A curved surface grid self-adaptive division method based on improved isoparametric line method

Abstract

This invention discloses an adaptive surface mesh generation method based on an improved isoparametric method. The method's process is as follows: First, the original surface is expanded. Based on the initially determined isoparametric design parameters, the isoparametric line spacing and segmentation starting points are corrected. Then, boundary points are snapped together according to the shortest path principle. Based on the processed point set, triangulation is performed to obtain the surface mesh. Finally, with the goal of minimizing the number of inferior meshes, an intelligent optimization algorithm is used to optimize the mesh design parameters to obtain the optimal mesh. This invention is applicable to surfaces with large curvature variations, effectively solving problems such as poor boundary mesh quality and non-smooth meshing in the original isoparametric method. Furthermore, it can adaptively optimize the mesh generation design parameters according to the surface characteristics, generating a regular and uniform mesh that can be directly used for subsequent structural design.

Description

Technical Field

[0001] This invention relates to the field of building structure design, and more specifically to an adaptive mesh generation method for curved surfaces based on an improved isoparametric method. Background Technology

[0002] Spatial grid structures are widely used in various large-scale building structures due to their excellent shaping capabilities. With the development of technology, more and more free-form surface shapes are being applied in architectural design. However, as structural shapes become increasingly complex, traditional component arrangement methods are difficult to meet the requirements of structural stress performance, building appearance, curtain wall construction, etc.

[0003] To achieve a reasonable arrangement of components, adaptive meshing of the curved surface of the grid structure is required. Traditional meshing methods, such as mapping, isoparametric methods, triangular mesh transformation, Delaunay triangulation, and wavefront methods, are mostly based on architectural perspectives, focusing only on the uniformity of mesh division and neglecting issues such as the arrangement of members and the treatment of members near the boundaries during the structural design process.

[0004] Among them, the equidistant reference line method (hereinafter referred to as the isoparametric line method) can effectively avoid the problem of mapping distortion in the mapping method because it directly performs meshing on the curved surface. It is applicable to curved surfaces with large curvature changes, but it also has shortcomings. There are often many thin-film mesh units with very sharp inner corners at the edge of the curved surface. Due to the influence of the curvature change of the curved surface, it is difficult to keep the spacing of the isoparametric lines consistent. In addition, the quality of meshing depends on the selection of its isoparametric line design parameters, and the selection of parameters depends on the designer's experience, which has a large degree of uncertainty. Summary of the Invention

[0005] This invention provides an adaptive surface mesh generation method based on the improved isoparametric method, which aims to solve the problems of inconsistent isoparametric line spacing, poor boundary mesh quality, and reasonable selection of design parameters for freeform surface mesh generation in the original isoparametric method, thereby achieving adaptive optimization of the surface mesh.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: an adaptive surface mesh generation method based on the improved isoparametric method, which achieves adaptive optimization of surface mesh generation by correcting the isoparametric line spacing and the starting point of the segmentation, absorbing the boundary point set, and combining it with an intelligent optimization algorithm, including the following steps:

[0007] (1) Surface extension: Based on the given original surface S, extract the boundary of the surface and extend the surface in the horizontal direction to obtain the extended new surface S';

[0008] (2) Initial parameters and value range: Initially determine the spacing d1 of isoparametric lines, the spacing d2 of isoparametric line points, the rotation angle a, and their corresponding value ranges;

[0009] (3) Correction of isoparametric line spacing: Based on the isoparametric line spacing d1 and the rotation angle a, draw an equally spaced curve L with a rotation angle of a+90° on the surface S', and divide the curve L according to the isoparametric line spacing d1 and the chord length, and then draw an isoparametric line with a rotation angle of a through the dividing point to obtain the corrected isoparametric line L' on the surface.

[0010] (4) Correction of the starting point of isoparametric line segmentation: Connect the midpoints of the first and last isoparametric lines L', and take the intersection of the connecting line with the other isoparametric lines on the surface as the starting point. According to the isoparametric line point spacing d2, the corrected isoparametric line L' is segmented by equal chord length to obtain the initial point set P.

