Density distribution and representation method for triangular surface element region in hexahedral mesh generation
By performing multi-resolution clustering and Gaussian kernel function estimation on triangular face elements, the problem of unused density information in the existing technology is solved, and efficient generation of non-uniform hexahedral mesh is achieved, and the quality and efficiency of mesh generation are improved.
Patent Information
- Application Number
- CN202510469648.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-15
- Publication Date
- 2025-07-18
AI Technical Summary
The prior art has not fully utilized density information in the transformation of triangular to hexahedral mesh, resulting in immature research on non-uniform algorithms and it is difficult to achieve efficient and accurate mesh generation.
By reading triangular element mesh data, multi-resolution clustering operations are performed, density features are estimated and classified into clusters, local density is estimated using Gaussian kernel function, linear interpolation is performed, and non-uniform hexahedral mesh generation is guided.
Accurate division of different regions and density information extraction are achieved, which significantly improves the quality and efficiency of hexahedral mesh generation.
Smart Images
Figure CN120337659A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of software development, and particularly to a density distribution and representation method for triangular face element regions in hexahedron mesh generation. Background Art
[0002] Triangular face element meshes are a common type of mesh, usually used in fields such as computer graphics, finite element analysis, computational fluid dynamics, and geographic information systems (GIS). A triangular face element mesh consists of multiple triangular elements (face elements), which are connected to form a large mesh for representing shapes or surfaces in two-dimensional or three-dimensional space. Triangular face element meshes are widely used because of the following characteristics.
[0003] Simplicity: Triangles are the simplest polygons with good mathematical properties, suitable for various complex geometric shapes.
[0004] Adaptability: It can handle complex and irregular regions well, especially suitable for representing curved surfaces, complex boundaries, and irregular shapes.
[0005] High computational efficiency: In finite element analysis, triangles can approximate and solve complex problems relatively accurately. Especially when dealing with numerical calculations in a finite region, they can converge relatively quickly.
[0006] Flexibility: Different refinement techniques can be used to flexibly change the mesh resolution to adapt to the different regional requirements of the problem.
[0007] In addition, the non-uniform encryption technology for triangular face elements has been quite mature. Nowadays, many commercial software and even open-source software (GMSH) support generating non-uniform triangular face element meshes of models to minimize the mesh generation error.
[0008] Cluster analysis is a common data analysis method aimed at dividing a data set into multiple groups or clusters according to the similarity between data, so that the data points in the same cluster have a high degree of similarity, while the similarity between different clusters is low. Cluster analysis has a wide range of applications in fields such as machine learning, data mining, and statistics, mainly used to discover potential structures and patterns in data. Commonly used distance metrics for cluster analysis include Euclidean distance, Manhattan distance, etc. This method uses Euclidean distance for clustering. Nowadays, there are various clustering algorithms, including but not limited to partitioning-based clustering methods, hierarchical clustering methods, density-based clustering methods, network-based clustering methods, model-based clustering methods, etc. This method uses a density-based clustering method for clustering.
[0009] At present, there have been many studies on the conversion of triangular facets to hexahedral meshes, but the research on non-uniform algorithms is not yet mature. Most researchers only use triangular facets to determine the contour of the model, but ignore the use of the density of triangular facets. Summary of the Invention
[0010] In order to make up for the deficiencies of the prior art and solve at least one technical problem proposed in the background art.
[0011] The present invention adopts the following technical solutions to solve the above technical problems: It provides a density distribution and representation method for triangular facet regions in hexahedral mesh generation, including the following steps:
[0012] S1. Read relevant information of triangular facet mesh data according to different file formats;
[0013] S2. Perform multi-resolution clustering operations on all triangular facets according to the read information to estimate the density characteristic data of triangular facets, and classify the triangular facets into clusters according to the density characteristic data;
[0014] S3. Perform Gaussian kernel function estimation on each cluster obtained by clustering to obtain the side lengths of each triangle in the cluster, and obtain the density of each cluster to obtain the local density of each cluster;
[0015] S4. Map the local density to the non-uniform hexahedral mesh density, perform linear interpolation on the local density, and calculate the mesh size of each region according to the density of each cluster;
[0016] S5. Complete the identification of the triangular facet region and the representation of the density, and guide the generation of non-uniform hexahedral meshes.
