CN117094197B - CDT parameterized grid and global isotropy re-gridding method - Google Patents
CDT parameterized grid and global isotropy re-gridding method Download PDFInfo
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Abstract
The invention discloses a CDT parameterized grid and global isotropy re-gridding method, which comprises the following steps: step 1: generating a visual triangle by using OCCT the CAD model; step 2: grid parameterization: based on the initial triangulation, the parameterized domain for each patch is reconstructed and CDT is reapplied to preserve the boundaries of each parameterized domain, and then the 2D triangulation is projected back into 3D space. Reconstructing the parameter domain of each curved surface piece through initial triangulation, generating a triangle with a better shape through the recovery and sampling of a boundary curve and angle optimization, and further accelerating the re-meshing process; through the price optimization of the inner vertex, the price regularization is improved, and the approximation error is kept, so that the accuracy of the model on a three-dimensional model display system and the success rate of various numerical analyses are increased.
Description
Technical Field
The invention relates to the technical field of geometric surface modeling, in particular to a method for reconstructing another high-quality triangular grid based on improved global isotropy re-gridding.
Background
Grid parameterization can convert complex grid model processing into relatively simple parameterized grid processing, and is widely applied in many fields, and meanwhile, the re-meshing of a three-dimensional grid model is an important content of computer graphics and is an important component of many geometric applications.
The mesh generation problem is a fundamental and important issue in computer graphics research, good meshes can often achieve a balance between quality and computation, while low quality meshes often prevent convergence of solutions and increase analysis errors. With the increase of computer processing power and the development of three-dimensional scanning techniques and visual reconstruction techniques, the generation of high quality grids has become a key to the success of numerical analysis. The grid parameterization method is one of the most important algorithms for repairing the grid quality, can be used for processing low-quality grids and improving the grid quality, and can further improve the grid quality if the grid parameterization method can be used for grid refinement at first and then the improved global isotropy re-gridding method is used for reconstructing the high-quality triangular grid.
Through retrieval, the Chinese patent with the application number CN109671154A discloses a curved surface non-iterative re-meshing method represented by triangular grids, which refers to the problem that the curved surface represented by the triangular grids is deformed as a result after reconstruction, and refers to the technical means of inputting a grid model firstly to restore the missing part when grid re-dividing is adopted;
The Chinese patent of application number CN105243688B discloses a non-obtuse angle re-gridding method based on a gravity center Voronoi diagram, which aims to solve the technical problem of how to enable the re-gridding result of a curved surface to not contain obtuse triangles and small-angle triangles.
The conventional repair grid quality algorithm can be mainly divided into local correction and global re-gridding. Local correction can only modify a single defect and the grid in the cell surrounding the defect; global re-meshing is typically based on repartitioning the input using some intermediate data structure. However, most schemes focus only on certain defect types, neglecting and even introducing other defects, and most algorithms currently do not consider improving the triangle quality of the output grid, generally cannot process grids with sharp features, and in practical applications, post-processing is generally required.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provides a CDT parameterized grid and global isotropy re-gridding method.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
A method of parameterizing a grid based on CDT and globally isotropic re-gridding, comprising the steps of:
Step 1: generating a visual triangle from the CAD model using OCCT, controlling the distance between the initial subdivision and the original analysis surface, preserving geometric fidelity, i.e., approximation error is small, and furthermore, collecting the original vertices of the input geometry from the B-rep model, which vertices are then identified in the initial triangulation, marked with "lock-in" markers;
step 2: grid parameterization: reconstructing the parameterized domain of each patch based on the initial triangulation and reapplying CDT to preserve boundaries of each parameterized domain, then projecting the 2D triangulation back into 3D space;
Step 3: global re-gridding: and (3) a global isotropy re-meshing technology is applied to perform price optimization of the segmentation edges, the angles, the folding edges and the vertexes and a tangential Laplace smoothing algorithm so as to realize grid optimization.
