JP2003091741A - Image forming system, program and information storage medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an image forming system, a program, and an information storage medium for changing a primitive image without making the changing process and the state after a change monotonous. SOLUTION: When an object before deformation in a frame n is deformed to an object after deformation in a frame (n+m), flow field information HFIn to HFIn+m equivalent to a continuous (m+1) frame is used. The flow field information HFIn to HFIn+m are determined by external cause-imparted fluid simulation by using a Navier-Stokes equation. The flow field information in the respective frames is successively applied on the object WOBJ before deformation in the frame n, and the object is deformed by changing a position of respective constitution points of the object according to the direction and the size of a speed vector set to respective lattice points. When applying the flow field information of a process of returning to the state before deformation from the state after deformation in inverse order, the deformation having viscosity inherent in fluid can be performed.

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention relates to an image generation system, a program, and an information storage medium.

[0002]

2. Description of the Related Art Conventionally, two-dimensional or three-dimensional object transformation is called morphing and is known as one of animation methods for providing a special effect image. In morphing, generally, an object before deformation and an object after deformation are prepared, and interpolation processing is performed so that the shape of the object before deformation gradually changes to the shape of the object after deformation.

Therefore, in the conventional morphing, it is necessary to prepare the deformed object and to associate the shape data of the object in the process before the deformation and after the deformation. In addition, not only the deformation process becomes constant, but also the shape other than the shape prepared in advance cannot be deformed. for that reason,
When the morphing was repeated, the effect of the effect image was gradually faded.

The present invention has been made in view of the above problems, and an object of the present invention is to improve the primitive shape and state without changing the primitive shape and state and the changed state. An object is to provide an image generation system, a program, and an information storage medium capable of changing an image.

[0005]

In order to solve the above-mentioned problems, the present invention is an image generation system for generating an image, which is obtained by calculating a change in physical quantity at each point in a simulation space by a fluid simulation calculation. , A simulation calculation means for obtaining a flow field for the physical quantity, a position of a configuration point or a control point of the primitive, information associated with the configuration point of the primitive or the control point, a method associated with the primitive based on the change of the flow field At least one of the direction and magnitude of the line vector,
And a means for changing at least one of the vertex information of the primitive, and a means for generating an image viewed from a given viewpoint in the object space in which the primitive is arranged. A program according to the present invention causes a computer to function as the above means. An information storage medium according to the present invention is a computer-readable information storage medium, and stores a program that causes a computer to function as the above means.

Here, the flow field refers to a region in which a physical quantity indicating a stationary state or a motion state of a fluid such as a liquid or a gas that changes its shape with respect to an external force and flows is spatially distributed. The shape of this flow field is not limited.

Here, the constituent points or control points of the primitive are, for example, definition points (for example, vertices) of the primitive and control points of the free-form surface, and the positions of the constituent points or control points of the primitive are, for example, the vertices of the primitive. Position coordinates or the position coordinates of free-form surface constituent points or control points.

The information associated with the constituent points of the primitive is, for example, color information or semitransparent information given to each vertex of the primitive, and the information associated with the control point of the primitive is, for example, control of a free-form surface. The weight given to each point.

Further, the normal vector associated with the primitive means a normal vector used when image processing such as shading is performed on the primitive, and can be provided for each vertex of the primitive.

Further, the vertex information of the primitive means texture coordinates, color (luminance) data, normal vector or α value.

The object space is a virtual three-dimensional space in which an object whose shape is specified by a definition point (vertex of polygon or control point of free-form surface) is arranged.

According to the present invention, the change in the physical quantity at each point in the simulation space is obtained by fluid simulation, and the flow field information regarding the change in the physical quantity is used to calculate
Since the positions of the constituent points or control points of the primitive are changed, a deformed image of the primitive reflecting the motion of the fluid can be generated and a more effective effect image can be provided.

Moreover, since it is not necessary to prepare the changed (deformed) primitive in advance, it is possible to reduce the amount of data required to change (deform) the image of the primitive. In this case, if only the flow field at a certain moment is prepared, it is not necessary to prepare all vertex information of the primitive in the changing process, and the amount of data for changing the image of the primitive can be significantly reduced. It will be possible.

Further, in the image generating system, the program and the information storage medium according to the present invention, the flow field information in the process of returning the flow field from the first state to the second state to the first state, or Based on the information affected by the flow field,
At least one of the position of the constituent point or control point of the primitive, the information associated with the constituent point or control point of the primitive, at least one of the direction and magnitude of the normal vector associated with the primitive, and at least one of the vertex information of the primitive; It is characterized by changing.

Here, the information affected by the flow field is
Information that changes based on the flow field information about the obtained physical quantity (in order to apply to the object, the result calculated based on the flow field information about the physical quantity,
For example, position information, speed information, temperature information, physical quantity, etc.).

According to the present invention, the flow field information in the process of returning the flow field from the first state (pre-change state) to the second state (post-change state) to the first state or Since the information affected by the flow field is used, it is possible to use the operation peculiar to the fluid in which the state of the flow field given the extrinsic condition returns to the original state, and the viscosity which could not be expressed so far is obtained. The image change of the primitive can be realized.

Further, the present invention is an image generation system for generating an image, wherein the flow field information about the physical quantity at each point of the simulation space obtained by the fluid simulation calculation or the information affected by the flow field. The storage means for storing a given time, based on the information of the flow field stored in the storage means, the position of the primitive configuration point or control point, information associated with the primitive configuration point or control point, Means for changing at least one of the orientation and size of the normal vector associated with the primitive and at least one of the vertex information of the primitive, and an image viewed from a given viewpoint in the object space in which the primitive is placed. And means for generating. A program according to the present invention causes a computer to function as the above means. An information storage medium according to the present invention is a computer-readable information storage medium, and stores a program that causes a computer to function as the above means.

Here, the information of the flow field for a given time or the information affected by the flow field is, for example, the information of the flow field generated in frame units or the information affected by the flow field. Means In this case, the flow field information for one or a plurality of frames or the information affected by the flow field is used to associate with the position of the primitive configuration point or control point, the primitive configuration point or control point in each frame. An image of the primitive with varying at least one of the information, the orientation and size of the normal vector associated with the primitive, and the vertex information of the primitive will be generated.

According to the present invention, since it is applied to the primitive using the result of the simulation performed in advance, it is not necessary to perform the simulation for each frame, and the processing load can be reduced.

Further, in the image generating system, the program and the information storage medium according to the present invention, in the storage means, the flow field in which the flow field changed from the first state to the second state returns to the first state. It is characterized in that it stores field information or information affected by the flow field.

According to the present invention, in addition to the effects described above,
An image change of a primitive with viscous properties that could not be expressed up to now can be realized by utilizing the fluid-specific motion in which the state of the flow field given an extrinsic condition returns to the state of the flow field before the application of an external factor. .

The present invention is also an image generation system for generating an image, the position of a constituent point or control point of a primitive, information associated with the constituent point or control point of the primitive, and a direction of a normal vector associated with the primitive. And reproduction data for generating an image for a given unit time including at least one of the size and at least one of the vertex information of the primitives, and each of the simulation space obtained by the fluid simulation calculation. Based on the information of the flow field about the physical quantity at the point or the information affected by the flow field, the position of the configuration point or control point of the primitive, the information associated with the configuration point of the primitive or the control point, associated with the primitive At least one of the direction and magnitude of the normal vector, and the vertex of the primitive Means for storing reproduction data obtained by changing at least one of the information for a given reproduction time, and means for generating an image viewed from a given viewpoint of the object space based on the stored reproduction data. It is characterized by including. A program according to the present invention causes a computer to function as the above means. An information storage medium according to the present invention is a computer-readable information storage medium, and stores a program that causes a computer to function as the above means.

Here, the reproduction data for generating an image for a given unit time is, for example, reproduction data for reproducing an image of one frame in the case of generating an image for each frame. Further, the reproduction data for a given reproduction time means reproduction data for one or a plurality of frames when the reproduction data is reproduced in frame units, for example. In this case, the reproduction data of one or a plurality of frames is used to determine the position of the primitive configuration point or control point, information associated with the primitive configuration point or control point, and the direction and magnitude of the normal vector associated with the primitive. An image of the primitive in which at least one and at least one of the vertex information of the primitive are changed will be generated.

According to the present invention, since the reproduction data of the primitive to which the flow field information is applied is used to reproduce the state in which the image of the primitive changes, for example, the flow field information or the flow field information of each frame is reproduced. It is no longer necessary to obtain the affected information and apply it to the primitive, and it is possible to contribute to real-time processing of image generation that reflects the fluid motion that is interactively affected by external factors.

Further, the image generation system, the program and the information storage medium according to the present invention are configured of a plurality of primitives set in the object space based on the information of one flow field or the information affected by the flow field. At least one of a position of a point or a control point, information associated with a constituent point or a control point of a plurality of primitives, at least one of a direction and a magnitude of a normal vector associated with the plurality of primitives, and at least one of vertex information of the plurality of primitives; It is characterized by changing.

According to the present invention, the information of one flow field or the information affected by the flow field is applied to the primitives at a plurality of positions, so that it is processed to change the image of the primitive at each position. Eliminates the need for heavy fluid simulations. Further, by shifting the application timing of, for example, the information of one flow field or the information affected by the flow field for each primitive, it is possible to change the image of a complicated primitive with a smaller processing load.

[0027]

BEST MODE FOR CARRYING OUT THE INVENTION Preferred embodiments of the present invention will be described below with reference to the drawings.

The present embodiment described below does not limit the content of the present invention described in the claims. Further, not all of the configurations described in the present embodiment are essential as the solving means of the present invention.

1. Configuration FIG. 1 shows an example of a functional block diagram of an image generation system (game system) of this embodiment.

In the figure, this embodiment may include at least the processing unit 100 (or the processing unit 100 and the storage unit 170, or the processing unit 100, the storage unit 170 and the information storage medium 180). Other blocks (for example, the operation unit 160, the display unit 190, the sound output unit 19
2. The portable information storage device 194 and the communication unit 196) may be arbitrary constituent elements.

