CN112381950B - Grid hole repairing method, electronic equipment and computer readable storage medium - Google Patents
Grid hole repairing method, electronic equipment and computer readable storage medium Download PDFInfo
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- CN112381950B CN112381950B CN202011221802.7A CN202011221802A CN112381950B CN 112381950 B CN112381950 B CN 112381950B CN 202011221802 A CN202011221802 A CN 202011221802A CN 112381950 B CN112381950 B CN 112381950B
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Abstract
The invention discloses a grid hole repairing method, which comprises the following steps: s1: extracting all holes on the grid of the input original grid data; s4: establishing a tetrahedral mesh of boundary points of the holes according to a Delaunay tetrahedral optimization method; s5: filling the holes by adopting a panel subset of the tetrahedral mesh to obtain filled holes; s6: newly adding space points on the filled holes to conduct grid subdivision; s7: and respectively establishing local multi-order Laplacian according to each newly added space point in grid subdivision, enabling each local multi-order Laplacian to be equal to 0 so as to obtain a multi-order Laplacian matrix, solving the Laplacian matrix to obtain three-dimensional coordinates of each newly added space point after deformation, and obtaining a grid hole repairing result. The invention overcomes the defects of poor hole repairing characteristic maintaining effect and low calculation efficiency for processing large holes in the prior art.
Description
Technical Field
The invention relates to the field of high-precision industrial measurement, in particular to a grid hole repairing method.
Background
With the rapid development of optical three-dimensional technology, the acquisition of a three-dimensional model of an object in space based on a three-dimensional scanning technology has become the most dominant technical means of geometric modeling, and has been widely applied in a plurality of fields. However, due to the limitations of the hardware of the scanning device and the algorithm, defects such as degraded triangles and holes often exist in the grid model reconstructed from the point cloud data obtained by three-dimensional scanning, which leads to poor quality and unattractive appearance of the grid model. Therefore, the rapid detection and high-precision repair of complex holes in a triangular mesh model become a challenging technical problem in the three-dimensional scanning geometric modeling research direction.
The existing triangular mesh model hole repairing algorithm has good hole repairing effect on plane holes or holes with small curvature of surrounding meshes, and has unsatisfactory hole processing effect on holes with large curvature of surrounding meshes. As a representative wavefront method, it is often a self-intersecting problem for some complex holes; and has the problem of low efficiency in processing large holes. Therefore, the development of a feature-preserving and high-efficiency grid hole repairing algorithm plays a vital role in three-dimensional optical modeling.
The foregoing background is only for the purpose of facilitating an understanding of the principles and concepts of the application and is not necessarily in the prior art to the present application and is not intended to be used as an admission that such background is not entitled to antedate such novelty and creativity by virtue of prior application or that it is already disclosed at the date of filing of this application.
Disclosure of Invention
Aiming at the defects of poor hole repairing characteristic maintaining effect and low calculation efficiency for processing large holes in the prior art, the invention provides a grid hole repairing method with characteristics maintaining and high efficiency.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the invention discloses a grid hole repairing method, which comprises the following steps:
s1: extracting all holes on the grid of the input original grid data;
S4: establishing a tetrahedral mesh of boundary points of the holes according to a Delaunay tetrahedral optimization method;
S5: filling the holes by adopting a panel subset of the tetrahedral mesh to obtain filled holes;
S6: newly adding space points on the filled holes to conduct grid subdivision;
S7: and respectively establishing local multi-order Laplacian according to each newly added space point in grid subdivision, enabling each local multi-order Laplacian to be equal to 0 so as to obtain a multi-order Laplacian matrix, solving the Laplacian matrix to obtain three-dimensional coordinates of each newly added space point after deformation, and obtaining a grid hole repairing result.
Preferably, the mesh hole repairing method further comprises the following steps: s2: dividing all holes into large holes and small holes according to the number n of the boundary points of each hole, judging the holes to be small holes when n is less than or equal to 10, and judging the holes to be large holes when n is more than 10; and executing steps S4-S7 for repairing the large holes.
Preferably, step S2 further comprises, for the small hole, performing step S3 to repair the hole; the step S3 comprises the following steps: and solving the mass center points of all the boundary points of the holes, sequentially connecting the mass center points with all the boundary points, connecting every two adjacent boundary points with the mass center points respectively to obtain a newly added patch, and connecting all the boundary points to obtain the mesh hole repairing result.
