Rapid self-adaptive re-gridding method for triangular mesh without self-intersection

Abstract

The invention discloses a rapid self-adaptive re-gridding method for a triangular mesh without self-intersection. According to the method, intersection detection is executed only in a key region by dynamically identifying the key region in a region with a complex structure. A flipping sensing energy mechanism is introduced, and triangular flipping and generation of irregular sharp edges are effectively avoided by constraining an optimization space of local re-gridding operation. On the basis of a discrete curvature initialization size field, in combination with Laplacian smoothing and quasi-geometric adjustment algorithms, smooth transition of the size field is rapidly achieved, the strip phenomenon is eliminated, and the grid quality is improved. The method is suitable for high-defect, non-manifold and multi-component input, and can quickly generate a high-quality triangular mesh on the premise of ensuring no intersection. Experiments show that when the method is used for processing complex models, the efficiency is improved by one order of magnitude compared with that of a traditional method, non-intersecting grids can be generated on all test models, and the method is suitable for computer graphics application such as numerical simulation, modeling and animation.

Description

Technical Field

[0001] The present invention relates to the fields of computer graphics and geometric processing, and in particular, to a fast adaptive remeshing method for triangle meshes without self - intersection. Background Art

[0002] Triangle meshes are a fundamental representation in computer graphics and geometric processing, and are widely used in numerical simulation, 3D modeling, animation and other fields. However, during the mesh remeshing process, local remeshing operations (such as edge collapse, edge split) may cause mesh intersection or triangle flipping, affecting the mesh quality and hindering downstream applications (such as constrained Delaunay tetrahedralization). These defects not only reduce the geometric accuracy, but also have a negative impact on tasks such as finite element analysis and shape thickness calculation.

[0003] In the prior art, the methods for solving the mesh intersection problem are mainly divided into two categories: 1. Global intersection detection methods based on surface meshes: Such methods detect intersections caused by local remeshing operations in real - time and reject operations that lead to intersections. Although spatial data structures (such as octrees) can accelerate the detection, due to the frequent modification of the mesh during the remeshing process, the data structure needs to be updated frequently and a large number of intersection detections are required, resulting in an efficiency bottleneck.

[0004] 2. Volume - based mesh methods: Such methods transform the surface mesh intersection problem into maintaining positive volume to avoid intersections by introducing tetrahedral meshes.

[0005] However, in the process of implementing the present invention, the inventors found that there are at least the following problems in the prior art: 1. Efficiency bottleneck: Global intersection detection methods need to update the spatial data structure frequently and perform a large number of detections, resulting in excessive computational overhead and being difficult to meet the requirements of real - time interactive applications.

[0006] 2. Limited flexibility: Volume - based mesh methods are limited by the complexity of tetrahedral meshes and are difficult to efficiently process complex geometric structures.

[0007] 3. Difficulty in balancing robustness and efficiency: Existing methods often sacrifice computational efficiency or mesh quality while pursuing intersection - free, and are difficult to meet the actual application requirements. Summary of the Invention

[0008] Based on the above problems, the embodiments of the present application provide a fast adaptive remeshing method for triangle meshes without self - intersection, which can effectively improve the robustness and efficiency of remeshing, and at the same time generate high - quality meshes suitable for downstream applications, and is applicable to applications such as numerical simulation, modeling, and animation.

[0009] According to an embodiment of the present application, a method for fast adaptive remeshing of a triangle mesh without self-intersection is provided, including: S1: Obtain a geometric model to be processed and perform mesh division on the geometric model to obtain a non-intersecting triangle mesh; S2: Perform remeshing on the non-intersecting triangle mesh to obtain a triangle mesh after remeshing; S3: Construct an octree data structure for the triangle mesh after remeshing to manage the triangles in the mesh, detect intersecting triangle pairs in the initial mesh, and generate an undirected graph; S4: Perform connected component analysis on the undirected graph, dynamically identify key regions, and generate axis-aligned bounding boxes for the key regions; S5: Detect whether the triangles in the mesh intersect with the axis-aligned bounding boxes of the key regions, perform local remeshing operations on the intersecting triangles, ensure no intersection after the local remeshing operation through an intersection detection algorithm, introduce a flip-aware energy mechanism for judgment, calculate the change in dihedral angle before and after the local remeshing operation, constrain the optimization space to prevent triangle flipping, and reject local remeshing operations that exceed a preset energy threshold; S6: For the geometric model after local remeshing operation, based on the initialized discrete curvature size field of the non-intersecting triangle mesh, eliminate noise by combining Laplacian smoothing, and achieve smooth transition of the size field through a quasi-geometric adjustment algorithm to eliminate the banding phenomenon; S7: Repeat S2 - S6 until a non-intersecting and high-quality triangle mesh of the geometric model is generated.