[0017] Preferably, in step S1, the relevant information includes the vertex and center point coordinates of the triangular facet, and the numbers of the three points forming the triangle.
[0018] Preferably, in step S2, the multi-resolution clustering operation extracts the density information of the triangular facets based on the vertices of all triangular facets.
[0019] Preferably, the density of the triangular facets is estimated by using the node density method.
[0020] Preferably, in step S3, the formula of the Gaussian kernel function is as follows:
[0021] ;
[0022] where is the estimated density function, is the point to be estimated, is the total number of data, is the bandwidth, is the Gaussian kernel function.
[0023] Preferably, the Gaussian kernel function is presented using the standard normal distribution, and the formula is specifically:
[0024] .
[0025] Preferably, the bandwidth is used for smoothing control.
[0026] Preferably, the calculation of the linear interpolation is specifically manifested as taking the calculated maximum local density and the minimum local density in the regional density of each cluster, then the local density is and the side length of the non-uniform grid in the area where the local density is
[0027] is:
[0028] Compared with the prior art, the present invention provides a density distribution and representation method for the triangular face element region in hexahedron mesh generation, having the following beneficial effects: By relying on the density characteristics of the triangular face elements, different regions can be accurately divided, and the density information of each region can be accurately extracted. On this basis, the size of the hexahedron mesh corresponding to each region can be further determined, providing scientific and effective guidance for the generation of non-uniform hexahedron meshes, thereby significantly improving the quality and efficiency of mesh generation. BRIEF DESCRIPTION OF THE DRAWINGS
[0029] Figure 1 is a schematic structural diagram of the program flow of the present invention;
[0030] Figure 2 is a schematic diagram for explaining the clustering process of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0031] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.
[0032] Please refer to Figure 1 , Figure 2 , a density distribution and representation method for the triangular face element region in hexahedron mesh generation, comprising the following steps:
[0033] S1. Read the relevant information of the triangular face element mesh data according to different file formats;
[0034] S2. Perform multi - resolution clustering operations on all triangular facets according to the read information to estimate the density feature data of the triangular facets, and classify the triangular facets into clusters according to the density feature data;
[0035] S3. Perform Gaussian kernel function estimation on each cluster obtained by clustering to obtain the side lengths of each triangle within the cluster, and obtain the density of each cluster to obtain the local density of each cluster;
[0036] S4. Map the local density to the non - uniform hexahedral grid density, perform linear interpolation on the local density, and calculate the grid size of each region according to the density of each cluster;
[0037] S5. Complete the identification of the triangular facet region and the representation of the density, and guide the generation of the non - uniform hexahedral grid.
[0038] In this embodiment, in step S1, the relevant information includes the vertex and center point coordinates of the triangular facets, and the numbers of the three points forming the triangle.
[0039] Specifically, first read the triangular facet grid data from the hard disk into the memory, and then read the relevant information of the triangular facets according to different file formats.
[0040] In this embodiment, in step S2, the multi - resolution clustering operation extracts the density information of the triangular facets based on the vertices of all triangular facets.
[0041] Specifically, the multi - resolution clustering operation can directly determine the accuracy of density region identification. In the triangular facet grid, the density of the grid is usually used to represent the size or distribution density of the triangles in the grid, and can be described by different mathematical methods.
[0042] In this embodiment, the density of the triangular facets is estimated using the node density method.
[0043] Specifically, when using node density to estimate the density of triangular facets, due to the characteristic that regions with higher density have higher priority in the multi - resolution clustering method, it means that if a region with lower density overlaps with a region with higher density, the overlapping part is determined by the region with higher density. Therefore, estimating the density of triangular facets by node density is more suitable for irregularly distributed grids. More specifically, this multi - resolution clustering method is similar to the Haar wavelet, that is, a scale function with lower resolution can be linearly represented by several scale functions with higher resolution. The multi - resolution clustering method first identifies regions with lower density, which may be large, even the entire region covered by the triangular facets, and then clusters these regions with higher - density parameters, repeating this process until the size of the clustering region is less than the set threshold region size before termination.