Preferably, step S1 specifically includes: the input original grid data is read, and the triangle grid of the original grid data is represented by using a half data structure so as to extract all holes on the triangle grid of the original grid data.
Preferably, step S4 specifically includes: traversing all boundary points of the hole one by one, constructing four boundary points which are not on the same plane into a tetrahedron, and connecting the boundary points with vertexes of the constructed tetrahedron to construct a new tetrahedron by judging the position relation between the newly traversed boundary points and the constructed tetrahedron, and when all boundary points are traversed, constructing and obtaining the tetrahedron grid.
Preferably, step S5 specifically includes: and filling the holes by adopting a subset of the surface patches of the tetrahedral mesh according to the principle of enabling the sum of the areas of all filling surfaces to be minimum.
Preferably, filling the holes with the subset of patches of tetrahedral mesh according to the principle of minimizing the sum of the areas of all the filling faces specifically comprises: and (3) taking W (D) to represent the area summation of the holes, starting from any boundary of the holes, enabling the boundary and the other boundary point to form a triangular surface patch t, dividing the area of the holes into two subareas of D1 and D2 and the triangular surface patch t, wherein W (D) is represented as: Wherein W (D1) represents the area of the sub-region D1, W (D2) represents the area of the sub-region D2, and W (t) represents the area of the triangular patch t; and recursively starting from any boundary of the hole, and filling all areas of the hole according to the optimization criterion of minimum W (D).
Preferably, step S6 specifically includes: counting the average side length of all boundary sides of the holeTraversing each newly added triangular patch, and calculating the average value of three side lengths of the triangular patchesIf it isThe centroid of the triangular patch is connected with three vertices of the triangular patch to decompose one triangle into three triangles, respectively.
Preferably, in step S6, after the corresponding triangular patches are subdivided, the method further includes: and judging whether two adjacent triangles meet the Delaunay triangulation criterion, if not, performing edge exchange operation until all triangular patches meet the condition, stopping segmentation, and obtaining a grid subdivided result.
Preferably, the newly added spatial point of the mesh subdivision refers to the centroid of the triangular patch newly added when the triangular patch is subdivided.
The invention also discloses an electronic device, which comprises a processor and a memory, wherein the memory stores computer executable instructions which can be executed by the processor, and the processor executes the computer executable instructions to realize the steps of the grid hole repairing method.
The invention further discloses a computer readable storage medium, wherein the computer readable storage medium stores computer executable instructions, and the computer executable instructions, when being called and executed by a processor, cause the processor to realize the steps of the grid hole repairing method.
Compared with the prior art, the invention has the beneficial effects that: according to the grid hole repairing method, when the grid holes are repaired, the extracted hole boundary points are subjected to Delaunay tetrahedron, and the original holes are filled by using the tetrahedron panel subsets, so that the hole rough repairing efficiency is improved; after the initial filling surface patch is obtained, a triangular surface patch similar to the boundary side length is obtained by utilizing a grid subdivision technology, and then deformed space three-dimensional coordinates of the newly added space points are obtained by solving the Laplacian operator to be equal to 0, so that the original grid characteristics can be recovered after repair to the greatest extent, and the defects of poor hole repair characteristic maintaining effect, low calculation efficiency for processing large holes and the like in the prior art are overcome.
Drawings
FIG. 1 is a flow chart of mesh hole repair according to a first embodiment of the present invention;
FIG. 2 is a flow chart of mesh hole repair according to a second embodiment of the present invention;
FIG. 3 is a schematic diagram of a half data structure;
FIG. 4 is a schematic diagram of centroid method filling holes;
FIG. 5 is a schematic diagram of a tetrahedral data structure;
FIG. 6a is a schematic diagram of a hole region in a hole coarsening step;
FIG. 6b is a schematic diagram showing the division of the hole region into a plurality of regions in the hole coarsening step;
FIG. 7a is a schematic diagram of the operation of grid subdivision;
FIG. 7b is a schematic diagram of the operation of an edge swap;
FIG. 8a is a schematic diagram of a woodcarving grid hole pattern before hole repair is performed;
FIG. 8b is a schematic diagram of a wood carving grid hole pattern after hole coarsening;
FIG. 8c is a schematic diagram of a woodcarving grid hole model after grid subdivision;
Fig. 8d is a schematic diagram of a wood carving grid hole model after laplace deformation.
