Rapid local repair method for self-intersecting triangular mesh

Abstract

The invention discloses a rapid local repair method for a self-intersecting triangular mesh. According to the method, local processing and rational number calculation are combined, aiming at an input low-quality triangular mesh, firstly, the mesh quality is optimized through a preprocessing step, intersection areas are positioned, then the mesh is partitioned based on octree division and connected component analysis, and the intersection areas and non-intersection areas are separated. In each intersection area, a shape-preserving boundary three-dimensional grid optimization method based on rational numbers is adopted to ensure the robustness of intersection calculation, and surface grids are extracted after successful conversion into floating-point number representation. And finally, seamlessly splicing the repaired local grid and the non-intersecting grid, and improving the overall grid quality through an edge re-gridding method based on curvature self-adaption. According to the method, the non-intersecting high-quality grid can be quickly generated, the method is suitable for downstream applications such as finite element analysis, meanwhile, the calculation overhead is remarkably reduced, and the algorithm robustness is improved.

Description

Technical Field

[0001] The present invention relates to the technical fields of computer graphics and mesh generation, and particularly to a fast local repair method for self-intersecting triangular meshes. Background Art

[0002] Triangular meshes are the basic geometric representations in computer graphics and are widely used in fields such as 3D modeling, simulation, and animation. However, due to various reasons, the triangular meshes generated may have defects such as intersections and low-quality elements. These defects not only affect the geometric accuracy of the mesh but also have a negative impact on subsequent applications (such as finite element analysis and volume discretization algorithms).

[0003] In the prior art, the methods for solving the mesh intersection problem are mainly divided into two categories: 1. Direct intersection detection and repair methods based on surface meshes. Such methods directly detect the intersecting triangles on the surface mesh and repair the intersecting regions. To improve the robustness of the calculation, some studies use indirect predicate methods to represent the intersection points to avoid floating-point precision errors. However, the indirect predicate method is prone to introducing new intersection problems when converting the results to floating-point numbers, which limits its practical application.

[0004] 2. Boundary-conforming tetrahedral mesh methods based on volume meshes. Such methods solve the triangle intersection problem by constructing boundary-conforming tetrahedral meshes. Although this method can improve the efficiency of intersection calculation, it still faces the challenge of floating-point errors. In addition, the existing methods usually need to globally process all surface meshes, and even non-intersecting regions will be processed, resulting in a high computational cost.

[0005] In the process of implementing the present invention, the inventors found that there are at least the following problems in the prior art: 1. Floating-point precision problem: Directly dealing with the intersection problem represented by floating-point numbers may lead to the non-robustness of the algorithm.

[0006] 2. Low global processing efficiency: It is necessary to uniformly process the entire surface mesh. Even if the intersecting region only accounts for a small part, it will still bring a large computational overhead.

[0007] 3. Difficulty in simultaneously achieving robustness and efficiency: The existing methods often sacrifice computational efficiency while pursuing accuracy and are difficult to meet the requirements of industrial applications. Summary of the Invention

[0008] Based on the above problems, the embodiments of the present application provide a fast local repair method for self-intersecting triangular meshes, which can effectively improve the robustness and efficiency of the repair, and at the same time generate high-quality meshes suitable for downstream applications.

[0009] According to an embodiment of the present application, a fast local repair method for self-intersecting triangular meshes is provided, including: S1: Preprocess the input triangular mesh; S2: Based on octree partitioning and connected component analysis, divide the preprocessed mesh into intersecting regions and non-intersecting regions, and extract the vertices and edges of the intersecting regions and non-intersecting regions; S3: In the intersecting regions, combine the extracted vertices and edges, construct an initial tetrahedral mesh with conformal boundaries through rational number calculations, and perform intersection repair; S4: Seamlessly splice the repaired intersecting region mesh and the non-intersecting region mesh to ensure consistent mesh topology; S5: Perform curvature-adaptive edge remeshing operations on the seamlessly spliced mesh.

