CN114970283A - Geometric model structure detection method, device, equipment and storage medium - Google Patents

Abstract

The invention relates to a method, a device, equipment and a storage medium for detecting a geometric model structure. The method comprises the following steps: receiving an input geometric model; after confirming that the number of vertexes of two geometric surfaces to be detected in the geometric model is the same and that the vertexes of the geometric surfaces are associated with arc edges, calculating a periodic surface rotation transformation matrix according to the arc edges; and after confirming that the boundary points of the two geometric surfaces have one-to-one correspondence according to the periodic surface rotation transformation matrix, confirming that the two geometric surfaces are a pair of rotation periodic surfaces. According to the scheme provided by the invention, whether the two geometric surfaces to be detected in the geometric model are a pair of rotation period surfaces can be quickly judged, so that the grid generation efficiency is favorably improved, and the calculation efficiency and precision of numerical simulation are improved.

Description

Geometric model structure detection method, device, equipment and storage medium

technical field

The present invention relates to the technical field of data processing, and in particular, to a geometric model structure detection method, device, equipment and storage medium.

Background technique

In the field of computer aided engineering, it is necessary to generate meshes for the geometric surfaces of the geometric model. The mesh generation is the key to digital simulation technology, and it is very important to the simulation efficiency and accuracy. In the geometric model, a pair of rotating periodic surfaces refers to two geometric surfaces that can be completely coincident by rotating about a specific axis. In the process of meshing each geometric surface of the geometric model, if it is determined that there are two geometric surfaces in the geometric model as a pair of rotating periodic surfaces, after meshing one of the rotating periodic surfaces, according to the rotation period The mesh that has been generated on the surface can quickly generate another mesh of the rotating periodic surface, which is beneficial to improve the mesh generation efficiency of the geometric model. The coincident periodic surface grids can be further improved by the rotation transformation, which can further improve the accuracy and efficiency of numerical simulation calculations.

However, in the related art, it is impossible to judge whether the two geometric surfaces to be detected in the geometric model are a pair of rotating periodic surfaces, which affects the grid generation efficiency and reduces the calculation efficiency of the numerical simulation.

SUMMARY OF THE INVENTION

In order to solve or partially solve the problems existing in the related art, the present invention provides a geometric model structure detection method, device, equipment and storage medium, which can quickly determine whether the two geometric surfaces to be detected in the geometric model are a pair of rotating periodic surfaces. , which is beneficial to improve the grid generation efficiency and improve the computational efficiency and accuracy of numerical simulation.

A first aspect of the present invention provides a geometric model structure detection method, comprising:

receive the input geometry;

After confirming that the number of vertices of the two geometric surfaces to be detected in the geometric model is the same, and after confirming that the vertices of the geometric surfaces are associated with arc edges, calculate the rotation transformation matrix of the periodic surface according to the arc edges;

After confirming that there is a one-to-one correspondence between the boundary points of the two geometric surfaces according to the rotation transformation matrix of the periodic surface, it is confirmed that the two geometric surfaces are a pair of rotating periodic surfaces.

In an embodiment, the method of confirming that the vertices of the geometric surface are associated with arc edges includes:

Obtain the geometric edges associated with the vertices of the geometric face;

Collect three sampling points from the geometric edge, and calculate the circumcircle determined by the three sampling points;

After determining that the geometric edge is an arc edge according to the circumscribed circle, it is confirmed that the vertex of the geometric surface is associated with an arc edge.

In an embodiment, the method for determining that the geometric edge is an arc edge according to the circumscribed circle includes:

collecting a preset number of checkpoints from the geometric edge;

After confirming that each of the check points is on the plane of the circumscribed circle, and the distance between each of the check points and the center of the circumscribed circle is the radius of the circumscribed circle, it is determined that the geometric edge is a circle arc edge.

In an embodiment, the calculating the rotation transformation matrix of the periodic surface according to the arc edge includes:

According to the arc edge, determine the center of the circle corresponding to the arc edge, the target center angle, and the rotation axis vector perpendicular to the plane where the arc edge is located; wherein, the target center angle is determined according to the arc edge. The circumscribed circle of and the vertexes of the two geometric surfaces located on the circumscribed circle are determined;

According to the center of the circle, the target center angle and the rotation axis vector, a rotation transformation matrix of the periodic surface is calculated.

In an embodiment, calculating the rotation transformation matrix of the periodic surface according to the center of the circle, the target center angle and the rotation axis vector includes:

Determine the movement transformation matrix by moving the center of the circle to the origin in the pre-built three-dimensional coordinate system;

Determine a first rotation transformation matrix by rotating the rotation axis vector by a first rotation angle to a target coordinate plane on the three-dimensional coordinate system;

Determine a second rotation transformation matrix by rotating the rotation axis vector by a second rotation angle to the target coordinate axis on the three-dimensional coordinate system;

Determine a third rotation transformation matrix by rotating the rotation axis vector by an angle corresponding to the size of the target central angle;

Calculate a periodic plane rotation transformation matrix according to the movement transformation matrix, the first rotation transformation matrix, the second rotation transformation matrix and the third rotation transformation matrix;

Wherein, the target coordinate plane and the target coordinate axis, according to the projection length of the rotation axis vector on the three coordinate planes in the three-dimensional coordinate system, respectively, from the three coordinate planes in the three-dimensional coordinate system Matching with the three axes is determined.

In an embodiment, the method for confirming that there is a one-to-one correspondence between boundary points of the two geometric surfaces according to the periodic surface rotation transformation matrix includes:

According to the rotation transformation matrix of the periodic surface, transform the boundary point of one of the geometric surfaces to obtain a transformation result;

After confirming that the transformation result has a one-to-one correspondence with the boundary points of the other geometric surfaces, confirm that the boundary points of the two geometric surfaces have a one-to-one correspondence.

In one embodiment, the boundary points of the geometric surface include vertices of the geometric surface and end points on the geometric edges of the geometric surface.

A second aspect of the present invention provides a geometric model structure detection device, comprising:

A receiving module for receiving the input geometric model;

The calculation module is used to calculate the rotation of the periodic surface according to the circular arc edge after confirming that the number of vertices of the two geometric surfaces to be detected in the geometric model is the same, and after confirming that the vertices of the geometric surface are associated with an arc edge transformation matrix;

The confirmation module is configured to confirm that the two geometric surfaces are a pair of rotating periodic surfaces after confirming that there is a one-to-one correspondence between the boundary points of the two geometric surfaces according to the periodic surface rotation transformation matrix.

