Fluid dynamic interactive simulation method based on 3D Gaussian sputtering and MPM

Abstract

The invention relates to a fluid dynamic interaction simulation method based on 3D Gaussian sputtering and MPM, and belongs to the field of three-dimensional reconstruction, and the simulation method comprises the steps: taking a fluid and a multi-view image of a simulation scene as initial input data, carrying out 3D Gaussian sputtering processing on the input multi-view image, and constructing object surface features; carrying out regional Gaussian kernel generation of the fluid, and carrying out scaling regularization processing on a 3D Gaussian kernel; performing fluid dynamic interaction simulation on the multiple physical fields by using a material point method; the fluid model is split, combined and optimized, simulation precision and details are enhanced, a fluid dynamic simulation result is finally presented, and a dynamic effect of interaction between the fluid and other models and scenes is displayed. According to the method, 3D Gaussian sputtering and a material point method are deeply fused, regional Gaussian kernel generation of the model is achieved, and high-precision fluid dynamic simulation interaction is achieved by combining external force analysis, splitting and merging of Gaussian kernels in the interaction process and a scene fusion technology.

Description

Technical Field

[0001] The present invention relates to the field of three-dimensional reconstruction, and in particular to a fluid dynamic interaction simulation method based on 3D Gaussian sputtering and MPM. Background Art

[0002] With the continuous development of virtual reality, digital twins and metaverse technologies, fluid dynamics simulation technology has become the key to enhancing the realism and interactivity of scenes. Fluid dynamics simulation can not only enhance the realism of virtual environments, but also improve the effectiveness of industrial simulations. In existing technologies, fluid dynamics simulation mainly relies on meshing technology, but traditional meshing methods have problems such as high computational complexity and low efficiency when dealing with complex geometric shapes and irregular boundary conditions. In addition, when traditional methods simulate drastic changes in fluids (such as splashing and collisions), the limitations of the mesh topology lead to insufficient simulation accuracy, and the cost of manually building scenes and rendering three-dimensional models is high, requiring a lot of manpower and computing resources, which makes it difficult to meet the needs of actual applications.

[0003] In the area of ​​water generation, traditional methods include those by Williams et al., who studied hydrodynamic properties through numerical simulation and characteristic function development; Jerry Tessendor, who used Fourier transforms to solve the surface wave equations of ocean water; Henry David, who used the Gerstner wave model to simulate periodic water waves; Gopala et al., who tracked the fluid volume fraction to simulate interfaces and fluid interactions; and Chorin, who introduced the use of the Navier-Stokes equations and discretization methods to solve fluid dynamics problems under complex boundary conditions. However, these methods primarily focus on visual presentation and ignore the realism required for real-world fluid simulations. In digital twins and industrial applications requiring realistic fluid interaction simulations, simply simulating the visual effects of the fluid surface is insufficient to reflect objective laws.

[0004] In terms of scene rendering with 3D Gaussian sputtering, although 3D Gaussian sputtering has become a major advancement in the field of computer graphics and can efficiently realize real-time rendering of new views; existing research mainly focuses on the dynamic simulation of rigid objects, such as introducing a 4D Gaussian scatter representation method to realize real-time rendering of dynamic scenes, and combining the MPM material algorithm to generate physically based dynamics and realistic rendering, but none of them involve fluid dynamic simulation rendering, and the technical development of fluid dynamic simulation rendering is still immature; at the same time, it is difficult to migrate them to fluid dynamic simulation. Fluid dynamic rendering based on 3D Gaussian sputtering is affected by independent Gaussian kernels, and there is a serious sense of roughness and graininess in the rendering process, especially the interaction between fluids, and there are serious visual artifacts. The reason is that they ignore the fusion and splitting process of the fluid, especially the surface interaction of the fluid, by calculating the spatial physical properties such as the position and rotation of independent Gaussians in the fluid model, resulting in significant differences between the simulation results and the actual situation. Summary of the Invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a fluid dynamic interaction simulation method based on 3D Gaussian sputtering and MPM, which solves the shortcomings of the prior art.

