Structure domination surface grid encryption method based on local self-adaption

Abstract

The invention discloses a structure domination surface grid encryption method based on local self-adaption, and the method comprises the steps: firstly carrying out the preprocessing of an input grid, and obtaining a to-be-encrypted vertex of a to-be-encrypted region through the screening of a topological relation; secondly, by judging whether the encryption method selected by the user is a bisection method or a trisection method, an encryption template corresponding to the encryption method is loaded, for the bisection method, a vertex to be encrypted is divided into boundary points and internal points, and boundary point rings are extracted in sequence; then marking boundary points and internal points based on a boundary point ring according to the type of the encryption template; and finally, encrypting the to-be-encrypted area units containing the mark vertexes to obtain a final encryption result, and completing grid encryption. According to the method, high-quality encryption of the encryption area and good transition between the encryption area and the transition area are achieved, time loss caused by reading of many irrelevant units which do not need to be encrypted during encryption of a large-size grid is avoided, and the encryption speed is increased.

Description

Technical Field

[0001] This invention relates to the fields of computational geometry and finite element analysis, and in particular to a locally adaptive quadrilateral dominant mesh refinement template and method. Background Technology

[0002] Mesh refinement is a key technology in fields such as finite element analysis, computer-aided design, and computer graphics. While there is considerable research on quadrilateral mesh re-minimization, a mature solution for refining quadrilateral-dominant meshes is still lacking. Quadrilateral-dominant meshes, which consist mostly of quadrilateral elements with a small number of triangular elements, combine the high computational accuracy of quadrilateral meshes with the strong adaptability of triangular meshes, and are widely used in engineering simulations.

[0003] The algorithmic challenge of mesh refinement lies in maintaining topological consistency, i.e., ensuring a smooth transition between the refined and unrefined portions of the mesh. Current techniques typically employ uniform refinement or adaptive refinement methods. Uniform refinement applies the same refinement strategy to all mesh cells, globally increasing mesh density and potentially wasting computational resources. While adaptive refinement can adjust the refinement density according to requirements, it is prone to mesh distortion when dealing with the transition regions between quadrilateral and triangular cells, leading to a decrease in numerical accuracy.

[0004] Furthermore, existing encryption templates often encounter compatibility issues between adjacent cells when processing boundary regions, leading to a decrease in mesh quality. Therefore, a quadrilateral-dominant mesh subdivision rule and adaptive encryption method that can balance encryption efficiency, mesh quality, and boundary compatibility are needed. Summary of the Invention

[0005] The purpose of this invention is to address the difficulty of local area encryption in quadrilateral dominant meshes by providing a complete quadrilateral dominant mesh encryption template and method, thereby solving the problems of low quality, poor compatibility, long encryption time, and slow efficiency in the encryption of transition areas in the prior art.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] A method for refining structure-dominant surface meshes based on local adaptation includes the following steps:

[0008] Step 1: Preprocess the input mesh by filtering it through topological relationships to obtain the vertices to be encrypted in the region to be encrypted.

[0009] Step 2: Preprocess the encryption template. By determining the encryption method selected by the user (binary or ternary), load the binary or ternary encryption template.

[0010] Step 3: For the binary search method, the vertices to be encrypted are divided into boundary points and internal points, and the boundary point cycle is extracted in sequence.

[0011] Step 3-1: Extract the boundary edge set and point set of the region to be encrypted.

[0012] Step 3-2: Extract one of the corner points from the point set.

[0013] Step 3-3: Starting from the corner point, take all the boundary points along one direction to obtain the boundary point loop.

[0014] Steps 3-4: Classify the non-boundary points in the vertices to be encrypted as internal points.

[0015] Step 4: Based on the type of encryption template, mark the boundary points and internal points according to the boundary point ring.

[0016] Step 4-1: For the bisection method, use interval marking for boundary points and full marking for interior points.

[0017] Step 4-2: For the three-part method, mark all points.

[0018] Step 5: Encrypt the region cells containing the marked vertices to be encrypted to obtain the final encryption result and complete the mesh encryption.

