A method and device for reconstructing a CAD model of a topology optimization result

Abstract

The application provides a CAD model reconstruction method and device for topology optimization results, and relates to the technical field of computer modeling. The method comprises the following steps: grid preprocessing, component type grid segmentation, sheet type grid segmentation, obtaining at least two sub-grid sheets, parameterizing each sub-grid sheet to obtain a final parameterization result, performing uniform interpolation sampling based on the final parameterization result to obtain sampling points, generating a spline surface by using the sampling points, assembling the spline surface, and generating a reconstructed CAD model corresponding to the three-dimensional topology optimization result. The grid model reconstruction method has the advantages of high automation degree, strong realizability, simple operation, etc., is not limited to a tubular topology optimization structure, has no obvious difference in processing tubular and non-tubular model characteristics, has stronger universality, can adapt to the diversity demand of industrial structure optimization, and can improve the reconstruction efficiency and reconstruction effect of the triangular grid model to the CAD model.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer modeling, and particularly relates to a CAD model reconstruction method and device for topology optimization results. BACKGROUND

[0002] Topology optimization is a method for finding the best material distribution and structure layout by iterative adjustment under design constraints. Topology optimization can be used to design high-strength and lightweight structures and has been widely used in engineering design.

[0003] However, the mesh model extracted from the topology optimization structure is usually a high-density and low-quality mesh model, which is difficult to directly apply to design verification, prototype manufacturing and other design iteration links. In order to meet the above redesign requirements, it is usually necessary to reconstruct the mesh model extracted from the topology optimization structure into a more easily processed CAD (Computer Aided Design) model.

[0004] At present, the vertex data of the mesh model extracted from the topology optimization structure can be directly fitted with a surface. This method not only involves too many variables, but also has poor reconstruction effect and low reconstruction efficiency. The model reconstruction method based on skeleton and contour line extraction, although better in reconstruction efficiency and effect, is only applicable to tubular topology optimization structure and has insufficient universality. The manual reconstruction method based on sketch drawing and Boolean operation and other operations is not only time-consuming and prone to error, but also has low efficiency. SUMMARY

[0005] In view of the deficiencies in the related art, the present application provides a CAD model reconstruction method and device for topology optimization results to solve the problems of poor reconstruction effect, low reconstruction efficiency and insufficient universality of the current triangular mesh reconstruction method.

[0006] In a first aspect, the present application provides a CAD model reconstruction method for topology optimization results, comprising:

[0007] generating a to-be-reconstructed triangular mesh model based on a three-dimensional topology optimization result;

[0008] performing mesh preprocessing on the to-be-reconstructed triangular mesh model to obtain a preprocessed triangular mesh model, wherein the to-be-reconstructed triangular mesh model is a mesh model extracted from a topology optimization structure, the to-be-reconstructed triangular mesh model has jagged boundaries and redundant vertices, and the preprocessed triangular mesh model does not have jagged boundaries and redundant vertices;

[0009] perform component-type grid segmentation on the preprocessed triangular mesh model to obtain at least two component sub-meshes, wherein a topological structure of the component sub-meshes is not a unit disc topological structure;

[0010] perform sheet-type grid segmentation on each of the component sub-meshes to obtain at least two sub-mesh sheets, wherein a topological structure of the sub-mesh sheets is a unit disc topological structure;

[0011] perform initial parameterization on each of the sub-mesh sheets to obtain an initial parameterization result of each sub-mesh sheet;

[0012] perform iterative parameterization on each of the sub-mesh sheets based on the initial parameterization result to obtain a final parameterization result of each sub-mesh sheet;

[0013] perform uniform interpolation sampling based on each of the final parameterization results to obtain a plurality of groups of sampling points;

[0014] generate a spline surface corresponding to each sub-mesh sheet by using the sampling points;

[0015] assemble the spline surfaces to generate a reconstructed CAD model corresponding to the three-dimensional topological optimization result.

[0016] Optionally, in the CAD model reconstruction method of the topological optimization result provided in the application, the preprocessed triangular mesh model is composed of triangular sheets and vertices, and the performing component-type grid segmentation on the preprocessed triangular mesh model to obtain at least two component sub-meshes comprises:

[0017] extract information features of all vertices of the preprocessed triangular mesh model;

[0018] perform classification prediction on each triangular sheet of the preprocessed triangular mesh model according to the information features;

[0019] perform component-type grid segmentation on the preprocessed triangular mesh model according to the classification prediction result of the triangular sheets to obtain at least two component sub-meshes.

[0020] Optionally, in the CAD model reconstruction method of the topological optimization result provided in the application, the performing sheet-type grid segmentation on each of the component sub-meshes to obtain at least two sub-mesh sheets comprises:

[0021] calculate an initial probability of each triangular sheet belonging to different segmentation regions according to distances between all adjacent triangular sheets in the component sub-meshes;

[0022] iteratively adjust the probability of each triangular sheet belonging to different segmentation regions based on the initial probability until convergence is achieved to obtain a final probability of each triangular sheet belonging to different segmentation regions.

[0023] determining a segmentation boundary based on the final probability;

[0024] performing a patch-type mesh segmentation on each of the component sub-meshes based on the segmentation boundary, to obtain at least two sub-mesh patches.

[0025] Optionally, the CAD model reconstruction method of the topological optimization result provided in the present application, the initial parameterization of each of the sub-mesh patches is performed, to obtain an initial parameterization result of each sub-mesh patch, which comprises:

[0026] creating a unit square parameter domain;

[0027] mapping the sub-mesh patches to the unit square parameter domain by using the Floater Shape-preserving method, to obtain the initial parameterization result of each sub-mesh patch, wherein the initial parameterization result is an initial two-dimensional parameter coordinate of the sub-mesh patch in the unit square parameter domain.

[0028] Optionally, the CAD model reconstruction method of the topological optimization result provided in the present application, the iterative parameterization of each of the sub-mesh patches based on the initial parameterization result is performed, to obtain a final parameterization result of each sub-mesh patch, which comprises:

[0029] iteratively mapping the sub-mesh patches to the unit square parameter domain based on the initial parameterization result, until the geometric stretching value in the parameterization process no longer decreases, to obtain the final parameterization result of each sub-mesh patch, wherein the final parameterization result is a final two-dimensional parameter coordinate of the sub-mesh patch in the unit square parameter domain, and the parameterization method adopted in the iterative parameterization is one of the convex combination method, the minimum energy method and the free boundary method.

