Boundary-maintained thin-wall structure curved surface triangular mesh alignment method

Abstract

The invention discloses a boundary-preserving thin-wall structure curved surface triangular mesh alignment method, which comprises the following steps of: reading a geometry and a mesh containing a thin-wall structure curved surface, and mapping a source curved surface and a target curved surface to a target curved surface geometric parameter space; detecting the intersection condition of the source curved surface grid and the target curved surface grid after mapping, and respectively splitting the source curved surface grid and the target curved surface grid into deletion and reservation areas; detecting a coincidence point of the reserved area and the deleted area of the target curved surface grid, and merging sub-areas in contact with the deleted area in the reserved area into the deleted area; boundary line grids of the source curved surface grid reserved area and the target curved surface grid deleted area are extracted and merged to form a transition area boundary line grid, and a transition area surface grid is generated; mapping reserved areas of the source curved surface grid and the target curved surface grid to a three-dimensional space, and combining the reserved areas with the transition area surface grid to obtain a combined surface grid; and extracting a triangular boundary of the source curved surface grid retaining region and an outer boundary of the combined surface grid as a constraint boundary line grid, and performing re-gridding optimization on the combined surface grid.

Description

Technical Field

[0001] This invention relates to the field of geometric modeling and numerical simulation technology, and in particular to a method for aligning triangular meshes on thin-walled structural surfaces while preserving boundaries. Background Technology

[0002] In complex geometric modeling and numerical simulation, curved triangular meshes serve as an important data structure for describing three-dimensional geometry and are widely used in CAD / CAM, finite element analysis, shape optimization, additive manufacturing, and other fields. With the increasing complexity of product designs and the growing frequency of using multi-source heterogeneous data, achieving high-quality stitching between multiple curved meshes and topological alignment of feature regions has become a crucial research direction for improving modeling efficiency and simulation accuracy.

[0003] Generating volume meshes between two closely spaced surfaces often presents a series of challenges: narrow gaps can easily generate poor-quality tetrahedral elements with excessively high aspect ratios, even leading to element flipping or mesh penetration; if the spacing is smaller than the set mesh size, it can also result in local voids or missing elements; furthermore, mesh generators often over-refine near the surface, causing element count inflation and a significant increase in computational overhead, while also reducing the numerical stability of the finite element solution. In practical engineering applications, these problems can be initially solved by aligning the curved mesh features of a local region (such as functional slots, external structural patches, or multiphysics interfaces) to another target mesh region, achieving seamless boundary stitching and topological consistency. Once the two surfaces are aligned, consistent interlayer thickness can be guaranteed, avoiding elements with extremely high aspect ratios. This type of task places high demands on the robustness, boundary preservation capabilities, and mesh quality control of geometric processing algorithms.

[0004] Existing methods mostly rely on traditional Boolean operations or processing strategies based on overall reconstruction. These methods have the following problems: (1) Severe loss or misalignment of boundary information. When performing mesh cutting and merging, conventional Boolean methods are prone to cracks, gaps or overlaps due to mismatched boundary node positions or inaccurate normal calculations; (2) Lack of control over the construction of transition regions. Traditional methods usually rely on automatic triangulation in the stitching region between source and target meshes, but lack boundary guidance or constraint mechanisms, making it difficult to guarantee geometric continuity and mesh quality; (3) Lack of unified processing methods for parameter space. Directly manipulating two surface meshes in three-dimensional space is easily affected by problems such as inconsistent coordinate systems and accumulation of geometric errors, reducing the accuracy and stability of the algorithm. In addition, actual engineering often involves mesh data from different sources (such as scanned meshes, CAE simulation outputs, CAD modeling results, etc.), and there are differences in size, resolution or structural complexity between these meshes. When processing such heterogeneous meshes, traditional methods usually require manual intervention and manual mesh repair, which is inefficient and lacks automation, making it difficult to adapt to the industrial needs of high-frequency iterative design and simulation optimization.

[0005] Therefore, there is an urgent need for a technical solution that can handle boundary alignment, topology reconstruction, and transition region generation between surface meshes in parameter space, which can ensure geometric consistency and boundary preservation, as well as have good automation and robustness. Summary of the Invention

[0006] Based on this, the present invention provides a method for aligning triangular meshes on thin-walled curved surfaces while maintaining boundaries, which solves problems such as boundary discontinuity, inconsistent geometric mapping, and unstable quality in transition regions that exist in the existing process of splicing curved surface meshes.