[0019] Step 5-1: Select the appropriate template based on the marker type and encryption template type.

[0020] Step 5-2: Determine the location and topological relationship of the new points based on the template.

[0021] Step 5-3: Add vertices based on the positions of the newly added points.

[0022] Step 5-4: Add new faces based on vertex topology.

[0023] Preferably, the method for preprocessing the input mesh in step 1 is as follows: traverse the cell to be encrypted, traverse the adjacent points of the cell to be encrypted, and store them in a set to prepare for the subsequent extraction of boundary points and interior points.

[0024] Preferably, the binary encryption template in step 2 includes a fully encrypted area template and a transition area template. The fully encrypted area template encrypts the user-specified units that need to be encrypted, while the transition area template encrypts the transition units between the encrypted and unencrypted areas. Furthermore, the fully encrypted area template and the transition area template can be further divided into templates suitable for quadrilateral units and templates suitable for triangular units, depending on the applicable unit type.

[0025] This invention has the following characteristics and beneficial effects: Using the above-mentioned template ensures excellent compatibility between templates, avoids the generation of T-shaped nodes, and achieves high-quality encryption of the encryption zone and a smooth transition with the transition zone. Furthermore, the above technical solution also optimizes time efficiency, avoiding the time loss caused by reading many irrelevant cells that do not need encryption during the encryption of large-volume meshes, thus improving the encryption speed. Attached Figure Description

[0026] To more clearly illustrate the implementation examples and specific schemes of the present invention, the following will briefly introduce the accompanying drawings used.

[0027] Figure 1 This is a flowchart of the present invention;

[0028] Figure 2 This is an illustration of a quadrilateral-dominant mesh subdivision template based on the bisection method in this invention;

[0029] Figure 3 This is an illustration of a quadrilateral-dominant mesh subdivision template based on the three-part method in this invention;

[0030] Figure 4 The input is the grid and the cell to be encrypted;

[0031] Figure 5 The boundary line of the region to be encrypted;

[0032] Figure 6 This is the result after labeling the vertices;

[0033] Figure 7 The segmentation effect after applying the encrypted template;

[0034] Figure 8 This is an example of the effect of using binary search template encryption;

[0035] Figure 9 Example 1 shows the effect of using the three-part template encryption.

[0036] Figure 10 Example 2 shows the effect of using the three-part template encryption. Detailed Implementation

[0037] This invention provides a locally adaptive quadrilateral dominant mesh encryption template and method, such as... Figure 1 As shown, it includes the following steps:

[0038] Step (1) Preprocess the input mesh: Traverse the cell to be encrypted, traverse the adjacent points of the cell, and store them in a set to prepare for the subsequent extraction of boundary points and interior points.

[0039] Step (2) Load the binary encryption template and the tri-encryption template

[0040] 2-1. A binary template, comprising a fully encrypted area template and a transition area template. The fully encrypted area template unit encrypts the user-specified units that require encryption; the transition area template unit encrypts the transition units between the encrypted and unencrypted areas. Further, the fully encrypted area template unit and the transition area template unit can be further divided into templates suitable for quadrilateral units and templates suitable for triangular units, depending on the applicable unit type. A schematic diagram of the binary template is shown below. Figure 2 As shown, it specifically includes:

[0041] The quadrilateral fully encrypted template based on the bisection method connects the midpoints of each side of the original quadrilateral unit to the unit center, dividing the original quadrilateral unit into four new smaller quadrilaterals.

[0042] Based on the bisection method, the first quadrilateral transition template is to connect the midpoint of the two adjacent edges of the unique marker point to the center of the unit, and to connect the diagonal point of the marker point to the center of the unit, thus dividing the original quadrilateral unit into 3 smaller quadrilaterals.

[0043] Based on the bisection method, the second quadrilateral transition template takes the midpoint of the adjacent edge of two adjacent marked points and connects the three points in pairs, dividing the original quadrilateral unit into one quadrilateral and two triangles.

