A 3D CAD Reconstruction Method for Pixel-based Topology Optimization Results
By smoothing the topological optimization results, skeleton line extraction and simplification, coarse skeleton generation and Catmull-Clark body segmentation methods, the problems of serratedization and large number of Bézier bodies when the topological optimization results are converted into Bézier body models are solved, and the smooth reconstruction and manufacturability of the model are achieved.
Patent Information
- Application Number
- CN202210452502.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-04-27
- Publication Date
- 2025-05-27
- Estimated Expiration
- 2042-04-27
AI Technical Summary
When the discrete voxel model generated by topology optimization is directly converted into a Bézier body model, it is prone to serration on the model surface and the large number of Bézier bodies generated, which reduces the manufacturability of the model.
A three-dimensional CAD reconstruction method for pixel-oriented topology optimization results is proposed, including smooth operation, extraction of triangular mesh skeleton lines, simplifying skeleton lines, generating thick skeleton models, and generating Bézier body models through Catmull-Clark body segmentation and projection operations.
Effectively eliminates the jagged structure of the discrete hexahedral mesh model, significantly reducing the number of generated Bézier blocks, and improving the smoothness and manufacturability of the model.
Smart Images
Figure CN114707388B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of CAD reconstruction after topology optimization, and specifically refers to a three-dimensional CAD reconstruction method for pixel-based topology optimization results. Background Art
[0002] With the improvement of computer computing power and the development of Computer Aided Engineering (CAE), through the analysis of the structural strength of the model calculated by computer simulation, the structural defects of the model can be found, and then the structural strength of the model can be improved by redesigning, which greatly increases the time cost required for the model design process. Generative Design emerged as the times require. Generative Design uses specific algorithm strategies to automatically design items to meet certain stiffness conditions, with the goal of minimizing the mass of the designed product or other corresponding design objectives. The commonly used algorithm strategies have evolved from simple size optimization at the beginning to more complex shape optimization later, and finally to the more difficult topology optimization currently. Topology optimization is to seek the optimal value of a certain index of the structure under the conditions that the structural components meet stress, displacement and other constraints. The common index is to minimize the mass of the structure or minimize the use of materials.
[0003] For the discrete voxel model generated by topology optimization, if it is directly converted into a Bézier solid model, there will be problems such as jaggedness on the model surface and a large number of generated Bézier solids, which reduces the manufacturability of the model.
[0004] In summary, how to effectively reconstruct the topology optimization results, generate a smooth model and keep the number of Bézier solid blocks of the model small is an urgent problem to be solved currently. Summary of the Invention
[0005] According to the deficiencies of the prior art, the present invention proposes a three-dimensional CAD reconstruction method for pixel-based topology optimization results.
[0006] To solve the above technical problems, the technical solution of the present invention is as follows:
[0007] A three-dimensional CAD reconstruction method for pixel-based topology optimization results includes the following steps:
[0008] S1. Perform a smoothing operation on the discrete voxel model generated by the topology optimization result, where the discrete voxel model is a three-dimensional object model represented by an ordered combination of regular cubes;
[0009] S2. Extract the triangular mesh on the surface of the smoothed discrete voxel model to generate the skeleton line of the triangular mesh model, that is, a curve with the same connectivity and topological structure as the original triangular mesh model;
[0010] S3. Simplify the skeleton lines of the triangular mesh model;
[0011] S4. Generate a coarse skeleton model
[0012] S4-1. Interactively adjust the skeleton nodes of the triangular mesh model;
[0013] S4-2. Optimize the angles of the skeleton nodes of the triangular mesh model;
[0014] S4-3. Establish intermediate connecting hexahedron elements and perform topological splitting operations to generate a coarse skeleton model;
[0015] S5. Perform Catmull-Clark volume subdivision on the coarse skeleton model and project the surface vertices onto the surface triangular mesh generated in step S2 to generate a Bézier volume model.
[0016] Preferably, in step S1, a hexahedron mesh smoothing operation is performed, and the hexahedron mesh adopts the Laplacian mesh smoothing method, and the expression is as follows:
[0017]
[0018] where Adj represents the neighborhood of a vertex, and U(P i ) is the coordinate mean of the neighborhood of a vertex.
