KR101110342B1 - System and method for shape controllable fluid simulation - Google Patents

Abstract

The fluid simulation shape control system includes a setting module for generating a local coordinate system and one or more vertices using shape information preset in a plurality of time steps; A first velocity field generation module for generating a first velocity field using a change in position of the one or more vertices in the local coordinate system; A second velocity field generation module for calculating a velocity of each vertex using a change in position of the one or more vertices in a reference coordinate system and generating a second velocity field by projecting the calculated velocity into the local coordinate system; And a simulation module that calculates positions of the one or more vertices for each time step based on the first velocity field and the second velocity field.

Description

Fluid simulation shape control system and method {SYSTEM AND METHOD FOR SHAPE CONTROLLABLE FLUID SIMULATION}

Embodiments relate to a fluid simulation shape control system and method.

In the field of computer graphics (CG), especially in the field of visual effects (VFX), fluid simulation requires a great deal of computation, and therefore, a lot of research and development is required even in recent years with improved computer performance. On the other hand, studies to quantify the flow of fluid numerically before the birth of the CG field have been discussed in the field of Computational Fluid Dynamics (CFD).

Most of the fluid movements encountered in everyday life can be seen as incompressible fluid flow, and in the field of CG and CFD, the Navier-Stokes equation is used as the governing equation to interpret incompressible fluid flow. Doing. Navier-Stokes equations do not have an analytical solution because many different partial differential equations are combined into one equation, and it is not until the 1970s that numerical solutions have been available using computers. In the field of CG, fluid simulations have been introduced, starting with Jos Stam's thesis, entitled "Stable Fluids".

Conventional fluid simulations were mainly used to express natural phenomena as it is, and to represent large-scale static liquids such as the surface of the sea. However, based on the development of technology, recently, unrealistic applications such as expressing the motion of dynamic fluids that are hard to find in the natural world are increasing.

According to an aspect of the present invention, by generating a velocity field corresponding to the movement of a portion of the character and a velocity field corresponding to the movement of the entire character, and performing the fluid simulation using the generated velocity field, the movement of the fluid It is possible to provide a fluid simulation shape control system and method that can be controlled as desired.

According to an embodiment, a fluid simulation shape control system includes: a setting module configured to generate a local coordinate system and one or more vertices using shape information preset in a plurality of time steps; A first velocity field generation module for generating a first velocity field using a change in position of the one or more vertices in the local coordinate system; A second velocity field generation module for calculating a velocity of each vertex using a change in position of the one or more vertices in a reference coordinate system and generating a second velocity field by projecting the calculated velocity into the local coordinate system; And a simulation module that calculates positions of the one or more vertices for each time step based on the first velocity field and the second velocity field.

According to one or more exemplary embodiments, a fluid simulation shape control method includes generating a local coordinate system and at least one vertex using shape information preset in a plurality of time steps; Generating a first velocity field using a change in position of the one or more vertices on the local coordinate system; Calculating a speed of each of the vertices using a change in position of the one or more vertices on a reference coordinate system, and generating a second velocity field by projecting the calculated speed into the local coordinate system; And calculating positions of the one or more vertices in each time step by using the first velocity field and the second velocity field.

Using a fluid simulation shape control system and method according to an aspect of the present invention, a first velocity field, which is a velocity field of a fluid corresponding to a movement of a portion of a character, and a second velocity field, which is a velocity field of a fluid corresponding to a movement of the entire character. By calculating the velocity fields and performing the uncompressed fluid flow simulation using the first velocity field and the second velocity field, the shape of the fluid can be controlled as desired.

1 is a block diagram showing a configuration of a fluid simulation shape control system according to an embodiment.
2 is a schematic diagram illustrating a reference coordinate system, a local coordinate system, a simulation grid, and one or more vertices for performing a fluid simulation.
3 is a schematic diagram illustrating a velocity field of one or more vertices calculated on a local coordinate system.
4 is a schematic diagram illustrating a velocity field calculated by applying a Poisson equation to the velocity field of FIG. 3.
5 is a schematic diagram illustrating a velocity field obtained by projecting the velocity of one or more vertices calculated on a reference coordinate system into a local coordinate system.
6 is a flowchart illustrating a fluid simulation shape control method according to an exemplary embodiment.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

1 is a block diagram showing a configuration of a fluid simulation shape control system according to an embodiment. Referring to FIG. 1, the fluid simulation shape control system may include a setting module 10, a first velocity field generation module 20, a second velocity field generation module 30, and a simulation module 40.

