A Feature-Preserving Surface Structure Mesh Generation Method Based on Piecewise Parameterization

Abstract

The present invention discloses a method for generating a feature-preserving structured surface quadrilateral mesh. Currently, for the method of generating a structured quadrilateral mesh, the generated mesh quality is poor, and it cannot effectively preserve features, making it difficult to meet the requirements of simulation calculations. The steps of the present invention are as follows: extracting feature lines; flood decomposition model; boundary first flattening parameterization; topology division based on a marked field; solving the mapping relationship between two-dimensional triangular mesh patches and three-dimensional triangular mesh patches; mapping two-dimensional streamlines to three dimensions to generate three-dimensional streamlines; solving the number of discrete segments of streamlines by integer programming; generating two-dimensional quadrilateral mesh patches by bilinear interpolation; mapping the two-dimensional quadrilateral mesh to three dimensions through the mapping relationship between two dimensions and three dimensions to generate three-dimensional quadrilateral mesh patches; splicing the three-dimensional quadrilateral mesh patches to generate a structured quadrilateral mesh model. The present invention can quickly generate a high-quality structured quadrilateral mesh model that preserves features.

Description

Technical Field

[0001] The present invention relates to the generation process of structured quadrilateral meshes in the pre - processing of the numerical simulation field, and particularly relates to a method for generating feature - preserving surface structure meshes based on piece - wise parameterization. Background Art

[0002] Mesh generation is a pre - processing process in numerical simulation technologies such as the finite element method, the finite volume method, and the finite difference method. This process is to convert a mesh model composed of structured triangular elements into a mesh model composed of structured quadrilateral elements. In numerical simulation, quadrilateral meshes are favored because they have higher solution accuracy, computational efficiency, and are easier to transform compared to triangular meshes.

[0003] Mesh parameterization was originally a method widely used in model surface mapping. Its main function is to map a three - dimensional model to a two - dimensional region, playing a bridging role between two - dimensional and three - dimensional. With the continuous maturity of mesh parameterization methods, there have been great improvements in both speed and mapping quality, providing theoretical support for the expansion of two - dimensional algorithms to three - dimensional algorithms.

[0004] Current structured quadrilateral mesh generation technologies cannot well preserve feature information, and the generated quadrilateral meshes often have more singular points and quadrilateral patches with low quality. This method can well preserve feature information and has fewer singular points and low - quality quadrilateral patches. Summary of the Invention

[0005] To improve the quality of quadrilateral meshes, the present invention provides a method for generating feature - preserving surface structure meshes based on piece - wise parameterization.

[0006] The technical solution of the present invention is as follows: by calculating the dihedral angle and manual method, the feature lines are extracted; through the flooding strategy, the feature lines are used as boundaries to decompose the three-dimensional triangular mesh model into several three-dimensional triangular mesh patches; through the boundaryfirst flattening parameterization method, each three-dimensional triangular mesh patch is mapped into a two-dimensional triangular mesh patch; the boundaries of the two-dimensional triangular mesh patches are extracted, and through the method based on the marked field, two-dimensional topological division is carried out, and for each two-dimensional triangular mesh patch, a two-dimensional streamline group is established; through the mapping relationship between the two-dimensional triangular mesh patch and the three-dimensional triangular mesh patch, the two-dimensional streamline group of each patch is mapped to three dimensions to generate a three-dimensional streamline group; an integer programming model is established according to the connection relationship of the three-dimensional streamline group and solved to obtain the discrete numerical values of each streamline group; the two-dimensional streamline group is interpolated by the bilinear interpolation method to generate two-dimensional quadrilateral patches; for the two-dimensional quadrilateral patches, the Winslow smoothing and patch inversion detection method is used for iterative smoothing; through the mapping relationship between the two-dimensional triangular mesh patch and the three-dimensional triangular mesh patch, the two-dimensional quadrilateral mesh is mapped to three dimensions to generate three-dimensional quadrilateral mesh patches; the three-dimensional quadrilateral mesh patches are spliced to generate a structured quadrilateral mesh model. The present invention can effectively retain the feature information, and the generated mesh model has fewer singular points and low-quality quadrilateral patches.

[0007] The method of the present invention specifically includes the following steps:

[0008] Step 1: Establish a three-dimensional triangular mesh model M of the analysis entity object t , and manually extract the set of feature lines CL to be retained through CAD software. Through this step, the feature information that the user wants to retain can be obtained.

