KR101022491B1 - System and method for rendering fluid flow - Google Patents

Abstract

A fluid flow rendering system includes: a velocity module for storing a velocity over time of a fluid divided into a first lattice; A particle module that calculates a time-dependent position of one or more particles located in the computational region of the fluid based on the velocity stored in the velocity module; A texture module that applies a predetermined texture to the one or more particles; And a density module for dividing the region in which the one or more particles are located into a second lattice to calculate the density of the fluid over time. By using the fluid flow rendering system and the fluid flow rendering method using the same, the shape of a fluid such as smoke can be rendered as a precise image.

Fluid, render, post-process, texture, density

Description

System and method for rendering fluid flow

Embodiments of the present invention relate to fluid flow rendering systems and methods.

In the field of computer graphics (CG), a series of processes for converting data obtained as a result of simulation into an image is called rendering. Objects such as fabrics can express the shape of the surface in the form of a mesh, and the object surface can be rendered as an image based on the mesh. However, fluids with unclear surfaces, such as smoke, require a completely different rendering method.

In the fluid flow simulation, volume data such as smoke is stored in a grid form, and density values may be stored in a real form for each cell, which is a basic unit constituting the grid. As a method of rendering such volume data defined in space, there is a volume ray marching method.

The volume ray projection method proceeds a virtual ray through a volume data defined in space from a specific viewpoint or a camera position, extracts volume data at a point where a ray passes at regular intervals, and then overlaps the extracted values. How to calculate the pixel value. It is an algorithm that mimics the way that real smoke is seen by the human eye or captured by the camera.

Since the density is stored as one real value for each cell of the grid in the volume data, one cell is shown in a single color in the rendered image. Therefore, in order to express the appearance of smoke in detail, a grid composed of a large number of cells should be used. The number of cells included in the grid is expressed in terms of resolution, and the higher the resolution, the more accurate an image can be generated.

However, in the simulation stage, it is difficult to use a high resolution grating due to problems such as computation time and memory. In general, a 3D grating uses a grating having a resolution of 256 x 256 x 256 or less. However, even when the grating having this resolution is simulated, it is difficult to realize a realistic rendering quality.

To solve this problem, a post-processing method may be used in which a rendering grid having a higher resolution than that used in the simulation step is separately created and the volume data simulated using the low resolution grid is rendered using a high resolution rendering grid. have. However, simply re-sampling the simulation results of a low resolution grid to use a high resolution rendering grid increases the size of the data and is difficult to produce good quality.

Meanwhile, there is a method of using texture as a method for obtaining a high resolution image from low resolution volume data. This is a method of applying a predetermined density distribution to the volume data, and the density distribution applied at this time is referred to as a texture.

There are two-dimensional, three-dimensional and four-dimensional textures in textures, and two-dimensional textures are the most intuitive but difficult to apply to objects such as smoke that are difficult to extract. In addition, the 3D texture has an unnatural problem because the texture is fixed without change over time. In order to overcome the problem of the three-dimensional texture, it is possible to use a four-dimensional texture that moves over time, but there is still an unnatural problem because the texture movement does not coincide with the fluid flow.

Embodiments of the present invention, fluid flow rendering that can be post-processed and rendered by applying a particle-based texture and a high resolution grid to the volume data simulated using a low resolution grid Systems and methods can be provided.

According to one embodiment, a fluid flow rendering system includes: a velocity module configured to store a velocity over time of a fluid divided into a first lattice; A particle module that calculates a time-dependent position of one or more particles located in the computational region of the fluid based on the velocity stored in the velocity module; A texture module that applies a predetermined texture to the one or more particles; And a density module for dividing the region in which the one or more particles are located into a second lattice to calculate the density of the fluid over time.

According to one or more exemplary embodiments, a fluid flow rendering method includes calculating a time-based position of one or more particles located in a calculation region of a fluid based on a time-based velocity of a fluid divided into a first lattice; Applying a preset texture to the one or more particles; And dividing the region in which the one or more particles are located in a second lattice form to calculate the density of the fluid over time.