[0019] Preferably, the Laplacian mesh smoothing method is specifically as follows:
[0020] 1) Initialize the entire hexahedron mesh, and extract the boundary vertices and internal vertices;
[0021] 2) Traverse the boundary vertices, then calculate the positions and S of the 1-neighborhood points of the boundary points, and the 1-neighborhood points of the boundary points do not include the internal vertices. Traverse the internal vertices and calculate the positions and S' of the 1-neighborhood points of the internal points;
[0022] 3) Place the boundary points at S / n, where n is the number of 1-neighborhood vertices, and place the internal points at S' / n.
[0023] Preferably, step S2 includes the following sub-steps:
[0024] S2-1. Traverse the discrete voxel model after step S1, and convert the boundary quadrilateral faces of the model into a triangular mesh model by adding an auxiliary edge in the faces, that is, the model structure with the surface represented by triangles;
[0025] S2-2. First, refine the extracted triangular mesh model through the Loop subdivision method. Then, utilize the extreme value property of the curvature of the triangular mesh to extract the skeleton line of the model, that is, a curve that is consistent with the connectivity and topological structure of the original triangular mesh model.
[0026] Preferably, the method for simplifying the skeleton line in step S3 is as follows:
[0027] S3-1. Segment the obtained skeleton line, and extract the skeleton segments by segmenting the nodes with a degree greater than 2 and the nodes with a degree equal to 1.
[0028] S3-2. Use the B-spline fitting algorithm to perform a fitting operation on the segmented skeleton line. By solving the coefficient matrix
[0029]
[0030] obtain the control vertices and knot vectors of the B-spline. Among them, Q k represents the vertex to be interpolated, and P i represents the obtained control vertex. represents the parameter of the B-spline curve, and is selected through chord length parameterization.
[0031] Let d be the total chord length.
[0032]
[0033] And let
[0034] S3-3. First, calculate the closest distance from the end points, that is, the skeleton nodes with a degree greater than 2 or a degree equal to 1, to the surface triangular mesh as its radius, and calculate the closest distance from the nodes at the middle position of the segmented skeleton to the surface triangular mesh, and judge whether the nodes at the middle position intersect with the nodes at both ends of this skeleton line.
[0035] S3-4. If they do not intersect, repeat steps S3-1 to S3-3 until they intersect, then stop the skeleton nodes and continue to step S3-5.
[0036] S3-5. Merge the skeleton nodes generated by multiple segments of skeleton lines to generate a globally simplified skeleton.
[0037] S3-6. Perform a merging operation on the intersecting skeleton nodes. Merge these two partially intersecting nodes, delete one of the nodes, and transfer the nodes it connects to the remaining node.
[0038] Preferably, in step S4-1, perform displacement, rotation, splitting, extension, addition, and deletion operations on the nodes of the skeleton.
[0039] Preferably, in the step S4-2,
[0040] 1) For nodes with a degree greater than 2, use the cube angle adjustment algorithm proposed by Usai. The expression is as follows:
[0041]
[0042] where U i , V i , W i are mutually perpendicular vectors with the length, width, and height of the node as the vector lengths, d i is the unit vector emitted by a node. By optimizing it, the node can reduce the number of node splits in the form of a rotation angle. ε is the iteration parameter, with an initial value of 0.5 and halved in each subsequent iteration;
[0043] 2) Adopt the rotation angle minimization method to adjust the angles of nodes with a degree of 2. Start generating a frame along the nodes with a degree greater than 2, then adjust the angles of the intermediate skeleton nodes, use the frame to generate a hexahedron of the skeleton nodes, and generate hexahedron skeleton nodes by extending in the direction of the frame.
[0044] Preferably, in the step S4-3, generate an intermediate connector, generate hexahedron units in the middle connecting the skeleton nodes. If one face of a node connects multiple skeleton nodes, perform a topological splitting operation, that is, split a node into multiple nodes and eliminate the characteristic that one face connects multiple skeleton nodes, and finally generate a coarse skeleton model.
[0045] Preferably, the step S5 includes the following sub-steps:
[0046] S5-1. Perform Catmull-Clark volume subdivision operation on the coarse skeleton model to generate coarse skeleton models with different resolutions;
[0047] S5-2. Perform a projection operation, project the surface vertices of the coarse skeleton model onto the surface triangular mesh model generated in step S2 using their vertex vectors;
[0048] S5-3. Convert the projected model into a Bézier volume model by generating a hexahedron mesh limit body approximation.