[0010] The technical solution provided by the embodiment of the present application may include the following beneficial effects: As can be seen from the above embodiments, the present application significantly reduces the computational cost of global intersection detection and improves the remeshing efficiency through adaptive intersection detection based on key regions and local remeshing operation optimization. By introducing a flip-aware energy mechanism, the optimization space of local remeshing operations is constrained, effectively avoiding triangle flipping and the generation of irregular sharp edges, thus significantly improving the mesh quality and robustness. In addition, the present application initializes the size field based on discrete curvature, combines Laplacian smoothing and a quasi-geometric adjustment algorithm, quickly realizes the smooth transition of the size field, eliminates the banding phenomenon, and further improves the overall quality of the mesh.

[0011] In the remeshing process of the present application, only the triangles intersecting with the key regions are subjected to local remeshing operations, and the intersection detection algorithm is used to ensure no intersection after the operation, avoiding the low efficiency problem of global detection of the entire mesh in traditional methods. At the same time, by dynamically updating the key region set, it is ensured that newly generated intersecting regions are timely identified and processed, further improving the robustness and adaptability of the algorithm.

[0012] In addition, by introducing a flip-aware energy mechanism, the present application calculates the change in dihedral angle before and after the local remeshing operation, constrains the optimization space to prevent triangle flipping, and rejects operations that exceed the preset energy threshold, effectively avoiding the degradation of mesh quality and the generation of sharp edges caused by flipping. By initializing the size field based on discrete curvature and combining Laplacian smoothing and quasi-geometric adjustment algorithms, a smooth transition of the size field is quickly achieved, eliminating the banding phenomenon caused by the low quality of the background mesh and further improving the overall quality of the mesh.

[0013] The method of the present application is applicable to high-genus, non-manifold, and multi-component inputs. It can quickly generate high-quality triangular meshes without intersection, significantly improving the efficiency and robustness of remeshing, and is applicable to computer graphics applications such as numerical simulation, modeling, and animation. Users can adjust geometric fidelity parameters, flip-aware energy thresholds, and size field scale factors according to actual needs, making the present invention highly flexible and adaptable.

[0014] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and do not limit the present application. Brief Description of the Drawings

[0015] Figure 1 is a text flow chart of a fast adaptive remeshing method for a non-self-intersecting triangular mesh shown according to an exemplary embodiment.

[0016] Figure 2 is a model flow chart of a fast adaptive remeshing method for a non-self-intersecting triangular mesh shown according to an exemplary embodiment.

[0017] Figure 3 is a schematic diagram of 4 local remeshing operations shown according to an exemplary embodiment.

[0018] Figure 4 is a full-process diagram of using this method for a gear model of an automotive transmission system shown according to an exemplary embodiment.

[0019] Figure 5 is a mesh model obtained by using this method for an aeroengine combustion chamber model shown according to an exemplary embodiment. Detailed Description of the Embodiments

[0020] Here, the exemplary embodiments will be described in detail. When the following description refers to the 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.

[0021] The method of the present invention combines local remeshing operation constraints with global size field optimization. Through the synergistic effect of key region detection, flip suppression, and size field smoothing techniques, the efficiency and quality of non-intersecting mesh generation are significantly improved. This method can be widely applied to the processing of complex geometric models, including high-genus, non-manifold, and multi-component structures. 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 the heart, brain, etc. in many fields of fluid, electromagnetic, thermal, and mechanical simulations. Taking some models as examples below, the application process of this method is elaborated in detail. Through the key region identification of this method, only local optimization is performed on the overlapping envelope region, and high-quality non-intersecting meshes are generated by combining size field adjustment, meeting the accuracy requirements of numerical simulations. Other complex models can be adapted according to this process, which will not be elaborated here.

