A self-intersection-free mesh assembly method based on volume parameterization

Abstract

The application discloses a self-intersection-free grid assembling method based on body parameterization, which comprises the following steps: inputting an arbitrary surface grid as a reference surface and a component grid, parameterizing the reference surface grid, generating a two-dimensional reference parameter plane, and establishing a first mapping function between a physical space and the parameter plane; placing the reference parameter plane on an XY plane, stretching along a Z axis to generate a three-dimensional parameter space, and converting the reference surface grid into a three-prism structure; synchronously expanding the reference grid into a three-prism grid in the physical space; according to a user-set assembling point and direction, mapping the component grid to the three-dimensional parameter space by using the first mapping function, and keeping the topology unchanged; constructing a second mapping function, mapping the component grid from the parameter space back to the physical space, and generating a component grid with an accurate assembling position; and merging the component and the reference grid, realizing node commonality and smooth transition, and eliminating the discontinuity of the assembling joint.

Description

Technical Field

[0001] This invention relates to the field of mesh generation, and more particularly to a method for assembling non-self-intersecting meshes based on volume parameterization. Background Technology

[0002] Numerical simulation plays an increasingly important role in various fields, such as fluid mechanics, electromagnetics, and structural mechanics. Mesh generation is a crucial preprocessing step in numerical simulation; the quality, size, shape, and dimensions of the mesh are critical because they directly affect the accuracy and stability of the simulation results. As a core verification method in modern engineering design, the computational accuracy and efficiency of numerical simulation are highly dependent on the quality of the preprocessing mesh generation. To achieve a reasonable mesh distribution, significant manual intervention is often required to design and adjust the topology. This inefficiency is particularly pronounced in the analysis of complex components with assembly characteristics. This essentially stems from the paradigm limitations of the linear "geometry-to-mesh" process—each design variant requires a complete cycle of geometric reconstruction and remeshing.

[0003] Traditional mesh generation methods face two major bottlenecks: First, the preparation of the input CAD model consumes more than 50% of the preprocessing time, requiring manual repair of geometric defects (such as gaps, overlaps, or non-manifold edges); second, the generation of special types of meshes (such as the central axis mesh of thin-walled structures) requires several hours of manual operation, involving surface offset, feature recognition, and quality verification. For assemblies with composite characteristics, these bottlenecks are further amplified: the strong coupling between the underlying geometric constraints and the topological assembly means that the geometric reconstruction and mesh generation process must be repeated for each design iteration. Summary of the Invention

[0004] In view of this, embodiments of the present invention provide a non-self-intersecting mesh assembly method based on volume parameterization to solve the problems existing in the background art.

[0005] The technical solutions adopted in the embodiments of the present invention are as follows:

[0006] A volume parameterization-based method for assembling self-intersecting meshes includes:

[0007] S1: Input an arbitrary surface mesh as a reference surface mesh and an arbitrary surface mesh as a component mesh. Parameterize the reference surface mesh to obtain a two-dimensional parameter plane. Use the obtained two-dimensional parameter plane as the reference parameter plane. Establish a first mapping function based on the mapping relationship between physical space and the reference parameter plane.

[0008] S2: Place the reference parameter plane on the XY plane of the Cartesian coordinate system and stretch it along the Z-axis to generate the top surface, thereby obtaining a three-dimensional parameter space. Transform the reference surface mesh in the reference parameter plane from a triangular mesh structure to a triangular prism mesh structure in the three-dimensional parameter space.

[0009] S3: In physical space, the reference surface mesh is expanded from a triangular mesh structure to a triangular prism mesh structure;

[0010] S4: Based on the specified assembly point coordinates, specified assembly direction vector, and first mapping function input by the user, map the node coordinates of the component mesh to the three-dimensional parameter space, while keeping the topology of the component mesh unchanged, to obtain the component mesh structure in the three-dimensional parameter space;

[0011] S5: Based on the triangular prism mesh structure in the three-dimensional parameter space and the triangular prism mesh structure in the physical space, establish a second mapping function, and map the node coordinates of the component mesh structure to the physical space according to the second mapping function, while keeping the topological relationship of the component mesh structure unchanged, to obtain the component mesh in the physical space.

