JP5050494B2 - A computer program that displays information on the predicted trajectory of a moving object. - Google Patents

Description

 The present invention relates to a computer program for displaying information on a predicted trajectory of a moving object and a game apparatus to which the computer program is applied, and particularly according to the output of an input device (pointing device) operated by a player (player). The present invention relates to a program for moving and displaying an object on a display device.

  Until now, based on the operation of the player, a game that displays the movement of a ball as a moving object on the screen of a display device and simulates a sport that handles the ball can be executed in various game devices.

  As a ball game, for example, as described in Patent Document 1, an expected ballistic trajectory of a ball is displayed based on shot elements before a golf shot operation, or as described in Patent Document 2. In addition, in a game simulating table tennis or the like, the swing hitting method is determined according to the input operation of the player, the ball trajectory corresponding to the hitting method is displayed on the display device, and reference information for the player is displayed. The invention to do is known.

  On the other hand, various new functions have been developed as input devices operated by players, and it has become possible to realize games that simulate new sports using these functions.

However, some new sports that are made into games are not common to players. Therefore, in such a case, it is important to enjoy the sport game while reflecting the rules and determination results in the game.
JP 2004-290657 A Japanese Patent No. 3763766

  In the conventional inventions described in the above Patent Documents 1 and 2, as described above, an expected trajectory of the ball is displayed to display information advantageous to the player. However, in the case of sports such as squash, for example, the rules are not common for players. In addition, the squash ball moves at high speed while bouncing off in the space of the rectangular parallelepiped on the five surfaces other than the ceiling, and moves in a complicated and intense manner.

  In addition, squash rules are complex. For example, it is a requirement to hit the front wall with no bound. Furthermore, even if it touches the four surrounding walls, it is not included in the number of bounces, but if you bounce two times on the floor, you will get a score on the other side.

  When simulating sports with such complicated rules and intense ball movement on the game, it is difficult to distinguish whether the ball bounces on the floor or the wall, so the predicted trajectory of the ball is always displayed in real time. However, it is preferable to give the player information on when to hit the ball and at what position.

  In addition, when it is affected by an unpredictable element, it is necessary to draw and display information that is immediately reflected, and it is desirable that information about rules is displayed in drawing a trajectory.

  Accordingly, an object of the present invention is to solve the above-mentioned demands and problems in the case of simulating a sport in which a complex and intense ball (moving object) such as squash moves and the rules are complex. It is an object of the present invention to provide a computer program for displaying information with a predicted trajectory of a moving object that performs the display.

  A first aspect of the present invention that solves the above problem is to determine a collision between a character and a ball that moves in response to an input operation of a player on a field having a plurality of planes provided in a virtual space. , A computer program for causing a computer system to execute a process of displaying a state of a game for changing the trajectory of the ball as an image viewed from a virtual viewpoint arranged in the virtual space, the program being moved to the computer system A trajectory calculation step for calculating the trajectory of the ball, a trajectory display step for displaying the trajectory on a screen, a frequency measurement step for measuring the number of times the trajectory touches a predetermined plane from the collision, and the measured frequency And a trajectory display changing step for changing and displaying the trajectory display form when the predetermined number of times is exceeded.

  In the above aspect, the trajectory display step can predict and display up to a predetermined time ahead of the ball.

  In the above, the trajectory calculation step may calculate the trajectory based on at least one of a movement direction, a movement speed, and a rotation direction of the ball.

  In addition, when the collision is determined based on the input operation of the player, the computer system is provided with at least one of the movement direction, the movement speed, and the rotation direction of the ball based on the acceleration of the input operation. You may make it perform further the parameter change step to change.

  In any of the above, a collision position determination step for determining a position where the collision occurs based on an input operation of the player, and a collision position display step for displaying the collision position on a screen in a predetermined form. May be further executed.

  Further, in the above, when the ball touches the predetermined surface for the predetermined number of times, a game ending step for ending the game is further executed.

  In the above, the trajectory display step may display the moving trajectory of the ball as a line or a point group.

  Embodiments of the present invention will be described below with reference to the drawings. In addition, although it demonstrates taking the case of the game which simulates squash as an example, application of this invention is not limited to this squash.

  FIG. 1 is a functional block diagram of a configuration example of a computer system that functions as a game device applied to the present invention. Each functional unit exchanges data through the bus 10.

