Curved surface grid generation method based on discrete grid parameterization

Abstract

The invention provides a curved surface grid generation method based on discrete grid parameterization, and belongs to the technical field of computer aided engineering (CAE) and computational geometry. Aiming at the problems of tedious geometric operation, parameter space fusion distortion, insufficient grid fitness and the like in grid subdivision of a complex curved surface formed by a plurality of sub-curved surfaces, the invention provides the following technical scheme: firstly, carrying out triangular grid pre-subdivision on an original curved surface, and constructing a virtual topological structure for inhibiting non-key features; the discrete grids are mapped to a low-distortion two-dimensional parameter space by adopting least square conformal mapping (LSCM), and seamless combination of multiple sub-surface parameter domains is realized; dynamically calculating a parameter space size field, and controlling grid density distribution; after a parameter space adaptive grid is generated through Delaunay triangulation, grid points are accurately attached to an original geometric surface by using a dual projection correction mechanism. According to the method, complex CAD geometric operation is avoided, the automation degree is remarkably improved, meanwhile, physical space grid uniformity and strict fitness are guaranteed, and the method is suitable for efficient and high-precision grid generation of complex curved surfaces in the fields of aerospace, automobiles, ships and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of computer-aided engineering (CAE) and computational geometry, and particularly relates to a surface mesh generation method based on discrete grid parameterization, which is applicable to high-quality mesh meshing of complex surfaces. Especially for composite surfaces composed of multiple sub-surfaces, through virtual topology construction, parameter space merging, and size field regulation, efficient and body-fitting mesh generation is realized. Background Art

[0002] With the development of CAE simulation and the growth of application requirements, in the fields of automotive, aerospace, shipbuilding, etc., simulation analysis of complex surface models is required. Complex surfaces are usually composite surfaces composed of multiple sub-surfaces, which often contain a large number of tiny patches, narrow edges and other geometric features. The existence of these features will lead to a significant decline in the quality of mesh generation, causing problems such as local mesh distortion and uneven density distribution, which will in turn affect the accuracy and reliability of engineering simulation. To address this challenge, the existing technologies mainly adopt two types of methods: geometric reconstruction method and discrete grid parameterization method.

[0003] The geometric reconstruction method stitches the sub-surfaces into a single continuous surface through surface re-fitting and Boolean operations, and selectively retains or suppresses the edges to form a topological loop. Its core processes include geometric stitching, surface trimming, global parameterization, and mesh mapping. However, this method relies on high-precision surface fitting and complex Boolean operations, which not only have high computational costs, but also are prone to introducing geometric errors during the reconstruction process. In addition, excessive suppression of tiny features may lead to the loss of key geometric details and reduce the fidelity of the model. More seriously, such methods rely strongly on manual intervention and are difficult to achieve automated processing of large-scale complex surfaces, greatly limiting the efficiency of engineering applications.

[0004] The discrete grid parameterization method realizes mesh generation by discretizing the sub-surfaces into triangular meshes and constructing a unified parameter space. This method avoids the geometric reconstruction step, but due to the lack of a dynamic size field regulation mechanism, it is difficult to balance the mesh density in key areas and the overall computational efficiency. In addition, when the generated mesh is mapped back to the physical space, it often deviates from the original surface due to the lack of geometric information, resulting in non-body-fitting meshes.

[0005] Generally speaking, the existing technologies generally face multiple contradictions among the complexity of geometric operations, the efficiency of parameter space fusion, and the body-fitting nature of meshes. Although the geometric reconstruction method can ensure geometric integrity, it comes at the cost of high computational costs and low automation. Although the discrete parameterization method simplifies geometric operations, it is limited by the quality of the parameter space and the lack of size field control. How to achieve efficient fusion of multi-sub-surface parameter spaces, precise regulation of dynamic size fields, and strict body-fitting of meshes without relying on complex CAD operations has become a technical problem that urgently needs to be broken through in the field of complex surface mesh generation. Summary of the Invention

[0006] In view of the limitations of the prior art, the present invention proposes a complex surface mesh generation method based on virtual topology construction, parameter space fusion, and dynamic size field regulation, aiming to solve the problems existing in the mesh generation of complex surfaces, such as complex geometric operations, difficulty in parameter space fusion, and insufficient grid uniformity and body-fittingness, and to achieve efficient and high-precision surface mesh generation. The present invention adopts the following technical solutions to achieve the purpose:

[0007] A surface mesh generation method based on discrete grid parameterization, comprising the following steps:

[0008] S1. Perform triangular mesh pre-dissection on the original surface geometry to obtain a background mesh for discrete grid parameterization. At the same time, suppress non-critical geometric features (such as feature lines on slender surfaces and geometric vertices on C1 continuous small broken edges), and construct a virtual geometric topology based on the discrete grid.

