Grasshopper-based parametric modeling method for polygon projection space distorted surface reticulated shell

Abstract

The invention discloses a Grasshopper-based parameterized modeling method for a polygon projection space distorted surface reticulated shell, which comprises the following steps of: S1, setting geometric parameters of a reticulated shell model in a Grasshopper platform through an input plug-in, and obtaining a corresponding projection surface of a space curved surface reticulated shell surface; s2, connecting vertexes of the projection surface to generate ridge lines forming a reticulated shell curved surface, and constructing a polygonal projection space distorted surface through curved surface generation operation based on the ridge lines; s3, performing grid division on the spatial warping surface by using an isoparametric method or a mapping method to generate grid points; and S4, based on the grid points, generating a single-layer polygonal projection space distorted surface latticed shell structure through a polyline connection plug-in. The method is used for solving the technical problems that an existing spatial reticulated shell structure with a complex shape is difficult to model, the modeling efficiency is low, and the repeated utilization rate is low.

Description

Technical Field

[0001] This invention relates to the field of auxiliary architectural design technology, specifically to a parametric modeling method for polygonal projection space twisted surface mesh shells based on Grasshopper. Background Technology

[0002] In the field of long-span spatial structures, reticulated shell structures have become the preferred form for landmark buildings due to their excellent mechanical properties and rich design possibilities. With the continuous improvement of architectural aesthetics and functional requirements, the application of spatially twisted reticulated shell structures with free-form and complex shapes is becoming increasingly widespread. These structures often involve complex geometric logic and spatial topological relationships.

[0003] Currently, modeling such complex reticulated shell structures mainly relies on traditional 3D modeling software, such as Rhinoceros and CATIA. Designers need to manually locate key control points, generate spatial surfaces, and then perform mesh generation and member connection. This method has drawbacks. When any design changes are encountered, such as adjusting the number of polygon sides, surface curvature, or reticulated shell thickness, it is necessary to start from scratch or perform tedious manual modifications. The design cycle is long and cannot meet the needs of rapid iteration. Moreover, for complex combinations of shapes such as edge folded plates and edge cylindrical surfaces that require a smooth transition with the central torsional surface, traditional methods lack a systematic generation logic and are difficult to directly and accurately convert into a structural calculation model, resulting in unsatisfactory modeling results.

[0004] To improve the morphology of spatial curved reticulated shell structures and enhance modeling efficiency, a parametric modeling method for polygonal projection twisted reticulated shells based on Grasshopper is proposed. Summary of the Invention

[0005] In order to overcome the problems in the prior art, the purpose of this invention is to provide a parametric modeling method for polygonal projection spatial twisted reticulated shells based on Grasshopper, so as to solve the technical problems of difficult modeling, low modeling efficiency and low reusability of existing complex spatial reticulated shell structures.

[0006] To achieve the above objectives, this invention provides a parametric modeling method for polygonal projection space twisted surface reticulated shells based on Grasshopper, comprising the following steps:

[0007] Step S1: In the Grasshopper platform, set the geometric parameters of the mesh shell model by inputting the plugin to obtain the corresponding spatial curved mesh shell surface projection surface;

[0008] Step S2: Connect the vertices of the projection plane to generate ridges that form the shell surface. Based on the ridges, construct a polygonal projection space twisted surface through surface generation operations.

[0009] Step S3: Use the isoparametric method or mapping method to mesh the spatial twisted surface and generate mesh points;

[0010] Step S4: Based on the grid points, generate a single-layer polygonal projection space twisted surface shell structure through a multi-segment line connection plug-in;

[0011] The geometric parameters in step S1 include: the radius and number of sides of the bottom polygon, the height of the center vertex, and the extension length and height of the outer corner points; the method for setting the geometric parameters is as follows:

[0012] Use the polygon plugin to generate the bottom polygon, and use its input plugin to set the parameters of the bottom polygon's radius and number of sides to control the polygon's shape;

[0013] Use the point generator plugin and parameterize the height of the center vertex by assigning a value to the Z coordinate;

[0014] The line segment generated by the extension segment plugin is used to extend the line segment formed by the center point of the polygon and the midpoint of the inner edge of the polygon. The extension length parameter is used to control the projection plane position of the outer corner point.

[0015] The point generation plugin is used again to parametrically adjust the spatial height of the outer corner points by assigning Z-coordinates to them.

[0016] Optionally, step S2 is used to construct a first type of polygonal projection space distortion surface, specifically including:

[0017] Step S2.1: Generate ridge lines connecting the center vertex to the polygon corners and outer corners;

[0018] Step S2.2: Based on the ridge line, generate a local spatial twist surface, and form a complete first-type polygonal projection spatial twist surface through array operation.

[0019] Optionally, step S2 is used to construct a second type of polygonal projection space distortion surface, specifically including:

[0020] Step S2.1': Generate ridge lines connecting the center vertex to the polygon corners and outer corners;

[0021] Step S2.2': Based on the ridge line, generate a local spatial twist surface;

[0022] Step S2.3': Use the mapping trimming method to remove the curved surface portion outside the bottom polygon projection area;

[0023] Step S2.4': Form a complete second type of polygonal projection space distortion surface through array operation.