[0022] Reference Figure 1 and Figure 2 , an embodiment of the present invention provides a fast adaptive remeshing method for non-self-intersecting triangular meshes, which may include the following steps: S1: Obtain the geometric model to be processed and perform mesh division on the geometric model to obtain non-intersecting triangular meshes; S2: Perform remeshing on the non-intersecting triangular meshes to obtain the triangular meshes after remeshing; S3: Construct an octree data structure for the triangular meshes after remeshing to manage the triangles in the mesh, and detect the intersecting triangle pairs in the initial mesh to generate an undirected graph; S4: Perform connected component analysis on the undirected graph, dynamically identify key regions, and generate axis-aligned bounding boxes for the key regions; S5: Detect whether the triangles in the mesh intersect with the axis-aligned bounding boxes of the key regions, perform local remeshing operations on the intersecting triangles, and ensure no intersection after local remeshing through an intersection detection algorithm. At the same time, introduce a flip-aware energy mechanism for judgment, calculate the dihedral angle change before and after local remeshing operations, constrain the optimization space to prevent triangle flipping, and reject local remeshing operations that exceed the preset energy threshold; S6: For the geometric model after local remeshing operations, based on the initialized discrete curvature size field of non-intersecting triangular meshes, combine Laplacian smoothing to eliminate noise, and achieve smooth transition of the size field through a quasi-geometric adjustment algorithm to eliminate striping phenomena; S7: Repeat S2 - S6 until non-intersecting and high-quality geometric model triangular meshes are generated.

[0023] As can be seen from the above embodiments, by adopting the adaptive non-intersecting remeshing method based on key regions, the present application transforms the complex mesh intersection problem into an efficient processing flow combining local optimization and global size field adjustment, and solves the problem of low efficiency of traditional global detection methods in large-scale mesh processing.

[0024] Through the key region dynamic recognition mechanism, using octree partitioning and connected component analysis, the input mesh is divided into key regions with complex structures and non-key regions. Only local remeshing operations (such as edge splitting and edge folding) and intersection detection are performed on the key regions, significantly reducing the computational complexity. Experiments show that the efficiency of this method is one order of magnitude higher than that of traditional methods when processing models with thin-walled structures and high-overlap envelopes.

[0025] The present invention proposes a flip-aware energy mechanism. By quantifying the positive change in the dihedral angle before and after local remeshing operations, the optimization space is constrained to avoid triangle flipping and the generation of sharp edges, significantly improving the mesh quality. Combining with the discrete curvature-driven size field optimization, dense meshes are generated in high-curvature regions to retain geometric details, and redundant cells are reduced in flat regions, ensuring a balance between geometric fidelity and uniformity of the mesh. In addition, this method only adjusts the vertex coordinates of the mesh (such as vertex smoothing and edge operations) without modifying the topology, thus maintaining the topological consistency of the mesh and avoiding connection anomalies caused by topological changes in traditional methods. By dynamically updating the set of key regions and real-time intersection detection, the stability of the algorithm and the reliability of the output mesh are further improved.

[0026] In the specific implementation of S1: Obtain the geometric model to be processed and perform mesh partitioning on the geometric model to obtain a non-intersecting triangular mesh; Specifically, obtain the geometric model to be processed. The geometric model may include high-genus, non-manifold, and multi-component structures. The specific application fields may 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 target bodies, etc.; Structural field: such as dams, bridges, etc.; Biomechanics field: such as hearts, brains, etc. in many fields for fluid, electromagnetic, thermal, mechanical, etc. simulation. This embodiment takes the gear model of the automotive transmission system as an example to elaborate.