Using the fluid flow rendering system and method according to the embodiments of the present invention, by applying a particle-based texture to the volume data, the shape of the fluid, such as smoke whose surface is unclear, to a precise image Rendering is possible. In addition, the low resolution grid is used in the simulation stage and the high resolution grid is used during the rendering process, so that high rendering quality can be obtained without significantly increasing calculation time or calculation amount. Furthermore, natural images can be generated by rotating the texture according to its position in the fluid.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. However, the present invention is not limited by the following examples. In describing the embodiments of the present invention, a detailed description of what can be easily understood by those skilled in the art from the known art in order to clarify the gist of the present invention will be omitted.

1 is a block diagram illustrating a configuration of a fluid flow rendering system according to an exemplary embodiment.

Referring to FIG. 1, the fluid flow rendering system may include a velocity module 10, a particle module 20, a texture module 30, and a density module 50. The velocity module 10 may store the velocity of the fluid over time calculated by the fluid flow simulation. Since the process of calculating the velocity of the fluid by the fluid flow simulation for each time can be performed by a known fluid flow simulation method, only a brief description thereof will be provided herein.

In the fluid flow simulation, the calculation region of the fluid may be divided into a lattice of a plurality of cells, and speed and density may be defined for each cell of the lattice. 2 is a schematic diagram showing a calculation region of a fluid divided into a lattice form by a fluid flow simulation. In FIG. 2, an arrow shown in each node of the grid represents a velocity vector defined in the node, and the velocity may be defined in the form of a velocity field for the entire grid. Meanwhile, in another embodiment, the velocity field may be defined with respect to the center point of each cell.

In fluid flow simulations, the calculation time can be divided into one or more time steps and the velocity of the fluid can be updated based on the flow equation for the velocity of the fluid in each time step. 2 (a) to 2 (c) show the results of updating the velocity field of the fluid in adjacent time steps. The velocity field and flow equation in the previous time step can be used to calculate the velocity field in the next time step, and this process can be repeated for all time steps to calculate the flow of fluid over time. The process of calculating the fluid flow based on the flow equation is well known to those skilled in the art.

The velocity module 10 may store the velocity field of the fluid calculated as a result of the fluid flow simulation as described above for each time step. The calculation region of the fluid in the velocity field of the fluid stored in the velocity module 10 may be divided in the form of the first grating 100. In the fluid flow simulation, it is difficult to use a high resolution grating due to limitations of calculation time, memory, etc., so that the first grating 100 may be a relatively low resolution grating compared to the second grating used in a rendering process described later. .

In the drawings attached to the present specification, the grating is shown in the form of a two-dimensional grating, but this may be a first grating used in the simulation process and a three-dimensional grating used in the rendering process.

The particle module 20 may set one or more particles in the calculation region of the fluid and calculate the position of the one or more particles over time using the velocity field of each time step stored in the velocity module 10.

3 shows one or more particles 200 set in the computational region of the fluid by the particle module 20. One or more particles 200 may be located regularly or irregularly, the number of particles 200 may be appropriately determined based on the size and calculation time of the calculation region of the fluid. Each particle 200 may be in the shape of a circle or sphere having a predetermined radius. Depending on the radius of the particle 200, the particle 200 may occupy an area smaller than one cell or occupy an area corresponding to a plurality of cells in the first grating 100.

However, the shape, number and size of the particles 200 is not limited to that shown in FIG. 3, and in other embodiments the particles may have other different shapes, numbers and sizes.

The particle module 20 may calculate the position of the particle 200 in each time step by using the velocity field stored in the speed module 10. 3 (a) to 3 (c) show the results of updating the position of particles in adjacent time steps.

4 is a schematic diagram illustrating a process in which the particle module 20 calculates the velocity of the particle 200 in one time step. Referring to FIG. 4, the velocity of the particle 200 at a particular time step may be calculated using the velocity vector of a location adjacent to the particle 200. For example, the velocity of the particle 200 is determined from the center point O of the particle 200 in the velocity vectors v ₁ , v ₂ , v ₃ and v _{4 of} adjacent nodes 101, 102, 103, 104. It may also be calculated by summing by applying a weight proportional to the distance to the nodes (101, 102, 103, 104). The particle module 20 may calculate the position of the particle 200 over time by applying a flow equation to the calculated velocity of the particle 200.