[0007] The technical solution adopted in this invention is as follows: A method for aligning triangular meshes on a boundary-preserving thin-walled structure surface includes: S1: Read the geometry and mesh files of the thin-walled structural surface, and use the geometry engine OCC to map the source surface and target surface that need to be aligned to the geometric parameter space of the target surface to obtain the mapped source surface mesh and target surface mesh; S2: Detect the intersection of the mapped source surface mesh and the target surface mesh, and separate them into deleted regions and retained regions respectively; S3: Detect the points where the retained and deleted regions of the target surface mesh overlap, and merge the sub-regions in the retained region that are in contact with the deleted region into the deleted region; S4: Extract and merge the boundary line meshes of the source surface mesh retention area and the target surface mesh deletion area to form the transition region boundary line mesh, and generate the transition region surface mesh; S5: Use the geometry engine OCC to map the source surface mesh preservation area and the target surface mesh preservation area to 3D space, and merge them with the transition area surface mesh to obtain a merged surface mesh; S6: Extract the triangular boundary of the source surface mesh retention region and the outer boundary of the merged surface mesh as the constraint boundary line mesh, and remesh to optimize the merged surface mesh. The technical solution provided by the embodiments of this application may include the following beneficial effects: This invention employs a parameter space-based mesh mapping and boundary recognition technique, significantly improving the boundary alignment accuracy between heterogeneous surface meshes. By uniformly mapping the source and target surface meshes to the target surface parameter space, and identifying and trimming deleted and retained regions within this space, it effectively avoids boundary misalignment caused by inconsistent normals and coordinate system differences in 3D space. During transition region construction and triangulation, this strategy ensures the continuity of boundary nodes and the closure of topological relationships, thereby improving the overall mesh merging quality and avoiding common defects such as "cracked meshes" or non-manifold structures.

[0008] This invention introduces an automatic transition region construction mechanism based on boundary line meshes. By extracting the boundary between the retained region of the source surface mesh and the deleted region of the target surface mesh and merging them into a continuous closed loop, it achieves automatic boundary identification and structural generation of transition patches. Compared with traditional Boolean operations that rely on wiring repair or manual patching, this invention can achieve high-quality region stitching without manual intervention. The triangulation results are controllable and have a good mesh quality distribution. It is particularly suitable for scenarios that require maintaining the continuity of boundary geometric features, such as high-precision simulation occasions involving local feature superposition, interface mesh fusion, and structural detail transfer.

[0009] This invention integrates the transition region with the original mesh in 3D space using mapping and constraint reconstruction techniques, and utilizes partial boundaries as constraints for unified retriangulation, significantly improving the robustness of the aligned mesh in terms of geometric fitting and topological consistency. This strategy can still achieve high-precision boundary closure and continuous splicing when dealing with large-scale models, irregular meshes, or locally refined regions, avoiding topological breaks or boundary overlaps, thus enhancing the method's adaptability and versatility in practical engineering modeling and cross-domain mesh integration. Attached Figure Description

[0010] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0011] Figure 1 This is a flowchart illustrating a method for aligning a boundary-preserving curved triangular mesh of a thin-walled structure, according to an exemplary embodiment.

[0012] Figure 2 This is a schematic diagram of a mobile phone case model with a thin-walled structure according to an exemplary embodiment.

[0013] Figure 3 This is a schematic diagram of the source surface mesh and the target surface geometry and mesh, according to an exemplary embodiment.

[0014] Figure 4 This is a schematic diagram illustrating the mapping of a target surface mesh to a parameter space according to an exemplary embodiment.

[0015] Figure 5 This is a schematic diagram illustrating the mapping of a source surface mesh to a parameter space according to an exemplary embodiment.

[0016] Figure 6 This is a schematic diagram illustrating the mapping of a source surface mesh and a target surface mesh to the same parameter space according to an exemplary embodiment.

[0017] Figure 7 This is a schematic diagram of the source surface mesh preservation region according to an exemplary embodiment.

[0018] Figure 8 This is a schematic diagram illustrating the retained and deleted regions of a target surface mesh according to an exemplary embodiment.

[0019] Figure 9 This is a schematic diagram of the contact and non-contact sub-regions of the target surface mesh retention area according to an exemplary embodiment.

[0020] Figure 10 This is a schematic diagram illustrating the merging of the target surface mesh retention area contact sub-region into the target surface mesh deletion area according to an exemplary embodiment.

[0021] Figure 11 This is a schematic diagram of the boundary line mesh of the annular transition region formed by the boundary of the source surface mesh retention region and the boundary of the target surface mesh deletion region, according to an exemplary embodiment.

[0022] Figure 12 This is a schematic diagram of a transition region surface mesh according to an exemplary embodiment.