Embodiments described herein may have aspects that are wholly hardware, partly hardware and partly software, or wholly software. For example, in this specification, a “unit”, “module” or “system” and the like may refer to hardware, a combination of hardware and software, or a computer related entity such as software. For example, a part, module or system may be, but is not limited to being, a running process, a processor, an object, an executable, a thread of execution, a program, and / or a computer. . For example, both an application running on a computer and a computer may correspond to a unit, module, or system described herein.

The setting module 10 is a part for storing and / or generating basic information for performing a fluid simulation. The setting module 10 may store shape information corresponding to an object to be expressed as a fluid for each time step. For example, the stored shape information may be a result of modeling the shape of a two-dimensional or three-dimensional character made of a fluid and the movement of the character in each time step.

Since the character to be expressed is moving, the shape information stored in the setting module 10 may be at least partially different in each time step. The time interval between each time step can be appropriately determined in consideration of the calculation amount of the fluid simulation. For example, each time step may be each frame subdividing one second of time, or each sub-frame subdividing one frame again.

In addition, the setting module 10 may set a simulation grid corresponding to the shape of the character in each time step. In the simulation grid, a character may be represented by one or more vertices corresponding to the vertices of the simulation grid located adjacent to the character's surface. As the character moves in each time step, the simulation grid also moves, so the position of one or more vertices also changes with each time step.

Also, the setting module 10 may generate a local coordinate located on the character to be expressed. The position of one or more vertices on the simulation grid is defined relative to a reference coordinate that is independent of the character's movement, while the local coordinate system moves in response to the character's movement while the origin is located on or adjacent to the character. Coordinate system.

2 is a schematic diagram illustrating a reference coordinate system, a local coordinate system, a simulation grid, and one or more vertices at a particular time step.

Referring to FIG. 2, the setting module 10 may generate the simulation grid 100 surrounding the character 1 according to the shape of the character 1 previously stored for the corresponding time step. In this case, the shape of the character 1 may be represented by one or more vertices 200 corresponding to each vertex in the simulation grid 100. In addition, the position of each vertex 200 may be defined based on a reference coordinate system consisting of x- and y-axes. In addition, the setting module 10 may generate a local coordinate system having an origin located on the character 1 and having an x 'axis and a y' axis.

In the embodiment described above with reference to FIG. 2, the simulation grid 100 is shown in a grid structure of square shape, but this is illustrative and in other embodiments a rectangular, hexagonal, triangular or other arbitrary polygonal shape is regularly arranged. The grid can also be used as a simulation grid.

In addition, in the above-described embodiment with reference to FIG. 2, the shape of the character 1, the reference coordinate system, the local coordinate system, the simulation grid 100, and the like have been described with reference to a two-dimensional plane. However, this is merely an example for convenience of description and may represent the shape and movement of the character located in the three-dimensional space in a fluid. In this case, the reference coordinate system and the local coordinate system may be three-dimensional coordinate systems, and the simulation grid may be in the form of a cube or another suitable polyhedron.

Referring back to FIG. 1, the first velocity field generation module 20 is a portion for generating a first velocity field, which is a velocity field of a fluid corresponding to movement of a portion of a character. For example, when the character is a human or animal form, the movement of the fluid corresponding to the movement of the limbs of the human or animal corresponds.

The first speed field generation module 20 may include a first converter 21 and a first speed calculator 22. The first transform unit 21 is a portion for projecting a position on the reference coordinate system of one or more vertices generated by the setting module 10 in the local coordinate system at each time step. This can be obtained as a result of calculating the transformation matrix between the reference coordinate system and the local coordinate system, and multiplying the position of each of the one or more vertices by the transformation matrix.

