CN114329668B - RAR grid optimization method and system based on CAD model - Google Patents
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Abstract
The invention discloses a RAR grid optimization method and system based on a CAD model, which are characterized in that characteristic edges and target edges are obtained by carrying out characteristic calculation on the CAD grid model stored according to the surface through triangular grid discretization, then grid optimization is carried out on the CAD grid model stored according to the surface through triangular grid discretization according to the obtained characteristic edges and target edges, grid optimization operation is carried out on all the surfaces simultaneously in parallel by utilizing the characteristic edges and the target edges, grid optimization can not interfere each other, the grid optimization time can be greatly saved, the accuracy of initial grid characteristics is ensured by approximating the grid model with an original CAD model, the original grid optimization operator is further constrained by introducing the boundary edges of the characteristic edges and the surface, and the characteristics of the original CAD model can not be eliminated in the grid optimization process under the condition of ensuring the grid optimization quality.
Description
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 dominant in discrete mesh models. The accurate mesh model can not only be highly approximated to the original geometric surface, but can also provide more stable numerical calculations. Therefore, how to accurately and efficiently convert a continuous solid model into a high quality discrete grid model is a critical issue.
In recent years, research not only searches breakthrough in the field of triangle mesh model generation algorithms, but also focuses on mesh model optimization algorithms, and at present, it can be shown that mesh model optimization can remarkably improve the quality of meshes. Representative algorithms are CVT (centroidal Voronoi Tessellation), CDT (centroidal Delaunay triangulation), ODT (optimal Delaunay triangulation), blue noise sampling and RAR (realtime adaptive remeshing), etc. The RAR algorithm is a simple and efficient adaptive local mesh optimization algorithm, which uses curvature fields of the model to perform local operations iteratively, but in practical application, the requirements on mesh processing time and the requirements on geometric feature preservation of the CAD model are still considered.
The traditional non-self-adaptive grid optimization operator sets the target side length as a set value, and the same characteristic side length as that of the smaller curvature is adopted at the position with larger curvature of the model, so that more sampling points are not added, and the characteristic performance of the position with larger curvature is also easily influenced. Secondly, boundary features between the CAD model surface and the surface are obvious, obvious feature curves exist in some surfaces, the appearance features of the CAD model cannot be well maintained when the original RAR grid optimization algorithm uses a grid optimization operator, and the features of the CAD model are easy to lose in the optimization process.
Disclosure of Invention
The invention aims to provide a RAR grid optimization method and system based on a CAD model, which are used for overcoming the defects of the prior art.
A RAR grid optimization method based on a CAD model comprises the following steps:
s1, performing feature calculation on a CAD grid model stored according to the surface through triangle grid discretization to obtain a feature edge and a target edge length;
s2, grid optimization is carried out on the CAD grid model stored according to the surface through discretization of the triangular grid according to the obtained characteristic edge and the target edge length.
Further, according to the normal vector n of two adjacent triangular surfaces 1 ,n 2 If the following conditions are satisfied:
cos(<n 1 ,n 2 >))>t
wherein t is a characteristic corner threshold value, and the common edge of two adjacent triangular faces 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 through the maximum curvature and the maximum geometric deviation.
Further, the maximum value of the interval of the target side length is 2 times of the surface average side length, and the minimum value is 1/2 of the surface average side length.
Further, specifically, a grid is adopted to approach a CAD model, then a local operation operator is used for parallel grid optimization on each surface of the CAD grid model, and finally the model after grid optimization is subjected to degradation triangle processing.
Further, triangles with the distance difference between the grid model and the original geometric model larger than the set precision u are decomposed one by one, and Hausdorff distance between the grid model and the original CAD model is reduced.
