Interpolation boundary-based rotating rigid body structure random generation method

Abstract

The invention discloses a rotating rigid body structure random generation method based on an interpolation boundary, and relates to the technical field of rotating rigid body processing, and the method comprises the following steps: S1, generating a random domain according to the size of a rotating rigid body, and determining a plurality of limiting points; s2, generating an interpolation function according to the plurality of limiting points; s3, drawing an interpolation curve corresponding to the interpolation function by using the plurality of fine points, and transforming the interpolation curve to generate a flexible hinge, a peripheral local structure of the flexible hinge and a rotating rigid body unit; and S4, generating a three-dimensional model of the rotating rigid body according to the flexible hinge, the peripheral local structure of the flexible hinge and the rotating rigid body unit. A large number of structures can be quickly generated, intermediate manpower is reduced, and priori knowledge and design experience are not needed; compared with a local topology generation method, the method is higher in randomness and globality, and complex constraint conditions and design targets do not need to be considered.

Description

Technical Field

[0001] The invention relates to the technical field of rotating rigid body processing, and in particular to a method for randomly generating a rotating rigid body structure based on an interpolation boundary. Background Art

[0002] Rotating rigid body structures are a type of metamaterial with unique mechanical properties, consisting of rigid units connected by flexible hinges. Since the applied load is not collinear between the upper and lower hinges, the unit body rotates, resulting in a negative Poisson's ratio effect close to -1. Predicting and controlling the motion of large-scale rotating rigid body structures, enhancing the mechanical properties of rotating rigid body structures to prevent damage, and their application in the fields of aerospace, biosensors, and transportation are of great strategic significance. The simulation and computational research methods for rotating rigid bodies are mainly divided into two categories, one is the traditional method based on finite elements or homogenization, and the other is a data-driven machine learning method, such as neural networks (generative adversarial networks, variational autoencoders, graph networks), random forests, vector machines, etc.

[0003] At present, some researchers have studied the complex motion of rotating rigid structures through machine learning and proved the feasibility and effectiveness of the method. However, the known rotating rigid structures are all generated through artificial design or local topology optimization, which is not conducive to the establishment of large-scale data sets. There are two major problems: insufficient data volume and insufficient randomness. It is impossible to achieve the diversified development of rotating rigid structures, which makes it difficult for data-driven methods to work. Summary of the invention

[0004] In order to solve the above problems, the present invention proposes a random generation method of a rotating rigid body structure based on an interpolation boundary.

[0005] The technical solution of the present invention is: a method for randomly generating a rotating rigid body structure based on an interpolation boundary comprises the following steps:

[0006] S1. Generate a random domain according to the size of the rotating rigid body and determine several limit points;

[0007] S2, generating an interpolation function according to a number of limit points;

[0008] S3, using a number of fine points to draw an interpolation curve corresponding to the interpolation function, and transforming the interpolation curve to generate a flexible hinge and its surrounding local structure and a rotating rigid body unit;

[0009] S4. Generate a three-dimensional model of a rotating rigid body according to the flexible hinge, its surrounding local structure and the rotating rigid body unit.

[0010] Furthermore, S1 includes the following sub-steps:

[0011] S11. Determine the design domain of the rotating rigid body unit and the design domain of the flexible hinge;

[0012] S12, generating a random domain according to the design domain of the rotating rigid body unit and the design domain of the flexible hinge;

[0013] S13. Determine several limit points in the random domain.

[0014] Furthermore, in S11, the design domain of the rotating rigid body unit is a square, and the design domain of the flexible hinge is a rectangle;

[0015] In S12, the range expression of the random domain is:

[0016] ;

[0017] In the formula, represents the horizontal axis of the random field, represents the ordinate of the random field, represents the side length of the square, Represents the length of the rectangle, Indicates the width of the rectangle.

[0018] Furthermore, S2 includes the following sub-steps:

[0019] S21, generate an index value, and divide the index value into several parts;

[0020] S22, using a plurality of index values, mapping a plurality of limit points to a plurality of fine points;

[0021] S23. Generate an interpolation function using a number of fine points.

[0022] Furthermore, in S22, the fine point coordinates The expression is:

[0023] ;

[0024] In the formula, The horizontal coordinate represents the fine point coordinate, The ordinate represents the fine point coordinates, Indicates the index value.