[0030] Optionally, the CAD model reconstruction method of the topological optimization result provided in the present application, uniform interpolation sampling based on the final parameterization result is performed, to obtain a plurality of groups of sampling points, which comprises:

[0031] setting a straight line grid in the unit square parameter domain;

[0032] in the straight line grid, uniform interpolation based on the final two-dimensional parameter coordinate is performed, to obtain a uniform interpolation point set;

[0033] determining the final two-dimensional parameter coordinates of the three vertices of the triangular patch of the sub-mesh patch closest to the uniform interpolation points in the uniform interpolation point set as reference two-dimensional parameter coordinates;

[0034] According to the two-dimensional coordinates of the uniform interpolation point and the reference two-dimensional parameter coordinates, a barycentric coordinate interpolation formula is used to calculate the barycentric coefficients corresponding to the uniform interpolation point, and the barycentric coordinate interpolation formula is:

[0035]

[0036] γ=1-α-β

[0037] Wherein, (x, y) is the two-dimensional coordinates of the uniform interpolation point, α, β, γ is the barycentric coefficient, (x A ,y A ),(x B ,y B ),(x C ,y C ) is the final two-dimensional parameter coordinates of the three vertices A, B, C of the triangular patch ΔABC of the sub-grid patch respectively.

[0038] According to the barycentric coordinate interpolation formula and the barycentric coefficients, the three-dimensional vertex space coordinates corresponding to the uniform interpolation point are calculated for the three-dimensional grid vertices of the sub-grid patch where the uniform interpolation point is located, wherein the three-dimensional vertex space coordinates corresponding to the uniform interpolation point are the three-dimensional space coordinates of the sampling point.

[0039] Optionally, according to the CAD model reconstruction method of the topological optimization result provided by the application, the at least two spline surfaces are generated by using the sampling points, which comprises:

[0040] According to the three-dimensional space coordinates corresponding to the uniform interpolation point, the uniform interpolation point is determined as a spline control point;

[0041] According to the spline control point, the spline surface is generated.

[0042] Optionally, according to the CAD model reconstruction method of the topological optimization result provided by the application, the spline surface is assembled to generate a reconstructed CAD model corresponding to the three-dimensional topological optimization result, which comprises:

[0043] All the spline surfaces are connected through adjacent edges to generate a reconstructed CAD model corresponding to the three-dimensional topological optimization result.

[0044] Optionally, according to the CAD model reconstruction method of the topological optimization result provided by the application, the grid preprocessing comprises Laplace smoothing and isotropic regridding, wherein the iteration number of the Laplace smoothing and isotropic regridding is not more than three times.

[0045] In the second aspect, the application provides a CAD model reconstruction device of a topological optimization result, which comprises:

[0046] A model generation unit is configured to generate a triangular mesh model to be reconstructed based on the three-dimensional topology optimization result;

[0047] A mesh preprocessing unit is configured to perform mesh preprocessing on the triangular mesh model to be reconstructed to obtain a preprocessed triangular mesh model, wherein the triangular mesh model to be reconstructed is a mesh model extracted from the topology optimization structure, the triangular mesh model to be reconstructed has jagged boundaries and redundant vertices, and the preprocessed triangular mesh model does not have jagged boundaries and redundant vertices;

[0048] A component-type mesh segmentation unit is configured to perform component-type mesh segmentation on the preprocessed triangular mesh model to obtain at least two component sub-meshes, wherein the topology structure of the component sub-meshes is not a unit disc topology structure;

[0049] A patch-type mesh segmentation unit is configured to perform patch-type mesh segmentation on each of the component sub-meshes to obtain at least two sub-mesh patches, wherein the topology structure of the sub-mesh patches is a unit disc topology structure;

[0050] An initial parameterization unit is configured to perform initial parameterization on each of the sub-mesh patches to obtain an initial parameterization result of each sub-mesh patch;

[0051] An iterative parameterization unit is configured to perform iterative parameterization on each of the sub-mesh patches based on the initial parameterization result to obtain a final parameterization result of each sub-mesh patch;

[0052] A sampling unit is configured to perform uniform interpolation sampling based on each of the final parameterization results to obtain a plurality of groups of sampling points;

[0053] A spline surface generation unit is configured to generate a spline surface corresponding to each sub-mesh patch by using the sampling points;

[0054] A CAD model assembly unit is configured to assemble the spline surfaces to generate a reconstructed CAD model corresponding to the three-dimensional topology optimization result.

[0055] The application firstly performs mesh preprocessing on the triangular mesh model extracted from the topology optimization structure, and the triangular mesh model after mesh preprocessing does not have jagged boundaries and redundant vertices, so it is more conducive to subsequent mesh model reconstruction. Then, the preprocessed triangular mesh model is subjected to component-type mesh segmentation to obtain at least two component sub-meshes. The mesh topology structure after component-type mesh segmentation is not a unit disc topology structure, and does not meet the parameterization requirement. Therefore, the component sub-meshes after segmentation are subjected to face-type mesh segmentation to obtain at least two sub-mesh faces. The mesh topology structure of the sub-mesh faces is a unit disc topology structure, so it meets the parameterization requirement, and the mesh model can continue to be subjected to subsequent parameterization. Then, initial parameterization is performed on each sub-mesh face to obtain an initial parameterization result. Iterative calculation is performed based on the initial parameterization result, that is, iterative parameterization is performed to obtain a final parameterization result. Finally, uniform interpolation sampling is performed based on the final parameterization result to obtain a plurality of groups of sampling points, and a spline surface corresponding to each sub-mesh face is generated. These spline surfaces are assembled to generate a reconstructed CAD model corresponding to the three-dimensional topology optimization structure.

[0056] The technical scheme provided by the application has the following beneficial effects:

[0057] Through a series of geometric processing such as smoothing, segmentation and parameterization, the topology optimization structure is reconstructed into a CAD model based on a parameter surface expression, which has the advantages of high automation degree, strong realizability and simple operation, and can solve the problem of redesign iteration of the topology optimization structure to a certain extent. At the same time, the generated model is in the commonly used IGES format, which is suitable for subsequent product structure analysis, prototype manufacturing verification and design verification parameterization design.

[0058] Compared with the reconstruction method of extracting the skeleton, the contour line and other topology optimization structures, the application scenario is not limited to the tubular topology optimization structure, and there is no obvious difference in the effect when processing tubular and non-tubular model features, which has stronger universality and can adapt to the diversity demand of industrial structure optimization.

