Curved surface grid adaptive division method based on improved isoparametric method

Abstract

The invention discloses a curved surface grid adaptive division method based on an improved isoparametric method, and the method comprises the following steps: firstly, carrying out the expansion of an original curved surface, carrying out the correction of isoparametric line spacing and a segmentation starting point according to the initially determined isoparametric line design parameters, carrying out the adsorption processing of boundary points according to the shortest path principle, and carrying out the adaptive division of a curved surface grid. And performing triangulation on the basis of the processed point set to obtain a curved surface grid, and finally optimizing grid design parameters by adopting an intelligent optimization algorithm to obtain an optimal grid by taking the minimum number of inferior grids as a target. The method can be suitable for a curved surface with large curvature change, the problems that an original isoparametric method boundary grid is poor in quality, the grid is not smooth and the like are effectively solved, self-adaptive optimization of grid division design parameters can be carried out according to the characteristics of the curved surface, and the generated grid is regular and uniform and can be directly used for subsequent structure design.

Description

Technical Field

[0001] The invention relates to the field of building structure design, and more specifically to a surface mesh adaptive division method based on an improved isoparametric method. Background Art

[0002] Spatial grid structures are widely used in various large-scale building structures due to their excellent modeling capabilities. With the development of technology, more and more free-form surface shapes are used in architectural design. However, as the structural modeling becomes increasingly complex, traditional component layout forms are difficult to meet the requirements of structural force performance, building appearance, curtain wall structure, etc.

[0003] In order to achieve a reasonable arrangement of components, it is necessary to perform adaptive meshing on the curved surface of the mesh structure. Traditional meshing methods, such as mapping method, isoparametric method, triangle mesh conversion method, Delaunay triangulation method, wavefront method, etc., mostly perform meshing from the perspective of architecture, focusing only on the uniformity of meshing, without considering the arrangement of rods in the structural design process and the treatment of rods near the boundary.

[0004] Among them, the equally spaced reference line method (hereinafter referred to as the isoparametric method) can effectively avoid the problem of mapping distortion of the mapping method because it directly performs meshing on the surface. It can be applied to surfaces with large curvature changes. However, it also has shortcomings. There are often many thin grid units with very sharp internal angles at the edge of the surface. Affected by the change of surface curvature, 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 design parameters, and the selection of parameters depends on the experience of the designer and has a large uncertainty. Summary of the invention

[0005] The present invention provides a surface mesh adaptive partitioning method based on the improved isoparametric method, aiming to solve the problems of inconsistent isoparametric spacing, poor boundary mesh quality, and reasonable selection of free-form surface mesh partitioning design parameters of the original isoparametric method, and realize adaptive optimization of the surface mesh.

[0006] To achieve the above object, the present invention adopts the following technical scheme: a surface mesh adaptive division method based on the improved isoparametric method, which realizes the adaptive optimization of surface mesh division by correcting the isoparametric spacing and the segmentation starting point, adsorbing the boundary point set and combining with the intelligent optimization algorithm, comprising the following steps:

[0007] (1) Surface extension: Based on the given original surface S, the boundary of the surface is extracted and the surface is extended horizontally to obtain the extended new surface S'.

[0008] (2) Preliminary parameters and value ranges: Preliminary determination of the isoparametric spacing d1, the isoparametric point spacing d2, 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 equidistant curve L with a rotation angle of a+90° on the surface S', and divide the curve L into equal chord lengths according to the isoparametric line spacing d1. Then draw isoparametric lines with a rotation angle of a through the dividing points to obtain the corrected isoparametric lines 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 use the intersection of this line and the remaining isoparametric lines on the surface as the starting point. According to the isoparametric line point spacing d2, the corrected isoparametric line L' is segmented into equal chord lengths to obtain the initial point set P;

[0011] (5) Boundary point adsorption processing: The point set near the boundary of the original surface S is projected back to the boundary of the original surface according to the shortest path principle 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, an intelligent optimization algorithm is used to optimize the mesh design parameters such as the spacing d1 of isoparametric lines, the spacing d2 of isoparametric points, and the rotation angle a. Steps (3) to (7) are repeated until the optimal mesh result and its mesh design parameters are found.

[0014] Furthermore, the expansion distance of the expanded surface in step (1) is 2 to 3 times the length of the required grid size.