Here, the processing section 100 performs various processing such as control of the entire system, instruction of instructions to each block in the system, game processing, image processing, sound processing, etc., and its function is Various processors (CPU, DSP
Etc.) or hardware such as ASIC (gate array etc.) or a given program (game program).

The operation section 160 is for the player to input operation data, and its function can be realized by hardware such as a lever, a button, a microphone, or a case.

The storage unit 170 includes the processing unit 100 and the communication unit 1.
A work area such as 96, whose function is RAM
It can be realized by hardware such as.

An information storage medium (storage medium that can be used by a computer) 180 stores information such as programs and data. Its function is that of an optical disc (C
D, DVD), magneto-optical disk (MO), magnetic disk, hard disk, magnetic tape, or memory (RO
It can be realized by hardware such as M). Processing unit 10
0 performs various processes of the present invention (this embodiment) based on the program (data) stored in the information storage medium 180. That is, the information storage medium 180 stores a program for causing a computer to realize (execute, function) the means of the present invention (the present embodiment) (particularly, the blocks included in the processing unit 100). Alternatively, it includes a plurality of modules (including objects in object orientation).

A part or all of the information stored in the information storage medium 180 is transferred to the storage unit 170 when the system is powered on. The information storage medium 1
80 includes a program for performing the process of the present invention, image data, sound data, shape data of a display object, information for instructing the process of the present invention, or information for performing the process according to the instruction. Can be made.

The display unit 190 outputs the image generated by the present embodiment, and its function is CRT,
LCD or HMD (head mounted display)
It can be realized by hardware such as.

The sound output unit 192 outputs the sound generated by this embodiment, and its function can be realized by hardware such as a speaker.

The portable information storage device 194 stores player's personal data, game save data, and the like. As the portable information storage device 194, consider a memory card, a portable game device, or the like. You can

The communication unit 196 performs various controls for communication with the outside (for example, a host device or another image generation system), and its function is various processors or communication ASICs. It can be realized by the hardware or the program.

A program (information) for realizing (execution, function) each means of the present invention (this embodiment) is information from an information storage medium of a host device (server) via a network and a communication unit 196. It may be delivered to the storage medium 180. Use of such an information storage medium of the host device (server) is also included within the scope of the present invention.

The processing unit (processor) 100 is the operation unit 1
Various processing such as game processing, image generation processing, or sound generation processing is performed based on operation data from 60, programs, and the like. In this case, the processing unit 100 includes the storage unit 17
Various processes are performed by using the main storage unit in 0 as a work area.

Here, as the processing performed by the processing unit 100, coin (price) acceptance processing, various mode setting processing, game progress processing, selection screen setting processing, objects (one or more primitives. The same applies to the description) processing for obtaining the position and rotation angle (rotation angle around the X, Y or Z axis), processing for moving the object (motion processing), position of the viewpoint (position of the virtual camera) and line-of-sight angle (virtual camera). Rotation angle), processing for arranging objects such as map objects in the object space, hit check processing, processing for computing game results (results, results), for allowing multiple players to play in a common game space Processing, game over processing, or the like can be considered.

The processing section 100 includes a simulation calculation section 110, a primitive processing section 130, and an image generation section 14.
0, the sound generator 150 is included. Note that the processing unit 100 does not need to include all of these functional blocks 110 to 150, and may have a configuration in which some functional blocks are omitted.

Here, the simulation calculator 110 is
Elapsed time at each point (lattice point in a narrow sense) of a two-dimensional or three-dimensional simulation space (game space, virtual space) (elapsed virtual time, elapsed real time, or progressing frame)
Physical quantities (such as velocity, acceleration, force, position, temperature,
Change of electricity or magnetism etc. is obtained by simulation calculation (fluid simulation or physical simulation etc.), and the field (fluid field, flow field, velocity field, acceleration field) or the virtual field affected by the field is calculated for the physical quantity. Ask. More specifically, the simulation calculator 110
Is the flow field (velocity vector field, fluid field, velocity field) for the velocity vector, which is the change in velocity vector (velocity) over time at each point in the fluid simulation space.
Ask for. Alternatively, the simulation calculation unit 110 may change the information based on the flow field information about the obtained physical quantity (for example, velocity vector) at each point (for applying to the object, the flow field information about the physical quantity may be used). A field that is a result of calculation based on, for example, position information, velocity information, temperature information, physical quantity, etc.) is obtained as a virtual field affected by the field of the physical quantity.

Here, the fluid simulation means, for example, numerically modeling and expressing a stationary state or a motion state of a fluid such as a liquid or gas which changes its shape with respect to an external force and flows. .

The flow field (field in a broad sense) means a region where the above-mentioned physical quantity indicating the stationary state or the operating state of the fluid is spatially distributed. For example, by dividing the simulation space to be processed into a grid shape and obtaining the physical quantity at each grid point, the state of the place can be represented. Then, by performing a given simulation calculation in accordance with the lapse of time (frame progression), it is possible to give each grid point a physical quantity according to its position and time, and it is possible to represent a change in the state of the field. Therefore,
The virtual field affected by the flow field can be represented by obtaining information at the same grid point or another grid point calculated based on the physical quantity at each grid point of the flow field.

The primitive processing unit 130 converts a field (including an object configured by the primitive and a particle primitive) at a position where the field or the virtual field affected by the field calculated by the simulation calculation section 110 is reflected. , A process of reflecting a change in the place is performed. More specifically, the primitive processing unit 1
Reference numeral 30 denotes a position of a primitive constituent point or a control point, a primitive constituent point or control for the primitive before simulation, using the information of the field obtained by the simulation calculation unit 110 or the information affected by the field. Information associated with the point, at least one of a direction and magnitude of a normal vector associated with the primitive,
Also, processing is performed to update the vertex information of the primitive, the position of the particle (particle primitive) and information associated with the particle (lifetime, size, color information, transparency information, temperature information, density, etc.).

Here, the constituent points of the primitive are, for example, definition points (for example, vertices) of the primitive, and the control points of the primitive are, for example, control points of the free-form surface.
The positions of the constituent points of the primitive are, for example, the position coordinates of the vertices of the primitive and the constituent points of the free-form surface, and the positions of the control points of the primitive are the position coordinates of the control points of the free-form surface.

The information associated with the constituent points of the primitive is, for example, color information or semi-transparent information given to each vertex of the primitive, and the information associated with the control points of the primitive is, for example, control of a free-form surface. The weight given to each point.

Further, the normal vector associated with the primitive means a normal vector used when image processing such as shading is performed on the primitive, and can be provided for each vertex of the primitive.

Furthermore, the vertex information of the primitive refers to texture coordinates, color (luminance) data, normal vector or α value.

The image generation section 140 performs image processing based on the results of various processing performed by the processing section 100 to generate a game image and outputs it to the display section 190. For example, in the case of generating a so-called three-dimensional game image, geometry processing such as coordinate conversion, clipping processing, perspective conversion, or light source calculation is performed first, and based on the processing result, primitive data (primitive configuration points Position coordinates of (vertices) or control points, texture coordinates, color (luminance) data, normal vector or α value, etc.) are created. Then, based on this primitive data (primitive data such as polygon, free-form surface or subdivision surface), the image of the object (one or more primitives) after the geometry processing is stored in the storage unit 17.
It is drawn in a drawing buffer of 0 (a buffer that can store image information in pixel units such as a frame buffer and a work buffer). As a result, an image viewed from the virtual camera (given viewpoint) in the object space is generated.

Here, the object space means a virtual three-dimensional space in which an object whose shape is specified by a definition point (eg, a vertex of a polygon or a control point of a free-form surface) is arranged.

In this embodiment, the image generator 140 performs the image generation process based on the field or the virtual field affected by the field obtained by the simulation calculator 110. More specifically, the image generation unit 140, in one or more fields set in the object space, based on the field information obtained by the simulation calculation unit 110 or the information affected by the field, Unshaped objects such as fluids (water,
Cloud, fog, smoke, airflow, electromagnetic waves, flames, etc.) is performed to generate an image representing the operation or state.

At this time, the image generation section 140 receives the field information of a plurality of consecutive frames (in a broad sense, a given time) stored in the flow field information storage section 172 or the influence of the field. By sequentially applying the obtained information to the object, a process of generating an image of the object that reflects the calculation result of the fluid simulation is performed.

Alternatively, the position of the constituent point or control point of the object, the position of the object constituent point or control point changed by using the information of the flow field obtained by the simulation calculation unit 110 or the information affected by the field is set. A storage unit for a plurality of consecutive frames as associated data, at least one of the direction and size of a normal vector associated with the object, and vertex information of the object as reproduction data for generating an image for at least one frame. It is stored in 170. The image generation unit 140 reads out the reproduction data from the storage unit 170 to generate an object image, and based on the flow field information reflecting the calculation result of the fluid simulation or the information affected by the flow field. To change the object image.

By doing so, it is not necessary to prepare in advance the states of the object before and after the change, so that the amount of data required for changing the image of the object can be reduced. . For example, the state of the flow field in an external factor is returned to the state of the flow field before the external factor is applied. Can be asked. In this case, if only the flow field at a certain moment is prepared, the flow field obtained for each frame or the virtual field affected by the flow field is sequentially applied to the object to change the image of the object. It is possible to significantly reduce the data amount of.

In particular, when an object is deformed, it is not necessary to prepare the shape of the deformed object in advance, and it is not necessary to have all vertex information of the object in the deformation process.

Further, by utilizing the action of the fluid in which the state of the flow field given the extrinsic state returns to the state of the original flow field before the application of the external factor, the flow field from after the change of the object to before the change of the object is changed. By applying the information or the information affected by the flow field to the object in the reverse order, it becomes possible to change the image of the object having the viscosity which could not be expressed so far.

The sound generation section 150 performs various kinds of sound processing according to the result of the game processing, generates a sound such as BGM, a sound effect, or a sound, and outputs it to the sound output section 192.

All the functions of the simulation calculation unit 110, the primitive processing unit 130, the image generation unit 140, and the sound generation unit 150 may be realized by hardware, or all of them may be realized by a program. Good. Alternatively, it may be realized by both hardware and a program.

