CN114970283A - Geometric model structure detection method, device, equipment and storage medium - Google Patents
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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
Technical Field
The invention relates to the technical field of data processing, in particular to a method, a device, equipment and a storage medium for detecting a geometric model structure.
Background
In the field of computer aided engineering, the generation of a grid is required to be carried out on a geometric surface of a geometric model, and the generation of the grid is the key of a digital simulation technology and is of great importance to the simulation efficiency and accuracy. In the geometric model, a pair of rotational periodic surfaces refers to two geometric surfaces that can be brought into perfect coincidence by rotating about a specific axis. In the process of generating the mesh for each geometric surface of the geometric model, if two geometric surfaces in the geometric model are judged to be a pair of rotation period surfaces, after the mesh is generated for one rotation period surface, the mesh of the other rotation period surface can be generated rapidly according to the generated mesh on the rotation period surface, so that the mesh generation efficiency of the geometric model is improved. The precision and the efficiency of numerical simulation calculation can be further improved by rotating and converting the periodic surface grids which can be superposed uniformly.
However, in the related art, it cannot be determined whether two geometric surfaces to be detected in the geometric model are a pair of rotation periodic surfaces, so that the grid generation efficiency is affected, and the calculation efficiency of the numerical simulation is reduced.
Disclosure of Invention
In order to solve or partially solve the problems in the related art, the invention provides a method, a device, equipment and a storage medium for detecting the structure of a geometric model, which can quickly judge whether two geometric surfaces to be detected in the geometric model are a pair of rotation periodic surfaces, are favorable for improving the grid generation efficiency and the calculation efficiency and precision of numerical simulation.
The invention provides a geometric model structure detection method in a first aspect, which 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.
In one embodiment, the manner of confirming that the vertex of the geometric surface is associated with the circular arc edge includes:
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.
In an embodiment, the determining that the geometric side is a circular arc side according to the circumscribed circle includes:
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.
In one embodiment, the calculating a periodic surface rotation transformation matrix according to the arc edge includes:
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.
In one embodiment, the calculating a periodic surface rotation transformation matrix according to the circle center, the target circle center angle and the rotation axis vector includes:
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.
In one embodiment, the determining that the boundary points of the two geometric surfaces have a one-to-one correspondence relationship according to the periodic surface rotation transformation matrix includes:
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.
In one embodiment, the boundary points of the geometric surface include vertices of the geometric surface and end points on a geometric edge of the geometric surface.
The second aspect of the present invention provides a geometric model structure detection apparatus, including:
a receiving module for receiving an input geometric model;
the calculation module is used for calculating a periodic surface rotation transformation matrix according to the arc edges after confirming that the vertexes of the two geometric surfaces to be detected in the geometric model are the same in number and confirming that the vertexes of the geometric surfaces are associated with the 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.
A third aspect of the present invention provides 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 as described above.
A fourth aspect of the invention provides 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 a method as described above.
The technical scheme provided by the invention can have the following beneficial effects:
according to the method, the input geometric model is received, the number of vertexes of two geometric surfaces to be detected in the geometric model is determined to be the same, the vertex of the geometric surface is associated with the arc edge, the periodic surface rotation transformation matrix is calculated according to the arc edge, and after the boundary points of the two geometric surfaces are determined to have one-to-one correspondence according to the periodic surface rotation transformation matrix, the two geometric surfaces are determined to be a pair of rotation periodic surfaces. Therefore, whether two geometric surfaces to be detected in the geometric model are a pair of rotation periodic surfaces can be quickly judged, the grid generation efficiency is favorably improved, and the calculation efficiency and precision of numerical simulation are improved.
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, as claimed.
Drawings
The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts.
FIG. 1 is a schematic flow chart of a geometric model structure detection method according to an embodiment of the present invention;
FIG. 2 is another schematic flow chart diagram illustrating a geometric model structure detection method according to an embodiment of the present invention;
FIG. 3 is a schematic structural diagram of a geometric model in a geometric model structure detection method according to an embodiment of the present invention;
FIG. 4 is a schematic diagram illustrating a rotation process of a rotation vector axis in a geometric model structure detection method according to an embodiment of the present invention;
FIG. 5 is a schematic structural diagram of a geometric model structure detection apparatus according to 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.
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
Embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. While embodiments of the invention are illustrated in the drawings, it should be understood that the invention can be embodied in various forms and should not be limited to 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 herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in this specification and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.