[0049] Preferably, the converted model has the advantages of a continuous surface and a small number of Bézier volume blocks forming the model. One hexahedron unit is converted into a Bézier volume block model with 64 control vertices. The specific conversion method is as follows:
[0050] The 64 control vertices of the generated Bézier volume element are as follows: 8 corner points are located at the 8 corners of the volume; 8 interior points are inside the volume element; 24 edge points are on the 12 edges of the volume, with 2 edge points on each edge; 24 face points are on the 6 faces of the volume, with 4 face points on each face.
[0051] 1) The 8 corner points correspond to the 8 corner points of a hexahedron element, and the generated 8 corner point control vertices are equal to the corresponding limit points of the Catmull-Clark subdivision volume.
[0052] 2) Calculation method of interior point control points. Denote the neighborhood of the hexahedron mesh element where point v is located as L = v, e 1 , e 2 , e 3 , f 1 , f 2 , f 3 , c, where e 1 , e 2 , e 3 represents the coordinates of adjacent edge points. Adjacent edge points refer to another point on the same edge as v. There are 3 adjacent edge points in a hexahedron mesh element; f 1 , f 2 , f 3 represents the coordinates of adjacent face points. Adjacent face points refer to points on the same face as v but not on the same edge. There are 3 adjacent face points in a hexahedron; c represents the coordinates of adjacent block points. Adjacent block points refer to points in the same hexahedron mesh as v but not on the same face. There is one adjacent block point in a hexahedron.
[0053] In the hexahedron mesh element, the coordinates v of the interior point adjacent to point v in The calculation formula is
[0054]
[0055] 3) If you want to calculate the coordinates of edge points, face points or corner points of a hexahedron mesh element, you only need to calculate the coordinates of the interior point closest to the edge point, face point or corner point to be calculated on each hexahedron mesh element containing the edge point, face point or corner point to be calculated, and then take the average of the coordinates of these interior points obtained, that is
[0056]
[0057] where n is the number of hexahedron mesh elements containing the edge point, face point or corner point to be calculated, is the coordinate of the interior point closest to the edge point, face point or corner point to be calculated on the t-th hexahedron mesh element containing the edge point, face point or corner point to be calculated.
[0058] The present invention has the following characteristics and beneficial effects:
[0059] By adopting the above technical solution, it is possible to conveniently and efficiently convert the discrete hexahedron mesh model generated by topology optimization into a Bézier solid model, which has a significant advantage in the number of generated Bézier solid models. At the same time, the jagged structure of the discrete hexahedron mesh model is eliminated, and it has application value in the field of topology optimization. Subsequently, the model reconstructed by CAD can also be applied to isogeometric analysis and has application value in the field of isogeometric analysis. BRIEF DESCRIPTION OF THE DRAWINGS
[0060] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.
[0061] Figure 1 It is the flowchart of the method for the embodiment of the present invention.
[0062] Figure 2 (a) It is the discrete voxel model diagram generated by topology optimization in the present invention.
[0063] Figure 2 (b) It is the surface triangular mesh model diagram extracted after hexahedron mesh smoothing in the present invention.
[0064] Figure 3 (a) It is the schematic diagram of the model skeleton extracted in the present invention.
[0065] Figure 3 (b) It is the model skeleton diagram generated after simplifying the skeleton in the present invention.
[0066] Figure 4 (a) It is the rough skeleton model diagram generated after adjustment.
[0067] Figure 4 (b) It is the Bézier solid model generated by projection in the present invention.
[0068] Figure 5 (a) It is the rough skeleton subdivision model diagram generated after adjustment.
[0069] Figure 5 (b) It is the Bézier solid model generated by projection in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0070] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.
[0071] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise stated, the meaning of "a plurality" is two or more than two.
[0072] In the description of the present invention, it should be noted that unless otherwise clearly specified and limited, the terms "mounted", "connected", and "coupled" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood through specific situations.