[0009] Step 2: Use the set of feature lines CL to decompose the three-dimensional triangular mesh model M through the flooding strategy t .

[0010] Sub-step 2.1: Arbitrarily select a point v t from the vertex set V mt of M mt , and add it to the detection queue Q;

[0011] Sub-step 2.2: Take out a point v from the detection queue Q, and detect a set of neighborhood points v t of v on M ring ;

[0012] Sub-step 2.3: Traverse the points v ring in v r . If v r does not belong to the patch point set v face and the set of feature lines CL, then v r to V faceWith Q; if v r does not belong to v face , but belongs to CL, then add v r to v face ; if v r belongs to v face , then skip this point;

[0013] Sub-step 2.4, if Q is not empty, go back to step b, if Q is empty then continue;

[0014] Sub-step 2.5, add V face to the set of detected points V used , use the v face set to generate the patch F, and add F to the three-dimensional triangular mesh patch set 3MF t , empty v face , if V mt is equal to V used , the algorithm ends; if V mt is not equal to V used , then continue;

[0015] Sub-step 2.6, select the vertex Add v to Q and go back to sub-step 2.2.

[0016] Through the above steps, the three-dimensional triangular mesh model M t can be decomposed into several three-dimensional triangular mesh patches and stored in the three-dimensional triangular mesh patch set 3MF t . This step realizes the decomposition of the complex three-dimensional triangular mesh model M t , and during the decomposition process, the feature information is converted into the boundaries of the three-dimensional triangular mesh patches.

[0017] Step 3, use the boundary first flattening mesh parameterization method to map the three-dimensional triangular mesh patch group to a two-dimensional region to generate a two-dimensional triangular mesh patch set 2MF t ;

[0018] For each three-dimensional triangular mesh patch 3F t in 3MF t , through the boundary first flattening parameterization method, map it to a two-dimensional region to generate a two-dimensional triangular mesh patch set 2MF t . This step realizes the effect of dimensionality reduction, converting three-dimensional information into two-dimensional information.

[0019] Step 4: Extract the boundaries of the two-dimensional triangular mesh patches, and use the marked field method for topological partitioning to generate a two-dimensional streamline group 2L. This step generates two-dimensional streamline information, which will be used in subsequent steps to construct an integer programming and generate structured quadrilateral mesh data.

[0020] The streamline group consists of several pairs of streamlines. Each pair of streamlines is composed of several internal streamlines plus two boundary streamlines. When generating the quadrilateral mesh later, the number of discrete segments of each pair of streamlines is equal.

[0021] Step 5: Map the two-dimensional streamline group to three dimensions through the mapping relationship between the three-dimensional triangular mesh patches and the two-dimensional triangular mesh patches to generate a three-dimensional streamline group 3L.

[0022] For any point v in 2L, map v to three dimensions to obtain the three-dimensional point v new The calculation formula is as follows:

[0023]

[0024] where v x , v y , v z represent the coordinates of point v on the x, y, and z axes respectively; represents the vertex of the triangular patch 2f in the two-dimensional triangular mesh patch where the point is located t ; represents the triangular patch 2f t mapped to the three-dimensional space, and the vertex of the triangular patch 3f in the three-dimensional triangular mesh patch t ;

[0025] Replace v with v new to generate the three-dimensional streamline group 3L. The three-dimensional streamline group and the two-dimensional streamline group have the characteristic that the number of discrete segments of the corresponding streamline pairs is equal. This step realizes the generation of three-dimensional streamline information, which will be used in subsequent steps to construct an integer programming model.

[0026] Step 6: Establish and solve an integer programming model through the topological relationship of the three-dimensional streamlines in the three-dimensional space;

[0027] The integer programming model takes the number of discrete segments of the two-dimensional streamline group as the independent variable x i . Set the shortest length of the streamline in two dimensions as the length of the unit segment number, and calculate the initial number of segments x of all streamlines i '. The integer programming model is as follows:

[0028]

[0029] R1: x i = x j + x k

[0030] R2: x i ≥ x i ′

[0031] where w i represents the discrete weight, and n is the total number of streamline pairs in the streamline group. R1 is a three-dimensional streamline constraint constructed from the equality relationship of the discrete segments of the three-dimensional streamline in three-dimensional space; R2 is a lower-bound constraint to ensure that the number of discrete segments is not a non-positive number.