[0010] The technical solutions provided by the embodiments of the present application may include the following beneficial effects: As can be seen from the above embodiments, the present application divides the input mesh into intersecting regions and non-intersecting regions through octree-based spatial partitioning and connected component analysis, and only repairs the intersecting regions, effectively reducing the computational cost of global processing and significantly improving the repair efficiency. By introducing rational number calculation technology, intersection points and conformal boundaries are accurately represented during the repair process of intersecting regions, avoiding error problems that may occur in traditional floating-point calculations, thereby significantly improving the robustness of the repair process and the accuracy of calculation results.

[0011] In addition, the present application introduces curvature-adaptive edge remeshing technology after mesh repair, which not only optimizes the triangle quality of the mesh but also avoids new intersection problems. The generated high-quality mesh can meet the requirements of downstream applications such as finite element analysis and volume mesh generation. In the present invention, only the coordinates of mesh points are adjusted, without involving modifications to the topological structure, ensuring that the repaired mesh remains unchanged in terms of topological consistency and solving the problem of inconsistent connection relationships between adjacent elements caused by topological changes in traditional methods.

[0012] A method combining local processing and volume optimization is proposed for the first time. By constructing an initial tetrahedral mesh and performing conformal boundary repair, it ensures that the volume of the generated mesh is positive, and at the same time realizes the high-quality generation of the overall mesh. The method of the present invention is applicable to complex geometric models, including meshes with rich details, boundary features, and multi-connectedness. Users can adjust mesh partitioning and optimization parameters according to actual needs, making the present invention highly flexible and adaptable.

[0013] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a flowchart of a fast local repair method for self - intersecting triangular meshes shown according to an exemplary embodiment.

[0015] Figure 2 It is a flowchart of a fast local repair method for self - intersecting triangular meshes shown according to an exemplary embodiment, showing the complete processing flow from pre - processing to remeshing.

[0016] Figure 3 It is an original model of an engine block shown according to an exemplary embodiment, showing many geometric errors contained in the original model.

[0017] Figure 4 It is a model of the engine block after pre - processing shown according to an exemplary embodiment, showing the effect of the pre - processed model.

[0018] Figure 5 It is the repair process of the engine block model shown according to an exemplary embodiment, showing multiple bounding box meshes constructed during the local repair process and the intersecting parts to be repaired.

[0019] Figure 6 It is a result comparison between the present method and a volume - based repair method on an engine block model shown according to an exemplary embodiment, where (a) is the processing result of the volume - based repair method and (b) is the processing result of the present method.

[0020] Figure 7 It is a model of the engine block after intersecting repair shown according to an exemplary embodiment, showing the effect of the model after intersecting repair.

[0021] Figure 8 It is a model of the engine block after remeshing shown according to an exemplary embodiment, showing the final model effect after all processes are completed.

[0022] Figure 9 It is the result of generating an engine block model and an oil pump jack by a volume - based repair method shown according to an exemplary embodiment.

[0023] Figure 10 It is a result comparison between the present method and a volume - based repair method on an oil pump jack model shown according to an exemplary embodiment, where Figure (a) is the processing result of the volume - based repair method and Figure (b) is the processing result of the present method. Detailed implementation manners

[0024] Exemplary embodiments will be described in detail herein. When the following description refers to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. On the contrary, they are merely examples of devices and methods consistent with some aspects of the present application as detailed in the appended claims.

[0025] Referring to Figure 1 and Figure 2 , an embodiment of the present invention provides a fast local repair method for self-intersecting triangular meshes, which may include the following steps: S1: Preprocess the input triangular mesh; S2: Based on octree partitioning and connected component analysis, divide the preprocessed mesh into intersecting regions and non-intersecting regions, and extract the vertices and edges of the intersecting regions and non-intersecting regions; S3: In the intersecting region, combine the extracted vertices and edges, construct an initial tetrahedral mesh with a conformal boundary through rational number calculations, and perform intersection repair; S4: Seamlessly splice the repaired intersecting region mesh and the non-intersecting region mesh to ensure consistent mesh topology; S5: Perform curvature-adaptive edge remeshing operations on the seamlessly spliced mesh.