[0006] The object of the present invention is achieved by the following technical solution: a fluid dynamic interaction simulation method based on 3D Gaussian sputtering and MPM, the simulation method comprising:

[0007] Step 1: Using multi-view images of the fluid and the simulation scene as the starting input data, perform 3D Gaussian sputtering on the input multi-view images to construct the surface features of the object;

[0008] Step 2: Generate a regional Gaussian kernel for the fluid and perform scaling regularization on the 3D Gaussian kernel;

[0009] Step 3: Use the material point method to simulate the fluid dynamic interaction of multiple physical fields and assign basic physical properties to each Gaussian model;

[0010] Step 4: Split and merge the fluid model through external force analysis to optimize the fluid simulation, solve the granularity problem, enhance the simulation accuracy and details, and finally present the results of the fluid dynamic simulation and demonstrate the dynamic effects of the fluid's interaction with other models and scenes.

[0011] The step 1 specifically includes the following contents:

[0012] Capturing fluid multi-view images in a virtual environment, as well as capturing real physical environments through cameras;

[0013] Using multiple multi-view images and SFM camera parameters as input, 3D Gaussian sputtering is used to generate discrete Gaussian kernels. These discrete Gaussian kernels use the G(M) function to determine their distribution and shape properties in space to form the surface features of the object. , where M represents the mean of the 3D Gaussian kernel position, M T represents the transpose of M, represents the covariance matrix;

[0014] During rendering, the 3D Gaussian kernel is projected onto the 2D plane, and the final two-dimensional image is obtained by mixing and calculating the pixel value and transparency. , It represents the multiplication of the opacity of the k-th Gaussian kernel and the 2D Gaussian distribution density of the pixel position projection. K represents the set of Gaussian kernels of different models, and p represents the number of factors involved in the multiplication calculation. Indicates the contribution of the kth Gaussian kernel to the pixel color under the lth influencing factor.

[0015] The second step specifically includes the following contents:

[0016] Generate regional Gaussian kernels based on the surface features of the object. By selecting points in the region to establish a data set, filter out holes and 3D Gaussian kernels with abnormal shapes to prevent the generated Gaussian kernels from becoming noise and reducing rendering realism. At the same time, control the number of generated 3D Gaussian kernels and ensure that the 3D Gaussian kernels are evenly distributed.

[0017] Scaling, deformation, regularization, and smoothing operations are performed on the 3D Gaussian kernel to avoid sharp shapes that may cause interactions between particles and the 3D Gaussian kernel, and to avoid deviations in the calculation of local physical quantities when simulating fluid motion, which may lead to abnormal fluid forces and reduce the realism of the fluid simulation.

[0018] The scaling deformation regularization constrains the size and shape of the 3D Gaussian kernel to prevent the 3D Gaussian kernel from being sharp, through the formula Implementation, where represents the amount of loss associated with scaling, Representative The maximum zoom value of an object, Representative The minimum scale value of an object, Represents the threshold parameter, which is used to participate in condition judgment.

[0019] The step three specifically includes the following contents:

[0020] In the material point method particle interaction simulation, the fluid is considered to be a mass carrier. and speed The distribution of these discrete Gaussian kernels in space constitutes a discretized expression of the fluid. The mass of each discrete Gaussian kernel is determined by the shape function Mapping to the background grid nodes, the mass information of the discrete Gaussian kernel is distributed to the background grid in a weighted form, so that the background grid can inherit the mass properties of the 3D Gaussian kernel. By mapping the background grid, the mass distribution at different positions can be perceived. is the position of material point i, j is the background grid node number;

[0021] The momentum of the material is mapped to the grid nodes based on the shape function. This mapping gives the grid nodes the motion information of the Gaussian kernel. The grid node momentum is updated by calculation based on the conservation law on the background grid, and the updated physical quantity is returned to the Gaussian kernel. Through this mapping, the 3D Gaussian kernel updates its own state based on the calculation results on the grid, realizing the cyclic transfer and update of physical quantities between the Gaussian kernel and the background grid, and continuously simulating the mechanical response of the material at different times.

