CN116664758A - Tetrahedral grid self-adaptive hierarchical refinement method based on fault plane - Google Patents
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Abstract
The invention provides a tetrahedral mesh self-adaptive hierarchical refinement method based on a fault plane, which relates to the field of computer graphics and the field of tetrahedral mesh model subdivision, and comprises the steps of firstly establishing a tetrahedral mesh model and a fault plane triangle mesh model according to stratum data, then adaptively determining a refinement range according to the fault plane, and determining a tetrahedral set in the range; determining the subdivision level of the tetrahedron grid and the subdivision level of the edges through the distance relation between the tetrahedron and the fault plane; and finally, classifying and adaptively refining the tetrahedral mesh according to the number of the tetrahedral edges. The method breaks through the defects of the self-adaptive refinement of the existing fault-containing three-dimensional slope grid, and optimizes the grid model near the fault plane.
Description
Technical Field
The invention relates to the field of computer graphics and the field of tetrahedral grid model subdivision, in particular to a tetrahedral grid self-adaptive hierarchical refinement method based on a fault plane.
Background
The complexity of the fault structure facing the three-dimensional space division of the rock ore leads to accident frequency of fault-containing areas, so that the three-dimensional solid modeling of the fault-containing areas becomes a key of numerical simulation. How to fully utilize the grid self-adaptive refinement method to generate finer grid at fault is a problem which needs to be researched and solved.
In the currently commonly adopted Adaptive Mesh Refinement (AMR) method, a new mesh is directly constructed mainly by adding or deleting nodes, so as to obtain a required mesh resolution. According to the method, because the data of the grid model is too large, an accurate grid model cannot be provided after the grid model is thinned, and the efficiency and cost of the adaptive grid thinning are greatly influenced. In order to improve the self-adaptive grid refinement effect and reduce the refinement cost, many scholars and engineering technicians have made many researches on grid division, refinement algorithm and the like. For example, peraire and Li Xiangrong et al, use adaptive re-meshing based on anisotropic front-edge-driven mesh generation techniques; inria et al adaptively repartitioned according to anisotropic Delaunay; rivara performs successive halving subdivision according to the longest edge refinement algorithm, liu and Joe control the segmentation order according to the affine transformation. None of these studies have involved improving the efficiency of the grid adaptive refinement method by adaptively classifying the tetrahedral grid based on fault planes due to technical limitations.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a tetrahedral mesh self-adaptive hierarchical refinement method based on a fault plane, which refines the tetrahedral mesh containing the fault plane and improves the mesh precision near the fault plane.
In order to solve the technical problems, the invention adopts the following technical scheme: a tetrahedral mesh self-adaptive hierarchical refinement method based on a fault plane comprises the following steps:
step 1: establishing a tetrahedral mesh model and a fault plane mesh model;
step 1.1: performing tetrahedral subdivision on stratum data to establish a tetrahedral mesh model;
step 1.2: establishing a fault plane grid model to obtain a grid plane top point set;
establishing a fault plane grid model by using a Delaunay triangulation method to obtain a fault plane grid top point set P= { P 0 ,p 1 ,…,p g ,…,p q P, where g For the g-th fault plane grid vertex, g E [0, q]Q is the total number of the grid vertices of the fault plane;
step 2: determining a refinement range and a tetrahedron set in the range, wherein the specific method comprises the following steps of:
step 2.1: determining a refining range R according to the influence range of faults;
