Closed grid model partitioning algorithm based on dihedral angle constraint optimization

Abstract

The invention discloses a closed grid model partitioning algorithm based on dihedral angle constraint optimization. The invention relates to the technical field of computer graphics, and aims to solve the problem that an interface grid and a segmentation domain surface grid intersect at an interface boundary in an existing grid model partitioning method. The algorithm comprises the steps of initial segmentation plane selection, interface boundary generation and interface boundary optimization. According to the invention, boundary node winding direction judgment is carried out based on a bounding box technology. After the model is segmented based on the segmentation surface, the interface boundary of the two decomposition domains is optimized based on dihedral angle constraint, and it can be guaranteed that a subsequent interface grid and a segmentation domain surface grid are not intersected. In the boundary optimization process of the interface, the segmentation plane may be moved. The moving segmentation surface only abandons boundaries contained in grids between the current optimized boundaries and the boundaries after moving the segmentation surface, and the boundaries of the interfaces which are not contained are reserved, so that one model may contain the boundaries generated by a plurality of segmentation surfaces.

Description

Technical Field

[0001] This invention relates to the field of computer graphics technology, and in particular to a partitioning algorithm for closed mesh models based on dihedral angle constraint optimization. Background Technology

[0002] Mesh model partitioning aims to divide a model into different regions and use these regions for multi-core parallel mesh generation, thereby improving the speed of overall model mesh generation. The main methods for model partitioning used in parallel mesh generation include the following: Recursive coordinate bisection: The computational domain is recursively divided into two parts along the longest coordinate axis (X, Y, or Z), ensuring that the geometric volume or number of vertices in the two parts is approximately equal. This process is repeated recursively until the number of partitions reaches the required number of processors. This method is prone to producing unbalanced loads or high aspect ratio partitions for models with complex geometries, resulting in very large communication interfaces between partitions.

[0003] Graph-based methods: These methods transform the region segmentation problem into a graph partitioning problem, fully considering the topological connections between cells, with the primary goal of minimizing inter-processor communication. The most well-known and widely used graph partitioning library, METIS / ParMETIS, provides efficient multi-level graph partitioning algorithms; however, this method faces significant challenges in generating meshes at subsequent interfaces.

[0004] Principal moment of inertia axis segmentation method: This method uses the principal moment of inertia axis, which includes the object's center of gravity and has the smallest relative moment of inertia, as the segmentation axis. However, this method may result in intersection problems between the generated interface mesh and surface mesh, requiring significant time for intersection detection and repair. Summary of the Invention

[0005] The purpose of this invention is to provide a closed mesh model partitioning algorithm based on dihedral angle constraint optimization, so as to solve the problem of intersection between the interface mesh and the surface mesh of the partitioned domain in the existing mesh model partitioning method.

[0006] This invention provides a partitioning algorithm for closed mesh models based on dihedral angle constraint optimization, comprising: Step 1, Selection of initial dividing surfaces: Given a mesh model The mesh model The position of the dividing surface is determined by the normal vector and the dividing base point, using the moment of inertia of the mesh model. The eigenvector corresponding to the smallest eigenvalue is used as the normal vector of the segmentation surface, and the initial segmentation surface is selected. ; Step 2, Interface Boundary Generation: Obtain the initial segmentation surface The mesh boundary of the interface is then calculated; the segmented region is then determined. as well as The surface mesh is used to calculate the three intersection points of the segmented surface and the coordinate axes of the Cartesian coordinate system. , , Determine the triangle Belongs to the segmented region; when the mesh edge of the triangle belongs to the region. and At that time, the grid edge is the boundary edge of the interface; Step 3, Interface Boundary Optimization: In the region where the interface boundary is located... It consists of multiple unconnected sub-regions. In the case of the configuration, obtain the sub-region. Maximum projected distance from the upper node to the segmentation plane k is the constitutive region The index number of the sub-region; if the maximum projection distance , For the set grid size, the area will be... All grid cells within the grid are moved to the corresponding segmented region; For a boundary mesh edge, when the dihedral angle between the surface mesh it belongs to and the dividing surface... Less than 0.11 If the boundary is not optimized, it is considered as a boundary mesh edge to be optimized. Traverse a boundary ring and calculate its boundary mesh edges to be optimized. If there are optimized boundary mesh edges, move the mesh connected by the mesh edge to the relative segmentation region, change the segmentation region where the mesh is located, and update the mapping relationship between the nodes of the moved mesh and the meshes connected to it, as well as the boundary of the entire segmentation region. Then, perform dihedral angle judgment on the newly added boundary mesh edges in the boundary.