The image generation system of this embodiment is
The system may be a system dedicated to the single player mode in which only one player can play, or a system having not only such a single player mode but also a multiplayer mode in which a plurality of players can play.

When a plurality of players play,
The game image and the game sound to be provided to the plurality of players may be generated using one terminal, or a plurality of terminals (game machine, mobile phone) connected by a network (transmission line, communication line) or the like. ) May be used.

2. Features of this Embodiment Next, features of this embodiment will be described with reference to the drawings.
In the following, a case where a fluid simulation calculation is performed using a flow field (velocity field, velocity field, fluid field) will be mainly described as an example. However, the present invention is not limited to the flow field, and can be applied to an image expression that reflects various fields other than the fluid expression.

In the following, unless otherwise stated, object deformation for changing the positions of the constituent points (vertices) or control points of an object (primitive) based on flow field information will be described. At least one of the information associated with the point, the orientation and magnitude of the normal vector associated with the primitive
The same can be applied to the case of changing the vertex information of one or primitive.

2.1 Flow Field In the present embodiment, by using the information of the flow field obtained by the fluid simulation or the information influenced by the flow field, the configuration points of the object (primitive in a broad sense) or At least one of the position of the control point, information associated with the object's constituent points or control points, the orientation and magnitude of the normal vector associated with the object,
And at least one of the vertex information of the object is changed. In particular, the object can be deformed by changing the positions of the constituent points (vertices) or the control points of the object. At this time, it is also possible to appropriately receive an external input as an external factor and generate a deformed image of the object in real time.

The flow field (field in a broad sense, the same applies in the following description) can be generated by dividing the simulation space (game space, virtual space) into an appropriate number in a grid pattern. For such a flow field, for example, each lattice point (each point in a broad sense.) Which changes with the passage of time (frame progression) by, for example, a fluid simulation calculation (a simulation calculation in a broad sense; the same applies in the following description). The same applies to the description of 1.), the flow field information (for example, the velocity vector) is obtained, and the flow field information is updated.

In the fluid simulation, the physical quantity to be obtained has continuity in terms of time and space under given boundary conditions, and the influence of a given external force (external factor) directly or indirectly affects the flow field. It is done by a given formula that can affect all grid points. When simulating the motion of a continuum such as water or air, the incompressible Navi
The flow field can be calculated using the er-Stokes equation.

Next, a procedure for performing fluid simulation (fluid dynamics calculation) will be described.

Space for simulating fluid (flow field)
After setting the state at a certain moment (for example, a certain frame), the Navier-Stokes equation or the like is solved to obtain the state of the flow field at the next moment (the next frame).

FIG. 2 shows a schematic diagram for explaining the procedure when performing fluid calculation. Further, FIG. 3 shows a flowchart for explaining the procedure when performing the fluid simulation calculation.

A1 in FIG. 2 is a flow field H at a certain moment.
2 schematically shows the state of F, and A2 in FIG.
It is a schematic representation of the state of the flow field HF at the next moment. In FIG. 2, the state of the flow field HF is the velocity vector (FV1, FV2, FV3 ...) Set at each grid point (GP1, GP2, GP3 ...) At a certain time.
-) Can be represented.

Although the flow field HF is shown two-dimensionally in FIG. 2 in order to make it easy to see, the flow field may be three-dimensional. In addition, in FIG. 2, each grid point (GP
1, GP2, GP3 ...) and velocity vector (FV1,
Although the start points of FV2, FV3 ...) Are shifted, they may be the same.

When obtaining the state of A2 from the state of A1 in FIG. 2, fluid calculation (fluid dynamics calculation) is performed in the procedure as shown in FIG.

First, for each grid point (grid point) in the simulation space, at a certain moment (frame "N-
1)), the flow field information (for example, velocity vector) is set (step S1. See A1 in FIG. 2). That is, the initial condition of the fluid simulation is set.

Next, fluid calculation is performed based on the flow field information set at each grid point (step S2).

Then, the flow field information of each grid point obtained by the fluid calculation becomes the flow field information (information of each grid point) representing the flow field at the next moment (frame "N") (step S3. FIG. 2 A2).

After that, the flow field information of each grid point obtained in step S3 is set as the flow field information of each grid point in step S1 (initial condition of fluid simulation), and the fluid of step S2 is set again. It is possible to change the state of the flow field by performing the calculation recursively.

Since the initial condition (step S1) can be basically freely set, it is also possible to apply an external force (for example, a velocity vector) to an arbitrary point at an arbitrary time.

In order to reflect the external force in the flow field, the corresponding grid point (for example, the grid point close to the position where the external force is applied)
On the other hand, flow field information corresponding to an external force (for example, when the external force is a velocity vector, a velocity vector having a magnitude and a direction corresponding to the external force) may be given.

The flow field H is shown in FIGS. 4 (A), (B) and (C).
The figure which represents typically the state change of the field when the velocity vector EFV corresponding to an external force is given with respect to F is shown.

Note that, in FIGS. 4A, 4B, and 4C, the grid points and the start points of the velocity vectors are deviated in order to make it easier to see, but they may be the same.

For example, if a velocity vector EFV corresponding to an external force as shown in FIG. 4 (B) is given to the flow field HF as shown in FIG. 4 (A), after fluid calculation, as shown in FIG. 4 (C). Such a flow field HF can be obtained.

Here, as a method of reflecting the external force in the fluid simulation, for example, a method of giving a velocity vector EFV obtained according to the direction and magnitude of the external force to the nearest grid point of the position to which the external force is applied as an initial condition. Can think of. Alternatively, the velocity vector EFV obtained in the magnitude and direction of the external force may be distributed to the lattice points GP13, GP14, GP18, GP19 around the position to which the external force is applied and given as the initial condition.

By applying the external force to the flow field in this way, it becomes possible to make the simulation space in which the fluid operation is performed interactive.

Next, the boundary condition when setting the flow field will be described. Here, how to give flow field information (for example, velocity vector) at the boundary of the space to be simulated is called a boundary condition.

The boundary condition is a very important factor in performing a fluid simulation, and various behaviors of a fluid can be virtually reproduced only by changing the way of giving this value.

For example, by setting the direction of the velocity vector at the lower boundary to be downward, it is possible to virtually express a fluid that moves like river water flowing from top to bottom.

If all the values at the boundary are set to 0,
It is possible to virtually express the movement of fluid in a closed space such as the surface of a bathtub in a bathroom, and to express how the fluid swirls.

For example, as shown in FIG. 5, if a velocity vector that blows upward is set as a boundary condition at the lower end, it is possible to generate a field in which gas always flows from bottom to top.

If left in this state, the flow becomes steady after a while, and the merit of performing the fluid simulation is diminished. However, by using the fluid simulation, it is possible to easily express the influence of the flow field to which an external factor such as “send the wind” is added.

2.2 Fluid simulation using the Navier-Stokes equation The equation governing the motion of a continuum such as water or air is Navi
Called the er-Stokes equation. If the fluid flow is sufficiently smaller than the speed of sound, incompressibility may be assumed, and the Navier-Stokes equation in this case is as follows.

[0093]

[Equation 1]

Where V is the flow velocity, p is the pressure, ρ is the density,
μ is the viscosity of the fluid. Further, ∇ represents a gradient operator and Δ represents Laplacian.

By differentiating these equations, the solution at each lattice point can be obtained numerically. The space to be analyzed by the difference is divided into a flow field (fluid field, vector field) in a grid shape, and each grid point is provided with flow field information (for example, velocity vector) for calculation.

Hereinafter, an example of the method of making a difference will be specifically described.

(E1) is a partial differential equation representing the law of conservation of mass, and is called "equation of continuity". Further, (E2) represents the law of conservation of momentum, and is called (Narrowly defined) Navier-Stokes equation.

In this equation, a typical length of flow is L and a typical velocity is U.

[0099]

[Equation 2]

Substituting these into (E1) and (E2) leads to the following equation.

[0101]

[Equation 3]

Re is a Reynolds number and is a dimensionless parameter defined by the following equation.

[0103]

[Equation 4]

There is only one parameter that appears in this equation, and when no external force acts, the flow changes according to the Reynolds number.

From the definition, the fact that the flow velocity is small, the scale of the flow is small, and the viscosity is large are all
It has the same effect in the sense of reducing the ynolds number. Re
The ynolds number physically represents the ratio of inertial force to viscous force, and Re
A small ynolds number means that viscous force is superior to inertial force. That is, it intuitively becomes a viscous fluid flow.

The following equations can be obtained by replacing the variables (E1) 'and (E2)' with x, V, t, and p.

[0107]

[Equation 5]

The expressions (E3) and (E4) are as follows (1)
Characteristic such as (3) is expressed. (1) The second term on the left side of the equation (E4) is non-linear. (2) The derivative of the highest rank is the second rank of the second term on the right side of the equation (E4) and further includes a parameter. (3) The velocity V is a time evolution type, but the pressure p is not a time evolution type.

In particular, (3) is a problem peculiar to incompressibility and is a factor that makes the numerical solution of the Navier-Stokes equation difficult. That is, when the velocity V is obtained over time, it is necessary to determine the pressure p so as to satisfy the continuous equation (E3) at each time step.

As a method of numerically solving the incompressible Navier-Stokes equation, the method of independently obtaining the pressure is adopted as follows.

In equation (E4), if the divergence on both sides is taken,

[0112]

[Equation 6]

When D = ∇ · V is set, the result is as follows.

[0114]

[Equation 7]

According to the equation (E3) of continuity, D = 0 should be obtained, but when the difference (E5) is solved, the discretization error may be accumulated and D may be a large value. , I left it on purpose. Now, in (E5), the pressure distribution obtained with D = 0 satisfies the following equation.

[0116]

[Equation 8]

However, (E6) does not necessarily mean D = 0. It can be seen from the fact that D = constant (≠ 0) satisfies (E6). If D = 0 is always satisfied on the boundary and the initial condition is given so that D = 0 is satisfied in all the regions, the formula (E6) means D = 0. Have difficulty.