the impact range of a fault is determined by the fault type and the fault length. The correlation between the fault influence range and the fault length obeys a power function distribution form, the fault influence band width is increased along with the increase of the fault scale, but the increasing amplitude is gradually reduced along with the increase of the fault scale, different types of faults have a fault influence band width threshold, the symmetrical distribution of translation faults is used as a reference, the influence range takes the maximum influence band width of a disc on the fault, so that the refinement range R is expanded to two sides by taking the fault as the center, and the width takes the maximum influence band width of the disc on the fault;
step 2.2: within the refinement range R of the fault, a tetrahedral grid set T= { T is obtained 0 ，t 1 ，…，t i ，…，t n }, t is i For the ith tetrahedral mesh, i ε [0, n]N is the total number of tetrahedral meshes; obtain tetrahedron center point set C= { C 0 ，c 1 ，…，c i ，…，c n }, wherein c i For the ith tetrahedron center point set, i E [0, n ]]The method comprises the steps of carrying out a first treatment on the surface of the Obtaining vertex set V= { V of tetrahedron grid 0 ，v 1 ，…，v j ，…，v m }, v is j Is the j-th tetrahedronVertices of the mesh, j E [0, m]M is the total number of vertices of the tetrahedral mesh; obtain tetrahedral edge set E= { E 0 ，e 1 ，…，e r ，…，e k E, where e r R is the r tetrahedron edge, r is E [0, k]K is the total number of tetrahedral sides;
step 3: determining a subdivision level G of a tetrahedral mesh i The specific method comprises the following steps:
step 3.1: the shortest distance from the tetrahedral set to the fault plane grid is calculated as follows:
d in i I is the shortest distance from the center point of the ith tetrahedral element to the fault plane, i is E [0, n]N is the total number of tetrahedral center points, p g The g-th fault plane grid vertex, q is the total number of the fault plane grid vertices;
step 3.2: calculating the number of stages G of a tetrahedral mesh i The subdivision level calculation formula is as follows:
g in i For the subdivision level of the ith tetrahedral mesh, i ε [0, n]N is the total number of tetrahedral meshes, if D i R is G i ＝0；
Step 3.3: determining subdivision level H of tetrahedral edges r The subdivision level of the edge is calculated as follows:
h in r For the subdivision level of the r-th edge, r E [0, k]K is the total number of tetrahedral sides, G i For the subdivision level of the ith tetrahedral mesh, i ε [0,l ]]L is the number of tetrahedral meshes containing the r-th edge;
step 4: for tetrahedronGrid hierarchical self-adaptive refinement and traversal tetrahedron set T= { T 0 ，t 1 ，…，t i ，…，t n And (3) classifying and subdividing the tetrahedrons according to the subdivision level of the edges contained in each tetrahedron, wherein the concrete method comprises the following steps of:
step 4.1: if the subdivision level of the tetrahedron edge is greater than 0, adding the midpoint of the edge to the vertex set V;
step 4.2: for tetrahedrons with subdivision level of more than 0, reconnecting the tetrahedrons by newly added vertexes and original vertexes, replacing the original tetrahedrons by newly generated tetrahedrons, and adding the newly generated tetrahedrons into a tetrahedron set T;
step 4.3: the subdivision level of the newly generated edge is equal to the subdivision level of the original edge minus 1, and the newly generated edge is added into the edge set E;
step 4.4: repeating the steps 4.1-4.3 until no tetrahedral edge progression is greater than zero cycle termination.
The beneficial effects of adopting above-mentioned technical scheme to produce lie in: the invention provides a tetrahedral mesh self-adaptive hierarchical refinement method based on a fault plane, which comprises the steps of establishing a tetrahedral mesh model and a fault plane mesh model, adaptively determining a refinement range according to the fault plane, and determining a tetrahedral set in the range; determining the subdivision level of the tetrahedron grid and the subdivision level of the edges through the distance relation between the tetrahedron and the fault plane; and carrying out grading self-adaptive refinement on the tetrahedral mesh according to the number of the tetrahedral edges. The method breaks through the defects of the self-adaptive refinement of the existing fault-containing three-dimensional slope grid, and optimizes the grid model near the fault plane.
