A method for automatic decomposition of solid models for hexahedral mesh generation

Abstract

The application discloses a kind of entity model automatic decomposition methods for hexahedral mesh generation, the method comprises: input entity model, generate triangular mesh and smooth two-dimensional frame field;Mark all the recess feature grid edge, generate feature cutting ring;According to feature cutting ring, generate feature cutting surface, and the surface is merged with triangular mesh;Generate model tetrahedral mesh;Establish three-dimensional frame field;Find all singular triangle, and be divided into several singular triangle groups;Calculate the singular value of each singular triangle group and the advancing direction of its singular cutting ring;Generate singular cutting ring;Generate a singular cutting surface with singular cutting ring as boundary;Complete the decomposition of model.The present application solves the problem that the block structure obtained by decomposition is unstable, there is singular structure in the interior, and it is not suitable for mesh division in the prior art by using geometry edge curvature or three-dimensional frame field to decompose entity model.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of hexahedral mesh generation, in particular to a solid model automatic decomposition method for hexahedral mesh generation. BACKGROUND

[0002] Hexahedral mesh generation has always been an important pre-processing step of finite element analysis. The existing automatic hexahedral mesh generation technology mainly includes mapping method and sweep method. These two algorithms can generate high-quality hexahedral meshes in simple solid models, but they cannot generate hexahedral meshes in complex solid models. In practical applications, operators usually decompose a complex solid model into several simple blocks based on their hexahedral mesh generation experience, and then try to mesh these blocks using the sweep method or the mapping method to obtain the hexahedral mesh of the complex solid model. For example, when meshing a pier model, the cylindrical surface feature on the pier cannot be directly processed by the mapping method and the sweep method, so the operator needs to divide the model near the cylindrical surface into small blocks that approximate cuboids. In addition, in some specific finite element analysis scenarios, the finite element solver has specific interface requirements for the hexahedral mesh of the solid model, and the small blocks obtained after model decomposition need to have corresponding interfaces. In summary, the manual decomposition of the hexahedral mesh of the solid model is very complex and time-consuming in practical applications, and a large amount of time is often required to obtain high-quality hexahedral meshes that meet the requirements of finite element analysis.

[0003] The existing automatic solid model decomposition techniques mainly include feature decomposition methods based on the geometry edges of the solid model and decomposition methods based on three-dimensional frame fields. However, the former cannot guarantee that the small blocks obtained after decomposition can be meshed using the sweep method or the mapping method. The latter is subject to the instability of the three-dimensional frame field technology, and cannot perform model decomposition when invalid singular structures appear in the three-dimensional frame field, or even cannot effectively decompose some simple solid models. SUMMARY

[0004] The purpose of the present application is to provide an efficient and stable model decomposition method for hexahedral mesh generation based on solid models, which is suitable for meshing.

[0005] Technical solution: To achieve the above purpose, the solid model automatic decomposition method for hexahedral mesh generation according to the present application comprises the following steps:

[0006] Step S1: input a known solid model, generate a triangular mesh containing the model surface and an internal user-defined cutting surface, and define a smooth two-dimensional frame field on the model surface;

[0007] Step S2: Based on the dihedral angle size of the feature edge, mark all the concave feature mesh edges and generate a series of feature cutting loops with the shortest possible total length passing through the concave feature mesh edges and whose tangent direction is approximately close to the direction of the two-dimensional frame field.

[0008] Step S3: For each feature cutting ring, generate a feature cutting surface with the feature cutting ring as the boundary, and merge the surface with the triangular mesh;

[0009] Step S4: Keep the existing triangular mesh unchanged, and generate a tetrahedral mesh for the solid model using the public library TetGen;

[0010] Step S5: Using the feature cutting surface and the user-defined cutting surface as internal constraint surfaces, and the surface normal of the solid model as the boundary constraint surface, establish a three-dimensional frame field defined on the mesh nodes with internal smoothness and aligned with the constraint surfaces.