Therefore, the equation (E5) is first discretized with respect to t.

[0119]

[Equation 9]

When D ^{n + 1} = 0 is set here, (E5) is as follows.

[0121]

[Equation 10]

Even if D ⁿ ≠ 0, p obtained in this way is determined so that D ^{n + 1} = 0. Therefore, p is always D with respect to inaccuracy of boundary conditions and error accumulation due to time progress.
Can be kept small.

If the pressure is determined from the expression (E7), the expression (E
By substituting the pressure into 4), it becomes possible to obtain V over time. This method is generally called the MAC method.

At (E7), since Δt is sufficiently small, it can be regarded as α = 0.

Therefore, in order to solve the incompressible Navier-Stokes equation, the following two equations must be solved.

[0126]

[Equation 11]

As a two-dimensional Cartesian coordinate system, (E
8) and (E9) are displayed as components as follows.

[0128]

[Equation 12]

The equation (E10) is the Poisson equation regarding pressure.

Regarding the equations (E11) and (E12), the following equations can be used for the respective nonlinear terms uu _x + vu _y and uv _x + vv _y .

[0131]

[Equation 13]

The cavity problem will be taken up below as an example of the calculation.

FIGS. 6A, 6B, and 6C are diagrams used for explaining a specific calculation example.

The cavity problem here is shown in FIG.
Consider a fluid that fills a square region like (A),
This is to numerically obtain the movement of the fluid inside when moving rightward on DC at speed 1.

First, considering the boundary condition of velocity, AD,
U = v = 0 on AB and BC, and u = 1 and v = 0 on CD.

Next, consider the boundary condition of pressure.

In the formula (E9), V =
When 0 is substituted, the following formula is established.

[0138]

[Equation 14]

In this equation, since u = 0 along the y direction on AD and BC, the following equation holds.

[0140]

[Equation 15]

Also, on AB and CD, v along the x direction
Since = 0, the following equation holds.

[0142]

[Equation 16]

Here, a grid called a staggered grid is used for the differentiation. This is because, as shown in FIG. 6B, the definitions of the individual physical quantities are not the same, and on the contrary, the lattice in which all the physical quantities are defined at the same point is called a regular lattice.

As can be seen from FIG. 6B, the advantage of the staggered grid is that the continuous expression can be naturally expressed in one grid cell, and the pressure gradient in each direction determines the velocity in that direction. The point is that the properties of the Stokes equation can be expressed naturally.

Specifically, the following formula is established by approximating the formula of continuity in the cell of FIG. 6 (B).

[0146]

[Equation 17]

As a point to be noted when solving the Navier-Stokes equations using a staggered lattice, for example, considering the equation for u, the following terms appear in the equation.

[0148]

[Equation 18]

Originally, v in this term should have a value at the defining point of u, but when a staggered grid is used, the value of v is not defined at that point. Therefore,
It is necessary to somehow determine the value from the definition point of v. Here, it is determined by the average value of surrounding points.

That is, in the case of the previous example, it is as follows.

[0151]

[Formula 19]

The same applies to the equation relating to v.

Also, the Poisson equation (E1 regarding pressure)
Similar processing is performed on the right side of 0).

Now that the conditions necessary to solve the Navier-Stokes equation have been set, the rest of (E10)
(E11) and (E12) may be differentiated and calculated.

As a precaution, the difference results will be shown below.

[0156]

[Equation 20]

In each of the expressions, the upper subscript n is omitted.

The procedure for solving the equation is as follows: The Poisson equation of (F1) is solved from the initial condition of the velocity or the velocity at the previous time step to obtain the pressure, and the pressure and the velocity are used (F2). , (F3), and the speed at the next time step is obtained. By repeating this procedure, it becomes possible to obtain a solution in a time evolution manner.

In this embodiment, (F1) to (F3) are solved for each grid point forming the flow field (fluid field, vector field), and the velocity vector given to each grid point is obtained.

Here, (F1) is an equation for obtaining the pressure, (F2) is an equation for obtaining the velocity in the x direction,
(F3) is an equation for obtaining the velocity in the y direction. I and j are two-dimensional flow fields (fluid field, vector field).
Is a subscript representing the x and y coordinates of each grid point in. The subscript n + 1 of u means the value of u at the next moment.

In this embodiment, when the velocity vector given to the flow field based on the external factor is reflected in the fluid simulation calculation, the x component of the velocity vector is used as u _{ij in the} equation (F2), and (F3 ), The y component of the velocity vector may be used as v _ij .

Finally, the boundary condition will be described.

For the boundary condition of velocity, see FIG.
At the position shown in (C), u _W= 0.

Regarding the boundary condition of the pressure, for example, if the pressure at the virtual point P'is p ', from the equation (E14),
It looks like this:

[0165]

[Equation 21]

The second-order differential of the velocity needs to be evaluated at the point W in the figure, but is approximated by the one-sided difference of the first-order accuracy as follows.

[0167]

[Equation 22]

The value of u at the virtual point A is required for approximation by the central difference. In this case, u _A = u _B.
When v needs a value at a virtual point, v _D = -v _E
Take (At this time, if v _W is an average of four surrounding points, v _W = 0 holds.) 2.3 Object Deformation Object deformation in the present embodiment will be described below.

In this embodiment, in the process of transitioning from a state before deformation (in a broad sense, before change; also in the following description) to a state after transformation (in a broad sense, after change; also in the following description). The object is deformed using the information on the flow field or the information on the flow field in the process of transitioning from the state after deformation to the state before deformation. Note that the information is not limited to the flow field information in the state transition process, and may be information affected by the flow field. Also, the flow field may be two-dimensional,
It may be three-dimensional, may be obtained in real time, or may be prepared in advance. The object may be two-dimensional or three-dimensional.

FIGS. 7A and 7B are diagrams for explaining the deformation of the object based on the flow field information in this embodiment.

Here, the case of deforming the object by changing the positions of the constituent points of the two-dimensional object is shown by using the information of the two-dimensional flow field. However, the information of the two-dimensional or three-dimensional flow field is used. The same applies when three-dimensional object transformation is performed.

In this embodiment, the modification in frame n
The previous object is transformed in frame (n + m)
When transforming into a later object, for example, it is continuous (m
+1) Flow field information HFI for one frame_n~ HFI_{n + m}For
There is. This flow field information HFI _n~ HFI_{n + m}Is the above Na
Fluid simulation with external factors using vier-Stokes equations
For each frame in real time
Alternatively, the flow field of the storage unit 170 may be set in advance.
Even if the information is stored in the information storage unit 172 and read out as appropriate.
Good.

For the object WOBJ before deformation in the frame n, the flow field information in each frame is applied in reverse order, and for example, according to the direction and size of the velocity vector set in each grid point, The object is deformed by changing the position. As a result, the deformed object WOBJ1 is generated in the frame (n + m).

At this time, it is not necessary to prepare the object after the deformation, and since it is not necessary to hold the object data (all vertex information of the object) of the deformation process, the data amount required for the object deformation is reduced. can do.

[0175] In particular, the flow field information HFI _n ~HFI _{n + m} in the frame n~ frame (n + m) is (broadly, a second state) after deformation in the object WOBJ1 deformation before (broad, first (State) of the flow field information in the process of returning to the object WOBJ, the flow field information can be applied to the object in the reverse order to express a state in which the fluid has a characteristic viscosity and is deformed.

In this case, for example, a frame (n + m) in which an external factor is given to the flow field in the frame n and gradually returns to the original state.
In each frame up to, the flow field information obtained by the fluid simulation may be saved.

Further, as shown in FIG. 7B, the flow field information HF of the transformation process is added to an arbitrary object WOBJ3.
The I _n ~HFI _{n + m} by applying in reverse order, it is possible to obtain the deformation object WOBJ4. The transformation process is
As described above, the fluid deforms with a viscosity peculiar to the motion of the fluid, and thus it is possible to provide an image of the deformation process of the object which has never existed before.

As described above, by deforming an object using the flow field information, the amount of data associated with the deformation is reduced, the image representation of the deformation process reflected in the motion of the fluid, the deformation process and the shape after the deformation are complicated. By this, it becomes possible to provide an effective effect image due to the deformation of an object that could not be obtained until now.

The present embodiment is not limited to the two-dimensional object deformation using the information of the two-dimensional flow field, but the two-dimensional or three-dimensional object using the information of the two-dimensional or three-dimensional flow field. The object transformation can be similarly performed.

FIG. 8 shows an example of an image of the transformation process of a three-dimensional object using the information of the three-dimensional flow field in this embodiment.

Here, an example of the transformation process of the cone object COBJ arranged in the object space is shown.

It is assumed that the positions of the constituent points of the three-dimensional conical object COBJ change based on the velocity vector of the lattice points of the three-dimensional flow field HF ₃₀ . Three-dimensional flow field H
F ₃₀ is the Navi described above as time passes (frame progress).
Updated according to the er-Stokes equation.

The conical object COBJ changes the position of its constituent points based on the direction and magnitude of the velocity vector at each grid point of the flow fields HF _{30 to} HF ₃₄ in each frame with the passage of time. Deformation takes place.

2.3.1 Object Deformation Based on Flow Field Information The above object deformation will be described in detail below.

In the present embodiment, the flow field information of the transformation process is stored, read sequentially and reflected in the object, so that an image in which the object is gradually transformed can be generated. Here, a case where a two-dimensional object is deformed by using information of a two-dimensional flow field will be described.
The same applies in principle when a three-dimensional or three-dimensional object is deformed.

Note that the case where the object is deformed based on the flow field information will be described below, but the same applies when the object is deformed based on the information affected by the flow field.

FIG. 9 schematically shows the flow field information of the transformation process stored in this embodiment.

[0188] In the present embodiment, the object Wobj ₀ in example frame 0, information (in a broad sense, given time duration) a plurality of frames consecutive affected by the flow field information (or the flow field ) Is sequentially applied in each frame to transform the object. Here, applying the flow field information (or information affected by the flow field) means, for example, using the flow field information (or information affected by the flow field), an object (in a broad sense, a primitive ) Of at least one of the configuration point or control point, the information associated with the configuration point or control point of the object, the orientation and size of the normal vector associated with the object, and at least one of the vertex information of the object. It means to let.