[0012] S6: Merge the component mesh and the reference surface mesh in the physical space to make the transition between the component mesh and the reference surface smooth, eliminate the discontinuity at the assembly joint, and make the assembly joint share nodes.

[0013] The technical solution provided by this invention has the following beneficial effects:

[0014] This invention can accept open surfaces (such as complex surfaces in thin-walled structures) and closed surfaces (such as geometric boundaries in multi-part assemblies) as input, and allows users to customize assembly parameters to flexibly assemble the reference surface mesh and the component mesh. It effectively solves the problems of cumbersome, complex and inefficient geometric reconstruction and mesh regeneration processes under complex geometric constraints in traditional methods, thereby significantly improving the automation level of mesh generation and assembly efficiency, and reducing manual intervention and the probability of errors.

[0015] This invention supports triangular mesh format input (such as STL files) and can be combined with a parametric standard part library to achieve rapid modeling and assembly of sub-parts. It overcomes the problem of needing a lot of geometric Boolean operations and manual processing in the traditional modeling process, thereby realizing efficient modeling and seamless integration of multiple parts in the additive manufacturing process, significantly shortening the product development cycle and improving the level of manufacturing automation.

[0016] This invention, through parametric imprinting, can automatically and precisely assemble the bottom surface mesh with the mesh of complex components, thereby directly generating high-quality meshes of complex structures such as the central axis surface mesh. This solves the problem of requiring a large amount of manual repair and quality verification in traditional central axis surface mesh generation methods, thus greatly improving the generation efficiency and stability of complex structure meshes, and is suitable for large-scale, refined engineering analysis scenarios. Attached Figure Description

[0017] Figure 1 A flowchart of a non-self-intersecting mesh assembly method based on volume parameterization provided in this application embodiment.

[0018] Figure 2 To verify the implementation example of the algorithm provided in this application, a schematic diagram of the surface mesh of a rabbit, a typical computer graphics model, is shown.

[0019] Figure 3 The semi-cylindrical quadrilateral surface mesh is used as a schematic diagram of the reference surface mesh.

[0020] Figure 4 This is a schematic diagram of the triangular mesh obtained by dividing the input datum plane quadrilateral mesh along the diagonal.

[0021] Figure 5 The input quadrilateral surface mesh of the part serves as a schematic diagram of the component mesh.

[0022] Figure 6 A schematic diagram of the triangular prism mesh generated for the rabbit's surface mesh.

[0023] Figure 7 A schematic diagram of the triangular prism mesh generated from the input semi-cylindrical surface mesh.

[0024] Figure 8 A schematic diagram showing the result of assembling a rabbit onto a mesh surface.

[0025] Figure 9 This is a schematic diagram showing the result of assembling parts on a mesh surface of a semi-cylindrical surface. Detailed Implementation

[0026] The method of the present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0027] This invention provides two examples, one of which is in Figure 2 The model rabbit shown has a scaled-down surface assembly. Figure 2 The model rabbit shown is one of them. Figure 4 The model shown has a semi-cylindrical surface assembly. Figure 5 The part models shown are, of course, not limited to these two examples.

[0028] like Figure 1 As shown, the present invention provides a non-self-intersecting mesh assembly method based on volume parameterization, comprising the following steps:

[0029] S1: Input an arbitrary surface mesh as a reference surface mesh and an arbitrary surface mesh as a component mesh. Parameterize the reference surface mesh to obtain a two-dimensional parameter plane. Use the obtained two-dimensional parameter plane as the reference parameter plane. Based on the mapping relationship between physical space and the reference parameter plane, establish a first mapping function, including the following sub-steps:

[0030] S11: Read the first input surface mesh as the reference surface mesh. It supports inputting triangular or quadrilateral meshes. When the input reference surface mesh is a quadrilateral mesh, it is divided into triangular meshes by the diagonal. Read the second input surface mesh as the part mesh. It supports inputting triangular or quadrilateral meshes.

[0031] Specifically, the arbitrary surface mesh refers to the surface mesh discretized based on the geometric model, including closed surfaces and non-closed surfaces, such as... Figure 2 It is the input closed surface. Figure 3 It is an open curved surface, represented by a triangular or quadrilateral mesh.