  The game is controlled by the main CPU 1 in accordance with a game program stored in an external memory or a ROM 2 represented as an internal memory.

  In this game execution control, the main CPU 1 as the control means performs coordinate conversion on the object data stored in the ROM 2 to form object data whose movement is controlled according to the game program in the virtual three-dimensional space. Further, the data of the object having the virtual three-dimensional coordinates to be moved is perspective-converted to the two-dimensional coordinates to be displayed on the display device 5 by the main CPU 1.

  At this time, the rendering processor 4 reads out the texture data from the texture memory 6 according to the game program for the object data whose coordinates are converted into the two-dimensional coordinates, pastes the read texture, and draws it in the video memory 7 as image data. To do.

  The image data drawn in the video memory 7 is read at a predetermined cycle and sent to the display device 5, whereby a game image including an object whose movement is controlled according to the game program is displayed on the display device 5.

  In contrast to the basic operation of such a game device, the present invention is processed according to a game program stored in the ROM 2, and is characterized by displaying information on the predicted movement trajectory of a moving object (ball in a squash game). Have

  Therefore, the aspect of the invention which is the subject of the present application resides in a game program for performing drawing by giving information to the predicted movement trajectory of such a moving object, and a game apparatus that is controlled by the game program.

  In FIG. 1, in addition, in the application of the present invention, the first controller used to control the movement of the character that performs squash on the screen by the player, and the timing at which the player hits the ball that is the moving object of the character that performs squash. The wireless receiver 8 which receives the signal from the 2nd controller which controls is provided.

  The wireless receiver 8 receives information generated by the first controller and the second controller wirelessly, for example, using Bluetooth (registered trademark).

  Further, although not directly related to the present invention in FIG. 1, an interface unit 9 connected to another external device is connected to the bus 10.

  FIG. 2 is a diagram for explaining the relationship between the wireless receiver 8 and the first and second controllers 20 and 21 operated by the player.

  The first controller 20 can be connected to the second controller 21 by wire. The second controller 21 has a wireless function, for example, the Bluetooth function described above, and the information generated by the first controller 20 and the information generated by the second controller 21 are built in the game apparatus body 30 in a predetermined format. To the wireless receiver 8 to be transmitted.

  As the first controller 20 and the second controller 21, for example, a remote control system called Wii (registered trademark) provided by Nintendo Co., Ltd. can be used.

  Since the first controller 20 and the second controller 21 are separated from the game apparatus body 30, the player can freely operate the first controller 20 and the second controller 21 with both hands. Is possible.

  In FIG. 2, a display screen 50 in which the display device 5 is connected to the game apparatus main body 30 and a squash game is drawn is shown.

  The first controller 20 is connected to the interface unit 8 (not shown in FIG. 2) of the game apparatus body 30 by wire. The second controller 21 is wirelessly connected to the wireless receiver 9 of the game apparatus body 30.

  Here, details of the first controller 20, the second controller and the roller 21 will be further described with reference to FIGS.

  FIG. 3 is a diagram for explaining the first controller 20. As shown in the figure, a joystick 200 is provided and can be tilted up, down, left and right. The main CPU 1 receives a signal indicating the direction in which the joystick 200 is tilted through the interface unit 8. Then, the main CPU 1 changes the two-dimensional coordinate position displayed on the display screen 50 of the character 40 so as to be displayed on the right side of FIG. 3 corresponding to the received signal.

  Thereby, the character 40 is moved and displayed on the display screen 50 of the display device 5 in accordance with the operation direction of the first controller 20.

  On the other hand, FIG. 4 is a diagram for explaining the second controller 21. The second controller 21 has various functions. The function used in the application of the present invention is that the second controller 21 detects and outputs the acceleration and the direction when the second controller 21 is swung by the player. It is a function to do.

  In order to have such a function, the second controller 21 is equipped with a triaxial acceleration sensor. A three-axis acceleration sensor is generally known as a sensor that detects acceleration, inclination, and vibration in a three-dimensional space by dividing them into three-axis components of the X, Y, and Z axes.

  For example, it has a weight part in the center, is supported by a beam in the X and Y axis directions and a peripheral frame, and is a combination of outputs of strain detection elements (piezoresistive elements) formed in the beam. It is possible to detect by dividing into three axis components of the Z axis.

  The second controller 21 further has a wireless function for transmitting the detected output to the wireless receiver 9 of the game apparatus body 30 wirelessly in a predetermined format.

