Method for reconstructing vane pump three-dimensional model based on STL (Standard Template Library) file

Abstract

The invention provides a vane pump three-dimensional model reconstruction method based on an STL file. The vane pump three-dimensional model reconstruction method specifically comprises the steps of vane pump STL model data reconstruction based on a half-side data structure; extracting feature edges of the vane pump STL model based on geometric maintenance; dividing vane pump STL model sub-regions based on included angle limitation; re-triangularization of the vane pump STL model based on the RAR algorithm comprises the following steps: constructing four operation operators; constructing constraint conditions of an operator on the basis of a geometric feature keeping thought, wherein the constraint conditions are used for keeping geometric features of the vane pump model; and determining a quality measurement index for locally performing iterative optimization on the vane pump STL model, and finally completing model reconstruction. According to the method, starting from the vane pump STL model, reconstruction of the vane pump STL model is achieved under the condition that the overall structure of the vane pump STL model is complete, and the triangular patch quality of the vane pump STL model is improved.

Description

Technical Field

[0001] The invention belongs to the field of fluid machinery design, and in particular relates to a three-dimensional model reconstruction method. Background Art

[0002] The vane pump CAD model designed by CAD software usually needs to be manually processed before meshing, but converting it to STL file format can avoid this operation. STL file is a file format that uses a discretized representation method. It can describe the surface of a three-dimensional model through a set of triangular facets, shielding the differences between different CAD systems. However, since the vane pump STL model directly exported by CAD software is usually of poor quality, if meshing is performed directly, it will seriously affect the quality of the mesh generated after the division. Summary of the invention

[0003] In view of this, the present invention provides a method for reconstructing a three-dimensional model of a vane pump based on an STL file. Starting from the vane pump STL model, the present invention realizes the reconstruction of the vane pump STL model while satisfying the integrity of the overall structure of the vane pump STL model, improves the quality of the triangular facets of the vane pump STL model, and establishes a method for reconstructing the vane pump STL model.

[0004] The present invention is achieved through the following technical scheme: three-dimensional reconstruction of the vane pump STL model is performed based on the half-edge data structure and the RAR algorithm.

[0005] The steps include:

[0006] a: Reconstruction of vane pump STL model data based on half-edge data structure

[0007] The STL (Stereolithography) model is a file format used to describe the surface of a three-dimensional object. The model consists of a series of triangular facets, each of which defines a part of the surface of the object. The three-dimensional model of the vane pump usually contains complex geometric shapes, which are approximated and represented by triangular facets in the STL model. In addition, the STL model does not store the connection information between nodes, edges and triangular facets in the mesh. Each element is independent of each other and has no clear topological structure. When reconstructing the vane pump STL model, the STL model must first be converted into a data structure that is more suitable for the mesh processing algorithm in order to perform topological reconstruction.

[0008] The data reconstruction means creating a face object F for each triangular face in the vane pump STL file, the face facing F includes the three vertices {V1, V2, V3} of the corresponding triangular face, and three half-edge objects are established by the three vertices, the half-edge objects are V1V2, V2V3, V3V1. V1V2 indicates that the direction of the half-edge is from V1 to V2;

[0009] b: Feature edge extraction of vane pump STL model based on geometry preservation

[0010] The STL model also contains some characteristic edges with significant geometric features, such as sharp edges or corners. These characteristic edges need to be identified and retained during the data reconstruction process to ensure the accuracy and integrity of the model. In order to ensure that the reconstructed vane pump STL model retains the key features of the original model, it is first necessary to identify and extract the key geometric feature edges from the original vane pump STL model.

[0011] In step b, the feature edge extraction step is as follows:

[0012] (1) According to the vane pump specific speed, the normal angle threshold α is given, and the low specific speed (specific speed n s ≤80) vane pump α is 50°, medium specific speed (80 <n s ≤220) vane pump is 55°, high specific speed (n s >220) The α of the vane pump is 60°.

[0013] (2) Traverse all the edges of the original vane pump STL model and use the topological data to find the two triangular facets connected by each edge. Measure the angle γ between the normal vectors of the two facets, and then calculate the angle β between the two facets, which is the complementary angle of γ. If β is greater than α, then this edge E is determined to be a feature edge and is retained in subsequent operations to maintain the geometric accuracy and details of the model, making the reconstructed model closer to the original design.

