CN116597117B - Hexahedral mesh generation method based on object symmetry - Google Patents
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Abstract
The invention provides a hexahedral mesh generating method based on object symmetry, which relates to the technical field of industrial image data processing and is used for generating hexahedral meshes of industrial devices with symmetrical characteristics, and comprises the following steps: preprocessing a series of CT images of a workpiece to obtain a three-dimensional target area with workpiece information; detecting three-dimensional symmetry characteristics of the workpiece in the three-dimensional target area, and dividing the workpiece into symmetrical parts according to the characteristics; taking a part as a main body, generating a core grid by adopting an octree method, and fitting a surface grid by adopting a gap filling method; adopting symmetrical operation, mirror image copying the built grids, and connecting the two symmetrical grids; and correcting the grid structure at the joint of the symmetrical surfaces by using a topology optimization method, and finally obtaining the three-dimensional full hexahedral grid of the workpiece. The full hexahedral mesh generated by the technical scheme of the invention can effectively restore the symmetrical characteristic of the industrial device and improve the mesh generation efficiency.
Description
Technical Field
The invention relates to the technical field of industrial image data processing, in particular to a hexahedral mesh generation method based on object symmetry.
Background
Reverse engineering is an important technology for product imitation and redevelopment. The industrial CT (Computed Tomography ) has the outstanding characteristics of non-destructive property, no influence of the complexity of the internal and external structures of the measured object, accurate recording of the internal structure of the object and distinguishing of different materials, and provides a good technical means for reverse design. The existing reverse design is mainly to sequentially generate an STL model, a surface model and a solid model from a CT image and then to a grid model, and is an indirect generation method which has the disadvantages of complicated process, complex operation, low efficiency and dependence on experience of operators and software proficiency.
The hexahedral mesh is an ideal finite element mesh because of remarkable advantages in terms of calculation accuracy, mesh unit number, distortion resistance degree, convergence speed, space complexity and the like, and is increasingly valued by researchers in various industries in recent years, so that the hexahedral mesh is widely applied to reconstruction work of a target object in a three-dimensional space. The method for directly generating hexahedral mesh by industrial CT image is the key work for solving the problem of product reverse design.
Symmetry is very common in nature, and human perception of symmetry features is also very strong, so most man-made objects are symmetrical. Symmetry is considered as a fundamental principle of human perception in psychology, influences the original attention mechanism of people and guides various processing procedures of objects in later stages. A symmetric feature is a significant overall feature of a three-dimensional object.
In summary, the method for generating the full hexahedral mesh directly from the industrial CT image according to the symmetrical characteristics of the target object has great significance for the reverse design of the industrial device. However, most of the current hexahedral mesh generating methods mostly consider the target workpiece as an integral body, neglect the symmetrical characteristic of the workpiece, and the generated mesh model has better quality but can not effectively restore the symmetrical structure of the workpiece.
There is therefore a need for a hexahedral mesh generation method that can effectively restore the symmetrical structure of a workpiece and improve the mesh generation efficiency.
Disclosure of Invention
The invention mainly aims to provide a hexahedral grid generation method based on object symmetry, which aims to solve the problems that the symmetric characteristics of a workpiece cannot be effectively restored and the grid generation efficiency cannot be improved in the prior art.
In order to achieve the above object, the present invention provides a hexahedral mesh generating method based on object symmetry, comprising the steps of: s1, preprocessing a series of CT images of a workpiece to obtain a three-dimensional target area with workpiece information; s2, detecting three-dimensional symmetry characteristics of the workpiece in the three-dimensional target area, and dividing the workpiece into symmetrical parts according to the characteristics; s3, taking a part of symmetry as a main body, generating a core grid by adopting an octree method, and fitting a surface grid by adopting a gap filling method; s4, adopting symmetrical operation, mirror image copying the built grids, and connecting the two symmetrical grids; s5, correcting the grid structure at the joint of the symmetrical surfaces by using a topology optimization method, and finally obtaining the three-dimensional full hexahedral grid of the workpiece.
Further, the step of preprocessing the series of CT images of the workpiece in step S1 includes: s1.1, performing median filtering with the template size of 5 multiplied by 5 on the original image.
S1.2, edge detection of a Canny operator is adopted to extract boundary information of the workpiece in the image.