[0073] The present invention provides a three-dimensional CAD reconstruction method for pixel-based topology optimization results, as Figure 1 shown, including the following steps:
[0074] S1. Perform a smoothing operation on the discrete voxel model generated from the topology optimization result, where the discrete voxel model is a three-dimensional object model represented by an ordered combination of a large number of regular cubes;
[0075] Specifically, perform a hexahedron mesh smoothing operation. The hexahedron mesh uses the Laplacian mesh smoothing method, and the expression is as follows:
[0076]
[0077] where Adj represents the neighborhood of a vertex, and U(P i ) is the coordinate mean of the neighborhood of a vertex.
[0078] Among them, the Laplacian mesh smoothing method is specifically as follows:
[0079] 1) Initialize the entire hexahedron mesh, and extract the boundary vertices and internal vertices;
[0080] 2) Traverse the boundary vertices, then calculate the positions and S of the 1-neighborhood points of the boundary points, and the 1-neighborhood points of the boundary points do not include the internal vertices. Traverse the internal vertices and calculate the positions and S' of the 1-neighborhood points of the internal points;
[0081] 3) Place the boundary points at S / n, where n is the number of 1-neighborhood vertices, and place the internal points at S' / n.
[0082] S2. Extract the triangular mesh on the surface of the smoothed discrete voxel model to generate the skeleton line of the triangular mesh model, that is, a curve with the same connectivity and topological structure as the original triangular mesh model;
[0083] Specifically, it includes the following sub-steps:
[0084] S2-1. Traverse the discrete voxel model after step S1, and convert the boundary quadrilateral faces of the model into a triangular mesh model by adding an auxiliary edge in the face, that is, a model structure represented by triangles on the surface;
[0085] S2-2. First, refine the extracted triangular mesh model by the Loop subdivision method, and then, utilize the extreme value property of the curvature of the triangular mesh to extract the skeleton line, that is, a curve with the same connectivity and topological structure as the original triangular mesh model.
[0086] S3. Simplify the skeleton line of the triangular mesh model;
[0087] Among them, the method for simplifying the skeleton line is as follows:
[0088] S3-1. Segment the obtained skeleton line, and segment and extract the skeleton segments for the nodes with degrees greater than 2 and the nodes with degree equal to 1;
[0089] S3-2. Use the B-spline fitting algorithm to fit the segmented skeleton lines. By solving the coefficient matrix
[0090]
[0091] Obtain the control vertices and knot vectors of the B-spline, where Q k represents the vertex to be interpolated, P i represents the obtained control vertex, represents the parameter of the B-spline curve, and is selected by chord length parameterization
[0092] Let d be the total chord length
[0093]
[0094] And let
[0095] S3-3. First, calculate the shortest distance from the endpoints, i.e., the skeleton nodes with a degree greater than 2 or equal to 1, to the surface triangular mesh as their radius. Calculate the shortest distance from the nodes at the middle position of the segmented skeleton to the surface triangular mesh, and determine whether the nodes at the middle position intersect with the nodes at both ends of this skeleton line.
[0096] S3-4. If they do not intersect, repeat steps S3-1 to S3-3 until they intersect, then stop the skeleton nodes and continue with step S3-5.
[0097] S3-5. Merge the skeleton nodes generated by multiple segments of skeleton lines to generate a globally simplified skeleton.
[0098] S3-6. Perform a merge operation on the intersecting skeleton nodes. Merge these two partially intersecting nodes, delete one of the nodes, and transfer the nodes it connects to the remaining node.
[0099] S4. Generate a coarse skeleton model
[0100] S4-1. Interactively adjust the skeleton nodes of the triangular mesh model, and perform displacement, rotation, splitting, extension, addition, and deletion operations on the nodes of the skeleton.
[0101] S4-2. Perform an optimization operation on the angles of the skeleton nodes of the triangular mesh model;
[0102] 1) For nodes with a degree greater than 2, use the cube angle adjustment algorithm proposed by Usai. The expression is as follows:
[0103]
[0104] Among them, U i , V i , W i are mutually perpendicular vectors with the length, width, and height of the node as the vector lengths, d i is the unit vector emitted by a node. By optimizing it, the node can reduce the number of node splits by rotating a certain angle. ε is the iteration parameter, with an initial value of 0.5, and it is halved in each subsequent iteration;
[0105] 2) Adopt the method of minimizing the rotation angle to adjust the angles of the nodes with a degree of 2. Start generating a frame from the nodes with a degree greater than 2, then adjust the angles of the intermediate skeleton nodes, use the frame to generate a hexahedron of skeleton nodes, and generate hexahedron skeleton nodes by extending a certain distance in the direction of the frame.