[0059] In the mesh segmentation process, a secondary segmentation strategy scheme is adopted, and according to the characteristics of the topology optimization structure having strong symmetry geometric characteristics, the "component" type mesh segmentation is applied first, and then the "face" type mesh segmentation is applied, so that the number of sub-meshes generated is small, and the reconstruction efficiency is improved.

[0060] For modular design, each link is highly independent, and for topology optimization structures with different geometric characteristics, other preprocessing methods, mesh segmentation methods and parameterization methods can be replaced modularly to further improve the reconstruction efficiency of the mesh model and optimize the reconstruction quality. BRIEF DESCRIPTION OF DRAWINGS

[0061] The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and together with the description serve to explain the application. In the drawings:

[0062] Figure 1 is a flow chart of the CAD model reconstruction method of the topology optimization result of the embodiment of the application;

[0063] Figure 2 is a schematic diagram of the triangular mesh model to be reconstructed in the embodiment of the application;

[0064] Figure 3 is Figure 2 is a schematic diagram of the preprocessed triangular mesh model obtained after the triangular mesh model to be reconstructed shown in the embodiment of the application is subjected to the mesh preprocessing of the embodiment of the application;

[0065] Figure 4 is a flow chart of the SDF segmentation method of the embodiment of the application;

[0066] Figure 5 is a schematic diagram of the component sub-mesh obtained after the preprocessed triangular mesh model shown in Figure 3 is subjected to the SDF segmentation method of the embodiment of the application; Figure 4

[0067] Figure 6 is a flow chart of the hierarchical fuzzy clustering segmentation method of the embodiment of the application;

[0068] Figure 7 is a schematic diagram of the sub-mesh patch obtained after the component sub-mesh shown in Figure 5 is subjected to the patch-type segmentation method of the embodiment of the application; Figure 6

[0069] Figure 8 is a flow chart of the parameterization method of the embodiment of the application;

[0070] Figure 9 is a schematic diagram of the parameterization effect display of the embodiment of the application;

[0071] Figure 10 is a flow chart of the uniform interpolation sampling method of the embodiment of the application;

[0072] Figure 11 is a schematic diagram of the comparison between the sampling point of a single sub-mesh patch and the original triangular patch mesh in the embodiment of the application;

[0073] Figure 12 is a schematic diagram of the reconstructed CAD model obtained after the triangular mesh model to be reconstructed shown in Figure 2 is subjected to the model reconstruction of the embodiment of the application;

[0074] Figure 13 ​​It is a CAD model reconstruction device schematic view of the topological optimization result of the embodiment of the application. DETAILED DESCRIPTION

[0075] For the purpose and implementation of the present application to be more clear, the exemplary embodiments of the present application will be described clearly and completely below in conjunction with the drawings of the exemplary embodiments of the present application. Obviously, the described exemplary embodiments are only a part of the embodiments of the present application, but not all the embodiments.

[0076] The grid model extracted from the topological optimization structure is mostly a high-density and low-quality grid model, which is difficult to be directly applied to design verification, prototype manufacturing and other design iteration links. In order to meet the above-mentioned redesign requirements, it is usually necessary to reconstruct the grid model extracted from the topological optimization result into a more easily processed CAD model.

[0077] At present, the vertex data of the grid model extracted from the topological optimization structure can be directly fitted with a surface. This method not only involves too many variables, but also has poor reconstruction effect and low efficiency. The model reconstruction method based on skeleton and contour line extraction, although better in reconstruction efficiency and effect, is only suitable for tubular topological optimization structure, and has insufficient universality. The manual reconstruction method based on sketch drawing and Boolean operation and other operations not only consumes time and is prone to errors, but also has low efficiency.

[0078] In order to solve the above-mentioned problems, the embodiment of the present application provides a CAD model reconstruction method of topological optimization result, which not only has high automation degree, strong realizability and simple operation, etc., and is not limited to tubular topological optimization structure, and has no obvious difference in effect when processing tubular and non-tubular model characteristics, has stronger universality, can adapt to the diversity demand of industrial structure optimization, and can improve the reconstruction efficiency and effect of triangular grid model.

[0079] As shown in the flowchart of the CAD model reconstruction method of topological optimization result, the method comprises the following steps: Figure 1

[0080] Step S101, generating a triangular grid model to be reconstructed based on a three-dimensional topological optimization result.

[0081] Step S102, performing grid preprocessing on the triangular grid model to be reconstructed to obtain a preprocessed triangular grid model, wherein the triangular grid model to be reconstructed is a grid model extracted from a topological optimization structure, the triangular grid model to be reconstructed has jagged boundaries and redundant vertices, and the preprocessed triangular grid model does not have jagged boundaries and redundant vertices;

[0082] ​The topological optimization structure of the embodiments of the present application is not limited to a tubular topological optimization structure, but can also be a non-tubular topological optimization structure. The generation process of the topological optimization structure can be: setting the application scenario and boundary conditions of a product, modeling and topological optimization solving based on the set content, obtaining the topological optimization structure required by the embodiments of the present application, and the corresponding triangular mesh model to be reconstructed of the topological optimization structure.

[0083] The extraction of the triangular mesh model to be reconstructed from the three-dimensional topological optimization result involves the following contents:

[0084] The input of the extraction process is usually a pseudo-density field or a level set function field, and the density distribution of each element unit in the optimization result is stored in a matrix form.

[0085] The output of the extraction process: the extraction result is a triangular mesh model, and the available data formats include STL, OBJ and OFF, etc. STL format is full name Stereolithographic, which is a three-dimensional model file format. It uses triangular approximation to represent a three-dimensional model, and is currently considered by the industry as a standard description file format in the field of rapid prototyping. OBJ file is a standard three-dimensional model file format developed for a set of workstation-based three-dimensional modeling and animation software, which is very suitable for mutual guidance between three-dimensional software models. OFF is an object file format used to represent the geometry of a model given a surface polygon. Here, the polygon can have any number of vertices.

[0086] Extraction method: the Marching Cubes (MC) based isosurface extraction method can be used in the embodiments of the present application to generate a triangular mesh model.