The process of calculating the position of the particles 200 over time in the particle module 20 may use the velocity field of each time step that is calculated in advance by the fluid flow simulation and stored in the velocity module 10. Thus, in comparison with the prior art, which calculates the density field of a fluid over time in a fluid flow simulation, the calculation time and the amount of calculation are relatively small, but as a result one or more particles 200 are calculated by the fluid flow simulation. It is located in a form similar to the density field.

The texture module 30 may apply a preset texture to each of the one or more particles 200 whose positions are calculated by the particle module 20. In the present specification, the texture refers to a density distribution that is preset as a result of a user's input or a numerical operation. The texture may be a two-dimensional texture, a three-dimensional texture, or a four-dimensional texture.

5A to 5C are exemplary schematic diagrams illustrating the results of applying a texture to one or more particles by the texture module 30 in time steps. In FIG. 5, a region having a relatively high density in each particle 200 is shown in a relatively dark color. In this way, by applying a predetermined texture to each particle 200, it is possible to generate volume data having a more precise density distribution than the resolution of the first grating 100 used in the simulation step.

The density distribution of the texture shown in FIG. 5 is exemplary, and the density distribution of the texture may be different from that shown in FIG. 5 and may be appropriately determined based on the nature and shape of the fluid to be expressed.

In one embodiment, when there are a plurality of particles, different textures may be applied to each particle 200. For example, the texture module 30 may generate a plurality of textures using a Perlin noise algorithm used to generate an irregular pattern. In this case, by using different seeding values for the respective textures, the textures may have different density distributions.

In one embodiment, the fluid flow rendering system may further include a rotation module 40 that rotates the texture applied to the particle 200 by the texture module 30 according to the position of the particle 200. Since the fluid such as smoke has a swirl-like movement, by rotating the texture applied to the particle 200 according to the position of the particle 200 can be expressed more precisely the fluid flow.

For example, when La u center point velocity field of the particles 200, referred to showing the angular velocity of the particles 200 in a quaternion (quaternion) Ω, Ω is local to the velocity field as shown in Equation 1 (curl Can be calculated by taking

In addition, when q represents the orientation of the center point of the particle 200 as quaternion, the direction q (t + Δt) at time t + Δt is the direction q (t) and rotation quaternion at time t. It can be expressed by the following equation (2) using Δ r (t).

In Equation 2, when the rotation angle of the particle (200) 2 △ α, referred to the unit rotation axis, v (t), the rotation quaternion △ r (t) is to be represented by the equation (3).

If smaller the value of △ α in the above equation (3) sufficiently, the rotation quaternion △ r (t) is to be represented by the equation (4).

Using the above Equations 2 and 4, the change amount according to time in the direction q of the particle 200, that is, the derivative value based on the time of q may be expressed by Equation 5 below.

In Equation 5, ω (t) is a vector representing the angular velocity of the particle 200 at time t, and the result of Equation 5 is represented by Equation 6 below using quaternion.

In Equation 6, q _vel is a quaternion representing the amount of change in the direction q over time. By multiplying the q _vel thus calculated by the time interval dt between each time step, the direction change q + of the particle 200 in one time step can be obtained by Equation 7 below.

The rotation module 40 may calculate the change in direction of the particle 200 in time steps by the process described above with reference to Equations 1 to 7 and the direction of the particle 200. You can update it over time. In addition, the rotation module 40 can rotate the texture applied to the particle 200 in accordance with the the q normalized (normalize) such that the length direction of the q of the particles 200, first, the normalized direction q. Since the texture applied to the particles 200 is rotated according to the direction of the particles 200, a natural density distribution may be calculated even when the fluid flows.

The density module 50 may calculate the density of the fluid in the form of a density field by dividing an area in which one or more particles 200 to which the texture is applied by the texture module 30 is located in a second lattice form.

