JP4467590B2 - Drawing apparatus, drawing method, and drawing program - Google Patents

Description

  The present invention relates to a technique for drawing an object represented by a three-dimensional image including a plurality of reference points.

  Conventionally, it is called RPG (Role Playing Game: A game in which a player plays the role of a character in the game world and enjoys the process of growing through various experiences while achieving a predetermined purpose). Various video games such as games are offered.

  In image drawing in recent video games, very realistic expression is possible. However, when expressing how a flat object such as cloth flutters in the wind or the like in a video game, in general, a morphing animation ("To express how a shape gradually changes from one shape to another." This means a moving image that expresses the state of the change using the created intermediate image.)) And uses a simple method to express how the object fluctuates. It was.

  However, in order to avoid a monotonous expression, it is necessary to complete the drawing of an object like a video game in a short time because the calculation becomes very complicated if the simulation is linked with the flow of the wind. It is not appropriate to adopt it for things.

  The ones that do not need to be simulated are to express the state in which a flat object such as a cloth fluctuates due to the wind in the virtual world. Similarly, there is a method in which calculation is performed using a force vector such as inertia that affects an object (see Patent Document 1).

  In addition, when recreating the movement of a liquid that flows along the surface of an object in the game, instead of the movement of the wind, a liquid simulation is performed by calculating the normal vector of the object surface and the vector of the liquid flow. (See Patent Document 2).

JP 2005-56251 A JP 2003-91738 A

  The invention described in Patent Document 1-2 described above does not need to perform an enormous calculation for simulation, but still requires a complicated calculation, so that a planar object such as a cloth fluctuates due to wind or the like. There was a problem that the situation could not be expressed realistically with simple calculations.

  In order to solve the above-described problem, an object of the present invention is to make it possible to realistically express how a planar object such as a cloth fluctuates due to a wind or the like by a simple calculation.

The drawing apparatus of the present invention is a drawing apparatus that draws an object represented by a three-dimensional image including a plurality of reference points, and includes a drawing unit that draws the object including the plurality of reference points, and the object Normal vector data storage means for storing normal vector data indicating normal vectors of a plurality of reference points, and acceleration vector data indicating movement acceleration vectors which are movement accelerations of the plurality of reference points included in the object Acceleration vector data storage means for storing action vector data, action vector data calculation means for calculating action vector data indicating action vectors indicating the contents of actions such as wind affecting the outer shape of the object, and action vector data calculation means. Calculated action vector data and included in the object And the normal vector data indicating a vector of each reference point that, based on the acceleration vector data representing the movement acceleration vector is a movement acceleration of the reference point included in the object, move the respective said each reference point Movement vector data calculation means for calculating movement vector data that can identify the data, and movement point calculation means for calculating a movement point indicating the movement destination of each reference point calculated by the movement vector data calculation means, The drawing means moves each reference point corresponding to each movement point calculated by the movement point calculation means, draws the object using the movement point as a new reference point , and the movement vector data calculation means Calculates the absolute value of the inner product of the unit action vector and the normal vector, and the product of the calculation result and the action vector. Calculated, and calculates a movement vector data indicating the motion vector by adding the movement acceleration vector calculated product.

  With the above configuration, it is possible to realistically express how a planar object such as a cloth fluctuates due to wind or the like with a simple calculation.

The drawing method of the present invention is a drawing method for drawing an object represented by a three-dimensional image including a plurality of reference points, the drawing process for drawing the object including the plurality of reference points, and the object Included in the object is action vector data calculation processing for calculating action vector data indicating action vectors indicating the contents of the action such as wind that affects the outer shape of the action vector, action vector data calculated by the action vector data calculation process, and The normal vector data stored in the normal vector data storage means for storing normal vector data indicating the normal vectors of each of the plurality of reference points, and the movement acceleration of each of the plurality of reference points included in the object. Acceleration vector data for storing acceleration vector data indicating a certain moving acceleration vector Based on the said acceleration vector data stored in憶means, using a predetermined arithmetic expression, a movement vector data calculation process of calculating the movement vector data capable of identifying the respective reference point each destination, the mobile A movement point calculation process for calculating a movement point indicating a movement destination of each reference point calculated in the vector data calculation process, and the drawing process corresponds to each movement point calculated in the movement point calculation process Each reference point to be moved, the object is drawn with the movement point as a new reference point, and in the movement vector data calculation process, the absolute value of the inner product of the unit action vector and the normal vector is calculated, The product of the calculation result and the action vector is calculated, and the movement vector data indicating the movement vector is obtained by adding the movement acceleration vector to the calculated product. Characterized in that it out.

