A Gaussian-based SPH fluid rendering method and system

Abstract

This invention discloses a Gaussian function-based SPH fluid rendering method and system, belonging to the field of computer graphics technology. The method includes: receiving fluid particle data simulated by SPH; constructing a particle connection graph based on particle neighborhood relationships; extracting local geometric features of each particle using a neural network based on the particle connection graph and aggregating them into global geometric features; parsing the global geometric features into Gaussian function parameters to generate multiple Gaussian functions for each particle; superimposing all Gaussian functions in space to form an implicit fluid surface; performing screen-space rendering on the implicit fluid surface to obtain the final fluid rendering image; and mapping foam particles generated by SPH simulation to Gaussian functions, followed by screen-space rendering to obtain a fluid rendering image containing foam visual effects. This invention can improve the smoothness and realism of the rendering results while ensuring computational efficiency, achieving a balance between fluid rendering efficiency and quality.

Description

Technical Field

[0001] This invention belongs to the field of computer graphics technology, specifically relating to a Gaussian function-based SPH fluid rendering method and system. Background Technology

[0002] Achieving highly realistic fluid effects has always been a long-standing challenge in the field of real-time graphics rendering. This stems not only from the fluid's unpredictable and rapidly changing form, but also from its complex optical interactions, such as refraction, reflection, and caustics. To obtain convincing visual effects, accurate modeling of the fluid surface is typically required, combined with realistic simulations of light transmission. However, simultaneously achieving both computational efficiency and visual realism under interactive constraints remains difficult, making real-time fluid rendering a key focus for both academia and industry.

[0003] Existing particle-based fluid simulation methods (such as Smoothed Particle Hydrodynamics, SPH) can capture fluid motion behavior well, possessing physical plausibility and scalability. However, their output is an unstructured collection of particles rather than a defined continuous surface representation. This characteristic makes it difficult to directly support high-precision optical effect simulation. In traditional offline rendering schemes, researchers typically transform particle data into explicit mesh surfaces using surface reconstruction methods (such as Marching Cubes and its improved algorithms), and then combine this with physically based rendering methods such as path tracing to achieve high-fidelity image generation. Although these methods can produce visually high-quality results, their computational cost is too high, often requiring offline rendering processes, thus making them unsuitable for real-time interactive scenarios. To improve efficiency, academia and industry have proposed various screen-space-based fluid rendering methods, such as particle projection, depth filtering, and ray stepping. These methods approximate the fluid surface directly in image space and simulate optical effects to some extent, thus balancing efficiency and dynamic performance. However, because they rely on screen space approximation, these methods still have significant shortcomings in terms of surface reconstruction accuracy, multi-view consistency, and simulation of complex lighting effects (such as caustics and global illumination), thus limiting their overall realism and making it difficult to meet the needs of next-generation high-fidelity real-time rendering.

[0004] In recent years, the development of point-based implicit representations has provided new possibilities for solving the aforementioned problems. Among them, 3D Gaussian Splatting (3DGS), as a neural rendering framework based on discrete Gaussian primitives, has achieved significant breakthroughs in visual quality and rendering efficiency. Although initially applied to novel view synthesis tasks, subsequent research has shown that this method also performs excellently in geometric detail modeling and point cloud rendering. With its explicit point-based organization, 3DGS has gradually expanded to application scenarios such as point cloud rendering, point cloud interactive computing, and mixed reality, demonstrating strong adaptability and application potential. However, existing point primitive-based methods still have significant limitations in practical applications: on the one hand, most frameworks rely on training and optimization for specific scenes, lacking cross-scene generality and making it difficult to directly transfer to complex dynamic scenes; on the other hand, in fluid rendering tasks, although particles are naturally suitable for mapping to Gaussian primitives, existing methods mostly focus on static geometric modeling, and still lack efficient real-time modeling and reconstruction capabilities for highly dynamic and unstructured fluid surfaces. Some studies have attempted to represent fluid particles as Gaussian elements and combine them with position-based dynamics (PBD) methods to handle fluid-structure interaction. While this has improved expressiveness to some extent, it still has significant shortcomings in terms of efficiency, scalability, and cross-scenario adaptability.

