KR102187066B1 - Method and apparatus of reaction-diffusion modeling based on lattice boltzmann method - Google Patents

Abstract

A reaction-diffusion modeling method and apparatus based on the lattice-Boltzmann technique are provided. The reaction-diffusion modeling apparatus includes a memory in which a reaction-diffusion modeling program according to the lattice-Boltzmann technique is stored, and a processor that executes a program stored in the memory, and the processor is, according to the execution of the reaction-diffusion modeling program, the lattice- A reaction-diffusion model that calculates the diffusion process of the medium using the Boltzmann method, and a reaction-diffusion model that calculates the reaction process of the medium using the Gray-Scott model equation, and the reaction-diffusion model for a set medium When the region is divided into a plurality of grids, a simulation is performed on the medium through the change of the amount of the medium present in each grid, but at least one of a simulation applying anisotropic control and a simulation applying flow resistance is performed, The pattern generated as a result of the simulation is output.

Description

Reaction-diffusion modeling method and apparatus based on the lattice-Boltzmann technique {METHOD AND APPARATUS OF REACTION-DIFFUSION MODELING BASED ON LATTICE BOLTZMANN METHOD}

The present invention relates to a reaction-diffusion modeling method and apparatus for generating a reaction-diffusion pattern based on a lattice-boltzmann technique.

Computer graphics technology plays an important role in the'realistic visual beauty' that enables users to immerse themselves in and enjoy content in games, movies, and animations. Also, as computer graphics technology develops, the demand for more realistic and high immersion is increasing, so research on related technologies is essential.

'Realistic visual beauty' can be realized through physical calculations found in the real world. However, as in the real world, if all physical calculations are considered, a lot of physical and time costs are incurred. Therefore, in computer graphics technology, it has been developed in a way that can give maximum realistic satisfaction to users while considering physical calculations with as little cost as possible.

One of the methods used for this is a method using textures. For example, when modeling a patterned 3D object, a 2D texture is mapped to make it easier to represent the pattern on the object's surface. In addition, a 3D object with a complex surface makes it look like it actually has a complex surface by using a texture that can represent a texture rather than manually modeling the complex surface. The texture used in this way can be produced by correcting the actual photographed material or by drawing it directly using a computer tool. However, the easiest and most effective way is to build it through a reaction-diffusion model.

On the other hand, in nature, various patterns can be found through the pattern of growing leaves, the shape of human fingers or the tentacles of living things, and the pattern of butterfly wings. These patterns are called biological patterns, and Alan Turing has shown that these patterns can be created through two processes. The two processes are called reaction and diffusion, and a model that creates biological patterns through these physical processes is called a reaction-diffusion model.

The technique of generating patterns through this reaction-diffusion model began to be used in the field of texture synthesis by Greg Turk and Andrew Witkin. Greg Turk created and used various animal skin patterns through a reaction-diffusion model, and Andrew Witkin proposed a model that could control the orientation of the pattern. Reaction-diffusion models are used to generate noise images that change over time and to create interesting and diverse patterns, and patterns have been used for texture synthesis or texture expression of 3D models, or artistic expressions of artists.

In general, reaction-diffusion models define reaction equations for how different fluids will react. At this time, diffusion of the fluid can be attempted in various ways, but there are differences in results depending on the diffusion method. Existing reaction-diffusion models mainly calculate the diffusion of fluids based on the finite difference fractional method, and generate various patterns by adjusting only the reaction coefficient values.

However, there is a need for a technology capable of controlling the patterns of patterns so that more diverse and dynamic patterns can be created. In particular, there is a need for a method of controlling the aspect of a reaction-diffusion pattern that generates various and dynamic textures so that it can be used for realistic image beauty of content or artistic expression of an artist.

US Patent Publication No. 2017-0255745 (Name of invention: System and Method for Medical Image Based Cardio-Embolic Stroke Risk Prediction)

An embodiment of the present invention is to solve the problems of the prior art described above, and not only control the reaction coefficient of the reaction equation in the reaction-diffusion model, but by controlling the pattern pattern locally, It is intended to provide a reaction-diffusion modeling method and apparatus based on the lattice-Boltzmann technique that can generate patterns.

However, the technical problem to be achieved by the present embodiment is not limited to the technical problem as described above, and other technical problems may exist.