[0087] The basic flow of the MC algorithm applied to the three-dimensional mesh model to be reconstructed in the embodiments of the present application includes: dividing the space into multiple cubes according to the arrangement of the units of the original topological optimization design domain, each cube corresponding to a density value in the density matrix, and setting the isosurface value C according to the density value; processing the cubes in the data field one by one, classifying the cubes intersecting with the isosurface, and using interpolation to calculate the intersection points of the isosurface and the edges of the cube; according to the relative position of each vertex of the cube and the isosurface, connecting the intersection points of the isosurface and the edges of the cube in a certain way to generate triangular faces as an approximate representation of the isosurface in the cube; connecting the triangular faces generated in each cube in the data field, and obtaining the extracted mesh model, i.e. the triangular mesh model to be reconstructed in the embodiments of the present application.

[0088] For the input topological optimization structure of the triangular mesh model to be reconstructed, the input triangular mesh model to be reconstructed (the embodiments of the present application take a Marshall beam as an example to illustrate the scheme, and the embodiments of the present application can also be applied to mesh models of other structures) is as followsFigure 2 Since the boundary of the triangle mesh model to be reconstructed is usually jagged, the reconstruction effect of the original mesh is not ideal. Therefore, Laplace smoothing and isotropic remeshing are performed on the original mesh respectively to reduce the anisotropy of the model and improve the smoothness, so as to improve the final reconstruction effect to a certain extent.

[0089] The topology optimization structure usually has a chessboard feature, so the triangle mesh model extracted from the isosurface of the optimization structure usually has jagged features and boundaries, the vertex data is large, and usually contains repeated points or coincident surfaces, forming a non-manifold mesh, and the model quality is low, which is not conducive to CAD model reconstruction. Therefore, before the subsequent steps of reconstruction, the input model needs to be pre-processed and optimized.

[0090] The mesh preprocessing method of the embodiment of the application can be Laplace smoothing and isotropic remeshing. Laplace smoothing, also known as add-one smoothing, is a technique used in statistical modeling to deal with zero probability problems. Laplace smoothing can make the original model jagged and the boundary smoother. Isotropic remeshing can eliminate redundant point and surface data, ensure that the mesh is a two-dimensional manifold, and also obtain a mesh with more uniform mesh distribution. Figure 2 The pre-processed triangle mesh model obtained after the triangle mesh model to be reconstructed shown in FIG. 1 is pre-processed is shown in FIG. 2. Figure 3

[0091] It should be noted that in the embodiment of the application, the iteration number of Laplace smoothing and isotropic remeshing in mesh preprocessing is usually not more than three, which can achieve an optimal mesh model optimization effect without changing the mechanical properties of the original topology optimization structure too much, and can also save operation steps and improve the efficiency of mesh preprocessing.

[0092] Step S103, performing component-type mesh segmentation on the pre-processed triangle mesh model to obtain at least two component sub-meshes, wherein the topology structure of the component sub-mesh is not a unit disc topology structure.

[0093] Step S104, performing patch-type mesh segmentation on each component sub-mesh respectively to obtain at least two sub-mesh patches, wherein the topology structure of the sub-mesh patch is a unit disc topology structure.

[0094] ​Topology optimization structure mostly has strong geometric symmetry characteristics. If surface-type mesh segmentation is directly performed on the entire model, a large number of sub-surface patches can be generated, thereby reducing the subsequent reconstruction efficiency. However, if only part-type mesh segmentation is performed on the entire model, the mesh patch obtained after part-type mesh segmentation has a mesh genus number greater than zero, and thus does not form a unit disc topology structure, which does not meet the parameterization requirement.

[0095] Therefore, the embodiment of the present application performs two segmentations on the preprocessed triangular mesh model: first, part-type mesh segmentation is performed, and then surface-type mesh segmentation is performed on the triangular mesh model after part-type mesh segmentation. Part-type mesh segmentation can divide the model into components (such as a person model, which can generate mesh distribution results such as head, hand, and foot) according to semantics such as “trunk” and “leg”. Surface-type mesh segmentation directly generates scattered surface patches according to model geometric information.

[0096] Specifically, part-type mesh segmentation can include the following steps:

[0097] Information features of all vertices of the preprocessed triangular mesh model are extracted. Each triangular surface patch of the preprocessed triangular mesh model is classified and predicted according to the information features. The preprocessed triangular mesh model is subjected to part-type mesh segmentation according to the classification and prediction results of the triangular surface patches, to obtain at least two component sub-meshes.

[0098] The above steps are actually a process of semantic segmentation of the preprocessed triangular mesh model. Semantic segmentation refers to dividing each element (pixel, vertex, surface patch, etc.) in image, vertex cloud, mesh, etc. data into different categories. In this embodiment, semantic segmentation is performed on each triangular surface patch in the triangular mesh model. Through the classification process, each triangular surface patch can be assigned to a corresponding category.

[0099] The preprocessed triangular mesh model is composed of triangular surface patches and vertices. Therefore, in some embodiments, a shape diameter function (SDF) segmentation method can also be used to perform part-type mesh segmentation on the preprocessed triangular mesh model. The SDF segmentation method is one of part-type mesh segmentation methods. As described above, the triangular mesh model can be divided into multiple components after part-type segmentation. The embodiment of the present application can divide the preprocessed triangular mesh model into multiple components based on the SDF segmentation method.

[0100] The SDF segmentation algorithm can include the following steps:

[0101] Step S401, calculate the SDF value. The calculation process of the SDF value: a vertex can be selected on the surface grid of the triangular mesh model, and a cone is made with the vertex as the cone vertex and the inverse direction of the vertex normal vector as the center line direction. Then, a plurality of rays are drawn from the vertex, which are limited in the cone range and intersect with the model surface grid. In order to avoid retaining the rays that may intersect with the error surface, only the rays with the normal direction consistent with the intersection point (i.e. the included angle between the ray and the normal is less than 90°) are selected. Finally, the length of all the rays is weighted and counted, and the SDF value of the vertex is obtained. SDF can establish the relationship between the surface of the mesh model and the volume of the enclosing body it is in, and obtain the local diameter (i.e. SDF value) of each patch position in the given mesh model. The SDF value represents the distance from the mesh surface to its corresponding enclosing region, which can be regarded as the thickness of the enclosing body of the patch.

[0102] Step S402, divide the grid of the preprocessed triangular mesh model into fixed regions with different widths or thicknesses according to the SDF value (similar local features usually have similar SDF values), that is, divide the preprocessed triangular mesh model into different component sub-meshes, and complete the component type mesh segmentation of the preprocessed triangular mesh model.

[0103] The SDF segmentation algorithm first performs soft clustering region segmentation on the mesh based on the SDF value size, and then combines the image segmentation algorithm based on the surface features to obtain the final segmentation result.