[0011] (5) Boundary point adsorption processing: Project the point set near the boundary of the original surface S back to the boundary of the original surface according to the principle of shortest path to obtain the final point set P';

[0012] (6) Triangulation to form a mesh: Perform Delaunay triangulation on the final point set P' and form a surface mesh with the boundary of the original surface S;

[0013] (7) Iterative optimization of mesh design parameters: With the goal of minimizing the number of inferior meshes, the intelligent optimization algorithm is used to optimize the isoparametric line spacing d1, isoparametric line point spacing d2, and rotation angle a in the mesh design parameters. Steps (3) to (7) are repeated until the optimal mesh result and its mesh design parameters are found.

[0014] Furthermore, in step (1), the extension distance of the extended surface is taken as 2 to 3 times the length of the required mesh size.

[0015] Furthermore, the definition of a substandard mesh in step (7) is determined based on the variance of the interior angle of each triangular mesh. A single mesh whose interior angle variance is greater than the limit value can be judged as a substandard mesh. The limit value can be adjusted according to actual use.

[0016] Furthermore, the limit is set between 130 and 150.

[0017] In summary, this invention first expands the original curved surface, corrects the isoparametric line spacing and segmentation starting point based on the initially determined isoparametric line design parameters, then performs boundary point snapping according to the shortest path principle, and obtains a curved surface mesh through triangulation based on the processed point set. Finally, with the goal of minimizing the number of inferior meshes, an intelligent optimization algorithm is used to optimize the mesh design parameters to obtain the optimal mesh. Compared with existing mesh generation methods, it has the following advantages:

[0018] Firstly, this invention is applicable to curved surfaces with large curvature variations, and the generated mesh is regular and uniform.

[0019] Secondly, by correcting the spacing of isoparametric lines and the starting point of segmentation on the curved surface, this invention effectively solves the problem of uneven mesh caused by inconsistent starting points and spacing when the curvature of the curved surface changes significantly, thus ensuring the consistency of mesh size.

[0020] Thirdly, this invention effectively solves the problem of poor quality of the original isoparametric boundary mesh by expanding the curved surface and adsorbing the boundary points, avoiding the generation of short boundary rods, and can be directly used for subsequent structural design.

[0021] Fourth, this invention can adaptively optimize the meshing design parameters according to the characteristics of the curved surface, effectively avoiding the limitations of manually setting design parameters and obtaining better meshing results;

[0022] Fifth, this invention can be programmed, enabling rapid adaptive optimization generation of meshes. Attached Figure Description

[0023] Figure 1 The flowchart of the method of this invention is shown below;

[0024] Figure 2 Let S be the original surface to be meshed and S' be the expanded surface;

[0025] Figure 3 This is a schematic diagram of the isoparametric line L';

[0026] Figure 4 The isoparametric line L' is corrected for equal chord length division;

[0027] Figure 5 To perform adsorption processing on points near the boundary of surface S;

[0028] Figure 6 For the problem of short rods near the boundary;

[0029] Figure 7 This is the initial mesh on the surface S;

[0030] Figure 8 This represents the final mesh generation result. Detailed Implementation

[0031] The following is in conjunction with the appendix Figures 1 to 8 The present invention provides a more detailed description of a specific implementation of an adaptive surface mesh generation method based on an improved isoparametric method. Specific implementation examples:

[0033] This embodiment involves a curved surface approximately 118m long, 109m wide, and with a maximum elevation difference of approximately 13m. The implementation steps of the method of this invention are as follows:

[0034] (1) Surface extension: such as Figure 2 As shown, the free surface that needs to be meshed is defined as the original surface S. The boundary of the surface is extracted and the surface is extended in the horizontal direction to obtain the extended new surface S'.

[0035] (2) Initial parameters and value range: The isoparametric line spacing d1 and the isoparametric line point spacing d2 are both set to 3m, the isoparametric line rotation angle a is set to 45°, the value range of the isoparametric line spacing d1 and the isoparametric line point spacing d2 is set to [2m, 4m], the parameter change accuracy is 0.05m, the value range of the isoparametric line rotation angle a is set to [30°, 120°], the parameter change accuracy is 1°;

[0036] (3) Correction of isoparametric line spacing: Based on the isoparametric line spacing d1 and the rotation angle a, draw an equally spaced curve L with a rotation angle of a+90° on the surface S'. Then, divide the curve L according to the isoparametric line spacing d1 and the chord length. Next, draw an isoparametric line with a rotation angle of a through the dividing point to obtain the corrected isoparametric line L' on the surface. The effect is as follows: Figure 3 As shown;