[0025] Furthermore, in S3, the calculation formula for transforming the interpolation curve is:

[0026] ;

[0027] In the formula, represents the abscissa of the interpolation curve, represents the ordinate of the interpolation curve, Indicates that the interpolation curve is intercepted, rotated 90° clockwise, and translated. The horizontal axis of Indicates that the interpolation curve is intercepted, rotated 90° clockwise, and translated. The vertical coordinate of Express The curve is rotated 90° clockwise and translated. The horizontal axis of Express The curve is rotated 90° clockwise and translated. The vertical coordinate of Express The horizontal coordinate of the curve after the curve is rotated 90° clockwise and translated. Express The vertical coordinate of the curve after the curve is rotated 90° clockwise and translated. represents the transposed matrix, represents the side length of the square, Indicates the width of the rectangle.

[0028] Further, S4 includes the following sub-steps:

[0029] S41, determining the length of the smooth curve according to the fine point coordinates corresponding to the flexible hinge and its surrounding local structure and the rotating rigid body unit;

[0030] S42, using a cubic spline curve to determine the geometric contour of the rotating rigid body unit, and connecting it through an interpolation function to form a smooth curve;

[0031] S43, triangulating the smooth curve to generate a plurality of triangular facets;

[0032] S44, filtering out triangular face patches whose centroids are located inside the contour curve, and generating a plurality of internal triangular face patches;

[0033] S45, generating a geometric mesh using a plurality of internal triangular facets;

[0034] S46. Based on the geometric mesh, traverse the boundary coordinates of several internal triangular facets to generate a three-dimensional model.

[0035] Furthermore, in S45, the expression of the geometric mesh is ; In the formula, Represents the horizontal coordinate of the first vertex of the triangle patch, Represents the horizontal coordinate of the second vertex of the triangle patch, Represents the abscissa of the third vertex of the triangle patch, Represents the ordinate of the first vertex of the triangle patch. Represents the ordinate of the second vertex of the triangle patch, Represents the ordinate of the third vertex of the triangle patch.

[0036] Furthermore, in S46, the number of top triangles of the three-dimensional model is The calculation formula is:

[0037] ;

[0038] In the formula, Indicates the number of internal triangle patches;

[0039] The number of base triangles of the 3D model The calculation formula is:

[0040] ;

[0041] The number of side triangles of the 3D model The calculation formula is:

[0042] ;

[0043] In the formula, Indicates the length of the fine point coordinate array;

[0044] The size of the 3D model The calculation formula is:

[0045] .

[0046] The beneficial effects of the present invention are:

[0047] (1) Compared with existing manual design methods, the present invention can quickly generate a large number of structures, reducing the number of intermediate manpower and requiring no prior knowledge or design experience. Compared with local topology generation methods, the present invention is more random and global, and does not require consideration of complex constraints and design goals.

[0048] (2) The present invention can generate large-scale random structures by controlling the boundary of a rotating rigid body through an interpolation function, thereby generating the necessary data set for the data-driven method and promoting the application of the method in the field of behavior prediction and performance optimization of rotating rigid body structures; the present invention can interpolate the generation function in the entire random domain to achieve global randomness, avoid the perspective limitation caused by local randomness, and meet the quality requirements of the data set;

[0049] (3) The present invention can generate a large number of rotational rigid body structures with different characteristics in a short period of time, instead of designing them one by one, to meet the quantity requirements of the data set; it can be completely driven by Python code to achieve automatic structure generation, and generate two types of structures, rotational rigid body units and flexible hinges, which can be widely used in different research. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 A flowchart of a random generation method for a rotating rigid body structure based on interpolation boundaries;

[0051] Figure 2 It is the dimension diagram of the rotating rigid body unit;

[0052] Figure 3 It is a schematic diagram of the flexible hinge and its surrounding local structure;

[0053] Figure 4 It is a schematic diagram of a rotating rigid body unit;

[0054] Figure 5 Schematic diagram of triangulation of the flexible hinge and its surrounding local structure;

[0055] Figure 6 Schematic diagram of the boundary triangulation of a rotating rigid body unit. DETAILED DESCRIPTION

[0056] The embodiments of the present invention are further described below in conjunction with the accompanying drawings.