[0027] For the obtained geometric model, the "Fast and Robust Mesh Arrangements using Floating-point Arithmetic" algorithm can be used. References: Cherchi, G., Livesu, M., Scateni, R., & Attene, M. (2020). Fast and robust mesh arrangements using floating-point arithmetic. ACM Transactions on Graphics , 39(6). https: / / doi.org / 10.1145 / 3414685.3417818》 or the "Exact and Efficient Intersection Resolution for Mesh Arrangements" algorithm. References: Guo, J.-P., & Fu, X.-M. (2024). Exact and efficient intersection resolution for mesh arrangements. ACM Transactions on Graphics , 43(6), 1–14. https: / / doi.org / 10.1145 / 3687925》, the geometric model to be processed is meshed to obtain a non-intersecting triangular mesh, which is beneficial to the subsequent remeshing step.

[0028] In the specific implementation of S2: The non-intersecting triangular mesh is remeshed to obtain a remeshed triangular mesh; this step may include the following sub-steps: S21: Perform a local remeshing operation on the non-intersecting triangular mesh, and at the same time introduce a flip-aware energy mechanism for judgment, calculate the change in dihedral angle before and after the local remeshing operation, constrain the optimization space to prevent triangle flipping, and reject local remeshing operations that exceed the preset energy threshold; this step may include the following sub-steps: S211: Perform a local remeshing operation, and the local remeshing operation includes edge splitting, edge collapsing, edge swapping, and vertex smoothing; Specifically, as Figure 3 shown, to perform a local remeshing operation.

[0029] S212: When performing edge collapsing, edge swapping, and vertex smoothing operations, calculate the change value of the dihedral angle of each associated edge before and after the operation; Specifically, for each local remeshing operation, traverse the affected edge set and calculate the dihedral angle change value of each triangular shared edge before and after the operation. Define the dihedral angle before the operation as and the dihedral angle after the operation as .

[0030] S213: Accumulate the positive change values of all edge dihedral angles to generate flip-aware energy. Specifically, accumulate the positive dihedral angle change values of all edges to generate flip-aware energy. .

[0031] S214: Compare the flip-aware energy value with a preset threshold. If it is greater, reject the operation; if it is less, accept the operation and update the mesh, while avoiding the generation of sharp edges and low-quality triangles caused by flipping.

[0032] Specifically, the preset threshold is default set to 30°. If , reject the operation; otherwise, accept the operation and update the mesh, which effectively avoids the generation of triangle flipping and irregular sharp edges, thus significantly improving the mesh quality and robustness.

[0033] S22: For the model after local remeshing, initialize the discrete curvature size field based on the non-intersecting triangle mesh, eliminate noise by combining Laplacian smoothing, and achieve smooth transition of the size field through the quasi-geometric adjustment algorithm to eliminate striping, obtaining the triangular mesh after remeshing. This step may include the following sub-steps: S221: Calculate the size field based on the initialization of discrete curvature of the non-intersecting triangle mesh; Specifically, for each vertex , calculate its maximum absolute curvature , where and are the maximum and minimum principal curvatures at . Calculate the initial size value according to the geometric fidelity parameter .

[0034] S222: Apply Laplacian smoothing to the size field to eliminate local size anomalies caused by noise data; Specifically, perform two Laplacian smoothing operations on the vertex size values at non-feature edge positions, which eliminates local size mutations caused by discrete curvature calculation errors or noise data.

[0035] S223: Limit the ratio of size differences between adjacent nodes through the quasi-geometric adjustment algorithm to achieve a smooth transition of the size field, eliminate the banding phenomenon caused by low-quality background meshes, and generate a high-quality size field.

[0036] Specifically, for each edge , where and are the coordinate values of the two endpoints of the edge respectively, calculate its length and the size difference . and are respectively and 's size values. According to , iteratively update the size values to meet the constraint conditions. The update formula is: (assuming ). This generates a dense mesh in high-curvature regions to retain geometric details and reduces redundant cells in flat regions, ensuring a balance between geometric fidelity and uniformity of the mesh.