A third aspect of the present invention provides an electronic device, comprising:

processor; and

A memory having executable code stored thereon which, when executed by the processor, causes the processor to perform the method as described above.

A fourth aspect of the present invention provides a computer-readable storage medium on which executable codes are stored, and when the executable codes are executed by a processor of an electronic device, the processor is caused to execute the above method.

The technical scheme provided by the present invention can include the following beneficial effects:

In the method provided by the present invention, by receiving the input geometric model, after confirming that the number of vertices of the two geometric surfaces to be detected in the geometric model is the same, and after confirming that the vertices of the geometric surfaces are associated with arc edges, the cycle is calculated according to the arc edges. Surface rotation transformation matrix. After confirming that there is a one-to-one correspondence between the boundary points of the two geometric surfaces according to the periodic surface rotation transformation matrix, confirm that the two geometric surfaces are a pair of rotating periodic surfaces. In this way, it can be quickly determined whether the two geometric surfaces to be detected in the geometric model are a pair of rotating periodic surfaces, which is beneficial to improve the efficiency of grid generation and the calculation efficiency and accuracy of numerical simulation.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention.

Description of drawings

The above and other objects, features and advantages of the present invention will become more apparent from the detailed description of the exemplary embodiments of the present invention in conjunction with the accompanying drawings, wherein the same reference numerals generally refer to the exemplary embodiments of the present invention. same parts.

1 is a schematic flowchart of a method for detecting a geometric model structure according to an embodiment of the present invention;

2 is another schematic flowchart of the geometric model structure detection method shown in the embodiment of the present invention;

3 is a schematic structural diagram of a geometric model in a method for detecting a geometric model structure according to an embodiment of the present invention;

4 is a schematic diagram of the rotation process of the rotation vector axis in the geometric model structure detection method shown in the embodiment of the present invention;

5 is a schematic structural diagram of a geometric model structure detection device shown in an embodiment of the present invention;

FIG. 6 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.

specific embodiment

Embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although embodiments of the present invention are shown in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

The terminology used in the present invention is for the purpose of describing particular embodiments only and is not intended to limit the present invention. As used in this specification and the appended claims, the singular forms "a," "the," and "the" are intended to include the plural forms as well, unless the context clearly dictates otherwise. It will also be understood that the term "and/or" as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.

It should be understood that although the terms "first", "second", "third", etc. may be used in the present invention to describe various information, such information should not be limited by these terms. These terms are only used to distinguish the same type of information from each other. For example, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information, without departing from the scope of the present invention. Thus, a feature defined as "first" or "second" may expressly or implicitly include one or more of that feature. In the description of the present invention, "plurality" means two or more, unless otherwise expressly and specifically defined.

In the related art, it is impossible to judge whether the two geometric surfaces to be detected in the geometric model are a pair of rotating periodic surfaces, which affects the grid generation efficiency and reduces the computational efficiency and accuracy of the numerical simulation.

In view of the above problems, the embodiments of the present invention provide a geometric model structure detection method, which can quickly determine whether the two geometric surfaces to be detected in the geometric model are a pair of rotating periodic surfaces, which is beneficial to improve the grid generation efficiency and improve the calculation of numerical simulation. Efficiency and Precision.

The technical solutions of the embodiments of the present invention are described in detail below with reference to the accompanying drawings.

FIG. 1 is a schematic flowchart of a method for detecting a geometric model structure according to an embodiment of the present invention.

Referring to Figure 1, the method includes:

S101. Receive an input geometric model.

In this step, the geometric model input by the user is received. The geometric model may refer to a 3D model file, for example, a 3D model file in different formats such as step, iges, and stl.

S102. After confirming that the number of vertices of the two geometric surfaces to be detected in the geometric model is the same, and after confirming that the vertices of the geometric surfaces are associated with arc edges, calculate the rotation transformation matrix of the periodic surface according to the arc edges.

The two geometric surfaces to be detected in the geometric model may be two geometric surfaces pre-selected by the user.

The manner of confirming that the vertices of the geometric face are associated with arc edges may include: acquiring the geometric edges associated with the vertices of the geometric face. Collect three sample points from the geometric edge, and calculate the circumcircle determined by the three sample points. After judging that the geometric edge is an arc edge according to the circumscribed circle, confirm that the vertex of the geometric surface is associated with an arc edge.

In this step, calculating the rotation transformation matrix of the periodic surface according to the arc edge may include: determining the center corresponding to the arc edge, the target center angle and the rotation axis vector perpendicular to the plane where the arc edge is located, according to the arc edge. The target central angle is determined according to the circumcircle where the arc edge is located and the vertices of the two geometric surfaces located on the circumcircle. Calculate the rotation transformation matrix of the periodic surface according to the center of the circle, the center angle of the target circle and the vector of the rotation axis.

S103 , after confirming that there is a one-to-one correspondence between the boundary points of the two geometric surfaces according to the rotation transformation matrix of the periodic surface, confirm that the two geometric surfaces are a pair of rotating periodic surfaces.

The method of confirming that there is a one-to-one correspondence between the boundary points of the two geometric surfaces according to the rotation transformation matrix of the periodic surface includes: transforming the boundary point of one of the geometric surfaces according to the rotation transformation matrix of the periodic surface to obtain a transformation result. After confirming that the transformation result has a one-to-one correspondence with the boundary points of another geometric surface, confirm that there is a one-to-one correspondence between the boundary points of the two geometric surfaces.

The boundary points of the geometric surface include vertexes of the geometric surface and endpoints on the geometric edges of the geometric surface.

It can be seen from this embodiment that, in the method provided by the embodiment of the present invention, by receiving the input geometric model, the number of vertices of the two geometric surfaces to be detected is the same in the confirmation geometric model, and the vertices of the confirmed geometric surface are associated with arcs After the edge, calculate the rotation transformation matrix of the periodic surface according to the arc edge. After confirming that there is a one-to-one correspondence between the boundary points of the two geometric surfaces according to the rotation transformation matrix of the periodic surface, confirm that the two geometric surfaces are a pair of rotating periodic surfaces. In this way, it can be quickly determined whether the two geometric surfaces to be detected in the geometric model are a pair of rotating periodic surfaces, which is beneficial to improve the efficiency of grid generation and the calculation efficiency and accuracy of numerical simulation.