[0005] Therefore, there is an urgent need for a new real-time rendering framework that can combine the advantages of particle simulation and Gaussian representation. This framework should not only be able to realistically reproduce complex optical effects such as refraction and reflection with interactive performance, but also have good versatility and scalability to break through the limitations of existing methods in terms of realism and applicability. Summary of the Invention

[0006] In view of the above, the purpose of this invention is to provide a Gaussian function-based SPH fluid rendering method and system. By mapping fluid particles to Gaussian functions, continuous modeling of the fluid surface is achieved. By combining graph structure organization and neural network feature decoding, the smoothness and realism of the rendering results are improved while ensuring computational efficiency, thus achieving a balance between fluid rendering efficiency and quality.

[0007] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0008] In a first aspect, the present invention provides a Gaussian-based SPH fluid rendering method, comprising the following steps:

[0009] Receive fluid particle data from SPH simulation and construct a particle connectivity graph based on particle neighborhood relationships;

[0010] Based on the particle connection graph, the local geometric features of each particle are extracted by a neural network and aggregated into global geometric features;

[0011] Global geometric features are parsed into Gaussian function parameters to generate multiple Gaussian functions for each particle, and all Gaussian functions are superimposed in space to form an implicit fluid surface;

[0012] The implicit fluid surface is screen-space rasterized to obtain a geometry buffer, and the final fluid rendering image is synthesized based on the geometry buffer.

[0013] Preferably, the method further includes:

[0014] After mapping the foam particles generated by SPH simulation to a Gaussian function, a fluid rendering image containing foam visual effects is obtained through screen space rendering.

[0015] Preferably, the construction of the particle connection graph based on particle neighborhood relationships includes:

[0016] Construct a particle connection graph using particles as nodes and the spatial neighborhood relationships between particles as edges;

[0017] For isolated particles, self-loop edges are introduced into the particle connectivity graph to ensure that their own characteristics are preserved in subsequent calculations.

[0018] Preferably, the local geometric features of each particle are extracted using a neural network, including:

[0019] The relative position vectors of a particle and other particles in its neighborhood are calculated. The relative position vectors are encoded by a multilayer perceptron to obtain high-dimensional features. Max pooling is then applied to the high-dimensional features to extract significant local geometric structure information, thus obtaining the local geometric features of each particle.

[0020] Preferably, the aggregation of local geometric features into global geometric features via a neural network includes:

[0021] A graph convolutional network is used to propagate features on the particle connection graph. The graph convolutional network performs feature weighting aggregation of neighborhood nodes based on the normalized adjacency matrix, so that the particles gradually integrate geometric information from a larger neighborhood and obtain the global geometric features of each particle.

[0022] Preferably, the Gaussian function parameters include:

[0023] The parameters describe the offset of the Gaussian function's center position relative to the particle's center position, the rotation parameter describes the Gaussian function's three-dimensional orientation, the scaling parameter describes the Gaussian function's three-dimensional orientation, and the custom parameter is used to express the fluid surface details.

[0024] Preferably, the step of performing screen-space rendering on the implicit fluid surface to obtain the final fluid rendering image includes:

[0025] After rasterizing the Gaussian function of the implicit fluid surface, a geometric buffer corresponding to the current viewpoint is generated. The reflection and refraction optical effects of the fluid are calculated based on the geometric buffer in screen space to synthesize the final fluid rendering image.

[0026] Secondly, embodiments of the present invention also provide a Gaussian function-based SPH fluid rendering system, which is implemented using the above-mentioned Gaussian function-based SPH fluid rendering method, including: a fluid particle data processing and graph construction module, a local geometric feature encoding and global feature aggregation module, a Gaussian function decoding and surface generation module, and a screen space rendering module;

[0027] The fluid particle data processing and graph construction module is used to receive fluid particle data from SPH simulation and construct a particle connection graph based on particle neighborhood relationships.

[0028] The local geometric feature encoding and global feature aggregation module is used to extract the local geometric features of each particle's neighborhood and aggregate them into global geometric features based on the particle connection graph and through a neural network.

