Complex mesh cutting method and apparatus based on an autonomous clipping algorithm

Abstract

The application provides a complex mesh cutting method based on an autonomous cutting algorithm, comprising the following steps: preprocessing a cutting mesh and a mesh body to be cut; performing collision detection on the preprocessed cutting mesh and the mesh body to be cut; performing intersection operation on intersecting triangles based on the detection result to obtain intersection lines; embedding the obtained intersection lines into the cutting mesh and the mesh body to be cut respectively; topologically separating the mesh body to be cut based on the intersection lines, and marking the part in the positive direction of the cutting mesh as a first sub-mesh; topologically separating the cutting mesh based on the intersection lines, and marking the part inside the mesh body to be cut as a second sub-mesh; and sewing the first sub-mesh and the second sub-mesh as a final cut sub-mesh body. The application solves the problem of low success rate of complex mesh Boolean operation.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of engineering digital modeling technology, and particularly relates to a complex mesh cutting method and device based on an autonomous shearing algorithm. BACKGROUND

[0002] A mesh model is an important three-dimensional shape representation method, in which a triangular mesh is most widely used. The mesh model can represent any complex surface and spatial shape with arbitrary precision. In the mesh model, the number of edges of each patch can vary, and the mesh model is referred to as a triangular mesh when each patch of the mesh model is a triangle. A non-triangular mesh can be converted into a triangular mesh by triangulation of each convex polygon patch in the mesh model.

[0003] In three-dimensional geological modeling research, a geological model is usually expressed by a boundary expression method to express a geological interface or a geological entity. The geological interface is generally composed of a single geometric surface, and the geological entity is composed of multiple geometric surfaces. In the modeling process, it is inevitable to cut the surfaces, and therefore a surface cutting algorithm is a key algorithm for implementing three-dimensional geological modeling and model analysis. The surface cutting algorithm has always been a research hotspot in the fields of computer graphics and computer-aided design. Generally, the surface cutting algorithm can be divided into two categories according to the type of the cut surface: one category is parameter surface cutting. Parameter surfaces have good mathematical properties, are easy to control and edit, and are widely used in engineering design fields, such as NURBS surfaces and subdivision surfaces. The other category is polygon surface cutting. Polygon surfaces are usually divided into polygons according to a set of discrete points. Since the polygon surfaces are represented by discrete irregular polygons for approximate approximation, cutting on the polygon surfaces is very complex. This method is suitable for three-dimensional visualization and analysis calculation in the engineering field, such as irregular triangular mesh and finite element mesh.

[0004] In the field of three-dimensional geology, since the geological interface is infinitely complex and is not suitable for being expressed by a parameter surface, most geological models use polygon surfaces, and the irregular triangular mesh is most widely used. Therefore, the research on the cutting algorithm of the irregular triangular mesh is particularly important.

[0005] According to the type of the cutting element, the cutting of the irregular triangular mesh can be divided into face / face cutting and line / face cutting. Compared with the mature face / face cutting algorithm, the complexity of the spatial curve makes it impossible to implement the arbitrary curve cutting surface algorithm, resulting in that the research on the line / face cutting algorithm of the irregular triangular mesh is not mature, and the computer interaction is mainly used to generate a reasonable cutting line to cut the model surface. In geological modeling, there are a large number of cutting problems of geological curves and geological surfaces. In this regard, the existing technology embeds the contour line into the face mesh by using the idea of embedding the constraint edge in the Delaunay triangular mesh division, and then cuts the face mesh. However, the contour line has special requirements, and the face mesh will be deformed after cutting.

[0006] In addition, when processing complex meshes (especially polygonal meshes with a large number of vertices), the success rate of mesh Boolean operation cutting will decrease significantly. This is mainly reflected in three aspects: first, the mesh model (compared with traditional NURBS surface or solid) itself is more prone to problems such as non-manifold geometry, holes, self-intersection, and inconsistent normals, increasing the difficulty of Boolean operation; second, the conventional algorithm is not fault-tolerant enough to edge cases such as coplanar and tangent contact, and is prone to failure when processing complex meshes; especially when the number of mesh vertices is large, the precision error of floating-point calculation will accumulate, causing key judgment errors (such as misjudging the state of surface intersection) or generating extremely small invalid geometric fragments during cutting, ultimately leading to operation failure. SUMMARY