[0044] The triangular fully encrypted template based on the bisection method connects the midpoints of each side of the original triangular unit to the unit center, dividing the original triangular unit into 3 small quadrilaterals.

[0045] The triangular transition template based on the bisection method takes the midpoint of the two adjacent sides of the unique marker point and connects them, dividing the original triangular unit into one triangle and one quadrilateral.

[0046] Under the binary search method, the encryption template rules applied to a cell based on its marker point type are as follows:

[0047] For quadrilateral cells, if three or more vertices are marked, or two diagonal vertices are marked, then a quadrilateral fully encrypted template based on the bisection method is used.

[0048] For quadrilateral elements, if only one vertex is marked, then the quadrilateral transition template one based on the bisection method is used.

[0049] For quadrilateral elements, if two adjacent vertices are marked, then a quadrilateral transition template based on the bisection method is used.

[0050] For a triangular unit, if two or more vertices are marked, a triangular fully encrypted template based on the bisection method is used.

[0051] For triangular units, if only one vertex is marked, a triangular transition template based on the bisection method is used.

[0052] 2-2. A diagram of the three-part template is shown below. Figure 3 As shown, it specifically includes:

[0053] The quadrilateral fully encrypted template based on the three-part rule is shaped like a "well" and divides each side into three equal parts. It further divides each part into 3×3 smaller units, thus dividing the original quadrilateral into 9 smaller quadrilaterals.

[0054] Based on the three-part quadrilateral transition template one, take the last third of the two adjacent edges of the unique marker point as the new edge, divide the interior into small quadrilaterals, and connect the vertices of the small quadrilaterals opposite to the marker point to the diagonal vertices of the original unit, and divide the remaining part into two small quadrilaterals. Thus, the original quadrilateral unit is divided into 4 small quadrilaterals.

[0055] Based on the trisection method, the second quadrilateral transition template is to take the points at one-third and two-thirds of the common edge of two adjacent points, and the points at the nearest one-third of the other two adjacent edges of the two points, thus dividing the original quadrilateral into 7 smaller quadrilaterals.

[0056] Based on the three-part quadrilateral transition template three, take the point at the nearest third of the adjacent edge of two opposite corner vertices to divide the original quadrilateral into 7 smaller quadrilaterals.

[0057] Based on the three-part quadrilateral transition template four, for an edge with two marked points, take the one-third point and the two-thirds point; for an edge with one marked point, take the one-third point closest to the marked point, thus dividing the original quadrilateral into 8 smaller quadrilaterals.

[0058] The triangular full encryption template based on the ternary method divides the three sides into three equal segments, and then divides a similar small triangle at the center of the triangular unit. Then, the three vertices of the small triangle are respectively adjacent to the new vertices on the original side, thereby dividing the original unit into 6 new small quadrilaterals and 1 small triangle.

[0059] Based on the trigonometric method, the first triangle transition template takes the last third of the two adjacent edges of the marked point and connects them, dividing the original triangle unit into a triangle and a quadrilateral.

[0060] Based on the trigonometric transition template 2, for an edge with two marked points, take the point at one-third and the point at two-thirds, and divide it into three equal segments. For an edge with one marked point, take the vertex at one-third of the distance from the marked point and divide it into two new edges. Take the center point of the face and connect it to the boundary point. In this way, the original triangle is divided into 3 triangles and 2 quadrilaterals.

[0061] Under the three-part method, the encryption template rules applied to a cell based on its marker type are as follows:

[0062] For quadrilateral cells, if all four vertices are marked, a quadrilateral fully encrypted template based on the ternary method is used.

[0063] For quadrilateral elements, if only one vertex is marked, then quadrilateral transition template one based on the ternary method is used.

[0064] For quadrilateral elements, if two adjacent vertices are marked, then quadrilateral transition template two based on the ternary method is used.

[0065] For quadrilateral elements, if two opposite vertices are marked, then a quadrilateral transition template based on the ternary method is used.