[0011] Step S6: Find all singular triangles from the 3D frame field of the solid model by calculating the differences between adjacent 3D frames, and divide all singular triangles into several singular triangle groups according to the node connectivity of the singular triangles;

[0012] Step S7: Calculate the singular valence of each singular triangle group and the direction of its singular cutting ring using the Poincaré-Hopf index;

[0013] Step S8: Starting from the triangles of each singular triangle group that intersect with the cutting surface or the boundary of the solid model, generate singular cutting loops on the surface of the solid model and the cutting surface whose tangential direction is approximately close to the direction of the three-dimensional frame field.

[0014] Step S9: For each singular cut ring, generate a singular cut surface with the singular cut ring as its boundary;

[0015] Step S10: Decompose the model based on singular cutting surfaces, feature cutting surfaces, and user-defined cutting surfaces.

[0016] In step S1, generating a triangular mesh containing a custom cut surface on the model surface and an internal surface, as well as a smooth two-dimensional frame field defined on the model surface, refers to generating a triangular mesh containing a custom cut surface on the model surface and an internal surface, as well as a smooth two-dimensional frame field defined on the model surface, using the public library Libigl.

[0017] The triangular mesh of the solid model has mesh edges corresponding to the geometric edges of the solid model. These mesh edges are marked as feature edges. When a 2D frame generated by the public library Libigl is near a feature edge, one direction of the 2D frame must be parallel to the feature edge.

[0018] Specifically, step S2, which involves marking all concave feature mesh edges based on the dihedral angle of the feature edge, is as follows: a smooth two-dimensional frame field is composed of two-dimensional frames defined in each triangular facet on the surface of the solid model. When a two-dimensional frame and a feature edge are adjacent, a certain direction of the two-dimensional frame is parallel to the feature edge. The detection method for concave feature edges is to determine whether its dihedral angle is less than 120°.

[0019] Specifically, step S3, which involves generating a feature cutting surface with the feature cutting loop as its boundary, includes the following sub-steps:

[0020] Step S301: For each feature cutting ring, the cross product vector of the coordinates of all nodes on the ring and the node normals with the mesh edge vectors is used as input information. The surface equation of the feature cutting surface is generated by the Hermit radial basis function method. Then, the cross product vector is changed to the node normals to generate the surface equation of the wrapping surface that wraps the feature cutting surface.

[0021] Step S302: Arrange the nodes on the feature cutting surface using the Marching Tetrahedra algorithm, and then use the Winding number algorithm and the corresponding wrapping surface equation to remove nodes that fall outside the feature cutting loop or outside the solid model. Record the nodes that meet the requirements as the node set V. inner ;

[0022] Step S303: Construct a triangular mesh for the feature-cut surface using the wavefront method.

[0023] Specifically, step S303, which involves constructing a triangular mesh for the feature-cut surface using the wavefront method, includes the following sub-steps:

[0024] Step S3031: Find the possible intersections between the feature-cut surface and the solid model, excluding the feature-cut ring, by using the surface equations of the feature-cut surface and the wrapping surface, and obtain the mesh edges of the potential intersections by using the mesh edge segmentation operation of the triangular mesh.

[0025] Step S3032: Use all mesh edges of the feature cutting loop and the potential intersection as the set of advancing edges E. s For E s A grid edge e in V inner and E s Find the node closest to it among the nodes and construct a triangular patch to form a triangular mesh of the feature cutting surface;

[0026] Step S3033: After constructing each triangle, update E. s and V inner And add the newly added mesh edges to E sRepeat the above steps until E s Given an empty set, construct the feature-cutting surface triangular mesh.

[0027] Specifically, step S5, which involves constructing a smooth, aligned 3D model frame field with internally smooth surfaces and user-defined cutting surfaces as internal constraint surfaces and solid model surface normals as boundary constraint surfaces, includes the following sub-steps:

[0028] Step S501: Place a 3D frame on each node of the tetrahedral mesh of the solid model;

[0029] Step S502: For a solid model tetrahedral mesh node constrained only by a boundary constraint surface or a single internal constraint surface, a certain direction of its 3D frame needs to be aligned with the surface normal or the node external normal.