Further, traversing edges in the surface, and performing edge segmentation on edges with the edge e length being greater than 4/3 of the target edge length L (e) and non-boundary edges; edge folding operation is carried out on edges, which are not characteristic edges, non-characteristic edge adjacent edges, non-boundary edges and non-boundary edge adjacent edges, wherein the length of the edge e is smaller than 2/5 of the target edge length L (e);
if the edge is a non-boundary edge and is not a characteristic edge, the two vertexes v of the edge are recorded 1 ,v 2 Opposite vertex v 3 ,v 4 Calculated value n 1 ＝|d(v 1 )-f(v 1 )| 2 +|d(v 2 )-f(v 2 )| 2 +|d(v 3 )-f(v 3 )| 2 +|d(v 4 )-f(v 4 )| 2 The edge is turned over and the value n is calculated again 2 ＝|d(v 1 )-f(v 1 )| 2 +|d(v 2 )-f(v 2 )| 2 +|d(v 3 )-f(v 3 )| 2 +|d(v 4 )-f(v 4 )| 2 If n 1 <n 2 And turning the edge back, otherwise, not performing other operations.
Further, points in the surface are traversed, and if the points are not boundary points and are not feature points, vertex movement is performed. Vertex movement refers to the area-weighted average position c of the center of gravity of all triangles that move each vertex to the point's neighborhood i And (3) the following steps:
wherein b j Is triangle t j Gravity center of (2), weight |t j The I is the area of the triangle, and the weight L (b) j ) Is the target side length L (e) i ) Average value of (2).
Further, if one angle in the triangle is smaller than a set threshold value, judging that the current plane is a degraded triangle plane; making a high line at the vertex from the vertex of the maximum angle of the triangle, and performing edge segmentation at the drop foot; edge collapse operations are performed along the 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 characteristic calculation on the CAD grid model which is stored according to the surface through the discretization of the triangular grid to obtain characteristic edges and target edge lengths;
and the optimization module is used for carrying out grid optimization on the CAD grid model stored according to the surface through the discretization of the triangular grid according to the acquired characteristic edge and the target edge.
Compared with the prior art, the invention has the following beneficial technical effects:
according to the RAR grid optimization method based on the CAD model, characteristic edges and target edges are obtained through characteristic calculation on the CAD grid model stored according to the surface through triangular grid discretization, grid optimization is carried out on the CAD grid model stored according to the surface through triangular grid discretization according to the obtained characteristic edges and target edges, grid optimization operation is simultaneously carried out on all the surfaces in parallel by utilizing the characteristic edges and the target edges, grid optimization can not be interfered with each other, and grid optimization time can be greatly saved.
Further, the accuracy of the initial grid features is ensured by approximating the grid model with the original CAD model.
Further, by introducing boundary edges of the feature edges and the faces, the original grid optimization operator is further constrained, and under the condition that the grid optimization quality is ensured, the features of the original CAD model are not eliminated in the grid optimization process.
Drawings
Fig. 1 is a schematic diagram of four grid optimization operators in the embodiment of the present invention, fig. 1 (a) is an edge segmentation schematic diagram, fig. 1 (b) is an edge folding schematic diagram, fig. 1 (c) is an edge turning schematic diagram, and fig. 1 (d) is a vertex movement schematic diagram.
Fig. 2 is a schematic diagram of a degraded triangle processing in the embodiment of the present invention, fig. 2 (a) is a schematic diagram of a degraded triangle, fig. 2 (b) is a schematic diagram of a maximum angle of the obtained triangle, fig. 2 (c) is a schematic diagram of edge segmentation performed at the foot drop, 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 invention.
Detailed Description
In order that those skilled in the art will better understand the present invention, a technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in which it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and the claims of the present invention and the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments of the invention described herein may be implemented in sequences other than those illustrated or otherwise 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, performing feature calculation on a CAD grid model stored according to the surface through triangle grid discretization;
according to the normal vector n of two adjacent triangular surfaces 1 ,n 2 If the following conditions are satisfied:
cos(<n 1 ,n 2 >))>t
and t is a characteristic corner threshold value, and is adjusted according to a specific experimental environment, and the common edge of the two adjacent triangular faces is set as a characteristic edge.
The maximum geometrical deviation from a smooth surface to a triangular mesh, i.e. the approximation threshold epsilon, is set.