[0066] For quadrilateral elements, if three vertices are marked, then a quadrilateral transition template based on the ternary method is used.

[0067] For a triangular unit, if all three vertices are marked, a triangular fully encrypted template based on the ternary method is used.

[0068] For triangular units, if only one vertex is marked, then the triangular transition template one based on the ternary method is used.

[0069] For a triangular unit, if two vertices are marked, then a triangular transition template based on the ternary method is used.

[0070] Step (3) For the binary search method, extract the boundary point rings of the region to be encrypted in sequence;

[0071] 3-1. Extract the boundary edge set BE and the point set BP of the region to be encrypted. For a closed region to be encrypted, such as... Figure 4 As shown, the boundary edges refer to those edges located at the region boundary and adjacent to the unencrypted region. First, a counting module is loaded, traversing all adjacent edges of all faces to be encrypted and counting the number of times each edge is traversed. Then, edges that count to 1 are taken out and added to the boundary edge set BE, as shown. Figure 5 As shown, the red boundary lines marked therein represent the boundary edges of the extracted region to be encrypted. The points on the boundary edges are the boundary points. Traverse all the adjacent points of the boundary edges and add them to the boundary point set BP.

[0072] 3-2. Extract a boundary corner point vc. A boundary corner point refers to a point located at a boundary inflection point in the region to be encrypted. These points are usually marked first to achieve a better transition effect. First, traverse the points in the boundary point set. For each point, extract the two adjacent edges of that point that exist in the boundary edge set. Then, determine whether these two edges are in the same face. If so, select that point as the corner point vc.

[0073] 3-3. Take all boundary points along one direction to obtain the boundary point cycle BC. First, denote the corner point vc taken in step 3-2 as vertex np and add it to the boundary point cycle. Then, traverse all adjacent points of vertex np and find a point xp that is located in the boundary point set and has not been added to the boundary point cycle. If xp is found, add it to the boundary point cycle and set np = xp. Then continue traversing all adjacent points of this vertex until all boundary points have been added to BC, indicating that the boundary point cycle has been taken.

[0074] 3-4. Classify the non-boundary points in the vertices to be encrypted as internal points. Traverse all vertices v in the vertex set BP to be encrypted. If vertex v is not in the boundary point cycle BC, add it to the internal point set NC.

[0075] Step (4) Mark the vertices according to the type of encryption template.

[0076] 4-1. For the bisection method, the points in the boundary point set BC are marked with intervals. First, the first vertex is marked. If the previous vertex is marked, the next vertex is not marked; otherwise, if the previous vertex is not marked, the next vertex is marked. For the internal point set NC, i.e., all non-boundary vertices within the local region are marked. The marking results are as follows: Figure 6 As shown, the vertices marked in red are the ones that have been labeled.

[0077] 4-2. For the three-part method, all points within the local area, including boundary points and internal points, are marked.

[0078] Step (5) encrypts the cell containing the marked vertex.

[0079] 5-1. For all the faces that need to be encrypted, find the corresponding template in step 2 based on the number of marked points and their adjacency relationships.

[0080] 5-2. Determine the coordinates pos of the newly added vertex according to the template. First, extract the coordinates of the original vertex of the face from the mesh, and then perform corresponding interpolation calculations on the vertex coordinates according to the target.

[0081] 5-3. Prepare a new vertex storage module to store the coordinates and IDs of all vertices added during the encryption process. Compare the new vertex pos with the coordinates ops of all previously added vertices. If the distance between the two points is greater than the threshold dmin, add the vertex to the grid and return its ID. Otherwise, consider them to be the same vertex, i.e., the vertex has already been added, and directly retrieve the vertex ID from ops in the storage module.

[0082] 5-4. After obtaining the vertex IDs of the face to be added, add the face to the mesh according to the connection relationships between vertices in the template. The final encryption result is as follows. Figure 7As shown, the fully encrypted area is marked in red and the transition area is marked in blue. It can be seen that the cells in the fully encrypted area are encrypted according to the "field" - shaped template rule, and the cells in the transition area are responsible for the transition between the encrypted grid and the original grid, with the property of becoming sparser from denser.

