CN114329668A - RAR grid optimization method and system based on CAD model - Google Patents

Abstract

The invention discloses a RAR grid optimization method and system based on a CAD model, which obtains the length of a characteristic edge and a target edge by carrying out characteristic calculation on the CAD grid model which is stored according to the surface through triangular grid discretization, then obtains the length of the characteristic edge and the target edge according to the obtained length of the characteristic edge and the target edge, carrying out mesh optimization on the CAD mesh model which is subjected to triangular mesh discretization and stored according to the surface one by one, utilizing the characteristic edge and the target edge length, the mesh optimization operation is simultaneously carried out on each surface in parallel, the mesh optimization of each surface can not interfere with each other, the time of grid optimization can be greatly saved, the accuracy of the initial grid characteristic is ensured by approximating the grid model with the original CAD model, and by introducing the boundary edge of the characteristic edge and the surface, and further constraining the original grid optimization operator, so that the characteristics of the original CAD model cannot be eliminated in the grid optimization process under the condition of ensuring the grid optimization quality.

Description

RAR grid optimization method and system based on CAD model

Technical Field

The invention belongs to the field of geometric processing, and particularly relates to a RAR grid optimization method and system based on a CAD model.

Background

In the field of computer graphics and geometric modeling, triangular mesh models have been dominated by discrete mesh models. An accurate mesh model not only can highly approximate the original geometric surface, but also can provide more stable numerical calculations. Therefore, how to accurately and efficiently convert a continuous solid model into a high-quality discrete mesh model is a crucial issue.

In recent years, researches seek breakthrough in the field of triangular mesh model generation algorithms, and also focus on mesh model optimization algorithms, so that at present, the mesh model optimization can remarkably improve the quality of meshes. Representative algorithms include CVT (Central Voronoi Tesselllation), CDT (Central Delaunay triangle), ODT (optimal Delaunay triangle), blue noise sampling, and RAR (temporal adaptive reconstruction). The RAR algorithm is a simple and efficient adaptive local mesh optimization algorithm, which uses the curvature field of the model to perform local operations iteratively, but in practical application, the requirements on mesh processing time and the requirements on geometric feature maintenance of the CAD model are still considered.

The traditional non-adaptive grid optimization operator sets the target side length as a fixed value, and the characteristic side length which is the same as that of the position with smaller curvature is still adopted at the position with larger curvature of the model, so that more sampling points are not added, and the characteristic performance at the position with larger curvature is easily influenced. Secondly, the boundary characteristics between the surfaces of the CAD model are obvious, and an obvious characteristic curve also exists in some surfaces, so that the appearance characteristics of the CAD model cannot be well maintained when the grid optimization operator is used in the original RAR grid optimization algorithm, and the characteristics of the CAD model are easily lost in the optimization process.

Disclosure of Invention

The invention aims to provide a RAR grid optimization method and system based on a CAD model, so as to overcome the defects of the prior art.

A RAR grid optimization method based on a CAD model comprises the following steps:

s1, carrying out feature calculation on the CAD mesh model which is subjected to triangular mesh discretization and stored according to the surface to obtain a feature edge and a target edge length;

and S2, carrying out mesh optimization on the CAD mesh model which is subjected to triangular mesh discretization and stored according to the side length of the obtained characteristic edge and the target edge one by one.

Further, according to the normal vector n of two adjacent triangular surfaces₁,n₂If the following conditions are met:

cos(<n₁,n₂>))>t

wherein t is a characteristic corner degree threshold value, and the common edge of two adjacent triangular surfaces is a characteristic edge.

Further, the maximum geometric deviation from the smooth curved surface to the triangular mesh is set, and the target side length is obtained through calculation of the maximum curvature and the maximum geometric deviation.

Further, the interval of the target side length has a maximum value of 2 times the average side length of the surface and a minimum value of 1/2 times the average side length of the surface.

Further, specifically, a grid approximation CAD model is adopted, then each surface of the CAD grid model is subjected to parallel grid optimization by using a local operation operator, and finally, the model subjected to grid optimization is subjected to regression triangle processing.

Furthermore, triangles with the distance difference from the original geometric model larger than the set precision u in the grid model are decomposed one by one, and the Hausdorff distance between the grid model and the original CAD model is reduced.