FIG. 2 is another schematic flowchart of a method for detecting a geometric model structure according to an embodiment of the present invention. FIG. 2 depicts the solution of the present invention in more detail with respect to FIG. 1 .

Referring to Figure 2, the method includes:

S201. Receive an input geometric model.

In this step, the geometric model input by the user is received. The geometric model may refer to a 3D model file, for example, a 3D model file in different formats such as step, iges, and stl.

S202. Confirm whether the number of vertices of the two geometric surfaces to be detected in the geometric model is the same.

The two geometric surfaces to be detected in the geometric model may be two geometric surfaces pre-selected by the user. Each geometric face is determined by the boundary formed by the geometric edge connection, and the vertex of the geometric face is the endpoint of the geometric edge. The two geometric surfaces to be detected may include a first geometric surface and a second geometric surface.

As shown in the geometric model in the embodiment of FIG. 3 , the two geometric surfaces to be detected in the geometric model are a first geometric surface A and a second geometric surface B, respectively. The first geometric surface A has four geometric edges, namely geometric edge A ₀ A ₁ , geometric edge A ₁ A ₂ , geometric edge A ₂ A ₃ , and geometric edge A ₀ A ₃ . The first geometric surface A has four vertices, namely vertex A ₀ , vertex A ₁ , vertex A ₂ , and vertex A ₃ . The second geometric surface B has four geometric edges, namely geometric edge B ₀ B ₁ , geometric edge B ₁ B ₂ , geometric edge B ₂ B ₃ , and geometric edge B ₀ B ₃ . The second geometric surface B has four vertices, namely, vertex B ₀ , vertex B ₁ , vertex B ₂ , and vertex B ₃ . It can be seen that the number of vertices of the first geometric surface A and the second geometric surface B is the same, and the number of vertices of the two geometric surfaces is four.

Further, the vertices of each geometric face can be recorded by building a set.

和

For example, in the embodiment of FIG. 3, the sets of vertices of the first geometric surface A and the second geometric surface B are:

and

It can be understood that since a pair of rotational periodic surfaces refers to two geometric surfaces that can be completely coincident by rotating around a specific axis, therefore, if the number of vertices of the two geometric surfaces is different, the two geometric surfaces are not a pair of rotational periodic surfaces.

In this step, if it is confirmed that the number of vertices of the two geometric faces to be detected in the geometric model is not the same, S203 is executed. If it is confirmed that the number of vertices of the two geometric faces to be detected in the geometric model is the same, S204 is executed.

S203, output the confirmation result that the two geometric surfaces are not a pair of rotating periodic surfaces.

In this step, the confirmation result that the two geometric surfaces are not a pair of rotational periodic surfaces is output, that is, it is confirmed that the two geometric surfaces to be detected in the geometric model are not a pair of rotational periodic surfaces.

S204 , confirming whether the vertices of the geometric surface are associated with arc edges.

In one of the embodiments, the method of confirming that the vertices of the geometric faces are associated with arc edges includes:

S204-1. Obtain the geometric edges associated with the vertices of the geometric surface.

记录。In this step, each geometric edge associated with each vertex of one of the geometric faces can be obtained. For example, each geometric edge associated with each vertex of the first geometric face is obtained. The geometric edges associated with vertices can use sets

Record.

As in the embodiment of FIG. 3 , each geometric edge associated with each vertex A _i of the first geometric surface A may be obtained, where i<4 and i≥0. For example, the geometric edges associated with vertex A ₀ are: geometric edge A ₀ A ₃ , geometric edge A ₀ A ₁ , and geometric edge A ₀ B ₀ .

S204-2, collect three sampling points from the geometric edge, and calculate the circumcircle determined by the three sampling points.

It should be noted that this step can be performed on each geometric edge obtained in S204-1. For example, in the embodiment of FIG. 3 , three sampling points are collected at geometric edge A ₀ A ₃ , three sampling points are collected at geometric edge A ₀ A ₁ , and three sampling points are collected at geometric edge A ₀ B ₀ .

It can be understood that three points can determine a unique circumcircle. Suppose the three sampling points are points P1, P2 and P3 respectively, and the formula for calculating the center of the circumcircle determined by the three sampling points is:

The radius of the circumscribed circle is the distance from the center C to any point among the points P1, P2 and P3.

S204-3, after determining that the geometric edge is an arc edge according to the circumscribed circle, confirm that the vertex of the geometric surface is associated with an arc edge.

In the embodiment of FIG. 3, it can be understood that the geometric edge A ₀ A ₃ and the geometric edge A ₀ A ₁ are straight geometric edges, and the three sampling points collected on the geometric edge A ₀ A ₃ and the geometric edge A ₀ A ₁ cannot be The calculation determines the circumcircle. If the three sampling points collected on the geometric edge A ₀ B ₀ can be calculated to determine the circumscribed circle, it can be determined whether the geometric edge A ₀ B ₀ is an arc edge according to the circumscribed circle.

In one of the embodiments, the manner of determining that the geometric edge is an arc edge according to the circumscribed circle may include:

S204-3-1. Collect a preset number of check points from geometric edges.

For example, in the embodiment of FIG. 3 , a preset number of check points are collected from the geometric edge A ₀ B ₀ , for example, 5 check points are collected, and the check points collected from the geometric edge are different from the sampling points. In order to improve processing efficiency and reduce computational overhead, the preset number can be set to be less than or equal to three.

S204-3-2. After confirming that each check point is on the plane of the circumscribed circle, and the distance between each check point and the center of the circumscribed circle is the radius of the circumscribed circle, determine that the geometric edge is an arc edge.

For example, in the embodiment of FIG. 3 , each check point collected from the geometric edge A ₀ B ₀ is on the plane of the circumscribed circle, and the distance between each check point and the center C of the circumscribed circle is the radius of the circumscribed circle (ie The distance from the center C to any point among the points P1, P2 and P3), it can be judged that the geometric edge A ₀ B ₀ is an arc edge. In this way, it can be confirmed that the vertex of the first geometric surface A in the embodiment of FIG. 3 is associated with an arc edge, that is, it can be confirmed that the vertex of one of the geometric surfaces to be detected in the geometric model is associated with an arc edge.

