Method for meshing a dome structure based on grasshopper

Abstract

The application discloses a dome structure grid division method based on grasshopper, and comprises the following steps: establishing a regular polygon with the origin as the center in grasshopper software, then splitting the regular polygon to form a plurality of grid units with the same shape, and then setting corresponding influence strength on the grid units, so that the grid units are deformed based on the influence strength; then importing a target curved surface, and matching the grid units, so that the grid units are deformed to be consistent with the shape of the target curved surface under software calculation, and a grid surface matched with the target curved surface is obtained. The application has the characteristics of small calculation amount, wide application range, good division and support effect.

Description

Technical Field

[0001] This invention relates to a design method for dome structures, and more particularly to a dome structure mesh generation method based on Grasshopper. Background Technology

[0002] Glass domes are commonly used to cap the tops of large buildings such as convention centers, stadiums, and high-speed rail stations. The overall shape of these glass domes is often constrained by the building's shape and the designer's requirements, resulting in various unconventional curved shapes. However, due to the complexity and large size of these curved glass domes, designers, to facilitate production and construction, must divide the monolithic curved structure into a grid surface composed of several interconnected grid units. Each grid unit represents a flat piece of dome glass, and the final curved effect is achieved by connecting these grid units at different angles. Based on this construction method, the traditional design approach for glass dome grid surfaces involves designers first creating a complete curved shape, then manually marking lines to divide the curved shape into several grid units. However, this method is not only labor-intensive and time-consuming, but the manual marking process also easily leads to difficulties in splicing grid units at uneven areas, resulting in significant segmentation challenges.

[0003] To address the aforementioned shortcomings, existing technicians have attempted to use Grasshopper software to replace manual line drawing for dividing the glass dome shape. The specific method, as shown in patent 202210514989.2, involves importing the curved surface shape of the glass dome into Grasshopper software and inputting the corresponding associated parameters. This allows Grasshopper to automatically divide the glass dome into a grid structure based on defined conditions, significantly improving the efficiency of glass dome division. However, this method has two drawbacks. First, the associated parameters for the grid units need to be manually input by technicians, requiring them to calculate the limiting formulas for the grid units based on the curved shape of the glass dome, thus increasing the computational difficulty for designers. Second, since the shape of a glass dome typically expands outwards from a certain point, the grid units generated by the software under parameter constraints are still affected by the curved surface shape, resulting in significant differences in shape and size. Specifically, grid units near the origin are smaller and tend to be uniform, while grid units farther from the origin are larger and more susceptible to the influence of the curved surface, forming several unconventional shapes. This further increases the actual construction and assembly difficulty of the glass dome.

[0004] Secondly, since the associated parameters of the aforementioned grid units need to be manually defined, the surface shape is limited to calculable conventional shapes. For example, the projected shape of the surface structure should be a circle or a regular polygon, and the protrusions or depressions of the surface structure should expand outwards from one or several points, with the expansion effect satisfying the automatic generation method of the software. However, for surface structures with unconventional projected shapes and unconventional surface shapes, it is impossible to define the shape of the surface shape through formulas, and therefore it is impossible to calculate the associated parameters of the grid units, thus reducing the divisible glass dome surface shapes.

[0005] Furthermore, to enhance the structural strength of the glass dome, a supporting grid is installed on the inner side of the dome at the top of the building. Support columns on this grid support multiple points on the glass dome. These support points need to be located at the corners of the glass panels, allowing a single column to support multiple glass sections simultaneously, thus improving the overall support effect. However, the current method of dividing the glass dome makes it impossible to pre-determine the corner positions. This forces designers to first divide the glass dome into grid cells, then adjust the column positions based on the corner positions. This method results in inconsistent column placement, where the column positions vary within a general range depending on the corner position, rather than being evenly spaced. This significantly increases the difficulty of designing and assembling the supporting grid. Moreover, as the column positions change with the corner positions, the support effect decreases, failing to achieve uniform stress distribution.

[0006] Therefore, existing methods for dividing glass domes suffer from problems such as high computational load, limited applicability, and poor division and support effects. Summary of the Invention

[0007] The purpose of this invention is to provide a Grasshopper-based mesh generation method for dome structures. It features low computational cost, wide applicability, and good mesh generation and support effects.

