KR101566484B1 - Apparatus and method for simulating fluid using weight between node and particle - Google Patents

Abstract

A fluid simulation apparatus includes a memory for storing instructions for simulating motion of a fluid, and a processor for simulating fluid motion in accordance with the instructions to generate a rendering image, wherein the instructions comprise inputting velocity, position and external force of each particle Calculating a weight corresponding to each particle, updating the velocity corresponding to the particle according to the weight and the external force, and projecting the particle according to the updated velocity and the density corresponding to the particle And a step of generating a rendering image.

Description

Field of the Invention [0001] The present invention relates to a fluid simulation apparatus and method using a weight between a node and a particle,

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to computer graphics technology, and more particularly, to an apparatus and method for simulating fluid.

Recently, computer graphics (CG) technology has been widely used in various fields including movies, animation, and advertisement, and its proportion is also increasing. Especially, the expression of fluids such as water and fire, which are representative special effects using CG technology, is an important part in the production of video objects.

The CG technique related to fluid representation consists of a process of scene representation, simulation, reconstruction, and rendering.

The modeling process is a process of reconstructing an external object that interacts with a fluid other than the fluid to be simulated, in a form suitable for simulation. For the method of performing the simulation at the uniform lattice position, the interacting object should also be expressed in the lattice form, and the initial conditions and the boundary conditions to be set before the simulation are made in the modeling process.

The simulation process is the process of calculating the fluid motion using an equation describing fluid motion, such as the Navier-Stokes equation, or using simple random elements.

The shaping process refers to the process of calculating the geometry from the simulation results for a fluid that has and maintains an external shape such as water. Computing the geometry from arbitrary points or updating the initially calculated geometry is available.

The rendering process is the process of creating the final image from the relationship between fluid and light, which is composed of points, faces, or arbitrary functions.

Generally, the most time is required in the simulation process, because a large amount of calculation must be performed in the simulation process.

The process of simulating fluids is the process of solving the Poisson equation.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a fluid simulation apparatus capable of expressing a detailed motion of a fluid.

According to an aspect of the present invention, there is provided a computer program product, comprising: a memory for storing instructions for simulating motion of a fluid; And a processor for simulating fluid movement according to the instruction to generate a rendered image, the instruction comprising: receiving a velocity, position and an external force applied to the particle; Calculating a weight corresponding to the particle; Updating a velocity corresponding to the particle according to the weight and the external force; And projecting the particles according to the updated velocity and the density corresponding to the particles to generate a rendered image.

The density corresponding to the particle may be a value obtained by multiplying the mass of each particle included in the cell in which the particle is located by the weight, and dividing the sum by the volume of the cell in which the particle is located.

The step of calculating a weight corresponding to each particle may be a step of calculating the weight by applying a difference between a coordinate of a node preset for the cell in which the particle is located and a coordinate of the particle to a preset weight function.

The weight function may be a B-spline function.

The step of updating the velocity corresponding to the particle according to the weight and the external force may include calculating a product of the external force and the weight for one or more nodes and calculating a product of the external force and the weight Calculating a velocity of the current time interval by multiplying a value obtained by multiplying the set unit time by a velocity corresponding to the particle in the previous time interval and updating the velocity corresponding to the particle at the velocity of the current time interval.

Wherein the command calculates a product of a velocity of the node and the weight, multiplies the sum of the products of the velocities of the respective nodes by the unit time and the position corresponding to the particles in the previous time interval, And calculating a position of a current time interval with respect to the particle.

According to another aspect of the present invention, there is provided a method of simulating fluid movement of a fluid simulation device, comprising: receiving a velocity, a position of each particle, and an external force applied to the particle; Calculating a weight corresponding to the particle; Updating a velocity corresponding to the particle according to the weight and the external force; And projecting the particles according to the updated speed and the density corresponding to the particles to produce a rendered image. A fluid simulation method is provided.

The density corresponding to the particle may be a value obtained by multiplying the mass of each particle included in the cell in which the particle is located by the weight, and dividing the sum by the volume of the cell in which the particle is located.

The step of calculating a weight corresponding to each particle may be a step of calculating the weight by applying a difference between a coordinate of a node preset for the cell in which the particle is located and a coordinate of the particle to a preset weight function.

The weight function may be a B-spline function.

The step of updating the velocity corresponding to the particle according to the weight and the external force may include calculating a product of the external force and the weight for one or more nodes and calculating a product of the external force and the weight Calculating a velocity of the current time interval by multiplying a value obtained by multiplying the set unit time by a velocity corresponding to the particle in the previous time interval and updating the velocity corresponding to the particle at the velocity of the current time interval.