[0024] Optionally, it also includes step S5 for generating a truss-type double-layer reticulated shell, which involves moving the nodes of the single-layer reticulated shell to obtain the lower chord layer nodes, and connecting the upper and lower chord layer nodes to form a double-layer reticulated shell. Specifically, this includes the following steps:

[0025] Step S5.1: Take the nodes of the single-layer reticulated shell as the upper chord layer nodes, and offset them along the normal or vertical direction to generate the lower chord layer nodes;

[0026] Step S5.2: Connect the lower chord nodes to form the lower chord member;

[0027] Step S5.3: Connect the corresponding upper chord layer nodes and lower chord layer nodes to form a web member system. The web member system includes inclined web members generated by pairing and connecting upper and lower chord nodes with different parities.

[0028] Optionally, the process also includes step S5' of generating a conical double-layer reticulated shell, which involves moving the nodes of the single-layer reticulated shell to obtain the lower chord layer nodes, and connecting the upper and lower chord layer nodes to form a double-layer reticulated shell. This specifically includes the following steps:

[0029] Step S5.1': Take the nodes of the single-layer shell as the upper chord nodes, and offset them along the normal of the upper chord surface of each grid cell to generate the lower chord nodes;

[0030] Step S5.2': Connect the lower chord nodes to form the lower chord;

[0031] Step S5.3': Each upper chord node is connected to its corresponding lower chord node and adjacent lower chord nodes to form a triangular pyramid or quadrangular pyramid web member system.

[0032] This embodiment also provides a parametric modeling method for polygonal projection space twisted surface reticulated shells based on Grasshopper, including:

[0033] Step S1a: In the Grasshopper platform, set the geometric parameters of the mesh shell model by inputting the plugin to obtain the corresponding spatial curved mesh shell surface projection surface;

[0034] Step S2a: Connect each vertex of the projection plane to generate ridges that constitute the shell surface. Based on the ridges, construct a polygonal projection space twisted surface through surface generation operations.

[0035] Step S3a: Use the isoparametric method or mapping method to mesh the spatial twisted surface and generate mesh points;

[0036] Step S4a: Based on the grid points, generate a single-layer polygonal projection space twisted surface shell structure through a multi-segment line connection plug-in;

[0037] The geometric parameters in step S1a include: the radius and number of sides of the bottom polygon, the height of the center vertex, and the height of the edge vertices; the method for setting the geometric parameters is as follows:

[0038] Use the polygon plugin to generate the bottom polygon, and use its input plugin to set the parameters of the bottom polygon's radius and number of sides to control the polygon's shape;

[0039] Use the point generator plugin and parameterize the height of the center vertex by assigning a value to the Z coordinate;

[0040] The height of the edge vertices is adjusted by using the point generation plugin and assigning a Z parameter to the center point height; the projection of each edge vertex is the midpoint of the corresponding edge of the bottom polygon.

[0041] Optionally, step S2a is used to construct a third type of polygonal projection space twisted surface with folded plate edges, specifically including:

[0042] Step S2.1a: Generate a straight ridge line connecting the edge vertices to the corner points and center vertex of the bottom polygon;

[0043] Step S2.2a: Using the adjacent straight ridge lines and their corresponding bottom edge lines as tracks, generate the edge folded plate surface through the dual-track sweeping plug.

[0044] Optionally, the surface constructed in step S2a is a fourth type of edge cylinder, wherein step S2 specifically includes:

[0045] Step S2.1a': Generate a central curved surface ridge frame and an edge curved surface ridge frame composed of circular arc ridges based on the center vertex, edge vertices and corner points of the bottom polygon;

[0046] Step S2.2a': For the edge region obtained by connecting the edge vertices and the corner points of the bottom polygon, use two adjacent circular arc ridges and the bottom edge as the track to generate a local cylinder through the dual-track sweep plugin, and obtain the complete edge cylinder surface through the array plugin.

[0047] For the central region obtained by connecting the central vertex with the edge vertices and the corner points of the bottom polygon, a local central surface is generated by using two central circular arc ridges and two edge circular arc ridges as boundaries, and the complete central twisted surface is obtained by using the array plugin.

[0048] Optionally, it also includes step S5a for generating a truss-type double-layer reticulated shell, which involves moving the nodes of the single-layer reticulated shell to obtain the lower chord layer nodes, and connecting the upper and lower chord layer nodes to form a double-layer reticulated shell, specifically including the following steps:

[0049] Step S5.1a: Take the nodes of the single-layer reticulated shell as the upper chord layer nodes, and offset them along the normal or vertical direction to generate the lower chord layer nodes;

[0050] Step S5.2a: Connect the lower chord nodes to form the lower chord member;

[0051] Step S5.3a: Connect the corresponding upper chord layer nodes and lower chord layer nodes to form a web member system, wherein the web member system includes inclined web members generated by pairing and connecting upper and lower chord nodes with different parity.

[0052] Optionally, the process also includes step S5a' of generating a conical double-layer reticulated shell, which involves moving the nodes of the single-layer reticulated shell to obtain the lower chord layer nodes, and connecting the upper and lower chord layer nodes to form a double-layer reticulated shell. This specifically includes the following steps:

[0053] Step S5.1a': Take the nodes of the single-layer shell as upper chord nodes, and offset them along the normal of the upper chord surface of each grid cell to generate lower chord nodes;

[0054] Step S5.2a': Connect the lower chord nodes to form the lower chord;

[0055] Step S5.3a': Each upper chord node is connected to its corresponding lower chord node and adjacent lower chord nodes to form a triangular pyramid or quadrangular pyramid web member system.