[0083] The above - mentioned template and steps have a wide range of application scenarios and are applicable to different cases of cells to be encrypted, such as Figure 8 , Figure 9 , Figure 10 as shown. Figure 8 The left - hand figure of Figure 8 shows the case where the area to be encrypted in the input contains triangular cells. At this time, singular points appear in the area, resulting in the vertices on the boundary line not being evenly divided. Figure 8 The right - hand figure of Figure 8 is the result figure after applying the binary encryption template and the above encryption steps. It can be seen that the cells in the transition area have successfully achieved the transition effect from dense to sparse, obtaining a topologically correct and well - performing encryption result. This is because the present invention has improved the previous binary template to make it applicable to the encryption of quadrilateral - dominant grids.

[0084] Figure 9 Figure Figure 9 is an example 1 of the application effect of the ternary template. The left - hand figure is the area to be encrypted in the input. This area fits the edge and has a relatively large number of triangles, which has a certain complexity in encryption. The right - hand figure is the encryption effect after applying the ternary encryption template. It can be seen that the boundary points of the area to be encrypted adopt a full - marking strategy, and the template is adaptively selected for encryption according to the type of marked points, achieving good encryption and transition of the area. Therefore, the method provided by the present invention can encrypt it correctly.

[0085] Figure 10 Figure Figure 10 is an example 2 of the application effect of the ternary template. The left - hand figure is the area to be encrypted in the input. This area is a discontinuous area, that is, there are multiple sub - areas to be encrypted, and there is a certain overlap in the transition areas of each cell to be encrypted, which brings certain difficulties to encryption. The right - hand figure is the encryption effect after applying the ternary encryption template. It can be seen that the method also has good adaptability to the encryption of discontinuous areas. In this case, each sub - area is encrypted separately, and global transition can also be achieved even when the transition areas of each sub - area overlap, and the final encryption result is correct.

[0086] In summary, the present invention provides a complete method for encrypting structure - dominant surface grids. This method can not only correctly implement grid encryption, but also optimize the time efficiency, avoid the time consumption caused by reading a lot of irrelevant cells that do not need to be encrypted during the encryption of large - volume grids, and improve the encryption speed.

Claims

1. A method for refining structure-dominant surface meshes based on local adaptive adaptation, characterized in that, Includes the following steps: Step 1: Preprocess the input mesh and filter the vertices of the region to be encrypted by topological relationships; Step 2: Determine whether the encryption method selected by the user is binary search or ternary search, and load the encryption template for the corresponding encryption method; Step 3: For the binary search method, divide the vertices to be encrypted into boundary points and interior points, and extract the boundary point cycles in sequence; Step 4: Based on the type of encryption template, mark the boundary points and internal points according to the boundary point ring; Step 5: Encrypt the cells in the region to be encrypted that contain the marked vertices to obtain the final encryption result and complete the mesh encryption.

2. The method for refining structure-dominant surface meshes based on local adaptation according to claim 1, characterized in that, The preprocessing of the input mesh in step 1 specifically involves: traversing the cell to be encrypted, traversing the adjacent points of the cell to be encrypted, and storing them in a set to prepare for the subsequent extraction of boundary points and interior points.