The curvature field of the input grid is calculated, and the target side length L (e) is obtained through the maximum curvature and the approximate threshold epsilon.
In the two-dimensional space of the tangent plane of the curved surface, the cross section of the curved surface is approximated by a straight line segment, namely a section of circular arc, under the condition that the approximate threshold epsilon is met, and 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=1/κ.
Due to L (e) i ) At vertex e i The position needs to meet the independence of the direction, and the side length of the straight line segment is selected as small as possible. Thus, the maximum absolute curvature value is chosen, i.e., κ=max { |κ min |,|κ max |}。
The equilateral triangle is provided with a side length L and the diameter length of the outer circle is LThen, at vertex e i L (e) at i ) Can pass through the maximum absolute curvature kappa i And the approximation error ε yields:
computing vertex e by computing average curvature value H and Gaussian curvature value K i Maximum absolute curvature at κ:
wherein θ i Is the vertex e i Angle of incidence at A i For its Voronoi area.
When the method is actually applied to the CAD grid model for calculating the characteristic side length, the maximum value of the section defining the target side length is 2 times of the surface average side length, and the minimum value is 1/2 of the surface average side length.
For edge e= (v 1 ,v 2 ) The size of the side length L (e) takes the minimum value of two endpoints:
L(e)＝min{L(v 1 ),L(v 2 )}
s2, according to the calculated CAD grid model characteristics, carrying out grid optimization on the CAD grid model stored according to the surface through triangular grid discretization.
S2.1: and decomposing triangles with the distance difference between the triangle and the original geometric model being larger than the set precision u in the grid model one by adopting the grid approximation CAD model, and reducing the Hausdorff distance between the grid model and the original CAD model.
Further, let the gravity center p of ΔABC in the mesh model be g The projection point on the original CAD model is p' g If p g And p' g Is greater than uDelete ΔABC from the grid, add point p' g Then increase Δp' g AB、△Cp′ g B、△p′ g CA。
S2.2: parallel grid optimization is carried out on each face of the CAD grid model by using a local operation operator, and each face is subjected to 5-10 operation iterations of S2.2.1-S2.2.4.
S2.2.1: traversing the edges in the surface, edge segmentation is performed on edges where the edge e is longer than the 4/3 target edge length L (e) and is not a boundary edge, 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, meanwhile, 2 triangles adjacent to the edge are updated into 4 triangles, and if the edge is a characteristic edge, the newly generated edge needs to be marked as the characteristic edge. Boundary edges refer to edges 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 with the length of the edge e being smaller than 2/5 of the target edge length L (e) and the edges being non-characteristic edges, non-characteristic edge edges, non-boundary edges and non-boundary edge edges, as shown in fig. 1 (b). The edge folding operation specifically refers to shrinking 2 vertices of the edge to 1 vertex, and the edge and its adjacent 2 triangles disappear from the mesh. Feature edge critical edges refer to edges where one vertex is on a feature edge and another vertex is on a non-feature edge. Boundary edge-to-edge refers to an edge where one vertex is on a face boundary and another vertex is not on a face boundary.
S2.2.3: traversing an edge in a face, if it is a non-boundary edge and a non-feature edge, noting two vertices v of the edge 1 ,v 2 Opposite vertex v 3 ,v 4 Calculated value n 1 ＝|d(v 1 )-f(v 1 )| 2 +|d(v 2 )-f(v 2 )| 2 +|d(v 3 )-f(v 3 )| 2 +|d(v 4 )-f(v 4 )| 2 The edge is turned over and the value n is calculated again 2 ＝|d(v 1 ) -f (v 1) |2+|d (v 2) -f (v 2) |2+|d (v 3) -f (v 3) |2+|d (v 4) -f (v 4) |2, if n1<n2, the edge is turned back, otherwise, no other operation is performed. Where d (v) represents the degree of the edge, f (v) =6 if v is a non-boundary point, and f (v) =4 if v is a boundary point. The edge flip operation represents a stripThe 2 triangles adjacent to the edge form a quadrangle, and the other diagonal line of the quadrangle is connected after the edge is deleted, so that the other 2 triangles are obtained, as shown in fig. 1 (c).