Wherein the fluid simulation method calculates the product of the velocity of the node and the weight, multiplies the sum of the products of the velocities of the respective nodes by the unit time and the position corresponding to the particles in the previous time interval , And calculating a position of a current time interval with respect to the particle.

According to an embodiment of the present invention, the detailed movement of the fluid under the influence of the strong surface tension can be realistically expressed.

BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 illustrates a fluid simulation apparatus in accordance with an embodiment of the present invention.
2 is a diagram illustrating a process of performing a fluid simulation by a fluid simulation apparatus according to an embodiment of the present invention;
3 is a view illustrating a rendering image generated by a fluid simulation apparatus according to an embodiment of the present invention and a rendering image generated through a conventional fluid simulation method.

While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the invention. It should be understood, however, that the invention is not intended to be limited to the particular embodiments, but includes all modifications, equivalents, and alternatives falling within the spirit and scope of the invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, the present invention will be described in detail with reference to the accompanying drawings. Furthermore, the singular terms used in this specification and the claims should generally be construed to mean one or more unless otherwise stated.

Fluid animation used in movies or TV commercials can be calculated realistically through the process of solving the Navier-Stokes equations from an Eulerian grid.

1 is a diagram illustrating a fluid simulation apparatus according to an embodiment of the present invention.

Referring to FIG. 1, a fluid simulation apparatus includes an input unit 110, a memory 120, a processor 130, and an output unit 140.

The input unit 110 receives particle velocity and position information from an external device (e.g., a terminal, a mobile storage device, etc.) through a predetermined protocol.

The memory 120 loads instructions that update the particle velocity and position information via Navier-Stokes equations.

The processor 130 updates the particle velocity and position information in accordance with the instructions loaded in the memory 120. The processor 130 projects each particle according to the updated particle velocity to generate a rendered image.

The output unit 140 transmits the rendered image to the output device. In this case, the output device may be a device for displaying a rendered image such as a monitor.

Hereinafter, a process of generating a rendering image through a fluid simulation according to an instruction of a fluid simulation apparatus according to an embodiment of the present invention will be described in detail.

FIG. 2 is a view illustrating a process of performing a fluid simulation according to an embodiment of the present invention. FIG. 3 is a flowchart illustrating a process of performing a fluid simulation using a rendering image generated by a fluid simulation apparatus according to an exemplary embodiment of the present invention, FIG. 2 is a diagram illustrating a rendering image generated through a simulation method. FIG.

Each of the processes described below describes a process performed by the processor 130 of the fluid simulation apparatus according to an embodiment of the present invention in accordance with an instruction loaded on the memory 120. However, for the sake of clarity and concise description of the invention, The process of confirming the command loaded in the memory 120 is omitted and a subject of each process is referred to as a fluid simulation device.

In step 210, the fluid simulation device receives mass, velocity, and position information for each particle from an external device via input 110. At this time, the node is a virtual particle located at the center of each cell formed by a grid.

In step 220, the fluid simulation device updates the velocity for each particle and node of the fluid. For example, the fluid simulation apparatus can calculate the velocity for the current time for each particle according to Equation (1) below.

[Equation 1]

는 현재 시간 구간(l+1번째 시간 구간)에 대한 노드 i에 대한 속도이고,

는 이전 시간 구간(l번째 시간 구간)에 대한 입자 p에 대한 속도이고,

는 현재 시간 구간(l+1번째 시간 구간)에 대한 입자 p에 대한 속도이고,

는 이전 시간 구간(l번째 시간 구간)에 대한 입자 p에 대한 속도이고,

는 단일 시간 구간의 시간 변화량이고,

는 노드 i와 입자 p 간의 가중치이고,

는 중력, 부력, 충격력 등의 노드 i에 가해지는 외력을 나타내는 벡터이다. 또한, 노드 i는 i번째 격자(Grid)의 중심 점에 위치하는 가상의 입자이고, 입자 p는 p번째 입자를 의미한다.

는 하기의 수학식 2에 따라 정의될 수 있다.At this time,

Is the velocity for node i for the current time interval (l + 1 < th > time interval)

Is the velocity for particle p over the previous time interval (lth time interval)

Is the velocity for particle p with respect to the current time interval (l + 1 < th > time interval)

Is the velocity for particle p over the previous time interval (lth time interval)

Is a time variation of a single time interval,

Is the weight between node i and particle p,

Is a vector representing an external force applied to a node i such as gravity, buoyancy, impact force, and the like. Also, the node i is a virtual particle located at the center point of the i-th grid (Grid), and the particle p means the p-th particle.

Can be defined according to the following equation (2).