Further, traversing the edges in the surface, and performing edge segmentation on the edges of which the length of the edge e is greater than 4/3 target edge length L (e) and which are not boundary edges; performing edge folding operation on edges of which the length of the edge e is less than the target edge length L (e) of 2/5 and which are non-characteristic edges, non-characteristic edge adjacent edges, non-boundary edges and non-boundary edge adjacent edges;

if the edge is a non-boundary edge and a non-characteristic edge, two vertexes v of the edge are recorded₁,v₂Relative vertex v₃,v₄Calculating a value n₁＝|d(v₁)-f(v₁)|²+|d(v₂)-f(v₂)|²+|d(v₃)-f(v₃)|²+|d(v₄)-f(v₄)|²The edge is turned over and the value n is calculated₂＝|d(v₁)-f(v₁)|²+|d(v₂)-f(v₂)|²+|d(v₃)-f(v₃)|²+|d(v₄)-f(v₄)|²If n is₁<n₂If so, the edge is flipped back, otherwise no other operation is performed.

Further, traversing the point in the surface, and if the point is not the boundary point and not the characteristic point, performing vertex movement. Vertex movement refers to moving each vertex to the area-weighted average position c of the center of gravity of all triangles that are adjacent to that point_iThe method comprises the following steps:

wherein, b_jIs a triangle t_jCenter of gravity, weight | t_jI is the area of the triangle, weight L (b)_j) Length L (e) of target edge at three vertices of triangle_i) Average value of (a).

Further, if one angle in the triangle is smaller than a set threshold, the current surface is judged to be a degenerated triangular surface; drawing a high line at the vertex from the vertex of the maximum angle of the triangle, and performing edge segmentation at the foot drop; the edge collapse operation is performed along a high line.

A RAR grid optimization system based on a CAD model comprises a preprocessing module and an optimization module;

the preprocessing module is used for carrying out feature calculation on the CAD mesh model which is subjected to triangular mesh discretization and stored according to the surface to obtain a feature edge and a target edge length;

and the optimization module is used for carrying out mesh optimization on the CAD mesh model which is subjected to the discretization of the triangular mesh and stored according to the side length of the obtained characteristic edge and the target edge one by one.

Compared with the prior art, the invention has the following beneficial technical effects:

the invention relates to a RAR (random access memory) grid optimization method based on a CAD (computer-aided design) model, which is characterized by calculating the characteristics of the CAD grid model which is stored according to the discretization of a triangular grid, so as to obtain the characteristic edge and the target edge length, then carrying out the grid optimization on the CAD grid model which is stored according to the discretization of the triangular grid one by one according to the obtained characteristic edge and the target edge length, simultaneously carrying out the grid optimization operation on each surface in parallel by utilizing the characteristic edge and the target edge length, and carrying out the grid optimization on each surface without mutual interference, thereby greatly saving the time for the grid optimization.

Furthermore, the accuracy of the initial grid characteristics is ensured by approximating the grid model with the original CAD model.

Furthermore, by introducing the boundary edge of the characteristic edge and the surface, the original grid optimization operator is further constrained, and the characteristics of the original CAD model cannot be eliminated in the grid optimization process under the condition of ensuring the grid optimization quality.

Drawings

Fig. 1 is a schematic diagram of four mesh optimization operators in an embodiment of the present invention, where fig. 1(a) is a schematic diagram of edge segmentation, fig. 1(b) is a schematic diagram of edge folding, fig. 1(c) is a schematic diagram of edge flipping, and fig. 1(d) is a schematic diagram of vertex movement.

Fig. 2 is a schematic diagram of a degenerate triangle processing according to an embodiment of the present invention, fig. 2(a) is a schematic diagram of a degenerate triangle, fig. 2(b) is a schematic diagram of obtaining a maximum angle of a triangle, fig. 2(c) is a schematic diagram of edge segmentation at a foot, and fig. 2(d) is a schematic diagram of an edge collapse result.

FIG. 3 is a block diagram of a system according to an embodiment of the present invention.

Detailed Description

In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.

A RAR grid optimization method based on a CAD model comprises the following steps:

s1, carrying out feature calculation on the CAD mesh model which is subjected to triangular mesh discretization and stored according to the surface;

according to the normal vector n of two adjacent triangular surfaces₁,n₂If the following conditions are met:

cos(<n₁,n₂>))>t

and t is a characteristic corner degree threshold value, adjustment is carried out according to a specific experimental environment, and a common edge of the two adjacent triangular surfaces is set as a characteristic edge.