In S204, if it is confirmed that no arc edge is associated with the vertex of the geometric surface, S203 is executed. If it is confirmed that the vertices of the geometric surface are associated with arc edges, S205 is executed.

S205 , according to the arc edge, determine the center of the circle corresponding to the arc edge, the target center angle, and the rotation axis vector perpendicular to the plane where the arc edge is located. The target central angle is determined according to the circumcircle where the arc edge is located and the vertices of the two geometric surfaces located on the circumcircle.

It can be understood that, if it is confirmed in S204 that the vertices of the geometric surface are associated with a plurality of arc edges, S205 can be executed for each arc edge respectively.

可以理解，根据圆弧边所在平面可以确定平面法向量，旋转轴向量

可以是指该平面法向量。根据该平面法向量与圆心C，则可以确定旋转轴。目标圆心角θ根据圆弧边所在的外接圆以及位于外接圆上的两个几何面的顶点确定。可以理解，如果第二几何面上也存在顶点在外接圆上，则根据第一几何面上位于外接圆上的顶点和第二几何面上同在外接圆上顶点可以计算目标圆心角θ。目标圆心角θ为：第一几何面位于外接圆上的顶点与圆心的连线，与第二几何面位于外接圆上的顶点与圆心的连线之间的夹角。In this step, according to the arc edge, the center C corresponding to the arc edge, the target center angle θ, and the rotation axis vector perpendicular to the plane where the arc edge is located can be determined

It can be understood that the plane normal vector and the rotation axis vector can be determined according to the plane where the arc edge is located.

Can refer to the plane normal vector. According to the plane normal vector and the circle center C, the rotation axis can be determined. The target central angle θ is determined according to the circumcircle where the arc edge is located and the vertices of the two geometric surfaces located on the circumcircle. It can be understood that if there are vertices on the circumscribed circle on the second geometric surface, the target central angle θ can be calculated according to the vertices on the first geometric surface and the vertices on the circumscribed circle on the second geometric surface. The target central angle θ is the included angle between the line connecting the vertex of the first geometric surface on the circumcircle and the center of the circle and the line connecting the vertex of the second geometric surface on the circumcircle and the center of the circle.

与向量

之间的夹角(由于第二几何面的顶点B0在外接圆上)。换句话说，向量

与向量

之间的旋转角的大小为目标圆心角θ。旋转轴向量

的起始点可以为圆心C，且旋转轴向量

可以垂直于圆弧边A₀B₀所在的平面。In the embodiment of Fig. 3, for the confirmed arc edge A ₀ B ₀ , the target central angle θ is a vector

with vector

The included angle between (because the vertex B0 of the second geometric face is on the circumcircle). In other words, the vector

with vector

The size of the rotation angle between them is the target central angle θ. Rotation axis vector

The starting point of can be the center C, and the rotation axis vector

Can be perpendicular to the plane where the arc edge A ₀ B ₀ is located.

S206: Calculate the rotation transformation matrix of the periodic surface according to the center of the circle, the angle of the target center of the circle, and the vector of the rotation axis.

It should be noted that the rotation transformation matrix of the periodic surface is calculated according to the rotation axis vector, the center of the circumcircle, and the central angle of the target circle. Correspondence can be determined. That is to say, the positions of the vertices on the first geometric surface associated with the arc edge, transformed by the periodic surface rotation transformation matrix, are the same as the positions of the other vertices on the circumcircle of the second geometric surface.

In one of the embodiments, according to the center of the circle, the target center angle and the rotation axis vector, calculating the rotation transformation matrix of the periodic surface may include:

S206-1. Determine the movement transformation matrix by moving the center of the circle to the origin in the pre-built three-dimensional coordinate system.

Remember the coordinates of the center C as (C _x , C _y , C _z ), and determine the movement transformation matrix T by moving the center C to the origin O in the pre-built three-dimensional coordinate system:

S206-2: Determine the first rotation transformation matrix by rotating the rotation axis vector by the first rotation angle α to the target coordinate plane on the three-dimensional coordinate system.

的坐标为(n_x,n_y,n_z)。Among them, the rotation axis vector

The coordinates are (n _x , n _y , n _z ).

的起点可以为三维坐标系中的原点O。通过将旋转轴向量

旋转第一旋转角α至三维坐标系上的目标坐标平面，可以确定第一旋转变换矩阵R_α。In this step, after moving the center of the circle to the origin in the pre-built three-dimensional coordinate system through S206-1, the rotation axis vector

The starting point can be the origin O in the three-dimensional coordinate system. By turning the axis of rotation vector

The first rotation transformation matrix R _α can be determined by rotating the first rotation angle α to the target coordinate plane on the three-dimensional coordinate system.

可以绕其中一个坐标轴旋转第一旋转角α至三维坐标系上的目标坐标平面，也就说，经过旋转后，旋转轴向量

位于目标坐标平面上。It should be noted that the three-dimensional coordinate system includes three coordinate planes, namely the X0Z plane, the XOY plane, and the YOZ plane. The target coordinate plane is one of the three coordinate planes. The three-dimensional coordinate system also includes three coordinate axes, which are an X coordinate axis, a Y coordinate axis, and a Z coordinate axis. Rotation axis vector

You can rotate the first rotation angle α around one of the coordinate axes to the target coordinate plane on the three-dimensional coordinate system, that is to say, after the rotation, the rotation axis vector

on the target coordinate plane.

S206-3. Determine the second rotation transformation matrix by rotating the rotation axis vector by the second rotation angle β to the target coordinate axis on the three-dimensional coordinate system.

旋转第二旋转角β至三维坐标系上的目标坐标轴，可以确定第二旋转变换矩阵R_β。In this step, the rotation axis vector located on the target coordinate plane can be

The second rotation transformation matrix R _β can be determined by rotating the second rotation angle β to the target coordinate axis on the three-dimensional coordinate system.

可以绕其中一个坐标轴旋转角α到目标坐标平面，再根据第二旋转角β变换至三维坐标系上的目标坐标轴。也就是说，经过旋转后，旋转轴向量

位于目标坐标轴上，旋转轴向量

与目标坐标轴重合。It should be noted that the target coordinate axis is one of the three coordinate axes in the three-dimensional coordinate system. Rotation axis vector

The angle α can be rotated around one of the coordinate axes to the target coordinate plane, and then transformed to the target coordinate axis on the three-dimensional coordinate system according to the second rotation angle β. That is to say, after rotation, the rotation axis vector

On the target axis, the rotation axis vector

coincides with the target axis.