[0007] Furthermore, in step one, the moment of inertia matrix of the model is calculated as follows: ; in, The center of gravity of the model, For mesh models The set of points composed of nodes in the middle, Let V contain nodes with coordinates as ; Given a symmetric positive definite matrix, solve for... The smallest eigenvalue corresponds to the eigenvector Then the normal vector of the dividing surface is: ; Obtain the segmented surface The equation is: ; x, y, z are variables in the equation of the partition surface, representing the coordinates of a point on the plane; determining an initial partition point to obtain value, d is a constant in the equation of the partition surface, and the normal vector n determines the position of the partition surface; the initial partition point The principle is to make the partition region and The grid size is similar; the weight method is used to determine the initial partition point, and the weight of the node is: ; is the set of grid edges containing the node , is the grid edge contained in , is the weight value of the node , is the length of the grid edge, and the point is obtained by projecting the point to , the weight of the point is , is the set of projection points; the distance between the projection point and the center of mass of the model: ; p c is the center of mass of the model.

[0008] Sort the nodes in according to the size of ; the projection point of the initial partition point divides into two subsets and , and satisfies the target: .

[0009] Further, in step two, the partition region to which the triangle belongs is determined by the following conditions: ; where ; is the value of the determinant of matrix A, , , are the intersection points of the partition surface and the X, Y, Z axes of the Cartesian coordinate system, respectively, is the triangle The coordinates of the center point.

[0010] Furthermore, in step two, after obtaining the interface boundary, the boundary edges of the interface are optimized. The optimization method is as follows: When boundary nodes When the number of connected grids in a partitioned domain is 1, then the nodes are... The connected mesh moves from one segmented region to another segmented domain; When boundary nodes Angle in a region Less than 0.4 When, then the node The connected mesh moves from one partition domain to another. , The angle between the grids connected to the boundary nodes at that point.

[0011] Furthermore, in step two, after the optimization is completed, the boundary of the interface is recalculated and the surrounding order of the boundary nodes is sorted; based on the connection relationship of the nodes, a closed boundary loop is obtained, which is a closed polygonal loop formed by the sequential connection of the nodes on the boundary. The algorithm for calculating boundary loops includes: when the number of boundary loops at the interface is greater than 1, determining the inner and outer boundary attributes of the boundary loops; when determining the inner and outer attributes of the boundary loops, establishing a local planar coordinate system on the segmentation surface and calculating the coordinates of the projection points of the boundary nodes on the segmentation surface in the local coordinate system; and determining the inner and outer boundary attributes of the boundary loops on the plane. After obtaining the internal and external attributes of the boundary loop at the interface, the nodes of the boundary loop are sorted by orientation; the extreme values ​​of the projection points of the boundary loop nodes onto the dividing surface in the x, y, and z directions are obtained. And the nodes with extrema; calculate the advance points for all extrema nodes, the positions of which are given by the following formula. ; In the formula: , where n is the normal vector of the dividing surface. , , For adjacent nodes on the boundary, For extreme nodes; calculate the extreme values ​​of the projection points of the propulsion points onto the segmentation plane in the x, y, and z directions. If the boundary loop is oriented correctly, then the calculation... The direction of r points outward from the boundary of the interface. exist The point of advancement in the direction is outside the boundary.

[0012] Further, for the outer boundary ring node, when the following conditions are met, the current boundary ring node's winding direction is adjusted by reversing the boundary node storage order; ; n x , n y , n z is the value of the normal vector of the split surface, z max0 , z max1 is the extreme value of the projection point of the boundary ring node on the split surface in the z direction; For the inner boundary ring node, when the following conditions are met, the current boundary ring node's winding direction is adjusted by reversing the boundary node storage order; .