[0032] By solving the integer programming, the number of discrete segments x of each streamline pair in the streamline group can be obtained.

[0033] The number of discrete segments of each streamline is calculated in this step and will be used to generate a structured quadrilateral mesh model in the subsequent steps.

[0034] Step 7: Using the number of discrete segments x of the streamline pairs calculated in Step 6, generate a two-dimensional quadrilateral mesh patch group 2MF using bilinear interpolation q .;

[0035] This step generates two-dimensional structured quadrilateral mesh patches, but there is a problem of uneven sparsity, which needs to be optimized.

[0036] Step 8: Optimize the two-dimensional quadrilateral mesh patch group 2MF q patches. By re-discretizing the sparse and uneven boundary streamlines in the two-dimensional streamline group, uniform boundary streamlines are obtained, as follows:

[0037] There are the following three cases for the equality constraints in the three-dimensional streamline:

[0038] c1: x i = x j

[0039] c2: x i = x j + x k …

[0040] c3: x i + x j … = x p + x q …

[0041] The coping strategies for the three cases are as follows:

[0042] a) For case c1, no processing is required as it will be automatically aligned in three dimensions;

[0043] b) For case c2, replace the long side with the short side, map the discrete points of the short side to three dimensions, and then map them to the two dimensions where the long side is located for replacement;

[0044] c) For case c3, map the discrete points on both sides to three dimensions, divide the streamline into multiple segments in three dimensions, recalculate the number of segments for each segment, map them to the corresponding two two-dimensional patches, and then discretize them at equal intervals.

[0045] Rediscretize the boundary streamlines in the three-dimensional streamline group as described above, and then map the boundary streamlines in the three-dimensional streamline group to the two-dimensional space to obtain a set L of rediscretized boundary uniform boundary streamlines. uni 。

[0046] This step obtains a uniformly distributed boundary discretization, which will be used to optimize the quality of the two-dimensional structured quadrilateral mesh patches in subsequent steps.

[0047] Step 9: Use the Winslow smoothing method that preserves the boundary and prevents patch inversion to iteratively smooth the two-dimensional quadrilateral mesh patches, specifically as follows:

[0048] Sub-step 9.1: For each streamline l in the set L of uniform boundary streamlines uni in, find the boundary line l of the corresponding two-dimensional quadrilateral mesh patch m ; where l b and l m are the discretizations of the same curve, both having the same number of discrete segments, the vertex distribution in l b is uniform, and the vertex distribution in l m is non-uniform; b

[0049] Sub-step 9.2: Fix the starting vertices of l m and l b , and calculate the ratio of the length from each vertex to the starting vertex to the total length of the line segment in each discrete line segment, denoted as r m and r b respectively;

[0050] Sub-step 9.3: Iteratively update r b until r b is equal to r m ; in each iteration, update the new vertex coordinates calculated using r b to l b and perform smoothing using the Winslow smoothing method that detects the patch Jacobian to prevent patch inversion. Through this step, high-quality two-dimensional structured quadrilateral mesh patches are obtained.

[0051] Step 10: Map the two-dimensional bilinear grid to three dimensions to generate a three-dimensional quadrilateral grid, and the mapping method is the same as the method for mapping streamlines in step five. Through this step, three-dimensional structured quadrilateral mesh patches are obtained.

[0052] Step 11: Merge the overlapping boundary points of the three-dimensional quadrilateral mesh patches to generate a three-dimensional structured quadrilateral mesh model.

[0053] Through this step, a structured surface quadrilateral mesh model with preserved features is obtained. This model retains the feature information that the user wants to preserve, has fewer singular points (points with a degree other than 4), and has higher quality.

