A polygonal structure curved surface laying modeling method suitable for a complex curved surface type with a curvature mutation feature

Abstract

The application provides a polygon structure curved surface laying modeling method suitable for a complex curved surface type with a curvature mutation feature, and comprises the following steps: obtaining a mutation composite curved surface; establishing a space right-angle coordinate system, and dividing the mutation composite curved surface along a turning line to establish a one-to-one mapping relationship from a three-dimensional coordinate to a two-dimensional plane parameter region; performing polygon structure pre-laying in the plane parameter region; projecting the laying result to a three-dimensional space to construct a hexagonal prism and a part of a triangular prism; optimizing the prism structure at the turning line; and covering the prism structure material on the mutation composite curved surface by using a 3D printing technology. The application solves the problems of great deformation and large cell structure array spacing of an electromagnetic structure in the prior art on a curvature mutation curved surface, and greatly reduces the electromagnetic performance. The polygon structure material can be conveniently laid on the curvature mutation complex curved surface, the polygon structure deformation is weak, the laying range is large, and the method is suitable for a wide type of curved surfaces.

Description

Technical Field

[0001] This invention relates to an electromagnetic design technique, and more particularly to a method for modeling polygonal structures with complex curved surfaces exhibiting abrupt curvature changes. Background Technology

[0002] In modern electromagnetic design, "conformal electromagnetic structural materials" are increasingly used, such as frequency selective surface (FSS) materials, metamaterials, cellular absorbing materials, and conformal antenna arrays. These materials are composed of a series of "units" arranged according to specific rules. In practical applications, these materials may be laid on the surfaces of aircraft, ships, missiles, and vehicles, such as radomes, wings, and fuselages. These surfaces are often complex curved surfaces. Arranging these complex curved surfaces while ensuring electromagnetic performance is a global modeling challenge. How to construct an "efficient, universally applicable method for laying out conformal curved arrays that guarantees specific electromagnetic performance" is a problem that urgently needs to be solved.

[0003] Patent CN 113378251 A discloses a modeling method for laying out unit structure surface arrays applicable to various continuous curved surface types. This method facilitates the laying of structural material unit structure arrays on surfaces of revolution, satisfying requirements such as weak unit deformation, consistent period intervals, wide applicability to various surface types, and the ability to lay out unit arrays on continuous curved surfaces. However, it does not yet address the issue of large "blank gap areas" (areas without structure) on surfaces with abrupt curvature changes, or the possibility of material deformation due to bending, which could affect electromagnetic performance. On the other hand, honeycomb structures offer advantages such as high load-bearing capacity, ingenious construction, and material savings. Utilizing the honeycomb (hexagonal) characteristics, honeycomb structures can be laid out on surfaces such as radomes, wings, and hulls of aircraft, ships, missiles, and vehicles. The resulting products are reliable and of stable quality. This not only enables radar-absorbing materials to possess broadband stealth capabilities but also allows them to be directly applied as structural load-bearing components in weaponry requiring mechanical support. Therefore, laying out honeycomb (hexagonal) unit structure arrays on curved surfaces may be more advantageous. Summary of the Invention

[0004] The main objective of this invention is to provide a polygonal structure surface tiling modeling method applicable to complex curved surfaces with abrupt curvature characteristics, solving the problem of difficult tiling of non-developable curved surfaces with abrupt curvature characteristics in electromagnetic design. It can meet the requirement that the deformation of polygonal tiling units is weak during the tiling process, and it is adaptable to a wide range of curved surface types, enabling the tiling of polygonal structure arrays on various curved surfaces with abrupt curvature characteristics.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for modeling polygonal structure surfaces with complex curved surface types having abrupt curvature changes, specifically including the following steps:

[0006] S1. Based on the required shape of the carrier object to which the structural material is to be laid, search for sharp points, connect adjacent sharp points to form a turning line, and extend a certain width to both sides of the turning line. This yields a mutational composite surface, while the remaining surfaces are arranged in a conventional array.