[0032] The reference surface mesh refers to the surface mesh used as the assembly carrier among the two input surface meshes, which maintains its spatial position, mesh node coordinates, and mesh topology unchanged during the assembly process. Figure 3 The component mesh refers to a surface model whose spatial location and mesh node coordinates are variable, but whose mesh topology remains unchanged, such as... Figure 5 .

[0033] The phrase "dividing a quadrilateral mesh into a triangular mesh by diagonals" refers to the situation where the input reference surface mesh is a quadrilateral mesh, such as... Figure 3 Before parametricating the surface, the quadrilateral mesh needs to be divided into two triangular meshes along its diagonal, such as... Figure 4 The processing of quadrilateral meshes introduces greater geometric complexity during parameterization compared to triangular meshes. Dividing a quadrilateral mesh into two triangular meshes effectively simplifies subsequent surface parameterization operations. Triangular meshes are more stable than quadrilateral meshes, exhibiting better adaptability in texture mapping, deformation calculations, and surface reconstruction. Furthermore, triangular meshes are more efficient in numerical optimization and algorithm implementation, reducing computational errors and instabilities. Therefore, employing diagonal partitioning preserves the mesh shape and topology while ensuring the accuracy and stability of subsequent operations.

[0034] S12: Using the coordinates of the assembly point on the reference surface mesh input by the user as the center, and the diagonal size of the bounding box of the component mesh as the search radius, obtain the triangular facets within the search radius on the reference surface mesh using a breadth-first search algorithm, and use them as a subset mesh;

[0035] Specifically, the breadth-first search algorithm is a graph traversal algorithm that starts from the assembly point of the reference plane grid and expands hierarchically to search for and select grid elements adjacent to the target region within a specified radius. By visiting grid nodes layer by layer, this algorithm ensures that the selected subset of grids has a relatively close spatial position to the assembly point in the reference plane grid.

[0036] The coordinates of the assembly point on the reference surface mesh are used as the center, meaning that the three-dimensional coordinate position of a given assembly point serves as the starting point for expanding the search area. A breadth-first search begins from this point. Based on a specified radius constraint, the breadth-first search explores the neighboring mesh layer by layer until the given radius is reached, ensuring that the selected mesh is located only within the valid area surrounding the assembly point.

[0037] The bounding box diagonal of the component mesh is defined as a radius, meaning that the length of the bounding box diagonal serves as the radius of the extended region in the three-dimensional space of the component mesh. During the search, the diagonal size of the bounding box directly affects the search range and accuracy, effectively constraining the search area and avoiding interference from invalid meshes during the search process.

[0038] In this way, the breadth-first search algorithm can accurately obtain a subset of the mesh corresponding to the component mesh on the reference surface mesh, providing accurate local mesh information for subsequent assembly operations. This operation not only optimizes search efficiency but also ensures accurate alignment and connection during mesh assembly.

[0039] S13: Parameterize a subset of the reference plane mesh to obtain the reference parameter plane;

[0040] S14: Based on the mapping relationship between the physical space and the reference parameter plane, establish a mapping function between the reference surface mesh and the coordinates of the points on the reference parameter plane, i.e., the first mapping function.

[0041] Specifically, the reference parameter plane is a two-dimensional plane obtained through parameterization operations, representing a local region of the reference surface mesh. This plane serves as a reference for the docking between the reference surface mesh and other meshes during assembly, providing concise mathematical expressions for subsequent assembly operations. On this plane, the relationship between the coordinates of mesh nodes and their positions in three-dimensional space is described by the mapping function F1. The mapping function F1 is a function that maps the coordinates of reference surface mesh points in three-dimensional space to the coordinates of points on the two-dimensional reference parameter plane.

[0042] The binary search tree BT1 is an efficient data structure that allows you to quickly find the index of the triangular facet to which a grid node belongs based on its coordinates. This significantly improves the efficiency of grid queries.

[0043] The user-specified size control parameters specifically include:

[0044] (1) Coordinates of assembly points of the reference surface mesh A reference point or starting point in three-dimensional space, specified by the user on the reference mesh, is used to determine the relative position of the reference mesh and the component mesh during assembly. The selection of this point is typically based on design requirements to ensure accurate alignment during assembly.

[0045] (2) Component mesh assembly point coordinates The coordinates of the assembly point specified by the user on the component mesh. This point is used to align with the assembly point coordinates of the reference plane mesh. During assembly, the component mesh is spatially matched with the reference plane mesh based on this point position to ensure accuracy and stability during assembly.