And S1.3, carrying out region filling on the image so as to separate the effective region from the background region of the workpiece.
S1.4, orderly arranging the processed serial images, and simulating three-dimensional space information of the workpiece.
Further, step S2 includes: s2.1, establishing a minimum bounding box of the workpiece in a three-dimensional space according to the industrial CT image, wherein the minimum bounding box comprises effective pixels of all CT images, and adjusting a three-dimensional coordinate system by taking the center of the minimum bounding box as an origin.
S2.2, through the origin of coordinates, symmetrically dividing lines in the minimum bounding box, including four body diagonal lines L 1 -L 4 And three central lines L 5 -L 7 Recording the intersection point of the symmetrical dividing line and the effective pixel as a mark point, wherein the intersection point of the ith symmetrical dividing line and the jth page CT image is recorded as the mark point。
S2.3, dividing each surface of the minimum bounding box, wherein the bottom surface and the front surface of the front viewThe right, back, left and top are F respectively 1 、F 2 、F 3 、F 4 、F 5 、F 6 。
S2.4, F n All marked points in half minimum bounding box on surfaceRecord as a set of marker point sets { B n Will { B } n Projection of points in F n Projection points obtained on a surfaceConstitute projection point set { T ] n N=1, 2, … …,6,i =1, 2, … …,7.
S2.5 for the marker Point set { B n -calculating its geometric centre (n=1, 2, … …, 6)（x,y,z）：Wherein, the method comprises the steps of, wherein,is { B n The length of the },is { B n Each mark point in }.
Each mark pointTo the corresponding projection pointAverage value D of Euclidean distance of (2) n The method comprises the following steps:wherein, the method comprises the steps of, wherein,is { B n Length of }.
S2.6, setting a geometric center error thresholdd 1 And projection error threshold d 2 Taking opposite faces of the smallest bounding box, e.g. F 1 And F 6 The geometric centers of the marked point sets are respectively points M 1 Sum point M 6 The average value of Euclidean distances from each marking point to the corresponding projection point is D 1 And D 6 。
S2.7, if point M 1 And point-M 6 The Euclidean distance of less than or equal to d 1 And D is 1 And D 6 The difference of less than or equal to d 2 The object is considered to be symmetrical about the plane of symmetry of the two faces.
S2.8, if M 1 And point-M 6 The Euclidean distance of (2) is greater than d 1 Or D 1 And D 2 Is greater than d 2 And if so, continuing to select the other two opposite faces, and repeating the step S2.7 until the symmetrical face of the object is found or no other opposite faces which are not judged.
Further, step S3 includes: s3.1, according to the industrial CT image, establishing a minimum bounding box of the workpiece in a three-dimensional space, wherein the minimum bounding box comprises effective pixels of all images, and the side length of the minimum bounding box is an integer power of 2.
S3.2, dividing a three-dimensional hexahedral space as a root node into 8 subspaces with the same size, namely child nodes, and continuing dividing each child node until a certain child node no longer contains effective pixels or reaches a grid specified level, thereby obtaining a core grid.
And S3.3, the surface of the core grid is divided into two layers by using a gap filling method to fit, the inner layer modifies the original grid and fills gaps, and the outer layer fits the surface vertexes of the core grid to the object boundary according to the shortest distance in the normal vector direction.
Further, step S4 specifically includes: and (3) copying the hexahedral mesh of the built part of the workpiece according to mirror-inverted coordinates of the symmetrical plane in a three-dimensional space to obtain the hexahedral mesh of the non-built part, and merging along the symmetrical plane.
Further, step S5 includes: s5.1, performing layer deletion operation on outer layers of grids at two sides of the symmetry plane, and reserving core grids far away from the symmetry plane.
S5.2, performing row and column insertion operation along the normal vector direction of the symmetry plane, and filling gaps among the core grids by using hexahedral grids.
The invention has the following beneficial effects: the invention focuses on the symmetrical characteristic of the target object, establishes a minimum outer bounding box, carries out symmetry detection through a simple geometric method, judges each symmetrical plane of the object, only takes a certain symmetrical part to generate a full hexahedral mesh model with high core mesh quality according to an octree method, and carries out mirror image copying, splicing and correcting on the rest parts. The method reduces the space complexity and the calculation time in the grid generation process, and also excellently restores the symmetrical characteristics of the target object, so that the symmetrical parts of the generated hexahedral grid model are completely the same, and the problem that the symmetrical characteristics of the workpiece cannot be effectively maintained in the normal conventional generation method is solved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the description of the embodiments or the prior art will be briefly described, and it is obvious that the drawings in the description below are some embodiments of the present invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
In the drawings: fig. 1 shows a flowchart of a hexahedral mesh generating method based on object symmetry according to the present invention.