[0023] Figure 13 This is a schematic diagram of a merged surface mesh obtained by merging the source surface mesh retention area, the target surface mesh retention area, and the transition area, according to an exemplary embodiment.

[0024] Figure 14 This is a schematic diagram of constraint edges extracted from a merged surface mesh according to an exemplary embodiment.

[0025] Figure 15This is a schematic diagram of a reconstructed surface mesh under constraint edge limitations, illustrating a merged surface mesh according to an exemplary embodiment.

[0026] Figure 16 This is a schematic diagram illustrating the alignment of the reconstructed surface mesh with the source surface mesh according to an exemplary embodiment.

[0027] Figure 17 This is a schematic diagram showing the effect of aligning the target curved surface mesh before and after on the thin-walled curved surface of a mobile phone case, according to an exemplary embodiment. Detailed Implementation

[0028] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0029] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0030] Figure 1 This is a flowchart illustrating a method for aligning triangular meshes on a boundary-preserving thin-walled structure surface according to an exemplary embodiment, such as... Figure 1 As shown, the method may include the following steps: S1: Read the geometry and mesh files containing the thin-walled structural surface, and use the geometry engine OCC to map the source and target surfaces that need to be aligned to the geometric parameter space of the target surface, obtaining the mapped source and target surface meshes; specifically, this may include the following sub-steps: S11: Read geometry and mesh files containing thin-walled structural surfaces; Specifically, the thin-walled structure is a lightweight load-bearing system composed of thin plates, thin shells, and slender rods. Its component thickness is much smaller than its dimensions in other directions. By optimizing material distribution, it achieves the characteristic of bearing a large load with a relatively small self-weight. Thin-walled structures typically meet the following conditions: in For wall thickness, This refers to the dimensions of the component. This type of structure can be found in aerospace, civil engineering, mechanical engineering, and automotive engineering, and can specifically be used for aircraft wings, fuselage skin, roof shells, pressure vessels, and body panels. For example... Figure 2 As shown, this application uses a mobile phone case model with thin-walled structural features as an example for detailed explanation.

[0031] In numerical simulations and mesh processing, especially in meshes with thin-walled structures, it is sometimes necessary to align a target surface with another source surface to achieve purposes such as structural information transfer, microstructure embedding, or geometric mapping. To ensure geometric accuracy and mesh quality, it is essential to accurately read the geometric model and mesh data of the surface containing the thin-walled structure. The geometric reading steps described in this application provide two types of input files for the source and target surfaces: one is a global geometry file (such as STEP or IGES formats), which provides basic CAD surface representation and parametric space mapping capabilities; the other is a triangular mesh file (such as STL or VTK formats), which describes the discretized topology and node coordinate information of its surface. Figure 3 As shown, the edge of the phone case contains a thin-walled curved surface region that is relatively thin compared to the overall structure. The two selected surfaces are the source surface and the target surface that need to be aligned, respectively. The overall geometry file and triangular mesh file of the phone case are read separately, and the geometric and mesh information of the source surface and the target surface are extracted from them. By establishing the correspondence between the geometric and mesh information of the source surface and the target surface, the foundation is laid for the subsequent parameter space mapping, boundary processing, and local reconstruction of the source surface mesh and the target surface mesh, which ensures accurate mesh alignment and high-quality simulation mesh generation.

[0032] S12: Use the geometry engine OCC to map the source surface mesh and target surface mesh that need to be aligned to the target surface geometry parameter space to obtain the mapped source surface mesh and target surface mesh; Specifically, before performing surface alignment and mesh fusion operations, to ensure the geometric alignment of different surface meshes on a unified surface, the meshes of both the source and target surfaces must be mapped to a parameter space (UV space) defined by the same geometric reference plane. This parameter space is typically defined by the target surface geometry and provides continuous mapping capabilities from points to the parameter space. A surface S(u,v) is defined as the mapping from two-dimensional parameters (u,v) to three-dimensional points (x,y,z): By obtaining the definition of the target surface geometry, given a three-dimensional point... , Find the surface parameters Make Minimize, that is, find the surface point closest to point P. Take its partial derivative: Solving this set of equations yields the mapping point. At the mapping point, the vector from the mapping point to the surface point is orthogonal to the tangent plane of the surface, and the direction of the shortest distance from the point to the surface is perpendicular to the tangent plane of the surface. The coordinates of each triangular element node on the source and target surface meshes are mapped to the parameter space defined by the target surface, resulting in its corresponding two-dimensional parameter coordinates (u, v). Through this mapping transformation, the discrete mesh points originally in three-dimensional space are mapped to the two-dimensional parameter space, creating a unified computational foundation for subsequent mesh processing. For example... Figure 4 and Figure 5 As shown, the target surface mesh and the source surface mesh are mapped from three-dimensional space to two-dimensional parameter space, respectively. Figure 6 As shown, the source surface mesh and the target surface mesh are mapped to the target surface geometric parameter space, allowing two original surface meshes located at different 3D positions to be computed in the same parameter space. Subsequent operations such as intersection detection, boundary extraction, reconstruction, and merging are all performed in the parameter space to avoid computational instability or deviation caused by 3D spatial errors. By uniformly mapping to the target surface geometric parameter space, different surface meshes obtain a consistent parametric representation on the same geometric reference plane. This ensures the precise alignment of the source and target surfaces in the geometric parameter domain and avoids geometric mismatch problems caused by coordinate errors or inconsistencies in normals when directly computed in 3D space, providing a unified and reliable computational foundation for subsequent processes.