[0054] The substantial effect of the present invention is that it can effectively retain the feature information, and the generated mesh model has fewer singular points and low-quality quadrilateral patches. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a three-dimensional triangular mesh model of an entity object;

[0056] Figure 2 is a set of diagrams of model feature lines;

[0057] Figure 3 is a group of three-dimensional triangular mesh patches;

[0058] Figure 4 is a group of parameterized two-dimensional triangular mesh patches;

[0059] Figure 5 is a group of two-dimensional streamline;

[0060] Figure 6 is a group of three-dimensional streamline;

[0061] Figure 7 is a group of unoptimized two-dimensional quadrilateral mesh patches;

[0062] Figure 8 is a group of optimized two-dimensional quadrilateral mesh patches;

[0063] Figure 9 is a group of three-dimensional quadrilateral mesh patches;

[0064] Figure 10 is a structured surface quadrilateral mesh model. DETAILED DESCRIPTION OF THE INVENTION

[0065] The technical solutions of the present invention will be further specifically described below through specific embodiments in conjunction with the accompanying drawings.

[0066] Step 1: Establish a three-dimensional triangular mesh model M of the analysis entity object t (as Figure 1 , this figure is a three-dimensional triangular mesh model. In the subsequent steps, the conversion of this three-dimensional triangular mesh model into a three-dimensional quadrilateral mesh model will be realized), and manually extract the set of feature lines CL to be retained through CAD software (as Figure 2, This figure shows the 3D feature information to be retained. The 3D quadrilateral mesh model generated by the method in this paper can still retain these features). Through this step, the feature information that the user wants to retain can be obtained;

[0067] Step 2: Use the set of feature lines CL and decompose the 3D triangular mesh model M through a flooding strategy t (As Figure 3 , In this figure, 15 3D triangular mesh patches are obtained by decomposing the 3D triangular mesh model. The boundaries of these patches are the feature information that the user wants to retain. These patches can be pieced together in 3D space to restore the 3D triangular mesh model);

[0068] a) Arbitrarily select a point v t from the vertex set V mt of M mt , and add it to the detection queue Q.

[0069] b) Take out a point v from the detection queue Q and detect a set of neighboring points v t of v on M ring .

[0070] c) Traverse the points v ring in v r . If v r does not belong to the patch point set v face and the set of feature lines CL, then add v r to V face and Q; if v r does not belong to v face , but belongs to CL, then add v r to v face ; if v r belongs to V face , then skip this point.

[0071] d) If Q is not empty, go back to step b; if Q is empty, continue.

[0072] e) Add V face to the set of detected points V used . Use the v face set to generate patches F and add F to the 3D triangular mesh patch set 3MF t , and clear v face . If V mt is equal to V used , the algorithm ends; if V mt is not equal to V used , then continue.

[0073] f) Select a vertex Add v to Q and go back to step b.

[0074] Through the above steps, the three-dimensional triangular mesh model M t can be decomposed into several three-dimensional triangular mesh patches and stored in the three-dimensional triangular mesh patch set 3MF t . This step realizes the decomposition of the complex three-dimensional triangular mesh model M t , and during the decomposition process, the feature information is converted into the boundaries of the three-dimensional triangular mesh patches.

[0075] Step 3: Use the boundary first flattening mesh parameterization method to map the group of three-dimensional triangular mesh patches to a two-dimensional region to generate a two-dimensional triangular mesh patch set 2MF t (as Figure 4 , in this figure, 15 two-dimensional triangular mesh patches are obtained by parameterization and dimensionality reduction from 15 three-dimensional triangular mesh patches);

[0076] For each three-dimensional triangular mesh patch 3F t in 3MF t , through the boundary first flattening

[0077] parameterization method, it is mapped to a two-dimensional region to generate a two-dimensional triangular mesh patch set 2MF t . This step realizes the effect of dimensionality reduction, converting three-dimensional information into two-dimensional information.

[0078] Step 4: Extract the boundaries of the two-dimensional triangular mesh patches, use the marked field method for topological partitioning to generate a two-dimensional streamline group 2L (as Figure 5 , in this figure, it is the partitioning result after re-topologically partitioning the boundaries in the two-dimensional triangular mesh patches).

[0079] This step generates two-dimensional streamline information, which will be used to construct integer programming and generate structured quadrilateral mesh data in subsequent steps.

[0080] Note: The streamline group is composed of several groups of streamline pairs. Each streamline pair consists of several internal streamlines plus two boundary streamlines. When generating quadrilateral meshes later, the number of discrete segments of each group of streamline pairs is equal.

[0081] Step 5: Through the mapping relationship between the three-dimensional triangular mesh patches and the two-dimensional triangular mesh patches, map the two-dimensional streamline group to three dimensions to generate a three-dimensional streamline group 3L (as Figure 6 , this figure shows 15 three-dimensional streamlines obtained by mapping the two-dimensional streamlines to three dimensions).