It is to be understood that, although the terms first, second, third, etc. may be used herein to describe various information, such information should not be limited by these terms. These terms are only used to distinguish one type of information from another. For example, first information may also be referred to as second information, and similarly, second information may also be referred to as first information, without departing from the scope of the present invention. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
In the related art, whether two geometric surfaces to be detected in the geometric model are a pair of rotation period surfaces cannot be judged, so that the grid generation efficiency is influenced, and the calculation efficiency and precision of numerical simulation are reduced.
In view of the above problems, embodiments of the present invention provide a method for detecting a geometric model structure, which can quickly determine whether two geometric surfaces to be detected in a geometric model are a pair of rotation periodic surfaces, and is beneficial to improving grid generation efficiency and improving calculation efficiency and precision of numerical simulation.
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 flow chart of a geometric model structure detection method according to an embodiment of the present invention.
Referring to fig. 1, the method includes:
and S101, receiving an input geometric model.
In this step, a geometric model of the user input is received. The geometric model may refer to a 3D model file, such as a 3D model file with different formats, such as step, iges, stl, and so on.
S102, after the number of vertexes of two geometric surfaces to be detected in the geometric model is the same and the vertexes of the geometric surfaces are associated with arc edges, calculating a periodic surface rotation transformation matrix according to the arc edges.
The two geometric surfaces to be detected in the geometric model may be two geometric surfaces selected in advance by a user.
The method for confirming that the vertex of the geometric surface is associated with the arc edge may include: and acquiring the geometric edges associated with the vertexes of the geometric surfaces. And collecting three sampling points from the geometric edge, and calculating the circumscribed circle determined by the three sampling points. And after judging that the geometric side is the arc side according to the circumscribed circle, confirming that the arc side is associated with the vertex of the geometric surface.
In this step, calculating the periodic surface rotation transformation matrix according to the circular arc edge may include: and determining the circle center, the target circle center angle and the rotation axis vector of the plane perpendicular to the arc edge corresponding to the arc edge according to the arc edge. The target central angle is determined according to the circumscribed circle where the arc edge is located and the vertexes of the 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.
S103, 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.
The method for confirming that the boundary points of the two geometric surfaces have one-to-one correspondence according to the periodic surface rotation transformation matrix comprises the following steps: and transforming the boundary point of one geometric surface according to the periodic surface rotation transformation matrix to obtain a transformation result. And after the one-to-one correspondence between the transformation result and the boundary point of the other geometric surface is confirmed, confirming that the boundary points of the two geometric surfaces have the one-to-one correspondence.
The boundary points of the geometric surface comprise the vertexes of the geometric surface and the end points on the geometric edges of the geometric surface.
It can be seen from this embodiment that, in the method provided in the embodiment of the present invention, by receiving an input geometric model, it is determined that the numbers of vertexes of two geometric surfaces to be detected in the geometric model are the same, and after it is determined that the vertexes of the geometric surfaces are associated with arc edges, a periodic surface rotation transformation matrix is calculated according to the arc edges, and after it is determined that the boundary points of the two geometric surfaces have a one-to-one correspondence relationship according to the periodic surface rotation transformation matrix, it is determined that the two geometric surfaces are a pair of rotation periodic surfaces. Therefore, whether two geometric surfaces to be detected in the geometric model are a pair of rotation period surfaces can be quickly judged, grid generation efficiency is improved, and calculation efficiency and accuracy of numerical simulation are improved.
Fig. 2 is another schematic flow chart of the geometric model structure detection method according to the embodiment of the present invention. Fig. 2 depicts the solution of the invention in more detail with respect to fig. 1.
Referring to fig. 2, the method includes:
s201, receiving an input geometric model.
In this step, a geometric model of the user input is received. The geometric model may refer to a 3D model file, such as a 3D model file with different formats, such as step, iges, stl, and so on.
S202, whether the number of vertexes of the two geometric surfaces to be detected in the geometric model is the same or not is confirmed.
The two geometric surfaces to be detected in the geometric model may be two geometric surfaces selected in advance by a user. Each geometric surface is determined by a boundary formed by connecting geometric edges, and the vertex of each geometric surface is an end point of each geometric edge. The two geometric surfaces to be detected may include a first geometric surface and a second geometric surface.