[0022] The splitting and merging optimization of the fluid model includes:

[0023] When the distance between adjacent 3D Gaussian kernels is less than the merging threshold and they belong to the same material and have similar physical states, the 3D Gaussian kernel merging strategy is implemented. The mass of the new Gaussian kernel is the sum of the masses of the Gaussian kernels before merging, and its velocity and surface tension are calculated according to the mass-weighted average rule.

[0024] For 3D Gaussian kernels with large deformation or abnormal force, a Gaussian kernel splitting strategy is adopted. The mass of each sub-Gaussian kernel is distributed according to a certain proportion to the original Gaussian kernel mass, and its velocity and stress are distributed according to the splitting direction and deformation.

[0025] When implementing the 3D Gaussian kernel merging strategy, by To indicate whether the 3D Gaussian kernel p and q are merged, is the distance between Gaussian kernels p and q, is the merging threshold;

[0026] when = 1, the mass of the new Gaussian kernel , the speed of the new Gaussian kernel , the surface tension of the new Gaussian kernel ,in 、 are the masses of Gaussian kernels p and q respectively, is the mass of the new Gaussian kernel after merging, 、 are the velocities of Gaussian kernels p and q, respectively, is the velocity of the new Gaussian kernel after merging, 、 are the surface tensions of Gaussian kernels p and q, is the surface tension of the new Gaussian kernel after merging.

[0027] When using the Gaussian kernel splitting strategy, Indicates whether the Gaussian kernel x is split, is the degree of deformation of the Gaussian kernel k, is the deformation threshold, is the external force on the Gaussian kernel k, is the stress threshold;

[0028] when 1 o'clock, 、 、 , where n is the number of sub-Gaussian kernels after splitting, is the mass of the original Gaussian kernel x, is the mass of the lth sub-Gaussian kernel, l=1,2,⋯,n, is the velocity of the original Gaussian kernel x, is the velocity of the lth sub-Gaussian kernel, is the stress of the original Gaussian kernel x, is the stress of the lth sub-Gaussian kernel, is the change in the velocity of the lth sub-Gaussian kernel relative to the original Gaussian kernel, is the stress change of the lth sub-Gaussian kernel relative to the original Gaussian kernel.

[0029] The present invention has the following advantages: a fluid dynamic interaction simulation method based on 3D Gaussian sputtering and MPM, which deeply integrates 3D Gaussian sputtering with the material point method (MPM), realizes the regional Gaussian kernel generation of the model, combines external force analysis and performs Gaussian kernel splitting and merging in the interaction process, and scene fusion technology to realize high-precision fluid dynamic simulation interaction; 3D Gaussian sputtering is combined with MPM. 3D Gaussian sputtering is used to generate discrete Gaussian kernels to construct the surface features of objects, and the material point method is used to realize dynamic interaction simulation of multi-physics fluids. This can effectively solve the shortcomings of traditional gridding methods in complex scenarios and open up a new path for high-precision fluid simulation. A dynamic and adaptive particle generation process is proposed to generate Gaussian kernels regionally according to the surface features of the object. The model realism is improved by screening point sets, filtering abnormal kernels, and reasonably controlling quantity and distribution. With the help of Gaussian scaling regularization, the size and shape of the kernel are constrained to solve problems such as visual artifacts and enhance the rationality and generalization ability of the model. The fluid is regarded as a set of discrete Gaussian kernels, and the data mapping of Gaussian kernels and background grids is used to transform physical quantities into continuous distributions. Gaussian kernels in special areas are accurately identified, and the merging and splitting strategies are used to optimize the layout, reduce noise, and enhance accuracy. In particular, Gaussian kernels on the fluid surface and interaction boundaries are used to solve the problem of granularity and truly display the mechanical response of the material. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a schematic diagram of the process of the present invention;

[0031] Figure 2 Generate schematic diagrams for fluid regionality;

[0032] Figure 3 This is a schematic diagram of the material point method;

[0033] Figure 4 Schematic diagram of 3D Gaussian kernel splitting and merging optimization;

[0034] Figure 5 Schematic diagram of fluid simulation interaction. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of the present application provided below in conjunction with the drawings is not intended to limit the scope of protection of the present application for which protection is claimed, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present application. The present invention is further described below in conjunction with the drawings.