[0029] The Gaussian function decoding and surface generation module is used to parse global geometric features into Gaussian function parameters to generate multiple Gaussian functions for each particle, and to superimpose all Gaussian functions in space to form an implicit fluid surface.

[0030] The screen space rendering module is used to perform screen space rasterization on the implicit fluid surface to obtain a geometry buffer, and then synthesize the final fluid rendering image based on the geometry buffer.

[0031] Preferably, the system further includes a foam enhancement module, used to map the foam particles generated by SPH simulation to a Gaussian function and then render the fluid rendering image containing the foam visual effect through screen space.

[0032] Thirdly, embodiments of the present invention also provide an electronic device, including a memory and one or more processors, wherein the memory is used to store a computer program, and the processor is used to implement the above-described Gaussian function-based SPH fluid rendering method when the computer program is executed.

[0033] Compared with the prior art, the beneficial effects of the present invention include at least the following:

[0034] The SPH fluid rendering framework provided by this invention introduces a Gaussian function as the basic unit of expression for the fluid surface, avoiding the voxelization of particle density fields and isosurface extraction processes in traditional mesh reconstruction methods, thus significantly reducing the computational overhead of geometric reconstruction. Compared to the traditional offline Marching Cube meshing method, its efficiency is improved by tens of times, meeting real-time requirements. Compared to traditional real-time screen space filtering schemes, the Gaussian function naturally possesses continuous and smooth characteristics, effectively eliminating the graininess caused by direct particle projection in the rendering results, making the fluid surface visually smoother and more natural. This invention combines graph structure with neural network decoding mechanisms, enabling each particle to generate a set of Gaussian function parameters adapted to its neighborhood geometry, thereby obtaining a smooth surface in dense regions and maintaining surface continuity and integrity in sparse regions or splash scenes. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a flowchart illustrating the SPH fluid rendering method based on Gaussian functions provided in an embodiment of the present invention.

[0037] Figure 2 This is a schematic diagram of the framework of the SPH fluid rendering method based on Gaussian function provided in the embodiments of the present invention;

[0038] Figure 3 This is a schematic diagram of the structure of the SPH fluid rendering system based on Gaussian functions provided in an embodiment of the present invention. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the scope of protection of this invention.

[0040] The inventive concept of this invention is as follows: Existing SPH-based fluid rendering methods generally rely on mesh reconstruction or screen-space filtering, which often suffers from problems such as time-consuming surface reconstruction, insufficient real-time performance, and rendering results prone to graininess and instability. This invention provides an SPH fluid rendering method and system based on Gaussian functions. Its core lies in transforming fluid particle data into a graph structure and utilizing a neural network to automatically learn the mapping relationship from particle distribution to a continuous fluid surface. Specifically, a graph neural network aggregates particle neighborhood information to obtain global geometric features, which are then decoded into a set of parameterized three-dimensional Gaussian functions. These Gaussian functions are superimposed in space to form a continuous, smooth implicit fluid surface. This method abandons the traditional explicit meshing or volume integration process, instead directly rasterizing this implicit surface to screen space, efficiently generating a geometric buffer and calculating optical effects, thereby achieving high-quality, real-time fluid rendering while ensuring consistency across multiple viewpoints. Furthermore, by embedding foam particles into the same rendering pipeline in the form of shared Gaussian functions, the visual realism of complex scenes such as splashes and turbulence is further enhanced.

[0041] like Figure 1 and Figure 2 As shown in the example, this embodiment provides a Gaussian function-based SPH fluid rendering method, including the following steps:

[0042] S1 receives fluid particle data from SPH simulation and constructs a particle connectivity graph based on particle neighborhood relationships.

[0043] In this embodiment, the open-source SPH simulation framework SPlisHSPlasH is used to output fluid particle data (including physical properties such as particle position, velocity, radius, and density) and the particle's neighborhood connection relationship (adjacency list) as input to the rendering system.