Further, the drawing program of the present invention is a drawing program for drawing an object represented by a three-dimensional image including a plurality of reference points, wherein the computer includes a drawing process for drawing the object including the plurality of reference points. , Action vector data calculation processing for calculating action vector data indicating action vectors indicating the contents of action such as wind that affects the outer shape of the object, action vector data calculated by the action vector data calculation process, Normal vector data stored in normal vector data storage means for storing normal vector data indicating normal vectors of a plurality of reference points included in the object, and each of the plurality of reference points included in the object Acceleration vector data indicating the movement acceleration vector, which is the movement acceleration Based on the stored the acceleration vector data to the acceleration vector data storage means for storing, using a predetermined arithmetic expression, movement vector data for calculating a movement vector data capable of identifying the respective reference point each destination A calculation process, and a movement point calculation process for calculating a movement point indicating a movement destination of each reference point calculated in the movement vector data calculation process. In the movement vector data calculation process, the unit action vector and the normal vector are executed by moving the respective reference points corresponding to the respective movement points and drawing the object using the movement point as a new reference point. The absolute value of the inner product is calculated, the product of the calculation result and the action vector is calculated, and the moving acceleration vector is added to the calculated product. Calculation is intended for executing a process of calculating the movement vector data indicating a movement vector by.

  According to the present invention, it is possible to realistically represent a state in which a planar object such as a cloth fluctuates due to wind or the like by a simple calculation.

  Hereinafter, an embodiment of the present invention will be described with reference to the drawings.

  FIG. 1 is a block diagram showing an example of the configuration of a video game apparatus 100 showing an example of a drawing apparatus according to an embodiment of the present invention. As shown in FIG. 1, the video game apparatus 100 of this example includes a video game apparatus main body 10, a display device 50, and a sound output device 60. The video game apparatus body 10 is configured by, for example, a commercially available video game machine. The display device 50 is configured by, for example, a television device or a liquid crystal display device, and includes an image display unit 51.

  The video game apparatus body 10 includes a control unit 11, a RAM 12, a hard disk drive (HDD) 13, a sound processing unit 14, a graphic processing unit 15, a DVD / CD-ROM drive 16, a communication interface 17, and an interface. A unit 18, a frame memory 19, a memory card slot 20, and an input interface unit 21 are included.

  The control unit 11, RAM 12, hard disk drive (HDD) 13, sound processing unit 14, graphic processing unit 15, DVD / CD-ROM drive 16, communication interface 17, and interface unit 18 are each connected to an internal bus 22. .

  The control unit 11 includes a CPU, a ROM, and the like, and controls the entire video game apparatus 100 according to a control program stored in the HDD 13 or the storage medium 70. The control unit 11 includes an internal timer that is used to generate a timer interrupt. The RAM 12 is used as a work area for the control unit 11. The HDD 13 is a storage area for storing control programs and various data.

  The sound processing unit 14 is connected to a sound output device 60 configured by, for example, a speaker. The sound processing unit 14 outputs a sound signal to the sound output device 60 in accordance with a sound output instruction from the control unit 11 executing processing according to the control program. The sound output device 60 may be built in the display device 50 or the video game apparatus main body 10.

  The graphic processing unit 15 is connected to a display device 50 having an image display unit 51 that displays a screen. The graphic processing unit 15 develops an image in the frame memory 19 according to a drawing command from the control unit 11 and outputs a video signal for causing the image display unit 51 to display an image to the display device 50. The switching time of the image displayed by the video signal is, for example, 1/30 second per frame.

  The DVD / CD-ROM drive 16 is loaded with a storage medium 70 storing a game control program such as a DVD-ROM or a CD-ROM. The DVD / CD-ROM drive 16 performs processing for reading various data such as a control program from the mounted storage medium 70.

  The communication interface 17 is connected to a communication network 80 such as the Internet by wireless or wired. The video game apparatus body 10 communicates with, for example, another computer via the communication network 80 using the communication function in the communication interface 17.

  An input interface unit 21 and a memory card slot 20 are connected to the interface unit 18. The interface unit 18 stores in the RAM 12 instruction data from the input interface unit 21 based on the operation of the keypad 30 by the player. Then, according to the instruction data stored in the RAM 12, the control unit 11 executes various arithmetic processes.