The flow field information is obtained as a physical quantity (for example, a velocity vector) at a grid point by fluid simulation in each frame. The information affected by the flow field is information that changes in each frame based on the flow field information about the physical quantity (for example, velocity vector etc.) at the grid point obtained by the fluid simulation (for applying to the object. , A result calculated based on the flow field information about the physical quantity).

Therefore, for example, when object transformation is performed using flow field information, a plurality of consecutive (m + 1)
The flow field information HFI _{n to} HFI _{n + m} for frames is stored and sequentially applied to the object WOBJ _n in the frame _n to obtain the objects WOBJ _{n to} WOBJ _{n + m} in the frame n to the frame (n + m). be able to.

The frame (n + k) (where 0 ≦
k ≦ m. object WOBJ _{n + k where} k is an integer
Should be obtained as a result of using the flow field HF _{n + k} . When the flow field information HFI _{n + k} is a change in the physical quantity with respect to the flow field information of the immediately preceding frame, the flow field information HF _{n to} HF _{n + k} are sequentially applied to the untransformed object to obtain the final result. Then, the object WOBJ _{n + k} in the frame (n + k) can be obtained. Furthermore, the flow field information HFI _{n + k} is, when a change in physical quantity to objects Wobj ₀ in frame 0, by applying the flow field information HFI _{n + k} to the object Wobj ₀ in frame 0, frame (n + k ) Object WOBJ _{n + k} can be obtained.

Therefore, by performing the object transformation using the flow field information or the information affected by the flow field, it is not necessary to prepare all the vertex information of the object in the transformation process, and the data amount accompanying the transformation can be reduced. Can be reduced.

Further, it is possible to carry out complex object deformation which could not be expressed so far, without performing fluid simulation in real time.

In order to obtain the flow field information HFI _{n to} HFI _{n + m} , the flow fields HF _{n to} HF _{n + m} may be obtained in real time for each frame from frame n to frame (n + m). . In this case, when only the flow field information HFI _n of the flow field HF _n at frame n is given, it is possible to determine the flow field information in each frame in real time according fluid simulation, the amount of data required to object deformation Will be able to be significantly reduced.

Also, in each frame, as a result of applying the flow field information to the object, the position of the constituent point or control point of the primitive, the information associated with the constituent point or control point of the primitive, and the normal vector associated with the primitive. Data for generating an image of one frame (in a broad sense, a given unit time) including at least one of the orientation and size and at least one of the vertex information of the primitive is stored as object data. Alternatively, this may be reproduced in reverse order as reproduction data. In this case, since it is not necessary to perform the fluid simulation, it is possible to provide a deformed image having a complicated deformation process that could not be expressed so far without imposing a processing load.

2.3.2 Deformation of Viscous Object In this embodiment, the flow field information in the process of returning from the state after the deformation to the state before the deformation is stored in advance, and this is stored in the reverse order before the deformation. An image that deforms with the viscosity peculiar to the motion of the fluid can be generated by applying (reverse reproduction) to the object of. Thereby, it is possible to express that the fluid slowly deforms by utilizing the characteristic that the fluid returns to the original state. Here, a case where a two-dimensional object is deformed by using information of a two-dimensional flow field will be described. However, a two-dimensional or three-dimensional object is deformed by using information of a two-dimensional or three-dimensional flow field. The same applies in principle.

FIG. 10 is a diagram for explaining reverse playback in this embodiment.

[0198] First of all, the object WOBJ flow field information HFI ₀ of the flow field HF ₀ is applied in the frame 0 ₀
Is the shape of the object before deformation.

[0199] For example determined flow field HF _n ~HF _{n + m} flow field information HFI _n ~HFI _{n + m} in advance a frame n~ frame (n + m), for example keep the flow field information storage unit of the storage unit . The flow fields HF _{n to} HF _{n + m} are, for example, by fluid simulation as states of the flow field in each frame up to the frame (n + m) due to an external factor given to a given position of the flow field HF _{n in} the frame n. Desired.

Then, using the flow field information HFI _{n + m} of the frame (n + m) stored in the frame n, the object WOBJ before deformation in the frame 0 is used.
By changing the position of the constituent point of ₀ , the object W
OBJ _{n + m} is generated. After that, similarly, the frame (n +
1) and (n + 2), the flow field information HFI of the stored frames (n + m-1) and (n + m-2)
By applying _{n + m-1} and HFI _{n + m-2,} and by applying the stored flow field information HFI _n of frame n in frame (n + m), the object WOBJ _n before deformation is generated. .

That is, frame n to frame (n +
m), viscous object WOBJ _{n + m}
Slowly deforms toward the object WOBJ _n (WOBJ ₀ ).

In this way, the flow of the process of returning from the state after deformation to the state before deformation (broadly speaking, the process in which the flow field changed from the first state to the second state returns to the first state) By applying the field information to the object in the reverse order, it becomes possible to generate an image of the process in which the object deforms with the viscosity peculiar to the motion of the fluid, which has been difficult to express.

Furthermore, in this embodiment, the information of the flow field in the process of returning from the state after the deformation to the state before the deformation is applied in the reverse order to change the positions of the constituent points of the arbitrary object. May be. In this case, it is possible to generate an image of the deformation process of an object having a viscosity peculiar to the motion of a fluid, which has been difficult to express up to now.

FIGS. 11A and 11B are views for explaining the object deformation to which the flow field information in the process of returning from the state after deformation to the state before deformation is applied.

In this embodiment, as shown in FIG. 11A, the flow field information in each frame can be applied to the object WOBJ _0A in the frame 0 to deform the object. In this case, the deformed object WOBJ _nA given an extrinsic has a viscosity peculiar to the fluid motion, and the objects WOBJ _nA and WOB
J _{(n + 1) A} , ..., WOBJ _{(n + m-1) A} are transformed, and the original object WOBJ _{(n + m) A} before transformation is gradually returned. At this time, flow field information HFI _n (flow field information after deformation) to HFI in the process of returning from the state after deformation to the state before deformation.
Save _{n + m} (flow field information before deformation).

Next, the flow field information HFI _{n to} HFI in the process of returning from the stored state after deformation to the state before deformation.
Apply _{n + m} in reverse order to any object. In this case, as shown in FIG. 11B, the objects WOBJ _nB , WOBJ _{(n + 1) B} , ...
.., WOBJ _{(n + m-1) B} and WOBJ _{(n + m) B} are generated.

At this time, the process of deforming the object is performed so as to gradually settle into the shape of the object after deformation with viscosity, so that an effect effect that cannot be expressed so far can be obtained.

2.3.3 Applying one flow field to a plurality of objects In this embodiment, one flow field or a virtual field influenced by the flow field is arranged in an object space. Can be applied to objects. Ie 1
In the above flow field, the plurality of objects can be deformed by using the information of the flow field of each frame obtained by the fluid simulation or the information affected by the flow field. Here, a case where a two-dimensional object is deformed by using information of a two-dimensional flow field will be described. However, a two-dimensional or three-dimensional object is deformed by using information of a two-dimensional or three-dimensional flow field. The same applies in principle.

FIG. 12 is a diagram for explaining a case where one flow field in this embodiment is applied to a plurality of objects.

In this embodiment, the two-dimensional flow field HF _{AD is used.}
Can be applied to each of the two-dimensional objects WOBJA to WOBJD. That is, the information of each grid point obtained by the fluid simulation in the two-dimensional flow field HF _AD is used as the information of the fields of WOBJA to WOBJD arranged at a plurality of positions in the object space.

Therefore, the fluid simulation in the one flow field HF _AD makes it possible to obtain the objects WOBJA ′ to WOBJD ′ in which the one flow field is similarly reflected on each object arranged at each position.

As a result, the above-described representation by object transformation can be realized with a smaller processing load.

Further, a two-dimensional flow field HF _AD ′, which is separate from the flow field HF _AD , is generated by the above-mentioned objects WOBJA ~.
You may make it apply to each WOBJD. That is, the information on each grid point obtained by the fluid simulation in the flow field HF _AD ′ is WOBJA to WOBJ arranged at a plurality of positions in the object space.
It is used as the information of D field.

[0214] Thus, the first flow field HF _AD 'by a fluid simulation in one of the flow field HF _AD'
The objects WOBJA ″ to WOBJD ″ can be obtained by similarly reflecting each of the objects on each of the positions.

The flow fields HF _AD and HF _AD ′ do not have to be applied to the objects WOBJA to WOBJD at the same timing. For example, the flow field information obtained by the fluid simulation for the flow field HF _AD may be stored, and the timing may be shifted for each of the objects WOBJA to WOBJD to be applied.

The flow fields HF _AD and HF _AD ′ applied to the same object may be applied to the object after a blending method such as averaging for each grid point.

Here, the case where the flow field information is applied to the object has been described, but the same applies to the case where the information affected by the flow field is applied to the object.

2.4 Others As described above, it is necessary to perform fluid simulation in order to obtain the flow field. In particular, when the fluid simulation is performed in each frame, the processing load becomes a problem. In that case, the processing load can be reduced by performing the following.

For example, in a fluid simulation, when the calculation is performed in a three-dimensional space, the amount of calculation becomes enormous, so that it is difficult to real-time process the generation of an image reflecting an external factor that occurs interactively. Here, the real-time processing means, for example, all processing such as game processing, image generation processing, and sound generation processing in one frame (1 /
It means to complete within 60 seconds, 1/30 second).

Therefore, as shown in FIG. 13, a flow field or a virtual field influenced by the flow field is obtained by performing a fluid simulation on a two-dimensional plane without considering the depth (flow field information or the influence of the flow field). The processing load may be reduced by determining the received information) and applying this flow field information or the information affected by the flow field to the three-dimensional object space.