[0037] In the specific implementation of S3: Construct an octree data structure for the triangular mesh after remeshing to manage the triangles in the mesh, and detect pairs of intersecting triangles in the initial mesh to generate an undirected graph. This step may include the following sub-steps: S31: Divide the triangular mesh after remeshing into spatial regions and construct an octree data structure, where each leaf node stores a subset of triangles; Specifically, divide the triangles in the input mesh into multiple leaf nodes according to their spatial positions, and each leaf node contains a subset of triangles (where represents the leaf node index of the octree). Through the octree structure , efficiently manage the triangles in the mesh and provide support for subsequent intersection detection.

[0038] S32: Perform intersection detection of triangle pairs in parallel in each leaf node, and independently judge the intersection relationships between all triangles within the leaf node; Specifically, in each octree leaf node , independently detect the intersection relationships between the subset of triangles it contains.

[0039] S33: According to the intersection relationships between triangles, record all intersecting triangle pairs to generate an intersecting triangle set; Specifically, record all intersecting triangle pairs to generate an intersecting triangle set , . represents the The remeshed grid after the next iteration.

[0040] S34: Based on the set of intersecting triangles, generate a set that contains all the intersecting triangles; Specifically, based on the set of intersecting triangles , generate a set that contains all the intersecting triangles , .

[0041] S35: If the generated set that contains all the intersecting triangles is empty, determine that there is no intersection in the current grid; otherwise, construct an undirected graph based on this set.

[0042] Specifically, if , determine that there is no intersection in the current grid; otherwise, construct an undirected graph based on , where the vertices represent the intersecting triangles, and the edges represent the intersection relationships between the triangles.

[0043] In the specific implementation of S4: Perform connected component analysis on the undirected graph, dynamically identify the key regions, and generate axis-aligned bounding boxes for the key regions; this step may include the following sub-steps: S41: Perform connected component analysis on the undirected graph and extract all the connected components; Specifically, perform connected component analysis on the undirected graph and extract all the connected components , where is the total number of connected components.

[0044] S42: Calculate the minimum and maximum coordinates of all the triangles contained in each connected component and generate an axis-aligned bounding box; Specifically, each connected component corresponds to a key region, and its axis-aligned bounding box , , where represents a vertex of and respectively represent the minimum and maximum coordinates of the triangle .

[0045] S43: Add the axis-aligned bounding box of each connected component to the key regions to generate the axis-aligned bounding boxes of the key regions.

[0046] Specifically, add the axis-aligned bounding box of each connected component to the set of key regions , , to form a dynamic detection range.

[0047] In the specific implementation of S5: Detect whether the triangles in the grid intersect with the axis-aligned bounding box of the key region, perform local remeshing operations on the intersecting triangles, and ensure no intersection after the local remeshing operation through the intersection detection algorithm. At the same time, introduce a flip-aware energy mechanism for judgment, calculate the change in dihedral angle before and after the local remeshing operation, constrain the optimization space to prevent triangle flipping, and reject local remeshing operations that exceed the preset energy threshold; this step may include the following sub-steps: S51: Calculate the axis-aligned bounding box of each triangle and detect whether it intersects with the set of key regions. If it intersects, mark the triangle as a triangle that needs intersection detection; Specifically, for each triangle , calculate its axis-aligned bounding box . If intersects with the set of key regions , mark , indicating that this triangle needs to perform intersection detection.

[0048] S52: Perform local remeshing operations and detect whether the newly generated triangles intersect with the existing triangles to ensure that the mesh remains non-intersecting after all local remeshing operations. The local remeshing operations include edge splitting, edge folding, edge swapping, and vertex smoothing.

[0049] Specifically, as Figure 3 shown, when performing local remeshing operations, use the intersection detection algorithm to temporarily remove all marked triangles ( ) to avoid misjudgment, perform intersection detection on the newly generated triangles and the existing triangles in the octree . If intersection is detected, reject the operation and restore the original mesh; otherwise, accept the operation and update the octree.

[0050] S53: When performing edge folding, edge swapping, and vertex smoothing operations, calculate the change value of the dihedral angle of each associated edge before and after the operation respectively; Specifically, for each local remeshing operation, traverse the affected edge set and calculate the change value of the dihedral angle of each triangle shared edge . Define the dihedral angle before the operation as , and the dihedral angle after the operation as .