As a technical means for achieving the above-described technical problem, the reaction-diffusion modeling method based on the lattice-Boltzmann technique according to the first aspect of the present invention calculates the diffusion process of the medium using the lattice-Boltzmann technique, and gray- Modeling a reaction-diffusion model for calculating the reaction process of the medium using the Scott model equation; When a region in which the medium exists is divided into a plurality of grids through the reaction-diffusion model for a set medium, a simulation is performed on the medium through a change in the amount of the medium present in each grid, but anisotropic control is applied. To simulate; And outputting a pattern generated as a result of the simulation, wherein the number of a plurality of directions each of the molecules of the medium existing in the lattice has is set in advance, and the anisotropy control is performed in a specific direction among a plurality of preset directions. An anisotropic function that controls the magnitude of the reaction of the molecules moving in the direction is applied to the diffusion process.

In addition, the reaction-diffusion modeling method based on the lattice-Boltzmann technique according to the second aspect of the present invention calculates the diffusion process of the medium using the lattice-Boltzmann technique, and the reaction process of the medium using the Gray-Scott model equation. Modeling a reaction-diffusion model that calculates When the region in which the medium exists is divided into a plurality of grids through the reaction-diffusion model for a set medium, a simulation is performed on the medium through a change in the amount of the medium present in each grid, but the flow resistance is applied. To simulate; And outputting a pattern generated as a result of the simulation, wherein the number of directions each of the molecules of the medium existing in the lattice has in advance is set, and the amount of the medium moves to another cell is controlled. The flow resistance according to the map is applied to the diffusion process of the medium, but the greater the flow resistance at a location on the style map corresponding to the cell to which the medium is to be moved, the smaller the amount of the moved medium, and the style map shows that the medium is As a still image having the same resolution as the area that can be diffused, the value of the flow resistance is set for each pixel.

In addition, a response-diffusion modeling apparatus based on a lattice-Boltzmann technique according to a third aspect of the present invention includes: a memory storing a reaction-diffusion modeling program according to the lattice-Boltzmann technique; And a processor that executes a program stored in the memory, wherein the processor calculates a diffusion process of the medium using a lattice-Boltzmann technique according to execution of the reaction-diffusion modeling program, and uses a Gray-Scott model equation. A reaction-diffusion model that calculates the reaction process of the medium is modeled, and the amount of medium present in each grid is divided into a plurality of grids through the reaction-diffusion model for a set medium. A simulation of the medium is performed through the change of, but at least one of a simulation to which anisotropic control is applied and a simulation to which flow resistance is applied is performed, and a pattern generated as a result of the simulation is output. In this case, the number of directions in each of the molecules of the medium existing in the lattice is set in advance. In addition, in the anisotropy control, an anisotropic function for controlling the magnitude of a reaction of the molecules moving in a specific direction among a plurality of preset directions is applied to the diffusion process. In addition, the flow resistance according to the style map that controls the amount of the medium moving to another cell is applied to the diffusion process of the medium, and the larger the flow resistance at a position on the style map corresponding to the cell to which the medium is moving, the moved medium The amount of is reduced, and the style map is a still image having the same resolution as a region in which the medium can be diffused, and a value of the flow resistance is set for each pixel.

Further, a fourth aspect of the present invention provides a computer-readable recording medium in which a program for implementing any one of the first and second aspects is recorded.

According to any one of the above-described problem solving means of the present invention, in a reaction-diffusion model used to express a realistic texture of a texture during 3D modeling of computer graphics, a response coefficient in changing the pattern of the pattern By applying constraints such as diffusion direction or flow resistance, not just the value, the pattern can be variously controlled and changed. In other words, through a reaction-diffusion model that is easier to control locally than the existing finite difference method, anisotropic control method that gives diffusion direction to the flow or reaction of fluid, and a method that applies flow resistance through a style map Pattern creation is possible.

In addition, according to any one of the problem solving means of the present invention, when the pattern aspect changes in the reaction-diffusion model, the user can set and adjust the constraint condition, so that the user can generate the pattern of the desired trend.

1 is a block diagram of a reaction-diffusion modeling apparatus according to an embodiment of the present invention.
2 and 3 are diagrams for explaining a lattice-Boltzmann technique applied to an embodiment of the present invention.
4 is a diagram showing a simulation result of a gray-Scott response-diffusion model based on a conventional finite difference method.
5 is a diagram showing an example of a simulation result of a response-diffusion model based on a lattice-Boltzmann technique according to an embodiment of the present invention.
6 is a diagram showing an example of a simulation result of a reaction-diffusion model to which anisotropic control is applied according to an embodiment of the present invention.
7 is a view showing an example of a simulation result of a reaction-diffusion model to which a flow resistance force according to a style map is applied according to an embodiment of the present invention.
8 is a flowchart illustrating a reaction-diffusion modeling method based on a lattice-Boltzmann technique according to an embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those of ordinary skill in the art can easily implement the present invention. However, the present invention may be implemented in various different forms and is not limited to the embodiments described herein. In order to clearly describe the present invention, parts irrelevant to the description are omitted in the drawings, and similar reference numerals are assigned to similar parts throughout the specification. In addition, while describing with reference to the drawings, the drawing numbers may vary depending on the drawings even if the configuration is indicated by the same name, and the drawing numbers are only described for convenience of description, and the concept, features, and functions of each configuration are indicated by the corresponding drawing numbers. Or the effect is not to be interpreted as limiting.