Fig. 2 shows a flow of a workpiece symmetry detection method of the hexahedral mesh generating method based on object symmetry according to the present invention.
Fig. 3 shows a schematic view of a nominal split line in a minimum bounding box of a workpiece.
Fig. 4 shows a schematic view of division of the sides of the minimum bounding box.
Fig. 5 shows a series of industrial CT images of a cylindrical workpiece.
FIG. 6 shows F of FIG. 5 3 The corresponding mark points and projection points of the surface are schematic diagrams.
FIG. 7 shows FIG. 5 at F 3 All projected points on the surface.
Fig. 8 shows two sets of hexahedral mesh grids of mirror symmetry of a cylindrical workpiece.
Fig. 9 shows a three-dimensional full hexahedral mesh of the cylindrical workpiece after two sets of mesh topology optimization in fig. 8.
Detailed Description
The following description of the embodiments of the present invention will be made apparent and fully in view of the accompanying drawings, in which some, but not all embodiments of the invention are shown. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The method provided by the invention is described in detail below by taking the generation of a three-dimensional hexahedral mesh for a certain cylindrical workpiece as an example.
The hexahedral mesh generating method based on object symmetry as shown in fig. 1 comprises the following steps: s1, preprocessing a series of CT images of a workpiece to obtain a three-dimensional target area with workpiece information.
Specifically, step S1 includes, S1.1, performing a median filtering of the original image with a template size of 5×5.
S1.2, the two-dimensional boundary of the workpiece in the extracted image is detected by adopting the edge detection of the Canny operator, the double threshold coefficient [ TL, TH ] = [0.05,0.25] of the two-dimensional boundary is detected as an edge pixel if the gradient of a pixel point is larger than the upper threshold value TH, the edge pixel is discarded if the gradient of the pixel point is lower than the lower threshold value TL, and the two-dimensional boundary is accepted only when the two-dimensional boundary is adjacent to the pixel point which is higher than the upper threshold value.
S1.3, carrying out region filling on the image, so as to separate the effective region from the background region of the workpiece, and achieving the effect of threshold segmentation.
S1.4, orderly arranging the processed serial images, and simulating three-dimensional space information of the workpiece.
S2, detecting three-dimensional symmetry characteristics of the workpiece in the three-dimensional target area, and dividing the workpiece into symmetrical parts according to the characteristics.
Specifically, as shown in fig. 2, step S2 includes: s2.1, establishing a minimum bounding box of the workpiece in a three-dimensional space according to the industrial CT image, wherein the minimum bounding box comprises effective pixels of all CT images, and adjusting a three-dimensional coordinate system by taking the center of the minimum bounding box as an origin.
S2.2, as shown in FIG. 3, wherein L 1 -L 4 Is 4 body diagonal lines L 5 -L 7 Is 3 centerlines. Symmetrical dividing lines in the minimum outer bounding box through the origin of coordinates, comprising four body diagonal lines L 1 -L 4 And three central lines L 5 -L 7 Recording the intersection point of the symmetrical dividing line and the effective pixel as a mark point, wherein the intersection point of the ith symmetrical dividing line and the jth page CT image is recorded as the mark point。
S2.3, as shown in FIG. 4, dividing each face of the minimum bounding box, wherein the front, right, back, left, and top faces of the front view are F respectively 1 、F 2 、F 3 、F 4 、F 5 、F 6 。
S2.4, as shown in FIGS. 5, 6 and 7, F n All marked points in half minimum bounding box on surfaceRecord as a set of marker point sets { B n Will { B } n Projection of points in F n Projection points obtained on a surfaceConstitute projection point set { T ] n N=1, 2, … …,6,i =1, 2, … …,7. Marking point B 3i Represents a symmetrical parting line L 3 Intersection point and projection point T of effective pixel in ith page CT image 3_3i Represents B 3i At F 3 Projection onto a surface, at F 3 All the marker points on the half side of the face form a set of marker point sets { B } 3 All projections on the F3 plane }The shadow points form a set of projection points { T ] 3 }。
S2.5 for the marker Point set { B n -calculating its geometric centre (n=1, 2, … …, 6)（x,y,z）：Wherein, the method comprises the steps of, wherein,is { B n The length of the },is { B n Each mark point in }.