[0051] S54: Accumulate the positive change values of all edge dihedral angles to generate flip-aware energy; Specifically, accumulate the positive dihedral angle change values of all edges to generate flip-aware energy .

[0052] S55: Compare the flip-aware energy value with a preset threshold. If it is greater, reject the operation; if it is less, accept the operation and update the mesh, while avoiding the generation of sharp edges and low-quality triangles caused by flipping.

[0053] Specifically, the preset threshold is default set to 30°. If , reject the operation; otherwise, accept the operation and update the mesh, which effectively avoids the generation of triangle flipping and irregular sharp edges, thereby significantly improving the mesh quality and robustness.

[0054] Through the key region dynamic recognition mechanism, using octree partitioning and connected component analysis, the input mesh is divided into key regions with complex structures and non-key regions. Only local remeshing operations (such as edge splitting and edge folding) and intersection detection are performed on the key regions, significantly reducing the computational complexity. Experiments show that the efficiency of this method is one order of magnitude higher than that of traditional methods when dealing with models with thin-walled structures and high-overlap envelopes.

[0055] The present invention proposes a flip-aware energy mechanism. By quantifying the positive change of the dihedral angle before and after local remeshing operations, the optimization space is constrained to avoid triangle flipping and sharp edge generation, significantly improving the mesh quality. Combining discrete curvature-driven size field optimization, dense meshes are generated in high-curvature regions to retain geometric details, and redundant cells are reduced in flat regions, ensuring a balance between geometric fidelity and uniformity of the mesh. In addition, this method only adjusts the vertex coordinates of the mesh (such as vertex smoothing and edge operations) without modifying the topology structure, thereby maintaining the topological consistency of the mesh and avoiding connection anomalies caused by topological changes in traditional methods. By dynamically updating the set of key regions and real-time intersection detection, the stability of the algorithm and the reliability of the output mesh are further improved.

[0056] In the specific implementation of S6: For the geometric model after local remeshing operations, based on the initialized discrete curvature size field of the non-intersecting triangle mesh, Laplace smoothing is combined to eliminate noise, and a quasi-geometric adjustment algorithm is used to achieve smooth transition of the size field and eliminate the striping phenomenon; this step may include the following sub-steps: S61: Calculate the size field based on the initialized discrete curvature of the non-intersecting triangle mesh; Specifically, for each vertex , calculate its maximum absolute curvature , where and are the maximum and minimum principal curvatures at . According to the geometric fidelity parameter , calculate the initial size value .

[0057] S62: Apply Laplacian smoothing to the size field to eliminate local size anomalies caused by noisy data; Specifically, perform two Laplacian smoothing operations on the vertex size values at non-feature edge positions, which eliminates local size mutations caused by discrete curvature calculation errors or noisy data.

[0058] S63: Limit the ratio of size differences between adjacent nodes through the quasi-geometric adjustment algorithm to achieve a smooth transition of the size field, eliminate the banding phenomenon caused by low-quality background meshes, and generate a high-quality size field.

[0059] Specifically, for each edge , where , are the coordinate values of the two endpoints of the edge respectively, calculate its length and the size difference , , are , 's size values respectively. According to , iteratively update the size values to meet the constraint conditions, and the update formula is: (assuming ), which generates a dense mesh in high-curvature regions to retain geometric details and reduces redundant cells in flat regions, ensuring a balance between geometric fidelity and uniformity of the mesh.

[0060] Compared with the remeshing step of S2, S5 and S6 introduce a key region dynamic recognition mechanism on the basis of S2. Using octree partitioning and connected component analysis, the input mesh is divided into key regions with complex structures and non-key regions, and only local remeshing operations (such as edge splitting and edge folding) and intersection detection are performed on the key regions, which can optimize the remeshing results of S2 and significantly reduce the computational complexity.

[0061] In the specific implementation of S7: Repeat S2 - S6 until a non-intersecting and high-quality geometric model triangular mesh is generated.

[0062] The following further illustrates the present invention through embodiments: In one embodiment, a gear model of an automotive transmission system is selected as the input. As Figure 4 shown, after the operation of this method, a non-structured surface mesh with high quality is generated.