Throughout the specification, when a part is said to be "connected" to another part, this includes not only "directly connected" but also "electrically connected" with another element interposed therebetween. . In addition, when a part "includes" a certain component, it means that other components may be further included, and one or more other components are not excluded unless specifically stated to the contrary. It is to be understood that the presence or addition of features, numbers, steps, actions, elements, parts, or combinations thereof, does not preclude the possibility of preliminary exclusion.

In this specification, the term'section' or'module' includes a unit realized by hardware or software, and a unit realized using both, and one unit is realized using two or more hardware. Alternatively, two or more units may be realized by one piece of hardware.

1 is a block diagram of a reaction-diffusion modeling apparatus according to an embodiment of the present invention.

As shown in FIG. 1, the reaction-diffusion modeling apparatus 100 includes a memory 110 and a processor 120.

The memory 110 stores a reaction-diffusion modeling program that models a reaction-diffusion model based on the lattice-Boltzmann technique, and generates a pattern through the modeled reaction-diffusion model. The reaction-diffusion modeling process and pattern generation process processed through the execution of the reaction-diffusion modeling program will be described in detail through the operation of the processor 120 below.

The memory 110 collectively refers to a nonvolatile storage device that continuously maintains stored information even when power is not supplied or a volatile storage device that requires power to maintain stored information.

The processor 120 controls the overall operation of the reaction-diffusion modeling apparatus 100. To this end, the processor 120 may be implemented by including at least one processing unit (CPU, micro-processor, DSP, etc.), random access memory (RAM), read-only memory (ROM), and the like, and the memory 110 The program stored in) can be read into RAM and executed through at least one processing unit. Meanwhile, according to embodiments, the term “control unit” may be interpreted as the same meaning as terms such as “processor”, “controller”, and “operation device”.

The processor 120 executes a reaction-diffusion modeling program stored in the memory 110, and processes an anisotropic control for the flow and reaction of a medium (eg, fluid) and a pattern generation operation in which flow resistance is applied.

The processor 120 processes the following operations as the reaction-diffusion modeling program is executed.

The reaction-diffusion model is divided into two processes. These two processes are a'diffusion process', a process in which a medium or substance spreads out, and a'reaction process' in which different mediums or substances cause a reaction. As a method of calculating the diffusion process, the processor 120 may use a lattice-Boltzmann method that can be precisely controlled locally. In addition, the processor 120 may use a Gray-Scott model equation capable of intuitive understanding of the reaction equation as an equation for calculating the reaction process.

First, an operation of calculating the spreading process by the processor 120 will be described.

For reference, a method of simulating a fluid can be largely divided into a method from an Euler perspective and a method from a Lagrangian perspective. From Euler's point of view, a fluid is simulated by dividing the area where the fluid can exist into grids and using the amount of fluid present in each grid. On the other hand, from the Lagrangian perspective, the fluid is simulated through the motion of each fluid molecule. Simulation methods from Euler's point of view include the Finite Differential Method (FDM) and the Lattice Boltzmann Method (LBM). At this time, compared to the finite difference method, the lattice-Boltzmann method does not require information about the surrounding lattice to calculate the motion of the fluid, so the computational speed can be faster by using parallel processing, and a more microscopic approach Easy to control.

The finite difference method applied to the existing reaction-diffusion model is a numerical calculation method that approximates the derivative with a finite difference equation to obtain a solution. Like the lattice-Boltzmann method, it is a method of fluid simulation from the Euler perspective. Divide the space that can exist into a grid. However, it does not consider the direction of the fluid molecules in the lattice, but only considers how much fluid there are in the lattice.

According to the lattice-Boltzmann technique, the processor 120 divides a region where a medium (hereinafter, referred to as “fluid”) can exist into a lattice, and a direction that molecules of fluid existing in one lattice can have. The fluid is simulated by limiting to a few.

For example, as shown in FIG. 2, nine directions can be considered in the case of two-dimensional including a stationary state, and it is assumed that the density in one grid is 1. In addition, in the case of three-dimensional, it is possible to consider 19 directions, and it is also assumed that the density in one grid is 1.