[0104] The triangular mesh model is composed of triangular patches, each triangular patch has three vertices, and each triangular patch contains a large number of features. The above semantic segmentation process extracts the information features of the vertices of the triangular patches, and the vertex information features can include the position, color, normal direction and other topological information of the vertices. Through the feature analysis of each vertex of the preprocessed triangular mesh model, combined with the corresponding relationship between each vertex and the triangular patch, the characteristics of each triangular patch in the model can be further understood, and then the triangular patches are classified.

[0105] For example, the triangular patches are classified into leg patches, top patches, connecting part patches, etc. Then, the preprocessed triangular mesh model can be segmented according to the classification results of the triangular patches to obtain leg, top, connecting part and other component sub-meshes. Figure 3 The segmentation result obtained after the component type mesh segmentation of the preprocessed triangular mesh model is shown in Figure 5 .

[0106] The face sheet type segmentation of the embodiments of the present application can adopt a hierarchical fuzzy clustering segmentation method (Hierarchical mesh decomposition using fuzzy clustering and cuts). The hierarchical fuzzy clustering segmentation method can segment a geometric model along a concave region into different geometric parts, and can avoid over-segmentation and jagged segmentation boundaries. The core idea of the hierarchical fuzzy clustering segmentation method is to first segment the geometric model using a fuzzy clustering method, and to retain a fuzzy region near the segmentation boundary, and then to find an accurate segmentation boundary in the fuzzy region using a minimum cut method.

[0107] In some embodiments, as shown in FIG. 6, applying the hierarchical fuzzy clustering segmentation method to the face sheet segmentation of the present application can include the following steps: Figure 6

[0108] Step S601: According to the distance between all adjacent triangular face sheets in the component sub-mesh, the initial probability of each triangular face sheet belonging to different segmentation regions is calculated. For example, for adjacent triangular face sheets A and B, the geodesic distance and the angular distance between them can be defined first. The geodesic distance is the distance between the centroids of A and B, and the angular distance is the angle between the perpendicular of A and the perpendicular of B. The two triangular face sheets farthest apart are selected as the seed face sheets of two segmentation regions M1 and M2, and the initial probability of face sheet A belonging to the two regions is calculated. For example, face sheet A is closer to region M1, and therefore the probability of face sheet A belonging to region M1 is greater.

[0109] Step S602: Based on the initial probability, the probability of each triangular face sheet belonging to different segmentation regions is iteratively adjusted until convergence, to obtain the final probability of each triangular face sheet belonging to different segmentation regions. The seed face sheets of the two segmentation regions M1 and M2 are iteratively updated using the fuzzy clustering method. The seed face sheets are recalculated. The above steps are iterated until the seed face sheets no longer change. The final probability of each face sheet belonging to the two regions is calculated.

[0110] Step S603: Based on the final probability, the segmentation boundary is determined. In the fuzzy region, the minimum cut method is used to find the accurate boundary. The result of the minimum cut in the mesh corresponds to the segmentation boundary with the largest dihedral angle in the fuzzy region in the mesh.

[0111] Step S604: Based on the segmentation boundary, the face sheet type mesh segmentation is performed on each component sub-mesh respectively, to obtain at least two sub-mesh face sheets.

[0112] It should be noted that in the embodiments of the present application, the face sheet type mesh segmentation is performed on each component sub-mesh respectively, and each component sub-mesh is segmented into several sub-face sheets. Based on the above hierarchical fuzzy clustering segmentation method, the component sub-mesh shown in FIG. 6 can be segmented into Figure 5 ​​Figure 7 The sub-grid patch result is shown.

[0113] In step S105, initial parameterization is performed on each sub-grid patch to obtain an initial parameterization result of each sub-grid patch. The initial parameterization can employ discrete harmonic mapping, discrete prolate mapping, or Floater mean coordinate method. The specific initial parameterization method is not limited in the embodiments of the present application.

[0114] In step S106, iterative parameterization is performed on each sub-grid patch based on the initial parameterization result to obtain a final parameterization result. The parameterization method employed in the initial parameterization can be different from the parameterization method employed in the iterative parameterization, or the same parameterization method can be employed.

[0115] Parameterization of a surface refers to establishing a one-to-one mapping relationship between the surface and a parameter domain. In essence, the parameter domain also belongs to the surface. Parameterization of a surface is to establish a one-to-one mapping relationship between two surfaces. Parameterization includes planar parameterization and spherical parameterization. The embodiments of the present application employ planar parameterization method for mapping.

[0116] Planar parameterization is a technology of unfolding a triangular mesh of a three-dimensional geometric model to a two-dimensional plane. The triangular mesh is converted into a planar mesh while ensuring the usability of the generated planar triangular mesh in applications. For a mesh with a closed or arbitrary topology, the surface thereof can be divided into a plurality of sub-patches, and each patch can be independently parameterized. The more the number of sub-patches, the smaller the deformation in the mapping process, but the continuity of the parameterization result can be reduced. Before planar parameterization, in order to reduce the distortion caused by parameterization mapping or when processing a mesh model with a complex topology, the mesh of the model is usually appropriately cut, i.e., the patch cutting process in the above embodiments. After cutting, planar parameterization is performed on each patch.

[0117] In some embodiments, as shown in FIG. 8, the specific process of parameterization of the present application includes the following steps: Figure 8

[0118] In step S801, a unit square parameter domain is created. The unit square parameter domain is the parameter domain to which the sub-grid patch structure needs to be mapped.

[0119] In step S802, the sub-grid patch is mapped to the unit square parameter domain by using Floater shape-preserving mapping method to obtain an initial parameterization result of each sub-grid patch. The initial parameterization result is the initial two-dimensional parameter coordinates of the sub-grid patch in the unit square parameter domain.

[0120] ​Step S803: Based on the initial parameterization result, i.e., based on the initial two-dimensional parameter coordinates, each sub-mesh patch is iteratively mapped to the unit square parameter domain using a mapping method until the geometric stretching value during the parameterization process no longer decreases. This yields the final parameterization result for each sub-mesh patch, where the final parameterization result is the final two-dimensional parameter coordinates of the sub-mesh patch in the unit square parameter domain. The parameterization method used for the iterative mapping does not have to be Floater Shape-preserving parameterization. For example, one of the following parameterization methods can be used: convex combination method, energy minimization method, and free boundary method.