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

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

[0017] In summary, the present invention first expands the original surface, and according to the initially determined isoparametric design parameters, corrects the isoparametric spacing and the segmentation starting point, then performs adsorption processing of the boundary points according to the shortest path principle, triangulates the processed point set to obtain the surface mesh, and finally optimizes the mesh design parameters using an intelligent optimization algorithm with the goal of minimizing the number of inferior meshes to obtain the optimal mesh. Compared with the existing mesh division method, it has the following beneficial effects:

[0018] First, the present invention is applicable to surfaces with large curvature changes, and the generated grid is regular and symmetrical;

[0019] Secondly, the present invention effectively solves the problem of grid unsmoothness caused by inconsistent segmentation starting points and spacing when the surface curvature changes greatly by correcting the surface isoparametric line spacing and segmentation starting points, thereby ensuring the consistency of grid size;

[0020] Thirdly, the present invention effectively solves the problem of poor quality of boundary mesh of the original isoparametric method by extending the surface and adsorbing the boundary points, avoids the generation of short boundary bars, and can be directly used for subsequent structural design;

[0021] Fourthly, the present invention can adaptively optimize meshing design parameters according to the surface characteristics, effectively avoiding the limitations of artificially set design parameters and obtaining better meshing results;

[0022] Fifthly, the present invention can be programmed and can quickly realize the adaptive optimization generation of the grid. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 A flow chart for dividing the method of the present invention;

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

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

[0026] Figure 4 The isoparameter L' modified by dividing the equal chord length;

[0027] Figure 5 To adsorb points close to the boundary of surface S;

[0028] Figure 6 For the short-shot problem near the boundary;

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

[0030] Figure 8 This is the final meshing result. DETAILED DESCRIPTION

[0031] The following is combined with Figures 1 to 8 The specific implementation of the method for adaptively dividing a surface mesh based on the improved isoparametric method of the present invention is further described in detail. Specific embodiment:

[0033] This embodiment is a curved surface with a length of about 118m, a width of about 109m, and a maximum height difference of about 13m. The method of the present invention is applied, and the implementation steps are as follows:

[0034] (1) Surface extension: 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 expanded in the horizontal direction to obtain the expanded new surface S';

[0035] (2) Initial parameters and value ranges: the isoparametric line spacing d1 and the isoparametric line point spacing d2 are both set to 3 m, the isoparametric line rotation angle a is set to 45°, the isoparametric line spacing d1 and the isoparametric line point spacing d2 have a value range of [2 m, 4 m], the parameter change accuracy is 0.05 m, the isoparametric line rotation angle a has a value range of [30°, 120°], and 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 equidistant curve L with a rotation angle of a+90° on the surface S', and divide the curve L into equal chord lengths according to the isoparametric line spacing d1. Then draw isoparametric lines with a rotation angle of a through the dividing points to obtain the corrected isoparametric lines L' on the surface. The effect is as follows: Figure 3 As shown;

[0037] (4) Correction of the starting point of isoparametric line segmentation: Connect the midpoints of the first and last isoparametric lines L', and use the intersection of this line and 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 with equal chord lengths to obtain the initial point set P. The effect is as follows: Figure 4 As shown;

[0038] (5) Boundary point adsorption processing: Points with a straight-line distance less than 1 m from the boundary of surface S are projected back to the original surface boundary according to the shortest path principle to obtain the final point set P', as shown in Figure 5 As shown, Figure 6 (Short rod problem near the boundary) additionally shows that if the boundary points are not sorted out, 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, as follows: Figure 7 As shown (preliminary mesh on surface S);

[0040] (7) Calculate the variance of the internal angles of all cells in the grid, and set the average angle to 60°, which is the internal angle of an equilateral triangle. In this embodiment, cells with a variance greater than 130 are considered to be poor-quality grids. The number of poor-quality 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 spacing d1, isoparametric point spacing d2, and rotation angle a). Steps (3) to (7) are repeated. Finally, after 40 cycles, the optimal solution for the mesh parameters is obtained: isoparametric spacing 3.5 m, isoparametric point spacing 4 m, and rotation angle 47°. The number of inferior meshes is reduced to 180. The mesh comparison results are as follows: Figure 8 As shown (left is before optimization, right is after optimization).

[0042] The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims

1. A surface mesh adaptive partitioning method based on improved isoparametric method, characterized in that: Adaptive optimization of surface meshing is achieved by modifying the isoparametric line spacing and segmentation starting point, adsorbing the boundary point set, and combining it with the intelligent optimization algorithm, including the following steps: (1) Surface extension: Based on the given original surface S, the boundary of the surface is extracted and the surface is extended horizontally to obtain the extended new surface S'. (2) Preliminary parameters and value ranges: Preliminary determination of the isoparametric spacing d1, the isoparametric point spacing d2, 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 equidistant curve L with a rotation angle of a+90° on the surface S', and divide the curve L into equal chord lengths according to the isoparametric line spacing d1. Then draw isoparametric lines with a rotation angle of a through the dividing points to obtain the corrected isoparametric lines 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 use the intersection of this line and the remaining isoparametric lines on the surface as the starting point. According to the isoparametric line point spacing d2, the corrected isoparametric line L' is segmented into equal chord lengths to obtain the initial point set P; (5) Boundary point adsorption processing: The point set near the boundary of the original surface S is projected back to the boundary of the original surface according to the shortest path principle 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, an intelligent optimization algorithm is used to optimize the mesh design parameters such as the spacing d1 of isoparametric lines, the spacing d2 of isoparametric points, and the rotation angle a. Steps (3) to (7) are repeated until the optimal mesh result and its mesh design parameters are found.

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

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

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

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