[0030] Step S503: For a mesh node that is simultaneously constrained by two or more constraint surfaces, it is necessary to find the two most orthogonal constraint directions from these constraints so that the 3D frame of the node is as close as possible to these two constraint directions.

[0031] Step S504: Minimize the value of the following formula using the L-BFGS algorithm from the public library ALGLIB to obtain an internally smooth, constraint-face-aligned 3D frame field.

[0032]

[0033] Where E is the set of all mesh edges of the tetrahedral mesh of the solid model, ij is a mesh edge in E consisting of nodes i and j, and F i Let i be the three-dimensional frame of node i.

[0034] Specifically, step S6 involves finding all singular triangles by calculating the differences between adjacent 3D frames. This process involves determining whether each triangular facet in the tetrahedral mesh of the solid model is a singular triangle by checking whether the sum of the differences between the 3D frames of the three nodes on the facet constitutes a rotation of more than 90°.

[0035] Specifically, step S9, which involves constructing a singular cut surface using a singular cut ring, means that the singular cut ring is limited to the coarse block surface of the solid model to which the singular triangle group belongs after being decomposed by the feature cut surface and the custom cut surface, and the advancing edge required to generate the singular cut surface only contains the singular cut ring.

[0036] Beneficial effects: The present invention has the following advantages:

[0037] 1. Compared with feature-based model decomposition algorithm, the application has the advantage of ensuring that the small pieces of the decomposed entity model can be used for hexahedral mesh partitioning by sweep method or mapping method.

[0038] 2. Compared with three-dimensional frame field-based decomposition algorithm, the application repairs the invalid 3-5 singular structure that may occur in the previous three-dimensional frame field generation process through feature cutting surface and user-defined cutting surface, and does not need to repair local invalid singular triangle, so that the quality of the final three-dimensional frame field is higher, and therefore some complex entity models can be successfully decomposed.

[0039] 3. The application is based on model features and three-dimensional frame field, realizes high-quality automatic decomposition of entity models, and the small pieces of the final entity model can be easily obtained by the mature sweep method and mapping method to obtain the hexahedral mesh of the entity model; the application can accelerate the hexahedral mesh partitioning speed of the entity model in the finite element simulation process, greatly improve the finite element simulation efficiency, and eliminate the tedious and extremely experience-dependent manual decomposition process of the entity model, for example, after the gate pier model is decomposed by the method proposed in the application, a series of small pieces that can be used for sweep method and mapping method are obtained, which greatly reduces the workload of manual decomposition of the entity model in the past and accelerates the finite element simulation efficiency of the gate pier model. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 is the work flow chart of the application;

[0041] Figure 2 is the decomposition process chart without user-defined cutting surface in the case of gate pier model as an embodiment;

[0042] Figure 3 is the decomposition process chart with user-defined cutting surface in the case of gate pier model as an embodiment;

[0043] Figure 4 is the schematic diagram of constructing cutting surface by cutting change in the application;

[0044] Figure 5 is the schematic diagram of generating three-dimensional frame field in the case of gate pier model as an embodiment;

[0045] Figure 6 is the hexahedral mesh schematic diagram of the model in the case of inputting user-defined cutting surface in the embodiment 1 of gate pier model;

[0046] Figure 7 is the hexahedral mesh schematic diagram of the model in the case of not inputting user-defined cutting surface in the embodiment 1 of gate pier model;

[0047] Figure 8Taking the spillway section model as Example 2, here is a schematic diagram of the hexahedral mesh of the model under the condition that a user-defined cutting surface is input to represent the layered casting of the spillway section structure;

[0048] Figure 9 Taking the pump station outlet model as an example, here is a schematic diagram of the hexahedral mesh of the model without inputting a user-defined cutting surface. Detailed Implementation

[0049] The technical solution of the present invention will be described in detail below with reference to the embodiments and accompanying drawings.