[0106] S4-3. Establish intermediate connecting hexahedron units and perform topological splitting operations to generate a coarse skeleton model.
[0107] Specifically, an intermediate connector is generated to connect the skeleton nodes, and hexahedron units are generated in the middle. If one face of a node is connected to multiple skeleton nodes, a topological splitting operation is performed on it, that is, a node is split into multiple nodes and the characteristic of one face being connected to multiple skeleton nodes is eliminated. Finally, a coarse skeleton model is generated.
[0108] S5. Perform Catmull-Clark volume subdivision on the coarse skeleton model, and project the surface vertices onto the surface triangular mesh generated in step S2 to generate a Bézier volume model.
[0109] Specifically, it includes the following sub-steps:
[0110] S5-1. Perform Catmull-Clark volume subdivision on the coarse skeleton model to generate coarse skeleton models with different resolutions;
[0111] S5-2. Perform a projection operation, and project the surface vertices of the coarse skeleton model onto the surface triangular mesh model generated in step S2 using their vertex vectors;
[0112] S5-3. Convert the projected model into a Bézier volume model by generating a hexahedral mesh limit body approximation.
[0113] It can be understood that the converted model has the advantages of a continuous surface and a small number of Bézier volume blocks that make up the model. One hexahedron unit is converted into a Bézier volume block model with 64 control vertices. The specific conversion method is as follows:
[0114] The 64 control vertices of the generated Bézier volume unit are respectively: 8 corner points are at the 8 corners of the volume; 8 inner points are inside the volume unit; 24 edge points are on the 12 edges of the volume, with 2 edge points on each edge; 24 face points are on the 6 faces of the volume, with 4 face points on each face.
[0115] 1) The 8 corner points correspond to the 8 corner points of one hexahedron unit, and the 8 generated corner point control vertices are equal to the corresponding limit points of the Catmull-Clark subdivision volume.
[0116] 2) The calculation method of the inner point control points. Denote the neighborhood of the hexahedron mesh unit where the point v is located as L = v, e 1 , e 2 , e 3 , f 1 , f 2 , f 3 , c, where e 1 , e 2 , e 3Indicates the coordinates of adjacent edge points. An adjacent edge point represents another point on the same edge as v. There are 3 adjacent edge points within a hexahedral mesh element; f 1 ,f 2 ,f 3 Indicates the coordinates of adjacent face points. An adjacent face point represents a point on the same face as v but not on the same edge. There are 3 adjacent face points within a hexahedron; c indicates the coordinates of adjacent block points. An adjacent block point represents a point within the same hexahedral mesh as v but not on the same face. There is one adjacent block point within a hexahedron.
[0117] The coordinates of the interior point v adjacent to point v in this hexahedral mesh element in The calculation formula is
[0118]
[0119] 3) If you want to calculate the coordinates of an edge point, face point, or corner point of a hexahedral mesh element, you only need to calculate the coordinates of the interior point closest to the edge point, face point, or corner point to be found on each hexahedral mesh element containing the edge point, face point, or corner point to be found, and then take the average of the coordinates of these interior points found, that is
[0120]
[0121] where n is the number of hexahedral mesh elements containing the edge point, face point, or corner point to be found, is the coordinates of the interior point closest to the edge point, face point, or corner point to be found on the t-th hexahedral mesh element containing the edge point, face point, or corner point to be found.
[0122] Reference Figure 2 , Figure 2 (a) is the discrete voxel model generated by topology optimization.
[0123] Figure 2 (b) is the triangular mesh model diagram converted from the hexahedral mesh smoothed and the surface quadrilateral mesh extracted.
[0124] Reference Figure 3 , Figure 3 (a) is the schematic diagram of the operation in step 2. The skeleton line of the triangular mesh model is generated.
[0125] Figure 3 (b) is the schematic diagram of the skeleton generated in step 3 after simplification, with hexahedrons as the skeleton nodes.
[0126] Reference Figure 4 , Figure 4 (a) is the rough skeleton model diagram generated in step 4.