[0009] S2. Adopt the least squares conformal mapping (LSCM) algorithm to map the discrete triangular mesh from the physical space (x, y, z) to the two-dimensional parameter space (u, v), ensuring low distortion in the parameter space and realizing seamless merging of multiple sub-face parameter domains.

[0010] S3. To ensure the uniformity of the physical space grid, introduce a grid size field regulation mechanism. Calculate the surface micro-elements from the physical space to the parameter space, and reversely correct the grid size in the parameter space, so that the grid mapped back to the physical space can adapt to the surface curvature change. Based on the grid size field, complete the grid dissection in the two-dimensional parameter space using Delaunay triangulation.

[0011] S4. Establish a double projection correction mechanism. First, judge the serial number of the unique pre-dissection background mesh where the generated grid nodes are located in the parameter space, and record the geometric patch number to which the background mesh belongs. Map each node from the parameter space to the parameter space of the CAD geometric surface through linear interpolation, and then calculate the physical space coordinates of this point through the CAD surface parameter equation analysis to ensure that the final grid strictly fits the geometric surface.

[0012] Further, in step S1, the pre-dissection grid can be dissected using a geometric curvature adaptive dissection algorithm, using small-sized grids in high-curvature regions and large-sized grids in flat regions to improve the geometric accuracy of the pre-dissection grid, while reducing the number of pre-dissection grids as much as possible and reducing the computational amount of discrete grid parameterization in step S2. Among them, the pre-dissection grid is only used to approximate the original analytical geometry and construct the parameter space, and does not require grid quality, so the grid quality improvement algorithm can not be adopted to reduce the calculation time.

[0013] Further, in step S1, the geometric continuity condition can be selected to automatically suppress points and edges to construct a virtual topology. Specifically, geometric continuity judgment is performed at the common edges of all adjacent faces. If the geometric continuity condition is satisfied, the edge is suppressed. Similarly, geometric continuity judgment is performed at the common nodes of all connected edges. If the geometric continuity condition is satisfied, the point is suppressed. It is also possible to manually specify the geometric features to be suppressed and retained. The retained edges need to be passed to the subsequent steps as line elements as well.

[0014] Further, in step S2, the geometric regions that need to be merged are grouped together for mesh discretization parameterization. The outer ring of the pre-meshed grid for parameterization needs to ensure no self-intersection and no large curvature changes, so as to ensure that the parameterized grid has no overlap and thus prevent parameterization failure.

[0015] Further, in step S3, the lines that do not need to be suppressed are first meshed and used as constraints in the Delaunay triangulation process. During the point insertion process of Delaunay triangulation, the density of the inserted points needs to be adjusted according to the mesh size field. Other triangulation algorithms such as AFT (Advancing Front Technique)-Delaunay can also be used for mesh generation in this step, or the triangular mesh can be converted into a quadrilateral hybrid mesh by using the element merging method after the triangular mesh is generated.

[0016] Further, in step S4, it is necessary to determine whether the node is inside a pre-meshed grid triangle. The AABB tree can be used to reduce the space, significantly reducing the number of judgments between the node and the triangular mesh and improving the calculation efficiency of the double projection. The interpolation of subsequent nodes and the CAD geometric calculation process are completely independent, and parallel computing can be used to accelerate.