[0026] As can be seen from the above embodiments, the present application effectively transforms the complex mesh intersection problem into an efficient repair process combining local optimization and global consistency by adopting an intersection triangle mesh repair method based on local processing and rational number calculations, and solves the problem of low efficiency of traditional methods in large-scale mesh processing.

[0027] Using the rational number calculation technology, intersection points and conformal boundaries can be accurately represented and processed, avoiding error problems that may occur in floating-point calculations, and significantly improving the robustness and reliability of the repair process. The octree partitioning and connected component analysis are introduced for the first time to divide the mesh into intersecting regions and non-intersecting regions, and only local repair is performed on the intersecting regions, greatly reducing the complexity of global calculations while ensuring that the non-intersecting region mesh maintains the original accuracy.

[0028] The present invention proposes a curvature-adaptive edge remeshing method based on the target edge length field, which can dynamically adjust the refinement degree of the mesh according to geometric features. Generate a higher density of meshes in high-curvature regions to capture details, while reduce unnecessary refinement in low-curvature regions, and the generated meshes reach a high level in terms of shape quality and distribution uniformity.

[0029] In addition, the present invention only adjusts the coordinates of the grid vertices without involving topological modifications of the grid, thereby ensuring topological consistency in the splicing area and avoiding connection problems caused by topological inconsistency in traditional methods. By detecting and repairing intersection problems in the real-time detection and optimization process, the present invention further improves the stability of grid optimization and the quality of the generated grid.

[0030] This application first proposes a method combining local processing and global optimization, which combines multiple technologies such as conformal boundary repair, tetrahedral mesh construction, and global smoothing processing, significantly improving the efficiency of intersecting mesh repair and the quality of the generated results. This method can be widely applied to processing mesh models of complex geometries, including three-dimensional models with richly detailed surfaces and complex boundary features. Specific application fields include: Aerospace: such as airplanes, rockets, etc.; Ship field: such as cargo ships, submarines, etc.; Engine field: such as cooling systems, ignition systems, etc.; Semiconductor field: such as chips, etc.; Nuclear physics field: such as targets, etc.; Structural field: such as dams, bridges, etc.; Biomechanics field: such as hearts, brains, etc. in many fields of fluid, electromagnetic, thermal, and mechanical simulations. Taking an engine block model as an example, the method of this application will be elaborated in detail below, and the rest of the three-dimensional models will not be elaborated one by one here.

[0031] In the specific implementation of S1: preprocess the input triangular mesh; this step may include the following sub-steps: S11: Adopt a remeshing algorithm based on edge operations to adjust the structure of the input mesh. This algorithm is guided by a constant-size field and constrained by a surface envelope to optimize the mesh size and quality while maintaining geometric fidelity; Specifically, remeshing gradually optimizes the mesh quality through local operations such as edge splitting, edge folding, edge swapping, and vertex smoothing on the input mesh. The constant-size field h is defined as 1% of the diagonal length of the model's axis-aligned bounding box to ensure that all edge lengths are uniform. The surface envelope is defined as a tolerance region with a thickness centered on the original surface and can be expressed as: where S is the original surface, is a three-dimensional vector space.

[0032] All modified triangles during the optimization process need to remain within this envelope. In addition, holes and gaps will be detected and repaired at this stage to ensure grid closure.

[0033] Taking the engine block model as an example, the initial mesh has a large number of triangles with uneven edge lengths, such as Figure 3As shown. Through the remeshing operation, the meshes in these regions are optimized into triangular meshes with uniform sizes, while the geometry is precisely retained, as Figure 4 shown.

[0034] S12: Meanwhile, by repairing holes and gaps, the input mesh is ensured to be closed, thereby generating a watertight mesh.

[0035] Specifically, the repair of holes and gaps includes identifying the non-closed parts of the boundary points, adding new vertices point by point and connecting them to the existing mesh structure to fill the voids. Meanwhile, redundant duplicate edges, isolated points, and non-manifold structures are detected and processed. The duplicate edges are merged, the isolated points are removed, and the non-manifold structures are transformed into manifold structures through local reconstruction, thus ensuring the topological integrity of the mesh.