[0127] Figure 4(b) Schematic diagram of the Bézier volume model generated by projecting onto the surface triangular mesh model.
[0128] Reference Figure 5 , Figure 5 (a) is Figure 4 (a) Schematic diagram of the model after Catmull-Clark volume subdivision.
[0129] Figure 5 (b) is Figure 5 (a) Schematic diagram of the Bézier volume model generated by projecting onto the surface triangular mesh model.
[0130] The embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, without departing from the principles and spirit of the present invention, various changes, modifications, substitutions, and variations to these embodiments including components still fall within the protection scope of the present invention.
Claims
1. A 3D CAD reconstruction method for pixel-based topology optimization results, characterized in that, it includes the following steps: S1. Perform smoothing on the discrete voxel model generated from the topology optimization result, where the discrete voxel model is a 3D object model represented by an ordered combination of regular cubes; S2. Extract the triangular mesh on the surface of the smoothed discrete voxel model and generate the skeleton line of the triangular mesh model, that is, a curve with the same connectivity and topological structure as the original triangular mesh model; S3. Simplify the skeleton line of the triangular mesh model; The method for simplifying the skeleton line is as follows: S3-1. Segment the obtained skeleton line, and segment and extract the skeleton segments for the nodes with a degree greater than 2 and the nodes with a degree equal to 1; S3-2. Use the B-spline fitting algorithm to perform fitting on the segmented skeleton line, and solve the coefficient matrix Obtain the control vertices and knot vectors of the B-spline, where Q k represents the vertices to be interpolated, P i represents the obtained control vertices, represents the parameter of the B-spline curve, which is selected by chord length parameterization Let d be the total chord length And let S3-3. First, calculate the closest distance from the end points, that is, the skeleton nodes with a degree greater than 2 or a degree equal to 1, to the surface triangular mesh as its radius, calculate the closest distance from the nodes at the middle position of the segmented skeleton to the surface triangular mesh, and determine whether the nodes at the middle position intersect with the nodes at both ends of this skeleton line; S3-4. If they do not intersect, repeat steps S3-1 to S3-3 until they intersect, then stop the skeleton nodes and continue with step S3-5; S3-5. Merge the skeleton nodes generated by multiple segments of skeleton lines to generate a globally simplified skeleton; S3-6. Perform a merging operation on the intersecting skeleton nodes to merge these two partially intersecting nodes, delete one of the nodes, and transfer the nodes it connects to the remaining node; S4. Generate a coarse skeleton model S4-1. Interactively adjust the skeleton nodes of the triangular mesh model; S4-2. Perform an optimization operation on the angles of the skeleton nodes of the triangular mesh model; The optimization method is as follows: 1) For the nodes with a degree greater than 2, use the cube angle adjustment algorithm proposed by Usai, and the expression is as follows: Among them, U i , V i , W i are vectors perpendicular to each other with the length and width and height of the node as the vector lengths, d i is the unit vector emitted by a node. By optimizing it, the node can reduce the number of node splits in the form of a rotation angle. ε is the iteration parameter, with an initial value of 0.5 and halved in each subsequent iteration; 2) Adopt the method of minimizing the rotation angle to adjust the angles of the nodes with a degree of 2. Start generating a frame from the nodes with a degree greater than 2, then adjust the angles of the middle skeleton nodes, use the frame to generate a hexahedron of skeleton nodes, and generate hexahedron skeleton nodes by extending in the direction of the frame; S4-3. Establish intermediate connecting hexahedron units and perform topological splitting operations to generate a coarse skeleton model; S5. Perform Catmull-Clark volume subdivision on the coarse skeleton model, and project the surface vertices onto the surface triangular mesh generated in step S2 to generate a Bézier volume model.
2. The 3D CAD reconstruction method for pixel-based topology optimization results according to claim 1, characterized in that, in step S1, a hexahedron mesh smoothing operation is performed, and the hexahedron mesh adopts the Laplacian mesh smoothing method, and the expression is as follows: Among them, Adj represents the neighborhood of a vertex, and U(P i ) is the coordinate mean of the neighborhood of a vertex.