[0033] S2: Detect the intersection of the mapped source surface mesh and the target surface mesh, and separate them into deleted regions and retained regions respectively; this may include the following sub-steps: S21: In the parameter space, the planar triangle intersection algorithm is used to detect the mapped source surface mesh and target surface mesh. The triangular elements in the source surface mesh that intersect with any triangular element of the target surface mesh but do not intersect with the outer boundary of the target surface mesh form the source surface mesh retention area, and the remaining triangular elements form the source surface mesh deletion area. Specifically, the source surface mesh is "trimmed," retaining only triangular regions that intersect the target surface but not its boundary, to ensure consistency and continuity in mesh fusion. A planar triangle intersection algorithm is used to detect the mapped source and target surface meshes, and the triangles from the source surface mesh are then processed. and any triangle from the target surface mesh The process checks for intersections, which can be categorized into partial overlap, complete containment, tangency, and no intersection. For partially overlapping intersections, the cross product of the triangle's edge segments is used for the check. This checks for the cross product of two line segments from two triangles. and cross product If at a given threshold The following satisfies If the line segments intersect, then the intersection of the triangles is considered a partial overlap. For intersections where any side of a triangle intersects, the intersection is determined by the fact that the line segments of the triangle intersect. For completely contained intersections, if all three vertices of the triangle are within another triangle, each vertex originating from a different triangle... Vertex P satisfies , Then the intersection of triangles is determined by complete containment. For the tangent intersection case, if triangles... If a vertex or edge of a triangle lies on another triangle, meaning the vertices are in contact or the boundaries are collinear, the triangles are considered tangent or intersecting. If neither of these conditions is met, they are considered non-intersecting. After determining triangle intersection, if triangles intersect, the intersection with the target surface mesh boundary is further assessed. First, the target surface mesh boundary is extracted. The triangular elements of the target surface mesh are traversed, and the occurrence count of each edge is counted. Boundary edges that appear only once are selected as boundary line meshes. The intersection of the triangle with the boundary line mesh is then determined; each of the three edges of the triangle intersects with the boundary line mesh. If they intersect, the triangle intersects with the boundary line mesh; otherwise, they do not. After these intersection checks, the triangular elements in the source surface mesh that intersect any triangular element of the target surface mesh but do not intersect the outer boundary of the target surface mesh form the retained region of the source surface mesh, while the remaining triangular elements form the deleted region of the source surface mesh. Figure 7 As shown, this represents the retained region of the source surface mesh. By employing a planar triangle intersection algorithm in the target surface parameter space for intersection detection, mesh trimming operations can be completed in the two-dimensional parameter space, reducing the numerical errors and computational complexity introduced by Boolean operations in three-dimensional space. By excluding triangular elements that intersect with the target surface boundary, boundary interference and topology errors are effectively avoided.

[0034] S22: In the parameter space, the planar triangle intersection algorithm is used to detect the target surface mesh and the source surface mesh retention area after mapping. The triangular elements in the target surface mesh that intersect with any triangular element in the source surface mesh retention area form the target surface mesh deletion area, and the remaining triangular elements form the target surface mesh retention area. Specifically, during mesh alignment, to achieve seamless fusion of the source and target surface meshes, it is necessary to pre-distinguish the regions in the target surface mesh that intersect with the source surface mesh. Failure to remove these regions will result in mesh redundancy and topological inconsistencies, leading to error propagation or failure in subsequent simulations. After source surface intersection trimming in step S21, the same planar triangle intersection detection algorithm is used to traverse all triangular elements of the target surface mesh in a unified parameter space, checking each element for intersection with triangles in the retained region of the source surface mesh. Triangular elements of the target surface mesh that intersect are deleted from the target surface mesh and marked as deleted regions; the remaining non-intersecting triangular elements are retained to form the retained regions. The final result is two independent mesh regions: one is the retained region of the target surface mesh, and the other is the deleted region of the target surface mesh. Figure 8 As shown, the retained and deleted regions of the target surface mesh are defined. By distinguishing between the deleted and retained regions, mesh overlap and topological redundancy are effectively eliminated, ensuring the boundary continuity of the subsequent fusion process, and also reducing the complexity of Boolean operations in three-dimensional space and the risk of error propagation.