[0037] (4) Correction of the starting point for isoparametric line segmentation: Connect the midpoints of the first and last isoparametric lines L', and take the intersection of this line with the remaining isoparametric lines on the surface as the starting point. Based on the isoparametric line point spacing d2, segment the corrected isoparametric line L' with equal chord lengths to obtain the initial point set P, as shown in the figure. Figure 4 As shown;

[0038] (5) Boundary point adsorption processing: Points whose straight-line distance from the boundary of surface S is less than 1m are projected back to the original surface boundary according to the shortest path principle to obtain the final point set P', such as Figure 5 As shown, Figure 6 (Short rod problem near the boundary) further demonstrates that if the boundary points are not properly organized, many short rods may appear;

[0039] (6) Triangulation to form a mesh: Perform Delaunay triangulation on the final point set P' and form a surface mesh with the boundary of the original surface S, such as... Figure 7 As shown (the initial mesh on surface S);

[0040] (7) Calculate the variance of the interior angle of all cells in the grid. The average angle is set to 60°, which is the interior angle of an equilateral triangle. In this embodiment, cells with a variance greater than 130 are judged as poor grids. The number of poor grids obtained in the initial iteration is 326.

[0041] (8) Iterative optimization of mesh design parameters: With the goal of minimizing the number of inferior meshes, an intelligent optimization algorithm is used to optimize the mesh design parameters (isoparametric line spacing d1, isoparametric line point spacing d2, and rotation angle a). Steps (3) to (7) are repeated. Finally, after 40 iterations, the optimal solution for the mesh parameters is obtained: isoparametric line spacing 3.5m, isoparametric line point spacing 4m, rotation angle 47°, and the number of inferior meshes is reduced to 180. Mesh comparison results Figure 8 As shown (left is before optimization, right is after optimization).

[0042] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A surface mesh adaptive generation method based on an improved isoparametric method, characterized in that, By correcting the isoparametric line spacing and segmentation starting point, performing boundary point set snapping, and combining with intelligent optimization algorithms, adaptive optimization of surface mesh generation is achieved, including the following steps: (1) Surface extension: Based on the given original surface S, extract the boundary of the surface and extend the surface in the horizontal direction to obtain the extended new surface S'; (2) Initial parameters and value range: Initially determine the spacing d1 of isoparametric lines, the spacing d2 of isoparametric line points, the rotation angle a, and their corresponding value ranges; (3) Correction of isoparametric line spacing: Based on the isoparametric line spacing d1 and the rotation angle a, draw an equally spaced curve L with a rotation angle of a+90° on the surface S', and divide the curve L according to the isoparametric line spacing d1 and the chord length, and then draw an isoparametric line with a rotation angle of a through the dividing point to obtain the corrected isoparametric line L' on the surface. (4) Correction of the starting point of isoparametric line segmentation: Connect the midpoints of the first and last isoparametric lines L', and take the intersection of the connecting line with the other isoparametric lines on the surface as the starting point. According to the isoparametric line point spacing d2, the corrected isoparametric line L' is segmented by equal chord length to obtain the initial point set P. (5) Boundary point adsorption processing: Project the point set near the boundary of the original surface S back to the boundary of the original surface according to the principle of shortest path to obtain the final point set P'; (6) Triangulation to form a mesh: Perform Delaunay triangulation on the final point set P' and form a surface mesh with the boundary of the original surface S; (7) Iterative optimization of mesh design parameters: With the goal of minimizing the number of inferior meshes, the intelligent optimization algorithm is used to optimize the isoparametric line spacing d1, isoparametric line point spacing d2, and rotation angle a in the mesh design parameters. Steps (3) to (7) are repeated until the optimal mesh result and its mesh design parameters are found.

2. The adaptive surface mesh generation method based on the improved isoparametric method according to claim 1, characterized in that: In step (1), the expansion distance of the expanded surface is 2 to 3 times the required mesh size.

3. The adaptive surface mesh generation method based on the improved isoparametric method according to claim 1, characterized in that: The definition of a substandard mesh in step (7) is determined based on the variance of the interior angle of each triangular mesh. A single mesh whose interior angle variance is greater than the limit can be judged as a substandard mesh. The limit can be adjusted according to actual use.

4. The adaptive surface mesh generation method based on the improved isoparametric method according to claim 3, characterized in that: The limit is set between 100 and 150.

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