[0121] This application uses an energy minimization method as the iterative parameterization method. The specific process is as follows: based on the initial parameterization structure, iterative calculations are performed. In each iteration, a weighted quadratic energy minimization operation is performed on the geometric stretching value of the target parameter to gradually reduce the geometric stretching value of the model until it no longer decreases. That is, the geometric stretching value corresponding to the parameterization result after the first iteration is less than the geometric stretching value corresponding to the initial parameterization result; the geometric stretching value corresponding to the parameterization result after the second iteration is less than the geometric stretching value corresponding to the parameterization result after the first iteration, and so on, until the geometric stretching value corresponding to the parameterization result after the Nth iteration is... The geometric stretching value is greater than the parameterization result corresponding to the (N-1)th iteration. End the iterative parameterization process. If the geometric stretch value obtained by the current parameterization is still less than the geometric stretch value obtained by the previous parameterization, continue the iterative parameterization process.

[0122] In each iteration, the locally weighted quadratic energy E(u) is gradually decreased. i ), which is defined as follows:

[0123] E(u i )=∑ j w ij (u j -u i ) 2 Among them, w ij For positive weights, the parameter domain grid point u i for

[0124] (i / (n-1),j / (n-1)), i,j=0,1,…,n-1.

[0125] During iteration, u is updated by solving the following sparse linear equation. i :

[0126] ∑ j w ij (u j -u i ) = 0.

[0127] The target parameter to be reduced in each iteration is the geometric stretch value, which is a measure of the parameterization effect and represents the distortion of the model in the two coordinate axes of the unit square parameter domain. Generally, the lower the geometric stretch value, the better the parameterization result of the model. The embodiments of the present application can use the L2 geometric stretch value (L ∞ The L2 geometric stretch value is generally used to measure the worst-case parameterization result of the model, and the L2 geometric stretch value is more universal. For any triangle T on the mesh model, an energy ∑ stretc h(T) corresponding to the average value of stretching in all directions is defined, and the local energy of each triangle T is combined into a global energy ∑ stretc h(S). The average value energy and the global energy are defined as follows:

[0128]

[0129] Where σ1 and σ2 are the axis lengths of the anisotropy ellipse, and A T represents the area of the triangle T. After the parameterization process, the mesh vertices p i (x, y, z) of each triangle T are mapped to the unit square parameter domain to generate a one-to-one corresponding two-dimensional parameter domain coordinate (i.e., the final two-dimensional parameter coordinate) u i (s, t). As shown in the figure, in order to verify the parameterization effect, the two-dimensional parameter domain coordinate can be used as a texture coordinate to add a black and white square texture to the model, and the parameterization effect is displayed. If the parameterization effect is not good, the parameterization process can be performed again. Figure 9

[0130] Step S106, based on the final parameterization result, uniform interpolation sampling is performed to obtain a plurality of groups of sampling points.

[0131] In some embodiments, as shown in the figure, the uniform interpolation sampling based on the final parameterization result can include the following steps: Figure 10

[0132] Step S1001, a straight line grid is set in the unit square parameter domain. The straight line grid is an (n x n) straight line grid.

[0133] Step S1002, in the straight line grid, uniform interpolation is performed based on the final two-dimensional parameter coordinate to obtain a uniform interpolation point set. On the (n x n) straight line grid, the two-dimensional parameter domain coordinate u i (s, t) is uniformly interpolated to obtain a uniform interpolation point u' i (i / (n-1), J / (n-1)), where i, j = 0, 1,..., n-1.

[0134] ​​Step S1003, determining the final two-dimensional parameter coordinates of the sub-grid patch closest to the uniform interpolation point in the uniform interpolation point set as the reference two-dimensional parameter coordinates. Assuming that the triangle patch closest to any uniform interpolation point p(x, y) in the unit square parameter domain plane is ΔABC, the final two-dimensional parameter coordinates x A ,x B ,x C ,y A ,y B ,y C of the three vertices of the triangle patch ΔABC are obtained, and the final two-dimensional parameter coordinates are determined as the reference two-dimensional parameter coordinates.

[0135] Step S1004, according to the two-dimensional coordinates (x, y) of the uniform interpolation point and the reference two-dimensional parameter coordinates x A ,x B ,x C ,y A ,y B ,y C of the sub-grid patch, the barycentric coordinate interpolation formula is used to calculate the barycentric coefficients corresponding to the uniform interpolation point, and the barycentric coordinate interpolation formula is:

[0136] (x, y) = αA + βB + γC, α + β + γ = 1,

[0137]

[0138] where (x, t) is the two-dimensional coordinates of the uniform interpolation point, α, β, γ are the barycentric coefficients, (x A ,t A ), (x B ,y B ), (x C ,y C ) are the final two-dimensional parameter coordinates of the three vertices A, B, C of the triangle patch ΔABC of the sub-grid patch, respectively.

[0139] Step S1005, for the three-dimensional grid vertices of the sub-grid patch where the uniform interpolation point is located, the barycentric coordinate interpolation formula and the barycentric coefficients are used to calculate the three-dimensional vertex space coordinates corresponding to the uniform interpolation point, wherein the three-dimensional vertex space coordinates corresponding to the uniform interpolation point are the three-dimensional space coordinates of the sampling point.

[0140] After obtaining the barycentric coefficients corresponding to the uniform interpolation point p from step S1004, through the parameterization mapping relationship, the three-dimensional grid vertices p i (x, y, z) of the triangle patch where the uniform interpolation point p is located are obtained again, and the barycentric coordinate interpolation formula is applied to obtain the coordinates p i(x',y',z'). The final sampling points are the uniform space vertices, and the comparison between the original triangular mesh and the sampling points is shown in FIG. 2. Figure 11 In FIG. 2, the black lines are the original triangular mesh, and the points covered on the black lines are the sampling points. Figure 11 In FIG. 2, the black lines are the original triangular mesh, and the points covered on the black lines are the sampling points.

[0141] In step S108, a spline surface corresponding to each sub-mesh patch is generated by using the sampling points. It should be noted that each sub-mesh patch can obtain a set of parameterization results and sampling point results, and one set of sampling points can only generate one spline surface. That is, one sub-mesh corresponds to one parameterization result, and corresponds to one set of sampling points and one spline surface. Therefore, in step S108, multiple spline surfaces can be generated by using multiple sets of sampling points.

[0142] The specific process of generating a spline surface by using the above set of sampling points is as follows: the control points of the spline patch are determined according to the geometric stretching values corresponding to the final parameterization results of each sub-mesh patch; and the spline surface is generated according to the three-dimensional space coordinates of the sampling points, the control points and the node vectors of the control points.