Each markTo the corresponding projection pointAverage value D of Euclidean distance of (2) n The method comprises the following steps:wherein, the method comprises the steps of, wherein,is { B n Length of }.
S2.6, setting a geometric center error threshold d 1 And projection error threshold d 2 Taking opposite faces of the smallest bounding box, e.g. F 1 And F 6 The geometric centers of the marked point sets are respectively points M 1 Sum point M 6 The average value of Euclidean distances from each marking point to the corresponding projection point is D 1 And D 6 。
S2.7, if point M 1 And point-M 6 The Euclidean distance of less than or equal to d 1 And D is 1 And D 6 The difference of less than or equal to d 2 The object is considered to be symmetrical about the plane of symmetry of the two faces.
S2.8, if M 1 And point-M 6 The Euclidean distance of (2) is greater than d 1 Or D 1 And D 2 Is greater than d 2 And if so, continuing to select the other two opposite faces, and repeating the step S2.7 until the symmetrical face of the object is found or no other opposite faces which are not judged.
S3, taking a part of symmetry as a main body, generating a core grid by adopting an octree method, and fitting the surface grid by adopting a gap filling method.
Specifically, step S3 includes: s3.1, according to the industrial CT image, establishing a minimum bounding box of the workpiece in a three-dimensional space, wherein the minimum bounding box comprises effective pixels of all images, and the side length of the minimum bounding box is an integer power of 2.
S3.2, dividing a three-dimensional hexahedral space as a root node into 8 subspaces with the same size, namely child nodes, and continuing dividing each child node until a certain child node no longer contains effective pixels or reaches a grid specified level, thereby obtaining a core grid.
And S3.3, the surface of the core grid is divided into two layers by using a gap filling method to fit, the inner layer modifies the original grid and fills gaps, and the outer layer fits the surface vertexes of the core grid to the object boundary according to the shortest distance in the normal vector direction.
S4, adopting symmetrical operation, mirror image copying the built grids, and connecting the two symmetrical grids.
Specifically, step S4 specifically includes: and (3) copying the hexahedral mesh of the built part of the workpiece according to mirror-inverted coordinates of the symmetrical plane in a three-dimensional space to obtain the hexahedral mesh of the non-built part, and merging along the symmetrical plane.
S5, correcting the grid structure at the joint of the symmetrical surfaces by using a topology optimization method, and finally obtaining the three-dimensional full hexahedral grid of the workpiece.
Specifically, as shown in fig. 8, step S5 includes: s5.1, performing layer deletion operation on outer layers of grids at two sides of the symmetry plane, and reserving core grids far away from the symmetry plane.
S5.2, performing row and column insertion operation along the normal vector direction of the symmetry plane, filling gaps among the core grids by using the hexahedral grids, and finally generating the three-dimensional full hexahedral grid of the cylindrical workpiece as shown in FIG. 9.
It should be understood that the above description is not intended to limit the invention to the particular embodiments disclosed, but to limit the invention to the particular embodiments disclosed, and that the invention is not limited to the particular embodiments disclosed, but is intended to cover modifications, adaptations, additions and alternatives falling within the spirit and scope of the invention.