[0063] In another embodiment, a combustion chamber model of an aerospace engine is selected as the input. As Figure 5 shown, after the operation of this method, a non-structured surface mesh with high quality is generated.

[0064] To verify the superiority of the method of the present invention, 5,469 non-intersecting models from the Thingi10K dataset were selected. As shown in Table 1, the method of the present invention successfully generated non-intersecting meshes for all models, with a success rate of 100%, which is better than the 90.13% success rate of CGAL (The Computational Geometry Algorithms Library) and the 73.19% success rate of MMGS (MmgTools). Moreover, it is also comprehensively superior to the other two methods in terms of computational performance and mesh quality.

[0065] Table 1: Comparison table of the success rate, computational performance, and mesh quality of the present invention and other methods on all 5,469 non-intersecting meshes from the Thingi10k (ten-thousand-models) dataset, where represents the number of triangular meshes, represents the number of intersecting triangles.

[0066]

[0067] After considering the specification and practicing the content disclosed herein, those skilled in the art will readily conceive of other embodiments of the present application. 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 the common general knowledge or conventional technical means in the technical field not disclosed in the present application. The specification and examples are only illustrative, and the true scope and spirit of the present application are pointed out by the claims.

[0068] 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 specific application scenarios already described, 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 adaptive remeshing method for a non-self-intersecting triangular mesh, characterized in that Including: S1: Obtain the geometric model to be processed and perform mesh division on the geometric model to obtain a non-intersecting triangular mesh; S2: Perform remeshing on the non-intersecting triangular mesh to obtain the triangular mesh after remeshing; S3: Construct an octree data structure for the triangular mesh after remeshing to manage the triangles in the mesh, detect the intersecting triangle pairs in the initial mesh, and generate an undirected graph; S4: Perform connected component analysis on the undirected graph, dynamically identify the key regions, and generate the axis-aligned bounding boxes of the key regions; S5: Detect whether the triangles in the mesh intersect with the axis-aligned bounding boxes of the key regions, perform local remeshing operations on the intersecting triangles, ensure no intersection after the local remeshing operation through the intersection detection algorithm, introduce a flip-aware energy mechanism for judgment, calculate the change in dihedral angle before and after the local remeshing operation, constrain the optimization space to prevent triangle flipping, and reject the local remeshing operations that exceed the preset energy threshold; S6: For the geometric model after the local remeshing operation, based on the initialized discrete curvature size field of the non-intersecting triangular mesh, eliminate noise by combining Laplacian smoothing, and achieve smooth transition of the size field through the quasi-geometric adjustment algorithm to eliminate the striping phenomenon; S7: Repeat S2 - S6 until a non-intersecting and high-quality triangular mesh of the geometric model is generated.

2. The method according to claim 1, characterized in that, Performing remeshing on the non-intersecting triangular mesh to obtain the triangular mesh after remeshing specifically includes: Perform local remeshing operations on the non-intersecting triangular mesh, introduce a flip-aware energy mechanism for judgment, calculate the change in dihedral angle before and after the local remeshing operation, constrain the optimization space to prevent triangle flipping, and reject the local remeshing operations that exceed the preset energy threshold; For the model after local remeshing, based on the initialized discrete curvature size field of the non-intersecting triangular mesh, eliminate noise by combining Laplacian smoothing, and achieve smooth transition of the size field through the quasi-geometric adjustment algorithm to eliminate the striping phenomenon, thereby obtaining the triangular mesh after remeshing.

3. The method according to claim 2, wherein Introducing a flip-aware energy mechanism for judgment, calculating the change in dihedral angle before and after the local remeshing operation, constraining the optimization space to prevent triangle flipping, and rejecting the local remeshing operations that exceed the preset energy threshold specifically includes: When performing edge collapse, edge swap, and vertex smoothing operations, calculate the change value of the dihedral angle of each associated edge before and after the operation respectively; Accumulate the positive change values of the dihedral angles of all edges to generate the flip-aware energy; Compare the flip-aware energy value with the preset threshold. If it is greater, reject the operation. If it is less, accept the operation and update the mesh, while avoiding the generation of sharp edges and low-quality triangles caused by flipping.