[0017] In summary, due to the adoption of this technical solution, the present invention demonstrates remarkable generality, flexibility, efficiency, and ease of use in solving complex surface mesh generation problems, providing a solution for high-quality surface mesh generation for engineering simulation calculations. The beneficial effects brought by the present invention are specifically manifested in the following aspects: 1. By constructing a virtual topology to replace complex geometric reconstruction, it reduces manual intervention and calculation costs and improves the automation degree of multi-subsurface processing. 2. The dynamic size field regulation combined with the low-distortion parameter space mapping ensures the uniformity of the physical space mesh, and the density in key regions (such as high-curvature edges) is adaptively encrypted to meet the high-precision simulation requirements. 3. The double mapping mechanism effectively eliminates the parameterization mapping error, making the final mesh strictly conform to the original surface. 4. It is applicable to complex surface structures such as aero-engine blades, automobile bodies, and ship hulls, and supports the rapid mesh generation requirements of large-scale engineering simulations. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a schematic diagram of the overall steps of the method of the present invention; Figure 2 Schematic diagram of the hull outer shell geometric model for illustration; Figure 3 Schematic diagram of the pre - meshed grid of the hull outer shell for illustration; Figure 4 Schematic diagram of the discrete grid parameterization of the hull outer shell; Figure 5 Schematic diagram of the result of the grid division of the hull outer shell parameter space for illustration; Figure 6 Schematic diagram of the final grid division result of the hull outer shell in the physical space Detailed implementation manners

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, rather than all, of the embodiments of the present invention. Usually, the components of the embodiments of the present invention described and illustrated herein can be arranged and designed in various different configurations.

[0020] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents the selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0021] Embodiment 1

[0022] A surface grid generation method based on discrete grid parameterization. The overall content of this method can be seen in the illustration of Figure 1 and its steps can be summarized as follows

[0023] S1. Perform a triangular grid pre - meshing on the original surface geometry to obtain the background grid for discrete grid parameterization. At the same time, suppress non - critical geometric features and construct a virtual geometric topology based on the discrete grid.

[0024] S2. Adopt the least - squares conformal mapping (LSCM) algorithm to map the discrete triangular grid from the physical space (x, y, z) to the two - dimensional parameter space (u, v), ensuring low distortion in the parameter space and realizing seamless merging of multiple sub - surface parameter domains.

[0025] S3. Use the surface micro - elements from the computational physical space to the parameter space to calculate the grid size field, and complete the grid division in the two - dimensional parameter space based on Delaunay triangulation.

[0026] S4. Through the double - projection correction mechanism, map the nodes in the parameter space to the physical space.

[0027] In this embodiment, the details of the method in each step will be introduced through a detailed method flow.

[0028] 1. Perform triangular mesh pre - meshing on the original surface geometry for the background mesh of discrete mesh parameterization. In this embodiment, geometric features that do not meet the continuity conditions will be automatically suppressed, and a virtual geometric topology based on discrete meshes will be constructed. Specifically, it includes the following sub - steps:

[0029] S101, Triangular mesh pre - meshing: The original surface geometry is meshed using a geometric curvature - adaptive meshing algorithm, and the mesh is refined in high - curvature regions. Among them, surface mesh meshing is performed on the parameter space (p, q) of the CAD geometric surface, and the node coordinates on the parameter space (p, q) of each sub - surface i are recorded. The node information, face element information (node ID, face ID), and line element information (node ID, line ID) in the physical space (x, y, z) of the entire model are recorded.

[0030] S102, Establish virtual topology: Automatically suppress points and edges using geometric continuity conditions to construct a virtual topology. Judge the topology of all points and faces in the model, suppress the internal edges and faces of sub - faces, and judge the common points and faces. Perform geometric continuity judgment at the common edges of all adjacent faces: Sample the common edges separately, and calculate the normal vectors of adjacent faces at the sampling points 、 , in this embodiment, the criterion used is (2° tolerance). If all sampling points meet the conditions, then suppress this edge; Similarly, perform geometric continuity judgment at the common nodes of all connected edges: Calculate the tangential vectors of adjacent lines at the common points 、 , in this embodiment, the criterion used is (2° tolerance). If the conditions are met, then suppress this point. Mark all the edges that need to be retained in their line element information.

[0031] 2. Use the least - squares conformal mapping (LSCM) algorithm to map the discrete triangular mesh from the physical space (x, y, z) to the two - dimensional parameter space (u, v). Specifically, it includes the following sub - steps:

[0032] S201, Free - edge calculation: Input the pre - meshed grid in the physical space, traverse the grid to calculate the free edges of the grid. Traverse the free - edge nodes, arrange them in a chain in sequence, and find the two points with the maximum arc - length distance on the chain as the constraint points, which are respectively constrained as the points (0, 0) and (1, 0) in the parameter space (u, v).