[0143] The B-spline surface can be divided into U and V directions in the parameter domain. The sampling points uniformly distributed on the unit square parameter domain are arranged as spline control points in U and V directions to generate a spline surface. For example, the B-spline surface is set to be of order 3, the number of control points is set according to the target reconstruction model, and the quasi-uniform node vector with a repetition degree node vector of [4, 1, 1, …, 1, 4] is selected to generate the spline surface.

[0144] In this embodiment, the number of spline patch control points can be dynamically set according to the geometric stretching values of each sub-mesh parameterization stage. When the stretching value ranges from 0 to 6, from 6 to 10, from 10 to 14, from 14 to 25 and from 25 to 35, the number of spline control points of the sub-mesh is set to (7x7), (9x9), (15x15), (21x21) and (41x41), respectively. Taking the (7x7) control points as an example, the node vectors in two directions are [0, 0, 0, 0, 1, 2, 3, 4, 4, 4, 4]. This embodiment finally includes 71 spline surfaces, and the number of control points of the patches with (7x7), (9x9) and (21x21) is 22, 37 and 12, respectively. The total number of control points is 9367.

[0145] The generated three-dimensional vertex coordinates usually have two processing methods: manually setting node vector data and the like, directly taking them as spline control points to generate a spline surface; or taking them as type value points to perform surface fitting operation to obtain new control points. The application directly takes the generated three-dimensional vertex coordinates as spline control points, and then generates a spline surface. This spline surface generation method can avoid complex surface fitting operation, and the calculation process is simpler, and it is also convenient for accurately adjusting the number of control points.

[0146] In step S109, the spline surface is assembled to generate a reconstructed CAD model corresponding to the topological optimization structure. The specific steps of generating the reconstructed CAD model by using the spline surface can include: connecting all the spline surfaces through adjacent edges to generate a reconstructed CAD model corresponding to the three-dimensional topological optimization result. The finally generated reconstructed CAD model corresponding to the topological optimization structure is as shown in Figure 12 .

[0147] As shown in Figure 13 , the embodiment of the application provides a CAD model reconstruction device for a topological optimization result, which includes:

[0148] The model generation unit 1301 is configured to perform: generating a triangular mesh model to be reconstructed based on a three-dimensional topological optimization result;

[0149] The mesh preprocessing unit 1302 is configured to perform: performing mesh preprocessing on the triangular mesh model to be reconstructed to obtain a preprocessed triangular mesh model, wherein the triangular mesh model to be reconstructed is a mesh model extracted from a topological optimization structure, the triangular mesh model to be reconstructed has jagged boundaries and redundant vertices, and the preprocessed triangular mesh model does not have jagged boundaries and redundant vertices; the component-type mesh segmentation unit 1303 is configured to perform: performing component-type mesh segmentation on the preprocessed triangular mesh model to obtain at least two component sub-meshes, wherein the topological structure of the component sub-mesh is not a unit disc topological structure;

[0150] The patch-type mesh segmentation unit 1304 is configured to perform: respectively performing patch-type mesh segmentation on each of the component sub-meshes to obtain at least two sub-mesh patches, wherein the topological structure of the sub-mesh patch is a unit disc topological structure;

[0151] The initial parameterization unit 1305 is configured to perform: performing initial parameterization on each of the sub-mesh patches to obtain an initial parameterization result of each sub-mesh patch;

[0152] The iteration parameterization unit 1306 is configured to perform: performing iterative parameterization on each of the sub-grid patches based on the initial parameterization result, to obtain a final parameterization result of each sub-grid patch, wherein the parameterization method used in the initial parameterization and the parameterization method used in the iterative parameterization can be different parameterization methods, or the same parameterization method is used.

[0153] The sampling unit 1306 is configured to perform: performing uniform interpolation sampling based on each of the final parameterization results, to obtain a plurality of groups of sampling points.

[0154] The spline surface generation unit 1307 is configured to perform: generating a spline surface corresponding to each sub-grid patch by using the sampling points.

[0155] The CAD model assembly unit 1308 is configured to perform: assembling the spline surfaces to generate a reconstructed CAD model corresponding to the three-dimensional topology optimization result.

[0156] In the CAD model reconstruction device of the topology optimization result according to the embodiments of the present application, each reconstruction link is realized by each unit, and therefore each reconstruction link is highly independent. In the application process, for topology optimization structures with different geometric characteristics, the preprocessing method, the mesh segmentation method, and the parameterization method can be replaced modularly, so as to further improve the reconstruction efficiency and the reconstruction quality.

[0157] The device embodiments described above are only schematic, and the units described as separate components can or can not be physically separate, and the components shown as units can or can not be physical units, that is, they can be located in one place, or distributed on multiple network units. Part or all of the modules can be selected according to actual needs to achieve the purpose of the embodiments. Those skilled in the art can understand and implement without creative labor.

[0158] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be realized by means of software and necessary general hardware platforms, and of course, it can also be realized by hardware. Based on such understanding, the above technical solutions can be embodied in the form of a software product, which can be stored in a computer readable storage medium, such as a ROM / RAM, a magnetic disk, an optical disk, etc., and includes a plurality of instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute the methods described in each embodiment or some parts of the embodiments.

[0159] It should be pointed out finally that the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit the same; and although the present application has been described in detail with reference to the foregoing embodiments, it should be appreciated by those skilled in the art that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features thereof can be replaced equivalently; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A CAD model reconstruction method of a topology optimization result, characterized by, The method comprises the following steps: generating a triangular mesh model to be reconstructed based on a three-dimensional topological optimization result; performing mesh preprocessing on the triangular mesh model to be reconstructed to obtain a preprocessed triangular mesh model, wherein the triangular mesh model to be reconstructed is a mesh model extracted from a topological optimization structure, the triangular mesh model to be reconstructed has jagged boundaries and redundant vertices, and the preprocessed triangular mesh model does not have jagged boundaries and redundant vertices; performing component-type mesh segmentation on the preprocessed triangular mesh model to obtain at least two component sub-meshes, wherein the topological structure of the component sub-meshes is not a unit disc topological structure; performing patch-type mesh segmentation on each of the component sub-meshes to obtain at least two sub-mesh patches, wherein the topological structure of the sub-mesh patches is a unit disc topological structure; performing initial parameterization on each of the sub-mesh patches to obtain an initial parameterization result of each sub-mesh patch; performing iterative parameterization on each of the sub-mesh patches based on the initial parameterization result to obtain a final parameterization result of each sub-mesh patch; performing uniform interpolation sampling based on each of the final parameterization results to obtain a plurality of groups of sampling points; generating a spline surface corresponding to each sub-mesh patch by using the sampling points; assembling the spline surfaces to generate a reconstructed CAD model corresponding to the three-dimensional topological optimization result.