Let the maximum geometric deviation from the smooth surface to the triangular mesh, i.e. the approximate threshold epsilon.

And (4) calculating a curvature field of the input grid, and obtaining the length L (e) of the target side through the maximum curvature and an approximate threshold epsilon.

In a two-dimensional space of a curved surface tangent plane, under the condition of meeting an approximate threshold epsilon, approximating the cross section of the curved surface by a straight line segment, namely a segment of circular arc, wherein the maximum side length l of the straight line segment can be obtained by the pythagorean theorem:

where r corresponds to the radius of the osculating circle, i.e. the inverse of the local curvature r is 1/κ.

Due to L (e)_i) At vertex e_iThe position needs to satisfy the direction independence, and the side length of the selected straight line segment is as small as possible. Therefore, the maximum absolute curvature value, i.e., κ ═ max { | κ, is selected_min|,|κ_max|}。

If the side length of the equilateral triangle is L and the diameter length of the circumscribed circle is L, then

Then, at vertex e_iL (e) of (C)_i) Can pass through the maximum absolute curvature k_iAnd the approximation error ε yields:

calculating the vertex e by calculating the mean curvature value H and the Gaussian curvature value K_iMaximum absolute curvature κ:

wherein, theta_iIs a vertex e_iAngle of incidence of, A_iIs its Voronoi area.

When the method is actually applied to a CAD grid model for feature side length calculation, the maximum value of the interval for defining the side length of the target is 2 times of the average side length of the surface, and the minimum value is 1/2 of the average side length of the surface.

For edge e ═(v₁,v₂) The size of the characteristic side length l (e) is the minimum of the two endpoints:

L(e)＝min{L(v₁),L(v₂)}

and S2, carrying out mesh optimization on the CAD mesh model which is subjected to triangular mesh discretization and stored according to the plane one by one according to the characteristics of the CAD mesh model obtained by calculation.

S2.1: and (3) adopting a grid approximation CAD model, and decomposing triangles, with the distance difference from the original geometric model being larger than the set precision u, in the grid model one by one to reduce the Hausdorff distance between the grid model and the original CAD model.

Further, let the gravity center point p of Δ ABC in the grid model_gProjected point on original CAD model is p'_gIf p_gAnd p'_gIf the distance of (d) is greater than u, deleting Delta ABC from the grid and adding point p'_gThen delta p 'is added'_gAB、△Cp′_gB、△p′_gCA。

S2.2: and performing parallel grid optimization on each surface of the CAD grid model by using a local operation operator, and performing S2.2.1-S2.2.4 operation iteration 5-10 times on each surface.

S2.2.1: traversing the edges in the surface, and performing edge segmentation on the edges in which the length of the edge e is greater than 4/3 the length L (e) of the target edge and the edges are not boundary edges, as shown in FIG. 1 (a). Specifically, a point is added to the midpoint of the edge, so that the edge is divided into 2 edges, and meanwhile, 2 triangles adjacent to the edge are updated to 4 triangles, and if the edge is a characteristic edge, a newly generated edge needs to be marked as the characteristic edge. A boundary edge refers to an edge where both vertices are on a face boundary.

S2.2.2: traversing the edges in the surface, and performing edge folding operation on the edges in which the length of the edge e is less than 2/5 target edge length L (e) and the non-characteristic edge, non-characteristic edge neighboring edge, non-boundary edge, and non-boundary edge neighboring edge, as shown in FIG. 1 (b). The edge folding operation specifically refers to shrinking 2 vertices of the edge into 1 vertex, and the edge and 2 triangles adjacent to the edge disappear from the mesh. The feature edge adjacent edge is an edge where one vertex is on the feature edge and the other vertex is on the non-feature edge. Boundary edge adjacent edges refer to edges where one vertex is on a face boundary and the other vertex is not.