As shown in the embodiment of fig. 3, the two geometric surfaces to be detected in the geometric model are the first geometric surface a and the second geometric surface B, respectively. The first geometric surface A has four geometric sides, which are geometric sides A 0 A 1 Geometric side A 1 A 2 Geometric side A 2 A 3 Geometric side A 0 A 3 . The first geometric surface A has four vertexes, namely vertexes A 0 Vertex A 1 Vertex A 2 Vertex A 3 . The second geometric surface B has four geometric sides which are respectively geometric sides B 0 B 1 Geometric side B 1 B 2 Geometric side B 2 B 3 Geometric side B 0 B 3 . The second geometric surface B has four vertexes B 0 Vertex B 1 Vertex B 2 Vertex B 3 . It can be seen that the number of vertexes of the first geometric surface a and the second geometric surface B is the same, and the number of vertexes of the two geometric surfaces is four.
Further, the vertices of each geometric surface may be recorded by constructing a set.
For example, in the embodiment of fig. 3, the set of vertices of the first geometric surface a and the second geometric surface B are:
and
it is to be understood that since a pair of rotation periodic surfaces means two geometric surfaces that can be brought into perfect coincidence by rotating about a specific axis, the two geometric surfaces are not a pair of rotation periodic surfaces if the number of vertexes of the two geometric surfaces is different.
In this step, if it is determined that the number of vertices of the two geometric surfaces to be detected in the geometric model is not the same, S203 is performed. If the number of the vertexes of the two geometric surfaces to be detected in the geometric model is the same, executing S204.
And S203, outputting a confirmation result that the two geometric surfaces are not the pair of rotation period surfaces.
In this step, a confirmation result that the two geometric surfaces are not a pair of rotation 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 rotation periodic surfaces.
And S204, confirming whether the vertex of the geometric surface is associated with the arc edge.
In one embodiment, the method for confirming that the vertex of the geometric surface is associated with the circular arc edge comprises the following steps:
s204-1, acquiring the geometric edge associated with the vertex of the geometric surface.
In this step, each geometric edge associated with each vertex of one of the geometric surfaces may be obtained. For example, each geometric edge associated with each vertex of the first geometric surface is obtained. Vertex-associated geometric edges may be aggregated
And (6) recording.
As in the embodiment of FIG. 3, each vertex A of the first geometric surface A may be obtained i Each geometric edge associated, where i<4 and i is more than or equal to 0. For example, vertex A 0 The associated geometric edges are: geometric edge A 0 A 3 Geometric side A 0 A 1 Geometric side A 0 B 0 。
And S204-2, collecting three sampling points from the geometric edge, and calculating a circumscribed circle determined by the three sampling points.
It should be noted that this step may be performed on each geometric side acquired in S204-1. For example, in the embodiment of FIG. 3, at geometric edge A 0 A 3 Three sampling points are collected on the geometric side A 0 A 1 Three sampling points are collected on the geometric side A 0 B 0 Three sampling points were collected.
It will be appreciated that three points may define a unique circumscribed circle. Three sampling points are respectively set as points P1, P2 and P3, and the center calculation formula of the circumscribed circle determined by the three sampling points is as follows:
the radius of the circumscribed circle is the distance from the center C to any of the points P1, P2, and P3.
And S204-3, after judging that the geometric side is the arc side according to the circumscribed circle, confirming that the vertex of the geometric surface is associated with the arc side.
In the embodiment of FIG. 3, it is to be understood that the geometric edge A 0 A 3 And a geometric edge A 0 A 1 Is a straight geometric side, at geometric side A 0 A 3 And a geometric edge A 0 A 1 The three sampling points collected above cannot be calculated to determine the circumscribed circle. If at the geometric side A 0 B 0 The circumscribed circle can be calculated and determined by the three sampling points collected, and the geometric edge A can be judged according to the circumscribed circle 0 B 0 Whether it is a circular arc edge.
In one embodiment, the determining that the geometric edge is the circular arc edge according to the circumscribed circle may include:
s204-3-1, collecting a preset number of check points from the geometric edge.
For example, in the FIG. 3 embodiment, from geometric edge A 0 B 0 And (3) collecting a preset number of check points, for example, collecting 5 check points, wherein the check points collected from the geometric side are different from the sampling points. In order to improve processing efficiency and reduce computational overhead, the preset number may be set to be less than or equal to three.