Drawings
FIG. 1 is a flow chart of a tetrahedral mesh adaptive hierarchical refinement method based on a fault plane provided by an embodiment of the present invention;
FIG. 2 is a diagram of a result of creating a tetrahedral mesh model by performing tetrahedral subdivision on formation data according to an embodiment of the present invention;
FIG. 3 is a diagram of a result of establishing a fault plane mesh model using a Delaunay triangulation method provided by an embodiment of the present invention;
FIG. 4 is a fault refinement scope box provided by an embodiment of the present invention;
fig. 5 is a diagram of a hierarchical adaptive refinement result of a three-dimensional slope grid with faults, which is provided by the embodiment of the invention.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
In the embodiment, the tetrahedral mesh containing faults in the adjacent end slope composite side slope area of a certain strip mine is taken as an example, the model range is 1.61km long and 1.1km wide, the fault length is 2.08km, and the tetrahedral mesh is graded and adaptively refined by the tetrahedral mesh self-adaptive grading refinement method based on the fault plane.
In this embodiment, a tetrahedral mesh adaptive hierarchical refinement method based on a fault plane, a flowchart is shown in fig. 1, includes the following steps:
step 1: establishing a tetrahedral mesh model and a fault plane mesh model;
step 1.1: performing tetrahedral subdivision on stratum data to establish a tetrahedral mesh model;
step 1.2: establishing a fault plane grid model to obtain a grid plane top point set;
establishing a fault plane grid model by using a Delaunay triangulation method to obtain a fault plane grid top point set P= { P 0 ，p 1 ，…，p g ,…，p q P, where g For the g-th fault plane grid vertex, g E [0, q]Q is the total number of the grid vertices of the fault plane;
the embodiment comprises the following steps of: the surface soil layer, the fourth system, the sandstone layer, the mudstone upper layer, the coal layer and the mudstone lower layer are subjected to tetrahedral subdivision on the stratum interface data, a tetrahedral mesh model is built, and 187897 tetrahedral meshes are obtained, as shown in fig. 2.
The fault plane triangle mesh model was established using the Delaunay triangulation method on the fault plane, resulting in 11749 mesh vertices and 7619 triangle meshes, as shown in fig. 3.
Step 2: determining a refinement range and a tetrahedron set in the range, wherein the specific method comprises the following steps of:
step 2.1: determining a refining range R according to the influence range of faults;
the impact range of a fault is determined by the fault type and the fault length. The correlation between the fault influence range and the fault length obeys a power function distribution form, the fault influence band width is increased along with the increase of the fault scale, but the increasing amplitude is gradually reduced along with the increase of the fault scale, different types of faults have a fault influence band width threshold, the symmetrical distribution of translation faults is used as a reference, the influence range takes the maximum influence band width of a disc on the fault, so that the refinement range R is expanded to two sides by taking the fault as the center, and the width takes the maximum influence band width of the disc on the fault;
step 2.2: within the refinement range R of the fault, a tetrahedral grid set T= { T is obtained 0 ，t 1 ，…，t i ，…，t n And t is }, where i For the ith tetrahedral mesh, i ε [0, n]N is the total number of tetrahedral meshes; obtain tetrahedron center point set C= { C 0 ，c 1 ，…，c i ，…，c n }, wherein c i For the ith tetrahedron center point set, i E [0, n ]]The method comprises the steps of carrying out a first treatment on the surface of the Obtaining a tetrahedral grid vertex set V= { V 0 ，v 1 ，…，v j ，…，v m }, v is j For the vertex of the jth tetrahedral mesh, j ε [0, m]M is the total number of vertices of the tetrahedral mesh; obtain tetrahedral edge set E= { E 0 ，e 1 ，…，e r ，…，e k E, where e r R is the r tetrahedron edge, r is E [0, k]K is the total number of tetrahedral sides;
in the embodiment, the fault is a positive fault with the length of 2.08km, according to the length and type of the fault, the refining range is determined by table 1, R=75m is selected, and the influence range of the fault is 75m on both sides of the fault, as shown in fig. 4;
obtaining a tetrahedral grid set T within a refinement range R, wherein the tetrahedral grid set T is 60896 tetrahedral grids in total; obtaining a tetrahedral grid vertex set V, wherein the total number of the tetrahedral grid vertices is 106536; a tetrahedral edge set E was obtained, for a total of 126387 tetrahedral edges.