[0050] Example 1, such as Figure 1 As shown, the automatic decomposition method for solid models used in hexahedral mesh generation described in this invention supports users inputting custom cutting surfaces while inputting the solid model. Taking the gate pier model in Example 1 as an example, as... Figure 2 and Figure 3 The figures show the block structures obtained by this invention for gate pier models with and without user-defined cutting surfaces, respectively. The specific steps include:

[0051] Step S1: The input gate pier model is used to create a triangular mesh on the surface and inside of the gate pier model using the triangular mesh generation algorithm in the public library Libigl. A smooth two-dimensional frame field defined on the model surface is generated using the two-dimensional frame field generation algorithm in the public library Libigl, and the feature edges in the triangular mesh corresponding to the geometric edges of the gate pier model are marked.

[0052] The triangular mesh of the gate pier model has mesh edges corresponding to the geometric edges of the gate pier model. These mesh edges are marked as feature edges. When the two-dimensional frame generated by the public library Libigl is near the feature edges, one direction of the two-dimensional frame needs to be parallel to the feature edges.

[0053] Step S2: The smooth two-dimensional frame field is composed of two-dimensional frames in each triangular facet defined on the surface of the gate pier model. When the two-dimensional frame and the feature edge are adjacent, a certain direction of the two-dimensional frame is parallel to the feature edge. The detection method of the concave feature edge is to determine whether its dihedral angle is less than 120°.

[0054] Based on the size of the dihedral angle of the feature edge, all concave feature mesh edges are marked, and a series of feature cutting loops with the shortest possible total length passing through the concave feature mesh edges and whose tangent direction is approximately close to the direction of the two-dimensional frame field are generated.

[0055] Step S3: For each feature cutting ring, generate a feature cutting surface with the feature cutting ring as the boundary, and merge the surface with the triangular mesh; specifically including the following sub-steps:

[0056] Step S301: For each feature cutting ring, the coordinates of all nodes on the ring and the cross product vector of the node normal and the mesh edge vector are taken as input information, and the surface equation of the feature cutting surface is generated by the Hermite radial basis function method, and then the cross product vector is changed to the node normal to generate the surface equation of the wrapping surface wrapping the feature cutting surface;

[0057] Step S302: As shown in Figure 4 , for the surface equation of each feature cutting surface, first arrange the nodes located on the feature cutting surface by the Marching Tetrahedra algorithm, and then remove the nodes falling outside the feature cutting ring or the pier model by the Winding number algorithm and the corresponding wrapping surface equation, and the nodes meeting the requirements are recorded as the node set V inner ;

[0058] Step S303: Construct a triangular mesh of the feature cutting surface by the wave front method.

[0059] The triangular mesh of the feature cutting surface by the wave front method in step S303 specifically includes the following sub-steps:

[0060] Step S3031: Find the possible intersection part of the feature cutting surface and the pier model except the feature cutting ring by the surface equation of the feature cutting surface and the surface equation of the wrapping surface, and obtain the mesh edge of the potential intersection part by the mesh edge division operation of the triangular mesh;

[0061] Step S3032: Take the feature cutting ring and all mesh edges of the potential intersection part as the set of advancing edges E s , and for a mesh edge e in E s , find the closest node from the nodes in V inner and E s , and construct a triangular patch to form the triangular mesh of the feature cutting surface;

[0062] Step S3033: After constructing a triangle, update E s and V inner , and add the newly added mesh edge to E s , repeat the above steps until E s is empty, and complete the construction of the triangular mesh of the feature cutting surface.

[0063] Step S4: Keep the existing triangular mesh unchanged, and generate a tetrahedral mesh of the pier model by the public library TetGen;

[0064] Step S5: As shown in Figure 5As shown, the internal smoothness is defined on the grid nodes, and the three-dimensional frame field is aligned with the constraint surface, with the feature cutting surface and the user-defined cutting surface as the internal constraint surface, and the surface normal of the pier model as the boundary constraint surface. The specific steps include the following sub-steps:

[0065] Step S501: Place a three-dimensional frame on each node of the tetrahedral grid of the pier model;