  In addition, the interface unit 18 stores data indicating the progress of the game stored in the RAM 12 in the memory card 90 installed in the memory card slot 20 according to an instruction from the control unit 11, The game data stored at the time of interruption is read out and transferred to the RAM 12.

  Various data such as a control program for playing a game on the video game apparatus 100 is stored in the storage medium 70, for example. Various data such as a control program stored in the storage medium 70 is read by the DVD / CD-ROM drive 16 in which the storage medium 70 is mounted and loaded into the RAM 12. The control unit 11 performs various processes such as a process of outputting a drawing command to the graphic processing unit 15 and a process of outputting a sound output instruction to the sound processing unit 14 according to the control program loaded in the RAM 12. Execute. It should be noted that while the control unit 11 is executing processing, data that is generated intermediately in the RAM 12 used as a work memory depending on the progress of the game (for example, data indicating the score of the game, the state of the player character, etc.) Is saved.

  The three-dimensional video game according to this embodiment is assumed to be a game that progresses on a field provided in a virtual three-dimensional space. Note that the virtual three-dimensional space in which the field is formed is indicated by the world coordinate system. The field is composed of a plurality of surfaces, and the coordinates of the vertices of each component surface are represented as feature points.

Next, the operation of the video game apparatus 100 of this example will be described.
Here, in order to simplify the description, the description may be omitted except for the processing particularly related to the present invention. In this example, it is assumed that video game control for RPG is executed.

  FIG. 2 is a flowchart showing an example of main processing in the video game apparatus 100 of the present example. The main process is a process for generating an image for one frame and a process necessary for controlling the video game, and is executed in response to a timer interrupt every 1/30 seconds. Note that “every 1/30 seconds” is an example, and the main process may be executed in response to a timer interrupt for each field period (1/60 seconds), for example, depending on the amount of processing. It may be executed in response to a timer interrupt every (1/15 seconds).

  In the main process, the control unit 11 determines whether or not the game is instructed to start by operating the keypad 30 before the game starts, and changes the scene (for example, changes in the field) if the game is being executed. It is determined whether or not it is time to perform (step S101). The timing for changing the scene is, for example, in order to end a scene (for example, a scene represented by a virtual three-dimensional space) that has been displayed on the image display unit 51 so far and switch to a new scene. 51 indicates the timing for displaying a virtual three-dimensional space indicating a new scene.

  When it is determined that there is an instruction to start the game, or when it is determined that it is time to change the scene (Y in step S101), the control unit 11 performs an initial screen (an initial screen at the start of the game, The initial screen when changing the scene is determined (step S102). Various data such as screens and characters used in the game are stored in the storage medium 70.

  Next, the control unit 11 determines the position of the viewpoint of the virtual camera, the direction of the visual axis, and the size of the viewing angle according to the control program, and performs initial setting of the virtual camera for performing perspective transformation (step S103). Then, the process proceeds to step S115.

  When it is determined that the game is being executed and it is not time to change the scene (N in Step S101), the control unit 11 receives instruction data based on the operation of the keypad 30 by the player (Step S104). When instruction data for instructing an action related to movement is received in step S104 (Y in step S105), the control unit 11 executes a movement process according to the received movement instruction data (step S106). Movement information is generated based on the position information of the player character derived from the movement process (step S107). Then, the process proceeds to step S113.

  When the instruction data for instructing the action related to the battle is received in step S104 (Y in step S108), the control unit 11 executes a battle process in accordance with the received battle instruction data (step S109). Battle information is generated based on the battle result and battle progress determined by the battle process (step S110). Then, the process proceeds to step S113.

  When instruction data for other instructions is received in step S104 (Y in step S111), the control unit 11 performs processing (for example, conversation, shopping, picking up, etc.) according to the received other instruction data. This is executed (step S112), and other various information according to the processing result is generated. Then, the process proceeds to step S113.

  In step S113, the control unit 11 updates the current position of the player character by storing the movement information generated in step S107 in a predetermined data area of the RAM 12. Further, in step S113, the control unit 11 stores the battle information generated in step S110 and other information generated after step S112 in a predetermined data area of the RAM 12, thereby allowing the player character to perform various types of information. The action history is stored and retained.

  Next, the control unit 11 executes an action evaluation process based on the information indicating the action history of the player character once stored in the RAM 12 (step S114).

