CN116797762A - Parameter curved surface grid generation method with controllable error - Google Patents

Abstract

The invention discloses a parameter curved surface grid generation method with controllable errors, and relates to the technical field of computer-aided geometric design. Comprising the following steps: s1, inputting a boundary representing a parameter curved surface model, and uniformly sampling the parameter curved surface model to obtain an initialization grid; s2, optimizing boundary sampling points to obtain an initial optimization grid; s3, optimizing the internal sampling points of the initial optimization grid to obtain a post-optimization grid; and S4, performing global optimization on the post-optimization grid to generate a final grid. In the grid generation process, the coordination of grid generation is ensured by synchronously editing the grid sharing operation, and the matching points of the coordinated grids are combined to generate watertight grids; in addition, two new target side length calculation methods are designed aiming at the error requirement, and the triangular grid meeting the error requirement can be generated by utilizing the target side length to carry out grid local editing operation.

Description

Parameter curved surface grid generation method with controllable error

Technical Field

The invention relates to the technical field of computer graphics processing, in particular to a parameter curved surface grid generation method with controllable errors.

Background

Both parametric and grid representations are important ways of representing three-dimensional geometries, which play a vital role in Computer Aided Design (CAD) and Computer Aided Engineering (CAE). The parametric representation has the characteristic of continuity and accuracy and is a common representation of geometric modeling in a CAD system. The grid representation is then a discrete representation, which is a commonly used representation of the physical simulation computation in a CAE system. Before CAE is imported into the parametric model obtained by CAD design for simulation calculation, the representation mode conversion is usually realized by using a parametric surface grid generation method.

Parametric surface models of boundary representations (Boundary Representation) are quite common in CAD systems, and these models are typically stored in IGES, STEP formats and are the underlying geometric representations employed by most surface modeling techniques. Generating grids from models of boundary representations is a major concern in many fields of numerical modeling, rapid prototyping, computational fluid dynamics, visualization, and the like. However, current mainstream CAD software such as Open Cascade, netGen, gmesh, etc. still generates an erroneous mesh structure, such as a degraded triangle, a mesh slit, etc., during the mesh generation process, and cannot control the error of generating the mesh. Although the wrong grid structure can be repaired using grid repair techniques, there is often a large error in the repair results.

One of the reasons for generating a false mesh structure for mesh generation is that the model itself of the boundary representation is not watertight. Since the common edges of the two patches on the boundary representation model are respectively stored in the parameter domains of the two parametric surfaces, gaps are generated under the influence of the truncation error of the computer. In addition, errors caused by design errors, boolean operation intersection errors, different accuracy requirements of different CAD software, and the like can destroy the water tightness of the model. Therefore, the grid generation process must perform special treatment on heavy edges and emphasis of the model. At present, the water tightness of a repair model usually adopts two means, namely filling and merging gaps on grids through local grid editing operation, the method is only suitable for stitching gaps with smaller intervals, grid edges which are overlapped with each other geometrically cannot be identified, and the hidden curved surface of the model is reconstructed globally firstly and then discretized to generate a water-tight grid, wherein the process can ensure the output of the water-tight grid, but the algorithm can blur important characteristics of sharp points, hard boundaries, thin plates and the like of the grid, so that a large error exists in the generated grid model. In addition, both methods cannot ensure that grid edges corresponding to parameter curved surface boundary lines exist in the generated grid, and are not beneficial to the viewing and modification of the model.

For applications such as physical simulation, besides maintaining water tightness, the surface grid model needs to reduce errors and resolution as much as possible and improve the quality of the triangular surface patches of the grid, and the goal can be achieved by adopting a grid simplifying method. The grid simplification algorithm based on local grid editing can use the characterization of continuous parameter curved surfaces and also can use the characterization of discrete grid curved surfaces. The method has the advantages that the geometric accuracy is high, the attributes such as the position, the tangent vector, the curvature and the like of the curved point can be calculated rapidly, but the related geometric calculation is usually nonlinear, the numerical stability problem exists, and the calculation of the projection point is time-consuming. The advantage of using mesh surface characterization is that the projection calculation is convenient, the correlation geometry calculation is linear, fast and effective, but certain discrete errors exist. Most of the current grid simplification algorithms only use grid characterization for calculation, and cannot accurately control errors in the discretization process.

Therefore, a method for generating a parameter curved surface grid with controllable errors is provided to solve the difficulties existing in the prior art, which is a problem to be solved by those skilled in the art.