And 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, judging that the geometric edge is an arc edge.
For example, in the FIG. 3 embodiment, from geometric edge A 0 B 0 The check points are located 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 (i.e. the distance from the center C to any one of the points P1, P2 and P3), so that the geometric edge a can be determined 0 B 0 Is a circular arc edge. Thus, it can be confirmed that the vertex of the first geometric surface a in the embodiment of fig. 3 is associated with the 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 the arc edge.
In S204, if it is confirmed that the vertex of the geometric surface is not associated with a circular arc edge, S203 is executed. If it is confirmed that the vertex of the geometric surface is associated with the arc edge, S205 is executed.
And S205, according to the arc edge, determining the circle center corresponding to the arc edge, the target central 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 circumscribed circle where the arc edge is located and the vertexes of the two geometric surfaces located on the circumscribed circle.
It is understood that if it is confirmed in S204 that a plurality of circular arc edges are associated with the vertices of the geometric surface, S205 may be executed for each circular arc edge.
In this step, according to the arc edge, the circle center C, the target central angle θ and the rotation axis vector perpendicular to the plane of the arc edge corresponding to the arc edge can be determined
It can be understood that the normal vector and the rotation axis vector of the plane can be determined according to the plane where the arc edge is positioned
May refer to the plane normal vector. And determining the rotating shaft according to the plane normal vector and the circle center C. The target central angle theta is determined according to the circumscribed circle where the arc edge is located and the vertexes of the two geometric surfaces located on the circumscribed circle. It will be appreciated that if there is also a vertex on the second geometric surface on the circumcircle, the target central angle θ may be calculated from the vertex on the first geometric surface on the circumcircle and the vertex on the second geometric surface on the circumcircle. The target central angle θ is: the included angle between the connecting line of the vertex of the first geometric surface on the circumscribed circle and the circle center and the connecting line of the vertex of the second geometric surface on the circumscribed circle and the circle center is formed.
In the embodiment of FIG. 3, for a confirmed arc edge A 0 B 0 With target central angle theta as vector
And vector
The included angle between (due to the vertex B0 of the second geometric surface being on the outer circle). In other words, vectors
And vector
The magnitude of the rotation angle therebetween is the target central angle θ. Vector of rotation axis
May be a circle center C, and the rotation axis vector
Can be perpendicular to the arc edge A 0 B 0 The plane of the plane.
And S206, calculating a periodic plane rotation transformation matrix according to the circle center, the target circle center angle and the rotation axis vector.
It should be noted that the periodic surface rotation transformation matrix is obtained by calculation according to the rotation axis vector, the center of the circumscribed circle and the target center angle, and the correspondence between the first geometric surface and the second geometric surface and two vertexes of the circumscribed circle can be determined by the periodic surface rotation transformation matrix. That is, the position of the vertex on the first geometric surface related to the arc edge, which is transformed by the periodic surface rotation transformation matrix, is the same as the position of the other vertex on the circumscribed circle of the second geometric surface.
In one embodiment, calculating the periodic surface rotation transformation matrix according to the circle center, the target circle center angle and the rotation axis vector may include:
s206-1, determining a movement transformation matrix by moving the circle center to the origin in the pre-constructed three-dimensional coordinate system.
The coordinate of the center C is (C) x ,C y ,C z ) And determining a movement transformation matrix T by moving the circle center C to an origin O in a pre-constructed three-dimensional coordinate system:
s206-2, a first rotation transformation matrix is determined by rotating the rotation axis vector by a first rotation angle alpha to a target coordinate plane on the three-dimensional coordinate system.
Wherein the rotation axis vector
Has the coordinates of (n) x ,n y ,n z )。
In this step, after the center of the circle is moved to the origin in the previously constructed three-dimensional coordinate system by S206-1, the axis vector of the rotation
The starting point of (b) may be an origin O in the three-dimensional coordinate system. By applying a rotation axis vector
By rotating the first rotation angle alpha to a target coordinate plane on the three-dimensional coordinate system, a first rotation transformation matrix R may be determined α 。
The three-dimensional coordinate system includes three coordinate planes, which are an X0Z plane, an XOY plane, and a YOZ plane. The target coordinate plane is one of three coordinate planes. The three-dimensional coordinate system also comprises three coordinate axes which are respectively an X coordinate axis, a Y coordinate axis and a Z coordinate axis. Vector of rotation axis
Can be rotated about one of the coordinate axes by a first rotation angle alpha to a target coordinate plane on the three-dimensional coordinate system, i.e. after rotation, the axis of rotation vector
Located on the target coordinate plane.