[0013] Further, in step three, the conditions for terminating the entire optimization process are as follows: Condition one: all boundary grid edges on the boundary do not meet the condition of becoming the boundary grid edge to be optimized; Condition two: when optimizing the boundary grid edge, the number of grid edges connected by the boundary node is greater than 2; Condition three: the difference between the maximum distance and the minimum distance of the optimized boundary node and its projection point on the split surface is greater than 1.5 ; Condition four: the projection of the optimized boundary ring on the split surface appears intersection of boundary edges; the scanning line algorithm can accurately realize the intersection judgment of boundary edges; When condition two is met, when the grid edges connected by the boundary node all belong to the current optimization boundary, the current boundary is divided into multiple boundaries, and then the multiple boundaries after division are optimized in turn; if the grid edges connected by the boundary node contain other boundaries, the current boundary intersects with other boundaries, and the boundary needs to be merged; when conditions three and four are met, the split base point needs to be selected again and the split surface needs to be moved; for condition three, the node with the maximum projection distance is selected as the split base point; for condition four, the node with the maximum projection distance in the intersecting grid edge is selected as the split base point.

[0014] Further, in step three, the operation process after the split surface is moved is as follows: Based on the normal vector of the split surface corresponding to the current optimization boundary and the split base point, the current split domain is split; Optimization is performed on the split boundary before obtaining the boundary ring, and after optimization, a new boundary ring is obtained, and the winding direction is judged and adjusted; The grid between the current optimization boundary and the new split boundary is obtained; If the grid between the current optimization boundary and the boundary generated after moving the split surface is not contained in the original remaining boundary, only the current optimization boundary is updated, and the original remaining boundary is retained; otherwise, the contained original remaining boundary is updated. The split region is merged, and the grid between the current optimization boundary and the new split boundary is added to the opposite split region of the current split region.

[0015] The application has the following beneficial effects: the closed mesh model partition algorithm based on dihedral angle constraint optimization of the application performs boundary node direction judgment based on the bounding box technology. After the model is partitioned based on the split surface and the boundary of the interface between the two split regions is optimized based on the dihedral angle constraint, the subsequent interface mesh and the split region surface mesh are guaranteed to be non-intersecting. In the boundary optimization process of the interface, the split surface may be moved. Moving the split surface will only discard the boundary contained in the grid between the current optimization boundary and the boundary after moving the split surface, and the original interface boundary that is not contained will be retained, so a model may contain multiple boundaries generated by split surfaces. BRIEF DESCRIPTION OF DRAWINGS

[0016] In order to more clearly illustrate the technical solutions of the application, the following will briefly introduce the drawings needed to be used in the embodiments. Obviously, for those skilled in the art, other drawings can also be obtained based on these drawings without any creative effort.

[0017] Figure 1 It is a node weight schematic diagram. Figure 2 It is a model partition schematic diagram. Figure 3 It is a boundary ring schematic diagram. Figure 4 It is a boundary point schematic diagram. Figure 5 It is a boundary partition schematic diagram. Figure 6 It is a split surface moving schematic diagram.

[0018] Figure 7 It is a hub model partition schematic diagram, in which (a) is an original model, and (b) is a partitioned model. DETAILED DESCRIPTION

[0019] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions of the present application will be described below in connection with the embodiments of the present application and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work belong to the protection scope of the present application. The technical solutions provided by the embodiments of the present application will be described in detail below in connection with the drawings.

[0020] The closed mesh model partitioning algorithm based on dihedral angle constraint optimization provided by the present application optimizes the partitioning boundary through the dihedral angle constraint of the boundary of the interface and the partitioning surface after the model is partitioned by the surface, so as to avoid the intersection of the subsequently generated interface mesh and the surface mesh at the boundary.

[0021] Referring to Figures 1 to 7 , the embodiment of the present application provides a closed mesh model partitioning algorithm based on dihedral angle constraint optimization, which comprises: Step 1: Selection of initial partitioning surface: given a mesh model , the position of the partitioning surface of the mesh model is determined by a normal vector and a partitioning base point, the inertia matrix of the mesh model is used , the eigenvector corresponding to the minimum eigenvalue is used as the normal vector of the partitioning surface, and the initial partitioning surface is selected.