[0036] Taking the engine block model as an example, there are multiple holes and gaps in the input mesh, such as Figure 3 shown. Through the repair operation, a complete watertight mesh is successfully generated, as Figure 4 shown, providing a reliable basis for subsequent intersection detection and optimization.

[0037] In the specific implementation of S2: Based on octree partitioning and connected component analysis, the preprocessed mesh is divided into intersecting regions and non-intersecting regions, and the vertices and edges of the intersecting regions and non-intersecting regions are extracted; this step may include the following sub-steps: S21: Construct an octree structure, divide the preprocessed mesh into multiple octree leaf nodes according to the spatial position, and each leaf node contains a subset of triangles; Specifically, the octree is a recursive spatial partitioning structure used to divide a three-dimensional mesh into multiple small regions, thereby improving the efficiency of intersection detection. The preprocessed mesh is denoted as: where is the total number of triangles in the mesh, is each triangular element.

[0038] Each leaf node of the octree contains a subset of triangles: Through this partitioning, the global detection problem can be decomposed into local sub-problems, thereby reducing the computational overhead.

[0039] S22: Perform intersection detection of triangle pairs in each octree leaf node and record all intersecting triangle pairs; Specifically, for each leaf node , for the subset of triangles it contains, for each pair of triangles , Perform intersection detection. The set of intersecting triangle pairs is defined as: In addition, extract all the triangles involved in the intersection to form a set of intersecting triangles: Taking the engine block model as an example, the intersection regions are accurately marked. The detection results show that there are intersections among multiple triangles, providing a clear target area for subsequent repair, as Figure 3 shown.

[0040] S23: Based on the intersection detection results, construct an undirected graph. The vertices of the graph represent the triangles involved in the intersection, and the edges represent the intersection relationships between these triangles; Specifically, according to the recorded intersecting triangle pairs, construct an undirected graph, where: where is the vertex set of the undirected graph, is the edge set of the undirected graph.

[0041] This undirected graph intuitively represents the intersection relationships between triangles and provides support for subsequent connected component analysis.

[0042] S24: Perform connected component analysis on the undirected graph, divide the intersecting triangles into multiple connected subgraphs, each subgraph corresponding to an independent intersection region, and at the same time classify the triangles that do not belong to any connected subgraph into the non-intersection region; Specifically, through connected component analysis, decompose the undirected graph into connected subgraphs: where, is the vertex set of the subgraph, is the edge set. Each subgraph The corresponding set of intersecting triangles is represented as: The set of non-intersecting triangles is: This division method effectively divides the mesh into intersection regions and non-intersection regions, providing a basis for subsequent repair operations.

[0043] S25: Extract the vertices and edges of the intersection regions and non-intersection regions.

[0044] Specifically, the vertex set and edge set of the intersection region are respectively defined as: Among them, , , represent the three vertices corresponding to each triangle.

[0045] The vertex set and edge set of the non-intersecting region are: In the specific implementation of S3: within the intersecting region, combining the extracted vertices and edges, construct an initial tetrahedral mesh with conformal boundaries through rational number calculations, and perform intersection repair; this step may include the following sub-steps: S31: Calculate the boundary bounding box of the intersecting region, slightly expand the bounding box to generate virtual vertices, and add these virtual vertices to the vertex set of the intersecting region; Specifically, for each intersecting region calculate its boundary bounding box, and slightly expand it based on its minimum and maximum points to generate 8 virtual vertices. These vertices together with the original vertex set of the intersecting region form a new vertex set . The expanded boundary bounding box can ensure that all intersecting regions are completely included within the mesh generation range.

[0046] Taking the engine block model as an example, after the bounding box is expanded, it completely covers the intersecting region, providing a complete geometric basis for generating the initial tetrahedral mesh, as Figure 5 shown.

[0047] S32: Based on the expanded vertex set, use the Bowyer-Watson algorithm to generate an initial tetrahedral mesh to ensure the topological integrity of the mesh; Specifically, use the Bowyer-Watson algorithm to construct an initial tetrahedral mesh on . This algorithm dynamically updates the tetrahedral elements by gradually inserting vertices, ensuring that the generated mesh conforms to the Delaunay property and has a good topological structure and geometric shape.