Disclosure of Invention

In view of this, the invention provides a method for generating a parametric surface grid with controllable errors, which designs a grid generation algorithm by using a grid local editing method, and converts a parametric surface model represented by a boundary into a watertight grid model meeting the error requirement.

In order to achieve the above purpose, the present invention adopts the following technical scheme:

a parameter curved surface grid generation method with controllable error comprises the following steps:

s1, inputting a boundary representing a parameter curved surface model, and uniformly sampling the parameter curved surface model to obtain an initialization grid;

s2, optimizing boundary sampling points to obtain an initial optimization grid;

s3, optimizing the internal sampling points of the initial optimization grid to obtain a post-optimization grid;

and S4, performing global optimization on the post-optimization grid to generate a final grid.

In the above method, optionally, in S1, the boundary parameter curved surface model is uniformly sampled according to the length of the three-dimensional curve, and the sampling points of two boundaries representing the same common edge are identical.

In the above method, optionally, in S2, one of two boundaries representing a common edge is optimized to enable the boundary line to meet a given distance error requirement, and then, according to the same length proportion, the other boundary line representing the same common edge is subjected to synchronous grid local editing operation to maintain the pairing relationship of the vertices of the two boundary lines;

after the boundary optimization is completed, an initial optimization grid is generated using the CDT.

The above method, optionally, the optimization method of two boundaries of the common edge adopts the following formula:

wherein ,is the boundary line v _a v _b Target length of->Is a curved surface->At v _c Minimum radius of curvature at ∈>Is at v as boundary line _c The radius of curvature at e is given as the error value.

In the above method, optionally, the operation of local editing of the synchronous grid is as follows: and when one boundary line performs edge splitting, edge merging and sampling point position optimization operations on two boundaries representing the same common edge, the other boundary line also performs edge splitting, edge merging and sampling point position optimization operations according to the same edge length proportion.

In the above method, optionally, in S3, the internal sampling points of the initial optimization grid are optimized, and the specific contents are: and judging the distance between the grid and the boundary parameter curved surface model by using the mapping distance, so that the internal grid meets the error, namely the optimization of the internal sampling points of the initial optimized grid is completed.

The above method, optionally, the method for making the internal grid satisfy the error adopts the following formula:

wherein ,is the vertex v _a Target length of l _a Is the minimum side length of the adjacent side, < ->Is the distance from the center of gravity of the triangular surface to the curved surface, +.>Is a curved surface->The minimum radius of curvature at e is the given error value, i=1, 2,.. _a V is _a Is provided.

In the above method, optionally, the specific content of performing global optimization on the post-optimization grid in S4 includes:

s4.1, optimizing an elongated triangle;

s4.2, global angle optimization;

and S4.3, global error optimization.

Compared with the prior art, the invention provides the parameter curved surface grid generating method with controllable errors, which has the following beneficial effects: in the grid generation process, the coordination of grid generation is ensured by synchronously editing the grid sharing operation, and matching points of the coordination grid are combined to generate watertight grids; in addition, two new target side length calculation methods are designed aiming at the error requirement, and the triangular grid meeting the error requirement can be generated by utilizing the target side length to carry out grid local editing operation; on the basis of controllable errors, the continuous parameter surface characterization and the discrete grid surface characterization are comprehensively utilized to perform global quality optimization, so that the triangular grid with high quality and low errors can be obtained.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.

FIG. 1 is a flow chart of a method for generating a parameter surface grid with controllable errors, which is provided by the invention;

FIG. 2 is a schematic diagram of a grid partial editing operation used in steps S1-S4 provided by the present invention;

FIG. 3 is a schematic diagram showing the results of steps S1-S4 according to the present invention;

FIG. 4 is a graph of the results of a mouse mesh model generated under different error requirements provided by the present invention;

FIG. 5 is a graph comparing the results of the Gmsh, netgen and the mesh model generated on the gear model according to the invention;

FIG. 6 is a graph comparing the results of the Gmsh, netgen and mesh model generated on the humming bird model according to the present invention;

FIG. 7 is a graph comparing the results of Gmsh, netgen and the mesh model generated on the turbine model according to the invention;

FIG. 8 is a graph comparing the results of the Gmsh, netgen and the grid model generated on the mouse model according to the invention;

fig. 9 is a graph comparing the results of the mesh model generated on the pillow model by Gmsh, netgen and the invention provided by 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. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

Referring to fig. 1, the invention discloses a parameter curved surface grid generation method with controllable errors, which comprises the following steps:

s1, inputting a boundary representing a parameter curved surface model, and uniformly sampling the parameter curved surface model to obtain an initialization grid;

s2, optimizing boundary sampling points to obtain an initial optimization grid;

s3, optimizing the internal sampling points of the initial optimization grid to obtain a post-optimization grid;

and S4, performing global optimization on the post-optimization grid to generate a final grid.