Further, the step S2 specifically further includes the following steps:
S201: dough sheet re-parameterization: firstly reconstructing a one-to-one mapping from each mesh patch to a simple 2D domain using SLIM (Scalable Locally Injective Mappings) parameterizations, resulting in an initial triangulation of a pair of parametric coordinates (u, v) for each vertex;
S202: boundary curve recovery and sampling: assuming the mesh is represented by a half-edge data structure, starting with one half-edge h 1 labeled "locked" by a vertex, recursively accessing its previous boundary half-edge until another half-edge labeled "locked" by another vertex is encountered. The linear segments then form a boundary curve c i＝{h1,...,hk, and after all halves are processed, a set of boundary curves is collected
S203: triangulation: refining each grid patch based on the reconstructed parameter space and the restored boundary curve, performing coarse triangulation by a parameterized grid method, and organizing sampling points on the boundary curve into a bounded region in a two-dimensional space, wherein the region is defined by PSLG, each part of PSLG is regarded as a constraint condition, and the constraint condition is input into our algorithm to construct CDT; then, an improved grid is obtained by invoking the Delaunay refinement method with default shape and size criteria; finally, each patch of the 2D mesh is mapped back into 3D space.
Further, the step3 specifically further includes the following steps:
S301: dividing edges: given a target length l target, all longer than Is a side of (2);
S302: and (3) angle optimization: if the sum of the two opposite angles of a side is greater than 180 degrees, the side is flipped, wherein this operation is performed only in the first iteration; s303: folding: folding all shorter than Is a side of (2);
s304: valence optimization of the inner vertex: when the condition is met, the non-characteristic edge is turned over;
S305: performing price optimization of the characteristic vertexes;
S306: tangential laplace smoothing: to optimize the vertex distribution, the locations are repositioned by calculating the optimal ODT.
Further, in step S304, the price of the inner vertex is optimized, and the non-feature edge is flipped when the following two conditions are satisfied:
1: reducing the square difference of the prices of the four vertices of the two associated triangles to an optimal value of 6;
2: the projected distance of the midpoint of the edge to the input CAD model is not increased.
Further, the specific step flow of the price optimization of the feature vertex in step S305 is as follows:
Vertex A is taken as a non-6-valent characteristic vertex, and two incident half sides h 1 and h 2 of the vertex A are on the same side of A;
Let θ be the angle between h 1 and h 2, n t be the number of triangles between h 1 and h 2, the number of triangles required calculated as
Optimizing according to the situation, wherein the different situations specifically comprise:
1: if n t＜n′t, where θ=180°, n t＝2,n′t =3: opposite sides BD of partition A;
2: if n t＞n′t, where n t＝4,n′t =3, the minimum angle of the opposite side CD is iteratively folded until n t＝n＇t:
Further, in step S306, each vertex is moved to its incident triangle The mean p i of the center of gravity b tj of (b) is weighted by the area of the triangle:
The new position p i is chosen to be projected back onto the original patch to reduce approximation errors.
Compared with the prior art, the invention has the beneficial effects that:
The invention reconstructs the parameter domain of each curved surface piece through initial triangulation, and obtains improved grids by recovering and sampling boundary curves and re-triangulating the boundary of the parameter domain by CDT, and then obtains improved curved surface subdivision with consistency by mapping each surface piece of the 2D grid back to 3D space. Through angle optimization, a triangle with a better shape is generated, and the re-meshing process is further accelerated. The price regularization is improved through the price optimization of the inner vertexes, the approximation error is kept, and the quality near the grid characteristic edges can be remarkably improved through the price optimization of the characteristic vertexes. And finally, using tangential Laplace smoothing to optimize vertex distribution and improve the angle quality of the grid.
The method greatly improves the regularity and the angle quality of the subdivision grid, thereby increasing the accuracy of the subdivision grid on a three-dimensional model display system and the success rate of various numerical analyses.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention.
FIG. 1 is a basic flow diagram of grid parameterization and global re-meshing in an embodiment of the present invention;
FIG. 2 is a schematic diagram of the price optimization of feature vertices in an embodiment of the invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments.
Referring to fig. 1-2, a method for parameterizing a grid based on CDT and globally isotropic regnet, comprising the steps of:
Step 1: generating a visual triangle from the CAD model using OCCT, controlling the distance between the initial subdivision and the original analysis surface, preserving geometric fidelity, i.e., approximation error is small, and furthermore, collecting the original vertices of the input geometry from the B-rep model, which vertices are then identified in the initial triangulation, marked with "lock-in" markers;
step 2: grid parameterization: reconstructing the parameterized domain of each patch based on the initial triangulation and reapplying CDT to preserve boundaries of each parameterized domain, then projecting the 2D triangulation back into 3D space;
step 3: global re-gridding: and (3) applying a global isotropy re-meshing technology, and carrying out price optimization of the segmentation edges, the angle optimization, the folding edges and the vertexes and a tangential Laplace smoothing algorithm according to the conditions defined by the invention to realize grid optimization.