[0056] This invention provides a logic for controlling the overall spatial distortion based on bottom polygon projection. All complex spatial morphological changes originate from the driving force of parameters such as the bottom polygon, central vertex, and external control points. Parametric modeling can not only generate a variety of novel spatial surface combinations but also improve the speed of model generation and modification, thus increasing work efficiency. Its application in assisting architectural design improves modeling efficiency and promotes the use of complex spatial reticulated shell structures. The parametric modeling design method based on Grasshopper employed in this invention is simple and efficient, greatly facilitating the stress analysis and structural design optimization of complex spatial reticulated shell structures under different types and parameters using finite element design software. Attached Figure Description

[0057] Figures 1(a) to 1(i) are schematic diagrams of the first type of polygonal projection space twisted surface single-layer reticulated shell or truss-type double-layer reticulated shell provided in Embodiment 1;

[0058] Figure 1(a) is a battery diagram of the first type of polygonal projection space twisted surface shell;

[0059] Figure 1(b) shows the geometric relationship of the first type of polygonal projection space twisted surface;

[0060] Figure 1(c) shows the first type of polygonal projection space twisted surface;

[0061] Figure 1(d) is a polygonal projection space twisted surface grid cell generated by parametric division of a single twisted surface in Figure 1(a).

[0062] Figure 1(e) is a schematic diagram of the first type of polygonal projection space twisted surface triaxial single-layer reticulated shell;

[0063] Figure 1(f) is a schematic diagram of a single-layer reticulated shell with a single oblique bar on a polygonal projection space twisted surface, belonging to the first type.

[0064] Figure 1(g) shows the battery diagram inside the lower chord and web members of the double-layer reticulated shell with a first type of polygonal projection space twisted surface generated according to the parameterized adjustment of the reticulated shell thickness in Figure 1(a).

[0065] Figure 1 (h) is a schematic diagram of the first type of polygonal projection space twisted surface truss type three-way double-layer reticulated shell;

[0066] Figure 1 (i) is a schematic diagram of the first type of polygonal projection space twisted surface truss type single diagonal bar type double-layer reticulated shell.

[0067] Figures 2(a) to 2(c) are schematic diagrams of the first type of polygonal projection space twisted surface triangular pyramidal double-layer reticulated shell;

[0068] Figure 2 (a) is a battery diagram of the first type of polygonal projection space twisted surface triangular pyramidal double-layer mesh shell;

[0069] Figure 2(b) shows the battery diagram inside the lower chord and the web of the double-layered reticulated shell with a triangular pyramidal twisted surface in the first type of polygonal projection space generated according to the parameterized adjustment of the reticulated shell thickness in Figure 2(a).

[0070] Figure 2(c) is a schematic diagram of the first type of polygonal projection space twisted surface triangular pyramidal double-layer reticulated shell.

[0071] Figures 3(a) to 3(f) are schematic diagrams of the second type of polygonal projection space twisted surface single-layer reticulated shell or truss-type double-layer reticulated shell provided in Example 2; Figure 3(a) is a battery diagram of the second type of polygonal projection space twisted surface truss type reticulated shell; Figure 3(b) shows the geometric relationship of the twisted surface in the projection space of the second type of polygon; Figure 3(b) shows the twisted surface of the second type of polygonal projection space; Figure 3(c) is a polygonal projection space twisted surface grid cell generated by parametric division of a single twisted surface in Figure 3(a); Figure 3(d) is a schematic diagram of a single-layer reticulated shell with a twisted surface in a polygonal projection space of the second type; Figure 3(e) shows the battery diagram inside the lower chord and web members of the double-layer reticulated shell with a twisted surface in the second type of polygonal projection space generated by adjusting the shell thickness according to parameters in Figure 3(a). Figure 3(f) is a schematic diagram of the second type of polygonal projection space twisted surface truss type double-layer reticulated shell; Figures 4(a) to 4(c) are schematic diagrams of the second type of polygonal projection space twisted surface triangular pyramidal double-layer reticulated shell; Figure 4 (a) is a battery diagram of the second type of polygonal projection space twisted surface triangular pyramidal double-layer reticulated shell; Figure 4(b) shows the battery diagram inside the lower chord and the web of the double-layered reticulated shell with a twisted surface of a triangular pyramidal shape in the second type of polygonal projection space generated according to the parameterized adjustment of the shell thickness in Figure 4(a). Figure 4(c) is a schematic diagram of the second type of polygonal projection space twisted surface triangular pyramidal double-layer reticulated shell; Figures 5(a) to 5(e) are schematic diagrams of the third type of polygonal projection space twisted surface edge with folded plate mesh shell provided in Example 3; Figure 5(a) is a battery diagram of the third type of polygonal projection space twisted surface edge is a folded plate mesh shell; Figure 5(b) shows the geometric relationship of the twisted surface of the third type of polygonal projection space with the edge of the folded plate surface; Figure 5(c) is a schematic diagram of the third type of polygonal projection space twisted surface with the edge of the folded plate surface model; Figure 5(d) is a schematic diagram of a single-layer reticulated shell with a twisted surface at the edge of a polygonal projection space of the third type. Figure 5(e) is a schematic diagram of a double-layer truss type third type polygonal projection space twisted surface edge with a folded plate surface mesh shell.

[0072] Figures 6(a) to 6(e) are schematic diagrams of the fourth type of polygonal projection space twisted surface with cylindrical reticulated shell at the edge, provided in Example 4;

[0073] Figure 6(a) is a battery diagram of the fourth type of polygonal projection space twisted surface with cylindrical mesh shell at the edge;

[0074] Figure 6(b) shows the geometric relationship of the twisted surface of the fourth type of polygonal projection space with cylindrical edges;

[0075] Figure 6(c) shows the cylindrical shape of the edge of the twisted surface in the fourth type of polygonal projection space.