[0033] S202. Calculate the coordinate of the node parameter space: Construct the conformal free energy through the Dirichlet energy and area, and establish a system of linear algebraic equations to minimize the conformal free energy. By solving the system of linear algebraic equations under constraints, the coordinate values of the parameter space of all nodes are obtained, the conformal mapping of the discrete triangular mesh is completed, and the pre-meshed grid on the two-dimensional parameter space is obtained.

[0034] III. Calculate the grid size field, and complete the grid division in the two-dimensional parameter space based on Delaunay triangulation, which specifically includes the following sub-steps:

[0035] S301. Calculate the grid size field: Loop through the face elements of the pre-meshed grid to calculate the surface microelement , where . Inside the triangular element is a constant and can be calculated through the coordinates of the physical space and the parameter space. At the node, average the connected elements can be calculated to obtain . The value of the grid size field at the node is , where D is the global grid size.

[0036] S302. Line re-meshing: Read the line information of the pre-meshed grid, exclude the suppressed edges, and then reconstruct the loop using the remaining discrete line grid. Under the parameter space, use the grid size field to complete the one-dimensional re-meshing of the line grid, which serves as a constraint for the two-dimensional grid division.

[0037] S303. Face re-meshing: Under the parameter space, insert points into the grid division area according to the grid size field, and use the Constrained Delaunay Triangulation (CDT) algorithm to complete the grid division on the parameter space.

[0038] IV. Establish the correspondence between the newly generated nodes and the pre-meshed grid, and map the nodes in the parameter space to the physical space through the double projection correction mechanism, which specifically includes the following sub-steps:

[0039] S401. Search for the grid to which the node belongs: First, establish an AABB tree for the pre-meshed grid in the parameter space. Then loop through the nodes generated by the re-meshing, and use the AABB tree to quickly filter the node neighborhood. For the pre-meshed grid in the neighborhood, first quickly judge through the bounding box, and then accurately judge through the area method whether the point is inside the pre-meshed grid. Thus, a one-to-one correspondence between the nodes and the pre-meshed grid is established.

[0040] S402, Parameter Space Projection: For all nodes in a loop, project the coordinates of the discrete parameter space (u, v) onto the original CAD surface parameter space (p, q) using linear interpolation. The coordinates of a node in the discrete parameter space are (u0, v0), and the coordinates of the three nodes corresponding to the pre-meshed grid are (u1, v1), (u2, v2), and (u3, v3) respectively; in the original CAD surface parameter space, the coordinates of the three nodes corresponding to the pre-meshed grid are (p1, q1), (p2, q2), and (p3, q3) respectively. The coordinates (p0, q0) of the node in the original CAD surface parameter space after linear interpolation can be calculated as follows: \left [ {{p}_{0},{q}_{0}} \right ]=\left [ {1,{u}_{0},{v}_{0}} \right ]\left [ {1,{u}_{1},{v}_{1};1,{u}_{2},{v}_{2};1,{u}_{3},{v}_{3}} \right ]{\,}^{-1}\left [ {{p}_{1},{q}_{1};{p}_{2},{q}_{2};{p}_{3},{q}_{3}} \right ]

[0041] S403, Physical Space Projection: Query the surface corresponding to the pre-meshed grid , and obtain the parametric equation (x, y, z) = F(p, q) of it. Substitute the parameter space coordinates (p0, q0) obtained by linear interpolation into the equation to get the physical space coordinates (x0, y0, z0) of this point, and the node fits exactly to the original geometric surface.

[0042] Example 2

[0043] Based on Example 1, this example uses the hull outer surface mesh generation for demonstration, and its geometric model is as shown in Figure 2 .

[0044] First, specify the pre-meshed grid size as 800, complete the mesh pre-generation of the geometric model, and the mesh generation result is as shown in Figure 3 . In this example, all common points and common edges inside the model will be suppressed. The entire pre-meshed grid information is passed as input to the next step.

[0045] Then use LSCM to complete the discrete parameterization of the pre-meshed grid, and the parameterized result is as shown in Figure 4 .