Detailed Description
The invention will be further described with reference to the following drawings in conjunction with the preferred embodiments.
As shown in fig. 1, a first embodiment of the present invention discloses a mesh hole repairing method, which includes the following steps:
s1: extracting all holes on the grid of the input original grid data;
S4: establishing a tetrahedral mesh of boundary points of the holes according to a Delaunay tetrahedral optimization method;
S5: filling the holes by adopting a panel subset of the tetrahedral mesh to obtain filled holes;
S6: newly adding space points on the filled holes to conduct grid subdivision;
S7: and respectively establishing local multi-order Laplacian according to each newly added space point in grid subdivision, enabling each local multi-order Laplacian to be equal to 0 so as to obtain a multi-order Laplacian matrix, solving the Laplacian matrix to obtain three-dimensional coordinates of each newly added space point after deformation, and obtaining a grid hole repairing result.
As shown in fig. 2, the second embodiment of the invention discloses a grid hole repairing method based on Delaunay tetrahedron optimization acceleration, which comprises the following steps:
S1: and inputting original grid data, establishing a half topological relation, and searching all hole boundaries.
The original grid data is read, a half data structure is shown in fig. 3 to represent the triangular grid of the input original grid data, all holes can be represented by continuous closed half, all holes on the grid are extracted by utilizing the characteristic of the half data structure, and all hole boundary information is stored in a computer storage container.
S2: the holes are divided into large holes and small holes according to the number of the hole boundary points.
Traversing each hole in the storage container, dividing the holes into a large hole and a small hole according to the number n of the boundary points of each hole, and identifying the holes as the small holes when n is less than or equal to 10 and identifying the holes as the large holes when n is more than 10. Step S3 is performed for small holes to repair holes, and steps S4 to S7 are performed for large holes to repair holes.
S3: and connecting the centroid of the boundary point with all boundary points by using a centroid method to form a new triangular patch.
All small holes were repaired using centroid method as shown in fig. 4. Firstly, the mass centers O of all boundary points are solved, then the mass center points are sequentially connected with all boundary points, two adjacent vertexes are respectively connected with the mass center points, a newly added face sheet can be obtained, all boundary points are connected completely, the mesh hole repairing result can be obtained, and the rapid repair of small holes is realized.
S4: establishing a tetrahedral mesh: boundary points are built up into the Delaunay tetrahedral structure.
The tetrahedron grid is established through all boundary points of the large hole according to the Delaunay tetrahedron optimization method, as shown in fig. 5, every four boundary points (such as boundary point a, b, c, d) which are not on the same plane can form a tetrahedron, all boundary points are added into a computer storage container point by point, the position relation between the newly added boundary points and the existing tetrahedron is judged, the newly added boundary points are connected with the vertices of the existing tetrahedron to form a new tetrahedron, and the final space tetrahedron structure is obtained until all boundary points are added.
S5: coarsely filling holes: and selecting a tetrahedral panel subset to fill the holes.
For a hole area D, as shown in fig. 6a, a tetrahedral panel subset is used to fill the hole area, and the optimization goal adopted in this embodiment is to sum the areas of all filling surfaces to a minimum, so as to ensure that the filling area is not self-intersected as much as possible.
Let W (D) denote the sum of the entire hole area, starting from one boundary edge, and assuming that it forms a triangular patch t with the other vertex, the patch divides the entire hole area into two sub-areas D1 and D2 and the patch itself, as shown in FIG. 6 b. W (D) may be represented as:
And recursively removing from one boundary edge, and filling all areas of the holes according to the optimization criterion of minimum total area.
S6: grid subdivision: the newly added surface patches are subdivided so that the newly added surface patches are similar in size to the boundary surface patches.