[0076] Figure 6(d) is a schematic diagram of a model of a fourth type of polygonal projection space twisted surface with cylindrical single-layer reticulated shell at the edge;

[0077] Figure 6(e) is a schematic diagram of a double-layer truss type fourth type polygonal projection space twisted surface edge cylindrical reticulated shell. Detailed Implementation

[0078] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. It should be noted that the following embodiments are used to more specifically explain the technical solutions defined in the claims of the present invention, and are not intended to limit the present invention. Any modifications based on the core concept of the present invention should be considered to fall within the protection scope of the present invention.

[0079] Example 1

[0080] The purpose of this embodiment is to explain in detail the modeling methods for the first type of reticulated shell and its single-layer and double-layer structures. Refer to Figures 1(a) to 2(c). Specifically, the following steps are included:

[0081] Step S1: In the Grasshopper platform, set the geometric parameters of the mesh shell model by inputting the plugin to obtain the corresponding spatial curved mesh shell surface projection surface.

[0082] The geometric parameters include: the radius and number of sides of the bottom polygon, the height of the central vertex O, and the extension length and height of the outer corner point B.

[0083] In specific operations, a polygon plugin is used to generate a bottom polygon. The radius and number of sides of the bottom polygon are set via its input plugin to control its shape. In this embodiment, the bottom polygon is a regular hexagon. The center point o of the polygon is obtained, and the height of the center vertex O is obtained by using a point generation plugin and assigning a value to its Z-coordinate. Taking two corner points a and c of the bottom polygon as examples, the heights of corner points a and c are parametrically adjusted using the point generation plugin and by assigning values ​​to their Z-coordinates to obtain new corner points A and C, respectively. Similarly, other new corner points are obtained. The line segment od, formed by the polygon center point o and the inner midpoint d of the bottom polygon's ac side, is extended outward using a line segment generation extension plugin. The extension length parameter is used to control the projection plane position of the outer corner point B, and multiple outer control points are obtained similarly. The point generation plugin is used again to parametrically adjust the spatial height of the outer corner point B by assigning a value to its Z-coordinate. The connection logic between the above parameter input module and the plugin is shown in the battery diagram of Figure 1(a). Each parameter can be adjusted in real time via an independent slider.

[0084] Step S2: Connect the vertices of the projection plane to generate ridges that form the reticulated shell surface. Based on these ridges, construct a polygonal projection space twisted surface through surface generation operations. This includes the following steps:

[0085] Step S2.1: Connect the center vertex, the outer corner points, and the polygon corner points to form a ridge line.

[0086] Referring to Figure 1(b), the line plugin is determined by two points. The center vertex O, the outer corner point B, and the polygon corner points A and C are connected to generate four ridge lines OA, OB, BA, and BC to form the spatial twisted surface.

[0087] Step S2.2: Based on the ridge line, generate a local spatial twist surface, and form a complete first-type polygonal projection spatial twist surface through array operation.

[0088] Using the ridge-generated-surface plugin, a local first-class polygonal projection space twist surface is constructed with adjacent ridges as boundaries. Subsequently, the generated local first-class polygonal projection space twist surface is arrayed in a ring using the array plugin to obtain a complete and closed first-class polygonal projection space twist surface, as shown in Figure 1(c).

[0089] Step S3: Use the isoparametric method or mapping method to mesh the spatial twisted surface and generate mesh points.

[0090] This embodiment uses the isoparametric method. By setting the mesh division number parameter, the complete twisted surface is uniformly divided to generate regularly distributed mesh points, as shown in the battery diagram of Figure 1(d).

[0091] Step S4: Based on the grid points, generate a single-layer polygonal projection space twisted surface shell structure through a multi-segment line connection plug-in.

[0092] Specifically, the grid points generated in step S3 are connected using a polyline plugin. Different connection rules can generate different types of single-layer mesh shells. For example, when the connection rule connects each point to all its adjacent points, a first-type polygonal projection space twisted surface three-dimensional single-layer mesh shell is generated, as shown in Figure 1(e). When a unidirectional diagonal bar rule is used for connection, a first-type polygonal projection space twisted surface single diagonal bar type single-layer mesh shell is generated, as shown in Figure 1(f).

[0093] Furthermore, based on the single-layer reticulated shell, step S5: the lower chord layer nodes are obtained by moving the nodes of the single-layer reticulated shell, and the upper and lower chord layer nodes are connected to form a double-layer reticulated shell. This embodiment discloses two types of double-layer reticulated shells.

[0094] The first type of double-layer structure is a truss type, and its web member system generation method includes the following steps:

[0095] Step S5.1: Take the nodes of the single-layer reticulated shell as the upper chord layer nodes, and offset them along the normal or vertical direction to generate the lower chord layer nodes.

[0096] Using the nodes of a single-layer reticulated shell as the upper chord nodes, the lower chord nodes are generated by vertically shifting all nodes of the upper chord by a set reticulated shell thickness distance using the reticulated shell thickness plugin.

[0097] Step S5.2: Connect the lower chord nodes to form the lower chord.

[0098] The lower chord nodes obtained after the downward movement are connected using a polyline plugin to form the lower chord mesh.

[0099] Step S5.3: Connect the corresponding upper chord layer nodes and lower chord layer nodes to form a web member system. The web member system includes inclined web members generated by pairing and connecting upper and lower chord nodes with different parities.