Claims (5)
1. The hexahedral mesh generation method based on object symmetry is characterized by comprising the following steps:
s1, preprocessing a series of CT images of a workpiece to obtain a three-dimensional target area with workpiece information;
s2, detecting three-dimensional symmetry characteristics of the workpiece in a three-dimensional target area, and dividing the workpiece into symmetrical parts according to the characteristics;
the step S2 comprises the following steps:
s2.1, establishing a minimum bounding box of a workpiece in a three-dimensional space according to an industrial CT image, wherein the minimum bounding box comprises effective pixels of all CT images, and adjusting a three-dimensional coordinate system by taking the center of the minimum bounding box as an origin;
s2.2, through the origin of coordinates, symmetrically dividing lines in the minimum bounding box, including four body diagonal lines L 1 -L 4 And three central lines L 5 -L 7 Recording the intersection point of the symmetrical dividing line and the effective pixel as a mark point, wherein the intersection point of the ith symmetrical dividing line and the jth page CT image is recorded as a mark point B ij ；
S2.3, dividing each surface of the minimum bounding box, wherein the front surface, the right surface, the back surface, the left surface and the upper surface are respectively F 1 、F 2 、F 3 、F 4 、F 5 、F 6 ；
S2.4, F n All marked points B in half minimum bounding box on surface ij Record as a set of marker point sets { B n Will { B } n Projection of points in F n Projection point T obtained on surface n_ij Constitute projection point set { T ] n N=1, 2, … …,6,i =1, 2, … …,7;
s2.5 for the marker Point set { B n -calculating its geometric centre M (n=1, 2, … …, 6) n (x，y，z)：
Wherein m is { B } n Length of B }, B ij Is { B n Each marker point in };
each marked point B ij To the corresponding projection point T n_ij Average value D of Euclidean distance of (2) n The method comprises the following steps:
wherein m is { B } n A length of };
s2.6, setting a geometric center error threshold d 1 And projection error threshold d 2 Taking opposite faces of the smallest bounding box, e.g. F 1 And F 6 The geometric centers of the marked point sets are respectively points M 1 Sum point M 6 The average value of Euclidean distances from each marking point to the corresponding projection point is D 1 And D 6 ；
S2.7, if point M 1 And Point-M 6 The Euclidean distance of less than or equal to d 1 And D is 1 And D 6 The difference of less than or equal to d 2 The object is considered to be symmetrical about the plane of symmetry of the two faces;
s2.8, if M 1 And Point-M 6 The Euclidean distance of (2) is greater than d 1 Or D 1 And D 2 Is greater than d 2 When the object is not judged, the other two opposite faces are selected continuously, and the step S2.7 is repeated until the symmetrical face of the object is found or no other opposite faces which are not judged are found;
s3, taking a part of symmetry as a main body, generating a core grid by adopting an octree method, and fitting a surface grid by adopting a gap filling method;
s4, adopting symmetrical operation, mirror image copying the built grids, and connecting the two symmetrical grids;
and S5, correcting the grid structure at the joint of the symmetrical surfaces by using a topology optimization method, and finally obtaining the three-dimensional full hexahedral grid of the workpiece.
2. The method of generating a hexahedral mesh based on object symmetry according to claim 1, wherein the step of preprocessing the series of CT images of the workpiece comprises:
s1.1, carrying out template size 5×5 median filtering on an original image;
s1.2, extracting boundary information of the workpiece in the image by adopting edge detection of a Canny operator;
s1.3, carrying out region filling on the image so as to separate an effective region from a background region of the workpiece;
s1.4, orderly arranging the processed serial images, and simulating three-dimensional space information of the workpiece.
3. The hexahedral mesh generating method according to claim 1, wherein step S3 comprises:
s3.1, establishing a minimum bounding box of the workpiece in a three-dimensional space according to the industrial CT image, wherein the minimum bounding box comprises effective pixels of all images, and the side length of the minimum bounding box is an integer power of 2;
s3.2, dividing a three-dimensional hexahedral space as a root node into 8 subspaces with the same size, namely child nodes, and continuing dividing each child node until a certain child node no longer contains effective pixels or reaches a grid specified level, thereby obtaining a core grid;
and S3.3, the surface of the core grid is divided into two layers by using a gap filling method to fit, the inner layer modifies the original grid and fills gaps, and the outer layer fits the surface vertexes of the core grid to the object boundary according to the shortest distance in the normal vector direction.
4. The hexahedral mesh generating method according to claim 1, wherein step S4 specifically comprises: and (3) copying the hexahedral mesh of the built part of the workpiece according to mirror-inverted coordinates of the symmetrical plane in a three-dimensional space to obtain the hexahedral mesh of the non-built part, and merging along the symmetrical plane.
5. The hexahedral mesh generating method according to claim 1, wherein step S5 comprises:
s5.1, performing layer deletion operation on outer layers of grids at two sides of the symmetry plane, and reserving core grids far away from the symmetry plane;
s5.2, performing row and column insertion operation along the normal vector direction of the symmetry plane, and filling gaps among the core grids by using hexahedral grids.
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