The ratio of directions of molecules in one lattice is determined differently. In the case of 9 two-dimensional directions, the ratio is 4/9 in the stationary state, 1/9 in the vertical direction, and 1/36 in the diagonal direction. In addition, in the case of 19 three-dimensional directions, the ratio is 1/3 in the stationary state, 1/18 in the vertical direction, and 1/36 in the diagonal direction.

In this case, in the case of 2D, the distribution function f in one direction within the grid is equal to Equation 1 below, and the density ρ of one lattice can be calculated as Equation 2 below through the distribution function.

<Equation 1>

<Equation 2>

격자의 위치, t는 시간이다. 분포 함수는

에 위치해 있는 격자에서 i 방향을 갖고 있는 분자들의 양을 의미하며, 한 격자의 모든 방향(즉, 9가지로 설정된 방향)에 대한 분포 함수 값을 합하면 해당 격자 안의 유체에 대한 밀도가 된다.In Equations 1 and 2, i is the direction of the molecule,

The position of the grid, t is the time. The distribution function is

It means the amount of molecules in the i-direction in the lattice located at, and the sum of the distribution function values for all directions of one lattice (that is, the directions set to nine) gives the density of the fluid in the lattice.

In the lattice-Boltzmann method, the flow of fluid is divided into a translation process and a collision process. Through the translation process, the molecules of each lattice move to the next lattice. The expression for the translation process is shown in Equation 3 below.

<Equation 3>

는 시간 변화량으로서 격자-볼츠만 방법에서는 보통 1을 사용하며,

는 j방향의 단위 벡터이고, j는 i의 반대 방향이다. 즉, 다음 시간에서 해당 격자의 i 방향에 해당하는 밀도 값은 i의 반대 방향으로 한 칸 건너간 격자의 i 방향의 밀도 값이 된다.In Equation 3,

Is the amount of time change, usually 1 in the Lattice-Boltzmann method,

Is the unit vector in the j direction, and j is the opposite direction of i. That is, the density value corresponding to the i-direction of the corresponding grid at the next time becomes the density value of the i-direction of the grid crossed one space in the opposite direction of i.

After the translation process, the collision process adjusts the collisions that occur as molecules move to the next grid and reflects the overall flow within one grid. This collision process can be represented through Equations 4 to 6 below.

<Equation 4>

<Equation 5>

<Equation 6>

는 평형 분포 함수이고,

는 해당 격자에서의 분자들의 전체적인 속도이고,

는 방향에 대한 가중 함수이며, "i=0"은 정지 상태, "i=1, 2, 3, 4"는 수직 방향, "i=5, 6, 7, 8"은 대각선 방향이다.At this time,

Is the equilibrium distribution function,

Is the overall velocity of the molecules in that lattice,

Is the weighting function for the direction, "i=0" is the stationary state, "i=1, 2, 3, 4" is the vertical direction, and "i=5, 6, 7, 8" is the diagonal direction.

For example, referring to FIG. 3, when the direction of the blue arrow is the i-direction, the opposite direction of the i-direction of the corresponding grid is the lower left, so the red arrow, which is the i-direction of the lower left grid, moves to the corresponding grid. Likewise, the blue arrow moves to the upper right grid.

The medium (eg fluid) that is diffused through the lattice-Boltzmann technique as described above may try to leave the simulation area or hit an obstacle in the simulation area. At this time, processing such a phenomenon is referred to as boundary surface processing.

As an interface for processing this, there are a no-slip boundary and a periodic boundary. The no-slip interface allows the relative velocity of the fluid with respect to the interface to be 0 when the fluid hits the interface, and the periodic interface can be regarded as infinite in size because the vertical and horizontal domains are connected respectively.

In an embodiment of the present invention, it is described that the processor 120 implements a no-slip interface so that when the fluid hits the interface, the flow of the fluid changes in a direction that is exactly opposite to the direction when the fluid hits the interface.

Next, an operation of calculating the reaction process by the processor 120 will be described.

The reaction equation that can be used in the reaction-diffusion modeling is not limited, but in an embodiment of the present invention, the implementation of the reaction-diffusion model will be described using a Gray-Scott reaction equation with excellent intuitive understanding.

The Gray-Scott reaction-diffusion model basically reacts two substances. At this time, if the corresponding two substances are respectively A and B, A is supplied at a constant rate each time the unit time elapses, and B is extinguished. At the same time, if there are 2 molecules B and 1 molecule A, a reaction occurs, and molecule A becomes molecule B.

Accordingly, the reaction equation for substances A and B can be expressed as Equation 7 below.