3. The method for refining structure-dominant surface mesh based on local adaptation according to claim 2, characterized in that, The encryption template for the binary search method in step 2 includes a fully encrypted area template and a transition area template. The fully encrypted area template encrypts the user-specified encrypted units. The transition area template encrypts the transition units between the encrypted and unencrypted areas. The fully encrypted area template and the transition area template are divided into templates applicable to quadrilateral units and templates applicable to triangular units, depending on the applicable unit type. Templates applicable to quadrilateral elements specifically include: The quadrilateral fully encrypted template based on the bisection method takes the midpoint of each side of the original quadrilateral unit and connects it with the center of the unit, dividing the original quadrilateral unit into 4 new sub-quadrilaterals. Based on the bisection method, the first quadrilateral transition template takes the midpoint of the two adjacent sides of the unique marker point and connects it to the center of the unit. The diagonal point of the marker point is also connected to the center of the unit, thus dividing the original quadrilateral unit into 3 sub-quadrilaterals. Based on the bisection method, the second quadrilateral transition template takes the midpoint of the adjacent edge of two adjacent marked points and connects the three points in pairs, dividing the original quadrilateral unit into 1 quadrilateral and 2 triangles. The templates applicable to triangular units specifically include: The triangular fully encrypted template based on the bisection method connects the midpoints of each side of the original triangular unit to the center of the unit, dividing the original triangular unit into 3 sub-quadrilaterals. The triangular transition template based on the bisection method takes the midpoint of the two adjacent sides of the unique marker point and connects them, dividing the original triangular unit into one triangle and one quadrilateral.

4. The method for refining structure-dominant surface meshes based on local adaptation according to claim 3, characterized in that, Based on the encryption template of the binary search method, the encryption template rules applied to the unit according to its marker point type are as follows: For quadrilateral cells, if three or more vertices are marked, or two diagonal vertices are marked, then a quadrilateral fully encrypted template based on the bisection method is used. For quadrilateral elements, if only one vertex is marked, then the quadrilateral transition template one based on the bisection method is used; For quadrilateral elements, if two adjacent vertices are marked, then a quadrilateral transition template based on the bisection method is used. For a triangular unit, if two or more vertices are marked, a triangular fully encrypted template based on the binary search method is used. For triangular units, if only one vertex is marked, a triangular transition template based on the bisection method is used.

5. The method for refining structure-dominant surface meshes based on local adaptation according to claim 4, characterized in that, The encryption template for the three-part method in step 2 includes: The quadrilateral fully encrypted template based on the three-part rule is shaped like a grid, dividing each side into three equal segments and further dividing the cell into 3×3 cells, thus dividing the original quadrilateral into 9 sub-quadrilaterals. Based on the three-part method, the first quadrilateral transition template takes the last third of the two adjacent edges of the unique marker point as the new edge, divides the interior into sub-quadrilaterals, and connects the vertices of the sub-quadrilaterals opposite to the marker point to the diagonal vertices of the original unit. The remaining part is divided into two sub-quadrilaterals, so the original quadrilateral unit is divided into 4 sub-quadrilaterals. Based on the three-part method, the second quadrilateral transition template is to take the point at one-third and two-thirds of the common side of two adjacent points, and the point at the nearest one-third of the other two adjacent sides of the two points, to divide the original quadrilateral into 7 sub-quadrilaterals. Based on the three-part method, the quadrilateral transition template three takes the point at the nearest third of the adjacent edge of two opposite corner vertices and divides the original quadrilateral into 7 sub-quadrilaterals. Based on the three-part quadrilateral transition template four, for an edge with two marked points, take the one-third point and the two-thirds point; for an edge with one marked point, take the one-third point closest to the marked point, thus dividing the original quadrilateral into 8 sub-quadrilaterals. The triangular full encryption template based on the ternary method divides the three sides into three equal segments, divides a similar sub-triangle at the center of the triangular unit, and then connects the three vertices of the sub-triangle to the new vertices on the original side, thereby dividing the original unit into 6 new sub-quadrilaterals and 1 sub-triangle. Based on the three-part triangle transition template one, take the last third of the two adjacent edges of the marked point and connect them to divide the original triangle unit into a triangle and a quadrilateral. Based on the trigonometric transition template 2, for an edge with two marked points, take the point at one-third and the point at two-thirds, and divide it into three equal segments. For an edge with one marked point, take the vertex at one-third of the distance from the marked point, divide it into two new edges, take the center point of the face, and connect it to the boundary point. In this way, the original triangle is divided into 3 triangles and 2 quadrilaterals.