The newly added triangular patches need to be subdivided, so that the size of the triangular patches is ensured to be similar to that of the boundary patches. Firstly, the average side length of all boundary sides is countedTraversing each newly added dough piece, if the average value of three side lengths of triangular dough piecesSubdividing the triangle as shown in fig. 7a, connecting the centroid of the patch with three vertices, and decomposing a triangle into three triangles; and if the three side length averages of the triangular patch No action is taken. When two adjacent triangles do not meet the Delaunay triangulation criterion, performing edge exchange operation on the triangles, and stopping segmentation until all triangular patches meet the conditions as shown in fig. 7b, so as to obtain a grid subdivided result; and if two adjacent triangles meet the Delaunay triangulation criterion, nothing is done.
S7: laplace deformation: and restoring the curvature of the newly added point by using Laplace deformation to obtain a final curvature restoration result.
Storing all newly added space points (patch centroid points added during subdivision) into a computer storage container, traversing all newly added space points, searching for two-ring neighborhood points of the newly added space points (namely, finding two surrounding circles of points by taking a certain newly added space point as the center), and establishing a local second-order Laplacian operator L 2 (v) in a recursion mode, wherein v represents the newly added space points, so that L 2 (v) =tetrode is used for guaranteeing smoothness and curvature continuity of a local area.
And combining m second-order Laplace operator equations listed by m newly added space points to obtain a Laplace matrix with m, and solving the Laplace matrix to obtain three-dimensional coordinates of each newly added space point after deformation to obtain a hole filling result after final curvature recovery.
In this embodiment, a local second-order laplace operator is established according to each newly added spatial point, and in other embodiments, a local multi-order laplace operator, for example, a local third-order laplace operator, a local fourth-order laplace operator, and the like, may also be established.
S8: the small holes and the large holes are repaired respectively through the step S3 and the step S7, and a complete grid can be output.
According to the grid hole repairing method based on Delaunay tetrahedron optimization acceleration, which is provided by the embodiment of the invention, when the grid holes are repaired, the extracted hole boundary points are subjected to Delaunay tetrahedron, and the tetrahedron panel subset is used for filling the original holes, so that the hole rough repairing efficiency is improved; after the initial filling surface patch is obtained, a triangular surface patch similar to the boundary side length is obtained by utilizing a grid subdivision technology, and then deformed space three-dimensional coordinates of the newly added space points are obtained by solving the Laplacian operator to be equal to 0, so that the original grid characteristics can be recovered after repair to the greatest extent, and the defects of poor hole repair characteristic maintaining effect, low calculation efficiency for processing large holes and the like in the prior art are overcome.
The following mesh hole repairing method based on Delaunay tetrahedron optimization acceleration in the second embodiment of the present invention performs hole repairing on the woodcarving mesh hole model shown in fig. 8a, the mesh model after the hole rough repairing treatment is shown in fig. 8b, the mesh model after the hole mesh subdivision treatment is shown in fig. 8c, the mesh model after the hole laplace deformation is shown in fig. 8d, it can be seen from fig. 8d that, when the mesh hole repairing method in the embodiment of the present invention repairs holes, the complex holes recover the shape characteristics of the hole area well after three operations of hole rough repairing, mesh subdivision and laplace deformation, and ensure the curvature continuity of the hole boundary area.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several equivalent substitutions and obvious modifications can be made without departing from the spirit of the invention, and the same should be considered to be within the scope of the invention.