At this time, a two-dimensional flow field HF or a primitive surface for mapping the influence of the flow field HF is set so as to substantially face the line-of-sight direction of a given viewpoint (virtual camera) VC in the object space. . Then, the information in the height direction of the primitive surface (the remaining one axis direction) is calculated by another calculation such as a proportional expression or a constant.

By doing so, for the image viewed from the given viewpoint VC, the movement on the plane capable of exerting the effect as the image effect effectively reflects the calculation result of the fluid simulation. As a result, it is possible to effectively generate an image in which the motion of the fluid is reflected, without impairing the expressiveness, with a smaller processing load.

Further, as shown in FIG. 14, the above-mentioned Navi
The flow field HF obtained by the fluid simulation using the er-Stokes equation can be mapped to the object OBJ arranged in the object space.

By mapping the flow field HF or the virtual field affected by the flow field on the surface of the object OBJ, for example, the change in the position of the primitive at the position reflecting the flow field HF and the information associated with the primitive. The motion of the fluid can be reflected in the change of the state of the primitive by the color information, the transparency information, and the like.
That is, the position and state of the primitive in the flow field HF can be controlled according to the fluid simulation.

Further, for example, when such a flow field HF or a virtual field affected by the flow field is mapped on the surface of the object OBJ by UV mapping, even if the shape of the object OBJ changes, the surface of the object OBJ also changes. Since the flow field HF can be mapped, the position or state of the primitive can be controlled according to the fluid simulation regardless of the shape of the surface of the object OBJ.

FIG. 15 is a diagram for explaining the UV mapping of the two-dimensional flow field HF performed on the object OBJ1.

Here, the vertex coordinates of the object OBJ1 are (X, Y) = (0, 0), (Xmax, 0), (0,
Ymax), (Xmax, Ymax). For such an object OBJ1, the vertex coordinates of the flow field HF subjected to UV mapping are (U, V) =
Let (0,0), (1,0), (0,1), (1,1).

In UV mapping, for example, each vertex of the flow field HF is associated with each vertex of the object OBJ1. That is, at the vertex coordinates (X, Y) = (0, 0) of the object OBJ1, the vertex coordinates (U,
V) = (0,0) to the vertex coordinates (X, Y) = (Xmax, 0) of the object OBJ1 and the vertex coordinates (U, V) = (1,0) of the flow field HF to the vertex of the object OBJ1. At the coordinates (X, Y) = (0, Ymax), the vertex coordinates (U, V) = (0,1) of the flow field HF are set to the object OBJ.
The vertex coordinates (U, V) = (1,1) of the flow field HF are coordinated with the vertex coordinates (X, Y) = (Xmax, Ymax) of 1.

By doing so, when the object OBJ1 is drawn, each point on the object OBJ1 becomes a flow field H.
Since it is possible to determine which position on F is referred to, when the velocity vector is obtained as the flow field information of each point, the velocity vector of the grid point GP of the flow field HF is set to the surface of the object OBJ1. Can be reflected on the primitive on the surface of the object OBJ1 as the velocity vector of the corresponding position GP ′.

The flow field to be mapped may be two-dimensional or three-dimensional, but in the case of two-dimensional,
As described above, the processing load can be reduced accordingly.

Further, even when it is not necessary to generate an image reflecting the flow field as described above, it is not efficient to perform the fluid simulation in each frame. When it is not necessary to generate an image that reflects the flow field, it is desirable to allocate the processing load for that to other processing.

Therefore, for example, at least one of the size, the number of divisions, the set position, the set number, and the shape of the flow field may be made variable.

FIG. 16 shows a diagram for explaining variable control of the flow field.

The case where the two-dimensional flow field is applied to the two-dimensional object will be described below, but the same applies to the case where the two-dimensional or three-dimensional flow field is applied to the two-dimensional or three-dimensional object.

Here, the flow field obtained by the fluid simulation using the Navier-Stokes equation described above or the virtual field affected by the flow field is defined as the object WOB.
Consider a case where an image reflected on JX is generated.

When the object WOBJX is arranged at a position that reflects the flow field or the virtual field influenced by the flow field, the information of each grid point of the flow field or the influence of the flow field obtained based on the information is displayed. The positions of the constituent points or control points of the object OBJX, the information associated with the constituent points (color information, transparency information, etc.), or the information associated with the control points (weighting, etc.) change based on the received information. As a result, the object WOBJX is generated with an image according to the size of the flow field or the number of divisions.

For example, as shown in FIG. 16, the flow field HFX1 of the object OBJX is different in size or number of divisions.
When the positions of the constituent points of each object are changed based on the flow field information (eg velocity vector) of each lattice point of HFX3 to HFX3, the objects OBJX1 to OBJX3
It transforms like.

Here, the flow field HFX1 and the flow field HFX2
Have the same number of divisions but different sizes. Also, the flow field H
The FX1 and the flow field HFX3 have the same size and different division numbers.

When the flow field HFX2 is set, the number of divisions is the same as in the case where the flow field HFX1 is set, so the accuracy of expressing the flow field is reduced. However, in this case, the state of the flow field can be expressed in an area wider than the flow field HFX1 without increasing the processing load of the fluid simulation.

On the other hand, when setting the flow field HFX3,
Compared to the case where the flow field HFX1 is set, the number of divisions is large, so the processing load of the fluid simulation becomes heavy. However, in this case, the flow field HFX1
Since the state of the flow field can be expressed more accurately than that, it becomes possible to generate a more realistic image.

As described above, by changing the size of the flow field or the number of divisions of the object in consideration of the processing load and the realistic expression, the flow field information obtained by the fluid simulation or the flow field is obtained. It is possible to optimize the image generation processing based on the information affected by.

In the present embodiment, the size or the number of divisions of the flow field is not limited, and the size of the flow field, the number of divisions of the flow field, the position to set the flow field, the number to be set and the shape of the flow field. At least 1 (including grid shape)
Similarly, it is possible to optimize the processing load and the highly accurate image generation.

3. Processing of this Embodiment Next, a processing example of object transformation in this embodiment as described above will be described.

Below, the case where the flow field is applied to the object is shown, but the same applies when the virtual field affected by the flow field is applied to the object.

First, a processing example using the two-dimensional and three-dimensional flow fields will be described.

FIG. 17 shows a flow chart of an example of the transformation process of a two-dimensional object using the two-dimensional flow field in this embodiment.

First, the processing unit 100 initializes various parameters (step S10) and sets a two-dimensional image (step S11). For example, the storage unit 17
The texture image stored in the texture image storage unit 0 is read out and set as a two-dimensional image.

Next, a two-dimensional object (eg plate polygon) is created (step S12), and step S1.
The two-dimensional image set in 1 is mapped as a texture (step S13).

Subsequently, the external force (external factor) applied to the two-dimensional flow field is set (step S14). This external force may be set in real time by an external interface, or may be set in advance by reading out a pre-stored one.

Then, the simulation operation section 110 performs the fluid simulation as described above,
Flow field information at each grid point of the flow field at the next moment (frame) is obtained (step S15).

Primitive processing unit 130 of processing unit 100
Uses the flow field information of each grid point to obtain, for example, a temperature distribution and a concentration change, and applies the temperature distribution and the concentration change to each vertex of a two-dimensional object to deform the object (step S1).
6) Generate this object as an image viewed from a given viewpoint in the object space, and output it to the display unit or the like (step S17).

Next, when a given reset condition is satisfied (step S18: Y), the process returns to step S11 and the two-dimensional image is set again. Further, when the given reset condition is not satisfied (step S18: N), it is determined whether or not the given end condition is satisfied (step S1).
9).

When a given end condition is satisfied (step S19: Y), a series of processing is ended (end), but when the end condition is not satisfied (step S19: N),
Returning to step S14, the external force applied to the flow field is set again.

By doing the above, image transformation (image effect) for a two-dimensional object (image such as a still image or a moving image) using a two-dimensional flow field
Can be realized in real time.

FIG. 18 shows a flow chart of an example of the transformation process of a three-dimensional object using the three-dimensional flow field in this embodiment.

First, in the processing section 100, various parameters are initialized (step S20), the model data stored in advance is read, or the shape of the deformed object is set (step S21).

Next, a three-dimensional polygon is created or FF
A three-dimensional object is created by setting object configuration points or control points such as D (Free Form Deformation), subdivision surface, and NURBS configuration points or control points (step S22).

Subsequently, an external force (external cause) applied to the two-dimensional flow field is set (step S23). This external force may be set in real time by an external interface, or may be set in advance by reading out a pre-stored one.

Then, the simulation operation section 110 performs the fluid simulation as described above,
Flow field information at each grid point of the flow field at the next moment (frame) is obtained (step S24).

The primitive processing section 130 of the processing section 100.
Obtains the flow field information of each grid point and applies it to the vertices of the three-dimensional object, the constituent points of the FFD, etc. to transform the three-dimensional object (step S25). It is generated as an object image viewed from a given viewpoint and is output to a display unit or the like (step S26).

Next, when the given reset condition is satisfied (step S27: Y), the process returns to step S21, and the shape of the deformed object is set again. Also,
When the given reset condition is not satisfied (step S
27: N), it is determined whether or not a given end condition is satisfied (step S28).

When a given termination condition is satisfied (step S28: Y), a series of processing is terminated (end), but when the termination condition is not satisfied (step S28: N),
Returning to step S23, the external force applied to the flow field is set again.

As described above, a three-dimensional object can be deformed using a three-dimensional flow field. In particular, by applying it to the constituent points of the FFD or the subdivision surface, the object can be deformed with fewer definition points, and thus the object can be efficiently deformed.

Next, a processing example for expressing the deformation process of the object having the viscosity peculiar to the fluid in this embodiment will be described. In this embodiment, as described above, the flow field information in the process of returning from the state after the deformation to the state before the deformation can be applied in the reverse order to express the deformation of the viscous object. Furthermore, by using the characteristics of the motion of the fluid that tries to return to a stable shape, the shape after deformation is given, and the object data (all vertex information) in the process of returning to the shape before deformation is saved as playback data, It is also possible to perform animation reproduction by reproduction or reverse reproduction.