[0036] The present invention specifically relates to a fluid dynamic interaction simulation method based on 3D Gaussian core sputtering and MPM, which aims to solve the problems of low simulation accuracy, complex and difficult scene construction, high computational complexity, and visual graininess on the fluid surface and neglect of objective physical laws in traditional fluid dynamic simulation methods, as well as the existing fluid simulation methods based on 3D Gaussian sputtering. At the same time, it solves the problem of 3D Gaussian model ignoring the internal structure of the model and the adverse effects of sharp Gaussian kernel on fluid simulation, and realizes smooth simulation of fluid dynamics in multiple physical fields. It improves the authenticity and visual consistency of the simulation, enhances the portability of the model, and provides more effective solutions for virtual reality, industrial simulation, digital twins and other fields involving complex fluid interaction simulation.

[0037] like Figure 1 As shown, specifically including the following:

[0038] Step 1: Using multi-view images of the fluid and the simulation scene as the starting input data, perform 3D Gaussian sputtering on the input multi-view images to construct the surface features of the object;

[0039] Furthermore, first, we capture multi-view images of the fluid in a virtual environment, and use a camera to capture the real physical environment, and then use 3D Gaussian sputtering to generate discrete Gaussian kernels to construct the surface features of the object. The specific operations are as follows:

[0040] Using multiple angle images and SFM (a 3D reconstruction method) camera parameters as input, discrete Gaussian kernels are generated through 3D Gaussian sputtering. These discrete Gaussian kernels use the G(M) function to determine their distribution, shape and other properties in space, forming the surface features of the object;

[0041] ,

[0042] Where M represents the mean of the 3D Gaussian kernel position, M T represents the transpose of M, Represents the covariance matrix. Position is used to determine the core area of ​​the Gaussian kernel in space, which is crucial for accurate modeling of spatial distribution, scene reconstruction, and object positioning, and helps to accurately describe the features near the center point.

[0043] During rendering, the 3D Gaussian kernel is projected onto a 2D plane, and the final two-dimensional image is obtained by mixing and calculating the pixel value and transparency. The specific formula is as follows:

[0044] ,

[0045] It represents the multiplication of the opacity of the k-th Gaussian kernel and the 2D Gaussian distribution density of the pixel position projection. The result is used to measure the degree to which the pixel point is affected by the Gaussian kernel on the projection plane. K represents the set of Gaussian kernels of different models. p represents the number of factors involved in the multiplication calculation. It reflects the contribution of the kth Gaussian kernel to the pixel color under the lth influencing factor (such as lighting from different directions, different material properties, etc.).

[0046] Step 2: Generate a regional Gaussian kernel for the fluid and perform scaling regularization on the 3D Gaussian kernel to improve the physical rationality and generalization ability of the model.

[0047] Furthermore, if Figure 2 The figure below illustrates the process of generating a 3D Gaussian kernel for a fluid and potential problems. The circle represents the generated area, the solid line represents a normal 3D Gaussian kernel, and the dashed line represents an abnormally shaped 3D Gaussian kernel. The circle on the right illustrates the potential for noise to be introduced if the generated particles are not properly screened and processed. Failure to properly handle abnormally shaped Gaussian kernels during the generation process can result in noise, affecting the realism of the fluid dynamics simulation.