[0022] The inertia matrix of the model is calculated as follows: ; wherein, is the center of gravity of the model, is a point set composed of nodes in the mesh model , and is a node contained in V, and the coordinates of the node are ; is a symmetric positive definite matrix, the eigenvector corresponding to the minimum eigenvalue of is solved , and the normal vector of the partitioning surface is: ; The equation of the partitioning surface is obtained as: ; x, y and z are variables in the equation of the partitioning surface, and represent the coordinates of a point on the plane.

[0023] An initial partitioning point is determined to obtain value, d is a constant in the equation of the partitioning surface, and together with the normal vector n determines the position of the partitioning surface; the initial partitioning point The selection principle is to make the segmented region and The grid sizes are similar; the initial partitioning points are determined using a weighted method, and the nodes... The weights are: ; for Contains nodes The set of grid edges, for The grid edges included For nodes The weight value, The length of the grid edge, such as Figure 1 As shown, node The weight value is the sum of the lengths of the thickened grid edges. The points... Projected to Points obtained later ,point The weight is , , The set of projection points; the distance between the projection points and the centroid of the model: ; p c This is the center of gravity of the model.

[0024] Will Middle node Sort by size; initial split point The projection point will Divided into two subsets and And it satisfies the objective: .

[0025] Step 2, Interface Boundary Generation: Obtain the initial segmentation surface The mesh boundary of the interface is then calculated; the segmented region is then determined. as well as The surface mesh is used to calculate the three intersection points of the segmented surface and the coordinate axes of the Cartesian coordinate system. , , Determine the triangle Belongs to the segmented region; when the mesh edge of the triangle belongs to the region. and When this occurs, the grid edge is the boundary edge of the interface.

[0026] Determine the triangle based on the following conditions. Part of the segmentation region: ; wherein ; is the value of the determinant of matrix A, , , are the intersection points of the partition surface and the Cartesian coordinate system X-axis, Y-axis, Z-axis respectively, is the center point of the triangle . As shown in Figure 2 , the surface mesh of the region and is obtained, and the vector is required to point to the region . When the mesh edge of the triangle belongs to both the region and , the mesh edge is the boundary edge of the interface. After the boundary of the interface is obtained, some sharp corners may occur at the nodes of the boundary, and thus the boundary edge of the interface needs to be optimized. The optimization method is as follows: When the number of the mesh connected by the boundary node in one partition region is 1, the mesh connected by the node is moved from the partition region to another partition region; When the included angle of the boundary node in one region is less than 0.4 , the mesh connected by the node is moved from the partition region to another partition region, , is the included angle of the mesh connected by the boundary node at the point.

[0027] After the optimization is completed, the boundary of the interface is recalculated, and the circumferential ordering of the boundary nodes is performed; based on the connection relationship of the nodes, a closed boundary ring is obtained, which is a closed polygon ring formed by sequentially connecting the nodes on the boundary. As shown in Figure 3 , the blue line is the boundary ring at the interface of the partition region. The algorithm for calculating the boundary ring is shown in Table 1. When the number of the boundary rings of the interface is greater than 1, the inner and outer boundary properties of the boundary ring need to be determined. When determining the inner and outer properties of the boundary ring, a local plane coordinate system is established on the partition surface, and the coordinates of the projection point of the boundary node on the partition surface in the local coordinate system are calculated. The inner and outer boundary properties of the boundary ring can be accurately determined on the plane.

[0028] Table 1: Algorithm for obtaining the boundary ring

[0029] After obtaining the internal and external attributes of the boundary loop at the interface, the nodes of the boundary loop are sorted by orientation; the extreme values ​​of the projection points of the boundary loop nodes onto the dividing surface in the x, y, and z directions are obtained. And the nodes with extrema; calculate the advance points for all extrema nodes, the positions of which are given by the following formula. ; In the formula: , where n is the normal vector of the dividing surface. , , For adjacent nodes on the boundary, For extreme nodes; calculate the extreme values ​​of the projection points of the propulsion points onto the segmentation plane in the x, y, and z directions. ;like Figure 4 As shown, the circular nodes are boundary points. The point of location. If the orientation of the boundary loop is correct, then the calculated... The direction of r points outward from the boundary of the interface. exist The point of advancement in the direction is outside the boundary.