S206-3, a second rotation transformation matrix is determined by rotating the rotation axis vector by a second rotation angle beta to the target coordinate axis on the three-dimensional coordinate system.
In this step, a rotation axis vector located on the target coordinate plane may be set
By rotating the second rotation angle β to the target coordinate axis on the three-dimensional coordinate system, a second rotation transformation matrix R may be determined β 。
It should be noted that the target coordinate axis is one of three coordinate axes in the three-dimensional coordinate system. Vector of rotation axis
The target coordinate axis can be transformed to the target coordinate axis on the three-dimensional coordinate system according to the second rotation angle beta after rotating the angle alpha to the target coordinate plane around one coordinate axis. That is, after rotation, the axis vector of rotation
On the target coordinate axis, the rotation axis vector
Coinciding with the target coordinate axis.
S206-4, rotating the rotation axis vector by an angle corresponding to the size of the target central angle, and determining a third rotation transformation matrix.
In this step, a rotation axis vector located on the target coordinate axis may be set
Rotating the angle theta corresponding to the central angle of the target, and determining a third rotation transformation matrix R θ 。
S206-5, 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.
According to the moving transformation matrix T and the first rotation transformation matrix R α A second rotation transformation matrix R β And a third rotation transformation matrix R θ And calculating a periodic surface rotation transformation matrix R.
In one embodiment, the formula for calculating the periodic surface rotation transformation matrix R is:
wherein, T -1 ，
Are respectively T, R α 、R β By inverse matrix of pairs T, R α 、R β And performing inverse transformation to obtain the final product.
The target coordinate plane and the target coordinate axis are based on the rotation axis vector
The projection lengths on three coordinate planes (i.e., X0Z plane, XOY plane, YOZ plane) in the three-dimensional coordinate system are respectively determined from matching of the three coordinate planes (i.e., X0Z plane, XOY plane, YOZ plane) in the three-dimensional coordinate system with three coordinate axes (i.e., X coordinate axis, Y coordinate axis, Z coordinate axis).
Vector of axis of rotation
Has the coordinates of (n) x ,n y ,n z )。
Vector of rotation axis
The length L of (a) is calculated as:
vector of rotation axis
Projection lengths L on YOZ plane respectively YZ Projection length L on X0Z plane ZX Projection length L on XOY plane XY Respectively as follows:
in one embodiment, the projection lengths (i.e., L) are based on three projection lengths YZ 、L ZX 、L XY ) Determining a target coordinate plane and a target coordinate axis according to the following three conditions (1), (2) and (3), and calculating a first rotation transformation matrix R α A second rotation transformation matrix R β And a third rotation transformation matrix R θ The value of (c).
(1) Vector of rotation axis
Projection length L on YOZ plane YZ In the maximum case (i.e. at L) YZ 、L ZX 、L XY Middle L YZ Maximum value of).
Matching determines that the target coordinate plane is an X0Z plane and the target coordinate axis is a Z coordinate axis.
Corresponding to the rotation axis vector in S206-2 to S206-4, see FIG. 4
Rotate about the X coordinate axis by a first rotation angle alpha to the X0Z plane (target coordinate plane), and then rotate about the Y coordinate axisThe axis is rotated by a second rotation angle β to the Z coordinate axis (target coordinate axis) so that the rotation axis vector
Coinciding with the Z coordinate axis.
It can be understood that the rotation axis vector
The rotation to the target coordinate plane is carried out according to a first circumferential axis, i.e. the axis vector of rotation
And rotating the first rotation angle alpha around the first surrounding shaft to the target coordinate plane. Vector of rotation axis
The rotation to the target coordinate axis is carried out according to a second axis of revolution, i.e. a rotation axis vector
And rotating the second rotation angle beta around the second ring axis to the target coordinate axis.
At the rotation axis vector
Projected length L in YOZ plane YZ Under the maximum condition, the first surrounding axis is an X coordinate axis, and the second surrounding axis is a Y coordinate axis.
First rotation transformation matrix R α A second rotation transformation matrix R β And a third rotation transformation matrix R θ Respectively as follows:
wherein,
(2) vector of rotation axis
Projection length L in X0Z plane ZX In the maximum case (i.e. at L) YZ 、L ZX 、L XY Middle L ZX Maximum value of (c).