[0100] Step S5.3 specifically involves directly connecting the corresponding upper and lower chord nodes using a two-point linear insertion plug to generate vertical web members. Next, a flow-dividing plug is used to divide the upper and lower chord nodes according to their odd or even numbering. Then, a weaving plug is used to pair the odd-numbered nodes of the upper chord with the even-numbered nodes of the lower chord (and vice versa). Finally, a two-point linear insertion plug is used to generate diagonal web members based on the pairing data. The core plug combination logic for generating the lower chord and web members is shown in the battery diagram of Figure 1(g). The resulting first type of truss-type three-dimensional double-layer reticulated shell is shown in Figure 1(h), and the truss-type single-diagonal double-layer reticulated shell is shown in Figure 1(i).

[0101] The second type of double-layer shape is a triangular pyramid, and its generation method includes the following steps:

[0102] First, based on the upper chord mesh of the first type of single-layer reticulated shell, the pyramidal upper chord surface corresponding to each mesh unit is generated using the edge-to-surface generation plugin. Then, the geometric center point of each pyramidal upper chord surface is obtained using the geometric center plugin. Finally, the surface analysis plugin is used to obtain the normal vector perpendicular to the upper chord plane at the geometric center point. The core plugin combination logic is shown in Figure 2(a).

[0103] Step S5.1': The nodes of the single-layer shell are taken as upper chord layer nodes, and lower chord layer nodes are generated by offsetting along the normal of the upper chord surface of each grid unit.

[0104] Step S5.2': Use a polyline plug-in to connect the lower chord layer nodes to form the lower chord.

[0105] In step S5.3', each upper chord node is connected to its corresponding lower chord node and adjacent lower chord nodes to form a triangular pyramidal or quadrangular pyramidal web member system.

[0106] By connecting each upper chord node of the linear plug to its corresponding lower chord node and adjacent lower chord nodes through two points, a triangular pyramid or quadrangular pyramid-shaped web system is formed. The connection logic of the web members is shown in the battery diagram of Figure 2(b). The schematic diagram of the final generated first-type triangular pyramid double-layer reticulated shell model is shown in Figure 2(c).

[0107] Example 2:

[0108] This embodiment details the modeling method for the second type of polygonal projection space twisted surface mesh shell. The core difference between this and the first type of polygonal projection space twisted surface mesh shell is that the surface needs to be mapped and trimmed after generation, as shown in Figures 3(a) to 4(c).

[0109] The specific implementation process is as follows:

[0110] First, step S1 is executed to set geometric parameters. The parameter types are the same as the first type in Example 1, including the radius and number of sides of the bottom polygon, the height of the center vertex O, and the extension length and height of the outer corner point B, which will not be described again here.

[0111] Next, step S2 is executed: connecting each vertex of the projection plane generates ridges that constitute the shell surface; based on the ridges, a polygonal projection space twisted surface is constructed through surface generation operations.

[0112] Step S2.1': Generate ridge lines connecting the center vertex with the polygon corners and external corners.

[0113] Step S2.2': Based on the ridge line, generate a local spatial twist surface.

[0114] Steps S2.1' and S2.2' are consistent with the logic for generating the first type of ridge line. Multiple ridge lines are generated based on the bottom polygon, the central vertex O, and the outer corner points B using a polygon plugin, a point generation plugin, and a two-point line determination plugin. A local spatial twisted surface is then generated based on these ridge lines using a ridge line surface generation plugin.

[0115] Step S2.3': Use the mapping trimming method to cut off the curved surface portion outside the bottom polygon projection area.

[0116] Using the mapping trimming method, the local spatial distortion surface generated in step S2.2' is cut off with the projection area of ​​the bottom polygon as the boundary, removing the excess curved surface outside the projection area of ​​the bottom polygon.

[0117] Step S2.4': Form a complete second type of polygonal projection space distortion surface through array operation.

[0118] The trimmed local spatial distortion surface is arrayed in a ring using an array plugin to obtain a complete second-type polygonal projection spatial distortion surface. The model is shown in Figure 3(b), and the core plugin combination logic is shown in Figure 3(a).

[0119] Step S3: Mesh the spatial twisted surface using the isoparametric method or the mapping method to generate mesh points. This embodiment can use the mapping method or the isoparametric method. By setting the mesh division number parameter, the trimmed complete twisted surface is divided to generate mesh points that fit its boundary. The core plug-in combination logic is shown in Figure 3(c).

[0120] Step S4: Based on the grid points, connect the multi-line connectors using the multi-line connector plugin.

[0121] A second type of polygonal projection space twisted surface single-layer mesh shell is generated, and its model schematic diagram is shown in Figure 3(d).

[0122] If a double-layered shell needs to be generated, then step S5 is executed: the lower chord layer node is obtained by moving the single-layered shell node, and the upper and lower chord layer nodes are connected to form a double-layered shell.

[0123] The method for generating the truss-type double-layer reticulated shell is exactly the same as the corresponding part in Example 1: that is, the upper chord node is moved down to generate the lower chord node, the lower chord node is connected, and the diagonal web members are generated through odd-even pairing. The core plug-in combination of this process is shown in the battery diagram of Figure 3(e), and the final model is shown in Figure 3(f).

[0124] The method for generating the triangular pyramidal double-layered reticulated shell is consistent with the corresponding part in Example 1: the normal is obtained by generating surfaces, geometric centers, and surface analysis plugins through edge lines, moving nodes along the normal, and finally connecting the web members. The core plugin components of this process are shown in the battery diagrams of Figures 4(a) and 4(b). Figure 4(a) is the battery diagram for generating the second type of polygonal projection space twisted surface triangular pyramidal double-layered reticulated shell, and Figure 4(b) is the battery diagram of the lower chord and web member battery packs in the second type of polygonal projection space twisted surface triangular pyramidal double-layered reticulated shell generated by parametrically adjusting the shell thickness in Figure 4(a). The final model is shown in Figure 4(c). Further details are omitted here.