[0057] like Figure 1 As shown, the present invention provides a method for randomly generating a rotating rigid body structure based on an interpolation boundary, comprising the following steps:

[0058] S1. Generate a random domain according to the size of the rotating rigid body and determine several limit points;

[0059] S2, generating an interpolation function according to a number of limit points;

[0060] S3, using a number of fine points to draw an interpolation curve corresponding to the interpolation function, and transforming the interpolation curve to generate a flexible hinge and its surrounding local structure and a rotating rigid body unit;

[0061] S4. Generate a three-dimensional model of a rotating rigid body according to the flexible hinge, its surrounding local structure and the rotating rigid body unit.

[0062] This paper innovatively invented a global random scheme based on interpolation function to generate structural boundaries for the diversified generation of rotating rigid bodies and their data set construction. 2D / 3D rotating rigid body structures with boundary differences of any scale are generated by Python script driving, and output as .stl files in the form of meshes, thereby facilitating the construction of data-driven method data sets, promoting neural networks to learn concise geometric information and mechanical properties, and achieving rapid prediction and design.

[0063] The rigid unit of the rotational rigid structure is a centrally symmetrical figure, that is, its geometric outline can be obtained by multiple rotations and translations of an edge, and the shape of the edge can be specified by a certain function form. The present invention, represented by the interpolation curve, demonstrates the random generation technology of the rotational rigid unit matrix and its flexible hinge. The three main tasks of two-dimensional geometric outline specification, two-dimensional / three-dimensional geometric grid drawing and output, and large-scale data set generation are respectively realized, breaking through the bottlenecks of low randomness, low versatility and optimization difficulties of manually designed rotational rigid structures, solving the problems of small data quantity and low quality in the context of data-driven design, and laying a good foundation for high-fidelity machine learning model training.

[0064] In this embodiment of the present invention, S1 includes the following sub-steps:

[0065] S11. Determine the design domain of the rotating rigid body unit and the design domain of the flexible hinge;

[0066] S12, generating a random domain according to the design domain of the rotating rigid body unit and the design domain of the flexible hinge;

[0067] S13. Determine several limit points in the random domain.

[0068] In the embodiment of the present invention, in S11, the design domain of the rotating rigid body unit is a square, and the design domain of the flexible hinge is a rectangle;

[0069] like Figure 2 As shown, in S12, the range expression of the random domain is:

[0070] ;

[0071] In the formula, represents the horizontal axis of the random field, represents the ordinate of the random field, represents the side length of the square, Represents the length of the rectangle, Indicates the width of the rectangle.

[0072] is the coordinate of the two-dimensional random field. A certain number of limit points are sown in the random field, and a unique interpolation curve is determined by multiple limit points. The number of limit points is preferably [5,15]. Since the two-dimensional coordinates of the data points are used as features in the subsequent data set generation process, too many features will lead to difficulties in network training, cause dimensionality disasters, and exponentially increase the data volume requirements; and insufficient data points will lead to insufficient randomness of the curve and reduce the quality of the data set. In addition, in order to further reduce the characteristics of the data set and prevent the randomly generated limit points from being too close, resulting in the problem of too large / too small interpolation curve values, it is recommended to fix each (or several) limit points. Values, random only This method greatly improves the representability of the interpolation function while sacrificing a small amount of randomness, and reduces the risk of self-interpolation, over-largeness, and under-smallness of the function.

[0073] In this embodiment of the present invention, S2 includes the following sub-steps:

[0074] S21, generate an index value, and divide the index value into several parts;

[0075] S22, using a plurality of index values, mapping a plurality of limit points to a plurality of fine points;

[0076] S23. Generate an interpolation function using a number of fine points.

[0077] In the embodiment of the present invention, in S22, the fine point coordinates The expression is:

[0078] ;

[0079] In the formula, The horizontal coordinate represents the fine point coordinate, The ordinate represents the fine point coordinates, Indicates the index value.

[0080] The interpolation function is through the limit points The only thing that is determined is the number of limit points. , the sequence of the restriction site is ,Right now: After the interpolation function is generated through the limit point process, the fine point Draw a curve. Introduce index value ,have , subdivide the index within a range for The number of fine points is called ,at this time, and They are The mapping of .

[0081] In addition, for The mapping of the last mapping value less than 0 corresponds to Recorded as ; The last mapping value less than 5 corresponds to Recorded as In order to prevent the generated structure from experiencing obvious stress concentration during mechanical simulation, the function curve is not required to be smooth and continuous. Therefore, the alternative functions include polynomial interpolation, spline interpolation, Bezier curve, B-spline curve and Catmull-Rom spline. The meanings and mathematical expressions of these functions are as follows.