  Then, the control unit 11 perspective-transforms the virtual three-dimensional space including the player character and the non-player character to be displayed from the virtual camera on the virtual screen according to the setting contents of the virtual camera and the like on the image display unit 51. A display process for generating a two-dimensional image to be displayed is performed (step S115). When the display process is terminated, the main process is terminated. Thereafter, when a timer interrupt occurs at the start timing of the next frame period, the next main processing is executed. Then, by repeatedly executing the main process, the character image is switched for each frame period, and the moving image is displayed on the image display unit 51.

  Here, the display process in step S115 will be briefly described. In step S115, the control unit 11 firstly, among the coordinates of the vertices of the polygons constituting the virtual three-dimensional space including the player character and the non-player character, at least the vertices of the polygons included in the range to be perspectively transformed on the virtual screen. Is converted from coordinates in the world coordinate system to coordinates in the viewpoint coordinate system. Next, the control unit 11 transmits the coordinates of the vertexes of the polygons in the viewpoint coordinate system for the player character and the non-player character to the graphic processing unit 15, and outputs a drawing command to the graphic processing unit 15.

  When a drawing command is input, the graphic processing unit 15 updates the contents of the Z buffer so that the point data on the front side remains for each point constituting each surface based on the coordinates of the viewpoint coordinate system. When the contents of the Z buffer are updated, the graphic processing unit 15 develops image data for the remaining points on the front side in the frame memory 19. The graphic processing unit 15 also performs processing such as shading and texture mapping on the developed image data.

  The graphic processing unit 15 sequentially reads the image data developed in the frame memory 19, adds a synchronization signal, generates a video signal, and outputs the video signal to the display device 50. The display device 50 displays an image corresponding to the video signal output from the graphic processing unit 15 on the image display unit 51. By switching the image of the image display unit 51 every frame time, the player can see an image including a state in which the player character and the non-player character move on the field.

  Next, the operation of the video game apparatus 100 of this example will be described.

  FIG. 3 is a flowchart showing an example of object drawing processing in the video game apparatus 100 of the present example. Here, for example, a description will be given of processing for drawing an object having a flat shape as shown in FIG. It should be noted that explanations may be omitted except for processing particularly related to the present invention. This object drawing process is a part of the display process (step S115) described above.

  An object drawn by the object drawing process is, for example, a cloth object for expressing a flag, a curtain, or the like. In this example, as shown in FIG. 5, for example, the structure of this object is specified by a so-called “wire frame” expressed by a contour line such as wirework, and each contact point of each wire is grasped as a reference point. That is, the cloth-like object is represented by a wire frame that uses the contact points of each wire as reference points. As described above, the cloth-like object is expressed by a three-dimensional image including a plurality of reference points. Each reference point is, for example, each definition point such as a vertex of a polygon forming an object or a control point of a free-form surface.

  In the object drawing process, the control unit 11 first stores the coordinate data and normal vector data of each reference point in the object to be drawn as the storage medium 70 (data (initial value) when displaying the initial state of the object). The data is read from the RAM 12 (in the case of reading out) or from the RAM 12 (in the case of reading out data when displaying the change state of the object) (step S201). For example, as shown in FIG. 6, the normal vector data is data indicating a normal vector of the reference point in order to specify the orientation of the object surface at the corresponding reference point. The initial values of the coordinate data and normal vector data of each reference point in the object are read from the storage medium 70 to the RAM 12 and managed in a normal vector data management area provided on the RAM 12.

  Next, the control unit 11 calculates action vector data (step S202). The action vector data is vector data indicating the contents (direction and strength) of actions such as wind direction and wind force that affect the change in the outer shape of the object. In this example, it is assumed that the action vector data is calculated based on wind data (wind direction, wind force) that causes the action.

  Next, if the acceleration vector data of each reference point in the object to be drawn is stored in an acceleration vector data management area described later, the control unit 11 reads the acceleration vector data from the RAM 12 (step S203). The acceleration vector data is vector data indicating a movement acceleration vector that is a movement acceleration of each of a plurality of reference points included in an object to be drawn. The acceleration vector data of each reference point in the object is managed in an acceleration vector data management area provided on the RAM 12.

  Next, the control unit 11 calculates a movement vector of each reference point by applying it to a predetermined arithmetic expression (step S204). In this example, the following formula 1 is used as the predetermined calculation formula. That is, the control unit 11 obtains the absolute value (abs) of the inner product of “unit movement vector (windNormal)” and “normal vector (crsNormal)” using Expression 1, and the result and the movement vector (windVector). The movement vector of each reference point is calculated by adding the movement acceleration vector if the movement acceleration vector (crsVelocity) is read. If the movement acceleration vector (crsVelocity) is not read, the absolute value (abs) of the inner product of the `` unit movement vector (windNormal) '' and `` normal vector (crsNormal) '', the movement vector (windVector) and Is calculated as a movement vector of each reference point.