 &Quot; (2) "

는 하기의 수학식 3과 같이 정의된다.

Is defined by the following equation (3).

&Quot; (3) "

는 deformation의 비율을 나타내는 tensor이고, tr(D)는 D의 trace이다.

및

는 미리 설정된 상수이다.Where p is the pressure applied to the particle, I is the second-order identity tensor,

Is the tensor representing the ratio of deformation, and tr (D) is the trace of D.

And

Is a predetermined constant.

In this case, the fluid simulation apparatus according to an embodiment of the present invention may calculate the external force for each node according to the above-described method, or separately receive the external force from the external apparatus.

는

및

가 성립하는 가중치로써, 미리 설정된 가중치 함수(B-splines function)를 통해 산출될 수 있다. 또한, 특정 입자 p에 대한 모든 노드에 대한 가중치를 합하면 1이 될 수 있다. 즉, 유체 시뮬레이션 장치는 각 입자의 위치에 따른

를 각각 산출할 수 있다.Also,

The

And

And can be calculated through a preset B-splines function. It can also be 1 if weights for all nodes for a particular particle p are summed. In other words, the fluid simulation device

Respectively.

는 하기의 수학식 4와 에 따라 산출될 수 있다. For example, if the coordinates of node _{i (x 1, y 1,} z 1) , and the coordinates of the particle _{p (x 2, y 2,} z 2),

Can be calculated according to the following equation (4).

&Quot; (4) "

At this time, w (a) is a preset weight function having the real number a as an input.

가 미리 산출되어 있지 않은 경우, 유체 시뮬레이션 장치는 하기의 수학식 5에 따라

를 이용하여

를 산출할 수 있다.In addition, the rate of the node i in the previous time interval

Is not calculated in advance, the fluid simulation apparatus calculates the following equation

Using

Can be calculated.

&Quot; (5) "

는 노드 i 에 대한 속도로써 수학식 1의

에 해당하는 값이고,

는 입자 p에 대한 속도로써 수학식 1의

에 해당하는 값이다. 또한, m_i는 노드 i의 질량이고, m_p는 전체 입자 중 p번째 입자에 대한 질량이다. m_i가 산출되는 과정은 추후 수학식 9에서 정의된다.
At this time,

Is the velocity of the node i,

, ≪ / RTI >

Is the velocity of the particle p,

. ≪ / RTI > Also, m _i is the mass of node i, and m _p is the mass for the pth particle of the total particles. The process of calculating m _i is defined in Equation (9).

를 산출할 때 사용될 수 있다.In step 230, the fluid simulation device updates location information for each particle of fluid. For example, the fluid simulation apparatus may calculate position information on the current time for each particle according to Equation (6) below. At this time, the position information of each particle is used as a weight

. ≪ / RTI >

&Quot; (6) "

는 현재 시간 구간(l+1번째 시간 구간)에 대한 입자 p에 대한 위치 정보이고,

는 이전 시간 구간(l번째 시간 구간)에 대한 입자 p에 대한 위치 정보이다.

Is the positional information on the particle p with respect to the current time interval (l + 1 < th > time interval)

Is the positional information on the particle p with respect to the previous time interval (lth time interval).

In step 240, the fluid simulation apparatus projects each particle to generate a rendering image. For example, the fluid simulation apparatus can project each particle according to the following equation.

The density and velocity of each particle can be expressed by the following equation (7).

&Quot; (7) "

는 특정 입자의 밀도이고,

는 특정 입자의 속도이다.
At this time,

Is the density of a particular particle,

Is the velocity of a particular particle.

Equation (7) can be transformed into Equation (8).

&Quot; (8) "

는 특정 입자에 대한 n+1 번째 시간 구간의 속도이고,

는 특정 입자에 대한 이전 시간 구간(n번째 시간 구간)의 속도이고,

는 n+1 번째 시간 구간 동안 특정 입자에 가해지는 압력의 그래디언트(gradient)이다.
At this time,

Is the velocity of the n + 1 < th > time interval for a particular particle,

Is the velocity of the previous time interval (nth time interval) for the particular particle,

Is the gradient of the pressure applied to a particular particle during the (n + 1) th time interval.

Also, equation (8) can be transformed into equation (9).

&Quot; (9) "

및

를 대해 동일한 상수

로 설정하는 경우, 하기의 수학식 10과 같이 푸아송(Poisson) 방정식을 나타낼 수 있다.
At this time,

And

The same constant for

The Poisson equation can be expressed by Equation (10). &Quot; (10) "

&Quot; (10) "

In this case, k is a constant preset as a control parameter. Also, P ⁿ is a value obtained by dividing the mass (m _i ) of each node by the volume of the cell in which the corresponding node is located.