S206-4: Determine a third rotation transformation matrix by rotating the rotation axis vector by an angle corresponding to the size of the target central angle.

旋转对应目标圆心角大小的角度θ，确定第三旋转变换矩阵R_θ。In this step, the rotation axis vector located on the target coordinate axis can be

Rotate the angle θ corresponding to the size of the central angle of the target circle to determine the third rotation transformation matrix R _θ .

S206-5: Calculate the periodic plane rotation transformation matrix according to the movement transformation matrix, the first rotation transformation matrix, the second rotation transformation matrix and the third rotation transformation matrix.

According to the movement transformation matrix T, the first rotation transformation matrix R _α , the second rotation transformation matrix R _β and the third rotation transformation matrix R _θ , the periodic plane rotation transformation matrix R is calculated.

In one of the embodiments, the calculation formula of the periodic surface rotation transformation matrix R is:

分别为T、R_α、R_β的逆矩阵，即通过对T、R_α、R_β进行逆变换得到。Among them, T ^-1 ,

are the inverse matrices of T, R _α , and R _β respectively, that is, obtained by inverse transformation of T, R _α , and R _β .

分别在三维坐标系中三个坐标平面(即X0Z平面、XOY平面、YOZ平面)上的投影长度，从三维坐标系中的三个坐标平面(即X0Z平面、XOY平面、YOZ平面)与三个坐标轴(即X坐标轴、Y坐标轴、Z坐标轴)中匹配确定。It should be noted that the target coordinate plane and the target coordinate axis are based on the rotation axis vector

The projection lengths on the three coordinate planes (ie X0Z plane, XOY plane, YOZ plane) in the three-dimensional coordinate system respectively, from the three coordinate planes in the three-dimensional coordinate system (ie X0Z plane, XOY plane, YOZ plane) and three The matching is determined in the coordinate axes (ie, the X coordinate axis, the Y coordinate axis, and the Z coordinate axis).

的坐标为(n_x,n_y,n_z)。Rotation axis vector

The coordinates are (n _x , n _y , n _z ).

的长度L的计算公式为：Rotation axis vector

The formula for calculating the length L is:

分别在YOZ平面的投影长度L_YZ、在X0Z平面的投影长度L_ZX、在XOY平面的投影长度L_XY分别为：Rotation axis vector

The projected length L _YZ on the YOZ plane, the projected length L _ZX on the X0Z plane, and the projected length L _XY on the XOY plane are respectively:

In one of the embodiments, according to the size of the three projection lengths (ie L _YZ , L _ZX , L _XY ), the following three cases (1), (2) and (3) are matched to determine the target coordinate plane and the target coordinate axis, and calculate the values of the first rotation transformation matrix R _α , the second rotation transformation matrix R _β and the third rotation transformation matrix R _θ .

在YOZ平面的投影长度L_YZ最大的情况下(即在L_YZ、L_ZX、L_XY中L_YZ的值最大)。(1) Rotation axis vector

In the case where the projected length L _YZ of the YOZ plane is the largest (that is, the value of L _YZ is the largest among L _YZ , L _ZX , and L _XY ).

The matching determines that the target coordinate plane is the X0Z plane, and the target coordinate axis is the Z coordinate axis.

绕X坐标轴旋转第一旋转角α至X0Z平面(目标坐标平面)，然后，再绕Y坐标轴旋转第二旋转角β至Z坐标轴(目标坐标轴)，使得旋转轴向量

与Z坐标轴重合。Corresponding to S206-2 to S206-4, see Fig. 4, the rotation axis vector

Rotate the first rotation angle α around the X coordinate axis to the X0Z plane (target coordinate plane), and then rotate the second rotation angle β around the Y coordinate axis to the Z coordinate axis (target coordinate axis), so that the rotation axis vector

Coincides with the Z coordinate axis.

旋转至目标坐标平面上需要依据第一环绕轴进行，也就是说，旋转轴向量

绕第一环绕轴旋转第一旋转角α至目标坐标平面。旋转轴向量

旋转至目标坐标轴上需要依据第二环绕轴进行，也就是说，旋转轴向量

绕第二环绕轴旋转第二旋转角β至目标坐标轴。It can be understood that the rotation axis vector

Rotation to the target coordinate plane needs to be performed according to the first surrounding axis, that is, the rotation axis vector

Rotate the first rotation angle α around the first surrounding axis to the target coordinate plane. Rotation axis vector

Rotation to the target coordinate axis needs to be performed according to the second surrounding axis, that is, the rotation axis vector

Rotate the second rotation angle β around the second surrounding axis to the target coordinate axis.

在YOZ平面的投影长度L_YZ最大的情况下，第一环绕轴为X坐标轴，第二环绕轴为Y坐标轴。vector in the axis of rotation

In the case where the projected length L _YZ of the YOZ plane is the largest, the first surrounding axis is the X coordinate axis, and the second surrounding axis is the Y coordinate axis.

The first rotation transformation matrix R _α , the second rotation transformation matrix R _β and the third rotation transformation matrix R _θ are respectively:

in,

在X0Z平面的投影长度L_ZX最大的情况下(即在L_YZ、L_ZX、L_XY中L_ZX的值最大)。(2) Rotation axis vector

In the case where the projected length L _ZX of the X0Z plane is the largest (that is, the value of L _ZX is the largest among L _YZ , L _ZX , and L _XY ).

The matching determines that the target coordinate plane is the X0Y plane, and the target coordinate axis is the X coordinate axis.

绕Y坐标轴旋转第一旋转角α至X0Y平面(目标坐标平面)，然后，再绕Z坐标轴旋转第二旋转角β至X坐标轴(目标坐标轴)，使得旋转轴向量

与X坐标轴重合。Corresponding to S206-2 to S206-4, the rotation axis vector

Rotate the first rotation angle α around the Y coordinate axis to the X0Y plane (target coordinate plane), and then rotate the second rotation angle β around the Z coordinate axis to the X coordinate axis (target coordinate axis), so that the rotation axis vector

coincides with the X-axis.