[0066] Step S502: For the tetrahedral grid nodes of the entity model which are only constrained by the boundary constraint surface or a single internal constraint surface, a certain direction of the three-dimensional frame needs to be aligned with the surface normal or the external normal of the node;

[0067] Step S503: For the grid nodes which are simultaneously constrained by two or more constraint surfaces, two most orthogonal constraint directions are found from the constraints, so that the three-dimensional frame of the node is as close as possible to the two constraint directions;

[0068] Step S504: The value of the following formula is minimized by the L-BFGS algorithm in the public library ALGLIB to obtain the three-dimensional frame field which is aligned with the internal smoothness and the constraint surface,

[0069]

[0070] Where E is a set of all grid edges of the tetrahedral grid of the pier model, ij is a grid edge composed of node i and node j in E, F i is the three-dimensional frame of node i.

[0071] Step S6: Find all singular triangles from the three-dimensional frame field of the pier model by calculating the difference between adjacent three-dimensional frames, and divide all singular triangles into several singular triangle groups according to the node connectivity of the singular triangles; Specifically, for each triangular patch in the tetrahedral grid of the pier model, whether the sum of the differences between the three-dimensional frames of the three nodes on the patch constitutes a rotation of more than 90° is judged to determine whether the triangle is a singular triangle.

[0072] Step S7: Calculate the singular valence and the advancing direction of the singular cutting ring of each singular triangle group by the Poincare-Hopf index;

[0073] Step S8: Starting from the triangle of each singular triangle group which intersects with the cutting surface or the boundary of the pier model, generate singular cutting rings on the surface of the pier model and the cutting surface, whose tangential direction is approximately close to the direction of the three-dimensional frame field;

[0074] Step S9: generating a singular cutting surface for each singular cutting loop, wherein the singular cutting surface is constructed by the singular cutting loop, and the singular cutting loop is limited to the rough block surface of the pier model decomposed by the feature cutting surface and the user-defined cutting surface, and the pushing edge required for generating the singular cutting surface only contains the singular cutting loop.

[0075] The singular cutting loop advances on the triangular patch in a straight line, and when it contacts a certain mesh edge, the next advancing direction is obtained by equally dividing the vector in the three-dimensional frame of the next triangle that is closest to the last advancing direction. The above operation is repeated until the singular cutting loop is generated.

[0076] For each singular cutting loop, the singular cutting surface is generated in a similar manner to the construction of the feature cutting surface, and the only difference is that the pushing edge required for generating the singular cutting surface only contains the singular cutting loop and does not contain other intersecting parts.

[0077] Step S10: completing the decomposition of the model based on the singular cutting surface, the feature cutting surface, and the user-defined cutting surface.

[0078] In the two cases of whether the pier model is decomposed by the user-defined cutting surface, the hexahedral meshes obtained by the mapping method from the two final block structures are shown in Figure 6 and Figure 7 . Figure 6 is the hexahedral mesh corresponding to the block structure obtained by the method of the present application for the case of the pier model with the user-defined cutting surface, Figure 7 is the hexahedral mesh corresponding to the block structure obtained by the method of the present application for the case of the pier model without the user-defined cutting surface. In Figure 2 and Figure 3 , the feature cutting surface obtained by the method of the present application is consistent regardless of whether the pier model is affected by the user-defined cutting surface. However, the three-dimensional frame field of the pier model affected by the user-defined cutting surface will change, so the singular cutting surface obtained by the method of the present application is different from the original case.

[0079] In Example 2, as shown in Figure 8 , the hexahedral meshes of different gray levels represent different pouring layers of the spillway section during the construction process. The interfaces between these pouring layers are represented by the input user-defined cutting surface, so the user-defined cutting surface supported by the present method can also enable the user to create hexahedral meshes that meet various self needs. Similarly, in Example 3, as shown in Figure 9As shown, the hexahedral mesh of different gray levels represents the different pouring layers of the outlet structure of the pump station during the construction process. However, the interfaces between the pouring layers are not represented by the input user-defined cutting surfaces, but are composed of the feature cutting surfaces of the model. Therefore, in the implementation process of the model, the feature cutting surfaces generated by the method can also replace part of the user-defined cutting surfaces that need to be manually defined and input by the user, and the finally generated hexahedral mesh can meet the requirements of the pouring layer interface in the finite element simulation process.