[0035] S3: Detect the points where the retained and deleted regions of the target surface mesh overlap, and merge the sub-regions in the retained region that contact the deleted region into the deleted region, including: S31: In the parameter space, extract the boundary point coordinates of the deleted region of the target surface mesh, traverse the triangles of the retained region of the target surface mesh, and form a contact sub-region between the retained region and the deleted region of the target surface mesh with triangle elements whose vertices coincide with the extracted boundary point coordinates, and form a non-contact sub-region with the remaining triangle elements. Specifically, the target surface mesh retention region has multiple topologically connected branches, some of which are in close contact with the target surface mesh deletion region, while others are completely isolated. The target surface mesh retention region is further subdivided to identify the contacting and non-contacting parts of the deletion region, providing a structural basis for subsequent region transition, boundary reconstruction, or differentiated mesh processing. First, based on the target surface mesh deletion region in S22, all boundary edges of the target mesh deletion region are extracted and its boundary line segment set is constructed. Based on this, its corresponding boundary point set is further extracted. Second, each triangular element of the target mesh retention region is traversed in the parameter space, determining whether at least one of its vertices is geometrically equal to a point in the aforementioned boundary point set to achieve region subdivision. If this condition is met, the triangle is considered to be in contact with the deletion region and marked as a "contacting sub-region"; otherwise, it is marked as a "non-contacting sub-region." For example... Figure 9As shown, the reserved region of the target surface mesh is divided into two sub-region meshes: a contact region and a non-contact region. By traversing the triangles of the reserved region of the target surface mesh to detect coincidence points, a secondary subdivision of the reserved region is achieved, providing more refined constraints for subsequent transition region construction and mesh fusion.

[0036] S32: Merge the target surface mesh retained area and the contact sub-region of the deleted area into the target surface mesh deleted area.

[0037] Specifically, based on the sub-region splitting results of the target surface mesh retention area in S31, the triangular elements of the contact sub-region are merged into the target surface mesh deletion area. For example... Figure 10 As shown, the contact sub-regions of the target surface mesh retention area are merged into the target surface mesh deletion area.

[0038] S4: Extract and merge the boundary line meshes of the source surface mesh retention area and the target surface mesh deletion area respectively to form the transition region boundary line mesh, generating the transition region surface mesh, including: S41: Extract the boundary line meshes of the source surface mesh retention area and the target surface mesh deletion area respectively to form the transition region boundary line mesh, and map the boundary line mesh from the two-dimensional geometric parameter space to the three-dimensional space; Specifically, to achieve a high-quality transition between the source and target surface meshes, after dividing their respective regions, the boundary information of both is further extracted as the basis for constructing the transition region surface mesh. First, boundary extraction operations are performed on the retained region of the source surface mesh and the deleted region of the target surface mesh, respectively. Based on local topological relationships, by counting the occurrence frequency of each edge, only edges that appear only once in the mesh are retained as boundary edges, thus constructing two sets of line segments representing the boundaries of the retained region of the source surface mesh and the deleted region of the target surface mesh, respectively. Second, considering that both the source and target surface meshes are processed in a two-dimensional parameter space (such as UV space) during the trimming process, the extracted boundary line meshes are mapped from the parameter space to the actual three-dimensional space. This mapping is achieved through the mapping function of the target surface geometry, and a spatial restoration operation is performed on the boundary endpoints to obtain their corresponding three-dimensional geometric coordinates. By first extracting the boundary in the parameter space and then uniformly restoring it in the three-dimensional space, the accumulation of errors caused by three-dimensional spatial operations is effectively reduced, improving the computational stability and accuracy of the algorithm, and providing reliable spatial constraints for the generation and splicing of the transition region surface mesh.

[0039] S42: Merge the boundary line meshes of the source surface mesh retention region and the target surface mesh deletion region, and use the leading edge advancement method to generate the transition region surface mesh within the transition region boundary line mesh.