旋转至目标坐标平面上需要依据第一环绕轴进行，也就是说，旋转轴向量

绕第一环绕轴旋转第一旋转角α至目标坐标平面。旋转轴向量

旋转至目标坐标轴上需要依据第二环绕轴进行，也就是说，旋转轴向量

绕第二环绕轴旋转第二旋转角β至目标坐标轴。It can be understood that the rotation axis vector

Rotation to the target coordinate plane needs to be performed according to the first surrounding axis, that is, the rotation axis vector

Rotate the first rotation angle α around the first surrounding axis to the target coordinate plane. Rotation axis vector

Rotation to the target coordinate axis needs to be performed according to the second surrounding axis, that is, the rotation axis vector

Rotate the second rotation angle β around the second surrounding axis to the target coordinate axis.

在XOZ平面的投影长度L_ZX最大的情况下，第一环绕轴为Y坐标轴，第二环绕轴为Z坐标轴。vector in the axis of rotation

In the case where the projected length L _ZX of the XOZ plane is the largest, the first surrounding axis is the Y coordinate axis, and the second surrounding axis is the Z coordinate axis.

The first rotation transformation matrix R _α , the second rotation transformation matrix R _β and the third rotation transformation matrix R _θ are respectively:

in,

在XOY平面的投影长度L_XY最大的情况下(即在L_YZ、L_ZX、L_XY中L_XY的值最大)。(3) Rotation axis vector

In the case where the projected length L _XY of the XOY plane is the largest (that is, the value of L _XY is the largest among L _YZ , L _ZX , and L _XY ).

The matching determines that the target coordinate plane is the YOZ plane, and the target coordinate axis is the Y coordinate axis.

绕Z坐标轴旋转第一旋转角α至YOZ平面(目标坐标平面)，然后，再绕X坐标轴旋转第二旋转角β至Y坐标轴(目标坐标轴)，使得旋转轴向量

与Y坐标轴重合。Corresponding to S206-2 to S206-4, the rotation axis vector

Rotate the first rotation angle α around the Z coordinate axis to the YOZ plane (target coordinate plane), and then rotate the second rotation angle β around the X coordinate axis to the Y coordinate axis (target coordinate axis), so that the rotation axis vector

coincides with the Y axis.

旋转至目标坐标平面上需要依据第一环绕轴进行，也就是说，旋转轴向量

绕第一环绕轴旋转第一旋转角α至目标坐标平面。旋转轴向量

旋转至目标坐标轴上需要依据第二环绕轴进行，也就是说，旋转轴向量

绕第二环绕轴旋转第二旋转角β至目标坐标轴。It can be understood that the rotation axis vector

Rotation to the target coordinate plane needs to be performed according to the first surrounding axis, that is, the rotation axis vector

Rotate the first rotation angle α around the first surrounding axis to the target coordinate plane. Rotation axis vector

Rotation to the target coordinate axis needs to be performed according to the second surrounding axis, that is, the rotation axis vector

Rotate the second rotation angle β around the second surrounding axis to the target coordinate axis.

在XOY平面的投影长度L_XY最大的情况下，第一环绕轴为Z坐标轴，第二环绕轴为X坐标轴。vector in the axis of rotation

In the case where the projected length LXY of the XOY plane is the largest, the first surrounding axis is the Z coordinate axis, and the second surrounding axis is the _X coordinate axis.

The first rotation transformation matrix R _α , the second rotation transformation matrix R _β and the third rotation transformation matrix R _θ are respectively:

in,

It can be understood that after the center of the circle is moved to the origin in the pre-built three-dimensional coordinate system, and the rotation axis vector is transformed twice by the first rotation angle α and the second rotation angle β, the rotation axis vector coincides with the target axis, The vertex of the associated arc edge on the first geometric surface can be transformed to the position of another vertex on the same circumcircle on the second geometric surface by rotating the angle corresponding to the size of the target central angle. The rotation transformation matrix R of the periodic surface obtained by the above calculation determines the transformation relationship between the two vertices on the first and second geometric surfaces. It can be seen that, according to the calculated periodic surface rotation transformation matrix R, it can be used to detect whether two geometric surfaces are a pair of rotating periodic surfaces.

S207 , confirming whether there is a one-to-one correspondence between the boundary points of the two geometric surfaces according to the rotation transformation matrix of the periodic surface.

In this step, if it is confirmed that there is no one-to-one correspondence between the boundary points of the two geometric surfaces according to the rotation transformation matrix of the periodic surface, S203 is executed. If it is confirmed that there is a one-to-one correspondence between the boundary points of the two geometric surfaces according to the rotation transformation matrix of the periodic surface, S208 is executed.

It should be noted that, if it is confirmed in S204 that the vertices of the geometric surface are associated with a plurality of circular arc edges, for the plurality of periodic surface rotation transformation matrices obtained by calculating respectively for the plurality of circular arc edges and the circumscribed circle, rotate according to one of the periodic surfaces. The transformation matrix confirms that there is a one-to-one correspondence between the boundary points of the two geometric surfaces, then execute S208; otherwise, execute S203. That is to say, it can be confirmed that there is a one-to-one correspondence between the boundary points of the two geometric surfaces through the rotation transformation matrix of one of the periodic surfaces, and then S208 is performed, otherwise, S203 is performed.

In one of the embodiments, the method of confirming that there is a one-to-one correspondence between the boundary points of the two geometric surfaces according to the rotation transformation matrix of the periodic surface may include:

S207-1, according to the rotation transformation matrix of the periodic surface, transform the boundary point of one of the geometric surfaces to obtain a transformation result.

In the embodiment shown in FIG. 3 , the boundary points of the first geometric plane A are transformed according to the periodic plane rotation transformation matrix R to obtain a transformation result.

The boundary points of the geometric surface include vertexes of the geometric surface and endpoints on the geometric edges of the geometric surface. That is, the boundary points of the first geometric surface A may be vertex A ₀ , vertex A ₁ , vertex A ₂ , and vertex A ₃ . The boundary point of the first geometric surface A may also be the end point on the geometric edge A ₀ A ₁ , the geometric edge A ₁ A ₂ , the geometric edge A ₂ A ₃ , and the geometric edge A ₀ A ₃ .

For example, transform the boundary point A ₀ of the first geometric surface A to obtain the transformation result a ₀ .