[0014] c: Sub-region division of vane pump STL model based on angle restriction

[0015] In the vane pump STL model, there may be continuous smooth structures such as cylindrical surfaces and various curved surfaces. These structures need to be represented by a series of continuous smooth triangular facets, but the edges of these smooth structures are usually not automatically identified as feature edges. Limiting the normal vector angles of the vane pump STL model triangular facets and dividing them into sub-regions can prevent the entire continuous smooth structure from being mistakenly identified as a separate sub-region. Independent sub-regions refer to the division of regions with significantly different geometric features in the model based on the differences in normal vector angles, so that each region can be processed more carefully. This division ensures that regions with different geometric features will not be confused during data reconstruction, thereby improving the accuracy and completeness of the model. The specific steps are as follows:

[0016] (1) Randomly select a triangle as the starting point of a separate sub-region. Starting from this starting triangle, expand outward along its three edges and classify adjacent triangles into the same sub-region.

[0017] (2) The expansion operation is repeated until the angle γ between the normal vectors of a pair of adjacent triangles is greater than α, then the expansion is stopped. At this time, the formed area is an independent sub-area.

[0018] d: Retriangulation of the vane pump STL model based on the RAR algorithm

[0019] Four operation operators are constructed to locally move and adjust the vertices of the triangular facets of the original vane pump STL model, and the original vane pump STL model is reconstructed. The side length of the triangular facet is used as a quality metric to iteratively optimize the local part of the vane pump STL model until the weighted side length of the curvature field is approximately consistent, thereby achieving the purpose of reconstruction.

[0020] The main operation operators in step d are as follows:

[0021] (1) Four geometric reconstruction algorithms are defined, namely vertex movement, edge flipping, edge collapse and edge cutting.

[0022] Vertex movement: By moving the vertices of the triangles to the point where the weighted area average position of the centroid of all triangles is formed, the overall shape and topological structure of the model are adjusted. Vertex movement is used to eliminate small fluctuations and irregularities on the surface of the model, making the surface smoother and more continuous.

[0023] Edge flipping: By adjusting the edges of adjacent triangles, the connection relationship of triangles is changed. Specifically, two triangles with adjacent edges are constructed into a quadrilateral, and the other diagonal line is reconnected to form two new triangles. Edge flipping can reduce the thin and long triangles in the STL model, making the distribution of triangles on the surface more natural and uniform, thereby improving the surface quality.

[0024] Edge Collapse: Eliminate redundant edges by merging two adjacent vertices into one vertex. Specifically, merge the two vertices of one edge of a triangle into one point and eliminate the two adjacent triangles. Edge Collapse simplifies the mesh structure by reducing the number of vertices and edges, thereby reducing the complexity of the model.

[0025] Edge cutting: This operator is used to insert new vertices and edges in the STL model, thereby increasing the fineness of the STL model. Edge cutting can significantly increase the resolution of the model and improve the smoothness of the model surface. By adding more vertices and edges, the model surface can better approximate a continuous surface, thereby reducing surface irregularities and roughness.

[0026] (2) Determine the target edge length as a quality metric

[0027] In the process of STL model reconstruction, determining the target edge length as a quality metric can not only help control the density and accuracy of the model's triangles, but also unify the structure of the entire model. Setting an appropriate target edge length helps ensure that the model has a suitable mesh resolution in different areas, thereby maintaining sufficient accuracy in geometric expression. Therefore, the edge length of the triangle is used as a quality metric to control the degree of re-triangulation of the triangle. If the edge is on a plane, the target edge length is the average triangle edge length of the input STL model; if the edge is on a quadratic surface, the target edge length is determined by the following formula:

[0028]

[0029] Where ε is the error, which is taken as 1% of the average side length of the triangle patch of the vane pump STL model; R is the radius of the inscribed circle of the arc corresponding to the edge, which can be determined by the parameter definition of the surface.

[0030] If the edge is on a NURBS surface, the target edge length is determined by the following formula:

[0031]

[0032] Where k is the maximum absolute curvature of the edge.

[0033] (3) Construction constraints

[0034] For the above four reconstruction geometry algorithms, the following constraints are constructed based on the idea of ​​geometric feature preservation to maintain the geometric features of the vane pump model.

[0035] Constraint 1: For vertex movement, the adjacent faces of the moved triangles are judged for triangle inversion and degeneration. If inversion and degeneration occur, the vertex movement operation is not performed.