[0046] (3) Alignment direction of the datum surface The alignment direction vector of the datum surface mesh is used to determine the directional constraints required for the datum surface during assembly. This direction is typically a vector in three-dimensional space that indicates the alignment direction of the datum surface mesh, ensuring that the datum surface mesh can be rotated, translated, and mated in the correct direction during assembly.

[0047] (4) Component assembly alignment direction The alignment direction vector of the component mesh is used to determine the orientation control of the component mesh during assembly. The alignment direction of the component mesh is opposite to the alignment direction of the reference plane mesh, and is used to precisely control the relative angle and direction between the component and the reference plane, so that the two can be accurately aligned during assembly and ensure that the final assembly result meets the design requirements.

[0048] S2: Place the reference parameter plane on the XY plane of the Cartesian coordinate system and extrude it along the Z-axis to generate the top surface, thus obtaining a three-dimensional parameter space. Transform the reference surface mesh in the reference parameter plane from a triangular mesh structure to a triangular prism mesh structure in the three-dimensional parameter space, including the following sub-steps:

[0049] S21: Embed the reference parameter plane into the Cartesian coordinate system and place it parallel to the XY plane, so that the reference parameter plane coincides with the XY plane of the Cartesian coordinate system;

[0050] S22: Perform a stretching operation on the reference parameter plane along the Z-axis direction, and set the stretching height to a predetermined value H to form a top surface parallel to the reference parameter plane;

[0051] S23: Based on the above reference parameter plane and top surface, a closed body is formed between the upper and lower planes by connecting the corresponding points, thus obtaining a three-dimensional parameter space. The bottom surface of this space is the reference parameter plane, the top surface is the extruded surface, and the side walls are formed by the corresponding boundaries between the reference plane mesh and the top surface mesh.

[0052] Specifically, the reference parameter plane, as a two-dimensional plane in the XY plane, is stretched along the Z-axis to form a three-dimensional structure. The bottom surface corresponds to the original reference parameter plane, while the top surface is obtained by extending the plane by a certain height. This extension transforms the original two-dimensional mesh into a three-dimensional spatial mesh, forming a triangular prism mesh structure extended from a triangular mesh structure, which can better represent the geometric shape in three-dimensional space.

[0053] During coordinate transformation, the mesh nodes on the reference parameter plane are transformed from the two-dimensional coordinate system. Extended to a three-dimensional coordinate system During this process, all nodes on the original reference plane h The coordinates are set to 0 to maintain their position in the XY plane. In contrast, the mesh nodes on the top surface... h The coordinates are defined as twice the height of the component mesh, thus ensuring the vertical expansion of the mesh structure.

[0054] S24: Divide the reference parameter plane into several triangular mesh units. Each triangular mesh consists of three vertices and three sides, forming a two-dimensional triangular mesh structure of the reference plane.

[0055] S25: For each triangular mesh element of the reference plane, stretch its three vertices to the corresponding positions on the top surface along the Z-axis to form the corresponding upper surface triangle. Connect the original triangular mesh with its corresponding top triangle to construct a triangular prism with two triangular faces and three rectangular sides. In this way, all the triangular meshes of the reference plane are transformed into triangular prism mesh elements in three-dimensional space.

[0056] S26: All triangular prism elements are combined in the three-dimensional parameter space to form a continuous triangular prism mesh structure.

[0057] Specifically, during the topology transformation process, each mesh node Ni on the reference parameter plane has a corresponding mesh node on the top surface. These two nodes are located on the bottom and top surfaces, respectively. The original triangular mesh topology... Expanded into a triangular prism mesh topology The nodes on the bottom and top surfaces form two triangular faces of a triangular prism. This topological transformation ensures that the geometry of the original mesh can be correctly extended into three-dimensional space, forming a stable triangular prism mesh structure.

[0058] S3: In physical space, the reference surface mesh is expanded from a triangular mesh structure to a triangular prism mesh structure, including the following sub-steps:

[0059] S31: Determine the stretching direction and construct an initial triangular prism mesh. Obtain the normal vector of each mesh node on the reference plane and perform Laplace smoothing on the normal vector. Replace the Z-axis direction in the Cartesian coordinate system with the smoothed normal vector and stretch the triangular mesh of the reference plane along this direction to construct a preliminary triangular prism mesh structure. If there is overlap or self-intersection between the triangular prism elements generated in this process, proceed to S32.