[0030] For outer boundary node, the surrounding direction of the current boundary node is adjusted by reversing the storage order of the boundary nodes when the following conditions are met; ; n x n y n z Let z be the value of the normal vector of the dividing surface. max0 , z max1 The extreme value of the projection point of the boundary node onto the dividing surface in the z-direction; For inner boundary node, the surrounding direction of the current boundary node is adjusted by reversing the storage order of the boundary nodes when the following conditions are met; .

[0031] Step 3, Interface Boundary Optimization: In the region where the interface boundary is located... It consists of multiple unconnected sub-regions. In the case of the configuration, obtain the sub-region. Maximum projected distance from the upper node to the segmentation plane k is the constitutive region The index number of the sub-region; if the maximum projection distance , For the set grid size, the area will be... All grids within the area are moved to the corresponding segmented region.

[0032] For the obtained interface boundaries, there may be cases where some boundary mesh edges and the dihedral angles of the dividing surface are too small. This can lead to intersection issues between the subsequent interface mesh generation and the surface mesh. For a boundary mesh edge, when the dihedral angle of the surface mesh it belongs to and the dividing surface is too small... Less than 0.11 If an edge is found to be an edge, it is considered a boundary mesh edge to be optimized. A boundary loop is traversed, and its boundary mesh edges to be optimized are calculated. If an optimized boundary mesh edge exists, the mesh connected to the edge is moved to the corresponding segmentation region, changing the segmentation region where the mesh resides. The mapping relationship between the nodes of the moved mesh and its connected meshes, as well as the boundary of the entire segmentation region, is updated. Then, the newly added boundary mesh edges in the boundary are judged for dihedral angles. The entire optimization process terminates under the following conditions: Condition 1: None of the boundary mesh edges on the boundary meet the conditions to become boundary mesh edges to be optimized; Condition 2: When optimizing boundary mesh edges, the number of mesh edges connected by boundary nodes is greater than 2; Condition 3: The difference between the maximum and minimum distances between the optimized boundary nodes and their projection points on the segmentation surface is greater than 1.5. ; Condition 4: The projection of the optimized boundary loop onto the segmentation surface shows the phenomenon of boundary edge intersection; the scan line algorithm can accurately realize the intersection judgment of boundary edges; When condition two is met, if all the mesh edges connected to the boundary nodes belong to the current optimized boundary, the current boundary is divided into multiple boundaries, and subsequent optimization judgments are performed on the multiple divided boundaries in sequence. If the mesh edges connected to the boundary nodes contain other boundaries, the current boundary intersects with other boundaries, and boundary merging is required. When conditions three and four are met, the dividing base point needs to be reselected and the dividing surface needs to be moved. For condition three, the node with the maximum projection distance is taken as the dividing base point. For condition four, the node with the maximum projection distance among the intersecting mesh edges is taken as the dividing base point.

[0033] The operation procedure after the segmentation plane is moved is as follows: Based on the normal vector of the segmentation surface corresponding to the current optimization boundary The current segmentation domain is segmented using the segmentation base point; The optimization is performed on the segmented boundary before obtaining the boundary loop, and the new boundary loop is obtained after optimization, and the around direction is judged and adjusted. Obtain the mesh between the current optimization boundary and the new split boundary; whether the grid between the current optimization boundary and the boundary generated after moving the split surface contains the original remaining boundary; if not, only the current optimization boundary is updated, and the original remaining boundary is retained; otherwise, the contained original remaining boundary is updated; thus, different interface boundaries in the model can correspond to different split surfaces. As shown in FIG. 8, only the boundary present in the yellow region grid needs to be updated. Figure 6

[0034] The split regions are merged, and the grid between the current optimization boundary and the new split boundary is added to the opposite split region of the current split region.