[0082] For any point v in 2L, map v to three dimensions to obtain the three-dimensional point v new . The calculation formula is as follows:

[0083]

[0084] where \(v\) x , \(v\) y , \(v\) z represent the coordinates of point \(v\) on the \(x\), \(y\), and \(z\) axes respectively; represents the vertices of triangular patch \(2f\) in the two - dimensional triangular mesh patch where the point is located t ; represents triangular patch \(2f\) t mapped into three - dimensional space, which are the vertices of triangular patch \(3f\) in the three - dimensional triangular mesh patch. t ;

[0085] Replace \(v\) with \(v\) new to generate the three - dimensional streamline group \(3L\). The three - dimensional streamline group and the two - dimensional streamline group have the characteristic that the number of discrete segments of the corresponding streamline pairs is equal.

[0086] This step realizes the generation of three - dimensional streamline information, which will be used to construct an integer programming model in subsequent steps.

[0087] Step 6: Establish and solve an integer programming model through the topological relationship of three - dimensional streamlines in three - dimensional space;

[0088] The integer programming model takes the number of discrete segments of the two - dimensional streamline group as the independent variable \(x\) i . Set the shortest length of the mid - streamline in two - dimensions as the length of a unit segment, and calculate the initial number of segments \(x\) i ' of all streamlines. The integer programming model is as follows:

[0089]

[0090] R1: \(x\) i = \(x\) j + \(x\) k

[0091] R2: \(x\) i ≥ \(x\) i '

[0092] where \(w\) i represents the discrete weight, and \(n\) is the total number of streamline pairs in the streamline group. R1 is the three - dimensional streamline constraint, constructed from the equality relationship of the number of discrete segments of three - dimensional streamlines in three - dimensional space; R2 is the lower - bound constraint to ensure that the number of discrete segments is not a non - positive number. By solving the integer programming, the number of discrete segments \(x\) of each streamline pair in the streamline group can be obtained.

[0093] This step calculates the number of discrete segments of each streamline, which will be used to generate a structured quadrilateral mesh model in subsequent steps.

[0094] Step 7: Using the number of discrete segments x of the streamline pairs calculated in Step 6, generate a two-dimensional quadrilateral mesh patch group 2MF by means of bilinear interpolation q (such as Figure 7 , this figure shows 15 two-dimensional structured quadrilateral mesh patches obtained after using bilinear interpolation. It can be seen that there are serious problems of uneven sparsity in the mesh, which need to be further optimized);

[0095] This step generates two-dimensional structured quadrilateral mesh patches, but there are problems of uneven sparsity, which need to be optimized.

[0096] Step 8: Optimize the two-dimensional quadrilateral mesh patch group 2MF q patches. Re-discretize the uneven boundary streamlines in the two-dimensional streamline group to obtain uniform boundary streamlines, as follows:

[0097] There are the following three cases for the equality constraints in three-dimensional streamlines:

[0098] c1: x i = x j

[0099] c2: x i = x j + x k …

[0100] c3: x i + x j … = x p + x q …

[0101] The coping strategies for the three cases are as follows:

[0102] a) For case c1, no processing is required as it will be automatically aligned in three dimensions;

[0103] b) For case c2, replace the long side with the short side. Map the discrete points of the short side to three dimensions and then map them to the two dimensions where the long side is located for replacement;

[0104] c) For case c3, map the discrete points of both sides to three dimensions. Divide the streamline into multiple segments in three dimensions, recalculate the number of segments for each segment, and map them to the corresponding two two-dimensional patches, and then discretize them at equal intervals.

[0105] Re-discretize the boundary streamlines in the three-dimensional streamline group as above, and then map the boundary streamlines in the three-dimensional streamline group to the two-dimensional space to obtain a set L of re-discretized boundary uniform streamlines uni .

[0106] This step obtains a uniformly distributed boundary discretization, which will be used in subsequent steps to optimize the quality of two-dimensional structured quadrilateral mesh patches.