[0044] In this embodiment, in step S3, the formula of the Gaussian kernel function is as follows:
[0045] ;
[0046] where, is the estimated density function, is the point to be estimated, is the total number of data, is the bandwidth, is the Gaussian kernel function, and the Gaussian kernel function is presented using the standard normal distribution, and the specific formula is:
[0047] .
[0048] Specifically, all clusters are obtained through clustering operations, and Gaussian kernel function estimation is performed on them, so that the local density can be conveniently obtained. By giving a set of data , Gaussian kernel density estimation is performed by applying a Gaussian kernel function at each data point, and then summing the kernel function values of all data points to finally obtain the density estimation of the data.
[0049] In this embodiment, the bandwidth is used for smoothing regulation.
[0050] Specifically, when (bandwidth) takes a small value, the characterization and estimation of the data are more delicate, and when the bandwidth takes a large value, the characterization and estimation of the data are smoother.
[0051] In this embodiment, the calculation of linear interpolation is specifically manifested as taking the calculated maximum local density and the minimum local density from the regional densities of each cluster, then the non-uniform grid side length of the region where the local density is is:
[0052] .
[0053] Specifically, when mapping the local density to the non-uniform hexahedron grid density, the calculated maximum local density and the minimum local density need to be calculated. If the set range of the non-uniform grid side length is , and the currently identified regions, then for the region where the current local density is , the non-uniform grid side length is:
[0054] .
[0055] It should be noted that in this text, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, such that a process, method, article or device comprising a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article or device.
[0056] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.
Claims
1. A density distribution and representation method for triangular face element regions in hexahedral mesh generation, characterized in that, Including the following steps: S1. Read the relevant information of the triangular element mesh data according to different file formats; S2. Perform multi-resolution clustering operations on all triangular elements based on the read information to estimate the density feature data of the triangular elements, and classify the triangular elements into clusters according to the density feature data; S3. Perform Gaussian kernel function estimation on each cluster obtained by clustering to obtain the side lengths of each triangle within the cluster, and obtain the density of each cluster to obtain the local density of each cluster; S4. Map the local density to the non-uniform hexahedral mesh density, perform linear interpolation on the local density, and calculate the mesh size of each region according to the density of each cluster; S5. Complete the identification of the triangular element region and the representation of the density, and guide the generation of the non-uniform hexahedral mesh.
2. A density distribution and representation method for triangular face element regions in hexahedral mesh generation, characterized in that: In step S1, the relevant information includes the vertex and center point coordinates of the triangular element, and the numbers of the three points forming the triangle.
3. A density distribution and representation method for triangular face element regions in hexahedral mesh generation, characterized in that: In step S2, the multi-resolution clustering operation extracts the density information of the triangular elements based on the vertices of all triangular elements.
4. A density distribution and representation method for triangular face element regions in hexahedral mesh generation, characterized in that: The density of the triangular element is estimated by using the node density method.
5. A density distribution and representation method for triangular face element regions in hexahedral mesh generation, characterized in that: In step S3, the formula of the Gaussian kernel function is as follows: ； Among them, is the estimated density function, is the point to be estimated, is the total number of data, is the bandwidth, is the Gaussian kernel function.
6. A density distribution and representation method for triangular face element regions in hexahedral mesh generation, characterized in that: The Gaussian kernel function is presented by using the standard normal distribution, and the formula is specifically: 。 7. A density distribution and representation method for triangular face element regions in hexahedral mesh generation, characterized by: The bandwidth is used for smoothing regulation.
8. A density distribution and representation method for triangular face element regions in hexahedral mesh generation, characterized in that: The calculation of the linear interpolation is specifically manifested as follows. Among the regional densities of each of the clusters, the maximum local density and the minimum local density are obtained. Then, the side length of the non-uniform grid for the region with a local density of is: 。