FIG. 19 shows an example of image generation processing in the deformation process of an object having a viscosity peculiar to a fluid in this embodiment.

First, the processing section 100 reads the flow field information of the transformation process stored in the flow field information storage section 172 of the storage section 170 or the reproduction data stored in the storage section 170 (step S30).

When performing reproduction (step S31: Y),
When the reverse reproduction is performed (step S32: Y), the flow field information in the process of returning from the deformed state to the undeformed state is sequentially applied to the object frame by frame in the reverse order. Alternatively, object data to which the flow field information in the process of returning from the state after deformation to the state before deformation is applied in the reverse order is sequentially set as object data for each frame (step S33).

Further, when performing the sequential reproduction (step S3)
2: N), flow field information in the process of returning from the state after deformation to the state before deformation (or flow field information in the process of transitioning from the state before deformation to the state after deformation) is sequentially applied to the object for each frame. Apply. Alternatively, the object data to which the flow field information in the process of returning from the state after the deformation to the state before the deformation (or the flow field information in the process of transiting from the state before the deformation to the state after the deformation) is sequentially applied is set to the frame. (Step S34).

On the other hand, if the reproduction is not performed in step S31 (step S31: N), for example, the flow field information is applied to the object to be deformed (step S35).

In step S33, step S34, and step S35, an object image of the deformed object viewed from a given viewpoint in the object space is generated and output to the display unit or the like (step S36).

After the image is output in step S36, when a given end condition is satisfied (step S37:
Y), when a series of processing is ended (END) but the end condition is not satisfied (step S37: N), the process returns to step S31.

As described above, by reproducing the flow field information sequentially or by reproducing the object data to which the flow field information is applied, the object deformation having the viscosity peculiar to the fluid, the indefinite deformation process, and the post-deformation It is possible to transform an object having a complicated shape.

The reproduction data described above may be generated and stored in the following processing.

FIG. 20 shows an example of processing for storing and reproducing the reproduction data in the transformation process.

First, it is determined whether or not there is reproduction data in the deformation process (step S40). When it is determined that there is no reproduction data (step S40: N), the processing section 100
Accept external input to the flow field (step S4)
1). Here, as external input, flow field information corresponding to external force is accepted. If the flow field information is a velocity vector,
Velocity vector EF with magnitude and direction corresponding to external force
V becomes an external input. The shape of the deformed object can be determined by the flow field to which this external force is applied.

When the external input is accepted in step S41, the simulation operation section 110 performs the fluid simulation as described above to obtain the flow field information of each grid point of the flow field at the next moment (frame) (step S42). That is, information about the flow field that gradually returns to the state before deformation is obtained.

The processing section 100 updates the flow field, for example, by obtaining the temperature distribution and the concentration change using the flow field information of each grid point (step S43).

Then, the primitive processing unit 130 changes the position of the constituent points of the object (primitive) at the position where the updated flow field is reflected by changing the position of the object using the field information. (Step S44).

Then, for each frame, the object data (vertex information) of the object deformed by applying the flow field information is stored in the storage section 170 as reproduction data (step S45).

Next, the deformed object is generated as an object image viewed from a given viewpoint in the object space, and is output to the display unit or the like (step S46).

If it is determined in step S40 that there is reproduced data in the deformation process (step S40: Y),
In each frame, using the reproduction data of the transformation process,
An object image viewed from a given viewpoint in the object space is generated and output to a display unit (step S4).
6).

After the image output in step S46, when a given end condition is satisfied (step S47:
Y), when a series of processing is ended (end), but when the end condition is not satisfied (step S47: N), the process returns to step S40 and the presence or absence of reproduction data is discriminated again.

As a result, the object data in the process of returning to the pre-deformation shape can be stored and reproduced. Therefore, it becomes possible to generate an image of a deformation process having a viscosity that could not be expressed so far. Also,
By storing the data as reproduction data, the processing load of real-time processing can be reduced.

In the processing example described above, only the deformation of the object (primitive) has been described, but at least the information associated with the constituent points or control points of the primitive, the direction and size of the normal vector associated with the primitive, and the like. The process of changing the vertex information of one or the primitives can be similarly performed.

4. Hardware Configuration Next, an example of a hardware configuration capable of realizing the present embodiment will be described with reference to FIG.

The main processor 900 is a CD982.
It operates based on a program stored in the (information storage medium), a program transferred via the communication interface 990, a program stored in the ROM 950 (one of the information storage media), game processing, image processing,
Various processing such as sound processing is executed.

The coprocessor 902 assists the processing of the main processor 900, has a product-sum calculator and a divider capable of high-speed parallel calculation, and executes matrix calculation (vector calculation) at high speed. For example, when a physical simulation for moving or moving an object requires a process such as a matrix calculation, a program operating on the main processor 900 instructs (requests) the coprocessor 902 to perform the process. ) Do.

The geometry processor 904 performs geometry processing such as coordinate transformation, perspective transformation, light source calculation, and curved surface generation, has a product-sum calculator and a divider capable of high-speed parallel calculation, and performs matrix calculation (vector calculation). Calculation) is executed at high speed. For example, when processing such as coordinate transformation, perspective transformation, and light source calculation is performed, the program running on the main processor 900 instructs the geometry processor 904 to perform the processing.

The data decompression processor 906 performs a decoding process for decompressing the compressed image data and sound data, and a process for accelerating the decoding process of the main processor 900. Accordingly, a moving image compressed by a given image compression method can be displayed on the opening screen, the intermission screen, the ending screen, the game screen, or the like. The image data and sound data to be decoded are stored in the ROM 95.
0, stored in the CD 982, or transferred from outside via the communication interface 990.

The drawing processor 910 is for executing the drawing (rendering) processing of an object composed of primitive surfaces such as polygons and curved surfaces at high speed. When drawing an object, the main processor 900
Uses the function of the DMA controller 970 to pass the object data to the drawing processor 910 and, if necessary, transfer the texture to the texture storage unit 924. Then, the drawing processor 910 draws the object in the frame buffer 922 at high speed while performing hidden surface removal using a Z buffer or the like based on these object data and texture. Also,
The drawing processor 910 can also perform α blending (semi-transparency processing), depth cueing, mip mapping, fog processing, trilinear filtering, anti-aliasing, shading processing, and the like. Then, when the image for one frame is written in the frame buffer 922, the image is displayed on the display 912.

The sound processor 930 incorporates a multi-channel ADPCM sound source, etc., and generates high-quality game sounds such as BGM, sound effects, and sounds. The generated game sound is output from the speaker 932.

Operation data from the game controller 942, save data from the memory card 944, and personal data are transferred via the serial interface 940.

The ROM 950 stores system programs and the like. In the case of the arcade game system, the ROM 950 functions as an information storage medium,
Various programs are stored in 950. A hard disk may be used instead of the ROM 950.

The RAM 960 is used as a work area for various processors.

The DMA controller 970 is a DM between processors and memories (RAM, VRAM, ROM, etc.).
It controls the A transfer.

The CD drive 980 is a CD 982 for storing programs, image data, sound data and the like.
(Information storage medium) is driven to enable access to these programs and data.

The communication interface 990 is an interface for transferring data with the outside via a network. In this case, a communication line (analog telephone line, ISDN), high-speed serial bus, or the like can be considered as the network connected to the communication interface 990. Then, by using the communication line, data transfer via the Internet becomes possible. Further, by using the high-speed serial bus, data transfer with another game system becomes possible.

Note that each of the means of the present invention may be executed entirely by hardware, or may be executed only by a program stored in an information storage medium or a program distributed via a communication interface. Good. Alternatively, it may be executed by both hardware and a program.

When each means of the present invention is executed by both hardware and a program, the information storage medium stores a program for executing each means of the present invention by using hardware. Will be. More specifically, the program instructs each processor 902, 904, 906, 910, 930, which is hardware, to perform processing, and passes data if necessary.
Then, each processor 902, 904, 906, 91
0, 930, etc. will execute each means of the present invention based on the instruction and the passed data.

FIG. 22A shows an example in which this embodiment is applied to an arcade game system. The player enjoys the game by operating the lever 1102, the buttons 1104, etc. while watching the game image displayed on the display 1100. Various processors, various memories, etc. are mounted on the built-in system board (circuit board) 1106. Information (program or data) for executing each unit of the present invention is stored in the memory 1108 which is an information storage medium on the system board 1106. Hereinafter, this information will be referred to as stored information.

FIG. 22B shows an example in which this embodiment is applied to a home game system. While watching the game image displayed on the display 1200, the player operates the game controllers 1202 and 1204 to enjoy the game. In this case, the above-mentioned stored information is stored in the CD 1206 or the memory cards 1208, 1209, which is an information storage medium that can be detachably attached to the main body system.

FIG. 22C shows a host device 1300,
This host device 1300 and network 1302 (LA
A terminal 130 connected via a small network such as N or a wide area network such as the Internet)
An example in which the present embodiment is applied to a system including 4-1 to 1304-n will be described. In this case, the stored information is, for example, a magnetic disk device that can be controlled by the host device 1300,
It is stored in an information storage medium 1306 such as a magnetic tape device or a memory. When the terminals 1304-1 to 1304-n are capable of standalone generation of game images and game sounds, the host device 1300 sends game images,
A game program or the like for generating a game sound is provided on the terminal 1
It is delivered to 304-1 to 1304-n. On the other hand, when it cannot be generated standalone, the host device 1300 generates a game image and a game sound, and the terminal device 1304-1 ...
It will be transmitted to 1304-n and output at the terminal.

In the case of the configuration shown in FIG. 22C, each means of the present invention may be distributed and executed by the host device (server) and the terminal. In addition, the above stored information for executing each means of the present invention is stored in the host device (server).
The information storage medium and the information storage medium of the terminal may be distributed and stored.

The terminal connected to the network may be a home game system or an arcade game system. When the arcade game system is connected to a network, a portable information storage device is capable of exchanging information with the arcade game system and also with the home game system. (Memory card, portable game device) is preferably used.

The present invention is not limited to that described in the above embodiment, and various modifications can be made.