Claims (6)
1. The grid hole repairing method is characterized by comprising the following steps of:
s1: extracting all holes on the grid of the input original grid data;
S4: establishing a tetrahedral mesh of boundary points of the holes according to a Delaunay tetrahedral optimization method;
S5: filling the holes by adopting a panel subset of the tetrahedral mesh to obtain filled holes;
S6: newly adding space points on the filled holes to conduct grid subdivision;
S7: respectively establishing local multi-order Laplacian according to each newly added space point in grid subdivision, enabling each local multi-order Laplacian to be equal to 0 so as to obtain a multi-order Laplacian matrix, solving the Laplacian matrix to obtain three-dimensional coordinates of each newly added space point after deformation, and obtaining a grid hole repairing result;
the step S5 specifically includes: filling the holes by adopting a subset of the face sheets of the tetrahedral mesh according to the principle of minimizing the sum of the areas of all the filling faces;
filling the holes with a subset of patches of tetrahedral mesh according to a principle that the sum of the areas of all filling surfaces is minimized specifically comprises: and (3) taking W (D) to represent the area summation of the holes, starting from any boundary of the holes, enabling the boundary and the other boundary point to form a triangular surface patch t, dividing the area of the holes into two subareas of D1 and D2 and the triangular surface patch t, wherein W (D) is represented as: wherein W (D1) represents the area of the sub-region D1, W (D2) represents the area of the sub-region D2, and W (t) represents the area of the triangular patch t; recursively descending any boundary of the hole, and filling all areas of the hole according to the optimization criterion of minimum W (D);
the step S6 specifically comprises the following steps: counting the average side length of all boundary sides of the hole Traversing each newly added triangular patch, and calculating the average value of three side lengths of the triangular patchesIf it isThe centroid of the triangular surface patch is respectively connected with three vertexes of the triangular surface patch to decompose one triangle into three triangles;
the method further comprises the following steps after the corresponding triangular patches are subdivided: judging whether two adjacent triangles meet Delaunay triangulation criteria or not, if not, performing edge exchange operation until all triangular patches meet the conditions, stopping segmentation, and obtaining a grid subdivided result;
The newly added space points of the grid subdivision refer to the mass centers of triangular patches which are newly added when the triangular patches are subdivided.
2. The mesh hole repair method of claim 1, further comprising the steps of:
S2: dividing all holes into large holes and small holes according to the number n of the boundary points of each hole, judging the holes to be small holes when n is less than or equal to 10, and judging the holes to be large holes when n is more than 10; wherein, for the large hole, steps S4 to S7 are executed to repair the hole; step S3 is executed for the small holes so as to repair the holes;
S3: and solving the mass center points of all the boundary points of the holes, sequentially connecting the mass center points with all the boundary points, connecting every two adjacent boundary points with the mass center points respectively to obtain a newly added patch, and connecting all the boundary points to obtain the mesh hole repairing result.
3. The mesh hole repair method according to claim 1, wherein step S1 specifically comprises: the input original grid data is read, and the triangle grid of the original grid data is represented by using a half data structure so as to extract all holes on the triangle grid of the original grid data.
4. The mesh hole repair method according to claim 1, wherein step S4 specifically comprises: traversing all boundary points of the hole one by one, constructing four boundary points which are not on the same plane into a tetrahedron, and connecting the boundary points with vertexes of the constructed tetrahedron to construct a new tetrahedron by judging the position relation between the newly traversed boundary points and the constructed tetrahedron, and when all boundary points are traversed, constructing and obtaining the tetrahedron grid.
5. An electronic device comprising a processor and a memory, the memory storing computer-executable instructions executable by the processor to perform the steps of the mesh hole repair method of any one of claims 1 to 4.
6. A computer readable storage medium storing computer executable instructions which, when invoked and executed by a processor, cause the processor to implement the steps of the grid hole repair method of any one of claims 1 to 4.
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| CN113593011A (en) * | 2021-07-12 | 2021-11-02 | 杭州思锐迪科技有限公司 | Hole repairing method, electronic device and storage medium |
| CN115077490B (en) * | 2022-06-24 | 2024-05-10 | 中铁二局第一工程有限公司 | Unmanned aerial vehicle naked eye 3D full-digital mapping method |
| CN117314786B (en) * | 2023-10-30 | 2025-07-08 | 浙江大学 | Three-dimensional grid repairing method based on deep learning |
| CN121725174A (en) * | 2026-02-27 | 2026-03-24 | 浙江省地矿勘察院有限公司 | Abnormality detection and restoration method for earth mine investigation drilling data |
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| CN102074052A (en) * | 2011-01-20 | 2011-05-25 | 山东理工大学 | Sampling point topological neighbor-based method for reconstructing surface topology of scattered point cloud |
| CN108230452B (en) * | 2017-12-18 | 2021-06-29 | 华侨大学 | A Model Hole Filling Method Based on Texture Synthesis |
| CN109615702B (en) * | 2018-10-23 | 2023-09-22 | 深圳市重投华讯太赫兹科技有限公司 | Grid hole filling method, image processing equipment and device with storage function |
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| CN101339670A (en) * | 2008-08-07 | 2009-01-07 | 浙江工业大学 | A computer-aided three-dimensional craniofacial reconstruction method |
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