[0040] Specifically, after the boundary line meshes of the source surface mesh retention region and the target surface mesh deletion region are extracted and successfully mapped back to 3D space, the boundary line meshes of the two are merged to construct a unified closed boundary loop. This closed loop serves as a transition region to ensure the topological and geometric continuity of the spliced ​​region. The line mesh objects of both the source surface mesh retention region boundary and the target surface mesh deletion region boundary consist of three parts: vertex coordinates, boundary line segment connection relationships, and region attribute labels. The merging process removes redundant vertices, rearranges connection relationships, and maintains the continuity of topological connections, ensuring that the line segment endpoints can be correctly spliced ​​into a closed structure. After merging, the boundary line segments will form a complete loop boundary, completely enclosing the region to be transitioned. Figure 11 As shown, this is the transition region line mesh formed by the retained boundary of the source surface mesh and the deleted boundary of the target surface mesh. Based on the principle of leading edge propagation, closed boundary segments are used as input, combined with the target surface geometry and parameter configuration, and the boundary is used as the starting leading edge to gradually fill the interior of the region, constructing a topologically closed, boundary-matching, and high-quality triangular mesh structure, automatically generating the transition region surface mesh on the 3D surface. Figure 12 The image shows a triangular transition region surface mesh generated by the leading-edge propulsion method. Generating the transition region surface mesh using this method not only ensures precise alignment between the transition region and the source and target surface boundaries, improving the geometric smoothness of the transition region, but also automatically generates a topologically closed, high-quality triangular network structure, reducing irregular meshes and sharp corners.

[0041] S5: Use the geometry engine OCC to map the source surface mesh preservation area and the target surface mesh preservation area to 3D space, and merge them with the transition area surface mesh to obtain a merged surface mesh; S51: Map the source surface mesh retention region and the target surface mesh retention region to three-dimensional space; Specifically, a mapping operation is performed on the coordinates of all vertices in the source surface mesh and the target surface retention area. The coordinates of points in the two-dimensional parameter space are mapped back to the three-dimensional space through the surface function of the target surface geometry to obtain accurate spatial positions, ensuring that the source surface mesh and the target surface retention area maintain the accuracy of their original surface shape in the three-dimensional space.

[0042] S52: Merge the source surface mesh retention area, the target surface mesh retention area, and the transition area surface mesh to obtain a merged surface mesh.

[0043] Specifically, both the source and target surface mesh regions have undergone boundary processing and region identification in a unified parameter space. The transition region surface mesh has been generated on the surface using a leading-edge propagation algorithm, possessing a geometric structure that strictly matches the interface boundaries on both sides. These three are merged to obtain a merged surface mesh. After all three meshes are mapped to 3D space, they are merged and stitched together. Specific operations include coordinate deduplication, element index reconstruction, and region label classification. For example... Figure 13 As shown, after merging, a merged surface mesh with complete structure, continuous boundaries, and topological closure is obtained. This mesh not only includes the source surface mesh retention areas and the target surface mesh retention areas, but also introduces intermediate transition areas to effectively fill the gaps or transition interfaces between the two surfaces. By uniformly merging the source surface mesh retention areas, target surface mesh retention areas, and transition area surface meshes in three-dimensional space, geometric continuity and topological consistency of the surface splicing area are achieved. By deduplicating node coordinates, reconstructing element indexes, and classifying region labels, boundary redundancy and topological breaks between different regions are effectively eliminated, ensuring that the merged surface mesh has a complete structure, continuous boundaries, and topological closure.

[0044] S6: Extract the triangular boundary of the source surface mesh retention region and the outer boundary of the merged surface mesh as the constraint boundary line mesh, and remesh and optimize the merged surface mesh. This may include the following sub-steps: S61: Extract the triangular boundary of the source surface mesh retention region and the outer boundary of the merged surface mesh as the constraint boundary line mesh; Specifically, to further improve the geometric quality and numerical stability of the merged surface mesh and avoid the propagation of simulation errors caused by irregular elements (such as excessively small, large, or acute-angled triangles), an optimization and reconstruction operation can be performed on the merged surface mesh. First, all external boundary segments are extracted from the merged surface mesh, and the occurrence frequency of each edge in all triangular elements is counted; edges appearing only once are considered external boundary edges. Second, to ensure that the source surface region remains undisturbed during optimization, all triangular boundary edges of the source surface mesh are extracted additionally and converted into corresponding boundary point indices in the merged surface mesh using coordinate mapping, thus constructing a set of boundary edges with geometric constraints. Finally, these boundary segments are uniformly set as "hard constraint edges," ensuring that boundary vertices and edges are not moved or topologically adjusted during triangular mesh optimization, providing a fixed framework for boundary morphology in the mesh reconstruction stage, and ensuring geometric continuity and stitching accuracy during optimization. Figure 14As shown, these are the constraint edges set for the triangular boundaries of the retained region of the source surface mesh and the outer boundaries of the merged surface mesh before reconstructing the surface mesh. By using the triangular boundaries of the retained region of the source surface mesh and the outer boundaries of the merged surface mesh as hard constraint boundaries in the remeshing optimization process, the geometric shape of the surface splicing boundaries can be kept unchanged during the mesh optimization process, avoiding boundary offset or topological breakage.