  In FIG. 4, when the second controller 21 is swung in the direction of the arrow, the acceleration sensor detects that the controller 21 has been lowered, and the result is transmitted to the game apparatus main body 30 side. Therefore, according to the program, the main CPU 1 generates an image that shakes the racket 41 of the character 40 based on the detection signal of the descending controller 21 and displays it on the display screen 50.

  Further, as the control, the acceleration sensor of the controller 21 detects the strength of descending the controller 21, so this information can also be sent to the game apparatus main body 30. Thereby, the launch strength of the ball hit by the racket 41 is controlled as will be described later.

  Further, as a control, as shown in FIG. 5, the direction B in which the ball is hit back is controlled in accordance with the timing at which the racket hits the direction A in which the ball flies.

  FIG. 5A shows the direction B in which the ball is hit back when the timing of swinging the racket 41 is early, and the ball is hit in the left direction. FIG. 5B shows a direction B in which the ball is hit back when the timing of swinging the racket 41 is intermediate, and the direction is the same as the direction A in which the ball flies. FIG. 5 (1) shows a direction B in which the ball is hit back when the timing of swinging the racket 41 is late, and the ball is hit in the right direction.

  Before explaining the details of the display control of the moving trajectory of the moving object (ball in squash) of the present invention executed based on such basic control, the outline of the display control of the moving trajectory of the moving object according to the present invention will be explained. Keep it.

  FIG. 6A to FIG. 6C and FIG. 7 are display screen examples (No. 1 to No. 4) of a squash game that are displayed on the display device 5 by the main CPU 1 in accordance with the game program.

  In FIG. 6A to FIG. 6C and FIG. 7, the fields of the front wall W1, the left and right walls W2, W3, and the floor (floor surface) W4 are displayed except for the rear wall. A character 40b whose movement is controlled by the player and an opponent character 40a whose movement is controlled by the computer according to the program are displayed. When a game is performed between two players, the character 40a is controlled to move by a player different from the player who operates the character 40b.

  Furthermore, the images on the display screens shown in FIGS. 6A to 6C display the expected movement trajectory of the ball when the character 40a hits the ball 50 with the racket 41a.

  FIG. 6A shows an expected movement trajectory 60, 61 at a certain frame time point when it hits with the racket 41a, hits the front wall W1, then falls to the floor surface W4, bounces and further rolls on the floor surface W4. Is displayed.

  FIG. 6B is an image of a frame display screen subsequent to FIG. 6A, and displays expected movement trajectories 60 and 61 after the timing when the ball 50 bounces on the floor surface W4. At this time, there is an input operation for operating the racket 41b by the player 40b whose number hits the ball 50, and it is determined whether or not the ball 50 is in the hit possible range 70 based on the position of the character 40b. If it is, the predicted hit point 51 is displayed.

FIG. 6C is an image of a display screen of a frame following FIG. 6B, in which the ball 50 bounces on the floor surface W <b> 4 and bounces higher, and almost reaches the expected hit point 51. At this time, a state in which the racket 41b of the character 40b operated by the player is closer to the predicted hit point 51 of the ball is displayed.

  Also, in FIGS. 6A to 6C, an expected movement locus 60 indicates a movement locus before two bounds on the floor surface W1, and the movement locus after the second bound is determined to be a failure in the game rules. The movement trajectory 60 is displayed on the display screen while being distinguished by a different line thickness or line color.

  Further, the expected movement trajectories 60 and 61 indicate the expected movement trajectories from the time when the ball 50 is hit with a racket to, for example, 2 seconds later.

  FIG. 7 is an example of an image displayed on the display screen after hitting the ball 50.

  When the racket 41b of the character 40b in the order to be hit is operated, the ball 50 is hit at the expected hit point 51, and new predicted movement trajectories 60a and 61a are formed and displayed with the hit point as the starting point 52. The

  The new predicted movement trajectories 60a and 61a at this time hit the front wall W1 and then hit the rear wall in a no-bound state, and then the expected movement trajectory 60a until the first bounce from the rear wall to the floor surface W4. An expected movement trajectory 61a after the bounce is shown.

  As described above, the expected movement trajectory 61a after the second bounce is displayed differently from the expected movement trajectory 60a until the first bounce (distinguishment by display / non-display such as the color of the trajectory display or the thickness of the line). Difference). In addition, the movement trajectory is not displayed after a predetermined time has elapsed since the ball was hit, for example, after 2 seconds.