4. The method according to claim 2, wherein For the geometric model after the local remeshing operation, based on the initialized discrete curvature size field of the non-intersecting triangular mesh, eliminate noise by combining Laplacian smoothing, and achieve smooth transition of the size field through the quasi-geometric adjustment algorithm to eliminate the striping phenomenon specifically includes: Calculate the size field based on the initialized discrete curvature of the non-intersecting triangular mesh; Apply Laplacian smoothing to the size field to eliminate local size anomalies caused by noisy data; Limit the ratio of size differences between adjacent nodes through the quasi-geometric adjustment algorithm to achieve a smooth transition of the size field, eliminate the banding phenomenon caused by low-quality background meshes, and generate a high-quality size field.

5. The method according to claim 1, wherein Construct an octree data structure for the triangular mesh after remeshing to manage the triangles in the mesh, and detect intersecting triangle pairs in the initial mesh to generate an undirected graph, specifically including: Divide the triangular mesh after remeshing into spatial regions and construct an octree data structure, where each leaf node stores a subset of triangles; Perform the intersection detection of triangle pairs in parallel in each leaf node and independently judge the intersection relationships between all triangles within the leaf node; Record all intersecting triangle pairs according to the intersection relationships between triangles to generate an intersecting triangle set; Generate a set that contains all intersecting triangles based on the intersecting triangle set; If the generated set that contains all intersecting triangles is empty, determine that there is no intersection in the current mesh, otherwise construct an undirected graph based on this set.

6. The method according to claim 1, characterized in that Perform connected component analysis on the undirected graph, dynamically identify key regions, and generate axis-aligned bounding boxes for the key regions, specifically including: Perform connected component analysis on the undirected graph to extract all connected components; Calculate the minimum and maximum coordinates of all triangles contained in each connected component to generate an axis-aligned bounding box; Add the axis-aligned bounding boxes of each connected component to the key regions to generate the axis-aligned bounding boxes of the key regions.

7. The method according to claim 1, wherein Detect whether the triangles in the mesh intersect the axis-aligned bounding boxes of the key regions, perform local remeshing operations on the intersecting triangles, and ensure no intersection after the local remeshing operation through the intersection detection algorithm, specifically including: Calculate the axis-aligned bounding box for each triangle and detect whether it intersects the key region. If it intersects, mark the triangle as a triangle that needs intersection detection; Perform local remeshing operations and detect whether the newly generated triangles intersect the existing triangles to ensure that the mesh remains intersection-free after all local remeshing operations. The local remeshing operations include edge splitting, edge folding, edge swapping, and vertex smoothing.

8. The method according to claim 1, characterized in that, Introduce a flip-aware energy mechanism for judgment, calculate the change in dihedral angles before and after local remeshing operations, constrain the optimization space to prevent triangle flipping, and reject local remeshing operations that exceed the preset energy threshold, specifically including: When performing edge folding, edge swapping, and vertex smoothing operations, calculate the change values of the dihedral angles of each associated edge before and after the operation respectively; Accumulate the positive change values of all edge dihedral angles to generate the flip-aware energy; Compare the flip-aware energy value with the preset threshold. If it is greater, reject the operation. If it is less, accept the operation and update the mesh, while avoiding the generation of sharp edges and low-quality triangles caused by flipping.

9. The method according to claim 1, characterized in that For the geometric model after local remeshing operations, based on the initialized discrete curvature size field of the intersection-free triangular mesh, combine Laplacian smoothing to eliminate noise, and achieve a smooth transition of the size field through the quasi-geometric adjustment algorithm to eliminate the banding phenomenon, specifically including: Initialize the discrete curvature calculation size field based on a non-intersecting triangular mesh; Apply Laplacian smoothing to the size field to eliminate local size anomalies caused by noisy data; Limit the ratio of size differences between adjacent nodes through the quasi-geometric adjustment algorithm to achieve a smooth transition of the size field, eliminate the banding phenomenon caused by low-quality background meshes, and generate a high-quality size field.

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