Matching determines the target coordinate plane as the X0Y plane and the target coordinate axis as the X coordinate axis.
Corresponding to the rotation axis vector in S206-2 to S206-4
Rotate the first rotation angle alpha to the X0Y plane (target coordinate plane) about the Y coordinate axis, and then rotate the second rotation angle beta to the X coordinate axis (target coordinate axis) about the Z coordinate axis, so that the rotation axis vector
Coinciding with the X coordinate axis.
It can be understood that the rotation axis vector
The rotation to the target coordinate plane is carried out according to a first circumferential axis, i.e. the axis vector of rotation
And rotating the first rotation angle alpha around the first surrounding shaft to the target coordinate plane. Vector of rotation axis
The rotation to the target coordinate axis is carried out according to a second axis of revolution, i.e. a rotation axis vector
And rotating the second rotation angle beta around the second ring axis to the target coordinate axis.
At the rotation axis vector
Length of projection L in XOZ plane ZX Under the maximum condition, the first surrounding axis is a Y coordinate axis, and the second surrounding axis is a Z coordinate axis.
First rotation transformation matrix R α A second rotation transformation matrix R β And a third rotation transformation matrix R θ Respectively as follows:
wherein,
(3) vector of rotation axis
Projection length L in XOY plane XY In the maximum case (i.e. at L) YZ 、L ZX 、L XY Middle L XY Maximum value of).
And matching to determine that the target coordinate plane is a YOZ plane and the target coordinate axis is a Y coordinate axis.
Corresponding to the rotation axis vector in S206-2 to S206-4
Rotating the first rotation angle alpha to the YOZ plane (target coordinate plane) about the Z coordinate axis, and then rotating the second rotation angle beta to the Y coordinate axis (target coordinate axis) about the X coordinate axis such that the rotation axis vector
Coinciding with the Y coordinate axis.
It can be understood that the rotation axis vector
The rotation to the target coordinate plane is carried out according to a first surrounding axis, i.e. a rotation axis vector
And rotating the first rotation angle alpha around the first surrounding shaft to the target coordinate plane. Vector of rotation axis
The rotation to the target coordinate axis is carried out according to a second axis of revolution, i.e. a rotation axis vector
And rotating the second rotation angle beta around the second ring axis to the target coordinate axis.
At the rotation axis vector
Projection length L in XOY plane XY Under the maximum condition, the first surrounding axis is a Z coordinate axis, and the second surrounding axis is an X coordinate axis.
First rotation transformation matrix R α A second rotation transformation matrix R β And a third rotation transformation matrix R θ Respectively as follows:
wherein,
it can be understood that after the circle center is moved to the origin in the pre-constructed three-dimensional coordinate system, and the rotation axis vector is rotated and transformed twice through the first rotation angle α and the second rotation angle β, the rotation axis vector coincides with the target axis, and the vertex of the related arc edge on the first geometric surface can be transformed to the position of the other vertex on the circumscribed circle on the second geometric surface by rotating the angle corresponding to the size of the target center angle. The periodic surface rotation transformation matrix R obtained by the calculation determines the transformation relation of two vertexes on the first and second geometric surfaces. Therefore, the calculated periodic surface rotation transformation matrix R can be used to detect whether two geometric surfaces are a pair of rotation periodic surfaces.
And S207, determining whether the boundary points of the two geometric surfaces have one-to-one correspondence according to the periodic surface rotation transformation matrix.
In this step, if it is determined from the periodic surface rotation transformation matrix that there is no one-to-one correspondence between the boundary points of the two geometric surfaces, S203 is performed. If it is determined that the boundary points of the two geometric surfaces have a one-to-one correspondence relationship according to the periodic surface rotation transformation matrix, S208 is performed.
It should be noted that if it is determined in S204 that a plurality of circular arc edges are associated with the vertices of the geometric surface, and for a plurality of periodic surface rotation transformation matrices obtained by calculation for the plurality of circular arc edges and the circumscribed circle, respectively, it is determined according to one of the periodic surface rotation transformation matrices that a one-to-one correspondence exists between boundary points of two geometric surfaces, S208 is executed, otherwise S203 is executed. That is, the boundary point of the two geometric surfaces can be confirmed to have a one-to-one correspondence by one of the periodic surface rotation transformation matrices, S208 is executed, otherwise S203 is executed.