[0125] Example 3:

[0126] This embodiment details the construction method of a third type of polygonal projection space twisted surface mesh shell with folded plate surfaces at the edges. Its characteristic is that the center is a first type of polygonal projection space twisted surface, but the edges are folded plate surfaces, and the modeling corresponds to the figures in Figures 5(a) to 5(e).

[0127] The specific implementation process is as follows:

[0128] First, perform step S1a to set the geometric parameters. Based on the geometric relationship in Figure 5(b), use the polygon plugin to generate the bottom polygon, input the polygon radius and number of sides, and parametrically control the shape of the polygon; use the point generation plugin to parametrically adjust the height of the center vertex O and the heights of the edge vertices A and C by assigning the center point height Z; wherein, the projection of the edge vertex A is the midpoint of the corresponding edge AB of the bottom polygon, and the position setting of the edge vertex C is similar, as shown in Figure 5(a). The principle of step S1a is the same as that of step S1 in embodiment 1, and will not be repeated here.

[0129] Next, step S2a is executed: connecting each vertex of the projection plane generates ridges that constitute the shell surface, and based on the ridges, constructing a polygonal projection space twisted surface through surface generation operations.

[0130] Step S2.1a: Generate a straight ridge connecting the edge vertices to the corner points and center vertex of the bottom polygon.

[0131] Referring to the geometric relationship diagram in Figure 5(b), the straight ridge is generated by connecting the center vertex O, the side vertices A and C, and the bottom polygon corner vertices B and D through two points.

[0132] S2.2a: Using the adjacent straight ridge lines and their corresponding bottom edge lines as tracks, generate the edge folded plate surface through the dual-track sweeping plug.

[0133] Specifically, using a dual-track sweep plugin, two adjacent ridges AB and AD are connected to the baseline BD to generate a local folded surface at the edge. The complete folded surface is then obtained through an array plugin, as shown in Figure 5(c). The central twisted surface and the edge folded surface together constitute a complete third-type composite surface.

[0134] Next, step S3a is executed, in which the spatial twisted surface is meshed using the isoparametric method or the mapping method to generate mesh points.

[0135] Using the isoparametric method, the central twisted surface and the edge folded plate surface are meshed separately or uniformly, and the meshing degree parameter is set to generate uniformly distributed mesh points. This step is the same as in Examples 1 and 2, and will not be repeated here.

[0136] Subsequently, step S4a is executed, and based on the grid points, a single-layer mesh shell with the edge of the twisted surface of the third type of polygonal projection space is generated by the polyline plugin. Its model schematic diagram is shown in Figure 5(d).

[0137] If a double-layered reticulated shell is required, then step S5a is executed to generate a truss-type web system.

[0138] The specific process is consistent with the generation logic of the truss-type double-layer mesh in Examples 1 and 2: the nodes of the single-layer mesh shell are moved down to generate the lower chord layer, and connected to form the lower chord members. Then, the upper and lower chord nodes with different odd and even numbers are connected to generate the diagonal web members, and finally the third type of double-layer truss-type mesh shell with folded plate surface at the edge is obtained. Its model schematic diagram is shown in Figure 5(e).

[0139] Example 4:

[0140] This embodiment details the construction method of a fourth type of polygonal projection space twisted surface mesh shell with cylindrical edges. Compared to Embodiment 3, this embodiment is characterized by a central twisted surface and curved cylindrical edges, as shown in Figures 6(a) to 6(e). The specific implementation process is as follows:

[0141] First, perform step S1a, in the Grasshopper platform, to set the geometric parameters of the shell model using the input plugin.

[0142] Based on the geometric relationship in Figure 6(b), a bottom polygon is generated using a polygon plugin. The polygon radius and number of sides are input, and the shape of the polygon is parametrically controlled. The center point of the bottom polygon is obtained, and the height of the center vertex O is adjusted parametrically by assigning a Z parameter to the center point height using a point generation plugin. The heights of the edge vertices A and C are also adjusted parametrically by assigning a Z parameter to the point generation plugin. The battery diagram is shown in Figure 6(a). This step is the same as in Example 3 and will not be repeated here.

[0143] Next, step S2a is executed: connecting each vertex of the projection plane generates ridges that constitute the shell surface, and based on the ridges, constructing a polygonal projection space twisted surface through surface generation operations.

[0144] S2.1a': Generate a central curved surface ridge frame and an edge curved surface ridge frame composed of circular arc ridges based on the central vertex, edge vertices and polygon corner points.

[0145] The connection method of the central arc ridge line is as follows:

[0146] The arc plugin connects the center vertex O and the edge vertex A by using two points and the slope of the endpoints, and sets the slope of endpoint O to 0 to generate the center arc ridge line OA;

[0147] Similarly, based on the slopes of the two points and endpoints, the arc plug-in connects the center vertex O and the edge vertex C, and sets the slope of endpoint O to 0 to generate the center arc ridge OC.

[0148] The connection method of the edge arc ridge line is as follows:

[0149] Based on the slope of the two points and the endpoint, the arc plug-in connects the edge vertex A and the polygon corner point B, and sets the slope of endpoint A to 0 to generate the edge arc ridge line AB;

[0150] Similarly, based on the slope of the two points and the endpoints, the arc plug-in connects the edge vertex A and the polygon corner point D, and sets the slope of endpoint A to 0 to generate the edge arc ridge line AD;

[0151] Similarly, based on the slope of the two points and the endpoints, the arc plug-in connects the edge vertex C and the polygon corner point B, and sets the slope of endpoint C to 0 to generate the edge arc ridge line CB.