[0046] Based on the parametric pre-meshing grid, specify the global mesh size as 2000 and calculate the mesh size field. Then, use the Constrained Delaunay Triangulation (CDT) algorithm to complete the mesh generation in the parametric space. The mesh generation results are shown as Figure 5 shown.

[0047] Establish a one-to-one correspondence between the nodes of the remeshed grid and the nodes of the pre-meshed grid. Through the double projection correction mechanism, first linearly interpolate the parametric space nodes to the surface parametric space of their respective original CAD geometric surfaces, and then map the parametric space nodes to the physical space through the surface parametric equation. The final mesh results are shown as Figure 6 shown.

Claims

1. A surface mesh generation method based on discrete grid parameterization, characterized in that It includes the following steps: S1. Perform triangular mesh pre - dissection on the original surface geometry and construct a virtual geometric topology: By suppressing non - critical geometric features, generate a discretized background mesh; S2. Parameter space mapping: Use the Least Squares Conformal Mapping (LSCM) algorithm to map the physical space mesh to a two - dimensional parameter space, realizing the seamless merger of multi - sub - surface parameter domains; S3. Dynamic size field regulation and parameter space mesh dissection: Based on the reverse correction of the mesh size field for surface micro - elements in the physical space and parameter space, use constrained Delaunay triangulation to generate a parameter space mesh; S4. Dual - projection correction: Map the parameter space nodes to the CAD surface parameter space through linear interpolation and then map them back to the physical space through an analytical equation to ensure that the mesh is strictly body - fitted.

2. The method according to claim 1, characterized in that, In step S1, any triangular surface mesh dissection method can be used for the triangular mesh pre - dissection, and adaptive densification at high - curvature locations can be selected to balance mesh accuracy and computational cost.

3. The method according to claim 1, wherein The method of suppressing non - critical geometric features in step S1 includes automated suppression based on geometric continuity conditions and manual feature suppression.

4. The method according to claim 1, wherein In step S1, methods other than the Least Squares Conformal Mapping (LSCM) algorithm can be used for the parameter space mapping method.

5. The method according to claim 4, wherein The pre - dissected mesh after parameterization needs to ensure that there are no overlaps in the parameterized mesh.

6. The method according to claim 1, wherein In the step S3, the calculation method of the dynamic size field is as follows: the value of the mesh size field at the node is , where D is the global mesh size. Among them, it is calculated on the triangular element , and averaged for the connected elements at the node can be calculated to obtain .

7. The method according to claim 1, wherein In step S3, the parameter space mesh dissection method can be selected as follows: the Constrained Delaunay Triangulation (CDT) algorithm, or use the Advancing Front Technique (AFT) and Delaunay hybrid algorithm to generate triangular meshes, or it can be converted into a quadrilateral hybrid mesh through element merging.

8. The method according to claim 1, wherein In step S4, the specific steps of dual - projection correction include: Use an AABB tree to accelerate the determination of the ownership of nodes and the pre - dissected background mesh, and determine the unique triangular element where the node is located; Map the parameter space nodes to the CAD surface parameter space through linear interpolation, and then calculate the physical coordinates through an analytical equation.

9. The method according to claim 8, characterized in that, The calculation method of the linear interpolation for the coordinates (p0, q0) of the node in the original CAD surface parameter space is: \left [ {{p}_{0},{q}_{0}} \right ]=\left [ {1,{u}_{0},{v}_{0}} \right ]\left [ {1,{u}_{1},{v}_{1};1,{u}_{2},{v}_{2};1,{u}_{3},{v}_{3}} \right ]{\,}^{-1}\left [ {{p}_{1},{q}_{1};{p}_{2},{q}_{2};{p}_{3},{q}_{3}} \right ] where (u0, v0) is the node parameter space coordinate, (u1, v1), (u2, v2), (u3, v3) are the parameter space coordinates of the corresponding pre - dissected mesh nodes, and (p1, q1), (p2, q2), (p3, q3) are the coordinates of the corresponding pre - dissected mesh nodes in the original CAD surface parameter space.

10. The method according to claim 8, wherein In step S4, the calculation of the node physical coordinates uses parallel processing to independently execute the analytical mapping of the CAD surface parameter equation for each node.

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