[0035] As shown in FIG. 9, where (a) is the original model, and (b) is the split model. Given the automobile hub model, the above scheme is used for splitting, and finally 8 split regions are successfully generated. The number of grids of each split region is shown in Table 2. The number of intersections between the interface grid generated at the interface of adjacent split regions and the grid of the split region is 0, which ensures that the grid of the split region can be successfully completed for subsequent tetrahedral meshing. The solid meshing time before splitting is 212 s, and the solid meshing time after splitting is 68.648 s. Figure 7

[0036] Table 2: Number of grids of each region

[0037] The above embodiments of the present application do not constitute a limitation on the protection scope of the present application.​​

Claims

1. A partitioning algorithm for a closed mesh model based on dihedral angle constraint optimization, characterized in that, include: Step 1, Selection of initial dividing surfaces: Given a mesh model The mesh model The position of the dividing surface is determined by the normal vector and the dividing base point, using the moment of inertia of the mesh model. The eigenvector corresponding to the smallest eigenvalue is used as the normal vector of the segmentation surface, and the initial segmentation surface is selected. ; Step 2, Interface Boundary Generation: Obtain the initial segmentation surface The mesh boundary of the interface is then calculated; the segmented region is then determined. as well as The surface mesh is used to calculate the three intersection points of the segmented surface and the coordinate axes of the Cartesian coordinate system. , , Determine the triangle Belongs to the segmented region; when the mesh edge of the triangle belongs to the region. and At that time, the grid edge is the boundary edge of the interface; Step 3, Interface Boundary Optimization: In the region where the interface boundary is located... It consists of multiple unconnected sub-regions. In the case of the configuration, obtain the sub-region. Maximum projected distance from the upper node to the segmentation plane k is the constitutive region The index number of the sub-region; if the maximum projection distance , If the set grid size is not specified, then the area will be... All grids within the area are moved to the corresponding segmented region; For a boundary mesh edge, when the dihedral angle between the surface mesh it belongs to and the dividing surface... Less than 0.11 If the boundary is not optimized, it is considered as a boundary mesh edge to be optimized. Traverse a boundary ring and calculate its boundary mesh edges to be optimized. If there are optimized boundary mesh edges, move the mesh connected by the mesh edge to the relative segmentation region, change the segmentation region where the mesh is located, and update the mapping relationship between the nodes of the moved mesh and the meshes connected to it, as well as the boundary of the entire segmentation region. Then, perform dihedral angle judgment on the newly added boundary mesh edges in the boundary.

2. The closed mesh model partitioning algorithm based on dihedral angle constraint optimization as described in claim 1, characterized in that, In step one, the moment of inertia matrix of the model is calculated as follows: ； in, The center of gravity of the model, For mesh models The set of points composed of nodes in the middle, Let V contain nodes with coordinates as ; Given a symmetric positive definite matrix, solve for... The smallest eigenvalue corresponds to the eigenvector Then the normal vector of the dividing surface is: ； Obtain the segmented surface The equation is: ； x, y, z are variables in the equation of the dividing surface, representing the coordinates of a point on the plane; Determine an initial split point To obtain The value d is a constant in the equation of the dividing surface, which, together with the normal vector n, determines the position of the dividing surface; the initial dividing point. The selection principle is to make the segmented region and The grid sizes are similar; the initial partitioning points are determined using a weighted method, and the nodes... The weights are: ； for Contains nodes The set of grid edges, for The grid edges included For nodes The weight value, Given the length of the grid edge, the point... Projected to Points obtained later ,point The weight is , , The set of projection points; the distance between the projection points and the centroid of the model. ； p c The center of gravity of the model; Will Middle node Sort by size; initial split point The projection point will Divided into two subsets and And it satisfies the objective: .

3. The closed mesh model partitioning algorithm based on dihedral angle constraint optimization as described in claim 1, characterized in that, In step two, the triangle is determined by the following conditions. Part of the segmentation region: ； In the formula ； Let A be the value of the determinant of matrix A. , , These are the intersection points of the dividing surface and the X, Y, and Z axes of the Cartesian coordinate system, respectively. It is a triangle The coordinates of the center point.

4. The closed mesh model partitioning algorithm based on dihedral angle constraint optimization as described in claim 3, characterized in that, In step two, after obtaining the interface boundary, the boundary edges of the interface are optimized. The optimization method is as follows: When boundary nodes When the number of connected grids in a partitioned domain is 1, then the nodes are... The connected mesh moves from one segmented region to another segmented domain; When boundary nodes Angle in a region Less than 0.4 When, then the node The connected mesh moves from one partition domain to another. , The angle between the grids connected to the boundary nodes at that point.