The first speed calculator 22 is a part for calculating the speed of each vertex using the position of each vertex converted into the local coordinate system. The aforementioned first transform unit 21 projects the position on the reference coordinate system of each of the one or more vertices in each local time step in the local coordinate system. In this case, the first speed calculator 22 may calculate the displacement of each vertex by comparing the position of each vertex projected to the local coordinate system in the current time step with the position projected to the local coordinate system in the previous time step. The calculated displacement may be divided by the time interval between each time step to calculate the speed of each vertex. By the above method, it is possible to generate the velocity field of one or more vertices corresponding to the movement of a part of the character.

3 is a schematic diagram illustrating a velocity field calculated by the first velocity calculator in a fluid simulation shape control system according to an exemplary embodiment. In Figure 3 the speed of each vertex is shown in a straight line extending in the direction of the length and speed proportional to the magnitude of the speed. On the other hand, since each vertex of the simulation grid generated by the setting module 10 is located adjacent to the surface of the character, the vertex does not exist in the internal region 300 of the character spaced more than a certain distance from the surface does not define the speed You may not.

In order to solve this problem, in one embodiment, the first speed field generation module 20 may further include a speed correction unit 23. The velocity correction unit 23 calculates the velocity field of the region 300 spaced apart from the character's surface by a distance by applying the Poisson equation to the velocity field calculated by the first velocity calculator 22. Can be calculated. Specifically, the calculation process of the Poisson equation by the speed correction unit 23 is as follows.

When the speed field calculated by the first speed calculating unit 22 is w and the divergence-free speed field to be calculated by the speed correcting unit 23 is u , the two speed fields are Helmholtz-low. According to Helmholtz-Hodge decomposition, the following Equation 1 is satisfied.

In Equation 1, q is a specific scalar value, and when q is obtained, u may be obtained by substituting q in Equation 1. To this end, first, by applying divergence to both sides of Equation 1, Equation 2 can be obtained.

In the above Equation 2, u is a no divergence field, so? u becomes 0, and thus Equation 2 becomes a Poisson equation such as Equation 3 below.

Using numerical analysis, the value of q can be obtained from Equation 3, and the velocity field u can be calculated by substituting the obtained value of q into Equation 1. In this case, as described above, the velocity field u becomes a velocity field including a velocity of an area spaced apart from the surface of the object by a predetermined distance or more. The velocity field u calculated as described above is a velocity field of the fluid corresponding to the projection of the movement of a part of the character in the local coordinate system, and is referred to as a first velocity field.

4 is a schematic diagram illustrating a first velocity field calculated in a fluid simulation shape control system according to an embodiment. Comparing FIG. 3 and FIG. 4, it can be seen that the velocity field is defined up to the inner region 300 spaced a predetermined distance or more from the character's surface as a result of the calculation by the velocity correction unit 23.

Referring back to FIG. 1, the second velocity field generator 30 is a portion for generating a second velocity field, which is a velocity field of a fluid corresponding to movement of the entire character to be represented by the fluid. For example, when a character made of a fluid moves in a specific direction, the motion such as fluid flowing in a direction opposite to the moving direction corresponds to this.

The second speed field generator 30 may include a second speed calculator 31 and a second converter 32. First, the second speed calculator 31 may calculate the speed of each vertex using the positions of one or more vertices in the reference coordinate system. The second speed calculator 31 calculates the displacement by comparing the position at the current time step of each vertex in the reference coordinate system with the position at the previous time step, and divides the calculated displacement by the time interval between each time step. Can be calculated.

The 2nd conversion part 32 is a part for projecting the speed | rate of the 1 or more vertices computed by the 2nd speed calculating part 31 to a local coordinate system. Projecting the velocity of each vertex to a local coordinate system can be obtained by multiplying the velocity of each vertex by a transformation matrix between the reference coordinate system and the local coordinate system, similar to the one described above with respect to the first transform unit 21. have. As a result, a second velocity field which is a velocity field of the fluid corresponding to the movement on the reference coordinate system of the character can be obtained.

5 is a schematic diagram illustrating a second velocity field calculated in a fluid simulation shape control system according to one embodiment. As shown, as a result of moving the entire character in one direction on the reference coordinate system, it can be seen that the velocity field is generated for the vertices located adjacent to the surface of the character.

Referring back to FIG. 1, the simulation module 40 is incompressible using the first speed field and the second speed field generated by the first speed field generation module 20 and the second speed field generation module 30, respectively. Incompressible fluid flow simulation can be performed. For example, the simulation module 40 may update the position of each vertex in time steps based on the speed field obtained by adding up the first speed field and the second speed field.