[0007] S2. Establish a spatial rectangular coordinate system, segment the abruptly changed composite surface along the turning line, and obtain the coordinates of the segmented surface point set. :

[0008] S3, 3D coordinates projected onto the 2D plane parameter region;

[0009] S4. Pre-lay out an array of polygonal structures in the two-dimensional planar parameter region and obtain a point set. :

[0010] S5. Project the pre-laid polygon structure result into three-dimensional space and obtain the point set. :

[0011] S6. Construct a hexagonal frustum and part of a triangular frustum;

[0012] S7. Combine the triangular frustums near the turning line and transform them into a combination of a central hexagonal frustum and an outer triangular frustum, then update the point set. and :

[0013] S8. Using 3D printing technology, the material of hexagonal frustum and part of triangular frustum structure is covered on the abrupt composite surface.

[0014] In the preferred embodiment, in step S2, with one end of the turning line as the origin, the tangent direction is... Axis, perpendicular The axes, perpendicular to the tangent direction, are respectively shaft and Axis, establish a spatial rectangular coordinate system, in which the abrupt composite surface is... The planar segmentation divides the surface into the first splicing surface along the turning line. Second spliced ​​surface Obtain the first spliced ​​surface Second spliced ​​surface coordinate point set

[0015] In the preferred embodiment, in step S3, a planar parameter region is given. Establish the first spliced ​​surface in a spatial rectangular coordinate system Second spliced ​​surface coordinate point set With planar parameter region One-to-one mapping relationship and The first spliced ​​surface in three-dimensional space Second spliced ​​surface Project onto the planar parameter region.

[0016] In the preferred embodiment, in step S4, a polygonal structure is pre-laid in an array in the two-dimensional planar parameter region to obtain a point set. This includes the following steps:

[0017] S01. Generate Delaunay triangular mesh;

[0018] S02, splicing hexagonal surfaces;

[0019] S03. Obtain the planar parameter point set of each point of the hexagon and the complementary triangle.

[0020] In the preferred embodiment, the generation of the Delaunay triangular mesh in step S01 specifically includes the following steps:

[0021] S11. Traverse all edges of the model;

[0022] S12. Generate boundary points: Traverse all faces of the model and collect the coordinates of its boundary points in the parameter region.

[0023] S13. Using the Delaunay triangulation algorithm, generate a Delaunay triangular mesh on the parameter region. For triangles whose side lengths are not less than the preset value, insert the centroid into the triangular mesh and use the Delaunay triangulation algorithm to obtain a new Delaunay triangulation until all triangles have side lengths that are less than the preset value.

[0024] In the preferred embodiment, step S02, which involves splicing the hexagonal surfaces, specifically includes the following steps:

[0025] S21. Randomly select a triangle, divide it into three triangles using its centroid, and extend outwards from the three triangles to find their common side triangles. Their common side triangles are called the principal triangles of the hexagon.

[0026] S22. Find the other two triangles that share a side as the main triangle of the hexagon, and use the centroid to divide these two triangles into three triangles respectively;

[0027] S23. The main triangle and three triangles sharing the same side together form a hexagon;

[0028] S24. Select any side of the hexagon and its corresponding triangle, find the main triangle that shares the same side, and repeat S22 to S24 until no more main triangles can be found. Keep these co-triangles and stop the loop.

[0029] In the preferred embodiment, in step S5, the mapping relationship is utilized. and The inverse mapping projects the pre-laid polygon structure result into three-dimensional space, and obtains the first polygon splicing surface, the second polygon splicing surface, and the corresponding point set. .

[0030] In the preferred embodiment, in step S6, on the first polygonal splicing surface... Second polygon splicing surface Extend outward at equal intervals along the tangent direction of each boundary point of the polygon And obtain the extended point set. Obtain the third and fourth polygonal splicing surfaces, and establish... and One-to-one mapping relationship Connect the corresponding points to obtain the wrapping on the first spliced ​​surface. Second spliced ​​surface The exterior features a hexagonal frustum and some triangular frustums.

[0031] In the preferred embodiment, the unit structure is laid using any one of the following materials: FSS material, metamaterial, or honeycomb absorbing material.