[0048] Because relying solely on a 3D Gaussian kernel on the object's surface cannot meet the realistic requirements of fluid dynamics simulations, it is necessary to generate a regional Gaussian kernel based on the object's surface characteristics within an area centered on the target region and with a radius of r (which can be determined based on the actual model size and simulation accuracy requirements). By selecting points within this area to establish a data set, 3D Gaussian kernels with holes and unusual shapes are filtered out to prevent the generated Gaussian kernels from becoming noise and reducing rendering realism. At the same time, the number of generated 3D Gaussian kernels should be properly controlled to ensure uniform distribution. Relying solely on points within a relatively close range is not the only option; a wider range should be selected. Furthermore, the number of generated 3D Gaussian kernels should not necessarily be higher; it should be kept within a certain range, otherwise rendering realism will be affected.

[0049] Because the shapes of the Gaussian kernels vary significantly, scaling, deformation, regularization, and smoothing are performed to better integrate them with the particles. This prevents sharp shapes from causing deviations in the calculation of local physical quantities when particles interact with the 3D Gaussian kernels and simulate fluid motion. This can lead to abnormal fluid forces and prevent precise physical motion. During rendering, sharp shapes can also cause unnatural abrupt changes in the rendering results, reducing the realism of the fluid simulation.

[0050] Gaussian scaling regularization prevents the 3D Gaussian kernel from being too sharp by constraining its size and shape.

[0051] ,

[0052] in represents the amount of loss associated with scaling, Representative The maximum zoom value of an object, Representative The minimum scale value of an object, is a threshold parameter used for conditional judgment. Regularization makes the 3D Gaussian shape smoother and more natural, improves the physical rationality of the model, and enhances the generalization ability of fluid simulation.

[0053] Step 3: Use the Material Point Method (MPM) to simulate the fluid dynamic interaction of multiple physical fields and assign basic physical properties to each Gaussian model;

[0054] Furthermore, if Figure 3 This figure illustrates the data mapping principle between the fluid Gaussian kernel and the background mesh in the Material Point Method (MPM). The solid circle in the center represents the target fluid Gaussian kernel, which is closely connected to the background mesh. The surrounding hollow circles are within its domain, interacting with it through the mesh. The dashed circles are outside the neighborhood and do not participate in the direct calculation of the central Gaussian kernel density. Using the background mesh as a medium, the formula utilizes information from the neighboring Gaussian kernels to accurately calculate the density of the central Gaussian kernel. This mapping allows for smoothing of the fluid simulation, ensuring that the simulation results faithfully reflect the continuity and stability of the fluid.

[0055] In MPM particle interaction simulation, the fluid is considered to be composed of ,speed The distribution of these discrete Gaussian kernels in space constitutes a discrete expression of the fluid and is the basic unit for simulating the complex mechanical behavior of the fluid. The mass of each discrete Gaussian kernel is determined by the shape function ( is the location of material point i, and j is the background grid node number) is mapped to a background grid node. This process distributes the mass information of the discrete Gaussian kernel to the background grid in a weighted manner, allowing the background grid to inherit the mass properties of the 3D Gaussian kernel, providing a quality foundation for subsequent mesh-based mechanical calculations. Through this mapping, the grid can perceive the mass distribution at different locations.

[0056] The momentum of matter is mapped to grid nodes based on shape functions. This mapping gives the grid nodes the motion information of the 3D Gaussian kernel. In complex mechanical response scenarios such as simulating the interaction between fluids and solids, the grid can use this momentum information, combined with conservation laws, to calculate physical quantities such as the node's velocity change, providing data support for the entire simulated dynamic process.

[0057] ,

[0058] in is the external force at node j, The internal force is calculated based on the conservation laws on the background mesh to update the mesh node momentum. The updated physical quantity needs to be transmitted back to the Gaussian core. Through this mapping, the 3D Gaussian core updates its own state based on the calculation results on the mesh, achieving a cyclic transfer and update of physical quantities between the Gaussian core and the background mesh, continuously simulating the mechanical response of the material at different times.

[0059] Step 4: Split and merge the fluid model through external force analysis to optimize the fluid simulation granularity. Finally, the results of the fluid dynamic simulation are presented, showing the dynamic effects of the fluid's interaction with other models and scenes.