[0107] Step 9. Use the Winslow smoothing method that maintains the boundary and prevents patch inversion to iteratively smooth the two-dimensional quadrilateral mesh patches, obtaining an optimized group of two-dimensional quadrilateral mesh patches (as Figure 8 , this figure shows 15 two-dimensional quadrilateral mesh patches after smoothing optimization, and it can be seen that the mesh distribution of the optimized mesh patches is uniform), specifically as follows:

[0108] a) For each streamline l uni in the set of uniform boundary streamlines L m , find the boundary line l b of the corresponding two-dimensional quadrilateral mesh patch. (Where l m and l b are the discretizations of the same curve, and they have the same number of discrete segments. Only the vertex distribution in l m is uniform, while the vertex distribution in l b is non-uniform);

[0109] b) Fix the starting vertices of l m and l b , and calculate the ratio of the length from each vertex to the starting vertex to the total length of the line segment in each discrete line segment, denoted as r m and r b respectively;

[0110] c) Update r b through multiple iterations until r b is equal to r m . In each iteration, update the new vertex coordinates calculated using r b to l b , and use the Winslow smoothing method that detects the patch Jacobian to prevent patch inversion for smoothing.

[0111] High-quality two-dimensional structured quadrilateral mesh patches are obtained through this step.

[0112] Step 10. Map the two-dimensional quadrilateral mesh to three dimensions to generate a group of three-dimensional quadrilateral mesh patches (as Figure 9 , this figure shows 15 three-dimensional structured quadrilateral mesh patches obtained by mapping the two-dimensional structured quadrilateral mesh patches to three dimensions), and the mapping method is the same as the mapping streamline method in Step 5.

[0113] Three-dimensional structured quadrilateral mesh patches are obtained through this step.

[0114] Step 11. Merge the overlapping boundary points of the three-dimensional quadrilateral mesh patches to generate a three-dimensional structured quadrilateral mesh model (as Figure 10, This figure is the finally generated structured quadrilateral mesh patch model. It can be seen that the model effectively preserves the feature information. At the same time, the model has fewer singular points and quadrilateral patches with poor quality, so it has higher quality).

[0115] Through this step, a structured surface quadrilateral mesh model with feature retention is obtained. The model preserves the feature information that the user wants to retain, has fewer singular points (points with a degree other than 4), and has higher quality.

Claims

1. A method for generating a feature-preserving structured surface quadrilateral mesh, characterized in that, it includes the following steps: Step 1, establish a three-dimensional triangular mesh model M of the analysis entity object t , and manually extract the set of feature lines CL to be retained through CAD software. Through Step 1, the feature information desired by the user can be obtained; Step 2, using the characteristic line set CL, decompose the three-dimensional triangular mesh model M through a flooding strategy t ; Step 3, use the boundary first flattening mesh parameterization method to map the three-dimensional triangular mesh patch group to a two-dimensional region, and generate a two-dimensional triangular mesh patch set 2MF t ; Step 4, extract the boundaries of the two-dimensional triangular mesh patches, use the marked field method for topological division, and generate a two-dimensional streamline group 2L; Step 5, map the two-dimensional streamline group to three dimensions through the mapping relationship between the three-dimensional triangular mesh patches and the two-dimensional triangular mesh patches to generate a three-dimensional streamline group 3L; Step 6, establish an integer programming model based on the topological relationship of the three-dimensional streamlines in three-dimensional space and solve it; Step 7: Using the number of discrete segments x of the streamline pairs calculated in Step 6, generate a two-dimensional quadrilateral mesh patch group 2MF by means of bilinear interpolation q ; Step 8, optimize the two-dimensional quadrilateral mesh patches group 2MF q for the patches, and re-discretize them through the sparse and uneven boundary streamlines in the two-dimensional streamline group to obtain uniform boundary streamlines; Step 9, use the Winslow smoothing method that preserves the boundary and prevents patch inversion to iteratively smooth the two-dimensional quadrilateral mesh patches; Step 10, map the two-dimensional bilinear grid to three dimensions to generate a three-dimensional quadrilateral mesh, and the mapping method is the same as the mapping streamline method in Step 5; Step 11, merge the overlapping boundary points of the three-dimensional quadrilateral mesh patches to generate a three-dimensional structured quadrilateral mesh model.