[0007] Based on the above background, the present application provides a complex mesh cutting method based on an autonomous cutting algorithm to solve the problem of low success rate of complex mesh Boolean operation. Specifically, the following technical solutions are adopted:

[0008] The first aspect of the present application provides a complex mesh cutting method based on an autonomous cutting algorithm, comprising the following steps:

[0009] Pretreating the cutting mesh and the mesh to be cut;

[0010] Performing collision detection on the pretreated cutting mesh and the mesh to be cut;

[0011] Performing intersection operation on the intersecting triangles based on the detection result to obtain the intersection line;

[0012] Embedding the obtained intersection line into the cutting mesh and the mesh to be cut, respectively;

[0013] Topologically separating the mesh to be cut based on the intersection line, and recording the part located in the positive direction of the cutting mesh as the first sub-mesh;

[0014] Topologically separating the cutting network based on the intersection line, and recording the part located inside the mesh to be cut as the second sub-mesh;

[0015] Stitching the first sub-mesh and the second sub-mesh as the final cut sub-mesh.

[0016] Further, the pretreatment of the cutting mesh and the mesh to be cut at least includes triangulation processing, and removing duplicate vertices and / or repairing non-manifold geometry.

[0017] Further, the collision detection on the pretreated cutting mesh and the mesh to be cut comprises:

[0018] Calculate whether the bounding box of any triangle in the cutting grid and any triangle in the grid body to be cut intersects or not;

[0019] If the two triangles intersect, proceed to the next step to find the intersection, if not, do not perform the intersection calculation.

[0020] Further, the intersection operation of the intersection triangle based on the detection result includes:

[0021] Find the intersection of the three edges of the first triangle with the second triangle, and then find the intersection of the three edges of the second triangle with the first triangle to obtain the intersection point set;

[0022] If there is only one intersection point in the intersection point set, it is determined that there is no intersection line segment;

[0023] If there are only two intersection points in the intersection point set and the two intersection points do not coincide, it is determined that the line connecting the two intersection points is the intersection line segment;

[0024] If there are more than two intersection points in the intersection point set, remove the duplicate intersection points, if there are only two intersection points after removing the duplicate intersection points, it is determined that the line connecting the two intersection points is the intersection line segment; if there are still more than two intersection points after removing the duplicate intersection points, it is determined that there is no intersection line segment;

[0025] All intersection line segments obtained are removed, and the remaining intersection line segments after removal are connected head to tail to form the intersection line.

[0026] Further, the embedding of the obtained intersection line into the cutting grid and the grid body to be cut includes:

[0027] Determine which triangle face in the grid body to be cut each intersection point on the intersection line is located on;

[0028] Perform constrained Delaunay triangulation on the triangle face containing the intersection point by unit of valid triangle, wherein the valid triangle contains the intersection point and the intersection line segment constraint;

[0029] Determine whether all intersection line segments on the intersection line have been embedded, if not, embed the unembedded intersection line segment into the grid body to be cut until all intersection line segments have been embedded.

[0030] Further, the topological separation of the grid body to be cut based on the intersection line includes:

[0031] Divide the grid body to be cut into two or more sub-triangle grids based on the intersection line;

[0032] The set of sub-triangle grids located in the positive direction of the cutting grid is taken as the result of the Boolean intersection, and the set of sub-triangle grids located in the negative direction of the cutting grid is taken as the result of the Boolean subtraction;

[0033] triangulation reconstruction is performed on the set of sub-triangle meshes obtained by Boolean intersection, as a first sub-mesh.

[0034] Further, the stitching of the first sub-mesh and the second sub-mesh comprises:

[0035] all the mesh nodes and triangular facets in the second sub-mesh are added to the first sub-mesh, with the first sub-mesh as the stitched object;

[0036] repeated mesh nodes after addition are removed, and the normals of all the triangular facets are adjusted to be uniform, from inside to outside;

[0037] the final sub-mesh after cutting is re-constructed based on the mesh nodes after removal of repetition and the triangular facets after adjustment of the normal direction.

[0038] The second aspect of the present application provides a computer device, comprising a memory and a processor, the memory stores computer instructions, and the processor executes the computer instructions to perform the complex mesh cutting method according to the first aspect.

[0039] The third aspect of the present application provides a computer readable storage medium, which stores computer instructions, and the computer instructions are executed by a computer to perform the complex mesh cutting method according to the first aspect.