[0060] Specifically, the normal vector of each mesh node on the surface is directly obtained. The normal vector is a vector describing the surface direction at each point on the surface, typically perpendicular to a local plane of the surface. The Laplacian smoothing method is similar to traditional Laplacian vertex smoothing, but it operates on the normal vector. It achieves a "smoothing" effect by adjusting the normal vector of a vertex to the average of the normal vectors of its neighbors. The smoothed normal vector replaces the original Z-axis direction (in 3D parametric processes, the Z-axis usually represents the vertical height of the surface). Therefore, the smoothed normal vector becomes the new "Z-axis" direction, determining the extension direction from the reference plane to the top surface. Figure 7 The image shows a triangular prism grid structure after the semi-cylindrical surface has been expanded.

[0061] S32: Robust triangular prism mesh generation based on bijective mapping. When there is a problem of triangular prism element intersection, a boundary layer prism mesh generation method is used to handle it. This method ensures that the triangular mesh is stably extended into non-overlapping triangular prism elements along the boundary normal direction by constructing a bijective mapping relationship, thus obtaining a triangular prism mesh structure without self-intersection.

[0062] S4: Based on the user-input specified assembly point coordinates, specified assembly direction vector, and first mapping function, map the node coordinates of the component mesh to the three-dimensional parameter space, while keeping the topology of the component mesh unchanged, to obtain the component mesh structure in the three-dimensional parameter space. This includes the following sub-steps:

[0063] S41: Based on the specified assembly point coordinates and assembly alignment direction input by the user and the first mapping function, calculate the parameter plane coordinates of the specified assembly point coordinates input by the user, and perform translation and rotation operations based on the parameter plane coordinates and the specified assembly direction to place the component mesh in the parameter plane.

[0064] Specifically, firstly, the user-input coordinates of the specified assembly points are converted into corresponding coordinates on the parameter plane using a first mapping function. Then, based on the specified assembly orientation, a series of geometric operations, including translation and rotation, are used to adjust the position and orientation of the component mesh, ensuring its correct alignment in 3D space. Through these operations, the node coordinates of the component mesh are mapped from the original space to 3D space, resulting in the final 3D point coordinates. Throughout this process, the topology of the component mesh remains unchanged, ensuring geometric consistency and accuracy during assembly.

[0065] S42: Map the nodes of the component mesh to three-dimensional space to obtain the three-dimensional space coordinates of the nodes of the component mesh, while keeping the topology of the component mesh unchanged.

[0066] S5: Based on the triangular prism mesh structure in the three-dimensional parameter space and the triangular prism mesh structure in the physical space, establish a second mapping function, and map the node coordinates of the component mesh structure to the physical space according to the second mapping function, while keeping the topological relationship of the component mesh structure unchanged, to obtain the component mesh in the physical space, including the following sub-steps:

[0067] S51: Construct a binary search tree BT1 based on the node coordinates and topological relationships of the grid. Through BT1, the index of the triangular facet to which any grid node belongs can be retrieved based on the spatial coordinates of the grid node. ; this index As an identifier for the triangular prism element, it enables a fast mapping from node coordinates to the triangular prism label;

[0068] S52: Decompose a triangular prism into n tetrahedrons to represent a structure in three-dimensional space. Each tetrahedron has a local index within its triangular prism. For any point P in the parameter space, project it onto the parameter plane, and obtain the label of the triangle to which point P belongs through the binary search tree BT1 of the triangles. At the same time, determine the triangular prism to which point P belongs;

[0069] S53: Inside a triangular prism, calculate the local tetrahedral index of point P using a volumetric algorithm. The centroid coordinate parameters represented by the four vertices of the tetrahedron are calculated using centroid coordinate interpolation. To obtain unique information for each point Substitute different spatial point coordinates into This allows us to obtain the coordinates of point P in different spaces, thereby establishing the second mapping function between the three-dimensional parameter space and the physical space triangular prism.

[0070] S54: Map the three-dimensional spatial coordinates of the nodes in the component mesh to the physical space through the second mapping function to obtain the point coordinates in the physical space, while keeping the topological relationship of the component mesh unchanged, and obtain the component mesh in the physical space.