[0082] Polynomial interpolation: ;in, is a polynomial difference function with coefficients Determined by a system of linear equations. The polynomial interpolation method is simple to calculate, but the calculation complexity is high, and high-order polynomials may have the Runge phenomenon, resulting in a large deviation between the value of the interpolation polynomial at the edge of the interval and the actual value. It is suitable for scenarios with few data points and need to accurately pass through all data points.

[0083] Spline interpolation (taking cubic spline as an example): ;in, It is The spline function at points, coefficients It is determined by ensuring that the first and second order derivatives at the point are continuous. The spline interpolation method uses a low-order polynomial between every two data points, which effectively reduces the oscillation phenomenon and can control the smoothness of the curve, but the calculation is relatively complex and requires additional constraints to ensure the smoothness of the curve. It is suitable for scenarios with many data points and a need for smooth curves, such as those requiring continuous derivatives in engineering and scientific computing.

[0084] Bezier curve: ;in, is the Bernstein basis function.

[0085] B-spline curve: ;in, is the B-spline function, is the B-spline basis function, defined recursively, is the order of the spline. The B-spline curve method has the characteristics of local control. Changing a control point only affects part of the curve. The control points can be flexibly increased or decreased to adjust the curve, but the calculation complexity is high and the implementation is relatively complex. It is suitable for complex geometric modeling in CAD / CAM systems and scenarios that require high flexibility and local control.

[0086] Catmull-Rom spline: ;in, It is the Catmull-Rom spline function. The Catmull-Rom spline method is simple and easy to implement. It passes through all control points and maintains the slope of the curve endpoints, but overshoot may occur. For non-uniformly distributed control points, the curve may not be smooth enough. It is suitable for simple curve design and smoothing.

[0087] In the embodiment of the present invention, in S3, the calculation formula for transforming the interpolation curve is:

[0088]

[0090] In the formula, represents the abscissa of the interpolation curve, represents the ordinate of the interpolation curve, Indicates that the interpolation curve is intercepted, rotated 90° clockwise, and translated. The horizontal axis of Indicates that the interpolation curve is intercepted, rotated 90° clockwise, and translated. The vertical coordinate of Express The curve is rotated 90° clockwise and translated. The horizontal axis of Express The curve is rotated 90° clockwise and translated. The vertical coordinate of Express The horizontal coordinate of the curve after the curve is rotated 90° clockwise and translated. Express The vertical coordinate of the curve after the curve is rotated 90° clockwise and translated. represents the transposed matrix, represents the side length of the square, Indicates the width of the rectangle.

[0091] In this embodiment of the present invention, S4 includes the following sub-steps:

[0092] S41, determining the length of the smooth curve according to the fine point coordinates corresponding to the flexible hinge and its surrounding local structure and the rotating rigid body unit;

[0093] S42, using a cubic spline curve to determine the geometric contour of the rotating rigid body unit, and connecting it through an interpolation function to form a smooth curve;

[0094] S43, triangulating the smooth curve to generate a plurality of triangular facets;

[0095] S44, filtering out triangular face patches whose centroids are located inside the contour curve, and generating a plurality of internal triangular face patches;

[0096] S45, generating a geometric mesh using a plurality of internal triangular facets;

[0097] S46. Based on the geometric mesh, traverse the boundary coordinates of several internal triangular facets to generate a three-dimensional model.

[0098] In the embodiment of the present invention, in S45, the expression of the geometric grid is: ; In the formula, Represents the horizontal coordinate of the first vertex of the triangle patch, Represents the horizontal coordinate of the second vertex of the triangle patch, Represents the abscissa of the third vertex of the triangle patch, Represents the ordinate of the first vertex of the triangle patch. Represents the ordinate of the second vertex of the triangle patch, Represents the ordinate of the third vertex of the triangle patch.

[0099] In this embodiment of the present invention, in S46, the number of top triangles of the three-dimensional model The calculation formula is:

[0100] ;

[0101] In the formula, Indicates the number of internal triangle patches;

[0102] The number of base triangles of the 3D model The calculation formula is:

[0103] ;

[0104] The number of side triangles of the 3D model The calculation formula is:

[0105] ;

[0106] In the formula, Indicates the length of the fine point coordinate array;

[0107] The size of the 3D model The calculation formula is:

[0108] .