[0008] The technical solution of this invention: a dome structure mesh generation method based on Grasshopper, comprising the following steps:

[0009] ① In Grasshopper software, set an origin, and input the radius and number of sides of the polygon with that origin as the center to obtain polygon A;

[0010] ② Connect each vertex of polygon A to the origin to form multiple first dividing lines, thus obtaining polygon B;

[0011] ③ Set n first dividing points at equal intervals on the first dividing line of polygon B, and then connect the first dividing points on adjacent first dividing lines in sequence to form multiple second dividing lines, thus obtaining polygon C;

[0012] ④ Set n second dividing points at equal intervals on each side of polygon C, and then connect the second dividing points and the first dividing points on both sides of the first dividing line in sequence to form multiple third dividing lines, thus obtaining polygon D;

[0013] ⑤ In polygon D, each edge and the first dividing line on both sides are divided into several grid cells by the second dividing line and the third dividing line, resulting in polygon E;

[0014] ⑥ Create the target surface, then import the E polygon into the target surface and scale it to match, so that the vertices and second division points of the mesh cells after overall scaling are close to overlapping with the edge lines of the target surface, and the edge lines of the E polygon do not exceed the edge lines of the target surface, thus obtaining the F polygon.

[0015] ⑦ Extract the parameters of the F polygon and set the influence intensity using Grasshopper software. Then deform the F polygon based on the target surface so that the shape of each mesh unit is automatically adjusted based on the influence intensity value during deformation, resulting in a mesh surface that matches the target surface.

[0016] In the aforementioned Grasshopper-based dome structure meshing method, step ⑦ involves extracting the side length of each mesh unit using Grasshopper software and setting the influence strength of the side length dimension, so that the variation range of the side length of each mesh unit during F-polygon deformation gradually decreases as the influence strength of the side length dimension increases; the value of the influence strength of the side length dimension is 100 to 200.

[0017] In the aforementioned Grasshopper-based grid division method for dome structures, step ⑦ involves extracting the side length of each grid cell using Grasshopper software and setting the influence intensity of the side length difference, so that the lengths of the longest and shortest sides in each grid cell tend to be equal as the influence intensity of the side length increases; the value of the influence intensity of the side length difference is 300 to 500.

[0018] In the aforementioned Grasshopper-based dome structure mesh generation method, step ⑦ involves dividing the edges of polygon F into m segments using the second dividing point and the vertices of polygon F as tangent points. These segments are then merged to form polylines. Grasshopper software is used to extract the scaling ratio of each segment within the polyline and set the segment influence intensity, ensuring that the scaling ratio of each segment approaches uniformity as the segment influence intensity increases. Furthermore, Grasshopper software is used to extract the angles of adjacent segments within the polyline and set the angle influence intensity, ensuring that the angles of adjacent segments approach 0° as the angle influence intensity increases. The values ​​of the segment influence intensity and the angle influence intensity are consistent, both ranging from 800 to 1000.

[0019] In the aforementioned Grasshopper-based dome structure mesh generation method, step ⑦ uses Grasshopper software to set the influence intensity of mesh points and the influence intensity of edge points, so that the vertices of each mesh unit and the target surface tend to overlap as the influence intensity of mesh points increases, and the vertices and second dividing points of the F polygon and the edge lines of the target surface tend to overlap as the influence intensity of edge points increases; the values ​​of the influence intensity of mesh points and the influence intensity of edge points are consistent, both ranging from 3000 to 10000.

[0020] In the aforementioned Grasshopper-based dome structure mesh generation method, step ⑦ involves extracting mesh cells containing the origin from the F polygon using Grasshopper software and setting the influence intensity of the first fixed point, such that the position of each vertex of the mesh cell tends to remain unchanged as the influence intensity of the first fixed point increases; the value of the influence intensity of the first fixed point is 100 to 500.

[0021] In the aforementioned Grasshopper-based dome structure mesh generation method, after the mesh surface matching the target curved surface in step ⑦ is formed, the vertex of the mesh unit closest to the support point of the space frame is selected and the influence intensity of the second fixed point is set so that the mesh unit vertex and the support point of the space frame tend to overlap as the influence intensity of the second fixed point increases. Then, the F polygon is deformed again based on the target curved surface to obtain the mesh surface matching the support point of the space frame.

[0022] In the aforementioned Grasshopper-based dome structure mesh generation method, the influence intensity of the second fixed point is 3000 to 10000.

[0023] Compared with the prior art, the present invention has the following characteristics:

[0024] (1) Based on Grasshopper software, this invention first divides regular polygons into several mesh units with the same shape. Then, based on this structure, the correlation between the mesh unit and the target surface is limited by logic cells, so that the polygon can overlap with the target surface by changing the number and shape of the mesh units, thereby realizing the division of the target surface. With the above combination, the target surface of this invention does not need to be manually limited by the correlation formula when dividing, which greatly reduces the amount of calculation for designers and can realize the division of any unconventional target surface.