S2.2.3: traversing an edge in the surface, if the edge is a non-boundary edge and a non-characteristic edge, recording two vertexes v of the edge₁,v₂Relative vertex v₃,v₄Calculating a value n₁＝|d(v₁)-f(v₁)|²+|d(v₂)-f(v₂)|²+|d(v₃)-f(v₃)|²+|d(v₄)-f(v₄)|²The edge is turned over and the value n is calculated₂＝|d(v₁) -f (v1) |2+ | d (v2) -f (v2) |2+ | d (v3) -f (v3) |2+ | d (v4) -f (v4) |2, if n1<n2, the edge is flipped back, otherwise no other operation is done. Where d (v) represents the degree of the side, and if v is a non-boundary point, f (v) is 6, and if v is a boundary point, f (v) is 4. The side flipping operation indicates that 2 triangles adjacent to one side form a quadrangle, and the other diagonal of the quadrangle is connected after the side is deleted, so as to obtain the other 2 triangles, as shown in fig. 1 (c).

S2.2.4: traversing a point in the surface, and if the point is not a boundary point and not a feature point, performing vertex movement, as shown in fig. 1 (d). Vertex movement refers to moving each vertex to the area-weighted average position c of the center of gravity of all triangles that are adjacent to that point_iThe method comprises the following steps:

wherein, b_jIs a triangle t_jCenter of gravity, weight | t_jI is the area of the triangle, weight L (b)_j) Length L (e) of target edge at three vertices of triangle_i) Average value of (a).

S2.3: and (3) carrying out degenerated triangle processing: if the three vertices of a triangle are collinear or nearly collinear, its actual role in the mesh has been degenerated to an edge, which we call a degenerated triangle. One of the main features of the degenerate triangle is that the angle of one of the corners is very small, i.e. less than a set threshold. As shown in fig. 2, finding a degenerated triangle, as shown in fig. 2(a), checking the angles of three angles of the triangle, and if one of the angles is found to be smaller than a set threshold, determining that the current surface is a degenerated triangle surface; finding the vertex of the triangle where the largest angle is located, as shown in fig. 2 (b); drawing a high line at the vertex, and performing edge segmentation at the foot drop, as shown in fig. 2 (c); the edge collapse operation is performed along the high lines, as shown in fig. 2(d), so that the current degenerate triangle is eliminated after the edge collapse operation.

In one embodiment of the present invention, a terminal device is provided that includes a processor and a memory, the memory storing a computer program comprising program instructions, the processor executing the program instructions stored by the computer storage medium. The processor is a Central Processing Unit (CPU), or other general purpose processor, Digital Signal Processor (DSP), Application Specific Integrated Circuit (ASIC), ready-made programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic device, discrete hardware component, etc., which is a computing core and a control core of the terminal, and is adapted to implement one or more instructions, and in particular, to load and execute one or more instructions to implement a corresponding method flow or a corresponding function; the processor of the embodiment of the invention can be used for the operation of the RAR grid optimization method based on the CAD model.

As shown in fig. 3, a RAR grid optimization system based on CAD model includes a preprocessing module and an optimization module;

the preprocessing module is used for carrying out feature calculation on the CAD mesh model which is subjected to triangular mesh discretization and stored according to the surface to obtain a feature edge and a target edge length;

and the optimization module is used for carrying out mesh optimization on the CAD mesh model which is subjected to the discretization of the triangular mesh and stored according to the side length of the obtained characteristic edge and the target edge one by one.

In still another embodiment of the present invention, the present invention further provides a storage medium, specifically a computer-readable storage medium (Memory), which is a Memory device in the terminal device and is used for storing programs and data. The computer-readable storage medium includes a built-in storage medium in the terminal device, provides a storage space, stores an operating system of the terminal, and may also include an extended storage medium supported by the terminal device. Also, one or more instructions, which may be one or more computer programs (including program code), are stored in the memory space and are adapted to be loaded and executed by the processor. It should be noted that the computer-readable storage medium may be a high-speed RAM memory, or may be a Non-volatile memory (Non-volatile memory), such as at least one disk memory. One or more instructions stored in a computer-readable storage medium may be loaded and executed by a processor to implement the corresponding steps of the RAR mesh optimization method applicable to CAD-based models in the above-described embodiments.

The input data of the invention adopts the CAD grid model with the surface data, each surface simultaneously carries out the grid optimization operation in parallel, the grid optimization of each surface can not interfere with each other, and the time of the grid optimization can be greatly saved. The accuracy of the initial grid characteristics is ensured by approximating the grid model with the original CAD model.