<Equation 7>

In Equation 7, A and B are values after diffusion is applied to each of the two materials, f is the feed rate of A, k is the extinction rate of B, and r is the reaction rate of the two materials.

For reference, the Gray Scott reaction-diffusion model equation based on the existing finite difference method is shown in Equation 8 below.

<Equation 8>

Here, γ represents the substance A or B, D _γ is the diffusion coefficient for the substance, and R _γ is the reaction equation for the substance.

Referring to FIG. 4, the result of the Gray-Scott response-diffusion model based on the existing finite difference method, r=0.1, and a resolution of 64X64.

On the other hand, the Grey-Scott reaction-diffusion model equation based on the lattice-Boltzmann technique according to an embodiment of the present invention is as Equation 9 below.

<Equation 9>

In Equation 9, f ^** is a distribution function after a translation process and a collision process, and R _γ is a reaction equation for a substance γ .

Referring to FIG. 5, a result of pattern generation through a gray-Scott reaction-diffusion model based on a lattice-Boltzmann technique according to an embodiment of the present invention can be confirmed. At this time, the horizontal axis is the feed rate, the vertical axis is the extinction rate, and each range is 0.00 to 0.09, indicating that the interval is 0.01. In addition, the result can be confirmed when r=0.5 and the resolution is 64X64.

Hereinafter, with reference to FIGS. 6 and 7, a method of generating a pattern by performing local control on a response-diffusion model based on the lattice-Boltzmann technique will be described.

The existing method of generating a pattern through a reaction-diffusion model has been limited to generating a pattern by simply adjusting the value of the reaction coefficient. However, because there are generally similar types of patterns within a single reaction equation, another way to change the movement of the pattern is needed. Accordingly, the processor 120 changes the pattern of the pattern by applying a constraint to the flow or reaction of the medium (ie, fluid) through anisotropy control and application of flow resistance. At this time, the diffusion equation used a lattice-Boltzmann method that simulates a fluid from a more microscopic point of view.

First, a process of processing the anisotropy control when the processor 120 generates a reaction-diffusion pattern will be described.

As described above, in the lattice-Boltzmann method, a total of nine directions are considered in one lattice, and information of this fluid is divided into nine directions for each lattice and stored as an example.

When the processor 120 calculates the reaction equation and stores the fluid information in nine directions, the processor 120 controls the magnitude of the reaction of the fluid molecules moving in a specific direction by applying an anisotropic function. In this way, the equation to which the anisotropic function is applied to the reaction equation can be expressed as Equation 10 below.

<Equation 10>

In Equation 10, f ^** is a distribution function after a translation process and a collision process, a _i is an anisotropic function, which determines how much reactions molecules in the i direction will cause, R is the reaction equation, and γ is the substance A Or B.

In this way, when applying the calculation result through the reaction equation to the change in the amount of a substance in the reaction process, the amount of reaction can be controlled by applying an anisotropic function together.

For example, a molecule has a direction in any of 9 directions, including stationary and 4 diagonal directions, up/down/left/right, and the anisotropy function controls the amount of reaction depending on which direction. At this time, there are 9 values corresponding to each of the 9 directions in the anisotropic function, and this value can be expressed as Equation 11 below.

<Equation 11>

That is, when a _i of Equation 11 is applied, 9 values a ₀ , a ₁ , a ₂ , a ₃ , a ₄ , a ₅ , a ₆ , a ₇ , a ₈ are applied to the anisotropic function of Equation 10. I can. At this time, each value may be set as a real number between 0 and 1, and if the value is 0, a reaction does not occur in a molecule having a corresponding direction. Also, the value of the anisotropic function may be determined by the user. To this end, the processor 120 may provide a user interface through which a user can input an anisotropic function value to be applied to anisotropic control.

Referring to FIG. 6, the result of pattern generation according to whether or not anisotropy is controlled is compared, and the result can be confirmed when f=0.06, k=0.04, r=0.7, and the resolution is 256X256.

At this time, Figure 6 (a) is the pattern generation result when the anisotropy control is not applied, and (b) is the pattern generation applying anisotropy control so that the reaction occurs only for molecules having a set direction (e.g., +x direction) It is the result.

By applying anisotropy control as shown in (b) of FIG. 6, it is possible to control a new pattern aspect different from the pattern as shown in (a) generated when only the response-diffusion model of the lattice-Boltzmann technique is applied.

Next, a description will be given of a process in which the processor 120 processes the application of the flow resistance through the style map when generating the reaction-diffusion pattern.

In this case, the processor 120 applies the flow resistance by modifying the translation process, but the equation for applying the flow resistance is as Equation 12 below.