  FIG. 8 is an enlarged view of an example of the ball trajectory. A ball trajectory is shown in which a plurality of balls are arranged in the depth direction from the front side P1 of the drawing. The display after the second bouncing point P2 of the ball is changed in color. In addition, the distance between the balls represents the speed of the ball movement.

  As described above, the present invention displays the predicted movement trajectory of the ball from the time when the ball 50 is hit until the predetermined time elapses, and changes the display of the predicted movement trajectory of the ball after two bounds on the losing floor surface W4. So that it is controlled.

  As a result, it is possible to predict the whereabouts of a ball that moves violently, and it is possible to guess the timing at which the ball should be returned in accordance with the rules, so that even a player who is not familiar with the sport can easily enjoy the game. Can do.

  FIG. 9 and FIG. 10 are operation flows for explaining the details of the computer program procedure for displaying information with the predicted moving trajectory of the moving object of the present invention described above.

  First, in FIG. 9, when the squash game is started, the main CPU 1 detects the operation of the second controller 21 (corresponding to the racket 41 in FIG. 9 and abbreviated as a device) corresponding to the player who hits the serve. (Step ST1).

  For detection of an operation on the device, the main CPU 1 stores the triaxial (X, Y, Z) gravity values of the device in the RAM 3 for a fixed time (1 second). Then, a change in the acceleration of the device over a certain time and a change in the direction of gravity from a stationary time are detected, and it is determined that the device is considered to be swung forward.

  The detection of the acceleration and the direction of gravity are both calculated based on the change in the triaxial gravity value of the acceleration sensor. When an acceleration sensor is not used, a conventional controller or the like is used to detect a change in an input signal caused by a player's button input operation, and when it is detected, it is determined that the device has been operated (hereinafter referred to as “device operation”). Is the same).

  When a device operation is accepted in step ST1, ball trajectory data from a ball trajectory process for calculating the trajectories of balls processed in parallel to a predetermined time (for example, after 2 seconds) is received, and the trajectory is displayed on the screen. (Step ST2).

  At this time, if the number of times that the ball trajectory bounces to the floor (court) W4 becomes 2 times or more, it is displayed differently from the color of the ball trajectory so far. Alternatively, it is possible to perform corresponding processing such as a line from a point group, a point to line group, and no display after two bounds. This is because the ball 50 is bound to the wall surfaces W2 and W3 and the trajectory of the ball is likely to change, so that the player can easily understand where and when to hit.

  The ball trajectory processing is performed when the ball 50 rebounds on the three-axis (X, Y, Z) speed parameter (including the rotation parameter if the ball is rotating) and the four wall surfaces or floor surface (court). Based on the elastic modulus of the ball, the ball trajectory up to 2 seconds later is calculated every frame. The elastic coefficient may be given not only to the ball but also to the four wall surfaces and the floor surface (court), and the three-axis velocity parameter of the ball may be given separately for the velocity and direction (vector).

  In this game, the four wall surfaces and the floor surface (court) are all along the coordinate axis direction.

  Details of the ball trajectory process (step ST2) are shown in the operation flow of FIG.

  Next, when the game end indication is displayed on the rule, such as when the ball 50 does not hit the front wall W1 with two bounds or the front wall W1, the game is ended (step ST3).

  If the game does not end in step ST3, it is detected whether the player who should hit the ball 50 has operated the device (step ST4). If no device operation is detected, the process returns to step ST2 (step ST4, NO).

  When a device operation is detected in ST4 (step ST4, YES), changes in acceleration and gravity direction (triaxial gravity value) due to the device operation from this time start to be recorded in the buffer RAM 3 (step ST5).

  When a conventional controller is used, recording is started in the RAM 3 in response to an input from a cross key or a button for shaking a racket.

  The positional relationship between the character 40 and the ball 50 is calculated, and it is detected whether the character 40 is in a range where the ball 50 can be hit (step ST6). This determination is made based on whether or not the ball 50 is present in a predetermined area (area within the hit possible range 70 in FIG. 6B) as described above.

  If the character 40 is not in the range where the character 40 can be hit in step ST6, an idle motion is drawn, and then the process returns to step S2 (YES in step ST7).

  If the character is within the range where the ball can be hit, the swing motion is determined from the positional relationship between the character and the ball, and display is started (step ST8).

