual area based on the result of the determination by the position determining means. Image processing device. 3. The image processing apparatus according to claim 2, wherein the virtual area generation means reduces the area of the virtual area as the speed of the first image decreases. 4. The image processing apparatus according to claim 1, wherein the virtual region has a shape extending in a direction perpendicular to a moving direction of the first image. 5. The image processing apparatus according to claim 1, wherein the image changing unit generates a second image having a shape corresponding to the position of the first image on the virtual area. 6. The image processing apparatus according to claim 1, wherein the image changing unit generates a second image having a shape corresponding to a height of the first image with respect to a reference plane image. 7. The first image represents a baseball ball, the second image represents a baseball fielder, and the image changing means gradually changes the posture of the fielder according to a catching operation. The image processing device according to claim 6. 8. A coordinate conversion means for projecting a plurality of polygons represented by a three-dimensional coordinate system onto a two-dimensional coordinate system and a display order of the plurality of polygons projected on the two-dimensional coordinate system.
In the image processing device, which is determined based on the magnitude of coordinate values in the depth direction with respect to the display screen, and which has a hidden surface processing unit that preferentially displays polygons according to this display order, the hidden surface processing unit is Only when it is determined that the display order of a polygon group including a plurality of polygons whose order is predetermined is determined based on the coordinate values in the depth direction of one polygon that constitutes the polygon group, and the polygon group is displayed. An image processing apparatus for preferentially displaying each polygon constituting the polygon group based on the above described order of description. 9. The image processing apparatus according to claim 8, wherein the hidden surface processing means determines the display order of the polygon group based on the coordinate values in the depth direction of the polygon having the highest description order. 10. The image processing apparatus according to claim 8, wherein the one polygon represents a uniform number, and the other polygon represents a uniform. 11. An image processing apparatus that determines a collision between a curved surface image having a radius R from a center point and a first image, calculates a distance r from the center point to the first image, and the distance r is the distance R.
The image processing apparatus that determines that the first image has collided with the curved surface image when the first image has reached. 12. The image processing apparatus according to claim 11, wherein the curved surface image represents a baseball fence, and the first image represents a ball. 13. In an image processing method for changing the shape of a second image when it is determined that the first image and the second image collide with each other, the first image moves within a predetermined time from the first image. A virtual area is generated at a position distant by the distance to be obtained, and it is determined whether or not the second image is located in the virtual area. If it is determined that the second image is located in the virtual area, Image processing method to change the shape. 14. The image processing method according to claim 12, wherein the moving speed and the position of the first image are determined, and the shape of the virtual region is changed based on the moving speed and the position. 15. A plurality of polygons represented by a three-dimensional coordinate system are projected on a two-dimensional coordinate system, and the display order of the plurality of polygons projected on the two-dimensional coordinate system is the depth direction with respect to the display screen. In the image processing method of determining the size of the coordinate values of the polygons, and displaying the polygons preferentially according to the display order, the display order of the polygon group including a plurality of polygons whose description order is predetermined is configured as the polygon group. The image processing that preferentially displays the respective polygons forming the polygon group based on the above description order, when the polygon group is determined based on the coordinate value of the polygon in the depth direction and only when the polygon group is displayed. Method. 16. An image processing method for determining a collision between a curved surface image having a radius R from a center point and a first image, wherein a distance r from the center point to the first image is calculated, and the distance r is the distance R.
Image processing method that determines that the first image has collided with the curved surface image when the first image has reached.