At this time, the mass of each node can be calculated by the following equation (9).

&Quot; (11) "

Where m _i is the mass of node i, and m _p is the mass for the pth particle of the total particles.

Thus, the fluid simulation apparatus can project each particle through the Poisson equation, as shown in equation (8). The process of projecting each particle according to the Poisson equation is a known matter, and a detailed description thereof will be omitted. In this case, the Poisson equation according to Equation (8) is an equation to which the velocity and position of each particle are applied by applying the weight. That is, the Poisson equation according to Equation (8) uses the density along the mass of each node calculated according to the updated speed and weight according to the weight.

Referring to FIG. 3, a fluid simulation apparatus according to an exemplary embodiment of the present invention generates a rendering image 320. In this case, the rendered image 320 is more distorted than the image 310 generated according to the conventional fluid simulation method, so that the fluid that rotates in a spread form appears to be more disturbed, resulting in a higher reality.

In operation 250, the fluid simulation apparatus outputs the rendering image generated in operation 240.

In this case, it is apparent to those skilled in the art that the above-described steps 220 to 250 are repeated for each time interval, and the rendered image output in step 250 is updated every time interval and output as an animation.

The above-described embodiments include examples of various aspects. While it is not possible to describe every possible combination for expressing various aspects, one of ordinary skill in the art will recognize that other combinations are possible. Accordingly, it is intended that the invention include all alternatives, modifications and variations that fall within the scope of the following claims.

Claims (12)

A memory for storing instructions for simulating fluid motion; And
A processor for simulating fluid motion according to the instruction to generate a rendered image;
, ≪ / RTI &
The command
Receiving a velocity, a position of each particle, and an external force applied to the particle;
Calculating a weight corresponding to the particle;
Updating a velocity corresponding to the particle according to the weight and the external force; And
Projecting the particles according to the updated speed and the density corresponding to the particles to generate a rendered image;
Comprising the steps of:
And updating the velocity corresponding to the particle according to the weight and the external force,
Calculating a product of the external force and the weight for one or more nodes, summing a product of the product of the external force and the weight for each node multiplied by a predetermined unit time and a velocity corresponding to the particle in a previous time interval Calculating the velocity of the current time interval and updating the velocity corresponding to the particle at the velocity of the current time interval.
The method according to claim 1,
Wherein the density corresponding to the particle is a value obtained by multiplying a mass of each particle included in the cell in which the particle is located by the weight, and dividing the sum by the volume of the cell in which the particle is located.
The method according to claim 1,
The step of calculating a weight corresponding to each particle
And calculating the weight by applying a difference between a coordinate of a node preset for the cell in which the particle is located and a coordinate of the particle to a predetermined weight function.
The method of claim 3,
Wherein the weight function is a B-spline function.
delete The method according to claim 1,
Wherein the command comprises:
Calculating a product of the velocity of the node and the weight, multiplying the sum of the product of the velocity of each node and the weight by the unit time, and summing the position corresponding to the particle in the previous time interval, Calculating a position of a current time interval
Further comprising instructions for performing the fluid simulation.
A method of simulating fluid motion in a fluid simulation device,
Receiving a velocity, a position of each particle, and an external force applied to the particle;
Calculating a weight corresponding to the particle;
Updating a velocity corresponding to the particle according to the weight and the external force; And
Projecting the particles according to the updated speed and the density corresponding to the particles to generate a rendered image;
, ≪ / RTI &
And updating the velocity corresponding to the particle according to the weight and the external force,
Calculating a product of the external force and the weight for one or more nodes, summing a product of the product of the external force and the weight for each node multiplied by a predetermined unit time and a velocity corresponding to the particle in a previous time interval Calculating the velocity of the current time interval, and updating the velocity corresponding to the particle at the velocity of the current time interval.
8. The method of claim 7,
Wherein the density corresponding to the particle is a value obtained by multiplying a mass of each particle contained in the cell in which the particle is located by the weight, and dividing the sum by the volume of the cell in which the particle is located.
8. The method of claim 7,
The step of calculating a weight corresponding to each particle
And calculating the weight by applying a difference between a coordinate of a node preset for the cell in which the particle is located and a coordinate of the particle to a predetermined weight function.
10. The method of claim 9,
Wherein the weight function is a B-spline function.
delete 8. The method of claim 7,
Calculating a product of the velocity of the node and the weight, multiplying the sum of the product of the velocity of each node and the weight by the unit time, and summing the position corresponding to the particle in the previous time interval, Calculating a position of a current time interval
Further comprising the steps of:

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