[0048] S33: Insert the triangles in the intersecting region into the initial tetrahedral mesh one by one, and achieve the restoration of the conformal boundary through rational number calculations to ensure that the mesh boundary is consistent with the original region; Specifically, insert the triangles in the intersecting region into the tetrahedral mesh one by one, and use rational number calculations to restore the boundary. When each triangle is inserted, use a binary space partitioning tree to clip the tetrahedral elements to ensure that the boundary is consistent with the original region. During the insertion process, all calculations are represented by rational numbers, ensuring the robustness of the calculations.

[0049] S34: Try to convert the tetrahedral mesh represented by rational numbers into a floating-point representation and detect whether the volume of the mesh is positive; Specifically, the vertex coordinates of the tetrahedral mesh are gradually converted from rational numbers to floating-point representations. During the conversion process, the volume of each tetrahedral element is calculated to ensure that all volumes are positive. If a negative-volume element is found, its vertices are recorded for further optimization.

[0050] S35: If there are negative-volume elements, perform volume mesh optimization under conformal boundary conditions, including inserting points on conformal edges, merging vertices, and optimizing the boundary shape, to ensure that the converted mesh maintains positive volume; Specifically, for negative-volume elements, adopt a local optimization strategy for repair, including: Inserting points: Add new vertices on conformal edges to adjust the mesh structure; Merging vertices: Merge two adjacent vertices into one to reduce sharp shapes in the mesh; Optimizing the boundary: Optimize the boundary shape by adjusting vertex positions to eliminate negative-volume elements.

[0051] During the optimization process, always comply with the boundary conformal conditions to avoid destroying the geometric features of the original region.

[0052] S36: After all points are successfully converted to floating-point numbers, extract the repaired surface mesh as the final result of the intersection repair.

[0053] Specifically, after the optimization is completed, extract the surface mesh from the tetrahedral mesh as the repair result. The surface mesh is consistent with the geometric shape of the original region, and at the same time, all intersection problems are eliminated, ensuring its applicability to subsequent downstream applications.

[0054] In the specific implementation of S4: Seamlessly splice the repaired intersection region mesh with the non-intersection region mesh to ensure the consistency of the mesh topology; this step may include the following sub-steps: S41: During the optimization process of the intersection region mesh, insert vertices on conformal edges; Specifically, during the repair phase of the intersection region, vertices have been inserted on conformal edges to ensure that the geometric properties of the conformal edges are retained. This process ensures the consistency of the boundaries of the intersection region and the non-intersection region, providing a basis for subsequent splicing operations.

[0055] S42: During the splicing phase, to ensure the consistency of the boundaries of the two regions, insert matching vertices on the corresponding boundaries of the non-intersection region mesh; Specifically, to ensure seamless splicing, insert vertices corresponding to the conformal edges of the intersection region on the boundaries of the non-intersection region mesh. The positions of these vertices are matched according to the conformal boundary of the intersection region, ensuring geometric consistency of the boundaries.

[0056] S43: Adjust the boundary grids of the non-intersecting region and the intersecting region to ensure consistent topology at the boundary; Through the alignment and insertion of boundary vertices, seamless splicing of the meshes of the two regions is completed to generate an overall mesh structure with consistent topology; Specifically, after the splicing is completed, the repaired intersecting region and non-intersecting region are seamlessly combined to generate an overall mesh structure, which has consistent topology and geometric seamlessness.

[0057] In the specific implementation of S5: Perform curvature-adaptive edge remeshing operation on the seamlessly spliced mesh; This step may include the following sub-steps: S51: Calculate the target edge length field based on discrete curvature. A smaller target edge length is used in the region with higher curvature to improve the mesh resolution; Specifically, the target edge length field is calculated from the discrete curvature of the vertices, where the curvature of each vertex is defined as: Target edge length Is calculated by the following formula: Among them, Is the geometric approximation tolerance defined by the user, which is used to control the mesh density in the region with higher curvature, Is the tolerance.

[0058] Reference Figure 6 , taking the engine block model as an example, a higher density target edge length field is generated in the high-curvature region, while the target edge length is sparser in the low-curvature region, thus realizing the efficient allocation of mesh resources, as shown in Figure 6 Shown in (b) of.