[0109] In the embodiment of the present invention, Figure 3 As shown in Figure 1, the flexible hinge and its surrounding local structure are composed of 8 line segments, among which curves ①②③④ are obtained by intercepting, translating and rotating the interpolation curve, and line segments ⑤⑥⑦⑧ are artificially drawn to generate closed geometric structures. The function representation of each line segment is shown in Table 1, and the coordinate origin is the (0,0) point of the random domain when generating the interpolation function. represents the interpolation function after fitting, Represents any fine point on the function coordinate, Represents any fine point on the function coordinate, and Indicates the set value.

[0110] Table 1

[0111]

[0112] like Figure 4 As shown in Figure 1, the rotating rigid body unit is composed of 8 segments, where curve ① is the original interpolation function, curve ② is obtained by intercepting, rotating and translating the interpolation curve ①, curve ③ is obtained by rotating and translating the interpolation curve ②, and curve ④ is obtained by rotating and translating the interpolation curve ③. They represent curves ①, ②, ③, and ④ respectively. is the clockwise rotation matrix. In addition, line segments ⑤⑥⑦⑧ are artificially drawn straight lines used to generate closed geometric structures, which are automatically generated when generating the mesh.

[0113] In the embodiment of the present invention, the .stl file is a triangular representation of the three-dimensional surface geometry, and the generation of the .stl file relies on mesh drawing and three-dimensional modeling.

[0114] like Figure 5 and Figure 6 As shown, the fine point coordinate array given by the flexible hinge and its surrounding local structure and rotating rigid body unit , whose length is defined as , use cubic spline curves to define the geometric outline of the rotating rigid body structure, and connect them through spline interpolation functions to form a smooth curve. Use the Lawson algorithm and Bowyer-Watson algorithm to implement the Delaunay triangulation network, triangulate these points, and generate a series of triangular facets. This algorithm can ensure that the generated triangles are as close to equilateral as possible, thereby improving the quality of the mesh.

[0115] The Lawson algorithm is as follows:

[0116] a) Build includes The super triangle of all points in △P O1 P O2 P O3 , forming the initial triangulation.

[0117] b) All points are inserted one by one into the existing triangulation In the , locate the point containing The triangle △P i P j P k .like Located in △P i P j P k Internally, connect it to the three vertices of the triangle to generate △P i P j P r , △P i P r P k , △P r P j P k Three triangles. Located in △P i P j P k On one edge of (assuming P i P j ), find P i P j The fourth vertex of another triangle ,Will Respectively , Connect them together so that they will be connected with P i P j The two triangles for the sides are divided into four triangles.

[0118] c) Check whether the newly generated edges meet the empty circle property. If not, perform edge flipping (replace the bad edge P i P j Flip to P r P k ), and perform empty circle detection on the newly generated edges. If there are bad edges, continue to flip until there are no bad edges. Repeat the operation to insert All points in .

[0119] d) The triangle △P O1 P O2 P O3 The vertices and edges of the triangles are deleted, and the remaining triangles form a point set Delaunay triangulation of T.

[0120] The Bowyer-Watson algorithm is as follows:

[0121] a) Build includes The super triangle of all points in △P O1 P O2 PO3 , forming the initial triangulation and placing it in the triangle list .

[0122] b) All points are inserted one by one into the existing triangulation in Find the circumcircle that contains the insertion point The triangle is called , delete the common edges of the affected triangles.

[0123] c) Connect all the vertices of the affected triangle to complete Linked list of Delaunay triangles Repeat the operation to insert All points in .

[0124] d) The super triangle △P O1 P O2 P O3 The vertices and edges of the triangles are deleted, and the remaining triangles form a point set Delaunay triangulation of T.

[0125] In the embodiment of the present invention, the edge of the three-dimensional model is defined by the coordinates in the two-dimensional array. Each internal triangle patch corresponds to a top face and a bottom face triangle, and each edge of the internal triangle patch corresponds to two side face triangles. Initialize the three-dimensional mesh object, size is the number of top, bottom, and side triangles , , The sum of .

[0126] Traverse the boundary coordinates of the internal triangle patch , for each patch, generate The top surface and The bottom surface of the patch generates two adjacent points on the bottom surface for each edge of the patch. The corresponding point of the top surface The two triangles, △P1P2P3 and △P2P4P3, form the side. The coordinates of are expressed as follows: , , and .