[0036] Constraint 2: For the edge flipping process, the projection of the constructed quadrilateral on the tangent plane is judged, and the flipping operation is performed only when its projection is not a convex polygon. After the flipping is completed, the difference between the diagonal midpoint of the quadrilateral before and after the flipping and the projection distance to the original STL model is checked. If it is greater than the set distance, the flipping operation is restored.

[0037] Constraint three: For the edge collapse process, determine whether the normal angle of the triangle face before and after the collapse exceeds 90°. If it exceeds 90°, the edge collapse operation will not be performed.

[0038] Constraint 4: For the edge cutting process, determine the edge length of the triangle before and after cutting. If it is less than the set distance, no edge cutting operation will be performed.

[0039] (4) Geometric reconstruction

[0040] Input: initial vane pump STL model, average side length L, error ε.

[0041] Step 1: Traverse all points on the feature edge. If the point is on the boundary, use formula (1) to calculate the target edge length L m Calculate; otherwise determine the surface type, if it is a plane, then L m =L; if it is a quadratic surface, then according to the surface parameters, the target side length L is determined by formula (1) m ; If it is a NURBS surface, the target edge length L m Determined by formula (2).

[0042] Step 2: Traverse each edge of the triangle patch, if the edge length is greater than the target edge length 0.75L m , perform edge cutting operation.

[0043] Step 3: Traverse each edge of the triangle patch, if the edge length is less than the target edge length 0.2L m And if it is not a feature edge, an edge flip operation is performed.

[0044] Step 4: Traverse each edge of the triangle. If the normal angle of the triangles on both sides of the edge is less than 30°, and the sum of the two angles opposite to the edge is greater than 180°, collapse the edge.

[0045] Step 5: Perform vertex movement operations on all non-boundary points.

[0046] Step 6: Repeat steps 1 to 4 until all side lengths meet the target side length requirements.

[0047] Output: reconstructed vane pump STL model.

[0048] Beneficial Effects

[0049] 1. The method of the present invention can greatly improve the quality of the triangular facets divided from the three-dimensional model of the vane pump, has the advantages of accurate recognition results, high efficiency, good repair effect, etc., and can greatly improve the quality of the three-dimensional model of the vane pump.

[0050] 2. The STL (Stereolithography) model is a file format used to describe the surface of a three-dimensional object. Its elements are independent of each other and have no clear topological structure. The present invention first reconstructs the data and converts the STL model into a data structure that is more suitable for the grid processing algorithm, which is conducive to subsequent topological reconstruction.

[0051] 3. The present invention extracts characteristic edges, which is beneficial to maintaining the geometric accuracy and details of the model, making the reconstructed model closer to the original design.

[0052] 4. The present invention divides regions with significantly different geometric features according to the difference in normal vector angles, so as to process each region more carefully. This division can ensure that regions with different geometric features will not be confused during data reconstruction, thereby improving the accuracy and integrity of the model.

[0053] 5. In the process of STL model reconstruction, the present invention determines the target side length as a quality metric, which can not only help control the density and accuracy of the triangular facets of the model, but also unify the structure of the entire model. Setting an appropriate target side length helps ensure that the model has a suitable mesh resolution in different areas, thereby maintaining sufficient accuracy in geometric expression. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is a schematic diagram of the half-edge data structure.

[0055] Figure 2a Schematic diagram of vertex movement operator;

[0056] Figure 2b Schematic diagram of edge flipping;

[0057] Figure 2c Schematic diagram of edge collapse operator;

[0058] picture Schematic diagram of edge cutting operator;

[0059] Figure 3 It is a heavy triangulation flow chart;

[0060] Figure 4 The feature edge recognition result of the embodiment;

[0061] Figure 5 Divide the results into sub-regions;

[0062] Figure 6 Reconstruct the STL model before the embodiment.

[0063] Figure 7 The STL model after reconstruction for the embodiment.

[0064] Figure 8 Flowchart of vane pump 3D model reconstruction DETAILED DESCRIPTION

[0065] The following is a detailed description of the embodiments of the present invention in conjunction with the accompanying drawings. This embodiment is implemented on the premise of the technical solution of the invention, and a detailed implementation method and a specific implementation process are given, but the protection scope of the present invention is not limited to the following embodiments. The present invention is a method for reconstructing the STL model of a vane pump based on a CAD platform.