S207-2. After confirming that the transformation result has a one-to-one correspondence with the boundary points of another geometric surface, confirm that the boundary points of the two geometric surfaces have a one-to-one correspondence.

That is to say, the positions corresponding to the transformation results are mapped one-to-one on the corresponding boundary points of another geometric surface, and it can be confirmed that there is a one-to-one correspondence between the boundary points of the two geometric surfaces.

For example, in the embodiment of FIG. 3 , if there is a one-to-one correspondence between the boundary points of the two geometric surfaces, the boundary point A ₀ of the first geometric surface A is transformed to obtain the transformation result a ₀ . The position corresponding to the transformation result a ₀ is the boundary point B ₀ of the second geometric surface B.

For another example, in the embodiment of FIG. 3 , if there is a one-to-one correspondence between the boundary points of the first geometric surface A and the boundary points of the second geometric surface B, the vertices A ₀ , A ₁ , A ₂ , A ₃ , the transformation result after transformation is performed according to the rotation transformation matrix R of the periodic surface, corresponding to the vertices B ₀ , B ₁ , B ₂ , and B ₃ on the second geometric surface B, respectively.

For another example, in the embodiment of FIG. 3 , if there is a one-to-one correspondence between the boundary points of the first geometric surface A and the boundary points of the second geometric surface B, the endpoint A on the geometric edge A ₀ A ₁ of the first geometric surface A ₀ , the transformation result after transformation is performed according to the rotation transformation matrix R of the periodic surface, which corresponds to the endpoint B ₀ on the corresponding geometric edge B ₀ B ₁ on the second geometric surface B. The endpoint A ₁ on the geometric edge A ₀ A ₁ of the first geometric surface A, the transformation result after the transformation is performed according to the periodic surface rotation transformation matrix R, corresponds to the corresponding geometric edge B ₀ B ₁ on the second geometric surface B. Endpoint B ₁ . In other words, the boundary ring of the first geometric surface A is A ₀ A ₁ A ₂ A ₃ , and the boundary ring of the second geometric surface B is B ₀ B ₁ B ₂ B ₃ . For any geometry of the first geometric surface A Edge A _i A _{(i+1)% 4} , any geometric edge B _i B _(i+1) % 4 of the second geometric surface B, where 0≤i<4, % is the remainder symbol. The endpoints on the geometric edge A _i A _{(i+1)% 4} can be in a one-to-one correspondence with the endpoint positions of the geometric edge B _i B _{(i+1) % 4} after being transformed by the periodic surface rotation transformation matrix R. That is to say, by checking whether there is a one-to-one correspondence between the end points of the geometric edges of one of the geometric surfaces and the corresponding end points of the geometric edges of the other geometric surface, it is determined whether the geometric edges on the two geometric surfaces are in a one-to-one correspondence.

To sum up, transform the boundary points of one of the geometric surfaces according to the rotation transformation matrix of the periodic surface. If the transformation result has a one-to-one correspondence with the boundary points of the other geometric surface, confirm that the boundary points of the two geometric surfaces exist one-to-one. Correspondence. Specifically, according to the rotation transformation matrix of the periodic surface, the vertices of one of the geometric surfaces are transformed. If there is a one-to-one correspondence between the transformation result and the vertices of the other geometric surface, and according to the rotation transformation matrix of the periodic surface, the vertices of one of the geometric surfaces are transformed according to the rotation transformation matrix of the periodic surface. The two endpoints on one of the geometric edges are transformed. If the transformation result has a one-to-one correspondence with the two endpoints on the corresponding geometric edge on the other geometric surface, confirm that the boundary points of the two geometric surfaces have a one-to-one correspondence. relation.

S208, output the confirmation result that the two geometric surfaces are a pair of rotating periodic surfaces.

In this step, the confirmation result that the two geometric surfaces are a pair of rotating periodic surfaces is output, that is, it is confirmed that the two geometric surfaces to be detected in the geometric model are a pair of rotating periodic surfaces.

For example, in the embodiment of FIG. 3 , it can be confirmed that the first geometric surface A and the second geometric surface B are a pair of rotational periodic surfaces.

It can be seen from this embodiment that the method provided by the embodiment of the present invention can quickly determine whether the two geometric surfaces to be detected in the geometric model are a pair of rotating periodic surfaces, which is beneficial to improve the efficiency of grid generation and the calculation efficiency of numerical simulation .

Corresponding to the foregoing application function implementation method embodiments, the present invention further provides a geometric model structure detection device, an electronic device, and corresponding embodiments.

FIG. 5 is a schematic structural diagram of an apparatus for detecting a geometric model structure according to an embodiment of the present invention.

Referring to FIG. 5 , a geometric model structure detection device 50 includes: a receiving module 510 , a calculating module 520 and a confirming module 530 .

The receiving module 510 is used for receiving the input geometric model.

The calculation module 520 is used to calculate the rotation transformation matrix of the periodic surface according to the circular arc edge after confirming that the number of vertices of the two geometric surfaces to be detected in the geometric model is the same and that the vertices of the geometric surface are associated with the arc edge.

The confirmation module 530 is configured to confirm that the two geometric surfaces are a pair of rotating periodic surfaces after confirming that there is a one-to-one correspondence between the boundary points of the two geometric surfaces according to the rotation transformation matrix of the periodic surface.

It can be seen from this embodiment that the device 50 provided by the embodiment of the present invention can quickly determine whether the two geometric surfaces to be detected in the geometric model are a pair of rotating periodic surfaces, which is beneficial to improve the grid generation efficiency and improve the calculation of numerical simulation Efficiency and Precision.

Regarding the apparatus in the above-mentioned embodiment, the specific manner in which each module performs the operation has been described in detail in the embodiment of the method, and will not be described in detail here.

FIG. 6 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.

Referring to FIG. 6 , an electronic device 600 includes a memory 610 and a processor 620 .

The processor 620 may be a central processing unit (Central Processing Unit, CPU), other general-purpose processors, a digital signal processor (Digital Signal Processor, DSP), an application specific integrated circuit (Application Specific Integrated Circuit, ASIC), a field-available processor Field-Programmable Gate Array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.