[0025] (2) Based on the above, by limiting the intensity of each influence, each grid unit can maintain the consistency of its shape and size values ​​as much as possible when deforming based on the target surface. That is, the overall shape change of the grid unit is used to replace the excessive deformation of the grid unit in the local position with the target surface. This effectively reduces the difference in shape of the grid unit in different parts after deformation, improves the division effect of the target surface and reduces the difficulty of post-processing of the dome glass.

[0026] (3) When Grasshopper automatically generates a mesh surface based on the target curved surface, it will produce several unconventional deformation effects due to the correlation and numerical influence of the influence strength. Moreover, the influence strengths will conflict with each other, causing the deformation effect of the mesh surface to fail to meet the set requirements. However, this invention further limits the correlation and specific values ​​of each influence strength based on the division requirements of the dome glass, so that the shape and size of each target curved surface are close to the same under the condition of achieving the division effect of the target curved surface. By limiting the generation method of the mesh unit and positioning the mesh unit at the vertex position, the mesh surface can also form an effect of spreading outward from the origin when it is generated, while reducing the offset of the center point of the mesh surface caused by deformation, thereby improving the overall display effect of the mesh surface.

[0027] (4) After the grid surface is generated based on the above battery logic, by selecting the grid unit vertex closest to the grid support point and setting the second fixed point influence intensity, and then generating it a second time after adding the influence intensity, the grid unit vertex can be displaced during the generation process, and the overall deformation of other grid units in the grid surface can be used to move the grid unit vertex to overlap with the grid support point, thereby enabling the grid unit vertex of the present invention to overlap with the preset grid support point, effectively reducing the difficulty of subsequent construction of the support grid and improving the support effect of the construction difficulty on the glass dome;

[0028] Therefore, this invention has the characteristics of low computational load, wide applicability, and good division and support effects. Attached Figure Description

[0029] Figure 1This is a process flow diagram of the present invention;

[0030] Figure 2 This is a plan view of the grid surface after it has been generated according to the present invention;

[0031] Figure 3 This is a three-dimensional view of the mesh surface that matches the target curved surface in this invention;

[0032] Figure 4 This is a three-dimensional view of the grid surface of the matching space frame support points in this invention;

[0033] Figure 5 It is a 3D diagram of an E-polygon;

[0034] Figure 6 It is a 3D view of the target surface.

[0035] The labels in the attached diagram are: 1-first dividing line, 2-first dividing point, 3-second dividing line, 4-second dividing point, 5-third dividing line, 6-grid cell, 7-line segment, 8-grid support point. Detailed Implementation

[0036] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the present invention.

[0037] Example. A Grasshopper-based mesh generation method for dome structures includes the following steps:

[0038] ① In Grasshopper software, set an origin, and input the radius and number of sides of the polygon with the origin as the center to obtain polygon A. Polygon A is inscribed in a circle with the origin as the center to form a regular polygon.

[0039] ② Connect each vertex of polygon A to the origin to form multiple first dividing lines 1, thus obtaining polygon B. The planar structure of polygon B is as follows: Figure 1 As shown in a;

[0040] ③ On the first dividing line 1 of polygon B, set n first dividing points 2 at equal intervals. Then connect the first dividing points 2 on adjacent first dividing lines 1 in sequence to form multiple second dividing lines 3, thus obtaining polygon C. The planar structure of polygon C is as follows: Figure 1 As shown in b;

[0041] ④ Set n second dividing points 4 at equal intervals on each side of polygon C, and then connect the second dividing points 4 and the first dividing points 2 on the first dividing lines 1 on both sides in sequence to form multiple third dividing lines 5, thus obtaining polygon D. The number of first dividing points 2 and second dividing points 4 can be automatically adjusted according to the subsequent algorithm.