[0152] S2.2a': For the edge region, using two adjacent circular arc ridges and the bottom edge as tracks, a local cylindrical surface is generated through the dual-track sweep plugin, and the complete edge cylindrical surface is obtained through the array plugin.

[0153] The dual-track sweep plugin is used to connect two adjacent edge arc ridges AB and AD and the bottom line BD to generate a local edge cylinder surface. The complete edge cylinder surface is obtained by using the array plugin.

[0154] For the central region, using two central circular arc ridges and two edge circular arc ridges as boundaries, and using the circular arc ridges as boundaries, a local central curved surface is generated through a four-sided surface plugin, and the complete central twisted surface is obtained through arraying.

[0155] Specifically, using the four circular arc ridges OA, OC, AB, and CB as boundaries, a local center surface is generated through the four-sided surface plugin, and then the complete center surface is obtained through the array plugin, as shown in Figure 6(c).

[0156] Next, step S3a is executed: the edge cylindrical surface and the center curved surface are divided by isoparametric method to obtain the edge cylindrical surface mesh points and the center curved surface mesh points respectively.

[0157] Subsequently, step S4a is executed, based on the grid points, all grid points are connected using a polyline plugin to generate a single-layer mesh shell with cylindrical edges on the twisted surface of the fourth type of polygonal projection space, as shown in Figure 6(d).

[0158] Steps S3a and S4a are in the same principle as steps S3 and S4 in Example 1, and will not be repeated here.

[0159] If a double-layer reticulated shell needs to be generated, step S5 is executed to generate a truss-type web system. The specific process is the same as in the previous embodiment: the nodes are moved down to generate the lower chord layer and the lower chord members are connected. Then, the diagonal web members are generated by connecting the upper and lower chord nodes with opposite odd and even numbers. Finally, a fourth type of double-layer truss-type reticulated shell with cylindrical edges is obtained, and its model schematic diagram is shown in Figure 6(e). It will not be described in detail here.

[0160] The above embodiments demonstrate in detail the specific process of generating four main types of polygonal projection spatial twisted reticulated shells based on the Grasshopper platform using parametric driving. This invention organizes the modeling steps through a visualized logical battery diagram, and all initial parameters can be adjusted in real time and dynamically updated through input plugins, achieving efficient and flexible parametric modeling of complex spatial reticulated shell structures. Any equivalent transformations or combinations based on the principles and technical solutions of this invention should be covered within the scope of protection of this invention.

Claims

1. A parametric modeling method for polygonal projection space twisted reticulated shells based on Grasshopper, characterized in that, Includes the following steps: Step S1: In the Grasshopper platform, set the geometric parameters of the mesh shell model by inputting the plugin to obtain the corresponding spatial curved mesh shell surface projection surface; Step S2: Connect the vertices of the projection plane to generate ridges that form the shell surface. Based on the ridges, construct a polygonal projection space twisted surface through surface generation operations. Step S3: Use the isoparametric method or mapping method to mesh the spatial twisted surface and generate mesh points; Step S4: Based on the grid points, generate a single-layer polygonal projection space twisted surface shell structure through a multi-segment line connection plug-in; The geometric parameters in step S1 include: the radius and number of sides of the bottom polygon, the height of the center vertex, and the extension length and height of the outer corner points; the method for setting the geometric parameters is as follows: Use the polygon plugin to generate the bottom polygon, and use its input plugin to set the parameters of the bottom polygon's radius and number of sides to control the polygon's shape; Obtain the center point of the bottom polygon, use the point generator plugin, and obtain the height of the center vertex by assigning a value to the Z coordinate; The line segment generated by the extension segment plugin is used to extend the line segment formed by the center point of the polygon and the midpoint of the inner edge of the polygon. The extension length parameter is used to control the projection plane position of the outer corner point. The point generation plugin is used again to parametrically adjust the spatial height of the outer corner points by assigning Z-coordinates to them.

2. The parametric modeling method for polygonal projection space twisted reticulated shells based on Grasshopper according to claim 1, characterized in that, Step S2 is used to construct the first type of polygonal projection space distortion surface, specifically including: Step S2.1: Generate ridge lines connecting the center vertex to the polygon corners and outer corners; Step S2.2: Based on the ridge line, generate a local spatial twist surface, and form a complete first-type polygonal projection spatial twist surface through array operation.

3. The parametric modeling method for polygonal projection space twisted surface mesh shells based on Grasshopper according to claim 1, characterized in that, Step S2 is used to construct the second type of polygonal projection space distortion surface, specifically including: Step S2.1': Generate ridge lines connecting the center vertex to the polygon corners and outer corners; Step S2.2': Based on the ridge line, generate a local spatial twist surface; Step S2.3': Use the mapping trimming method to remove the curved surface portion outside the bottom polygon projection area; Step S2.4': Form a complete second type of polygonal projection space distortion surface through array operation.