6. The method for refining structure-dominant surface meshes based on local adaptation according to claim 5, characterized in that, Based on the three-part encryption template, the encryption template rules applied to the cell according to its marker point type are as follows: For quadrilateral cells, if all four vertices are marked, then a quadrilateral fully encrypted template based on the ternary method is used. For quadrilateral elements, if only one vertex is marked, then the quadrilateral transition template based on the ternary method is used. For quadrilateral elements, if two adjacent vertices are marked, then quadrilateral transition template two based on the ternary method is used; For quadrilateral elements, if two opposite vertices are marked, then a quadrilateral transition template based on the ternary method is used. For quadrilateral elements, if three vertices are marked, then a quadrilateral transition template based on the ternary method is used. For a triangular unit, if all three vertices are marked, a triangular fully encrypted template based on the ternary method is used. For triangular units, if only one vertex is marked, then the triangular transition template based on the three-part rule is used. For a triangular unit, if two vertices are marked, then a triangular transition template based on the ternary method is used.

7. The method for refining structure-dominant surface meshes based on local adaptation according to claim 6, characterized in that, The specific implementation process of step 3 is as follows: 3-1. Extract the boundary edge set BE and the point set BP of the region to be encrypted. For a closed region to be encrypted, its boundary edge refers to the edge located at the boundary of the region and adjacent to the unencrypted region. First, load a counting module, traverse all adjacent edges of all faces to be encrypted, and count the number of times they are traversed. Then, extract the edges that have been counted once and add these edges to the boundary edge set BE. The points on the boundary edges are the boundary points. Traverse all adjacent points of the edges in the boundary edge set and add them to the boundary point set BP. 3-2. Extract a boundary corner point vc; A boundary corner point refers to a point located at the boundary turning point in the region to be encrypted. First, traverse the points in the boundary point set. For each point, extract the two adjacent edges of that point that exist in the boundary edge set. Then, determine whether these two edges are in the same face. If so, extract the point as the corner point vc. 3-3. Take all boundary points along one direction to obtain the boundary point cycle BC; first, denote the corner point vc taken in step 3-2 as vertex np and add it to the boundary point cycle; then traverse all adjacent points of vertex np to find a point xp that is located in the boundary point set and has not been added to the boundary point cycle. If xp is found, add it to the boundary point cycle and set np = xp. Then continue to traverse all adjacent points of the vertex until all boundary points have been added to BC, which means that the boundary point cycle has been completed. 3-4. Classify the non-boundary points in the vertices to be encrypted as internal points; traverse all vertices v in the vertex set BP to be encrypted. If vertex v is not in the boundary point ring BC, add it to the internal point set NC.

8. The method for refining structure-dominant surface meshes based on local adaptation according to claim 7, characterized in that, The specific implementation process of step 4 is as follows: 4-1. For the bisection method, the points in the boundary point set BC are marked at intervals. First, the first vertex is marked. If the previous vertex is marked, the next vertex is not marked. Otherwise, if the previous vertex is not marked, the next vertex is marked. For the internal point set NC, all points in the non-boundary vertices of the local region are marked. 4-2. For the three-part method, all points within the local area, including boundary point BC and internal point NC, are marked.

9. The method for refining structure-dominant surface meshes based on local adaptation according to claim 8, characterized in that, The specific implementation process of step 5 is as follows: 5-1. For all encrypted patches, find the corresponding template in step 2 based on the number of marked points and their adjacency relationships; 5-2. Determine the coordinates pos of the newly added vertex according to the template. First, extract the coordinates of the original vertex of the face from the mesh, and then perform corresponding interpolation calculations on the vertex coordinates according to the target. 5-3. Prepare a new vertex storage module to store the coordinates and IDs of all vertices added during the encryption process through interpolation calculation; Compare the new vertex pos with the coordinates ops of all previously added vertices. If the distance between the two points is greater than the threshold dmin, add the vertex to the grid and return its id. Otherwise, assume that the vertex has already been added and retrieve the vertex id from the storage module directly. 5-4. After obtaining all the vertex IDs of the newly added face, add the face to the mesh according to the vertex connection relationship in the template to complete the mesh encryption.

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