Incompressible fluid flow simulation may be a process of updating the position of each vertex in a time step by calculating the velocity field of the fluid calculated by the above-described process to the Navier-Stokes equation. . Since a detailed calculation process of fluid simulation by the simulation module 40 is well known to those skilled in the art, a detailed description thereof will be omitted. For example, the simulation module 40 may perform fluid simulations using known fluid simulators.

In one embodiment, the fluid simulation shape control system may further include a particle module 50. The particle module 50 is a part for generating one or more fluid particles based on the first velocity field and the second velocity field generated by the above-described process. Fluid particles may be represented by one or more vertices.

For example, if there is a portion of the velocity field in which the magnitude of the velocity is greater than or equal to a preset threshold value, the particle module 50 may generate a new vertex adjacent to the portion. As a result, it is possible to express a splash shape in which water particles splash on the surface of the character when the character made of water moves fast. An operation for generating particles in the particle module 50 includes a method for generating particles in a bubble or foam shape in addition to the above-described splash based method. Specific methods for generating particles in a splash, bubble, and / or foam shape are well known to those skilled in the art, and thus detailed descriptions thereof will be omitted.

6 is a flowchart illustrating a fluid simulation shape control method according to an exemplary embodiment.

Referring to FIG. 6, first, a local coordinate system and a simulation grid positioned on a character may be generated using shape information stored in advance for each character to be represented by a fluid (S1). In this case, the shape of the character may be represented by one or more vertices corresponding to each vertex of the simulation grid.

Next, it is determined whether the current time step is the first time step (S2). If the current time step is the first time step, no operation is performed, and the process proceeds directly to the next step after step S10 of determining whether the current time step is the last time step.

If the current time step is not the first time step, the position of each vertex generated in the above-described step S1 may be projected to the local coordinate system on the character (S3). This can be obtained as a result of calculating a transformation matrix between the reference coordinate system and the local coordinate system, and multiplying the calculated transformation matrix by each position of one or more vertices.

Next, the displacement is calculated by comparing the position of each vertex in the local coordinate system with the position in the previous time step, and the speed of each vertex may be calculated by dividing the calculated displacement by the time interval between each time step (S4). . At this time, since each vertex is located adjacent to the surface of the character, the speed may not be defined in the inner region spaced more than a predetermined distance from the surface of the character.

Therefore, in order to define the velocity of the character internal region, the first velocity field may be generated by calculating the velocity of the entire region of the character using the velocity of each vertex calculated in step S4 described above (S5). The first velocity field may be a no-dispersion velocity field calculated by applying the Poisson equation to the velocity of each vertex calculated in step S4.

The first velocity field generated by the above-described steps S3 to S5 is the velocity field of the fluid corresponding to the movement of the portion of the character. For example, when a character of human or animal shape is to be represented by a fluid, the movement of a fluid corresponding to the movement of a limb of a human or an animal corresponds to this.

Meanwhile, the velocity field of the fluid corresponding to the movement of the entire character may be separately calculated. To do this, first calculate the displacement of each vertex by comparing the position of each of the one or more vertices in the reference coordinate system with the position in the previous time step, and calculate the velocity of each vertex by dividing the calculated displacement by the time interval between each time step. It may be (S6).

Next, the second velocity field may be generated by projecting the velocity of each vertex calculated in the above-described step S6 to a local coordinate system located on the character (S7). The second velocity field calculated as described above is a velocity field of a fluid corresponding to the movement of the entire character. For example, when a character made of fluid moves in one direction, the fluid flowing on the surface of the character in a direction opposite to the movement direction may be used. Yes.

In the above-described embodiment, steps S3 to S5 of generating the first velocity field corresponding to the movement of the portion of the character are first performed, and then generating the second velocity field corresponding to the movement of the entire character. (S6, S7) was performed. However, as an example, the order of generating the first speed field (S3 to S5) and generating the second speed field (S6, S7) may be changed or may be performed simultaneously.