In one embodiment, the method for confirming that the boundary points of the two geometric surfaces have the one-to-one correspondence according to the periodic surface rotation transformation matrix may include:
s207-1, transforming the boundary point of one geometric surface according to the periodic surface rotation transformation matrix to obtain a transformation result.
In the embodiment shown in fig. 3, the boundary points of the first geometric surface a are transformed according to the periodic surface rotation transformation matrix R to obtain the transformation result.
The boundary points of the geometric surface comprise the vertexes of the geometric surface and the end points on the geometric edges of the geometric surface. That is, the boundary point of the first geometric surface a may be the vertex a 0 Vertex A 1 Vertex A 2 Vertex A 3 . The boundary point of the first geometric surface A may be a geometric edge A 0 A 1 Geometric side A 1 A 2 Geometric side A 2 A 3 Geometric side A 0 A 3 The upper endpoint.
For example, a boundary point A to the first geometric surface A 0 Performing transformation to obtain a transformation result a 0 。
S207-2, after the fact that the transformation result is in one-to-one correspondence with the boundary point of the other geometric surface is confirmed, the fact that the boundary points of the two geometric surfaces are in one-to-one correspondence is confirmed.
That is, the positions corresponding to the transformation results are mapped on the corresponding boundary points of the other geometric surface one by one, so that it can be confirmed that the boundary points of the two geometric surfaces have a one-to-one correspondence relationship.
For example, in the embodiment of fig. 3, if there is a one-to-one correspondence relationship between the boundary points of the two geometric surfaces, the boundary point a of the first geometric surface a is referred to 0 Performing transformation to obtain a transformation result a 0 . Transformation result a 0 The corresponding position is the boundary point B of the second geometric surface B 0 。
For another example, in the embodiment of fig. 3, if the boundary point of the first geometric surface a and the boundary point of the second geometric surface B have a one-to-one correspondence relationship, the vertex a of the first geometric surface a 0 、A 1 、A 2 、A 3 The transformation results transformed according to the periodic surface rotation transformation matrix R respectively correspond to the vertexes B on the second geometric surface B 0 、B 1 、B 2 、B 3 。
For another example, in the embodiment of fig. 3, if the boundary point of the first geometric surface a and the boundary point of the second geometric surface B have a one-to-one correspondence relationship, the geometric edge a of the first geometric surface a 0 A 1 Endpoint A of 0 According to the transformation result after the transformation of the periodic surface rotation transformation matrix R, corresponding to the corresponding geometric side B on the second geometric surface B 0 B 1 Endpoint B of 0 . Geometric edge A of first geometric surface A 0 A 1 Endpoint A of 1 According to the transformation result after the transformation of the periodic surface rotation transformation matrix R, corresponding to the corresponding geometric side B on the second geometric surface B 0 B 1 Endpoint B of 1 . In other words, the boundary ring of the first geometric surface A is A 0 A 1 A 2 A 3 The boundary ring of the second geometric surface B is B 0 B 1 B 2 B 3 For any geometric edge A of the first geometric surface A i A (i+1)％4 Any geometric side B of the second geometric surface B i B (i+1)％4 Wherein, 0 is less than or equal to i<4,% is the remainder symbol. Geometric edge A i A (i+1)％4 The end points on the geometric side B can be in one-to-one correspondence after being transformed by the periodic surface rotation transformation matrix R i B (i+1)％4 At the position of the end point of (a). That is, whether the geometric edges on the two geometric surfaces correspond one to one is determined by checking whether the end points of the geometric edges of one geometric surface have a one-to-one correspondence with the end points of the corresponding geometric edges of the other geometric surface.
In summary, the boundary points of one of the geometric surfaces are transformed according to the periodic surface rotation transformation matrix, and if the transformation result has a one-to-one correspondence relationship with the boundary points of the other geometric surface, it is determined that the boundary points of the two geometric surfaces have a one-to-one correspondence relationship. Specifically, the vertex of one of the geometric surfaces is transformed according to the periodic surface rotation transformation matrix, if the transformation result has a one-to-one correspondence with the vertex of the other geometric surface, and the two endpoints on one of the geometric sides on one of the geometric surfaces are transformed according to the periodic surface rotation transformation matrix, and if the transformation result has a one-to-one correspondence with the two endpoints on the corresponding one of the geometric sides on the other geometric surface, it is determined that the boundary points of the two geometric surfaces have a one-to-one correspondence.