[0071] Specifically, volume parameterization refers to the extension of surface parameterization, that is, from planar triangles to spatial tetrahedrons.

[0072] S6: Merge the component mesh with the reference surface mesh using an imprinting technique to smooth the transition between the component mesh and the reference surface, eliminate discontinuities at the assembly joints, and ensure common nodes at the assembly joints to obtain the assembled mesh. This includes the following sub-steps:

[0073] S61: Merge the mesh nodes of the component mesh obtained in S5 and the mesh nodes of the reference plane to the output result mesh nodes, update the topology of the component mesh and the topology of the reference plane mesh, and merge them;

[0074] Specifically, the operation involves combining all mesh nodes of the component mesh and the reference surface mesh to form a unified point set. At this point, all nodes are merged sequentially to form a new point set containing all nodes of both the component mesh and the reference surface mesh. Then, the topology is updated to reflect the order of the new point set. This step does not immediately change the connectivity between nodes, but rather prepares the site for subsequent seam processing and mesh optimization.

[0075] S62: The seam between the component mesh and the reference surface mesh is processed by embossing technology.

[0076] As can be seen from the above technical solutions, this invention proposes a novel mesh assembly method that decouples topological assembly from geometric constraints by constructing a parameterized assembly space. Unlike traditional geometry-driven paths, this framework directly combines existing mesh components based on user input parameters, effectively avoiding the geometric reconstruction step. This method demonstrates significant advantages in several typical scenarios:

[0077] (1) Parametric Mesh Generation: When generating the axial surface mesh using AI, a large amount of geometric and mesh datasets are required. The geometric dataset can be generated through geometric parametric modeling, while generating the mesh dataset manually presents several challenges. First, there is the issue of labor costs. If the dataset requires 10,000 mesh sets, and the workload for each mesh set is 1, then the workload for 10,000 mesh sets would be 10,000. Second, there is the issue of mesh quality, requiring manual intervention to refine the mesh. The axial surface mesh has a characteristic that the bottom surface and the component are independent and separable. However, since the bottom surface is curved, it is impossible to fit the component to the bottom surface through simple translation. For the batch creation of axial surface meshes for thin-walled structures, the method in this paper is parametric mesh generation. By parameterizing the bottom surface, the position of the component can be determined, and then the bottom surface and the component can be assembled together through an imprinting operation.

[0078] (2) Multi-part 3D Modeling and Manufacturing: In recent years, new technologies such as additive manufacturing processes (3D printing) and digital CFAO chains (computer-aided design and manufacturing) for the medical field have emerged. All of these technologies traditionally rely on the STL (Standard Triangle Language) file format to model the geometric information of parts or shapes. This 3D file format contains only the minimum information required to describe the 3D model, making it compact and easy to use. The STL file format is based on the polyhedral surface model of the object (i.e., triangular mesh), which is essentially a surface without thickness or fill. When manufacturing models with assembly features, generating a separate STL file for each model can be too redundant. This invention can achieve seamless integration of parts without geometric Boolean operations by using STL files of pre-built parametric standard sub-part libraries (such as gear sets, connecting mechanisms, etc.).

[0079] Specifically, the imprinting technique transforms the joints between the component mesh and the reference surface mesh into shared nodes by processing the non-shared nodes at the interface. Through mutual imprinting, the nodes in the interface area between the reference surface mesh and the component mesh are locally adjusted to ensure precise alignment and the formation of shared nodes. This technique effectively handles the joint areas of different meshes, eliminates discontinuities, and ensures node consistency at the joints, thereby improving the overall mesh quality and smoothness of the transition after assembly. Figure 8 and Figure 9 The image shows the final results for two instances.

[0080] 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.