<Equation 12>

In Equation 12, d is a diffusion coefficient and β is a flow resistance coefficient. At this time, as the value of n increases, the difference in flow resistance can be more clearly confirmed.

Referring to FIG. 7, in (a) to (c), each left represents a style map having information on flow resistance. For example, in the style maps of FIGS. 7A to 7C, the closer to black, the weaker the flow resistance is, and the reverse case, the stronger the flow resistance.

At this time, in (a) of FIG. 7 shows the result of pattern generation by applying the flow resistance based on the circle-shaped style map, and the result in the case of f=0.09 and k=0.04 can be confirmed. In (b) of FIG. 7 shows the result of pattern generation in which the flow resistance based on the square style map is applied, and the result in the case of f=0.07 and k=0.07 can be confirmed. In addition, in (c) of FIG. 7 shows the result of pattern generation by applying the flow resistance based on the wood grain pattern style map, and the result in the case of f=0.06 and k=0.04 can be confirmed. In addition, r=0.7, n=3, and 256X256 were applied in all of FIGS. 7A to 7C.

The shape and variable conditions (eg, diffusion coefficient and flow resistance coefficient, etc.) of the style map are not limited, and may be applied regularly or randomly, or may be selected by a user. To this end, the processor 120 may provide a user interface through which a user can check and select a plurality of shapes and conditions stored in advance. In this case, the plurality of style maps may be stored in a separate storage space (not shown) controlled by the memory 110 or the processor 120. In addition, the processor 120 may provide a user interface through which a user can register or edit and store a new style map in the device 100.

Specifically, the style map controls the amount by which the material moves to another cell during the diffusion process. The style map is a still image having the same resolution as the area in which the material can be diffused, and may be set to have a real value between 0 and 1 per pixel. The value set for each pixel is called flow resistance. The greater the flow resistance at the location on the style map corresponding to the cell to which the material is moving, the less the amount of material to be moved.

At least one method may be used for the anisotropy control method and the flow resistance application method used in the reaction-diffusion model based on the lattice-Boltzmann method described above, and the order of application is not limited. In addition, the processor 120 may allow a user to select at least one of an anisotropic control method and a flow resistance application method, and may provide a user interface that allows the user to select an application order when both methods are selected.

In addition, the processor 120 outputs a pattern generated as a result of the simulation according to the above process. That is, the processor 120 applies the patterns generated according to at least one of the anisotropic control method and the flow resistance application method used in the response-diffusion model based on the grid-Boltzmann method as texture data used when modeling a 3D object. Alternatively, it may be provided with a 3D computer graphics device (not shown).

Hereinafter, an operation of generating a reaction-diffusion model by the processor 120 and generating a pattern through it will be described in detail with reference to FIG. 8.

First, a reaction-diffusion model that calculates a reaction process of a medium is modeled using a lattice-Boltzmann technique and a Gray-Scott model equation (S810).

At this time, as described above, the diffusion process includes a distribution function based on the direction of the molecule, the position of the lattice, and time, the expression of the translation process based on the distribution function, the amount of time change, and the direction opposite to the direction of the molecule, and the expression of the translation process. , The equilibrium distribution function, the overall velocity of the molecules in the lattice, and the equation of the collision process based on the weighting function for the direction. In addition, the reaction process is the value after applying the diffusion reaction to two or more substances contained in the medium, the supply rate of the first substance among two or more substances, the extinction rate of the second substance among two or more substances, and the first and second substances. 2 It is calculated based on the reaction equation based on the reaction rate of the substance and the distribution function after the translation and collision process.

In addition, the boundary surface processing is performed on a predetermined simulation region, but a no-slip boundary is applied so that the speed becomes 0 when the medium hits the boundary surface.

Next, when the region in which the medium exists is divided into a plurality of grids through the modeled reaction-diffusion model, simulation of the medium is performed through a change in the amount of the medium present in each grid (S820).

At this time, simulation is performed by applying at least one of anisotropic control and flow resistance application.

When anisotropic control is applied, an anisotropy function that controls the magnitude of the reaction of molecules moving in a specific direction among a plurality of preset directions is applied to the diffusion process.

Specifically, the anisotropy function includes a plurality of values corresponding to a predetermined number of directions, but the plurality of values are real numbers between 0 and 1, respectively, and when the value is 0, the molecule having the corresponding direction does not cause a reaction. do.

In addition, when the simulation is performed by applying anisotropic control, the step of providing a user interface for allowing the user to input the value of the anisotropic function is further included, wherein the value of the anisotropic function is set to a value input by the user.