By introducing the boundary edges of the characteristic edges and the surfaces, the original grid optimization operator is further constrained, and the characteristics of the original CAD model cannot be eliminated in the grid optimization process under the condition of ensuring the grid optimization quality.

Claims (10)

1. A RAR grid optimization method based on a CAD model is characterized by comprising the following steps:

s1, carrying out feature calculation on the CAD mesh model which is subjected to triangular mesh discretization and stored according to the surface to obtain a feature edge and a target edge length;

and S2, carrying out mesh optimization on the CAD mesh model which is subjected to triangular mesh discretization and stored according to the side length of the obtained characteristic edge and the target edge one by one.

2. The RAR mesh optimization method based on CAD model as recited in claim 1, wherein the normal vector n according to two adjacent triangular faces₁，n₂If the following conditions are met:

cos(＜n₁，n₂＞))＞t

wherein t is a characteristic corner degree threshold value, and the common edge of two adjacent triangular surfaces is a characteristic edge.

3. The RAR mesh optimization method based on CAD model as recited in claim 1, wherein the maximum geometric deviation from smooth surface to triangular mesh is determined, and the target side length is calculated from the maximum curvature and the maximum geometric deviation.

4. The RAR grid optimization method based on CAD models of claim 3, characterized in that the interval of the target edge length has the maximum value 2 times the average edge length of the surface and the minimum value 1/2.

5. The RAR grid optimization method based on the CAD model as recited in claim 1, wherein specifically, a grid approximation CAD model is adopted, then each face of the CAD grid model is subjected to parallel grid optimization by using a local operator, and finally, the model after grid optimization is subjected to regression triangle processing.

6. The RAR mesh optimization method based on the CAD model as recited in claim 5, wherein triangles in the mesh model with a distance difference from the original geometric model larger than a set precision u are decomposed one by one to reduce the Hausdorff distance between the mesh model and the original CAD model.

7. The RAR mesh optimization method based on CAD model as recited in claim 5, wherein traversing the edge in the face, edge-segmenting the edge whose edge e length is greater than 4/3 target edge length L (e) and is not boundary edge; performing edge folding operation on edges of which the length of the edge e is less than the target edge length L (e) of 2/5 and which are non-characteristic edges, non-characteristic edge adjacent edges, non-boundary edges and non-boundary edge adjacent edges;

if the edge is a non-boundary edge and a non-characteristic edge, two vertexes v of the edge are recorded₁，v₂Phase of changeFor vertex v₃，v₄Calculating a value n₁＝|d(v₁)-f(v₁)|²+|d(v₂)-f(v₂)|²+|d(v₃)-f(v₃)|²+|d(v₄)-f(v₄)|²The edge is turned over and the value n is calculated₂＝|d(v₁)-f(v₁)|²+|d(v₂) -f (v2) |2+ | d (v3) -f (v3) |2+ | d (v4) -f (v4) |2, if n1 < n2, the edge is turned back, otherwise no other operation is performed.

8. The RAR mesh optimization method based on CAD model as recited in claim 7, wherein traversing a point in the plane, if the point is not a boundary point and not a feature point, performing vertex movement; vertex movement refers to moving each vertex to the area-weighted average position c of the center of gravity of all triangles that are adjacent to that point_iThe method comprises the following steps:

wherein, b_jIs a triangle t_jCenter of gravity, weight | t_jI is the area of the triangle, weight L (b)_j) Length L (e) of target edge at three vertices of triangle_i) Average value of (a).

9. The RAR mesh optimization method based on the CAD model of claim 5, wherein if an angle in a triangle is smaller than a set threshold, it is determined that the current surface is a degenerated triangle surface; drawing a high line at the vertex from the vertex of the maximum angle of the triangle, and performing edge segmentation at the foot drop; the edge collapse operation is performed along a high line.

10. A RAR grid optimization system based on a CAD model is characterized by comprising a preprocessing module and an optimization module;

the preprocessing module is used for carrying out feature calculation on the CAD mesh model which is subjected to triangular mesh discretization and stored according to the surface to obtain a feature edge and a target edge length;

and the optimization module is used for carrying out mesh optimization on the CAD mesh model which is subjected to the discretization of the triangular mesh and stored according to the side length of the obtained characteristic edge and the target edge one by one.

Images