[0060] Furthermore, if Figure 4 As shown in the figure, the complex mechanical behavior of the fluid is demonstrated through the splitting and merging of Gaussian kernels. The upper part shows the merging process, where two 3D Gaussian kernels merge into a larger Gaussian kernel after meeting certain conditions. The lower part shows the splitting process, where a larger elliptical 3D Gaussian kernel, when subjected to excessive deformation or force, splits into multiple sub-Gaussian kernels. The dashed circle in the figure represents the kernel before splitting, and the solid circle represents the new Gaussian kernel formed after splitting.

[0061] To accurately simulate the complex mechanical behavior between fluids and solid materials during simulation, it is necessary to automatically identify Gaussian kernels in specific regions. Furthermore, to avoid the graininess associated with independent Gaussian kernels, Gaussian kernel merging and splitting are introduced during the simulation. In particular, the mechanical behavior of Gaussian kernel particles at the fluid surface and near interaction boundaries is significantly affected by boundary conditions.

[0062] When the distance between adjacent 3D Gaussian kernels is less than the merging threshold, and they belong to the same material and have similar physical states, a 3D Gaussian kernel merging strategy is implemented. The mass of the new Gaussian kernel is the sum of the masses of the previous Gaussian kernels, and its physical quantities such as velocity and surface tension are recalculated according to the mass-weighted average rule. Gaussian kernel merging can reduce the number of Gaussian kernels and reduce noise interference in numerical calculations, while maintaining accurate simulation of overall mechanical behavior and avoiding the accumulation of numerical errors caused by too many Gaussian kernels. This achieves smooth interaction between Gaussian fluid models and solves the graininess that exists in traditional Gaussian fluid simulation methods.

[0063] ,

[0064] in, Indicates whether the 3D Gaussian kernels p and q are merged (p, q are Gaussian kernel numbers). is the distance between Gaussian kernels p and q, is the merging threshold.

[0065] when =1, 、 、 ,in 、 are the masses of Gaussian kernels p and q respectively, is the mass of the new Gaussian kernel after merging, 、 are the velocities of Gaussian kernels p and q, respectively, is the velocity of the new Gaussian kernel after merging, 、 are the surface tensions of Gaussian kernels p and q, is the surface tension of the new Gaussian kernel after merging.

[0066] For 3D Gaussian kernels with excessive deformation or abnormal stress, a Gaussian kernel splitting strategy is employed. The mass of each daughter Gaussian kernel is proportionally distributed to the original Gaussian kernel, while physical quantities such as velocity and stress are appropriately distributed based on the splitting direction and deformation. This Gaussian kernel splitting increases the particle density in localized regions, better reflecting the mechanical changes within the material, enhancing the accuracy and detail of the simulation results, and ensuring that the simulation process truly represents the mechanical response of the material under complex stress conditions, maintaining simulation stability and fidelity.

[0067]

[0068] in Indicates whether the Gaussian kernel x is split (x is the Gaussian kernel number), is the degree of deformation of the Gaussian kernel k, is the deformation threshold, is the external force on the Gaussian kernel k, is the stress threshold.

[0069] when 1 o'clock, 、 , It represents the change in the velocity of the lth sub-Gaussian core relative to the original Gaussian core, which is determined by the splitting direction and deformation. , It represents the change of the stress of the lth sub-Gaussian core relative to the original Gaussian core, which is determined according to the splitting direction and deformation. Among them, n is the number of sub-Gaussian cores after splitting. is the mass of the original Gaussian kernel x, is the mass of the lth sub-Gaussian kernel (l=1,2,⋯,n), is the velocity of the original Gaussian kernel x, is the velocity of the lth sub-Gaussian kernel, is the stress of the original Gaussian kernel x, is the stress of the lth sub-Gaussian kernel.