[0066] Example:

[0067] Taking a vane pump with a specific speed of 118 as an example, its main geometric parameters are: impeller outlet width b2=30mm, impeller outlet diameter D2=315mm, base circle diameter D3=342, and inlet width b3=60.

[0068] Step 1: Reconstruction of vane pump STL model data based on half-edge data structure

[0069] For the embodiment, the half-edge data structure is established in the following steps:

[0070] For each triangular face in the embodiment, a face object F is created, and the face facing F includes the three vertices {V1, V2, V3} of the corresponding triangular face, and three half-edge objects are established by the three vertices, and the half-edge objects are V1V2, V2V3, and V3V1, respectively. V1V2 indicates that the direction of the half-edge is from V1 to V2.

[0071] The specific steps of data reconstruction are as follows:

[0072] (1) According to the triangular patch data of the vane pump STL model, a vertex table, a half-edge table and a surface table are established respectively;

[0073] (2) Process each triangle in the vane pump STL file, create a face object F for it, and record the vertex coordinates of the triangle; if a vertex already exists in the vertex table, use the index of the vertex directly; otherwise, mark the three vertices as {V1, V2, V3}, and create corresponding vertex objects and store them in the vertex table;

[0074] (3) Create three half-edge objects from the three vertices in (2), namely V1V2, V2V3, and V3V1. V1V2 indicates that the direction of the half-edge is from V1 to V2.

[0075] (4) Associate these three half-edges with the face object F, and check and record the half-edges issued by each vertex. For example, if vertex V1 has not yet been associated with any issued half-edges, record the half-edge V1V2 from V1, set its next half-edge to V2V3, and set its own face to face F.

[0076] (5) Traverse all triangular faces in the vane pump STL file and repeat (2) to (4).

[0077] (6) Traverse the half-edge table and check each half-edge V1V2. If there is a half-edge V2V1 that is symmetrical to it, set the symmetrical half-edge of V1V2 to V2V1.

[0078] Step 2: Extraction of feature edges from the vane pump STL model based on geometry preservation

[0079] The specific steps are as follows:

[0080] (1) According to the vane pump specific speed, the normal angle threshold α is given, and the low specific speed (specific speed n s ≤80) vane pump α is 50°, medium specific speed (80 <n s ≤220) vane pump is 55°, high specific speed (n s >220) The α of the vane pump is 60°.

[0081] (2) Traverse all the edges of the original vane pump STL model and use the topological data to find the two triangular facets connected by each edge. Measure the angle γ between the normal vectors of the two facets, and then calculate the angle β between the two facets, which is the complementary angle of γ. If β is greater than α, then this edge E is determined to be a feature edge and is retained in subsequent operations.

[0082] In this embodiment, the angle threshold α of the medium specific speed vane pump is set to 55°. Figure 5 shown.

[0083] Step 3: Sub-area division of the vane pump STL model based on angle restriction

[0084] The specific steps are as follows:

[0085] (1) Randomly select a triangle as the starting point of a separate sub-region. Starting from this starting triangle, expand outward along its three edges and classify adjacent triangles into the same sub-region.

[0086] (2) The expansion operation is repeated until the angle γ between the normal vectors of a pair of adjacent triangles is greater than α, then the expansion is stopped. At this time, the formed area is an independent sub-area.

[0087] The threshold value of this embodiment is 55°. The schematic diagram of the embodiment division is as follows: Figure 6 a. Figure 6 b. Figure 6 As shown in c.

[0088] Step 4: Retriangulation of the vane pump STL model based on the RAR algorithm

[0089] The specific construction geometry algorithm is as follows:

[0090] Vertex movement: Adjust the overall shape and topology of the model by moving the triangles locally. Specifically, each vertex is moved to the average position of the area weighted by the center of gravity of all triangles formed by that point.

[0091] Edge flipping: By adjusting the edges of adjacent triangles, the connection relationship of triangles is changed. Specifically, two triangles with adjacent edges are constructed into a quadrilateral, and the other diagonal line is reconnected to form two new triangles.

[0092] Edge Collapse: Eliminate redundant edges by merging two adjacent vertices into one vertex. Specifically, merge the two vertices of one edge of a triangle into one point and eliminate the two adjacent triangles.