[0045] S62: Use the remeshing algorithm to optimize and merge the surface mesh with the constrained boundary line mesh as the constraint.

[0046] Specifically, based on the constraint edge set extracted in step S61, immovable boundary conditions are set for the merged surface mesh to ensure that the boundary structure remains unchanged during the optimization process. Subsequently, surface mesh optimization parameters are set, such as the maximum number of iterations, the allowed number of topology operations (e.g., edge folding, edge splitting, point relocation), and the control unit's target shape and size, to achieve a locally uniform and globally continuous target mesh structure. During optimization, the algorithm locally adjusts the triangular units within the surface mesh, continuously improving the quality of the facets through vertex smoothing, edge flipping, and triangle regeneration. This process uses quality indicators such as the minimum angle of the triangle, area uniformity, and side length ratio as optimization targets, dynamically adjusting the distribution of nodes within the face until convergence or the set number of iterations is reached. The final generated surface mesh not only achieves structural alignment and fusion of the source surface mesh, target surface mesh, and transition region, but also achieves a high level in terms of mesh quality, shape regularity, and simulation usability, providing a reliable foundation for subsequent construction of 3D volume meshes or physical simulations. Figure 15 As shown, the optimized mesh boundary remains unchanged, while the internal cells are regular and the angle distribution is reasonable. Figure 16 As shown, the final aligned target surface triangle mesh and the source surface mesh are aligned sequentially at corresponding points and on the triangles. Figure 17 The image shows a comparison of the effects of aligning the target surface mesh before and after aligning the thin-walled curved surface of a mobile phone casing. By performing remeshing optimization on the merged surface mesh with the constraint boundary line mesh as a fixed condition, the geometry and distribution of the internal triangular elements are improved while keeping the boundaries unchanged. This effectively improves the element quality and numerical stability of the merged surface mesh, and enhances the accuracy and reliability of the surface mesh in subsequent simulation and manufacturing processes, demonstrating high practical value.

[0047] As can be seen from the above technical solution, this invention first maps the source surface mesh and the target surface mesh to the parameter space of the target geometry, achieving coordinate consistency processing for meshes from different sources. Then, by identifying and dividing the retained and deleted regions of the source and target meshes, and expanding and merging the adjacent contact regions of the target mesh, the integrity of the boundary stitching is ensured. Next, by extracting the boundary line mesh, constructing the transition region, and performing triangulation, the transition surface between the source and target regions is effectively connected. Finally, by mapping back to three-dimensional space and setting constraint boundaries for unified triangulation reconstruction, a boundary-aligned and topologically continuous surface triangular mesh is generated.

[0048] This invention employs a parameter space-based mesh mapping and boundary recognition technique, significantly improving the boundary alignment accuracy between heterogeneous surface meshes. By uniformly mapping the source and target surface meshes to the target surface parameter space, and identifying and trimming deleted and retained regions within this space, it effectively avoids boundary misalignment caused by inconsistent normals and coordinate system differences in 3D space. During transition region construction and triangulation, this strategy ensures the continuity of boundary nodes and the closure of topological relationships, thereby improving the overall mesh merging quality and avoiding common defects such as "cracked meshes" or non-manifold structures.

[0049] This invention introduces an automatic transition region construction mechanism based on boundary line meshes. By extracting the boundary between the retained region of the source surface mesh and the deleted region of the target surface mesh and merging them into a continuous closed loop, it achieves automatic boundary identification and structural generation of transition patches. Compared with traditional Boolean operations that rely on wiring repair or manual patching, this invention can achieve high-quality region stitching without manual intervention. The triangulation results are controllable and have a good mesh quality distribution. It is particularly suitable for scenarios that require maintaining the continuity of boundary geometric features, such as high-precision simulation occasions involving local feature superposition, interface mesh fusion, and structural detail transfer.

[0050] This invention integrates the transition region with the original mesh in 3D space using mapping and constraint reconstruction techniques, and utilizes partial boundaries as constraints for unified retriangulation, significantly improving the robustness of the aligned mesh in terms of geometric fitting and topological consistency. This strategy can still achieve high-precision boundary closure and continuous splicing when dealing with large-scale models, irregular meshes, or locally refined regions, avoiding topological breaks or boundary overlaps, thus enhancing the method's adaptability and versatility in practical engineering modeling and cross-domain mesh integration.