When the first velocity field and the second velocity field are calculated, an uncompressed fluid flow simulation may be performed using the first velocity field and the second velocity field (S8). For example, an uncompressed fluid flow simulation can be performed using the velocity field, which is the sum of the first velocity field and the second velocity field. Uncompressed fluid flow simulation may be a process of updating the position of each vertex in a time step by applying a Navier-Stokes equation to a velocity field. Detailed computation of fluid flow simulation is well known to those skilled in the art, and thus detailed description thereof will be omitted.

In one embodiment, after the fluid flow simulation is performed, one or more fluid particles may be generated based on the first velocity field and the second velocity field (S9). The resulting fluid particle may be represented by one or more vertices. This is for expressing a fluid shape such as a splash, bubble, or foam, and the detailed description of the specific particle generation method is well known to those skilled in the art.

When each of the above-described steps S3 to S9 in the current time step is completed, it is determined whether the corresponding time step is the last time step (S10). If it is not the last time step, the above-described steps (S3 to S9) are repeatedly performed in the next time step with the position of each vertex calculated in the current time step as an initial value, and the simulation is terminated in the last time step. do.

The fluid simulation shape control method according to the embodiments herein has been described with reference to the flowchart shown in the drawings. Although the method is shown and described in a series of blocks for the sake of simplicity, the invention is not limited to the order of the blocks, and some blocks may occur in different order or simultaneously with other blocks than those shown and described herein. Various other branches, flow paths, and blocks may be implemented in order to achieve the same or similar results. In addition, not all illustrated blocks may be required for the implementation of the methods described herein.

Although the present invention described above has been described with reference to the embodiments illustrated in the drawings, this is merely exemplary, and it will be understood by those skilled in the art that various modifications and variations may be made therefrom. However, such modifications should be considered to be within the technical protection scope of the present invention. Therefore, the true technical protection scope of the present invention will be defined by the technical spirit of the appended claims.

Claims (10)

A setting module for generating a local coordinate system and at least one vertex using shape information preset in a plurality of time steps;
A first velocity field generation module for generating a first velocity field using a change in position of the one or more vertices in the local coordinate system;
A second velocity field generation module for calculating a velocity of each vertex using a change in position of the one or more vertices in a reference coordinate system and generating a second velocity field by projecting the calculated velocity into the local coordinate system; And
And a simulation module for calculating the position of the one or more vertices in each time step based on the first velocity field and the second velocity field.
The method of claim 1,
The first speed field generation module,
A first converter converting a position on a reference coordinate system of the one or more vertices into a position on the local coordinate system; And
And a first speed calculator for calculating the speed of each of the vertices by comparing the converted positions of the respective vertices with the positions of the previous time steps.
The method of claim 2,
The first speed field generation module,
And a velocity correction unit for converting the velocity of the one or more vertices into a no-dissipation velocity field.
The method of claim 1,
The second speed field generation module,
A second speed calculator configured to calculate a speed of each of the vertices by comparing the position of the one or more vertices on a reference coordinate system with a position in a previous time step; And
And a second transform unit converting the calculated velocities of the vertices into velocities on the local coordinate system.
The method of claim 1,
And a particle module that generates one or more vertices based on the first velocity field and the second velocity field.
Generating a local coordinate system and one or more vertices using shape information preset in a plurality of time steps;
Generating a first velocity field using a change in position of the one or more vertices on the local coordinate system;
Calculating a speed of each of the vertices using a change in position of the one or more vertices on a reference coordinate system, and generating a second velocity field by projecting the calculated speed into the local coordinate system; And
And calculating positions of the one or more vertices in each time step by using the first velocity field and the second velocity field.
The method of claim 6,
Generating the first velocity field may include:
Converting a location on a reference coordinate system of the one or more vertices to a location on a local coordinate system; And
And calculating the velocity of each vertex by comparing the transformed position of each vertex with a position in a previous time step.
The method of claim 7, wherein
Generating the first velocity field may include:
And generating a no-dissipation velocity field using the calculated velocities of the respective vertices.
The method of claim 6,
Generating the second velocity field may include:
Calculating the speed of each vertex by comparing the position of the one or more vertices with a position in a previous time step; And
And converting the calculated velocity of each vertex into a velocity on the local coordinate system.
The method of claim 6,
Generating one or more vertices based on the first velocity field and the second velocity field.

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