On the other hand, when the flow resistance is applied, the flow resistance according to the style map that controls the amount of the medium moving to another cell is applied to the diffusion process of the medium. At this time, the larger the flow resistance at the location on the style map corresponding to the cell to which the medium is to be moved, the smaller the amount of the moved medium. In addition, the style map is a still image having the same resolution as a region in which a medium can be diffused, and a value of flow resistance is set for each pixel.

Specifically, the flow resistance may be applied based on the expression of the translation process further including the diffusion coefficient and the flow resistance coefficient.

In addition, when the simulation is performed by applying the flow resistance, the method further comprises providing a user interface that allows a user to select a shape of a style map or input at least one of a diffusion coefficient and the flow resistance coefficient, Apply the shape, diffusion coefficient, and flow resistance coefficient of the style map according to selection or input.

Next, a pattern generated as a result of the simulation is output (S830).

At this time, patterns generated according to at least one of an anisotropic control method and a flow resistance application method used in a reaction-diffusion model based on the lattice-Boltzmann method are output. In addition, the output patterns may be applied as texture data used when modeling a 3D object or may be provided to a 3D computer graphics device (not shown).

The reaction-diffusion modeling method based on the lattice-Boltzmann technique according to the embodiment of the present invention described above may be implemented in the form of a recording medium including instructions executable by a computer such as a program module executed by a computer. have. Such recording media include computer-readable media, and computer-readable media may be any available media that can be accessed by a computer, and include both volatile and nonvolatile media, and removable and non-removable media. In addition, computer-readable media includes computer storage media, which are volatile and nonvolatile embodied in any method or technology for storage of information such as computer-readable instructions, data structures, program modules or other data. , Both removable and non-removable media.

The above description of the present invention is for illustrative purposes only, and an investigator of ordinary knowledge in the technical field to which the present invention pertains will be able to understand that it can be easily transformed into other specific forms without changing the technical spirit or essential features of the present invention. will be. Therefore, it should be understood that the embodiments described above are illustrative in all respects and not limiting. For example, each component described as a single type may be implemented in a distributed manner, and similarly, components described as being distributed may also be implemented in a combined form.

Further, although the method and system of the present invention have been described in connection with specific embodiments, some or all of their components or operations may be implemented using a computer system having a general-purpose hardware architecture.

The scope of the present invention is indicated by the claims to be described later rather than the detailed description, and all changes or modified forms derived from the meaning and scope of the claims and their equivalent concepts should be interpreted as being included in the scope of the present invention. .

100: reaction-diffusion modeling device
110: memory
120: processor

Claims (13)