[0127] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for randomly generating a rotating rigid body structure based on an interpolation boundary, characterized in that: The following steps are involved: S1. Generate a random domain according to the size of the rotating rigid body and determine several limit points; S2, generating an interpolation function according to a number of limit points; S3, using a number of fine points to draw an interpolation curve corresponding to the interpolation function, and transforming the interpolation curve to generate a flexible hinge and its surrounding local structure and a rotating rigid body unit; S4. Generate a three-dimensional model of a rotating rigid body according to the flexible hinge, its surrounding local structure and the rotating rigid body unit.

2. The method for randomly generating a rotating rigid body structure based on an interpolation boundary according to claim 1, characterized in that: The S1 comprises the following sub-steps: S11. Determine the design domain of the rotating rigid body unit and the design domain of the flexible hinge; S12, generating a random domain according to the design domain of the rotating rigid body unit and the design domain of the flexible hinge; S13. Determine several limit points in the random domain.

3. The method for randomly generating a rotating rigid body structure based on an interpolation boundary according to claim 2, characterized in that: In S11, the design domain of the rotating rigid body unit is a square, and the design domain of the flexible hinge is a rectangle; In S12, the range expression of the random domain is: ； In the formula, represents the horizontal axis of the random field, represents the ordinate of the random field, represents the side length of the square, Represents the length of the rectangle, Indicates the width of the rectangle.

4. The method for randomly generating a rotating rigid body structure based on an interpolation boundary according to claim 1, characterized in that: The S2 comprises the following sub-steps: S21, generate an index value, and divide the index value into several parts; S22, using a plurality of index values, mapping a plurality of limit points to a plurality of fine points; S23. Generate an interpolation function using a number of fine points.

5. The method for randomly generating a rotating rigid body structure based on an interpolation boundary according to claim 4, characterized in that: In S22, the fine point coordinates The expression is: ； In the formula, The horizontal coordinate represents the fine point coordinate, The ordinate represents the fine point coordinates, Indicates the index value.

6. The method for randomly generating a rotating rigid body structure based on an interpolation boundary according to claim 1, characterized in that: In S3, the calculation formula for transforming the interpolation curve is: ； In the formula, represents the abscissa of the interpolation curve, represents the ordinate of the interpolation curve, Indicates that the interpolation curve is intercepted, rotated 90° clockwise, and translated. The horizontal axis of Indicates that the interpolation curve is intercepted, rotated 90° clockwise, and translated. The vertical coordinate of Express The curve is rotated 90° clockwise and translated. The horizontal axis of Express The curve is rotated 90° clockwise and translated. The vertical coordinate of Express The horizontal coordinate of the curve after the curve is rotated 90° clockwise and translated. Express The vertical coordinate of the curve after the curve is rotated 90° clockwise and translated. represents the transposed matrix, represents the side length of the square, Indicates the width of the rectangle.

7. The method for randomly generating a rotating rigid body structure based on an interpolation boundary according to claim 1, characterized in that: The S4 comprises the following sub-steps: S41, determining the length of the smooth curve according to the fine point coordinates corresponding to the flexible hinge and its surrounding local structure and the rotating rigid body unit; S42, using a cubic spline curve to determine the geometric contour of the rotating rigid body unit, and connecting it through an interpolation function to form a smooth curve; S43, triangulating the smooth curve to generate a plurality of triangular facets; S44, filtering out triangular face patches whose centroids are located inside the contour curve, and generating a plurality of internal triangular face patches; S45, generating a geometric mesh using a plurality of internal triangular facets; S46. Based on the geometric mesh, traverse the boundary coordinates of several internal triangular facets to generate a three-dimensional model.

8. The method for randomly generating a rotating rigid body structure based on an interpolation boundary according to claim 7, characterized in that: In S45, the expression of the geometric grid is: ; In the formula, Represents the horizontal coordinate of the first vertex of the triangle patch, Represents the horizontal coordinate of the second vertex of the triangle patch, Represents the abscissa of the third vertex of the triangle patch. Represents the ordinate of the first vertex of the triangle patch. Represents the ordinate of the second vertex of the triangle patch, Represents the ordinate of the third vertex of the triangle patch.

9. The method for randomly generating a rotating rigid body structure based on an interpolation boundary according to claim 7, characterized in that: In S46, the number of top triangles of the three-dimensional model The calculation formula is: ； In the formula, Indicates the number of internal triangle patches; The number of base triangles of the 3D model The calculation formula is: ； The number of side triangles of the 3D model The calculation formula is: ； In the formula, Indicates the length of the fine point coordinate array; The size of the three-dimensional model The calculation formula is: 。

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