[0051] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0052] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A method for aligning triangular meshes on a thin-walled structure surface while preserving boundaries, characterized in that, include: S1: Read the geometry and mesh files of the thin-walled structural surface, and use the geometry engine OCC to map the source surface and target surface that need to be aligned to the geometric parameter space of the target surface to obtain the mapped source surface mesh and target surface mesh; S2: Detect the intersection of the mapped source surface mesh and the target surface mesh, and separate them into deleted regions and retained regions respectively; S3: Detect the points where the retained and deleted regions of the target surface mesh overlap, and merge the sub-regions in the retained region that are in contact with the deleted region into the deleted region; S4: Extract and merge the boundary line meshes of the source surface mesh retention area and the target surface mesh deletion area to form the transition region boundary line mesh, and generate the transition region surface mesh; S5: Use the geometry engine OCC to map the source surface mesh preservation area and the target surface mesh preservation area to 3D space, and merge them with the transition area surface mesh to obtain a merged surface mesh; S6: Extract the triangular boundary of the source surface mesh and the outer boundary of the merged surface mesh as the constraint boundary line mesh, and remesh to optimize the merged surface mesh.

2. The method according to claim 1, characterized in that, Read the geometry and mesh files of the thin-walled structural surfaces, and use the geometry engine OCC to map the source and target surfaces that need to be aligned to the geometric parameter space of the target surface, obtaining the mapped source and target surface meshes, including: S11: Read geometry and mesh files containing thin-walled structural surfaces; S12: Use the geometry engine OCC to map the source surface mesh and target surface mesh that need to be aligned to the target surface geometry parameter space to obtain the mapped source surface mesh and target surface mesh.

3. The method according to claim 1, characterized in that, The intersection of the mapped source and target surface meshes is detected, and both are then divided into deleted and retained regions, including: S21: In the parameter space, the mapped source surface mesh and target surface mesh are detected. The triangular elements in the source surface mesh that intersect with any triangular element of the target surface mesh but do not intersect with the outer boundary of the target surface mesh form the source surface mesh retention area, and the remaining triangular elements form the source surface mesh deletion area. S22: In the parameter space, detect the target surface mesh and the source surface mesh retention area after mapping. The triangular elements in the target surface mesh that intersect with any triangular element in the source surface mesh retention area form the target surface mesh deletion area, and the remaining triangular elements form the target surface mesh retention area.

4. The method according to claim 1, characterized in that, Detect the points where the retained and deleted regions of the target surface mesh overlap, and merge the sub-regions in the retained region that contact the deleted region into the deleted region, including: S31: In the parameter space, extract the boundary point coordinates of the deleted region of the target surface mesh, traverse the triangles of the retained region of the target surface mesh, and form a contact sub-region between the retained region and the deleted region of the target surface mesh with triangle elements whose vertices coincide with the extracted boundary point coordinates, and form a non-contact sub-region with the remaining triangle elements. S32: Merge the target surface mesh retained area and the contact sub-region of the deleted area into the target surface mesh deleted area.

5. The method according to claim 1, characterized in that, The boundary line meshes of the source surface mesh retention region and the target surface mesh deletion region are extracted and merged to form the transition region boundary line mesh, generating the transition region surface mesh, including: S41: Extract and merge the boundary line meshes of the source surface mesh retention area and the target surface mesh deletion area respectively to form the transition region boundary line mesh, and map the boundary line mesh from the two-dimensional geometric parameter space to the three-dimensional space; S42: Using the leading edge propagation method, generate the transition region surface mesh within the transition region boundary line mesh.

6. The method according to claim 1, characterized in that, The geometry engine OCC is used to map the source surface mesh preservation region and the target surface mesh preservation region to 3D space, and merge them with the transition region surface mesh to obtain a merged surface mesh, including: S51: Map the source surface mesh retention region and the target surface mesh retention region to three-dimensional space; S52: Merge the source surface mesh retention area, the target surface mesh retention area, and the transition area surface mesh to obtain a merged surface mesh.

7. The method according to claim 1, characterized in that, Extract the triangular boundary of the source surface mesh retention region and the outer boundary of the merged surface mesh as the constraint boundary line mesh, and remesh and optimize the merged surface mesh, including: S61: Extract the triangular boundary of the source surface mesh retention region and the outer boundary of the merged surface mesh as the constraint boundary line mesh; S62: Use the remeshing algorithm to optimize and merge the surface mesh with the constrained boundary line mesh as the constraint.

Images