In a specific embodiment of the present application, step S2 specifically further includes the following steps:
S201: dough sheet re-parameterization: firstly reconstructing a one-to-one mapping from each mesh patch to a simple 2D domain using SLIM (Scalable Locally Injective Mappings) parameterizations, resulting in an initial triangulation of a pair of parametric coordinates (u, v) for each vertex;
S202: boundary curve recovery and sampling: assuming the mesh is represented by a half-edge data structure, starting with one half-edge h 1 labeled "locked" by a vertex, recursively accessing its previous boundary half-edge until another half-edge labeled "locked" by another vertex is encountered. The linear segments then form a boundary curve c i＝{h1,...,hk, and after all halves are processed, a set of boundary curves is collected
Currently, each curve c of the input geometry has been identified in its two input mesh patches (the adjacency relationship between the different patches has been pre-stored in the initial triangulation), corresponding to c i and c' i, respectively.
To achieve consistent discretization of each common curve c, we generate the same number of uniform samples on c i and c' i, respectively. The length of the curve c is denoted as l c, and the sampling interval of the curve is denoted as δ=αl target (α is set to 0.6-0.8). Therefore, the number of points to be sampled isWherein max (a, b) function returns the larger of a and b. Finally, N samples are uniformly generated over the sheet-like linear segments of c i and c' i. The parameter coordinates (u, v) for each sample are interpolated using the values defined on the vertices of c i and c' i.
S203: triangulation: refining each grid patch based on the reconstructed parameter space and the restored boundary curve, performing coarse triangulation by a parameterized grid method, and organizing sampling points on the boundary curve into a bounded region in a two-dimensional space, wherein the region is defined by PSLG, each part of PSLG is regarded as a constraint condition, and the constraint condition is input into our algorithm to construct CDT; then, an improved mesh is obtained by calling the Delaunay refinement method with default shape and size criteria (default shape criteria b=0.125, size criteria s=0.5); finally, each patch of the 2D mesh is mapped back into 3D space.
In a specific embodiment of the present application, step 3 specifically further includes the following steps:
S301: dividing edges: given a target length l target, all longer than Is a side of (2);
s302: and (3) angle optimization: if the sum of the two opposite angles of a side is greater than 180 degrees, the side is flipped, wherein this operation is performed only in the first iteration; as the inputs for subsequent iterations have been shaped. Thus, this operation does not conflict with the price optimization in subsequent iterations;
S303: folding: folding all shorter than Is a side of (2);
s304: valence optimization of the inner vertex: when the condition is met, the non-characteristic edge is turned over;
S305: performing price optimization of the characteristic vertexes;
S306: tangential laplace smoothing: to optimize the vertex distribution, the locations are repositioned by calculating the optimal ODT.
As a preferred embodiment of the present application, in step S304, the price optimization of the inner vertex is performed, and the non-feature edges are flipped when the following two conditions are satisfied:
Reducing the square difference of the prices of the four vertices of the two associated triangles to an optimal value of 6 (assuming that no boundary edge exists for the closed model CAD model);
the projected distance of the midpoint of the edge to the input CAD model is not increased.
As another preferred embodiment of the present application, the specific step flow of the price optimization of the feature vertex in step S305 is as follows:
The price optimization scheme of the feature vertices is shown in fig. 2. Vertex A is taken as a non-6-valent characteristic vertex, and two incident half sides h 1 and h 2 of the vertex A are on the same side of A;
Let θ be the angle between h 1 and h 2, n t be the number of triangles between h 1 and h 2, the number of triangles required calculated as
Optimizing according to the situation, wherein the different situations specifically comprise:
As shown in fig. 2 (a), if n t＜n′t, where θ=180°, n t＝2,n′t =3: opposite sides BD of partition A;
BD is selected because the valence optimum of vertex C is smaller than the valence of E. However, segmentation introduces another vertex G with a valence of 4, and thus local edge flipping is performed to increase the valence of G (as shown in fig. 2 (b)).
As shown in fig. 2 (c), if n t＞n′t, where n t＝4,n＇t =3, the opposite side CD of the minimum angle is iteratively folded until n t＝n＇t.