[0032] This invention provides a method for modeling polygonal surface tiling of complex curved surfaces with abrupt curvature changes. It facilitates the tiling of polygonal element arrays on complex curved surfaces with abrupt curvature changes, ensuring element non-deformation and a large tiling range. This method is well-suited for tiling non-developable surfaces with abrupt curvature changes. The combination of the Delaunay triangulation algorithm and the common-edge selection algorithm of this invention during modeling offers several advantages: 1) The Delaunay triangulation algorithm avoids the formation of elongated triangles, and the hexagons formed by the common-edge selection algorithm are close to regular hexagons, thus possessing the advantages of strong load-bearing capacity, ingenious construction, and material saving characteristic of honeycomb structures; 2) Using triangles as the basic element structure allows for 3D printing for covering and tiling. Attached Figure Description

[0033] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0034] Figure 1 It is a complex surface with abrupt curvature changes in the present invention;

[0035] Figure 2 This is the abrupt composite surface in this invention;

[0036] Figure 3 This is a schematic diagram of the hexagonal splicing process in this invention;

[0037] Figure 4 This is a schematic diagram of the hexagonal splicing of the present invention;

[0038] Figure 5 This is a schematic diagram of the side of the hexagon after splicing according to the present invention.

[0039] In the figure: main triangle 1; abrupt composite surface 2; first spliced ​​surface 201; second spliced ​​surface 202; first polygon spliced ​​surface 203; second polygon spliced ​​surface 204; third polygon spliced ​​surface 205; fourth polygon spliced ​​surface 206; complementary triangle 3. Detailed Implementation

[0040] Example 1

[0041] like Figures 1-5 As shown, a method for modeling polygonal structures with complex surfaces exhibiting abrupt curvature changes is proposed, which includes the following steps:

[0042] S1. Based on the required shape of the carrier object to which the structural material is to be laid, search for sharp points, connect adjacent sharp points to form a turning line, and extend a certain width to both sides of the turning line. This yields the abrupt composite surface 2, while the remaining surfaces are arranged in a conventional array.

[0043] S2. Establish a spatial rectangular coordinate system, divide the abruptly changed composite surface 2 along the turning line, and obtain the coordinates of the point set of the divided surface. :

[0044] S3, 3D coordinates projected onto the 2D plane parameter region;

[0045] S4. Pre-lay out an array of polygonal structures in the two-dimensional planar parameter region and obtain a point set. :

[0046] S5. Project the pre-laid polygon structure result into three-dimensional space and obtain the point set. :

[0047] S6. Construct a hexagonal frustum and part of a triangular frustum;

[0048] S7. Combine the triangular frustums near the turning line and transform them into a combination of a central hexagonal frustum and an outer triangular frustum, then update the point set. and :

[0049] S8. Using 3D printing technology, the material of the hexagonal frustum and part of the triangular frustum structure is covered on the abrupt composite surface 2.

[0050] Identify abrupt changes in curvature by finding sharp points, connect adjacent sharp points to form a turning line, and extend the turning line a certain width to both sides. This yields the abrupt composite surface 2 to be laid, with a width of... The arrangement can be determined according to the actual situation. The remaining part consists of surfaces with small curvature changes, which can be arranged in a conventional array. This solves the problem of laying out abrupt composite surfaces and reduces the amount of computation.

[0051] The conventional array layout is arranged using the method described in CN113378251A.

[0052] In the preferred embodiment, in step S2, with one end of the turning line as the origin, the tangent direction is... Axis, perpendicular The axes, perpendicular to the tangent direction, are respectively shaft and Axis, establish a spatial rectangular coordinate system, in which the abrupt composite surface 2 is... The planar segmentation divides the surface into the first splicing surface along the turning line. Second spliced ​​surface Obtain the first spliced ​​surface Second spliced ​​surface coordinate point set .

[0053] Dividing the abrupt composite surface 2 into two splicing surfaces along the turning line allows the abrupt composite surface 2 to be modeled as two separate surfaces, reducing the difficulty of modeling.

[0054] In the preferred embodiment, in step S3, a planar parameter region is given. Establish the first spliced ​​surface in a spatial rectangular coordinate system Second spliced ​​surface coordinate point set With planar parameter region One-to-one mapping relationship and The first spliced ​​surface in three-dimensional space Second spliced ​​surface Project onto the planar parameter region.

[0055] Because laying directly in three-dimensional space will cause the laying material to deform due to the different curvature of the surface, establishing a mapping relationship from three-dimensional to two-dimensional helps to model the array pre-laying of curved surfaces in two-dimensional space.

[0056] In the preferred embodiment, in step S4, a polygonal structure is pre-laid in an array in the two-dimensional planar parameter region to obtain a point set. This includes the following steps:

[0057] S01. Generate Delaunay triangular mesh;

[0058] S02, splicing hexagonal surfaces;

[0059] S03. Obtain the planar parameter point set of each point of the hexagon and the complementary triangle. .