[0059] S52: Apply Laplacian smoothing operation to the target edge length field to reduce noise and ensure smooth transition of the edge length field; Specifically, perform Laplacian smoothing on the target edge length field to eliminate local noise and discontinuities, so as to ensure smooth transition of the target edge length field on the mesh surface and improve the stability of subsequent mesh optimization.

[0060] S53: Under the guidance of the target edge length field, iteratively perform local mesh optimization operations.

[0061] Specifically, optimize the mesh quality through operations such as edge splitting, edge folding, edge swapping, and vertex smoothing. These operations ensure the improvement of the triangle quality of the mesh and avoid the generation of new intersection problems.

[0062] The present invention is further described below through embodiments: Embodiment 1: In this embodiment, to verify the method of the present application, an engine block model is selected, such asFigure 3 As shown. The model contains 490 intersecting triangles and multiple gaps and slender triangles. After preprocessing, the model becomes closed and contains only 61 intersecting triangles. The number of intersections in the mesh is significantly reduced. In addition, in areas where the mesh topology is correct but there are geometric errors, the intersection problems are solved after remeshing. This improvement is attributed to local operations performed during preprocessing, such as smoothing, which makes the originally intersecting meshes non-intersecting through untangling. As Figure 4 shown, the preprocessing results of the model are presented. After the partitioning algorithm, the model is divided into multiple sets. For each intersecting set, a robust intersection operation based on rational numbers is introduced, and the rational numbers are gradually converted to floating-point numbers using volume mesh optimization. As Figure 5 shown, the partitioning results and the bounding box elements constructed for each intersecting set are presented. A total of 11 intersecting sets are identified. Finally, the repaired intersecting sets and non-intersecting sets are stitched together to obtain a surface mesh without intersections, as Figure 7 shown. The entire repair process is executed sequentially in three steps: partitioning, repair, and stitching, which only takes 4.04 seconds. This shows that the proposed local method significantly improves efficiency by reducing the problem scale. As Figure 8 shown, the final remeshing results are presented.

[0063] Example 2: To verify the superiority of the method of the present invention, it is compared with the current advanced volume mesh-based repair method. The volume mesh-based repair method is selected as the benchmark because it achieves a balance between computational efficiency and result validity in floating-point representation, while other existing methods either have difficulty handling floating-point precision problems or have low computational efficiency. To ensure fairness, the tolerance is set to 10 -4 times the diagonal length of the model bounding box, and the maximum number of iterations of the volume mesh-based repair method is limited to 30. As Figure 9 shown, the results of the volume mesh-based repair method for processing the engine block model and the oil pump jack model are presented. The detailed comparison is as Figure 6 and Figure 10 shown. It can be seen from the figures that the method of the present invention generates higher-quality meshes and correctly preserves the feature edges. In contrast, the volume mesh-based repair method shows excessive refinement locally, which is the result of continuous refinement to improve quality. The performance comparison is shown in Table 1. Although the method of the present invention is executed serially, its running time is still one order of magnitude faster than that of the volume mesh-based repair method. This shows that the method of the present invention has a significant advantage in terms of efficiency.

[0064] Table 1: Performance comparison data table of the method of the present invention and the volume mesh-based repair method for the engine block model and the oil pump jack model. Those skilled in the art will readily conceive of other embodiments of the present application after considering the specification and practicing the content disclosed herein. The present application is intended to cover any variations, uses, or adaptations of the present application, which follow the general principles of the present application and include well-known common general knowledge or conventional technical means in the technical field not disclosed in the present application. The specification and examples are only regarded as exemplary, and the true scope and spirit of the present application are pointed out by the claims.

[0065] It should be understood that the present application is not limited to the exact structures already described and shown in the drawings, nor is it limited to the application fields and their specific application scenarios already described above, and various modifications and changes can be made without departing from its scope. The scope of the present application is only limited by the appended claims.