[0042] ⑤ In polygon D, each edge and the first dividing line 1 on both sides are divided by the second dividing line 3 and the third dividing line 5 to form several grid cells 6, resulting in polygon E. The shape of the grid cell 6 is triangular, and the planar structure of polygon E is as follows. Figure 1 As shown in c, the 3D diagram of polygon E is as follows: Figure 5 As shown;

[0043] ⑥ Create the target surface, and its 3D representation is shown below. Figure 6 As shown; then, after importing the E polygon into the target surface, it is scaled and matched so that the vertices and second segmentation points of the mesh elements after overall scaling are close to overlapping with the edge projection contours of the target surface, and the edges of the E polygon do not exceed the edge lines of the target surface, resulting in the F polygon. The planar structure of the F polygon and the edge projection contours of the target surface after matching is shown in the figure. Figure 1 As shown in d;

[0044] ⑦ Extract the parameters of the F-polygon using Grasshopper software and set the influence intensity. Then, deform the F-polygon based on the target surface. During deformation, the shape of each mesh unit 6 is automatically adjusted according to the influence intensity value to obtain a mesh surface that matches the target surface. This influence intensity is the existing GH battery logic in Grasshopper software. By changing the value of any battery logic, the weight of that battery logic can be adjusted. The values ​​of each influence intensity can be readjusted according to the exported mesh surface shape so that the mesh surface meets the designer's design requirements for the dome structure. The planar structure of this mesh surface is as follows: Figure 2 As shown, the three-dimensional structure of the grid surface is as follows: Figure 3 As shown;

[0045] ⑧ After the mesh surface matching the target curved surface is formed, the vertex of the mesh unit closest to the support point 8 of the space frame is selected, and the influence strength of the second fixed point is set so that the vertex of the mesh unit and the support point 8 of the space frame tend to overlap as the influence strength of the second fixed point increases. Then, the mesh surface is deformed again to obtain the mesh surface matching the support point 8 of the space frame. The value of the influence strength of the second fixed point is 5000. The three-dimensional structure of the mesh surface matching the support point 8 of the space frame is as follows: Figure 4 As shown.

[0046] In step ⑦, the side length of each mesh unit 6 is extracted using Grasshopper software, and the influence strength of the side length dimension is set so that the change in the side length of each mesh unit 6 during F polygon deformation gradually decreases as the influence strength of the side length dimension increases; the value of the influence strength of the side length dimension is 100.

[0047] In step ⑦, the side length of each grid cell 6 is extracted using Grasshopper software, and the influence intensity of the side length difference is set so that the lengths of the longest and shortest sides in each grid cell 6 approach equal lengths as the influence intensity of the side length increases; the value of the influence intensity of the side length difference is 300.

[0048] In step ⑦, the edges of polygon F are divided into m segments using the second dividing point 4 and the vertices of polygon F as tangent points. These segments are then merged to form a polyline. The scaling ratio of each segment in the polyline is extracted using Grasshopper software, and the influence intensity of the segment is set so that the scaling ratio of each segment approaches the same value as the influence intensity increases. The angles of adjacent segments in the polyline are extracted using Grasshopper software, and the influence intensity of the angle is set so that the angles of adjacent segments approach 0° as the influence intensity increases. The values ​​of the influence intensity of the segment and the influence intensity of the angle are the same, both being 1000.

[0049] In step ⑦, the influence intensity of grid points and the influence intensity of edge points are set using Grasshopper software, so that the vertices of each grid cell 6 and the target surface tend to overlap as the influence intensity of grid points increases, and the vertices of the F polygon and the second dividing point 4 and the edge lines of the target surface tend to overlap as the influence intensity of edge points increases; the values ​​of the influence intensity of grid points and the influence intensity of edge points are the same, both being 3000.

[0050] In step ⑦, the Grasshopper software is used to extract the mesh cell 6 containing the origin of the F polygon and set the influence intensity of the first fixed point. This makes the position of each vertex of the mesh cell 6 approach its original position as the influence intensity of the first fixed point increases, meaning that the deformation of the mesh cell 6 during the export process is smaller than that of the mesh cell 6 itself. The value of the influence intensity of the first fixed point is 500. The mesh cell 6 containing the origin is as follows: Figure 4 The grid cell x is shown in the figure.

[0051] The working principle of this invention is as follows: First, regular polygons are divided in Grasshopper software to form several mesh units 6 with identical shapes. Then, parameters such as the length, shape, and position of each mesh unit 6 are defined, allowing the mesh unit 6 to deform based on the target surface. This ensures that the vertices of the mesh unit 6 approach the overlapping position with the target surface, thus achieving the division of the target surface. During the deformation process, by limiting various battery logic parameters, the mesh unit 6 maintains consistency in its shape and size, mitigating excessive deformation of local mesh units 6 to match the shape of the target surface. With the above combination, this invention can divide glass domes with arbitrary projected contours and curved surface shapes, and the shape and size of each mesh unit 6 tend to be consistent after division, without significant differences arising from changes in the surface shape. Simultaneously, designers do not need to set separate division formulas for different surface shapes, thereby reducing their workload.