For example, in the present embodiment, the fluid simulation calculation has been mainly described as an example, but the simulation calculation of the present invention is not limited to the fluid simulation calculation. Further, the present invention is not limited to the flow field, and the present invention can be applied to fields related to various physical quantities.

Also, the method of simulation calculation is shown in FIG.
The method is not limited to the method described in FIG. 6, and the simulation calculation may be performed based on an equation different from the Navier-Stokes equation.

[0308] Further, in the present embodiment, the grid point is taken as an example of the point belonging to the vector field, but the present invention is not limited to this. The points may not be arranged in a grid pattern.

Further, in the present embodiment, the description has been made mainly using the information of the two-dimensional flow field, but the present invention is not limited to this, and the information of the three-dimensional flow field can be used as described above. May be.

Further, in the present embodiment, a flow field (flow field information) can be applied to a virtual field affected by the flow field by the same method (information affected by the flow field).
Can be applied. In addition, a virtual field that is influenced by the flow field (information that is influenced by the flow field) can be applied to the flow field (information of the flow field) by a similar method.

In the invention according to the dependent claim of the present invention, a part of the constituent elements of the claim on which the invention is dependent can be omitted. Further, a main part of the invention according to one independent claim of the present invention can be made dependent on another independent claim.

The present invention is also applicable to various games (fighting games,
It can be applied to shooting games, robot battle games, sports games, competition games, role playing games, music playing games, dance games, etc.).

The present invention is also applicable to various image generation systems (games) such as an arcade game system, a home game system, a large attraction system in which many players participate, a simulator, a multimedia terminal, and a system board for generating game images. System).

[Brief description of drawings]

FIG. 1 is an example of a functional block diagram of an image generation system of this embodiment.

FIG. 2 is a schematic diagram for explaining a procedure when performing a fluid simulation.

FIG. 3 is a flowchart for explaining a procedure when performing a fluid simulation.

4 (A), (B), and (C) are diagrams schematically showing changes in the state of the field when a velocity vector corresponding to an external force is applied to the flow field.

FIG. 5 is a diagram for explaining boundary conditions.

6A, 6B, and 6C are diagrams for explaining a cavity problem as a specific calculation example.

7A and 7B are explanatory diagrams of deformation of an object based on flow field information in the present embodiment.

FIG. 8 is a diagram showing an example of an image of a deformation process of a three-dimensional object using the information of the three-dimensional flow field in the present embodiment.

FIG. 9 is an explanatory diagram schematically showing flow field information of a deformation process stored in the present embodiment.

FIG. 10 is an explanatory diagram of reverse playback in the present embodiment.

11A and 11B are explanatory diagrams of object deformation to which flow field information in the process of returning from a state after deformation to a state before deformation is applied.

FIG. 12 is an explanatory diagram of a case where one flow field in the present embodiment is applied to a plurality of objects.

FIG. 13 is an explanatory diagram for the case of applying a two-dimensional flow field to a three-dimensional object space.

FIG. 14 is an explanatory diagram of a case where a flow field is mapped to an object.

FIG. 15 is an explanatory diagram of UV mapping of a two-dimensional flow field performed on an object.

FIG. 16 is an explanatory diagram of variable control of a flow field.

FIG. 17 is a flowchart showing an example of a two-dimensional object transformation process using a two-dimensional flow field in the present embodiment.

FIG. 18 is a flowchart showing an example of a three-dimensional object transformation process using a three-dimensional flow field in the present embodiment.

FIG. 19 is a flowchart showing an example of image generation processing in the deformation process of an object having a viscosity peculiar to a fluid in the present embodiment.

FIG. 20 is a flowchart showing an example of a process of storing and reproducing reproduction data in the transformation process in the present embodiment.

FIG. 21 is a diagram showing an example of a hardware configuration capable of realizing the present embodiment.

22 (A), (B), and (C) are diagrams showing examples of various types of systems to which the present embodiment is applied.

[Explanation of symbols]

100 processing unit 110 simulation calculation unit 130 primitive processing unit 140 image generation unit 150 sound generation unit 160 operation unit 170 storage unit 172 flow field information storage unit 180 information storage medium 190 display unit 192 sound output unit 194 portable information storage device 196 communication Part HFI _{n to} HFI _{n + m} Flow field information WOBJ, WOBJ1, WOBJ3, WOBJ4 objects

Continued front page    F-term (reference) 2C001 AA03 AA06 AA11 AA14 AA16                       BA02 BA04 BA05 BA06 BA07                       BB01 BB02 BB03 BB04 BC02                       BC03 BC04 BC05 BC06 CA02                       CB01 CB02 CB04 CB06 CB08                       CC01 CC08 DA04                 5B050 BA08 EA24

Claims (13)

[Claims] 1. An image generation system for generating an image, comprising: a simulation calculation means for calculating a flow field for the physical quantity by calculating a change in the physical quantity at each point in a simulation space by a fluid simulation calculation; The location of the constituent or control points of the primitive, information associated with the constituent or control points of the primitive, at least one of the orientation and magnitude of the normal vector associated with the primitive, and the vertex of the primitive based on the change in field. An image generation system comprising: means for changing at least one of information; and means for generating an image viewed from a given viewpoint in an object space in which the primitive is arranged. 2. The flow field according to claim 1, wherein the flow field changed from the first state to the second state is changed to information of a flow field in the process of returning to the first state or information affected by the flow field. Based on at least one of the positions of the constituent points or control points of the primitive, information associated with the constituent points or control points of the primitive, at least one of the orientation and size of the normal vector associated with the primitive, and at least vertex information of the primitive. An image generation system characterized by changing one. 3. An image generation system for generating an image, wherein the flow field information about the physical quantity at each point of the simulation space obtained by the fluid simulation calculation or the information affected by the flow field is stored. Storage means for storing a given time, based on the information of the flow field stored in the storage means or the information affected by the flow field, the position of the primitive configuration point or control point, the primitive configuration point or Means for changing at least one of information associated with control points, at least one of the direction and size of a normal vector associated with the primitive, and vertex information of the primitive; and a place in the object space in which the primitive is placed. An image generation system comprising: a unit for generating an image viewed from a given viewpoint. 4. The storage device according to claim 3, wherein the storage unit stores information about a flow field in a process in which a flow field changed from the first state to the second state returns to the first state or an influence of the flow field. An image generation system characterized by storing the received information. 5. An image generation system for generating an image, the position of a primitive configuration point or control point, information associated with the primitive configuration point or control point, and the orientation and size of a normal vector associated with the primitive. Which is reproduction data for generating an image for a given unit time including at least one of the above and at least one of the vertex information of the primitives, and is at each point of the simulation space obtained by the fluid simulation calculation. Based on the information of the flow field about the physical quantity or the information affected by the flow field, the position of the configuration point or control point of the primitive, the information associated with the configuration point or control point of the primitive, the normal vector associated with the primitive At least one of the orientation and size of the A means for storing at least one changed reproduction data for a given reproduction time; and a means for generating an image viewed from a given viewpoint in the object space based on the stored reproduction data. An image generation system characterized by the above. 6. The composition point or control point of a plurality of primitives set in an object space based on the information of the flow field of 1 or the information affected by the flow field according to any one of claims 1 to 5. Position, information associated with constituent points or control points of the plurality of primitives, at least one of orientation and size of a normal vector associated with the plurality of primitives, and at least one of vertex information of the plurality of primitives. Characteristic image generation system. 7. A simulation calculation unit for obtaining a flow field for the physical quantity by calculating a change in the physical quantity at each point in the simulation space by a fluid simulation calculation, and a constituent point of the primitive based on the change in the flow field. Or a means for changing at least one of a position of a control point, information associated with a constituent point or control point of the primitive, orientation and size of a normal vector associated with the primitive, and vertex information of the primitive. A program causing a computer to function as a means for generating an image viewed from a given viewpoint in an object space in which the primitives are arranged. 8. The flow field according to claim 7, wherein the flow field changed from the first state to the second state is changed to information of a flow field in the process of returning to the first state or information affected by the flow field. Based on at least one of the positions of the constituent points or control points of the primitive, information associated with the constituent points or control points of the primitive, at least one of the orientation and size of the normal vector associated with the primitive, and at least vertex information of the primitive. A program characterized by changing one. 9. Storage means for storing, for a given time, flow field information about physical quantities at each point in the simulation space obtained by fluid simulation calculation or information affected by the flow field, Based on the information of the flow field stored in the storage means or the information affected by the flow field, the position of the configuration point or control point of the primitive, the information associated with the configuration point or control point of the primitive, or the primitive As means for changing at least one of the direction and size of the normal vector and at least one of vertex information of the primitive, and as means for generating an image viewed from a given viewpoint in the object space in which the primitive is arranged. A program that causes a computer to function. 10. The storage device according to claim 9, wherein the storage unit stores information about a flow field in a process in which a flow field changed from the first state to the second state returns to the first state or an influence of the flow field. A program for storing the received information. 11. The position of a constituent point or control point of the primitive, information associated with the constituent point or control point of the primitive, at least one of the direction and magnitude of a normal vector associated with the primitive, and vertex information of the primitive. Reproduction data for generating an image for a given unit time including at least one of them, and flow field information about the physical quantity at each point of the simulation space obtained by the fluid simulation calculation or the flow field Based on the information affected by the, the position of the constituent points or control points of the primitive, information associated with the constituent points or control points of the primitive, at least one of the orientation and magnitude of the normal vector associated with the primitive, and The reproduction data obtained by changing at least one of the primitive vertex information is A program for causing a computer to function as means for storing a given reproduction time and means for generating an image viewed from a given viewpoint of an object space based on the stored reproduction data. 12. The composition point or control point of a plurality of primitives set in an object space based on the information of the flow field of 1 or the information affected by the flow field according to any one of claims 7 to 11. Position, information associated with constituent points or control points of the plurality of primitives, at least one of orientation and size of a normal vector associated with the plurality of primitives, and at least one of vertex information of the plurality of primitives. Characteristic program. 13. An information storage medium readable by a computer, which stores the program according to any one of claims 7 to 12.