[0081] 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 assembling self-intersecting meshes based on volume parameterization, characterized in that, include: S1: Input an arbitrary surface mesh as a reference surface mesh and an arbitrary surface mesh as a component mesh. Parameterize the reference surface mesh to obtain a two-dimensional parameter plane. Use the obtained two-dimensional parameter plane as the reference parameter plane. Establish a first mapping function based on the mapping relationship between physical space and the reference parameter plane. S2: Place the reference parameter plane on the XY plane of the Cartesian coordinate system and stretch it along the Z-axis to generate the top surface, thereby obtaining a three-dimensional parameter space. Transform the reference surface mesh in the reference parameter plane from a triangular mesh structure to a triangular prism mesh structure in the three-dimensional parameter space. S3: In physical space, the reference surface mesh is expanded from a triangular mesh structure to a triangular prism mesh structure; S4: Based on the specified assembly point coordinates, specified assembly direction vector, and first mapping function input by the user, map the node coordinates of the component mesh to the three-dimensional parameter space, while keeping the topology of the component mesh unchanged, to obtain the component mesh structure in the three-dimensional parameter space; S5: Based on the triangular prism mesh structure in the three-dimensional parameter space and the triangular prism mesh structure in the physical space, establish a second mapping function, and map the node coordinates of the component mesh structure to the physical space according to the second mapping function, while keeping the topological relationship of the component mesh structure unchanged, to obtain the component mesh in the physical space. S6: Merge the component mesh and the reference surface mesh in the physical space to make the transition between the component mesh and the reference surface smooth, eliminate the discontinuity at the assembly joint, and make the assembly joint share nodes.

2. The method for assembling a non-self-intersecting mesh based on volume parameterization according to claim 1, characterized in that, Input an arbitrary surface mesh as a reference surface mesh and another arbitrary surface mesh as a component mesh. Parameterize the reference surface mesh to obtain a two-dimensional parameter plane. Use the obtained two-dimensional parameter plane as the reference parameter plane. Based on the mapping relationship between physical space and the reference parameter plane, establish a first mapping function, specifically including: S11: Read the first input surface mesh as the reference surface mesh. It supports inputting triangular or quadrilateral meshes. When the input reference surface mesh is a quadrilateral mesh, it is divided into triangular meshes by the diagonal. Read the second input surface mesh as the part mesh. It supports inputting triangular or quadrilateral meshes. S12: Using the coordinates of the assembly point on the reference surface mesh input by the user as the center, and the diagonal size of the bounding box of the component mesh as the search radius, obtain the triangular facets within the search radius on the reference surface mesh using a breadth-first search algorithm, and use them as a subset mesh; S13: Parameterize a subset of the reference plane mesh to obtain the reference parameter plane; S14: Based on the mapping relationship between the physical space and the reference parameter plane, establish a mapping function between the reference surface mesh and the coordinates of the points on the reference parameter plane, i.e., the first mapping function.

3. The method for assembling a non-self-intersecting mesh based on volume parameterization according to claim 1, characterized in that, The reference parameter plane is placed on the XY plane of the Cartesian coordinate system and stretched along the Z-axis to generate the top surface, thus obtaining a three-dimensional parameter space. The reference surface mesh in the reference parameter plane is transformed from a triangular mesh structure into a triangular prism mesh structure in the three-dimensional parameter space, specifically including: S21: Embed the reference parameter plane into the Cartesian coordinate system and place it parallel to the XY plane, so that the reference parameter plane coincides with the XY plane of the Cartesian coordinate system; S22: Perform a stretching operation on the reference parameter plane along the Z-axis direction, and set the stretching height to a predetermined value H to form a top surface parallel to the reference parameter plane; S23: Based on the above reference parameter plane and top surface, a closed body is formed between the upper and lower planes by connecting the corresponding points, thus obtaining a three-dimensional parameter space. The bottom surface of this space is the reference parameter plane, the top surface is the extruded surface, and the side walls are formed by the corresponding boundaries between the reference plane mesh and the top surface mesh. S24: Divide the reference parameter plane into several triangular mesh units. Each triangular mesh consists of three vertices and three sides, forming a two-dimensional triangular mesh structure of the reference plane. S25: For each triangular mesh element of the reference plane, stretch its three vertices to the corresponding positions on the top surface along the Z-axis to form the corresponding upper surface triangle. Connect the original triangular mesh with its corresponding top triangle to construct a triangular prism with two triangular faces and three rectangular sides. In this way, all the triangular meshes of the reference plane are transformed into triangular prism mesh elements in three-dimensional space. S26: All triangular prism elements are combined in the three-dimensional parameter space to form a continuous triangular prism mesh structure.