[0044] To better describe the spatial relationships between particles, a particle connectivity graph is constructed using the adjacency list generated by the SPH simulation framework, based on the neighborhood search results obtained during the SPH simulation. In this graph, particles are treated as nodes, and neighborhood relationships are used as edges. Self-loops are automatically introduced for isolated particles to ensure they retain their characteristics in subsequent calculations. This process transforms the unstructured particle set into a graph structure with topological relationships, guaranteeing data sparsity and providing a computational foundation for subsequent neural network feature propagation.

[0045] S2, based on the particle connection graph, extracts the local geometric features of each particle through a neural network and aggregates them into global geometric features.

[0046] In the embodiments, in order to accurately capture the local geometric features of particles Instead of directly using the absolute coordinates of the particles, it employs relative position encoding. Specifically, for each particle... Calculate its relationship with neighboring particles The relative position vectors between them, and through the first multilayer perceptron A nonlinear mapping is performed to encode the relative position vectors into high-dimensional features. To avoid redundancy in neighborhood information, max pooling is used on the high-dimensional features. This allows for the extraction of the most significant geometric changes while avoiding information redundancy. This relative encoding method ensures the robustness of features to translation and temporal variations. The process can be described by the following formula:

[0047] ,

[0048] in, and They represent particles respectively Its neighboring particles Spatial position vector, Represents particles defined by a particle connection graph. The set of neighboring particles.

[0049] Furthermore, a Graph Convolutional Network (GCN) is employed for global feature aggregation, and multi-hop feature propagation is achieved based on the particle connection graph. GCN identifies features based on a multi-layer network structure and performs weighted aggregation using a normalized adjacency matrix, allowing particles to gradually fuse geometric information from a wider neighborhood, thereby obtaining more global geometric features. This process effectively eliminates local ambiguity and improves the integrity and consistency of surface reconstruction. The process can be described as follows:

[0050] ,

[0051] in, This indicates a single-layer GCN network.

[0052] S3 resolves global geometric features into Gaussian function parameters to generate multiple Gaussian functions for each particle, and then superimposes all Gaussian functions in space to form an implicit fluid surface.

[0053] In the embodiment, the rich global geometric features on each particle are... Through the second multilayer perceptron This is resolved into a set of Gaussian function parameters representing a high-quality fluid surface. A single Gaussian parameter includes: a parameter describing the offset of the Gaussian function's center position relative to the particle's center position. Rotational parameters describing the three-dimensional orientation of Gaussian functions , Describe the scaling parameters of the Gaussian function in three dimensions and custom parameters used to express detailed information about the fluid surface. Among them, custom parameters This includes: fourth-order spherical harmonic coefficients for representing the xyz positive semi-axis normal space; three-dimensional coordinates for representing the three-dimensional positional properties of the fluid surface; and probability weighting labels for representing the presence or absence of the fluid surface. Each particle can correspond to multiple Gaussian functions, thus maintaining sufficient expressive power in sparse, splashing, and other regions. This process can be described as follows:

[0054] ,

[0055] Among them, subscript and superscript It still represents the index of a particle and its neighboring particles. Represents particles The total number of neighborhood particles. When all Gaussian functions are superimposed in space, a continuous and smooth implicit fluid surface can be formed.

[0056] The above processes, including local geometric feature extraction, global geometric feature aggregation, global geometric feature parsing, and implicit fluid surface generation, are constructed into a complete neural network structure. The PyTorch framework is used to implement operator construction and complete training.

[0057] S4 performs screen-space rendering on the implicit fluid surface to obtain the final fluid rendering image.

[0058] In this embodiment, an efficient screen-space rendering pipeline is employed based on the implicit fluid surface obtained above. Specifically, the core process includes: firstly, rasterizing the Gaussian function corresponding to the implicit fluid surface using a custom CUDA operator to obtain the fluid surface geometry buffer (G-Buffer) information from the target viewpoint—the normal buffer, depth buffer, and weight buffer indicating the presence of fluid (a mask formed by binary values ​​of 0-1). Subsequently, using a rendering pipeline built with PythonGL, screen-space refraction and reflection calculations are implemented in the Compute Shader to generate basic fluid optical effects, thus synthesizing a preliminary fluid rendering image. Specifically, the normal buffer and depth buffer of the valid fluid surface are marked using the weight buffer in screen space, and combined with the depth buffer of the non-fluid portion (from the basic rendering pipeline), reflection and refraction effects are calculated as the basic appearance of the fluid. This process avoids display mesh reconstruction and volume integration, significantly reducing computational overhead, ensuring real-time rendering performance, and the Gaussian representation provides multi-view consistency, overcoming the viewpoint inconsistency problem of traditional screen-space fluid rendering.