[0070] like Figure 5 As shown, the image on the left displays multiple fluid models and several object models, presenting the model morphology from different perspectives. The simulated interaction process on the right illustrates the interaction between the fluid model and the object model. When the fluid model comes into contact with the object model, its morphology changes. Some of the fluid model covers the object model, while others change shape due to contact. This intuitively demonstrates the mechanical behavior and morphological evolution of the fluid and object during the simulated interaction process, demonstrating the effectiveness of the technology in simulating the interaction between fluids and objects.

[0071] Integrate the optimized 3D Gaussian kernel fluid model with other 3D Gaussian models into the same scene to perform dynamic fluid simulations. Through scene fusion, users can quickly add or remove fluid models from complex scenes without extensive modification or reconfiguration, streamlining the development process for large-scale simulations while maintaining the consistency and accuracy of physical simulations. Finally, render the dynamic effects of fluid interaction with other models and scenes.

[0072] The foregoing description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein and should not be construed as excluding other embodiments. Rather, the present invention is capable of various other combinations, modifications, and improvements, and is capable of modifications within the scope of the concepts described herein, through the above teachings, or through techniques or knowledge in the relevant fields. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention are intended to be within the scope of the appended claims.

Claims

1. A fluid dynamic interaction simulation method based on 3D Gaussian sputtering and MPM, characterized by: The simulation method comprises: Step 1: Using multi-view images of the fluid and the simulation scene as the starting input data, perform 3D Gaussian sputtering on the input multi-view images to construct the surface features of the object; Step 2: Generate a regional Gaussian kernel for the fluid and perform scaling regularization on the 3D Gaussian kernel; Step 3: Use the material point method to simulate the fluid dynamic interaction of multiple physical fields and assign basic physical properties to each Gaussian model; Step 4: Split and merge the fluid model through external force analysis to enhance the accuracy and details of the simulation, ultimately presenting the results of the fluid dynamics simulation and demonstrating the dynamic effects of the fluid's interaction with other models and scenes.

2. The fluid dynamic interaction simulation method based on 3D Gaussian sputtering and MPM according to claim 1, characterized in that: The step 1 specifically includes the following contents: Capturing fluid multi-view images in a virtual environment, as well as capturing real physical environments through cameras; Using multiple multi-view images and SFM camera parameters as input, 3D Gaussian sputtering is used to generate discrete Gaussian kernels. These discrete Gaussian kernels use the G(M) function to determine their distribution and shape properties in space to form the surface features of the object. , where M represents the mean of the 3D Gaussian kernel position, M T represents the transpose of M, represents the covariance matrix; During rendering, the 3D Gaussian kernel is projected onto the 2D plane, and the final two-dimensional image is obtained by mixing and calculating the pixel value and transparency. , It represents the multiplication of the opacity of the k-th Gaussian kernel and the 2D Gaussian distribution density of the pixel position projection. K represents the set of Gaussian kernels of different models, and p represents the number of factors involved in the multiplication calculation. Indicates the contribution of the kth Gaussian kernel to the pixel color under the lth influencing factor.

3. The fluid dynamic interaction simulation method based on 3D Gaussian sputtering and MPM according to claim 1, characterized in that: The second step specifically includes the following contents: Generate regional Gaussian kernels based on the surface features of the object. By selecting points in the region to establish a data set, filter out holes and 3D Gaussian kernels with abnormal shapes to prevent the generated Gaussian kernels from becoming noise and reducing rendering realism. At the same time, control the number of generated 3D Gaussian kernels and ensure that the 3D Gaussian kernels are evenly distributed. Scaling, deformation, regularization, and smoothing operations are performed on the 3D Gaussian kernel to avoid sharp shapes that may cause interactions between particles and the 3D Gaussian kernel, and to avoid deviations in the calculation of local physical quantities when simulating fluid motion, which may lead to abnormal fluid forces and reduce the realism of the fluid simulation.