4. A parametric modeling method for polygonal projection space twisted reticulated shells based on Grasshopper according to any one of claims 2 or 3, characterized in that, It also includes step S5 for generating a truss-type double-layer reticulated shell: obtaining the lower chord layer nodes based on the movement of the single-layer reticulated shell nodes, and connecting the upper and lower chord layer nodes to form a double-layer reticulated shell, specifically including the following steps: Step S5.1: Take the nodes of the single-layer reticulated shell as the upper chord layer nodes, and offset them along the normal or vertical direction to generate the lower chord layer nodes; Step S5.2: Connect the lower chord nodes to form the lower chord member; Step S5.3: Connect the corresponding upper chord layer nodes and lower chord layer nodes to form a web member system. The web member system includes inclined web members generated by pairing and connecting upper and lower chord nodes with different parities.

5. A parametric modeling method for polygonal projection space twisted reticulated shells based on Grasshopper according to any one of claims 2 or 3, characterized in that, It also includes step S5' of generating a conical double-layer reticulated shell: obtaining the lower chord layer nodes based on the movement of the single-layer reticulated shell nodes, and connecting the upper and lower chord layer nodes to form a double-layer reticulated shell, specifically including the following steps: Step S5.1': Take the nodes of the single-layer shell as the upper chord nodes, and offset them along the normal of the upper chord surface of each grid cell to generate the lower chord nodes; Step S5.2': Connect the lower chord nodes to form the lower chord; Step S5.3': Each upper chord node is connected to its corresponding lower chord node and adjacent lower chord nodes to form a triangular pyramid or quadrangular pyramid web member system.

6. A parametric modeling method for polygonal projection space twisted reticulated shells based on Grasshopper, characterized in that, Includes the following steps: Step S1a: In the Grasshopper platform, set the geometric parameters of the mesh shell model by inputting the plugin to obtain the corresponding spatial curved mesh shell surface projection surface; Step S2a: Connect each vertex of the projection plane to generate ridges that constitute the shell surface. Based on the ridges, construct a polygonal projection space twisted surface through surface generation operations. Step S3a: Use the isoparametric method or mapping method to mesh the spatial twisted surface and generate mesh points; Step S4a: Based on the grid points, generate a single-layer polygonal projection space twisted surface shell structure through a multi-segment line connection plug-in; The geometric parameters in step S1a include: the radius and number of sides of the bottom polygon, the height of the center vertex, and the height of the edge vertices; The method for setting the geometric parameters is as follows: Use the polygon plugin to generate the bottom polygon, and use its input plugin to set the parameters of the bottom polygon's radius and number of sides to control the polygon's shape; Obtain the center point of the polygon, use the point generator plugin, and obtain the height of the center vertex by assigning a value to the Z coordinate; The height of the edge vertices is adjusted parametrically; the projection of each edge vertex is the midpoint of the edge corresponding to the bottom polygon.

7. The parametric modeling method for polygonal projection space twisted reticulated shells based on Grasshopper according to claim 6, characterized in that, Step S2a is used to construct a third type of polygonal projection space twisted surface with folded plate edges, specifically including: Step S2.1a: Generate a straight ridge line connecting the edge vertices to the corner points and center vertex of the bottom polygon; Step S2.2a: Using the adjacent straight ridge lines and their corresponding bottom edge lines as tracks, generate the edge folded plate surface through the dual-track sweeping plug.

8. The method for parametric modeling of polygonal projection space twisted reticulated shells based on Grasshopper according to claim 6, characterized in that, The surface constructed in step S2a is a fourth type of edge cylinder surface, wherein step S2 specifically includes: Step S2.1a': Generate a central curved surface ridge frame and an edge curved surface ridge frame composed of circular arc ridges based on the center vertex, edge vertices and corner points of the bottom polygon; Step S2.2a': For the edge region obtained by connecting the edge vertices and the corner points of the bottom polygon, use two adjacent circular arc ridges and the bottom edge as the track to generate a local cylinder through the dual-track sweep plugin, and obtain the complete edge cylinder surface through the array plugin. For the central region obtained by connecting the central vertex with the edge vertices and the corner points of the bottom polygon, a local central surface is generated by using two central circular arc ridges and two edge circular arc ridges as boundaries, and the complete central twisted surface is obtained by using the array plugin.

9. A parametric modeling method for polygonal projection space twisted reticulated shells based on Grasshopper according to any one of claims 7 or 8, characterized in that, It also includes step S5a for generating a truss-type double-layer reticulated shell: obtaining the lower chord layer nodes based on the movement of the single-layer reticulated shell nodes, and connecting the upper and lower chord layer nodes to form a double-layer reticulated shell, specifically including the following steps: Step S5.1a: Take the nodes of the single-layer reticulated shell as the upper chord layer nodes, and offset them along the normal or vertical direction to generate the lower chord layer nodes; Step S5.2a: Connect the lower chord nodes to form the lower chord member; Step S5.3a: Connect the corresponding upper chord layer nodes and lower chord layer nodes to form a web member system, wherein the web member system includes inclined web members generated by pairing and connecting upper and lower chord nodes with different parity.

10. A parametric modeling method for polygonal projection space twisted reticulated shells based on Grasshopper according to any one of claims 7 or 8, characterized in that, It also includes step S5a' of generating a conical double-layer reticulated shell: obtaining the lower chord layer nodes based on the movement of the single-layer reticulated shell nodes, and connecting the upper and lower chord layer nodes to form a double-layer reticulated shell, specifically including the following steps: Step S5.1a': Take the nodes of the single-layer shell as upper chord nodes, and offset them along the normal of the upper chord surface of each grid cell to generate lower chord nodes; Step S5.2a': Connect the lower chord nodes to form the lower chord; Step S5.3a': Each upper chord node is connected to its corresponding lower chord node and adjacent lower chord nodes to form a triangular pyramid or quadrangular pyramid web member system.

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