Further, in S1, the boundary parametric surface model is uniformly sampled according to the length of the three-dimensional curve, and the sampling points are identical for two boundaries representing the same common edge.

Specifically, CAD models (IGES or STEP format) are input as boundary representationsThe model comprises n pieces of parameter curved surfaces represented by boundaries>The user is then required to provide a given error value e representing the unilateral Hausdorff distance of the surface to the triangular mesh. The output of the algorithm is a triangular mesh that satisfies the error e.

S1, an initialization grid (shown in FIG. 3 b) is obtained by utilizing the isoparametric lines of the parameter domain, and the specific contents are as follows: firstly, generating an isoparametric line grid in a parameter domain; uniformly sampling boundary lines according to the length of the three-dimensional curve, and ensuring that the sampling points of two boundaries representing the same common edge are consistent; finally, generating an initialization grid by using Constrained Delaunay Triangulation (CDT) and obtaining the curved surface grid through a curved surface parameter equation.

Further, in S2, one of two boundaries representing the common edge is optimized to enable the boundary line to meet a given distance error requirement, and then the other boundary line representing the same common edge is subjected to synchronous grid local editing operation according to the same length proportion so as to maintain the pairing relationship of the vertices of the two boundary lines;

after the boundary optimization is completed, an initial optimization grid is generated using the CDT.

Further, the optimization method of the two boundaries of the common edge adopts the following formula:

wherein ,is the boundary line v _a v _b Target length of->Is a curved surface->At v _c Minimum radius of curvature at ∈>Is at v as boundary line _c The radius of curvature at e is given as the error value.

Further, the synchronous grid local editing operation is as follows: and when one boundary line performs edge splitting, edge merging and sampling point position optimization operations on two boundaries representing the same common edge, the other boundary line also performs edge splitting, edge merging and sampling point position optimization operations according to the same edge length proportion.

Specifically, the optimization process for optimizing the boundary sampling points in S2 includes the following steps:

step S2.1, calculating a target side length: a target side length is calculated for each line segment on the boundary line, so that the boundary line can meet the distance error when the line segment length is the target side length. Given a vertex ofLine segment v of (2) _a v _b The corresponding curve is a parametric curve +.>And->A section of intersection line between them. Let->Is a line segment v _a v _b Corresponding to the midpoint of the curve segment. In order to make the side length meet the distance error requirement, first a curved surface +.>At v _c Minimum radius of curvature at ∈>Curved surface->At v _c Minimum radius of curvature at ∈>And curve segment v _c Radius of curvature +.>Then press the followingCalculating line segment v _a v _b Is +.> Finally, in order to avoid that the generated line segment is too long or too short, the target length may be +.>Limited to a given range [ l ] _min ,l _max ]And (3) inner part.

Step S2.2, edge splitting optimization: when line segment v _a v _b Is of the side length l _ab Greater thanAt the time of line segment v _a v _b Intermediate insert segment v _a v _b Midpoint v of corresponding curve segment _c And update v _c Target side length of adjacent line segments.

Step S2.3, edge merging optimization: when line segment v _a v _b Is of the side length l _ab Less thanMerging line segments v _a v _b To the midpoint v of its corresponding curve segment _c And updates segment v _a-1 v _c and v_c v _b+1 Wherein v is _a-1 V is _a V _c v _b+1 V is _b Is the next sample point of (c).

Step S2.4, optimizing sampling point positions: for two line segments v _a v _b and v_b v _d Is a common point v of (2) _b According to the target side lengthAndoptimization Point v _b Is positioned so that it satisfies-> wherein />Respectively represent line segments v _a v _b and v_b v _d Corresponding to the length of the curve segment.

Further, in S3, the internal sampling points of the initial optimization grid are optimized, which specifically includes: and judging the distance between the grid and the boundary parameter curved surface model by using the mapping distance, so that the internal grid meets the error, namely the optimization of the internal sampling points of the initial optimized grid is completed.