[0060] In the preferred embodiment, the generation of the Delaunay triangular mesh in step S01 specifically includes the following steps:

[0061] S11. Traverse all edges of the model;

[0062] S12. Generate boundary points: Traverse all faces of the model and collect the coordinates of its boundary points in the parameter region.

[0063] S13. Using the Delaunay triangulation algorithm, generate a Delaunay triangular mesh on the parameter region. For triangles whose side lengths are not less than the preset value, insert the centroid into the triangular mesh and use the Delaunay triangulation algorithm to obtain a new Delaunay triangulation until all triangles have side lengths that are less than the preset value.

[0064] Using the Delaunay triangulation algorithm, the abrupt composite surface 2 is decomposed into triangles with side lengths less than 2-10 mm. Furthermore, based on the characteristics of the algorithm, it can avoid generating elongated triangles, which is helpful for the further hexagonal splicing step.

[0065] The side length of the triangle is less than the preset value, which is 2-10mm.

[0066] In the preferred embodiment, step S02, which involves splicing the hexagonal surfaces, specifically includes the following steps:

[0067] S21. Randomly select a triangle, divide it into three triangles using its centroid, and extend outwards from the three triangles to find their common side triangles. Their common side triangle is called the principal triangle 1 of the hexagon.

[0068] S22. Find the other two triangles sharing the same side as the main triangle 1 of the hexagon, and use the centroid to divide these two triangles into three triangles respectively;

[0069] S23, the main triangle 1 and three triangles sharing the same side together form a hexagon;

[0070] S24. Select any side of the hexagon and its corresponding triangle, find the main triangle 1 that shares a side, and repeat S22 to S24 until no more main triangle 1 can be found. Keep these co-triangles 3 and stop the loop.

[0071] Using the above steps, the hexagons are divided by the center of gravity and spliced ​​together. The spliced ​​hexagons are approximately regular hexagons, which helps to strengthen the material structure. After the splicing process is completed, a small number of triangles may be generated at the edges, but since the number is small, it will not affect the laying structure.

[0072] In the preferred embodiment, in step S5, the mapping relationship is utilized. and The inverse mapping projects the pre-laid polygon structure result into three-dimensional space, and obtains the first polygon splicing surface 203 and the second polygon splicing surface 204 and the corresponding point set. .

[0073] Using mapping relationships and The inverse mapping can project the pre-laid hexagonal and triangular structures on the planar parameter region into three-dimensional space, and obtain the pre-laid hexagonal and triangular point set in three-dimensional space.

[0074] In the preferred embodiment, in step S6, on the first polygonal splicing surface... 203 and the second polygon splicing surface 204 extends outward at equal intervals along the tangent directions at each boundary point of the polygon. And obtain the extended point set. Obtain the third polygon splicing surface 205 and the fourth polygon splicing surface 206, and establish... and One-to-one mapping relationship Connect the corresponding points to obtain the wrapping on the first spliced ​​surface. Second spliced ​​surface 02. Hexagonal frustum and part of triangular frustum.

[0075] In the pre-laid hexagonal and triangular point sets Establish an equidistant and enlarged set of pre-laid hexagonal and triangular points on the periphery. These point sets together form a wrapping around the first spliced ​​surface. Second spliced ​​surface The set of points of the external hexagonal frustum and part of the triangular frustum.

[0076] In the preferred embodiment, the unit structure is laid using any one of the following materials: FSS material, metamaterial, or honeycomb absorbing material.