  Specifically, the control unit 11 uses, for example, a normal vector (crsNormal) of a certain reference point and a wind unit vector (windNormal) that is a unit movement vector as shown in FIG. Find the inner product vector as shown. And the control part 11 calculates | requires the absolute value (abs) of the value which the inner product vector shows, calculates the product (refer FIG.7 (C)) of the result and the wind vector (windVector) which is a movement vector, and movement acceleration If the vector (crsVelocity) has been read, the movement acceleration vector is added (see FIG. 7D) to calculate the movement vector of each reference point. The control unit 11 executes such arithmetic processing for each reference point.

  When the movement vector of each reference point is calculated, the control unit 11 calculates the movement position of each reference point using the coordinate data of each reference point read in step S201 and the calculated movement vector of each reference point ( Step S205). For example, as shown in FIG. 8, the new reference point, which is the movement position of each reference point, is a point moved from the old reference point by the direction and size (length) indicated by the corresponding movement vector.

  Then, the control unit 11 draws an object using the calculated movement position as a reference point (step S206).

  By repeatedly executing the processes in steps S201 to S206, the control unit 11 displays on the display screen 51 of the display device 50 a state in which the object is flickering as shown in FIG. indicate.

  As described above, in the above-described embodiment, the control unit 11 includes the RAM 12 and the storage medium 70 that store normal vector data indicating the normal vectors of the plurality of reference points included in the object. A drawing process (step S206) for drawing an object expressed by a three-dimensional image including a plurality of reference points, and action vector data indicating action vectors indicating action contents such as wind affecting the outer shape of the object are calculated. Based on the action vector data calculation process (step S202), the calculated action vector data, and the normal vector data indicating the normal vector of each reference point included in the object, A movement vector data calculation process for calculating movement vector data that can specify the movement destination of each reference point. (Step S204) and a movement point calculation process (Step S205) for calculating a movement point indicating the movement destination of each calculated reference point, and a drawing process and a movement point calculation process. Each reference point corresponding to the moving point is moved, and the object is drawn using the moving point as a new reference point, so it is easy to calculate how a flat object such as cloth fluctuates due to wind. To be able to express realistically.

  In other words, it is possible to reduce the display control burden of the control unit 11 when the planar object such as the cloth is realistically expressed as being shaken by the wind.

  In the above-described embodiment, the RAM 12 stores acceleration vector data indicating the movement acceleration vector that is the movement acceleration of each of the plurality of reference points included in the object represented by the three-dimensional image including the plurality of reference points. In the movement vector data calculation process (step S204), the control unit 11 also calculates the movement vector data using the acceleration vector data indicating the movement acceleration vector that is the movement acceleration of each reference point included in the object. Therefore, it is possible to realistically express how the object fluctuates due to wind or the like in consideration of the acceleration vector.

  In the above-described embodiment, the predetermined arithmetic expression is the movement acceleration vector + = movement vector × | unit movement vector / normal vector |, and the control unit 11 performs the movement vector data calculation process (step S204). Because the movement vector data is calculated using the calculation formula, the normal vector at each reference point and the virtual world in the game can be seen. It will be possible to express realistically with simple calculations using action vectors due to the wind blowing in, etc., and also support what needs to complete drawing of objects like video games in a short time Is possible. That is, it becomes possible to draw an object in a video game easily and at high speed.

  In the above-described embodiment, the video game apparatus 100 has been described as an example of a drawing apparatus that displays an object represented by a three-dimensional image including a plurality of reference points. Any device can be suitably applied.

  INDUSTRIAL APPLICABILITY According to the present invention, the present invention is useful for application to a drawing apparatus such as a video game apparatus that can realistically express a state in which a planar object such as a cloth fluctuates due to wind or the like by a simple calculation.

It is a block diagram which shows the structural example of the video game device in one embodiment of this invention. It is a flowchart which shows the example of a main process. It is a flowchart which shows the example of an object drawing process. It is the front view which looked at planar objects, such as cloth, from the front. It is explanatory drawing which shows the example of the object expressed by the wire frame. It is explanatory drawing which shows the example of the normal vector set to each reference point in an object. It is explanatory drawing for demonstrating the example of vector calculation. It is explanatory drawing for demonstrating an old reference point and a new reference point. It is the front view which looked at a mode that planar objects, such as cloth, are shaking.