It is noted that n t＞n′t is rare because the above-described optimization of the price of the folded edge and the inner vertex can largely prevent this from occurring.
As another preferred embodiment of the present application, in step S306, each vertex is moved to its incident triangleThe mean P i of the center of gravity b tj of (b) is weighted by the area of the triangle:
Then, the new position p i is chosen to be projected back onto the original patch to reduce approximation errors. Since a good balance between meshing speed and approximation error is to be achieved, projection is applied only in the first iteration. After all iterations, the edges are flipped again by angle. This operation improves angle quality and does not interfere with price regularization.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.
Claims (2)
1. A method for parameterizing a grid based on CDT and globally isotropic re-gridding, comprising the steps of:
Step 1: generating a visual triangle from the CAD model using OCCT, controlling the distance between the initial subdivision and the original analysis surface, preserving geometric fidelity, i.e., approximation error is small, and furthermore, collecting the original vertices of the input geometry from the B-rep model, which vertices are then identified in the initial triangulation, marked with "lock-in" markers;
step 2: grid parameterization: reconstructing the parameterized domain of each patch based on the initial triangulation and reapplying CDT to preserve boundaries of each parameterized domain, then projecting the 2D triangulation back into 3D space;
Step 3: global re-gridding: grid optimization is carried out by using a global isotropy re-gridding technology through price optimization of dividing edges, angle optimization, folding edges and vertexes and a tangential Laplace smoothing algorithm;
the step 3 specifically further comprises the following steps:
S301: dividing edges: given a target length l target, all longer than Is a side of (2);
S302: and (3) angle optimization: if the sum of the two opposite angles of a side is greater than 180 degrees, the side is flipped, wherein this operation is performed only in the first iteration;
S303: folding: folding all shorter than Is a side of (2);
s304: valence optimization of the inner vertex: when the condition is met, the non-characteristic edge is turned over;
S305: performing price optimization of the characteristic vertexes;
S306: tangential laplace smoothing: repositioning the locations by calculating the optimal ODT in order to optimize the vertex distribution;
In step S304, the price optimization of the inner vertex is performed, and the non-feature edge is flipped when the following two conditions are satisfied:
1: reducing the square difference of the prices of the four vertices of the two associated triangles to an optimal value of 6;
2: the projection distance from the middle point of the edge to the input CAD model is not increased;
the specific step flow of the price optimization of the feature vertex in step S305 is as follows:
Vertex A is taken as a non-6-valent characteristic vertex, and two incident half sides h 1 and h 2 of the vertex A are on the same side of A;
Let θ be the angle between h 1 and h 2, n t be the number of triangles between h 1 and h 2, the number of triangles required calculated as
Optimizing according to the situation, wherein the different situations specifically comprise:
1: if n t＜n′t, where θ=180°, n t＝2,n′t =3: opposite sides BD of partition A;
2: if n t>n′t, where n t＝4,n′t = 3, iteratively folding the opposite side CD of the minimum angle until n t＝n′t;
In step S306, each vertex is moved to its incident triangle The mean p i of the center of gravity b tj of (b) is weighted by the area of the triangle:
The new position p i is chosen to be projected back onto the original patch to reduce approximation errors.
2. The method of CDT-based parameterized meshing and globally isotropic regorarization of claim 1, wherein step S2 specifically further comprises the steps of:
S201: dough sheet re-parameterization: firstly reconstructing a one-to-one mapping from each mesh patch to a simple 2D domain using SLIM parameterization, resulting in an initial triangulation of a pair of parameter coordinates (u, v) for each vertex;
S202: boundary curve recovery and sampling: assuming the mesh is represented by a half-edge data structure, recursively accessing its previous boundary half-edge starting from one half-edge h 1 labeled "locked" by the vertex until encountering another half-edge labeled "locked" by the vertex; the linear segments then form a boundary curve c i＝{h1,...,hk, and after all halves are processed, a set of boundary curves is collected
S203: triangulation: refining each grid patch based on the reconstructed parameter space and the restored boundary curve, performing coarse triangulation by a parameterized grid method, and organizing sampling points on the boundary curve into a bounded region in a two-dimensional space, wherein the region is defined by PSLG, each part of PSLG is regarded as a constraint condition, and the constraint condition is input into our algorithm to construct CDT; then, an improved grid is obtained by invoking the Delaunay refinement method with default shape and size criteria; finally, each patch of the 2D mesh is mapped back into 3D space.
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