4. The method for assembling a non-self-intersecting mesh based on volume parameterization according to claim 1, characterized in that, In physical space, the reference surface mesh is expanded from a triangular mesh structure to a triangular prism mesh structure, specifically including: S31: Determine the stretching direction and construct an initial triangular prism mesh. Obtain the normal vector of each mesh node on the reference plane and perform Laplace smoothing on the normal vector. Replace the Z-axis direction in the Cartesian coordinate system with the smoothed normal vector and stretch the triangular mesh of the reference plane along this direction to construct a preliminary triangular prism mesh structure. If there is overlap or self-intersection between the triangular prism elements generated in this process, proceed to S32. S32: Robust triangular prism mesh generation based on bijective mapping. When there is a problem of triangular prism element intersection, a boundary layer prism mesh generation method is used to handle it. This method ensures that the triangular mesh is stably extended into non-overlapping triangular prism elements along the boundary normal direction by constructing a bijective mapping relationship, thus obtaining a triangular prism mesh structure without self-intersection.

5. The method for assembling a non-self-intersecting mesh based on volume parameterization according to claim 1, characterized in that, Based on the user-input specified assembly point coordinates, specified assembly direction vector, and first mapping function, the node coordinates of the component mesh are mapped to the three-dimensional parameter space, while the topology of the component mesh remains unchanged, resulting in the component mesh structure in the three-dimensional parameter space, specifically including: S41: Based on the specified assembly point coordinates and assembly alignment direction input by the user and the first mapping function, calculate the parameter plane coordinates of the specified assembly point coordinates input by the user, and perform translation and rotation operations based on the parameter plane coordinates and the specified assembly direction to place the component mesh in the parameter plane. S42: Map the nodes of the component mesh to three-dimensional space to obtain the three-dimensional space coordinates of the nodes of the component mesh, while keeping the topology of the component mesh unchanged.

6. The method for assembling a non-self-intersecting mesh based on volume parameterization according to claim 1, characterized in that, The specified assembly point coordinates include: assembly point coordinates on the reference plane grid. and component mesh assembly point coordinates The specified assembly direction vector includes the datum plane assembly alignment direction. Alignment direction of component assembly .

7. The method for assembling a non-self-intersecting mesh based on volume parameterization according to claim 1, characterized in that, Based on the triangular prism mesh structure in the three-dimensional parameter space and the triangular prism mesh structure in the physical space, a second mapping function is established. The node coordinates of the component mesh structure are mapped to the physical space using this second mapping function, while maintaining the topological relationships of the component mesh structure, to obtain the component mesh in the physical space. Specifically, this includes: S51: Construct a binary search tree BT1 based on the node coordinates and topological relationships of the grid. Through BT1, the index of the triangular facet to which any grid node belongs can be retrieved based on the spatial coordinates of the grid node. ; this index As an identifier for the triangular prism element, it enables a fast mapping from node coordinates to the triangular prism label; S52: Decompose a triangular prism into n tetrahedrons to represent a structure in three-dimensional space. Each tetrahedron has a local index within its triangular prism. For any point P in the parameter space, project it onto the parameter plane, and obtain the label of the triangle to which point P belongs through the binary search tree BT1 of the triangles. At the same time, determine the triangular prism to which point P belongs; S53: Inside a triangular prism, calculate the local tetrahedral index of point P using a volumetric algorithm. The centroid coordinate parameters represented by the four vertices of the tetrahedron are calculated using centroid coordinate interpolation. To obtain unique information for each point Substitute different spatial point coordinates into This allows us to obtain the coordinates of point P in different spaces, thereby establishing the second mapping function between the three-dimensional parameter space and the physical space triangular prism. S54: Map the three-dimensional spatial coordinates of the nodes in the component mesh to the physical space through the second mapping function to obtain the point coordinates in the physical space, while keeping the topological relationship of the component mesh unchanged, and obtain the component mesh in the physical space.

8. The method for assembling a non-self-intersecting mesh based on volume parameterization according to claim 1, characterized in that, Merging the component mesh and the reference plane mesh in the physical space to achieve a smooth transition between the component mesh and the reference plane specifically includes: S61: Merge the mesh nodes of the component mesh and the reference surface mesh in the physical space into the output result mesh node, update the topology of the component mesh and the topology of the reference surface mesh, and merge them; S62: The seam between the component mesh and the reference surface mesh is processed by mesh embossing technology.

Images