Memory 610 may include various types of storage units, such as system memory, read only memory (ROM), and persistent storage. The ROM may store static data or instructions required by the processor 620 or other modules of the computer. Persistent storage devices may be readable and writable storage devices. Permanent storage may be a non-volatile storage device that does not lose stored instructions and data even if the computer is powered off. In some embodiments, persistent storage devices employ mass storage devices (eg, magnetic or optical disks, flash memory) as persistent storage devices. In other embodiments, the persistent storage device may be a removable storage device (eg, a floppy disk, an optical drive). System memory can be a readable and writable storage device or a volatile readable and writable storage device, such as dynamic random access memory. System memory can store some or all of the instructions and data that the processor needs at runtime. Additionally, memory 610 may include any combination of computer-readable storage media, including various types of semiconductor memory chips (eg, DRAM, SRAM, SDRAM, flash memory, programmable read only memory), and magnetic and/or optical disks may also be employed. In some embodiments, memory 610 may include a removable storage device that is readable and/or writable, such as a compact disc (CD), a read-only digital versatile disc (eg, DVD-ROM, dual-layer DVD-ROM), Read-only Blu-ray Disc, Ultra-Density Disc, Flash Card (eg SD Card, Min SD Card, Micro-SD Card, etc.), Magnetic Floppy Disk, etc. Computer-readable storage media do not contain carrier waves and transient electronic signals transmitted over wireless or wireline.

Executable codes are stored on the memory 610, and when the executable codes are processed by the processor 620, the processor 620 can be caused to execute some or all of the above-mentioned methods.

Furthermore, the method according to the present invention can also be implemented as a computer program or computer program product comprising computer program code instructions for performing some or all of the steps in the above-described method of the present invention.

Alternatively, the present invention can also be implemented as a computer-readable storage medium (or a non-transitory machine-readable storage medium or a machine-readable storage medium) having executable code (or computer program or computer instruction code) stored thereon, When the executable code (or computer program or computer instruction code) is executed by a processor of an electronic device (or server, etc.), the processor is caused to perform some or all of the steps of the above-described method according to the present invention.

Various embodiments of the present invention have been described above, and the foregoing descriptions are exemplary, not exhaustive, and not limiting of the disclosed embodiments. Numerous modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or improvement over the technology in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.

Claims (10)

1. A geometric model structure detection method is characterized by comprising the following steps:

receiving an input geometric model;

after confirming that the number of vertexes of two geometric surfaces to be detected in the geometric model is the same and that the vertexes of the geometric surfaces are associated with arc edges, calculating a periodic surface rotation transformation matrix according to the arc edges;

and after confirming that the boundary points of the two geometric surfaces have one-to-one correspondence according to the periodic surface rotation transformation matrix, confirming that the two geometric surfaces are a pair of rotation periodic surfaces.

2. The method according to claim 1, wherein the confirming that the vertex of the geometric surface is associated with the arc edge comprises:

acquiring a geometric edge associated with a vertex of the geometric surface;

collecting three sampling points from the geometric side, and calculating circumscribed circles determined by the three sampling points;

and after judging that the geometric side is an arc side according to the circumscribed circle, confirming that the vertex of the geometric surface is associated with the arc side.

3. The method according to claim 2, wherein the determining that the geometric side is a circular arc side according to the circumscribed circle comprises:

collecting a preset number of check points from the geometric side;

and after confirming that each check point is on the plane of the circumscribed circle and the distance between each check point and the circle center of the circumscribed circle is the radius of the circumscribed circle, judging that the geometric side is an arc side.

4. The method of claim 1, wherein computing a periodic surface rotation transformation matrix from the circular arc edge comprises:

according to the arc edge, determining a circle center corresponding to the arc edge, a target central angle and a rotation axis vector perpendicular to a plane where the arc edge is located; the target central angle is determined according to a circumscribed circle where the arc edge is located and vertexes of two geometric surfaces located on the circumscribed circle;

and calculating a periodic surface rotation transformation matrix according to the circle center, the target circle center angle and the rotation axis vector.

5. The method of claim 4, wherein said computing a periodic surface rotation transformation matrix from the center of the circle, the target center angle, and the rotation axis vector comprises:

determining a movement transformation matrix by moving the circle center to an origin in a pre-constructed three-dimensional coordinate system;

determining a first rotation transformation matrix by rotating the rotation axis vector by a first rotation angle to a target coordinate plane on the three-dimensional coordinate system;

determining a second rotation transformation matrix by rotating the rotation axis vector by a second rotation angle to a target coordinate axis on the three-dimensional coordinate system;

determining a third rotation transformation matrix by rotating the rotation axis vector by an angle corresponding to the size of the target central angle;

calculating a periodic surface rotation transformation matrix according to the movement transformation matrix, the first rotation transformation matrix, the second rotation transformation matrix and the third rotation transformation matrix;

and the target coordinate plane and the target coordinate axis are determined by matching the three coordinate planes and the three coordinate axes in the three-dimensional coordinate system according to the projection lengths of the rotation axis vectors on the three coordinate planes in the three-dimensional coordinate system.

6. The method according to claim 1, wherein the determining the boundary points of the two geometric surfaces have a one-to-one correspondence relationship according to the periodic surface rotation transformation matrix comprises:

according to the periodic surface rotation transformation matrix, transforming the boundary point of one of the geometric surfaces to obtain a transformation result;

and after confirming that the transformation result has one-to-one correspondence with the boundary point of the other geometric surface, confirming that the boundary points of the two geometric surfaces have one-to-one correspondence.

7. The method of claim 1, wherein:

the boundary points of the geometric surface include vertices of the geometric surface and end points on geometric edges of the geometric surface.

8. A geometric model structure detection apparatus, comprising:

the receiving module is used for receiving the input geometric model;

the calculation module is used for calculating a periodic surface rotation transformation matrix according to the circular arc edges after confirming that the number of vertexes of two geometric surfaces to be detected in the geometric model is the same and that the vertexes of the geometric surfaces are associated with the circular arc edges;

and the confirming module is used for confirming that the two geometric surfaces are a pair of rotating periodic surfaces after confirming that the boundary points of the two geometric surfaces have one-to-one correspondence according to the periodic surface rotating transformation matrix.

9. An electronic device, comprising:

a processor; and

a memory having executable code stored thereon, which when executed by the processor, causes the processor to perform the method of any one of claims 1-7.

10. A computer-readable storage medium having stored thereon executable code, which when executed by a processor of an electronic device, causes the processor to perform the method of any one of claims 1-7.

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