3. The 3D CAD reconstruction method for pixel-based topology optimization results according to claim 2, characterized in that, the Laplacian mesh smoothing method is specifically as follows: 1) Initialize the entire hexahedron mesh, and extract the boundary vertices and internal vertices; 2) Traverse the boundary vertices, then calculate the positions and S of the 1-neighborhood points of the boundary points, and the 1-neighborhood points of the boundary points do not include the internal vertices. Traverse the internal vertices and calculate the positions and S' of the 1-neighborhood points of the internal points; 3) Place the boundary points at S / n, where n is the number of 1-neighborhood vertices, and place the internal points at S' / n.
4. A three-dimensional CAD reconstruction method for pixel-based topological optimization results according to claim 1, characterized in that, the step S2 includes the following sub-steps: S2-1. Traverse the discrete voxel model after step S1, and convert the boundary quadrilateral faces of the model into a triangular mesh model by adding an auxiliary edge in the face, that is, the model structure with the surface represented by triangles; S2-2. First, refine the extracted triangular mesh model by the Loop subdivision method, and then, using the extreme value property of the curvature of the triangular mesh, extract the skeleton line of the model, that is, a curve consistent with the connectivity and topological structure of the original triangular mesh model.
5. A three-dimensional CAD reconstruction method for pixel-based topological optimization results according to claim 1, characterized in that, in the step S4-1, displacement, rotation, splitting, extension, addition and deletion operations are performed on the nodes of the skeleton.
6. A three-dimensional CAD reconstruction method for pixel-based topological optimization results according to claim 5, characterized in that, in the step S4-3, an intermediate connector is generated, and hexahedral elements are generated to connect the skeleton nodes. If one face of a node is connected to multiple skeleton nodes, a topological splitting operation is performed on it, that is, a node is split into multiple nodes and the property that one face is connected to multiple skeleton nodes is eliminated, and finally a coarse skeleton model is generated.
7. A three-dimensional CAD reconstruction method for pixel-based topological optimization results according to claim 1, characterized in that, the step S5 includes the following sub-steps: S5-1. Perform Catmull-Clark volume subdivision operation on the coarse skeleton model to generate coarse skeleton models with different resolutions; S5-2. Perform a projection operation, and project the surface vertices of the coarse skeleton model onto the surface triangular mesh model generated in step S2 using their vertex vectors; S5-3. Convert the projected model into a Bézier volume model by generating a hexahedral mesh limit body approximation.
8. A three-dimensional CAD reconstruction method for pixel-based topological optimization results according to claim 7, characterized in that, in the step S5-3, when converting into a Bézier volume model, the specific conversion method is as follows: The 64 control vertices of the generated Bézier volume elements are respectively: 8 corner points are at the 8 corners of the volume; 8 inner points are inside the volume element; 24 edge points are on the 12 edges of the volume, and there are 2 edge points on each edge; 24 face points are on the 6 faces of the volume, and there are 4 face points on each face; The 8 corner points correspond to the 8 corner points of a hexahedral element, and the generated 8 corner point control vertices are equal to the corresponding limit points of the Catmull-Clark subdivision volume; Calculation method of interior point control points. Denote the neighborhood of the hexahedral mesh element where point v is located as L = v, e 1 , e 2 , e 3 , f 1 , f 2 , f 3 , c, where e 1 , e 2 , e 3 represents the coordinates of adjacent edge points. Adjacent edge points represent another point on the same edge as v. There are 3 adjacent edge points in a hexahedral mesh element; f 1 , f 2 , f 3 represents the coordinates of adjacent face points. Adjacent face points represent points on the same face as v but not on the same edge. There are 3 adjacent face points in a hexahedron; c represents the coordinates of adjacent block points. Adjacent block points represent points in the same hexahedral mesh as v but not on the same face. There is one adjacent block point in a hexahedron; The coordinates v of the interior point adjacent to point v in the hexahedral mesh element in The calculation formula is To calculate the coordinates of the edge points, face points, or corner points of a hexahedral mesh cell, simply calculate the coordinates of the inner point closest to the edge point, face point, or corner point to be found on each hexahedral mesh cell containing the edge point, face point, or corner point to be found, and then take the average of the coordinates of these inner points found, that is where n is the number of hexahedral mesh cells containing the edge point, face point or corner point to be determined, and is the coordinate of the in-point closest to the edge point, face point or corner point to be determined on the t-th hexahedral mesh cell containing the edge point, face point or corner point to be determined.