Claims

1. A fast local repair method for self-intersecting triangular meshes, characterized in that: include: S1: preprocess the input triangle mesh; S2: Based on octree partitioning and connected component analysis, the preprocessed mesh is divided into intersecting areas and non-intersecting areas, and the vertices and edges of the intersecting areas and non-intersecting areas are extracted; S3: In the intersection area, the extracted vertices and edges are combined to construct the initial tetrahedral mesh of the conformal boundary through rational number calculation, and the intersection repair is performed; S4: seamlessly splice the repaired mesh of the intersecting area with the mesh of the non-intersecting area to ensure the consistency of the mesh topology; S5: Perform curvature-adaptive edge re-meshing on the seamlessly joined mesh.

2. The method according to claim 1, characterized in that Preprocess the input triangle mesh, including: S11: An edge-based remeshing algorithm is used to adjust the structure of the input mesh. The algorithm is guided by a constant size field and constrained by the surface envelope to optimize the mesh size and quality while maintaining geometric fidelity. S12: At the same time, the input mesh is ensured to be closed by repairing holes and gaps, thus generating a watertight mesh.

3. The method according to claim 1, characterized in that Based on octree partitioning and connected component analysis, the preprocessed mesh is divided into intersecting areas and non-intersecting areas, and the vertices and edges of the intersecting areas and non-intersecting areas are extracted, including: S21: construct an octree structure, divide the preprocessed mesh into multiple octree leaf nodes according to the spatial position, and each leaf node contains a triangle subset; S22: Perform intersection detection of triangle pairs in each octave leaf node and record all intersecting triangle pairs; S23: Based on the intersection detection result, an undirected graph is constructed, where the vertices of the graph represent the triangles involved in the intersection, and the edges represent the intersection relationship between these triangles; S24: performing connected component analysis on the undirected graph, dividing the intersecting triangles into multiple connected subgraphs, each subgraph corresponding to an independent intersecting region, and classifying triangles that do not belong to any connected subgraph into non-intersecting regions; S25: Extracting vertices and edges of the intersecting area and the non-intersecting area.

4. The method according to claim 1, characterized in that: In the intersection area, the extracted vertices and edges are combined to construct the initial tetrahedral mesh of the conformal boundary through rational number calculation, and the intersection repair is performed, including: S31: Calculate the bounding box of the intersection area, slightly expand the bounding box to generate virtual vertices, and add these virtual vertices to the vertex set of the intersection area; S32: Based on the expanded vertex set, the Bowyer-Watson algorithm is used to generate the initial tetrahedral mesh to ensure the topological integrity of the mesh; S33: inserting the triangles in the intersection area into the initial tetrahedral mesh one by one, and restoring the conformal boundary through rational number calculation to ensure that the mesh boundary is consistent with the original area; S34: Try to convert the tetrahedral mesh represented by rational numbers into floating point representation and detect whether the volume of the mesh is positive; S35: If negative volume cells exist, perform volume mesh optimization under conformal boundary conditions, including inserting points on conformal edges, merging vertices, and optimizing boundary shapes to ensure that the converted mesh maintains positive volume; S36: After all points are successfully converted to floating point numbers, the repaired surface mesh is extracted as the final result of the intersection repair.

5. The method according to claim 1, characterized in that: Seamlessly splice the repaired meshes in the intersecting area with the meshes in the non-intersecting area to ensure the consistency of the mesh topology, including: S41: Insert vertices on conformal edges during mesh optimization in intersection regions; S42: In the stitching stage, to ensure the consistency of the boundaries of the two regions, matching vertices are inserted on the corresponding boundaries of the meshes of the non-intersecting regions; S43: Adjust the boundary meshes of the non-intersecting area and the intersecting area to ensure the topological structure at the boundary is consistent.

6. The method according to claim 1, characterized in that Perform curvature-adaptive edge re-meshing operations on the seamlessly spliced ​​mesh, including: S51: Calculate the target edge length field based on discrete curvature, and use smaller target edge lengths in areas with higher curvature to improve grid resolution; S52: Apply Laplace smoothing operation to the target edge length field to reduce noise and ensure smooth transition of the edge length field; S53: Under the guidance of the target edge length field, iteratively perform local mesh optimization operations.

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