[0093] Edge cutting: This operator is used to insert new vertices and edges into the STL model, thereby increasing the refinement of the STL model.

[0094] The specific reconstruction steps are as follows:

[0095] (1) Determine quality metrics

[0096] The quality metric is determined as the side length of the triangle to control the degree of re-triangulation of the triangle. The target side length is calculated in units of sides. The type of surface the triangle is located on is first determined. If the edge is on a plane, the target side length is the average side length of the triangle in the input STL model; if the edge is on a quadratic surface, it is determined by the following formula:

[0097]

[0098] Where ε is the error, which can be taken as 1% of the average side length of the triangle patch of the vane pump STL model; R is the radius of the inscribed circle of the arc corresponding to the edge, which can be determined by the parameter definition of the surface.

[0099] If the edge is on a NURBS surface, it is determined by the following formula:

[0100]

[0101] Where k is the maximum absolute curvature of the edge.

[0102] (2) Construction constraints

[0103] For the above four geometric algorithms, the following constraints are constructed based on the idea of ​​geometric feature preservation to maintain the geometric features of the vane pump model.

[0104] Constraint 1: For vertex movement, the adjacent faces of the moved triangles are judged for triangle inversion and degeneration. If inversion and degeneration occur, the vertex movement operation is not performed.

[0105] Constraint 2: For the edge flipping process, the projection of the constructed quadrilateral on the tangent plane is judged, and the flipping operation is performed only when its projection is not a convex polygon. After the flipping is completed, the difference between the diagonal midpoint of the quadrilateral before and after the flipping and the projection distance to the original STL model is checked. If it is greater than the set distance, the flipping operation is restored.

[0106] Constraint three: For the edge collapse process, determine whether the normal angle of the triangle face before and after the collapse exceeds 90°. If it exceeds 90°, the edge collapse operation will not be performed.

[0107] Constraint 4: For the edge cutting process, determine the edge length before and after cutting. If it is less than the set distance, no edge cutting operation will be performed.

[0108] (3) Geometric reconstruction

[0109] Input: initial implementation, average edge length L, error ε.

[0110] Step 1: Traverse all points on the feature edge. If the point is on the boundary, calculate the target edge length Lm by multiplying the corresponding coefficient using formula (1); otherwise, determine the surface type. If it is a plane, then L m =L; if it is a quadratic surface, then according to the surface parameters, the target side length L is determined by formula (1) m ; If it is a NURBS surface, the target edge length L m Determined by formula (2).

[0111] Step 2: Traverse each edge of the triangle patch, if the edge length is greater than the target edge length 0.75L m , perform edge cutting operation.

[0112] Step 3: Traverse each edge of the triangle patch, if the edge length is less than the target edge length 0.2L m And if it is not a feature edge, an edge flip operation is performed.

[0113] Step 4: Traverse each edge of the triangle. If the normal angle of the triangles on both sides of the edge is less than 30°, and the sum of the two angles opposite to the edge is greater than 180°, collapse the edge.

[0114] Step 5: Perform vertex movement operations on all non-boundary points.

[0115] Step 6: Repeat steps 1 to 4 until all side lengths meet the target side length requirements.

[0116] Output: Refactored example.

[0117] Comparison diagram of the embodiment before and after reconstruction Figure 7 a. Figure 7 As shown in b.

Claims

1. A method for reconstructing a three-dimensional model of a vane pump based on an STL file, characterized in that The following specific steps are included: a: Reconstruction of vane pump STL model data based on half-edge data structure; b: Feature edge extraction of vane pump STL model based on geometry preservation: c: Sub-region division of the vane pump STL model based on angle restriction; d: Retriangulation of the vane pump STL model based on the RAR algorithm, including: constructing four operation operators; constructing the constraints of the operation operators based on the idea of ​​geometric feature preservation to maintain the geometric features of the vane pump model; determining the quality measurement index to iteratively optimize the local part of the vane pump STL model and finally completing the model reconstruction.

2. The method for reconstructing a three-dimensional model of a vane pump based on an STL file according to claim 1, characterized in that: The data reconstruction refers to creating a face object F for each triangular face in the vane pump STL file, the face facing F includes the three vertices {V1, V2, V3} of the corresponding triangular face, and three half-edge objects are established by the three vertices, and the half-edge objects are V1V2, V2V3, and V3V1 respectively. V1V2 indicates that the direction of the half-edge is from V1 to V2.