Table 1 fault influence range table
Step 3: determining a subdivision level G of a tetrahedral mesh i The specific method comprises the following steps:
step 3.1: the shortest distance from the tetrahedral set to the fault plane grid is calculated as follows:
d in i I is the shortest distance from the center point of the ith tetrahedral element to the fault plane, i is E [0, n]N is the total number of tetrahedral center points, p g The g-th fault plane grid vertex, q is the total number of the fault plane grid vertices;
step 3.2: calculating the number of stages G of a tetrahedral mesh i The subdivision level calculation formula is as follows:
g in i For the subdivision level of the ith tetrahedral mesh, i ε [0, n]N is the total number of tetrahedral meshes, if D i R is G i ＝0；
Step 3.3: determining subdivision level H of tetrahedral edges r The subdivision level of the edge is calculated as follows:
h in r For the subdivision level of the r-th edge, r E [0, k]K is the total number of tetrahedral sides, G i For the subdivision level of the ith tetrahedral mesh, i ε [0,l ]]L is the number of tetrahedral meshes containing the r-th edge;
according to the embodiment, the subdivision level of 60896 tetrahedral grids is calculated through a tetrahedral grid subdivision level calculation formula;
according to the subdivision level of the tetrahedral mesh and the subdivision level calculation formula of the edges, the subdivision level of 126387 edges of the tetrahedron is calculated respectively.
Step 4: self-adaptive hierarchical refinement of tetrahedral meshes, and traversal of tetrahedral set T= { T 0 ，t 1 ，…，t i ，…，t n And (3) classifying and subdividing the tetrahedrons according to the subdivision level of the edges contained in each tetrahedron, wherein the concrete method comprises the following steps of:
step 4.1: if the subdivision level of the tetrahedron edge is greater than 0, adding the midpoint of the edge to the vertex set V;
step 4.2: for tetrahedrons with the edge subdivision level being greater than 0, reconnecting the tetrahedrons by newly added vertexes and original vertexes, replacing the original tetrahedrons by newly generated tetrahedrons, and adding the newly generated tetrahedrons into a tetrahedron set T;
step 4.3: the subdivision level of the newly generated edge is equal to the subdivision level of the original edge minus 1, and the newly generated edge is added into the edge set E;
step 4.4: repeating the steps 4.1-4.3 until no tetrahedral edge progression is greater than zero cycle termination.
In the embodiment, all tetrahedral grids in the refinement range R are adaptively classified and refined to obtain an adaptive classifying and refining result of the grid of the three-dimensional slope containing the fault, as shown in fig. 5, and the result proves that the adaptive classifying and refining method of the tetrahedral grid based on the fault plane is applicable to the grid of the three-dimensional slope containing the fault.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced with equivalents; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions, which are defined by the scope of the appended claims.
Claims (5)
1. A tetrahedral grid self-adaptive hierarchical refinement method based on a fault plane is characterized by comprising the following steps of: the method comprises the following steps:
step 1: establishing a tetrahedral mesh model and a fault plane mesh model;
step 2: determining a refining range and a tetrahedron set in the range, determining a refining range R of the grid model through a fault influence range table, and obtaining a tetrahedron grid set T, a tetrahedron grid top point set V and a tetrahedron edge set E in the refining range R;
step 3: determining a subdivision level G of a tetrahedral mesh i Determining the subdivision level H of tetrahedral edges r ；
Step 4: and carrying out self-adaptive hierarchical refinement on the tetrahedral mesh, traversing the tetrahedral set, and carrying out hierarchical subdivision on the tetrahedron according to the subdivision level of the edges contained in each tetrahedron.
2. The tetrahedral mesh adaptive hierarchical refinement method based on the fault plane according to claim 1, wherein: the specific method of the step 1 is as follows:
step 1: establishing a tetrahedral mesh model and a fault plane mesh model;
step 1.1: performing tetrahedral subdivision on stratum data to establish a tetrahedral mesh model;
step 1.2: establishing a fault plane grid model to obtain a grid plane top point set;
establishing a fault plane grid model by using a Delaunay triangulation method to obtain a fault plane grid top point set P= { P 0 ,p 1 ,…,p g ,…,p q P, where g For the g-th fault plane grid vertex, g E [0, q]Q is the total number of fault plane mesh vertices.