Explanation of symbols

10 Video Game Device Body 11 Control Unit 12 RAM
13 HDD
14 sound processing unit 15 graphic processing unit 16 DVD / CD-ROM
DESCRIPTION OF SYMBOLS 17 Communication interface 18 Interface part 19 Frame memory 20 Memory card slot 21 Input interface part 22 Internal bus 30 Keypad 50 Display device 51 Image display part 60 Sound output device 70 Storage medium 80 Communication network 90 Memory card 100 Video game device

Claims (3)

A drawing device for drawing an object represented by a three-dimensional image including a plurality of reference points,
Drawing means for drawing the object including the plurality of reference points;
Normal vector data storage means for storing normal vector data indicating normal vectors of each of a plurality of reference points included in the object;
Acceleration vector data storage means for storing acceleration vector data indicating a movement acceleration vector that is a movement acceleration of each of a plurality of reference points included in the object;
Action vector data calculating means for calculating action vector data indicating an action vector indicating the content of action such as wind that affects the outer shape of the object;
Action vector data calculated by the action vector data calculating means, normal vector data indicating a normal vector of each reference point included in the object, and movement acceleration that is a movement acceleration of each reference point included in the object based on the acceleration vector data indicating a vector, and motion vector data calculation means for calculating a movement vector data capable of identifying the respective reference point each destination,
Movement point calculation means for calculating a movement point indicating the movement destination of each reference point calculated by the movement vector data calculation means,
The drawing means moves each reference point corresponding to each movement point calculated by the movement point calculation means, draws the object using the movement point as a new reference point ,
The movement vector data calculation means calculates the absolute value of the inner product of the unit action vector and the normal vector, calculates the product of the calculation result and the action vector, and adds the movement acceleration vector to the calculated product. A drawing apparatus characterized by calculating movement vector data indicating a movement vector . A drawing method for drawing an object represented by a three-dimensional image including a plurality of reference points,
A drawing process for drawing the object including the plurality of reference points;
Action vector data calculation processing for calculating action vector data indicating action vectors indicating the contents of action such as wind that affects the outer shape of the object;
The method stored in the normal vector data storage means for storing the action vector data calculated in the action vector data calculation process and the normal vector data indicating the normal vectors of the plurality of reference points included in the object. Based on the line vector data and the acceleration vector data stored in the acceleration vector data storage means for storing the acceleration vector data indicating the movement acceleration vector that is the movement acceleration of each of the plurality of reference points included in the object , a predetermined value is obtained. A movement vector data calculation process for calculating movement vector data that can specify the movement destination of each reference point,
A movement point calculation process for calculating a movement point indicating a movement destination of each reference point calculated in the movement vector data calculation process,
In the drawing process, each reference point corresponding to each movement point calculated in the movement point calculation process is moved, the object is drawn using the movement point as a new reference point ,
In the movement vector data calculation process, the absolute value of the inner product of the unit action vector and the normal vector is calculated, the product of the calculation result and the action vector is calculated, and the movement acceleration vector is added to the calculated product. A drawing method characterized by calculating movement vector data indicating a movement vector . A drawing program for drawing an object represented by a three-dimensional image including a plurality of reference points,
On the computer,
A drawing process for drawing the object including the plurality of reference points;
Action vector data calculation processing for calculating action vector data indicating action vectors indicating the contents of action such as wind that affects the outer shape of the object;
The method stored in the normal vector data storage means for storing the action vector data calculated in the action vector data calculation process and the normal vector data indicating the normal vectors of the plurality of reference points included in the object. Based on the line vector data and the acceleration vector data stored in the acceleration vector data storage means for storing the acceleration vector data indicating the movement acceleration vector that is the movement acceleration of each of the plurality of reference points included in the object , a predetermined value is obtained. A movement vector data calculation process for calculating movement vector data that can specify the movement destination of each reference point,
A movement point calculation process for calculating a movement point indicating a movement destination of each reference point calculated in the movement vector data calculation process;
In the drawing process, each reference point corresponding to each movement point calculated in the movement point calculation process is moved, and a process of drawing the object using the movement point as a new reference point is executed.
In the movement vector data calculation process, the absolute value of the inner product of the unit action vector and the normal vector is calculated, the product of the calculation result and the action vector is calculated, and the movement acceleration vector is added to the calculated product. A drawing program for executing a process of calculating movement vector data indicating a movement vector .

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