2. A method for generating a feature-preserving structured surface quadrilateral mesh according to claim 1, characterized in that, the said Step 2 includes the following sub-steps: Sub-step 2.1, take any point v t from the vertex set V mt of M mt , and add it to the detection queue Q; Sub-step 2.2: Take a point v from the detection queue Q and detect a set of neighboring points v of v on M t ; ring ; Sub-step 2.3, traverse the points v ring in r if v r does not belong to the patch point set v face and the feature line set CL, then add v r to V face and Q; if v r does not belong to v face , but belongs to CL, then add v r to v face ; if v r belongs to v face , then skip this point; Sub-step 2.4, if Q is not empty, go back to Step b, if Q is empty, continue; Sub-step 2.5, add V face to the detected point set V used . Use the v face set to generate the patch F, and add F to the 3D triangular mesh patch set 3MF t . Clear v face . If V mt is equal to V used , end the algorithm; if V mt is not equal to V used , then continue; Sub-step 2.6, select a vertex Add v to Q and return to sub-step 2.

2.

3. A method for generating a feature-preserving structured surface quadrilateral mesh according to claim 1, characterized in that, In step 5 described above, for any point v in 2L, map v to three dimensions to obtain the three-dimensional point v new The calculation formula is as follows: where v x , v y , v z represent the coordinates of point v on the x, y, and z axes respectively; represents the vertices of triangular patch 2f in the two-dimensional triangular mesh patch where the point is located t ; represents the vertices of triangular patch 3f in the three-dimensional triangular mesh patch after triangular patch 2f t is mapped into the three-dimensional space t ; Use v new Replace v to generate a three-dimensional streamline group 3L; the three-dimensional streamline group and the two-dimensional streamline group have the characteristic that the number of discrete segments of the corresponding streamline pairs is equal.

4. A method for generating a feature-preserving structured surface quadrilateral mesh according to claim 1, characterized in that, In the integer programming model described in step 6, the number of discrete segments of the two-dimensional streamline group is used as the independent variable x i , set the shortest length of the middle streamline in two dimensions as the length of a unit segment, and calculate the initial number of segments x i ′; The integer programming model is as follows: R1: x i = x j + x k R2: x i ≥ x i ′ where w i represents the discrete weight, n is the total number of streamline pairs in the streamline group; R1 is the three-dimensional streamline constraint, constructed by the equality relationship of the discrete segments of the three-dimensional streamline in three-dimensional space; R2 is the lower bound constraint to ensure that the number of discrete segments is not a non-positive number; by solving the integer programming, the number of discrete segments x of each streamline pair in the streamline group is obtained.

5. A method for generating a feature-preserving structured surface quadrilateral mesh according to claim 1, characterized in that, in the said Step 8, it is defined that there are equality constraints in the three-dimensional streamlines: c1: x i = x j c2: x i = x j + x k … c3: x i +x j … = x p +x q … There are three cases; The coping strategies for the three cases are as follows: a) For case c1, no processing is required, and this case will be automatically aligned in three dimensions; b) For case c2, replace the long side with the short side, map the discrete points of the short side to three dimensions, and then map them to the two dimensions where the long side is located for replacement; c) For case c3, map the discrete points on both sides to three dimensions, divide the streamline into multiple segments in three dimensions, recalculate the number of segments for each segment, map them to the corresponding two two-dimensional patches, and then discretize them at equal intervals; rediscretize the boundary streamlines in the three-dimensional streamline group, and then map the boundary streamlines in the three-dimensional streamline group to the two-dimensional space to obtain the rediscretized boundary uniform boundary streamline set L uni 。 6. A method for generating a feature-preserving structured surface quadrilateral mesh according to claim 1, characterized in that, the said Step 9 includes the following sub-steps: Sub-step 9.1, for each streamline l in the set L of uniform boundary streamlines uni find the boundary line l of the corresponding two-dimensional quadrilateral mesh patch m ; where l b and l m are the discretizations of the same curve, and both have the same number of discrete segments. The vertex distribution in l b is uniform, while the vertex distribution in l m is non-uniform; b ​ Sub-step 9.2, fix l m With l b For the starting vertex of, calculate the ratio of the length from the vertex to the starting vertex to the total length of the line segment in each discrete line segment, and denote them as r m And r b ; Sub-step 9.3, iterate and update r b , until r b equals r m ; in each iteration, update the newly calculated vertex coordinates with r b into l b , and perform smoothing using the Winslow smoothing method that detects the patch Jacobian to prevent patch inversion.

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