2. The method of claim 1, wherein, The preprocessed triangular mesh model is composed of triangular patches and vertices. The component-type mesh segmentation on the preprocessed triangular mesh model to obtain at least two component sub-meshes comprises the following steps: extracting information features of all vertices of the preprocessed triangular mesh model; performing classification prediction on each triangular patch of the preprocessed triangular mesh model according to the information features; performing component-type mesh segmentation on the preprocessed triangular mesh model to obtain at least two component sub-meshes according to the classification prediction results of the triangular patches.

3. The method of claim 2, wherein, The patch-type mesh segmentation on each of the component sub-meshes to obtain at least two sub-mesh patches comprises the following steps: calculating an initial probability that each triangular patch belongs to different segmentation regions according to the distances between all adjacent triangular patches in the component sub-meshes; iteratively adjusting the probability that each triangular patch belongs to different segmentation regions based on the initial probability until convergence to obtain a final probability that each triangular patch belongs to different segmentation regions; determining a segmentation boundary based on the final probability; performing patch-type mesh segmentation on each of the component sub-meshes based on the segmentation boundary to obtain at least two sub-mesh patches.

4. The method of claim 1, wherein, The initial parameterization on each of the sub-mesh patches to obtain an initial parameterization result of each sub-mesh patch comprises the following steps: creating a unit square parameter domain; mapping the sub-mesh patches to the unit square parameter domain by using the Floater Shape-preserving method to obtain an initial parameterization result of each sub-mesh patch, wherein the initial parameterization result is an initial two-dimensional parameter coordinate of the sub-mesh patch in the unit square parameter domain.

5. The method of claim 4, wherein, The iterative parameterization of each of the sub-grid patches based on the initial parameterization result comprises: Based on the initial parameterization result, the sub-grid patches are iteratively mapped to the unit square parameter domain until the geometric stretching value in the parameterization process no longer decreases, to obtain the final parameterization result of each sub-grid patch, wherein the final parameterization result is the final two-dimensional parameter coordinates of the sub-grid patch in the unit square parameter domain, and the parameterization method adopted in the iterative parameterization is one of the convex combination method, the minimum energy method and the free boundary method.

6. The method of claim 5, wherein, The uniform interpolation sampling based on each of the final parameterization results comprises: A straight grid is set in the unit square parameter domain; In the straight grid, uniform interpolation is performed based on the final two-dimensional parameter coordinates to obtain a uniform interpolation point set; The final two-dimensional parameter coordinates of the three vertices of the triangular patch of the sub-grid patch closest to the uniform interpolation point in the uniform interpolation point set are determined as reference two-dimensional parameter coordinates; According to the two-dimensional coordinates of the uniform interpolation point and the reference two-dimensional parameter coordinates, the barycentric coordinate interpolation formula is used to calculate the barycentric coefficients corresponding to the uniform interpolation point, and the barycentric coordinate interpolation formula is: γ=1-α-β wherein (x, y) is the two-dimensional coordinate of the uniform interpolation point, a, b, g are the barycentric coefficients, (x A ,y A ),(x B ,y B ),(x C ,y C ) are the final two-dimensional parametric coordinates of the three vertices A, B, C of the triangular patch ΔABC of the sub-grid patch, respectively. The barycentric coordinate interpolation formula and the barycentric coefficients are used to calculate the three-dimensional vertex space coordinates corresponding to the uniform interpolation point for the three-dimensional grid vertices of the sub-grid patch where the uniform interpolation point is located, wherein the three-dimensional vertex space coordinates corresponding to the uniform interpolation point are the three-dimensional space coordinates of the sampling point.

7. The method of claim 6, wherein the CAD model reconstruction of the topology optimization result is performed by a computer. The generation of at least two spline surfaces using the sampling points comprises: The uniform interpolation points are determined as spline control points according to the three-dimensional space coordinates corresponding to the uniform interpolation points; The spline surfaces are generated according to the spline control points.

8. The method of claim 7, wherein, The assembly of the spline surfaces to generate a reconstructed CAD model corresponding to the three-dimensional topological optimization result comprises: All the spline surfaces are connected through adjacent edges to generate a reconstructed CAD model corresponding to the three-dimensional topological optimization result.

9. The method of claim 1, wherein, The grid preprocessing comprises Laplace smoothing and isotropic regridding, wherein the number of iterations of the Laplace smoothing and isotropic regridding is not more than three.

10. A CAD model reconstruction apparatus of a topology optimization result, characterized by, The grid model reconstruction device of the topologically optimized structure comprises: A model generation unit configured to perform: generating a triangular grid model to be reconstructed based on a three-dimensional topological optimization result; A grid preprocessing unit configured to perform: performing grid preprocessing on the triangular grid model to be reconstructed to obtain a preprocessed triangular grid model, wherein the triangular grid model to be reconstructed is a grid model extracted from a topologically optimized structure, the triangular grid model to be reconstructed has jagged boundaries and redundant vertices, and the preprocessed triangular grid model does not have jagged boundaries and redundant vertices; A component-type grid segmentation unit configured to perform: performing component-type grid segmentation on the preprocessed triangular grid model to obtain at least two component sub-grids, wherein the topological structure of the component sub-grid is not a unit disc topological structure; The patch-type mesh segmentation unit is configured to perform patch-type mesh segmentation on each of the component sub-meshes to obtain at least two sub-mesh patches, wherein the sub-mesh patches have a unit disc topology structure. The initial parameterization unit is configured to perform initial parameterization on each of the sub-mesh patches to obtain initial parameterization results of the sub-mesh patches. The iterative parameterization unit is configured to perform iterative parameterization on each of the sub-mesh patches based on the initial parameterization results to obtain final parameterization results of the sub-mesh patches. The sampling unit is configured to perform uniform interpolation sampling based on the final parameterization results to obtain a plurality of groups of sampling points. The spline surface generation unit is configured to generate a spline surface corresponding to each of the sub-mesh patches by using the sampling points. The CAD model assembly unit is configured to assemble the spline surfaces to generate a reconstructed CAD model corresponding to the three-dimensional topology optimization result.

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