  The ball hitting point is calculated from the positional relationship in step ST6 and displayed in a predetermined form (for example, a red ball 51 enlarged on the screen than the track display 60: refer to FIG. 6B) to teach the part where the track changes. Step ST9).

  In the swing motion display started in step ST8, the process waits for a process for determining whether the ball and the racket collide (step ST10).

  When the collision determination between the ball and the racket is obtained in step ST10, the three axes (X, Y, Z) of the ball are determined based on the gravitational and acceleration changes for the latest 25 frames that have been stored in the buffer RAM 3 in step ST5. ) The speed parameter and the rotation parameter are changed (step ST11).

  When the acceleration change is large, increase the speed of the ball, or tilt the ratio of the three-axis speed (X and Y) of the ball according to the speed of the collision timing as shown in FIG. Can do.

  Furthermore, in order to preferentially reflect the device operation when it is close to the collision, the degree of influence on the ball is evaluated in order from the new value in 25 frames.

  Change the device operation (acceleration, etc.) so that the game continues as much as possible.

  Further, the direction in which the ball is hit is corrected so as to approach the center of the front wall W1.

  Similarly, in the case of a conventional controller, the direction of hitting the ball can be determined based on the value of the cross key for 25 frames, or the strength of hitting the ball can be determined by the input time and input pattern of the button for shaking the racket. it can.

Next, it is determined whether or not the collision display between the ball and the racket has been completed (step ST12).
When the collision display between the ball and the racket is completed (step ST12), the bounce count is reset and the character for detecting the collision between the ball and the racket is changed, and the process returns to step ST2 to continue the above processing (step ST13). .

  Next, details of the ball trajectory process in step ST2 will be described with reference to the operation flowchart of FIG.

  When the ball trajectory drawing process is started, a series of data indicating the state of a certain frame of the ball (ball information having information such as position, speed, rotation, drawing color, etc. for one frame) and data having the current state (Ball information C) needs to be prepared.

  First, various parameters are initialized. As initialization of various parameters, the following four types of parameters need to be secured for the ball trajectory drawing process.

Orbit display buffer Processing frame counter (N)
Bound counter (B)
Work memory for ball trajectory drawing processing (ball information A)
These four types are initialized as follows. Note that the upper buffer and the counter can be generated in the RAM 3.
i Initialize the trajectory display buffer.

The trajectory display buffer can duplicate and hold ball information for the number of frames for which trajectory prediction is performed. Here, all the trajectory display buffers are once erased.
ii Initialize the processing frame number counter (step ST14)
Let N = 1.
iii Initialize the bounce counter.

Let B = 0.
iv Duplicate the current state of the ball.

    The current ball state data (ball information C) is copied to the work memory (ball information A) for ball trajectory drawing processing.

  The processing frame counter is compared with the number of frames for trajectory prediction. If the processing frame number counter has already exceeded the number of frames for which trajectory prediction is performed (step ST15, YES), the trajectory is drawn based on the content of the generated trajectory display buffer (step ST26), and the processing is finished (FIG. Return to the flow of 9).

  If the processing frame number counter does not yet exceed the number of frames for which trajectory prediction is performed (step ST15, NO), the ball information A is evaluated and updated as follows, and the state of the ball information A is set to the future direction by one frame. Proceed to

  For this purpose, the following processing is performed as evaluation / update of the ball information A.

  i As an initialization process, clear the flag indicating the state of interference between the ball and the terrain (touching the floor, touching the wall, etc.).

  ii In the ball information A, the position is moved by one frame based on the speed and rotation, and the position is updated (step ST16).

  iii Next, in the ball information A, the speed and rotation are changed by one frame based on parameters such as air resistance and gravity.

  iv As reflection processing, if the ball position in the ball information A is in contact with the wall surface or the floor surface (step ST17, YES)), the ball information A is based on the ball parameters (elastic coefficient, etc.) and the wall parameters. The position, speed, and rotation of are changed (step ST18), and the ball position after N frames is recalculated (step ST19).

  In addition, a flag indicating an interference state between the ball and the terrain is set according to the touched surface.

  That is, if the updated ball information A is touching the floor surface W4 (if a flag indicating that the floor surface has been touched is set) (step ST20, YES), the bound number counter is incremented (step ST21). .