[0040] The present application has the following beneficial effects:

[0041] The complex mesh cutting method based on the autonomous cutting algorithm of the present application significantly improves the success rate and stability of complex mesh Boolean operation based on the innovative pre-processing, collision detection, intersection line calculation, intersection line embedding, bidirectional topological separation and sub-mesh stitching process, effectively solving the industry core pain point of low success rate of complex mesh Boolean operation. By using the method of the present application, the designer's rework and manual repair time can be greatly reduced, the work efficiency and model quality can be improved, and reliable basic tool support is provided for three-dimensional digital design, which has significant engineering practical value and broad industrial application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 The figure is a flowchart of the embodiment of the complex mesh cutting method of the present application.

[0043] Figure 2 The figure is a schematic diagram of the relationship between two triangles in space.

[0044] Figure 3 The figure is a schematic diagram of the division of the mesh body to be cut into multiple sub-triangle meshes in the embodiment of the present application.

[0045] Figure 4An example schematic diagram of cutting a terrain mesh using the method of the present application. DETAILED DESCRIPTION

[0046] Embodiments of the present application will be described in more detail with reference to the drawings. While several embodiments of the application are shown in the drawings, it is understood that the application can be embodied in various forms and should not be interpreted in a limited sense. On the contrary, these embodiments are provided so that this disclosure will be thorough and complete and will fully convey the scope of the application to those skilled in the art. It should be understood that the drawings and detailed description are not intended to limit the scope of the present application.

[0047] Referring to Figure 1 , the first embodiment of the present application provides a complex mesh cutting method based on an autonomous clipping algorithm, comprising the following steps:

[0048] S1, preprocessing the cutting mesh and the mesh to be cut.

[0049] As a preferred embodiment, in this embodiment, the preprocessing of the cutting mesh and the mesh to be cut at least includes triangulation processing, and removing duplicate vertices and / or repairing non-manifold geometry.

[0050] S2, collision detection is performed on the preprocessed cutting mesh and the mesh to be cut.

[0051] The purpose of collision detection is to quickly determine which triangles in the cutting mesh and the mesh to be cut intersect, without accurately calculating the coordinate position of the intersection point, so as to reduce the complexity of subsequent calculation.

[0052] Referring to Figure 2 , the relationship between two triangles in space is usually one of four cases:

[0053] 1) intersecting, as shown in (a) of Figure 2 , the common part is a straight line segment; at this time, the planes of the two triangles intersect.

[0054] 2) overlapping, the common part is a plane area, as shown in (b) of Figure 2 , at this time the two triangles are coplanar.

[0055] 3) apart, no common part, as shown in (c) of Figure 2 , regardless of whether the planes of the two triangles intersect, are parallel or overlap, the two triangles can be apart.

[0056] 4) collision, the two triangles are in a critical state of contact, including two states of common point and common boundary, as shown in (d) of Figure 2 ; it can also be regarded as a singular state of intersection or overlap.

[0057] As a preferred embodiment, in this embodiment, the collision detection is performed using the following scheme:

[0058] Calculate whether the bounding boxes of any triangle in the cutting grid and any triangle in the grid body to be cut overlap one by one;

[0059] If the two triangles overlap, proceed to the next step of intersection, if not, do not perform intersection calculation.

[0060] S3, based on the detection result, perform intersection operation on the intersecting triangles to obtain the intersection line.

[0061] The accurate intersection of intersecting triangles is reflected on a single primitive, which is to calculate the intersection point position information of the triangle and the triangle.

[0062] As a preferred embodiment, in this embodiment, the intersection operation is performed to obtain the intersection line using the following scheme:

[0063] Intersect the three edges of the first triangle with the second triangle respectively, and then intersect the three edges of the second triangle with the first triangle respectively to obtain the intersection point set;

[0064] If there is only one intersection point in the intersection point set, it is determined that there is no intersection line segment;

[0065] If there are only two intersection points in the intersection point set and the two intersection points do not overlap, it is determined that the line connecting the two intersection points is the intersection line segment;

[0066] If the intersection points in the intersection point set are more than two, remove the duplicate intersection points, if there are only two intersection points after removing the duplicate intersection points, it is determined that the line connecting the two intersection points is the intersection line segment; if there are still more than two intersection points after removing the duplicate intersection points, it is determined that there is no intersection line segment;

[0067] Perform a de-duplication operation on all the intersection line segments obtained, and connect the heads and tails of the remaining intersection line segments after de-duplication to form the intersection line.