And S208, outputting a confirmation result that the two geometric surfaces are a pair of rotation period surfaces.
In this step, the result of confirmation that the two geometric surfaces are a pair of rotation periodic surfaces is output, that is, the two geometric surfaces to be detected in the geometric model are confirmed as a pair of rotation 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 two geometric surfaces to be detected in the geometric model are a pair of rotation periodic surfaces, which is beneficial to improving the grid generation efficiency and improving the calculation efficiency of the numerical simulation.
Corresponding to the embodiment of the application function implementation method, the invention also provides a geometric model structure detection device, electronic equipment and a corresponding embodiment.
Fig. 5 is a schematic structural diagram of a geometric model structure detection apparatus according to an embodiment of the present invention.
Referring to fig. 5, a geometric model structure detecting apparatus 50 includes: a receiving module 510, a calculating module 520, and a confirming module 530.
A receiving module 510, configured to receive an input geometric model.
And the calculating module 520 is configured to calculate a periodic surface rotation transformation matrix according to the circular arc edges after the number of the vertexes of the two geometric surfaces to be detected in the geometric confirmation model is the same and the circular arc edges are associated with the vertexes of the geometric confirmation model.
A confirming module 530, configured to confirm that the two geometric surfaces are a pair of rotational periodic surfaces after confirming that the boundary points of the two geometric surfaces have a one-to-one correspondence according to the periodic surface rotational transformation matrix.
It can be seen from this embodiment that the apparatus 50 provided in the embodiment of the present invention can quickly determine whether two geometric surfaces to be detected in the geometric model are a pair of rotation periodic surfaces, which is beneficial to improving the grid generation efficiency and improving the calculation efficiency and precision of the numerical simulation.
With regard to the apparatus in the above embodiment, the specific manner in which each module performs the operation has been described in detail in the embodiment related to the method, and will not be elaborated herein.
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 (CPU), other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic, discrete hardware components, etc. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory 610 may include various types of storage units such as system memory, Read Only Memory (ROM), and permanent storage. Wherein the ROM may store static data or instructions that are required by the processor 620 or other modules of the computer. The persistent storage device may be a read-write storage device. The persistent storage may be a non-volatile storage device that does not lose stored instructions and data even after the computer is powered off. In some embodiments, the persistent storage device employs a mass storage device (e.g., magnetic or optical disk, flash memory) as the persistent storage device. In other embodiments, the persistent storage may be a removable storage device (e.g., floppy disk, optical drive). The system memory may be a read-write memory device or a volatile read-write memory device, such as a dynamic random access memory. The system memory may store instructions and data that some or all of the processors require at runtime. In addition, the memory 610 may include any combination of computer-readable storage media, including various types of semiconductor memory chips (e.g., DRAM, SRAM, SDRAM, flash memory, programmable read-only memory), magnetic and/or optical disks, as well. In some embodiments, memory 610 may include a removable storage device that is readable and/or writable, such as a compact disc laser (CD), a read-only digital versatile disc (e.g., DVD-ROM, dual layer DVD-ROM), a read-only Blu-ray disc, an ultra-dense optical disc, a flash memory card (e.g., SD card, min SD card, Micro-SD card, etc.), a magnetic floppy disk, or the like. Computer-readable storage media do not contain carrier waves or transitory electronic signals transmitted by wireless or wired means.
The memory 610 has stored thereon executable code that, when processed by the processor 620, may cause the processor 620 to perform some or all of the methods described above.
Furthermore, the method according to the invention may also be implemented as a computer program or computer program product comprising computer program code instructions for carrying out some or all of the steps of the above-described method of the invention.
Alternatively, the invention may also be embodied as a computer readable storage medium (or non-transitory machine-readable storage medium or machine-readable storage medium) having stored thereon executable code (or a computer program or computer instruction code) which, when executed by a processor of an electronic device (or server, etc.), causes the processor to perform part or all of the steps of the above-described method according to the invention.
While embodiments of the present invention have been described above, the above description is illustrative, not exhaustive, and not limited to the disclosed embodiments. Many 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 is chosen in order to best explain the principles of the embodiments, the practical application, or improvements made to 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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