Further, the method for making the internal grid satisfy the error adopts the following formula:

wherein ,is the vertex v _a Target length of l _a Is the minimum side length of the adjacent side, < ->Is the distance from the center of gravity of the triangular surface to the curved surface, +.>Is a curved surface->The minimum radius of curvature at e is the given error value, i=1, 2,.. _a V is _a Is provided.

Specifically, in S3, the internal sampling points of the initial optimization grid are optimized, and the specific contents are:

estimating grid using mapping distanceDistance from the curved surface. The mapping distance of the triangular patch f on the curved surface grid is f, and the curved surface point p represented by the gravity center of the f on the parameter domain ₁ And the center of gravity p of f ₂ Distance between them. The optimization procedure of this step is given by algorithm 2, which comprises the following steps.

Step S3.1, calculating a target side length: the purpose of this step is for each point v on the grid _a Calculating a target lengthSo that the grid satisfies the distance error when each side length of the grid does not exceed the sum of target lengths of the end points of the two sides. For each vertex v on the mesh _a Calculating the minimum side length l of the adjacent sides _a . Let->V is _a Is adjacent to the triangular face->Is the center of gravity of triangular surface +.>Is the distance from the center of gravity of the triangular surface to the curved surface, +.>Is->To a curved surface->Is>Is a curved surface->A minimum radius of curvature at the point. Vertex v _a Is +.>The method comprises the following steps: />

Step S3.2, edge splitting optimization: v _a v _b Is of the side length l _ab With the target side lengthSatisfy->When the grid is subjected to edge splitting operation, i.e. at edge v _a v _b Midpoint v of the middle insertion edge _c And split with edge v _a v _b Adjacent patches. After all the grid edges are processed, the target edge length of the grid is updated.

Step S3.3, edge merging optimization: when grid edge v _a v _b Is of the side length l _ab With the target side lengthSatisfy the following requirementsMerging line segments v _a v _b To line segment v _a v _b Midpoint v of corresponding curve segment _c . After all the grid edges are processed, the target edge length of the grid is updated.

Step S3.4, vertex degree optimization: the number of adjacent edges of the grid vertex is called the degree of the grid vertex, the mesh scale of the internal grid vertex is 6, and the mesh scale of the boundary grid vertex isWhere θ is the internal angle between the boundary edges. The goal of this step is to bring the mesh vertices as close to the mesh scale as possible. For each grid edge v _a v _b Let adjacent triangles thereof be v _a v _b v _c and v_a v _b v _d Wherein four grid points v _a ,v _b ,v _c ,v _d Degree of (D) _a ,D _b ,D _c ,D _d Target degrees are respectively O _a ,O _b ,O _c ,O _d . If the edge roll-over operation is capable of optimizing the degree of four grid points, i.e. |D _a -1-O _a |+|D _b -1-O _b |+|D _c +1-O _c |+|D _d +1-O _d |＜|D _a -O _a |+|D _b -O _b |+|D _c -O _c |+|D _d -O _d I, turn over edge v _a v _b And updates the target side length of the grid.

Step S3.5, vertex position optimization: first, for each internal vertex v _a Calculate all adjacent patchesCenter of gravity->Then according to three vertexes v of each face sheet _a ,/>Weights of the patches are calculated +.> wherein />Is the average of the target lengths of all vertices. Finally, the vertex v is updated _a Is defined by the position of: wherein />Is triangle->Dough sheet->P (P) represents the projection of the spatial point P onto the curved surface.

Step S3.6, angle optimization: the goal of this step is to optimize the angular energy wherein θ_i ,i＝1,...,n _angle Is the interior angle of all triangles within the mesh. For triangle to each internal grid edge v _a v _b Checking whether edge-turning can reduce the angle energy E _angle If it is possible, the edge v is turned over _a v _b 。

Further, the specific content of performing global optimization on the post-optimization grid in S4 includes:

s4.1, optimizing an elongated triangle;

s4.2, global angle optimization;

and S4.3, global error optimization.

Specifically, S4.1 elongated triangle optimization

The step is that under the condition of fixed boundary sampling points, each parameter surface is sequentially processedThe optimization is carried out, comprising the following steps.

Step S4.1.1, edge splitting optimization: for all triangles f containing angles less than 15 degrees, the length l of the shortest side is calculated _s If the triangle f is not bordered by edge e _i Length of greater than 2l _s The edges of such a strip are optionally split. Recording the newly added vertex number N in the splitting process _inserted 。

Step S4.1.2 edge merge optimization: combining the opposite sides of the small angles in sequence from small angles to large angles, when the combination quantity reachesAnd ending the combination.