[0059] S5 maps the foam particles generated by SPH simulation to a Gaussian function, and then renders them in screen space to obtain a fluid rendering image containing the visual effect of foam.

[0060] In this embodiment, to further enhance visual realism, it also supports processing foam particles introduced in areas of severe turbulence. Using CUDA parallel operators, the foam particles are also mapped to Gaussian functions, their appearance characteristics determined by reflection, refraction, and weak self-emission. Without concern for the specific geometry of the foam particles, the ambient lighting features are directly decoded (the environment map uses a CNN convolutional network to obtain lighting features). A multilayer perceptron (MLP) maps the foam particles to the same set of Gaussian functions (custom attributes include transmittance and foam appearance). Based on the spatial position of the foam particles derived from the fluid simulation framework, this shared set of Gaussian functions is translated. By rasterizing the Gaussian functions, the transmittance buffer and foam appearance buffer of the foam in the target viewpoint in screen space are obtained. Then, the foam results are blended with the fluid surface results through the Compute Shader post-processing channel, outputting a final fluid rendering image containing foam details. This process, through foam enhancement operations, uses transmittance-weighted summation to create rich secondary visual effects by combining the fluid's appearance and the foam's appearance, making it particularly suitable for depicting complex scenes such as wave breaking and water splashing.

[0061] In summary, through the above implementation methods, the present invention realizes a complete SPH fluid rendering method based on Gaussian function. On common GPU platforms (such as workstations equipped with NVIDIA RTX series graphics cards), this embodiment can achieve a real-time rendering performance of 30-60 frames per second at 1080p resolution.

[0062] Based on the same inventive concept, such as Figure 3 As shown, this embodiment of the invention also provides a Gaussian function-based SPH fluid rendering system 300, including: a fluid particle data processing and graph construction module 310, a local geometric feature encoding and global feature aggregation module 320, a Gaussian function decoding and surface generation module 330, a screen space rendering module 340, and a foam enhancement module 350.

[0063] The fluid particle data processing and graph construction module 310 is used to receive fluid particle data from SPH simulation and construct a particle connection graph based on particle neighborhood relationships.

[0064] The local geometric feature encoding and global feature aggregation module 320 is used to extract the local geometric features of each particle's neighborhood and aggregate them into global geometric features based on the particle connection graph through a neural network.

[0065] The Gaussian function decoding and surface generation module 330 is used to resolve global geometric features into Gaussian function parameters to generate multiple Gaussian functions for each particle, and to superimpose all Gaussian functions in space to form an implicit fluid surface.

[0066] The screen space rendering module 340 is used to perform screen space rasterization on the implicit fluid surface to obtain a geometry buffer, and then synthesize the final fluid rendering image based on the geometry buffer.

[0067] The foam enhancement module 350 is used to map the foam particles generated by SPH simulation to a Gaussian function and then render them in screen space to obtain a fluid rendering image containing foam visual effects.

[0068] Based on the same inventive concept, embodiments of the present invention also provide an electronic device, including a memory and one or more processors, wherein the memory is used to store a computer program, and the processor is used to implement the above-described Gaussian function-based SPH fluid rendering method when executing the computer program.

[0069] It should be noted that the Gaussian function-based SPH fluid rendering system and electronic device provided in the above embodiments belong to the same inventive concept as the Gaussian function-based SPH fluid rendering method. For details of their implementation process, please refer to the embodiments of the Gaussian function-based SPH fluid rendering method, which will not be repeated here.