In the reaction-diffusion modeling method based on the lattice-Boltzmann technique of the reaction-diffusion modeling device,
Modeling a reaction-diffusion model that calculates the diffusion process of the medium using the lattice-Boltzmann technique and calculates the reaction process of the medium using the Gray-Scott model equation;
When a region in which the medium exists is divided into a plurality of grids through the reaction-diffusion model for a set medium, a simulation is performed on the medium through a change in the amount of the medium present in each grid, but anisotropic control is applied. To simulate; And
And outputting the pattern generated as a result of the simulation,
In advance, the number of directions in a plurality of directions each molecule of the medium existing in the lattice has is set,
The anisotropy control is to apply an anisotropy function for controlling the magnitude of the reaction of the molecules moving in a specific direction among a plurality of preset directions to the diffusion process,
The diffusion process includes a distribution function based on a direction of a molecule, a position of a lattice, and a time, an equation of a translation process based on the distribution function, an amount of change in time, and a direction opposite to the direction of the molecule, an equation of the translation process, and an equilibrium distribution function. , Calculated based on the equation of the collision process based on the weight function for the overall velocity and direction of the molecules in the corresponding lattice,
The reaction process includes a value after applying the diffusion reaction to two or more substances contained in the medium, a supply rate of a first substance among the two or more substances, an extinction rate of a second substance among the two or more substances, and the first And a reaction equation based on the reaction rate of the second substance, and a distribution function after the translation process and collision process,
The anisotropic function includes a plurality of values corresponding to the predetermined number of directions,
Each of the plurality of values is a real number between 0 and 1, and when the value is 0, a molecule having a corresponding direction does not cause a reaction. delete delete The method of claim 1,
The step of simulating by applying the anisotropy control,
Further comprising the step of providing a user interface for allowing a user to input the value of the anisotropic function,
The value of the anisotropic function is set to a value input by a user, a reaction-diffusion modeling method. The method of claim 1,
The step of performing the simulation through the reaction-diffusion model,
A reaction-diffusion modeling method that performs boundary surface treatment on a preset simulation area, but applies a no-slip boundary so that the velocity becomes 0 when the medium hits the boundary surface. In the reaction-diffusion modeling method based on the lattice-Boltzmann technique of the reaction-diffusion modeling device,
Modeling a reaction-diffusion model that calculates the diffusion process of the medium using the lattice-Boltzmann technique and calculates the reaction process of the medium using the Gray-Scott model equation;
When the region in which the medium exists is divided into a plurality of grids through the reaction-diffusion model for a set medium, a simulation is performed on the medium through a change in the amount of the medium present in each grid, but the flow resistance is applied. To simulate; And
And outputting the pattern generated as a result of the simulation,
In advance, the number of directions in a plurality of directions each molecule of the medium existing in the lattice has is set,
Applying the flow resistance according to the style map for controlling the amount of the medium moving to another cell to the diffusion process of the medium,
The larger the flow resistance at the location on the style map corresponding to the cell to which the medium is to be moved, the smaller the amount of the medium moved,
The style map is a still image having the same resolution as a region in which the medium can be diffused, and a value of the flow resistance is set for each pixel. The method of claim 6,
The diffusion process includes a distribution function based on a direction of a molecule, a position of a lattice, and a time, an equation of a translation process based on the distribution function, an amount of change in time, and a direction opposite to the direction of the molecule, an equation of the translation process, and an equilibrium distribution function. , Calculated based on the equation of the collision process based on the weight function for the overall velocity and direction of the molecules in the corresponding lattice,
The reaction process includes a value after applying the diffusion reaction to two or more substances contained in the medium, a supply rate of a first substance among the two or more substances, an extinction rate of a second substance among the two or more substances, and the first And a reaction equation based on the reaction rate of the second material and a distribution function after the translation and collision process. The method of claim 7,
A reaction-diffusion modeling method for applying the flow resistance based on an equation of the translation process further including a diffusion coefficient and a flow resistance coefficient. The method of claim 8,
The step of simulating by applying the flow resistance force,
Providing a user interface that allows a user to select a shape of the style map or to input at least one of the diffusion coefficient and the flow resistance coefficient, further comprising:
To apply the shape, diffusion coefficient, and flow resistance coefficient of the style map according to the user's selection or input. The method of claim 6,
The step of performing the simulation through the reaction-diffusion model,
A reaction-diffusion modeling method that performs boundary surface treatment on a predetermined simulation region, and applies a no-slip boundary to ensure that the velocity becomes zero when the medium hits the boundary surface. In the response-diffusion modeling apparatus based on the lattice-Boltzmann technique,
A memory storing a response-diffusion modeling program according to the lattice-Boltzmann technique; And
And a processor that executes a program stored in the memory,
According to the execution of the reaction-diffusion modeling program, the processor calculates the diffusion process of the medium using a lattice-Boltzmann technique, and models a reaction-diffusion model for calculating the reaction process of the medium using the Gray-Scott model equation. And, when the region in which the medium exists is divided into a plurality of grids through the reaction-diffusion model for a set medium, simulation of the medium is performed through a change in the amount of the medium present in each grid, but anisotropy control Perform at least one of the simulation to which is applied and the simulation to which the flow resistance is applied, and output the pattern generated as a result of the simulation,
In advance, the number of directions in a plurality of directions each molecule of the medium existing in the lattice has is set,
The anisotropy control is to apply an anisotropy function for controlling the magnitude of the reaction of the molecules moving in a specific direction among a plurality of preset directions to the diffusion process,
The flow resistance according to the style map that controls the amount of the medium moving to another cell is applied to the diffusion process of the medium, and the greater the flow resistance at a position on the style map corresponding to the cell to which the medium is moving, the greater the amount of the medium moved. Is reduced, and the style map is a still image having the same resolution as a region in which the medium can be diffused, and a value of the flow resistance is set for each pixel. The method of claim 11,
The diffusion process includes a distribution function based on a direction of a molecule, a position of a lattice, and a time, an equation of a translation process based on the distribution function, an amount of change in time, and a direction opposite to the direction of the molecule, an equation of the translation process, and an equilibrium distribution function. , Calculated based on the equation of the collision process based on the weight function for the overall velocity and direction of the molecules in the corresponding lattice,
The reaction process includes a value after applying the diffusion reaction to two or more substances contained in the medium, a supply rate of a first substance among the two or more substances, an extinction rate of a second substance among the two or more substances, and the first And a reaction equation based on a reaction rate of the second material and a distribution function after the translation process and the collision process. A computer-readable recording medium in which a program for implementing the method of any one of claims 1, 4 to 10 is recorded.

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