S4.2 Global Angle optimization

At this stage, firstly, the grids of all the curved sheets obtained in the previous step are combined to generate a watertight grid M _w Then for M _w Global optimization is performed. In the optimization process, grid points corresponding to the vertexes of the parameter curved surface sheet are kept fixed, boundary edges corresponding to the boundaries of the parameter curved surface sheet are kept marked, and endpoints on the boundary edges are always located on the boundary of the curved surface sheet. Due to the mesh M _w Having been sufficiently close to the surface, spatial point to M can be used in the process of global optimization _w Instead of the projection of the spatial point onto the curved surface. Global optimization involves the following steps.

Step S4.2.1 calculates the target side length: unlike step S2.1, this step uses the current mesh to estimate the minimum radius of curvature r at the vertices _a Rather than using a parametric surface to estimate the minimum radius of curvature. Each vertex v on the mesh _a Target length of (2)The method comprises the following steps: />Minimum radius of curvature r on the mesh _a The mean curvature and gaussian curvature of the mesh can be used to determine the mean curvature and gaussian curvature of the mesh.

Step S4.2.2 edge splitting optimization: calculating the number n of obtuse triangles _obtuse For all obtuse triangles f, splitting is performed before the obtuse angles are sequentially split from big to smallThe longest edge of the obtuse triangle is recorded and the newly added vertex number N is recorded _inserted . And under the condition that the longest side is a curved surface boundary side, the newly added vertex needs to be projected onto the curved surface boundary.

Step S4.2.3 edge merge optimization: combining the opposite sides of the small angles in sequence from small angles to large angles, when the combined number reaches N _inserted Ending at the time, in addition, when merging edges v _a v _b When the vertices of (a) include vertices on boundary edges, the merged vertices are projected onto the merged vertexAnd then, the method. When merging edges v _a v _b Comprises vertex v of parametric surface _a V when (v) _a v _b Is combined to v _a The corresponding curved surface boundary is positioned; when the vertices of the merge edge include vertices on two different boundary edges, the merge is canceled.

Step S4.2.4 vertex position optimization: this step is similar to step S3.5, except that the target side length used in step S3.5 for calculating the weights is changed to the target side length obtained in step S4.2.1, and the projection P (·) of the spatial point to the curved surface is changed to the watertight grid M _w Is a projection of (a).

S4.3 Global error optimization

The grid error global optimization stage firstly changes the condition of edge splitting (step S4.2.2) in global angle optimization from an obtuse triangle to a triangle with larger error, namely the edge splitting step is an edge splitting step for optimizing error, and then circularly executes the following steps for 3-4 times: edge splitting step to optimize error, vertex degree optimization (step S3.4), computing grid target edge length (step S4.2.1), and updating vertex position optimization (step S4.2.4).

FIG. 2 shows a schematic diagram of the grid partial editing operation used in steps S1-S4 of the present invention, the first behavior editing the pre-grid, the second behavior editing the post-grid; 2a is edge splitting, 2b is edge merging, 2c is edge flipping, and 2d is vertex position optimization.

FIG. 3 shows a schematic diagram of the results of the steps S1-S4, wherein 3a is a boundary representation parameter surface model input by S1, and consists of six parameter surfaces; 3b is the grid initialization result of S1; 3c is the boundary sampling point optimization result of S2; 3d is an internal sampling point error optimization result of S3; and 3e is the global angle and error optimization result of S4.

FIG. 4 illustrates different resolution mouse mesh models generated by different error limits. The corresponding grid quality index is given in table 1. Under different given errors, the grid model generated by the method can meet the error requirement. Where 4a is e=0.03, 4b is e=0.12, 4c is e=0.3, and 4d is e=0.6.

Table 1 quality index of mouse mesh model generated by different error requirements

Wherein, mouse model bounding box length is 229.36.e is the input distance error. And V is the number of model top points. h is the unilateral Hausdorff distance from the parameter model to the grid model. d is the average distance from the parametric model to the mesh model. θ _min Is the minimum angle of the grid. θ _max Is the grid maximum angle.Is the average of the minimum angles of all mesh patches. θ _＜30° % is the triangle duty cycle with a minimum angle of less than 30 degrees.