3. The tetrahedral mesh adaptive hierarchical refinement method based on the fault plane according to claim 1, wherein: the specific method of the step 2 is as follows:
step 2.1: the impact range of a fault is determined by the fault type and the fault length. The correlation between the fault influence range and the fault length obeys a power function distribution form, the fault influence band width is increased along with the increase of the fault scale, but the increasing amplitude is gradually reduced along with the increase of the fault scale, different types of faults have a fault influence band width threshold, the symmetrical distribution of translation faults is used as a reference, the influence range takes the maximum influence band width of a disc on the fault, so that the refinement range R is expanded to two sides by taking the fault as the center, and the width takes the maximum influence band width of the disc on the fault;
step 2.2: within the refinement range R of the fault, a tetrahedral grid set T= { T is obtained 0 ,t 1 ,…,t i ,…,t n }, t is i For the ith tetrahedral mesh, i ε [0, n]N is the total number of tetrahedral meshes; obtain tetrahedron center point set C= { C 0 ,c 1 ,…，c i ,…,c n }, wherein c i For the ith tetrahedron center point set, i E [0, n ]]The method comprises the steps of carrying out a first treatment on the surface of the Obtaining a tetrahedral grid vertex set V= { V 0 ,v 1 ,…,v j ,…,v m }, v is j For the vertex of the jth tetrahedral mesh, j ε [0, m]M is the total number of vertices of the tetrahedral mesh; obtain tetrahedral edge set E= { E 0 ,e 1 ,…,e r ,…,e k E, where e r R is the r tetrahedron edge, r is E [0, k]K is the total number of tetrahedral sides.
4. The tetrahedral mesh adaptive hierarchical refinement method based on the fault plane according to claim 1, wherein: the specific method of the step 3 is as follows:
step 3.1: the shortest distance from the tetrahedral set to the fault plane grid is calculated as follows:
d in i I is the shortest distance from the center point of the ith tetrahedral element to the fault plane, i is E [0, n]N is the total number of tetrahedral center points, p g The g-th fault plane grid vertex, q is faultThe total number of face mesh vertices;
step 3.2: calculating the number of stages G of a tetrahedral mesh i The subdivision level calculation formula is as follows:
g in i For the subdivision level of the ith tetrahedral mesh, i ε [0, n]N is the total number of tetrahedral meshes, if D i >R is G i ＝0；
Step 3.3: determining subdivision level H of tetrahedral edges r The subdivision level of the edge is calculated as follows:
h in r For the subdivision level of the r-th edge, r E [0, k]K is the total number of tetrahedral sides, G i For the subdivision level of the ith tetrahedral mesh, i ε [0,l ]]L is the number of tetrahedral meshes containing the r-th edge.
5. The tetrahedral mesh adaptive hierarchical refinement method based on the fault plane according to claim 1, wherein: the specific method of the step 4 is as follows:
step 4.1: if the subdivision level of the tetrahedron edge is greater than 0, adding the midpoint of the edge to the vertex set V;
step 4.2: for tetrahedrons with the edge subdivision level being greater than 0, reconnecting the tetrahedrons by newly added vertexes and original vertexes, replacing the original tetrahedrons by newly generated tetrahedrons, and adding the newly generated tetrahedrons into a tetrahedron set;
step 4.3: the subdivision level of the newly generated edge is equal to the subdivision level of the original edge minus 1, and the newly generated edge is added into the edge set E;
step 4.4: repeating the steps 4.1-4.3 until no tetrahedral edge progression is greater than zero cycle termination.
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| CN117272759A (en) * | 2023-11-20 | 2023-12-22 | 埃洛克航空科技（北京）有限公司 | Method and device for splitting triangular mesh in three-dimensional reconstruction process and computer equipment |
| CN117272759B (en) * | 2023-11-20 | 2024-03-15 | 埃洛克航空科技（北京）有限公司 | Method and device for splitting triangular mesh in three-dimensional reconstruction process and computer equipment |
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