[0077] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for modeling polygonal structures with complex surfaces exhibiting abrupt curvature changes, characterized by: Specifically, the steps include the following: S1. Based on the required shape of the carrier object to which the structural material is to be laid, search for sharp points, connect adjacent sharp points to form a turning line, and extend a certain width to both sides of the turning line. , thus obtaining the abrupt composite surface (2), and the remaining surfaces are arranged in a conventional array; S2. Establish a spatial rectangular coordinate system, divide the abrupt composite surface (2) along the turning line, and obtain the coordinates of the point set of the divided surface. ; S3, 3D coordinates projected onto the 2D plane parameter region; S4. Pre-lay out an array of polygonal structures in the two-dimensional planar parameter region and obtain a point set. ; In step S4, a preset polygon structure is arrayed in the two-dimensional planar parameter region to obtain a point set. This includes the following steps: S01. Generate Delaunay triangular mesh; S02, splicing hexagonal surfaces; Step S02 involves assembling the hexagonal surfaces, specifically including the following steps: S21. Randomly select a triangle, divide it into three triangles using its centroid, and extend outward from the three triangles to find their common side triangles. Their common side triangles are called the main triangle of the hexagon (1). S22. Find the other two common-side triangles of the main triangle (1) of the hexagon, and divide these two triangles into three triangles using the centroid respectively; S23, the main triangle (1) and three triangles sharing the same side together form a hexagon; S24. Select any side of the hexagon and its corresponding triangle, find the main triangle (1) that shares the same side, and repeat S22 to S24 until no more main triangles (1) can be found. Keep these co-triangles (3) and stop the loop. S03. Obtain the planar parameter point set of each point of the hexagon and the complementary triangle. ; S5. Project the pre-laid polygon structure result into three-dimensional space and obtain the point set. ; S6. Construct a hexagonal frustum and part of a triangular frustum; S7. Combine the triangular frustums near the turning line and transform them into a combination of a central hexagonal frustum and an outer triangular frustum, then update the point set. and ; S8. Using 3D printing technology, the material of the hexagonal frustum and part of the triangular frustum structure is covered on the abrupt composite surface (2).

2. The method for modeling polygonal structures with complex surface types exhibiting abrupt curvature changes, as described in claim 1, is characterized by: In step S2, taking one end of the turning line as the origin, its tangent direction is... The axes, perpendicular to the tangent direction, are respectively shaft and Axis, establish a spatial rectangular coordinate system, in which the abrupt composite surface (2) is... The planar segmentation divides the surface into the first splicing surface along the turning line. (201) and the second spliced ​​surface (202) Obtain the first spliced ​​surface (201) and the second spliced ​​surface The set of coordinate points of (202) .

3. The method for modeling polygonal structures with complex surface types exhibiting abrupt curvature changes, as described in claim 1, is characterized by: In step S3, a planar parameter region is given. Establish the first spliced ​​surface in a spatial rectangular coordinate system (201) and the second spliced ​​surface The set of coordinate points of (202) With planar parameter region One-to-one mapping relationship and The first spliced ​​surface in three-dimensional space (201) and the second spliced ​​surface (202) Project onto the plane parameter region.

4. The method for modeling polygonal structures with complex surface types exhibiting abrupt curvature changes, as described in claim 1, is characterized by: Step S01 generates the Delaunay triangular mesh, which specifically includes the following steps: S11. Traverse all edges of the model; S12. Generate boundary points: Traverse all faces of the model and collect the coordinates of its boundary points in the parameter region. ; S13. Using the Delaunay triangulation algorithm, generate a Delaunay triangular mesh on the parameter region. For triangles whose side lengths are not less than the preset value, insert the centroid into the triangular mesh and use the Delaunay triangulation algorithm to obtain a new Delaunay triangulation until all triangles have side lengths that are less than the preset value.

5. The method for modeling polygonal structures with complex surface types exhibiting abrupt curvature changes, as described in claim 3, is characterized by: In step S5, the mapping relationship is used. and The inverse mapping projects the pre-laid polygon structure result into three-dimensional space, and obtains the first polygon splicing surface. (203) and the second polygon splicing surface (204) and the corresponding point set .

6. The method for modeling polygonal structures with complex surface types exhibiting abrupt curvature changes, as described in claim 1, is characterized by: In step S6, on the first polygonal splicing surface (203) and the second polygon splicing surface (204) Extend outward at equal intervals along the tangent direction of each boundary point of the polygon. And obtain the extended point set. Obtain the third polygon splicing surface (205) and the fourth polygon splicing surface (206), and establish... and One-to-one mapping relationship Connect the corresponding points to obtain the wrapping on the first spliced ​​surface. (201) and the second spliced ​​surface (202) The hexagonal frustum and part of the triangular frustum outside.

7. The method for modeling polygonal structures with complex surface types exhibiting abrupt curvature changes, as described in claim 1, is characterized by: The unit structure can be laid using any one of the following materials: FSS material, metamaterial, or honeycomb absorbing material.

Images