  It is evaluated whether the bound number counter has reached twice (the number of bounds regarded as a mistake in the game rules) (step ST22). If it has already been reached (step ST22, YES), the ball information A is retained. The drawing color is set and stored in the trajectory display buffer so as to be displayed in a color (for example, purple) indicating that an error occurs at the ball position after N frames (step ST23).

  On the other hand, if not reached yet, the drawing color held by the ball information A is set in the trajectory display buffer so as to display a color (for example, red) indicating that there is no mistake at the ball position after N frames (for example, red). Step ST24).

  Next, the processing frame number counter is counted N (step ST25), and the process returns to step ST15 to repeat the above processing.

  As described in accordance with the above-described embodiment, when a sport in which a complex ball like a squash and a violent ball (moving body object) moves according to the present invention is simulated in a game, information is stored in the predicted trajectory of the moving object. It can be displayed.

  In other words, when there is no display of the predicted trajectory, it is difficult to inform the player of which surface of the floor (court) or wall surface the ball has bounced, but by displaying the predicted trajectory, the player Can be visually informed.

  In addition, this makes it possible to notify the timing and position of hitting the ball within the number of bounces defined in the rules, and to suppress the difficulty of the game. Therefore, the rally can be continued by the player, and the player who is not familiar with the rules can be more entertained.

  Accordingly, it is possible to provide a game system that allows a player who is not familiar with the rules to easily enjoy the game.

It is a functional block diagram of the structural example of the computer system which functions as a game device applied to this invention. It is a figure explaining the relationship between an interface part, a radio | wireless receiver, and the 1st and 2nd controller operated by the player. It is a figure explaining a 1st controller. It is a figure explaining a 2nd controller. It is a figure explaining the control of the direction in which a ball is hit back according to the timing which hits a racket. It is a display screen example (1) of a frame with a squash game whose display is controlled on the display device 5 by the main CPU 1 according to the game program. FIG. 6B is a display screen example (part 2) of a frame subsequent to the frame of FIG. FIG. 6B is an example of a frame display screen (part 3) following the frame of FIG. 6B; It is the example of a display screen after hitting the ball of the squash game controlled to be displayed on the display device 5 by the main CPU 1 according to the game program (part 4). It is the figure which expanded and displayed an example of the ball locus. It is an operation | movement flow explaining the detail of the computer program procedure which gives and displays information on the prediction track | orbit of the moving object of this invention. It is a flow explaining the detail of step ST2 (ball trajectory process) in the operation | movement flow of FIG.

Explanation of symbols

1 Main CPU
2 ROM
3 RAM
4 Rendering processor 5 Display device 6 Texture memory 7 VRAM
8 Interface unit 9 Wireless receiver 10 Bus 20 First controller 200 Joystick 21 Second controller 30 Game device body 40 Character 41 Racket 50 Display screen 60 Expected movement trajectory

Claims (7)

A state of a game in which a collision between a character that moves in response to an input operation of a player and a ball on a field having a plurality of planes provided in a virtual space is determined and the trajectory of the ball is changed is described above. A computer program for causing a computer system to execute processing to display an image viewed from a virtual viewpoint placed in a space,
A trajectory calculating step for calculating a trajectory of the moving ball in the computer system;
A trajectory display step for displaying the trajectory on a screen;
A frequency measurement step of measuring the number of times the trajectory touches a predetermined plane from the collision;
A trajectory display changing step for changing and displaying the trajectory display when the measured number exceeds a predetermined number of times;
A computer program for executing In claim 1,
The trajectory display step predicts and displays a predetermined time ahead of the ball. In claim 1 or claim 2,
The trajectory calculating step calculates the trajectory based on at least one of a moving direction, a moving speed, and a rotating direction of the ball. In claim 3,
When the collision is determined based on the input operation of the player, the computer system changes at least one of the moving direction, the moving speed, and the rotating direction of the ball based on the acceleration of the input operation. A parameter change step;
Is further executed. In any one of Claims 1 thru | or 4,
In the computer system,
A collision position determination step of determining a position where the collision occurs based on an input operation of the player;
A collision position display step for displaying the collision position on a screen in a predetermined form;
Is further executed. In any one of Claims 1 thru | or 5,
A computer program for further executing a game ending step of ending the game when the ball touches the predetermined surface for the predetermined number of times. In any one of Claims 1 thru | or 6,
The trajectory display step displays a moving trajectory of the ball as a line or a point group.

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