[0070] The specific embodiments described above illustrate the technical solution and beneficial effects of the present invention in detail. It should be understood that the above description is only the most preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for SPH fluid rendering based on Gaussian function, characterized in that, Includes the following steps: Receive fluid particle data from SPH simulation and construct a particle connection graph based on particle neighborhood relationships. This includes: using particles as nodes and the spatial neighborhood relationships between particles as edges to construct the particle connection graph. For isolated particles, introduce self-loop edges into the particle connection graph to ensure that their own characteristics are preserved in subsequent calculations. Based on the particle connection graph, the local geometric features of each particle are extracted by a neural network, and a graph convolutional network is used to propagate the features on the particle connection graph. The graph convolutional network performs weighted aggregation of the local geometric features of the neighborhood nodes based on the normalized adjacency matrix, so that the particles gradually integrate geometric information from a larger neighborhood and obtain the global geometric features of each particle. Global geometric features are parsed into Gaussian function parameters to generate multiple Gaussian functions for each particle, and all Gaussian functions are superimposed in space to form an implicit fluid surface; The final fluid rendering image is obtained by screen-space rendering of the implicit fluid surface.

2. The SPH fluid rendering method based on Gaussian functions according to claim 1, characterized in that, The method further includes: After mapping the foam particles generated by SPH simulation to a Gaussian function, a fluid rendering image containing foam visual effects is obtained through screen space rendering.

3. The SPH fluid rendering method based on Gaussian functions according to claim 1 or 2, characterized in that, Local geometric features of each particle are extracted using a neural network, including: The relative position vectors of a particle and other particles in its neighborhood are calculated. The relative position vectors are encoded by a multilayer perceptron to obtain high-dimensional features. Max pooling is then applied to the high-dimensional features to extract significant local geometric structure information, thus obtaining the local geometric features of each particle.

4. The SPH fluid rendering method based on Gaussian function according to claim 1 or 2, characterized in that, The parameters of the Gaussian function include: The parameters describe the offset of the Gaussian function's center position relative to the particle's center position, the rotation parameter describes the Gaussian function's three-dimensional orientation, the scaling parameter describes the Gaussian function's three-dimensional orientation, and the custom parameter is used to express the fluid surface details.

5. The SPH fluid rendering method based on Gaussian functions according to claim 1 or 2, characterized in that, The process of performing screen-space rendering on the implicit fluid surface to obtain the final fluid rendering image includes: After rasterizing the Gaussian function of the implicit fluid surface, a geometric buffer corresponding to the current viewpoint is generated. The reflection and refraction optical effects of the fluid are calculated based on the geometric buffer in screen space to synthesize the final fluid rendering image.

6. A Gaussian function-based SPH fluid rendering system, implemented using the Gaussian function-based SPH fluid rendering method according to any one of claims 1 to 5, characterized in that, include: The modules include: fluid particle data processing and graph construction, local geometric feature encoding and global feature aggregation, Gaussian function decoding and surface generation, and screen space rendering. The fluid particle data processing and graph construction module is used to receive fluid particle data from SPH simulation and construct a particle connection graph based on particle neighborhood relationships. The local geometric feature encoding and global feature aggregation module is used to extract the local geometric features of each particle's neighborhood and aggregate them into global geometric features based on the particle connection graph and through a neural network. The Gaussian function decoding and surface generation module is used to parse global geometric features into Gaussian function parameters to generate multiple Gaussian functions for each particle, and to superimpose all Gaussian functions in space to form an implicit fluid surface. The screen space rendering module is used to perform screen space rasterization on the implicit fluid surface to obtain a geometry buffer, and then synthesize the final fluid rendering image based on the geometry buffer.

7. The SPH fluid rendering system based on Gaussian functions according to claim 6, characterized in that, The system also includes a foam enhancement module, which maps the foam particles generated by SPH simulation to a Gaussian function and then renders them in screen space to obtain a fluid rendering image containing foam visual effects.

8. An electronic device comprising a memory and one or more processors, the memory for storing a computer program, characterized in that, The processor is used to implement the Gaussian function-based SPH fluid rendering method as described in any one of claims 1 to 5 when executing a computer program.

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