S2.2.4: if a point in the surface is traversed and the point is not a boundary point or a feature point, the vertex is moved as shown in fig. 1 (d). Vertex movement refers to the area-weighted average position c of the center of gravity of all triangles that move each vertex to the point's neighborhood i And (3) the following steps:
wherein b j Is triangle t j Gravity center of (2), weight |t j The I is the area of the triangle, and the weight L (b) j ) Is the target side length L (e) i ) Average value of (2).
S2.3: degradation triangle processing: if the three vertices of a triangle are collinear or nearly collinear, its actual effect in the mesh has 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. smaller than the set threshold. Finding a degenerated triangle as shown in fig. 2, checking the angles of three angles of the triangle as shown in fig. 2 (a), and if one of the angles is found to be smaller than a set threshold value, determining that the current face is a degenerated triangle face; finding the vertex where the maximum angle of this triangle is located, as shown in fig. 2 (b); making a high line at the vertex, and performing edge segmentation at the drop foot, as shown in fig. 2 (c); the edge collapse operation is performed along the high line as shown in fig. 2 (d), so that the current degenerate triangle can be eliminated after the edge collapse operation.
In one embodiment of the present invention, there is provided a terminal device including a processor and a memory for storing a computer program including program instructions, the processor for executing the program instructions stored by the computer storage medium. The processor adopts a Central Processing Unit (CPU), or adopts other general purpose processors, digital Signal Processors (DSPs), application Specific Integrated Circuits (ASICs), ready-made programmable gate arrays (FPGAs) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components and the like, which are a computation core and a control core of the terminal, and are suitable for realizing one or more instructions, in particular for loading and executing one or more instructions so as to realize corresponding method flows or corresponding functions; the processor disclosed by the embodiment of the invention can be used for operating the RAR grid optimization method based on the CAD model.
As shown in fig. 3, a RAR grid optimization system based on a CAD model includes a preprocessing module and an optimization module;
the preprocessing module is used for carrying out characteristic calculation on the CAD grid model which is stored according to the surface through the discretization of the triangular grid to obtain characteristic edges and target edge lengths;
and the optimization module is used for carrying out grid optimization on the CAD grid model stored according to the surface through the discretization of the triangular grid according to the acquired characteristic edge and the target edge.
In still another embodiment of the present invention, a storage medium, specifically a computer readable storage medium (Memory), is a Memory device in a terminal device, 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 stored in the memory space are one or more instructions, which may be one or more computer programs (including program code), adapted to be loaded and executed by the processor. The computer readable storage medium may be a high-speed RAM memory or a Non-volatile memory (Non-volatile memory), such as at least one magnetic 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 above-described embodiments that may be used in CAD model-based RAR grid optimization methods.
The input data of the invention adopts the CAD grid model with the surface data, all surfaces simultaneously and parallelly carry out grid optimization operation, all surfaces do not interfere with each other in grid optimization, and the time of grid optimization can be greatly saved. The accuracy of initial grid features is ensured by approximating the grid model with the original CAD model.
By introducing boundary edges of the feature edges and the faces, the original grid optimization operator is further constrained, and under the condition that the grid optimization quality is ensured, the features of the original CAD model are not eliminated in the grid optimization process.