6A to 6C are exemplary schematic diagrams illustrating a process of calculating a density field by dividing an area in which particles are located by the density module 50 into a lattice form in time steps. Referring to FIG. 6, a calculation region of a fluid in which one or more particles 200 to which a texture is applied is located may be divided into a shape of a second grating 500. In this case, each cell of the second grating 500 may be assigned an average value of the density distribution of the corresponding cell as the density value. Since the calculation is performed only on the region where the particle 200 is located in the second grating 500, the calculation time and the amount of calculation are reduced.

The second grating 500 used by the density module 50 may include a greater number of cells than the first grating 100 used in the fluid flow simulation process. As a result, the fluid flow simulation is performed using the relatively low resolution first grid 100 and the rendering is performed using the relatively high resolution second grid 500, thereby increasing the computational burden of the fluid flow simulation process. The advantage is that you get a high rendering quality without having to.

In one embodiment, the fluid flow rendering system may further include a conversion module 60 that converts the density of the fluid calculated by the density module 50 into an image. The processes performed by the particle module 20, the texture module 30, the rotation module 40 and the density module 50 correspond to the step of post-processing the velocity field resulting from the fluid flow simulation into the density field. The module 60 may serve to convert the post-processed density field into an actual image.

Operation of the transform module 60 may be performed using known techniques for converting the density field into an image. For example, the conversion module 60 may convert the density field into an image by a volume ray marching method, but this is exemplary, and the operation of the conversion module 60 may change the volume ray projection method. It is not limited to the one used.

Using the fluid flow rendering system and method according to the embodiments of the present invention described above, by applying a particle-based texture and a high-resolution rendering grid to the volume data, to accurately image the shape of the fluid, such as smoke whose surface is unclear Can be rendered as: In addition, since a low resolution grid is used in the simulation step and a high resolution grid is used in the rendering process, high rendering quality can be obtained without significantly increasing calculation time or calculation amount. Furthermore, natural images can be generated by rotating the texture according to its position in the fluid.

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.

1 is a block diagram illustrating a fluid flow rendering system according to one embodiment.

2 is a schematic diagram exemplarily showing a velocity field of a fluid calculated by a fluid flow simulation.

Figure 3 is a schematic diagram showing the results of calculating the position of the particles in each time step by the particle module by way of example.

4 is a schematic diagram illustrating a process of calculating the velocity of particles from the velocity field by the particle module.

FIG. 5 is a schematic diagram exemplarily illustrating a result of applying a texture to particles at each time step by a texture module. FIG.

6 is a schematic diagram illustrating a process of converting a region where particles are located in each density step into a density field by the density module.

Claims (10)

A velocity module for storing the velocity of the fluid divided into a first lattice form in a plurality of time steps; A particle module that calculates the position of one or more particles located in the calculation region of the fluid in the plurality of time steps based on the speed stored in the velocity module; A texture module for applying a preset texture to the one or more particles; And And a density module for dividing an area in which the one or more particles are located into a second lattice shape to calculate a density of the fluid in the plurality of time steps. The method of claim 1, Wherein said first grating and said second grating each comprise one or more cells, said second grating comprising a greater number of cells than said first grating. The method of claim 1, And a conversion module for converting the density of the fluid calculated by the density module into an image. The method of claim 1, The particle is a plurality of, And the texture module applies a different texture to each of the plurality of particles. The method of claim 1, And a rotation module for calculating a direction of the one or more particles using the speed stored in the speed module, and rotating the texture applied to the one or more particles according to the calculated direction. Calculating positions of one or more particles located in the calculation region of the fluid in the plurality of time steps based on a plurality of time step speeds of the fluid divided into a first lattice shape; Applying a preset texture to the one or more particles; And And dividing the region in which the one or more particles are located in a second lattice form to calculate the density of the fluid in the plurality of time steps. The method of claim 6, Wherein the first grating and the second grating each consist of one or more cells, the second grating comprising a greater number of cells than the first grating. The method of claim 6, And converting the calculated density of the fluid into an image. The method of claim 6, The particle is a plurality of, The applying of the preset textures includes applying different textures to each of the plurality of particles. The method of claim 6, Before calculating the density of the fluid in the plurality of time step, Calculating an angular velocity from the velocities of the one or more particles; Calculating a direction from the angular velocity of the at least one particle; And And rotating the texture applied to the one or more particles according to the calculated direction.

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