4. The fluid dynamic interaction simulation method based on 3D Gaussian sputtering and MPM according to claim 3, characterized in that: The scaling deformation regularization constrains the size and shape of the 3D Gaussian kernel to prevent the 3D Gaussian kernel from being sharp, through the formula Implementation, where represents the amount of loss associated with scaling, Representative The maximum zoom value of an object, Representative The minimum scale value of an object, Represents the threshold parameter, which is used to participate in condition judgment.

5. The fluid dynamic interaction simulation method based on 3D Gaussian sputtering and MPM according to claim 3, characterized in that: The step three specifically includes the following contents: In the material point method particle interaction simulation, the fluid is considered to be a mass carrier. and speed The distribution of these discrete Gaussian kernels in space constitutes a discretized expression of the fluid. The mass of each discrete Gaussian kernel is determined by the shape function Mapping to the background grid nodes, the mass information of the discrete Gaussian kernel is distributed to the background grid in a weighted form, so that the background grid can inherit the mass properties of the 3D Gaussian kernel. By mapping the background grid, the mass distribution at different positions can be perceived. is the position of material point i, j is the background grid node number; The momentum of the material is mapped to the grid nodes based on the shape function. This mapping gives the grid nodes the motion information of the Gaussian kernel. The grid node momentum is updated by calculation based on the conservation law on the background grid, and the updated physical quantity is returned to the Gaussian kernel. Through this mapping, the 3D Gaussian kernel updates its own state based on the calculation results on the grid, realizing the cyclic transfer and update of physical quantities between the Gaussian kernel and the background grid, and continuously simulating the mechanical response of the material at different times.

6. The fluid dynamic interaction simulation method based on 3D Gaussian sputtering and MPM according to claim 1, characterized in that: The splitting and merging optimization of the fluid model includes: When the distance between adjacent 3D Gaussian kernels is less than the merging threshold and they belong to the same material and have similar physical states, the 3D Gaussian kernel merging strategy is implemented. The mass of the new Gaussian kernel is the sum of the masses of the Gaussian kernels before merging, and its velocity and surface tension are calculated according to the mass-weighted average rule. For 3D Gaussian kernels with large deformation or abnormal force, a Gaussian kernel splitting strategy is adopted. The mass of each sub-Gaussian kernel is distributed according to a certain proportion to the original Gaussian kernel mass, and its velocity and stress are distributed according to the splitting direction and deformation.

7. The fluid dynamic interaction simulation method based on 3D Gaussian sputtering and MPM according to claim 6, characterized in that: When implementing the 3D Gaussian kernel merging strategy, by To indicate whether the 3D Gaussian kernel p and q are merged, is the distance between Gaussian kernels p and q, is the merging threshold; when = 1, the mass of the new Gaussian kernel , the speed of the new Gaussian kernel , the surface tension of the new Gaussian kernel ,in 、 are the masses of Gaussian kernels p and q respectively, is the mass of the new Gaussian kernel after merging, 、 are the velocities of Gaussian kernels p and q, respectively, is the velocity of the new Gaussian kernel after merging, 、 are the surface tensions of Gaussian kernels p and q, is the surface tension of the new Gaussian kernel after merging.

8. The fluid dynamic interaction simulation method based on 3D Gaussian sputtering and MPM according to claim 6, characterized in that: When using the Gaussian kernel splitting strategy, Indicates whether the Gaussian kernel x is split, is the degree of deformation of the Gaussian kernel k, is the deformation threshold, is the external force on the Gaussian kernel k, is the stress threshold; when 1 o'clock, 、 、 , where n is the number of sub-Gaussian kernels after splitting, is the mass of the original Gaussian kernel x, is the mass of the lth sub-Gaussian kernel, l=1,2,⋯,n, is the velocity of the original Gaussian kernel x, is the velocity of the lth sub-Gaussian kernel, is the stress of the original Gaussian kernel x, is the stress of the lth sub-Gaussian kernel, is the change in the velocity of the lth sub-Gaussian kernel relative to the original Gaussian kernel, is the stress change of the lth sub-Gaussian kernel relative to the original Gaussian kernel.

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