[0080] The method realizes the feature decomposition of the model through the feature cutting surfaces and the user-defined cutting surfaces, meets the application requirement of decomposing the solid model into small blocks that are easy to be hexahedral meshed, and generates the internal constraints in the three-dimensional frame field generation process based on the two types of surfaces, so that the quality of the final three-dimensional frame field is better, the generation process is more stable, the singular structure is more correct, part of the wrong 3-5 singular structure can be repaired, the repair step for the wrong singular triangle is avoided, and the block structure obtained finally has no internal singular structure, and each small block can obtain high-quality hexahedral mesh through the mapping method or the sweeping method. The application can no longer rely on the grid division experience, speeds up the grid division speed, reduces the labor cost, and improves the finite element simulation efficiency. In addition, the application supports the user-defined cutting surface, so that the output hexahedral mesh can meet various requirements of the user on the hexahedral mesh.

Claims

1. A method for automatic decomposition of solid models for hexahedral mesh generation, characterized in that: The method comprises the following steps: Step S1: input a known entity model, generate a triangular mesh containing model surface and internal custom cutting surface, and generate a smooth two-dimensional frame field defined on the model surface, which means generating a triangular mesh containing model surface and internal custom cutting surface and generating a smooth two-dimensional frame field defined on the model surface by using a public library Libigl; the triangular mesh of the entity model has mesh edges corresponding to the geometric edges of the entity model, and these mesh edges are marked as feature edges; when the two-dimensional frame generated by the public library Libigl is near the feature edge, a certain direction of the two-dimensional frame needs to be parallel to the feature edge; the entity model is a pier model or an overflow dam section model, and when the entity model is an overflow dam section model, the hexahedral mesh represents the pouring layer of the overflow dam section in the construction process; Step S2: based on the size of the feature edge dihedral angle, mark all the concave feature mesh edges, and generate a series of feature cutting rings that pass through the concave feature mesh edges, have the shortest total length as possible, and have a tangent direction close to the direction of the two-dimensional frame field; Step S3: for each feature cutting ring, generate a feature cutting surface with the feature cutting ring as the boundary, and combine the surface with the triangular mesh; Step S4: keep the existing triangular mesh unchanged, and generate a tetrahedral mesh of the entity model by using a public library TetGen; Step S5: take the feature cutting surface and the user-defined cutting surface as internal constraint surfaces, and take the normal of the entity model surface as a boundary constraint surface, to establish an internal smooth defined on the grid nodes, and align the three-dimensional frame field with the constraint surface; Step S6: find all singular triangles from the entity model three-dimensional frame field by calculating the difference between adjacent three-dimensional frames, and divide all the singular triangles into several singular triangle groups according to the node connectivity of the singular triangles; Step S7: calculate the singular valence and the advancing direction of the singular cutting ring of each singular triangle group by using the Poincare-Hopf index; Step S8: start from the triangle of each singular triangle group that intersects with the cutting surface or the boundary of the entity model, and generate a singular cutting ring on the surface of the entity model and the cutting surface, which has a tangent direction close to the direction of the three-dimensional frame field; Step S9: for each singular cutting ring, generate a singular cutting surface with the singular cutting ring as the boundary; Step S10: complete the decomposition of the model based on the singular cutting surface, the feature cutting surface and the user-defined cutting surface.

2. The method for automatic decomposition of solid models for hexagonal mesh generation according to claim 1, wherein: In step S2, the concave feature mesh edges are marked based on the size of the feature edge dihedral angle, and specifically, the smooth two-dimensional frame field is composed of two-dimensional frames defined on each triangular patch of the entity model surface; when the two-dimensional frame is adjacent to the feature edge, a certain direction of the two-dimensional frame is parallel to the feature edge; the concave feature edge is detected by judging whether the dihedral angle is less than 120°.