3. The method for reconstructing a three-dimensional model of a vane pump based on an STL file according to claim 1, characterized in that: The steps of feature edge extraction are as follows: (1) The normal angle threshold α is given according to the specific speed of the vane pump. Specifically, under low specific speed conditions, the normal angle threshold α of the vane pump is 50°; under medium specific speed conditions, the normal angle threshold α of the vane pump is 55°; under high specific speed conditions, the normal angle threshold α of the vane pump is 60°; (2) Traverse all the edges of the vane pump STL model and use the topological data to find the two triangular facets connected by each edge; measure the angle γ between the normal vectors of the two facets, and then calculate the angle β between the two facets. β is the complementary angle of γ. If β is greater than α, then this edge E is determined to be a feature edge.

4. The method for reconstructing a three-dimensional model of a vane pump based on an STL file according to claim 1, characterized in that: The sub-model division specifically includes: (1) Select a triangle as the starting point of a specific sub-region, and expand outward along its three edges from this starting triangle to include adjacent triangles in the same sub-region; (2) The expansion operation is repeated until the angle γ between the normal vectors of a pair of adjacent triangles is greater than α, then the expansion is stopped. At this time, the formed area is an independent sub-area.

5. The method for reconstructing a three-dimensional model of a vane pump based on an STL file according to any one of claims 1 to 4, characterized in that: The four operation operators are specifically vertex movement, edge flipping, edge collapse and edge cutting.

6. The method for reconstructing a three-dimensional model of a vane pump based on an STL file according to claim 5, characterized in that: The constraints include: Constraint 1: For vertex movement, the adjacent faces of the moved triangles are subjected to triangle inversion and degeneration judgment. If inversion and degeneration occur, the vertex movement operation is not performed; Constraint 2: For the edge flipping process, the projection of the constructed quadrilateral on the tangent plane is judged, and the flipping operation is performed only when its projection is not a convex polygon; after the flipping is completed, the difference between the diagonal midpoint of the quadrilateral before and after the flipping and the projection distance to the original STL model is checked. If it is greater than the set distance, the flipping operation is restored; Constraint 3: For the edge collapse process, determine whether the normal angle between the two triangles before and after the collapse exceeds 90°. If it exceeds 90°, the edge collapse operation will not be performed. Constraint 4: For the edge cutting process, determine the edge length before and after cutting. If it is less than the set distance, no edge cutting operation will be performed.

7. The method for reconstructing a three-dimensional model of a vane pump based on an STL file according to claim 6, characterized in that: The quality metric is determined as the side length of the triangle to control the degree of re-triangulation of the triangle. The target side length is calculated in units of sides. The type of surface on which the triangle is located is first determined. If the edge is on a plane, the target edge length is the average triangle edge length of the input STL model; If the edge is located on a quadratic surface, it is determined by the following formula: Where ε is the error; R is the radius of the inscribed circle of the arc corresponding to the edge, which is determined by the parameter definition of the surface; If the edge is on a NURBS surface, it is determined by the following formula: Where k is the maximum absolute curvature of the edge.

8. The method for reconstructing a three-dimensional model of a vane pump based on an STL file according to claim 7, characterized in that: The re-triangulation of the vane pump STL model based on the RAR algorithm specifically includes: Input: initial vane pump STL model, average side length L, error ε. Step 1: Traverse all points on the feature edge. If the point is on the boundary, use formula (1) to calculate the target edge length L m Calculate; otherwise determine the surface type, if it is a plane, then L m =L; if it is a quadratic surface, then according to the surface parameters, the target side length L is determined by formula (1) m ; If it is a NURBS surface, the target edge length L m Determined by formula (2); Step 2: Traverse each edge of the triangle patch, if the edge length is greater than the target edge length 0.75L m , perform edge cutting operation; Step 3: Traverse each edge of the triangle patch, if the edge length is less than the target edge length 0.2L m If it is not a characteristic edge, an edge flipping operation is performed; Step 4: Traverse each edge of the triangle patch. If the normal angle of the triangle patches on both sides of the edge is less than 30°, and the sum of the two angles opposite to the edge is greater than 180°, then collapse the edge. Step 5: Perform vertex movement operations on all non-boundary points; Step 6: Repeat steps 1 to 5 until all side lengths meet the target side length requirements; Output: reconstructed vane pump STL model.

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