Claims (6)
1. The RAR grid optimization method based on the CAD model is characterized by comprising the following steps of:
s1, performing feature calculation on a CAD grid model stored according to the surface through triangle grid discretization to obtain a feature edge and a target edge length;
according to the normal vector n of two adjacent triangular surfaces 1 ，n 2 If the following conditions are satisfied:
cos(<n 1 ，n 2 >))>t
wherein t is a characteristic corner threshold value, and the common edge of two adjacent triangular faces is a characteristic edge;
setting the maximum geometric deviation from the smooth curved surface to the triangular mesh, and calculating to obtain the target side length through the maximum curvature and the maximum geometric deviation;
the maximum value of the interval of the target side length is 2 times of the surface average side length, and the minimum value is 1/2 of the surface average side length;
s2, carrying out grid optimization on the CAD grid model stored according to the surface through discretization of the triangular grid according to the obtained characteristic edge and the target edge length;
and (3) approximating the CAD model by adopting the grid, carrying out parallel grid optimization on each surface of the CAD grid model by using a local operation operator, and finally carrying out degradation triangle processing on the model after grid optimization.
2. The RAR grid optimization method based on the CAD model according to claim 1, wherein triangles with the distance difference from the original geometric model being larger than the set precision u in the grid model are decomposed one by one, and Hausdorff distance between the grid model and the original CAD model is reduced.
3. The method of claim 1, wherein edges in the surface are traversed and edges in which the edge e length is greater than 4/3 of the target edge length L (e) and non-boundary edges are edge segmented; edge folding operation is carried out on edges, which are not characteristic edges, non-characteristic edge adjacent edges, non-boundary edges and non-boundary edge adjacent edges, wherein the length of the edge e is smaller than 2/5 of the target edge length L (e);
if the edge is a non-boundary edge and is not a characteristic edge, the two vertexes v of the edge are recorded 1 ，v 2 Opposite vertex v 3 ，v 4 Calculated value n 1 ＝|d(v 1 )-f(v 1 )| 2 +|d(v 2 )-f(v 2 )| 2 +|d(v 3 )-f(v 3 )| 2 +|d(v 4 )-f(v 4 )| 2 The edge is turned over and the value n is calculated again 2 ＝|d(v 1 )-f(v 1 )| 2 +|d(v 2 )-f(v 2 )| 2 +|d(v 3 )-f(v 3 )| 2 +|d(v 4 )-f(v 4 )| 2 If n 1 ＜n 2 And turning the edge back, otherwise, not performing other operations.
4. A method of optimizing a RAR mesh based on a CAD model according to claim 3, wherein points in the surface are traversed, and if the points are not boundary points and are not feature points, vertex movement is performed; vertex movement refers to the area-weighted average position c of the center of gravity of all triangles that move each vertex to the point's neighborhood i And (3) the following steps:
wherein b j Is triangle t j Gravity center of (2), weight |t j The I is the area of the triangle, and the weight L (b) j ) Is the target side length L (e) i ) Average value of (2).
5. The method for optimizing an RAR mesh based on a CAD model according to claim 1, wherein if one angle in the triangle is smaller than a set threshold, determining that the front face is a degraded triangle face; making a high line at the vertex from the vertex of the maximum angle of the triangle, and performing edge segmentation at the drop foot; edge collapse operations are performed along the high line.
6. The RAR grid optimization system based on the CAD model is characterized by comprising a preprocessing module and an optimization module;
the preprocessing module is used for carrying out characteristic calculation on the CAD grid model which is stored according to the surface through the discretization of the triangular grid to obtain characteristic edges and target edge lengths;
according to the normal vector n of two adjacent triangular surfaces 1 ，n 2 If the following conditions are satisfied:
cos(<n 1 ，n 2 >))>t
wherein t is a characteristic corner threshold value, and the common edge of two adjacent triangular faces is a characteristic edge;
setting the maximum geometric deviation from the smooth curved surface to the triangular mesh, and calculating to obtain the target side length through the maximum curvature and the maximum geometric deviation;
the maximum value of the interval of the target side length is 2 times of the surface average side length, and the minimum value is 1/2 of the surface average side length;
the optimization module is used for carrying out grid optimization on the CAD grid model stored according to the surface through the discretization of the triangular grid according to the acquired characteristic edge and the target edge length; and (3) approximating the CAD model by adopting the grid, carrying out parallel grid optimization on each surface of the CAD grid model by using a local operation operator, and finally carrying out degradation triangle processing on the model after grid optimization.
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