5-9, wherein 5a, 6a, 7a, 8a, 9a represent Gmsh generated gear, buzzer, turbine, mouse and pillow grid models, respectively; 5b, 6b, 7b, 8b, 9b represent gear, buzzer, turbine, mouse and pillow mesh models generated by NetGen, respectively; 5c, 6c, 7c, 8c, 9c represent gear, buzzer, turbine, mouse and pillow mesh models, respectively, generated by the present invention. The error indexes e used for generating the graphic grid are 0.2,1.0,0.06,0.12,0.4 respectively. The corresponding grid quality index is given in table 2.

Table 2 comparison of the present algorithm with open source grid Generation software Gmsh and Netgen

Wherein L is the diagonal length of the model bounding box. P is the number of model patches. And V is the number of model top points. h is the unilateral Hausdorff distance from the parameter model to the grid model. d is the average distance from the parametric model to the mesh model. θ _min Is the minimum angular angle of the grid. θ _max Is the grid maximum angle.Is the average of the minimum angles of all mesh patches. θ _＜30° % is the triangle duty cycle with a minimum angle of less than 30 degrees.

The index of Table 2 shows that the invention can still generate grids with lower maximum error and average error under the condition that the grid resolution is greatly lower than that of the grids generated by Gmsh and Netgen, and the grids can meet the error requirement. In the aspect of grid angle quality, the overall indexes of the minimum angle, the maximum angle and the small angle triangle of the algorithm are better than Gmsh, the index level is equivalent to Netgen, and meanwhile, the invention has optimal precision and quality indexes on a mouse and a pillow model. In particular, on the mouse model of fig. 8, neither Gmsh nor Netgen generate a grid that is watertight, whereas the present invention generates a grid that is watertight.

The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (8)

1. The parameter curved surface grid generating method with controllable error is characterized by comprising the following steps:

s1, inputting a boundary representing a parameter curved surface model, and uniformly sampling the parameter curved surface model to obtain an initialization grid;

s2, optimizing boundary sampling points to obtain an initial optimization grid;

s3, optimizing the internal sampling points of the initial optimization grid to obtain a post-optimization grid;

and S4, performing global optimization on the post-optimization grid to generate a final grid.

2. The method for generating an error-controllable parametric surface grid as claimed in claim 1, wherein,

in S1, uniformly sampling the parametric curved surface model according to the length of the three-dimensional curve, and the sampling points are consistent for two boundaries representing the same common edge.

3. The method for generating an error-controllable parametric surface grid as claimed in claim 1, wherein,

s2, optimizing one of two boundaries representing the common edge to enable the boundary line to meet a given distance error requirement, and then carrying out synchronous grid local editing operation on the other boundary line representing the same common edge according to the same length proportion so as to keep the pairing relation of the vertexes of the two boundary lines;

after the boundary optimization is completed, an initial optimization grid is generated using the CDT.

4. An error-controllable parametric surface mesh generation method as claimed in claim 3, wherein,

the optimization method of the two boundaries of the common edge adopts the following formula:

wherein ,is the boundary line v _a v _b Target length of->Is a curved surface->At v _c Minimum radius of curvature at ∈>Is at v as boundary line _c The radius of curvature at e is given as the error value.

5. An error-controllable parametric surface mesh generation method as claimed in claim 3, wherein,

the synchronous grid local editing operation is as follows: and when one boundary line performs edge splitting, edge merging and sampling point position optimization operations on two boundaries representing the same common edge, the other boundary line also performs edge splitting, edge merging and sampling point position optimization operations according to the same edge length proportion.

6. The method for generating an error-controllable parametric surface grid as claimed in claim 1, wherein,

and S3, optimizing the internal sampling points of the initial optimization grid, wherein the specific contents are as follows: and judging the distance between the grid and the boundary parameter curved surface model by using the mapping distance, so that the internal grid meets the error, namely the optimization of the internal sampling points of the initial optimized grid is completed.

7. The method for generating an error-controllable parametric surface grid as claimed in claim 6, wherein,

the method for making the internal grid satisfy the error uses the following formula:

wherein ,is the vertex v _a Target length of l _a Is the minimum side length of the adjacent side, < ->Is the distance from the center of gravity of the triangular surface to the curved surface,is a curved surface->The minimum radius of curvature at e is the given error value, i=1, 2,.. _a V is _a Is provided.

8. The method for generating an error-controllable parametric surface grid as claimed in claim 1, wherein,

the specific content of performing global optimization on the post-optimization grid in the S4 comprises the following steps:

s4.1, optimizing an elongated triangle;

s4.2, global angle optimization;

and S4.3, global error optimization.