Claims

1. A method for mesh generation of dome structures based on Grasshopper, characterized in that, Includes the following steps: ① In Grasshopper software, set an origin, and input the radius and number of sides of the polygon with that origin as the center to obtain polygon A; ② Connect each vertex of polygon A to the origin to form multiple first dividing lines, thus obtaining polygon B; ③ Set n first dividing points at equal intervals on the first dividing line of polygon B, and then connect the first dividing points on adjacent first dividing lines in sequence to form multiple second dividing lines, thus obtaining polygon C; ④ Set n second dividing points at equal intervals on each side of polygon C, and then connect the second dividing points and the first dividing points on both sides of the first dividing line in sequence to form multiple third dividing lines, thus obtaining polygon D; ⑤ In polygon D, each edge and the first dividing line on both sides are divided into several grid cells by the second dividing line and the third dividing line, resulting in polygon E; ⑥ Create the target surface, then import the E polygon into the target surface and scale it to match, so that the vertices and second division points of the mesh cells after overall scaling are close to overlapping with the edge lines of the target surface, and the edge lines of the E polygon do not exceed the edge lines of the target surface, thus obtaining the F polygon. ⑦ Extract the parameters of the F polygon and set the influence intensity using Grasshopper software. Then deform the F polygon based on the target surface so that the shape of each mesh unit is automatically adjusted based on the influence intensity value during deformation, resulting in a mesh surface that matches the target surface. In step ⑦, after the mesh surface matching the target curved surface is formed, the vertex of the mesh unit closest to the support point of the space frame is selected and the influence intensity of the second fixed point is set so that the mesh unit vertex and the support point of the space frame tend to overlap as the influence intensity of the second fixed point increases. Then, the F polygon is deformed again based on the target curved surface to obtain the mesh surface matching the support point of the space frame.

2. The dome structure mesh generation method based on Grasshopper according to claim 1, characterized in that: In step ⑦, the side length of each mesh unit is extracted using Grasshopper software, and the influence strength of the side length dimension is set so that the change in the side length of each mesh unit during F polygon deformation gradually decreases as the influence strength of the side length dimension increases; the value of the influence strength of the side length dimension is 100 to 200.

3. The dome structure mesh generation method based on Grasshopper according to claim 1, characterized in that: In step ⑦, the side length of each grid cell is extracted using Grasshopper software, and the influence intensity of the side length difference is set so that the lengths of the longest and shortest sides in each grid cell approach to be equal as the influence intensity of the side length increases; the value of the influence intensity of the side length difference is 300 to 500.

4. The dome structure mesh generation method based on Grasshopper according to claim 1, characterized in that: In step ⑦, the edges of polygon F are divided into m segments using the second dividing point and the vertices of polygon F as tangent points. These segments are then merged to form a polyline. The scaling ratio of each segment in the polyline is extracted using Grasshopper software, and the influence intensity of the segment is set so that the scaling ratio of each segment approaches the same value as the influence intensity increases. The angles of adjacent segments in the polyline are extracted using Grasshopper software, and the influence intensity of the angle is set so that the angles of adjacent segments approach 0° as the influence intensity increases. The values ​​of the influence intensity of the segment and the influence intensity of the angle are the same, both ranging from 800 to 1000.

5. The dome structure mesh generation method based on Grasshopper according to claim 1, characterized in that: In step ⑦, the influence intensity of grid points and the influence intensity of edge points are set using Grasshopper software, so that the vertices of each grid cell and the target surface tend to overlap as the influence intensity of grid points increases, and the vertices and second dividing points of the F polygon and the edge lines of the target surface tend to overlap as the influence intensity of edge points increases. The values ​​of the influence intensity of grid points and the influence intensity of edge points are the same, both ranging from 3000 to 10000.

6. The dome structure mesh generation method based on Grasshopper according to claim 1, characterized in that: In step ⑦, the grasshopper software is used to extract the mesh cells containing the origin of the F polygon and set the influence intensity of the first fixed point so that the position of each vertex of the mesh cell tends to remain unchanged as the influence intensity of the first fixed point increases. The value of the influence strength of the first fixed point is 100 to 500.

7. The dome structure mesh generation method based on Grasshopper according to claim 1, characterized in that: The value of the influence intensity of the second fixed point is 3000 to 10000.

Images