5. The closed mesh model partitioning algorithm based on dihedral angle constraint optimization as described in claim 4, characterized in that, In step two, after the optimization is completed, the boundary of the interface is recalculated and the orientation of the boundary nodes is sorted. Based on the connection relationship of the nodes, a closed boundary loop is obtained. The boundary loop is a closed polygonal loop formed by the sequential connection of the nodes on the boundary. The algorithm for calculating boundary loops includes: when the number of boundary loops at the interface is greater than 1, determining the inner and outer boundary attributes of the boundary loops; when determining the inner and outer attributes of the boundary loops, establishing a local planar coordinate system on the segmentation surface and calculating the coordinates of the projection points of the boundary nodes on the segmentation surface in the local coordinate system; and determining the inner and outer boundary attributes of the boundary loops on the plane. After obtaining the internal and external attributes of the boundary loop at the interface, the nodes of the boundary loop are sorted by orientation; the extreme values ​​of the projection points of the boundary loop nodes onto the dividing surface in the x, y, and z directions are obtained. And the nodes with extrema; calculate the advance points for all extrema nodes, the positions of which are given by the following formula. ； In the formula: , where n is the normal vector of the dividing surface. , , For adjacent nodes on the boundary, For extreme nodes; calculate the extreme values ​​of the projection points of the propulsion points onto the segmentation plane in the x, y, and z directions. ; If the boundary loop is oriented correctly, then the calculation... The direction of r points outward from the boundary of the interface. exist The point of advancement in the direction is outside the boundary.

6. The closed mesh model partitioning algorithm based on dihedral angle constraint optimization as described in claim 5, characterized in that, For outer boundary node, the surrounding direction of the current boundary node is adjusted by reversing the storage order of the boundary nodes when the following conditions are met; ； n x n y n z Let z be the value of the normal vector of the dividing surface. max0 , z max1 The extreme value of the projection point of the boundary node onto the dividing surface in the z-direction; For inner boundary node, the surrounding direction of the current boundary node is adjusted by reversing the storage order of the boundary nodes when the following conditions are met; 。 7. The closed mesh model partitioning algorithm based on dihedral angle constraint optimization as described in claim 1, characterized in that, In step three, the conditions for terminating the entire optimization process are as follows: Condition 1: None of the boundary mesh edges on the boundary meet the conditions to become boundary mesh edges to be optimized; Condition 2: When optimizing boundary mesh edges, the number of mesh edges connected by boundary nodes is greater than 2; Condition 3: The difference between the maximum and minimum distances between the optimized boundary nodes and their projection points on the segmentation surface is greater than 1.

5. ; Condition 4: The projection of the optimized boundary loop onto the segmentation surface shows the phenomenon of boundary edge intersection; the scan line algorithm can accurately realize the intersection judgment of boundary edges; When condition two is met, if all the mesh edges connected to the boundary nodes belong to the mesh edges of the current optimization boundary, the current boundary is divided into multiple boundaries, and the subsequent optimization judgments are performed on the multiple divided boundaries in sequence; if the mesh edges connected to the boundary nodes contain other boundaries, the current boundary intersects with other boundaries, and boundary merging is required; when conditions three and four are met, the dividing base point needs to be reselected and the dividing surface needs to be moved. For condition three, the node with the maximum projected distance is used as the splitting point; for condition four, the node with the maximum projected distance in the intersecting grid edges is used as the splitting point.

8. The closed mesh model partitioning algorithm based on dihedral angle constraint optimization as described in claim 7, characterized in that, In step three, the operation procedure after the segmentation plane is moved is as follows: Based on the normal vector of the segmentation surface corresponding to the current optimization boundary The current segmentation domain is segmented using the segmentation base point; The optimization is performed on the segmented boundary before obtaining the boundary loop, and the new boundary loop is obtained after optimization, and the around direction is judged and adjusted. Obtain the mesh between the current optimization boundary and the new split boundary; Determine whether the mesh between the current optimized boundary and the boundary generated after moving the split surface contains the original remaining boundaries; if not, only update the current optimized boundary and retain the original remaining boundaries; otherwise, update the original remaining boundaries that are contained. Merge the segmented regions by adding the mesh between the current optimized boundary and the new segmentation boundary to the relative segmentation domain of the current segmentation domain.

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