3. The method for automatic decomposition of solid models for hexagonal mesh generation according to claim 1, wherein: In step S3, the feature cutting surface with the feature cutting ring as the boundary is generated, which specifically includes the following substeps: Step S301: For each feature cutting ring, the coordinates of all nodes on the ring and the cross product vectors of the node normals and the mesh edge vectors are taken as input information, the surface equation of the feature cutting surface is generated by the Hermite Radial Basis Function method, and then the cross product vectors are changed to node normals to generate the surface equation of the wrapping surface wrapping the feature cutting surface; Step S302: arranging nodes on the feature cutting surface by the Marching Tetrahedra algorithm, and then removing nodes outside the feature cutting ring or the solid model by the Winding number algorithm and the corresponding wrapping surface equation, and the nodes meeting the requirements are recorded as a node set ; Step S303: Construct a triangular mesh of the feature cutting surface by the wave front method.

4. The method for automatic decomposition of solid models for hexagonal mesh generation according to claim 3, wherein: The triangular mesh of the feature cutting surface constructed by the wave front method in step S303 specifically includes the following sub-steps: Step S3031: Find the possible intersection part of the feature cutting surface and the entity model except for the feature cutting ring through the surface equation of the feature cutting surface and the surface equation of the wrapping surface, and obtain the mesh edges of the potential intersection part through the mesh edge segmentation operation of the triangular mesh; Step S3032: take all mesh edges of feature cutting loop and potential intersection part as the set of advancing edges For each mesh edge in the set of advancing edges , find the closest node from the nodes of the feature cutting loop and the potential intersection part, and construct a triangular patch, consisting of the triangular mesh of the feature cutting surface. and , find the closest node from the nodes of the feature cutting loop and the potential intersection part, and construct a triangular patch, consisting of the triangular mesh of the feature cutting surface. Step S3033: After constructing one triangle, update and and add the new grid edge to Repeat the above steps until is empty, and complete the construction of the feature cut surface triangle grid.

5. The method for automatic decomposition of solid models for hexagonal mesh generation according to claim 1, wherein: Step S5: Take the feature cutting surface and the user-defined cutting surface as internal constraint surfaces, and take the entity model surface normal as a boundary constraint surface to construct a model three-dimensional frame field with internal smoothness and constraint surface alignment, which specifically includes the following sub-steps: Step S501: Place a three-dimensional frame on each node of the entity model tetrahedral mesh; Step S502: For the entity model tetrahedral mesh nodes constrained only by the boundary constraint surface or a single internal constraint surface, a certain direction of the three-dimensional frame of the node needs to be aligned with the surface normal or the node outer normal; Step S503: For mesh nodes constrained by two or more constraint surfaces, find two most orthogonal constraint directions from these constraints, so that the three-dimensional frame of the node is as close as possible to these two constraint directions; Step S504: Minimize the value of the following formula through the L-BFGS algorithm in the public library ALGLIB to obtain an internal smoothness and constraint surface alignment three-dimensional frame field, ， wherein, is a set of all grid edges of the tetrahedral mesh of the solid model, is a set of all nodes of the tetrahedral mesh of the solid model, is a grid edge of the tetrahedral mesh of the solid model, consisting of a node and a node is a three-dimensional frame of reference of the node .

6. The method for automatic decomposition of solid models for hexagonal mesh generation according to claim 1, wherein: Step S6: Find all singular triangles by calculating the difference between adjacent three-dimensional frames, which is specifically: for each triangular patch in the entity model tetrahedral mesh, judge whether the triangular patch is a singular triangle by whether the sum of the differences between the three-dimensional frames of the three nodes on the patch constitutes a rotation of more than 90°.

7. The method for automatic decomposition of solid models for hexagonal mesh generation according to claim 1, wherein: Step S9: Construct a singular cutting surface through a singular cutting ring, which is specifically: the singular cutting ring is limited to the rough block surface of the entity model to which the singular triangle group belongs after the entity model is decomposed by the feature cutting surface and the user-defined cutting surface, and the push edges required to generate the singular cutting surface only contain the singular cutting ring.

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