[0068] S4, embed the obtained intersection line in the cutting grid and the grid body to be cut respectively.

[0069] The intersection line embedding is the premise of topological separation, that is, the nodes in the intersection line (i.e. the endpoints of the intersection line segments constituting the intersection line) are interpolated into the triangular mesh, and the intersection line is used as a constraint to reconstruct the triangular mesh.

[0070] As a preferred embodiment, in this embodiment, the intersection line embedding is performed using the following scheme:

[0071] Determine which triangular patch in the grid body to be cut each intersection point on the intersection line is located on one by one;

[0072] The intersection triangle patches are subjected to the constrained Delaunay triangulation one by one, with an effective triangle as a unit, wherein the effective triangle contains the intersection point and the intersection line segment constraint;

[0073] It is judged whether all intersection line segments on the intersection line have been embedded, and if not, the unembedded intersection line segment is embedded into the cutting grid body until all intersection line segments have been embedded.

[0074] For the cutting grid body A and the intersection line C, one specific implementation example of the above process is as follows:

[0075] Firstly, the indices of all nodes and triangular patches in the cutting grid body A are obtained, and all intersection points in the intersection line C are obtained, and the serial number of the intersection line segment where the intersection point is located is stored;

[0076] Then, the intersection points in the intersection line C are traversed, it is judged whether the intersection point is a new node, and the triangular index where the intersection point is located in the cutting grid body A and the vertex number where the intersection point is embedded in the cutting grid body A are recorded;

[0077] Next, the intersection line C is divided into effective triangles according to the triangular index where the intersection point is located, so that the intersection line is embedded into the effective triangle in the cutting grid body A (the effective triangle refers to the triangle in which there is a new intersection point and an intersection line segment passing through it);

[0078] Then, the effective triangle is subjected to the constrained Delaunay triangulation based on the intersection point and the intersection line segment in the effective triangle, that is, the mesh subdivision;

[0079] Finally, it is checked whether there is still an intersection line segment to be embedded in the cutting grid body A, and if so, the grid in the cutting grid body A is adjusted, until all intersection line segments participate in the network construction in the cutting grid body A.

[0080] In this embodiment, the specific implementation of the constrained Delaunay triangulation includes:

[0081] Firstly, the nodes in the intersection line are inserted into the triangle one by one, and it is ensured that the inserted nodes satisfy the planar Delaunay condition, that is, whether the new node is in the circumscribed circle of the triangle is used to judge whether the triangle is the minimum cavity triangle;

[0082] Secondly, it is judged whether the constrained intersection line segment participates in the triangle network construction, and if not, the intersection line segment is divided into left and right sub-cavities with the intersection line segment as a boundary, and the network is reconstructed.

[0083] S5, topologically separate the cutting grid body based on the intersection line, and record the part in the positive direction of the cutting grid as a first sub-grid.

[0084] As a preferred embodiment, in this embodiment, the topological separation adopts the following scheme:

[0085] Firstly, the cutting grid body is divided into two or more sub-triangle meshes by the intersection line, as shown in Figure 3 The specific implementation is as follows: starting from the first triangle, taking the edge of the triangle as the boundary, topologically searching the triangles in the remaining triangles that share the edge with the boundary, then taking the boundary edge formed by the triangles sharing the edge as the starting point of the next judgment, and not taking the edge as the boundary for topology when the intersection line is encountered, until all the triangles are divided into sub-triangle meshes.

[0086] Then, the sub-triangle mesh set located in the positive direction of the cutting grid is taken as the result of Boolean intersection, and the sub-triangle mesh set located in the negative direction of the cutting grid is taken as the result of Boolean subtraction, as shown in Figure 3 Part I and Part II in

[0087] Finally, the sub-triangle mesh set obtained by Boolean intersection is reconstructed into a triangle mesh, that is, the vertex indexes are renumbered in sequence from 1, 2, 3, …, and the triangles in the sub-triangle mesh set are renumbered according to the new vertex indexes, so as to finally generate an independent sub-triangle mesh as the first sub-mesh.

[0088] S6, topologically separating the cutting mesh based on the intersection line, and recording the part located inside the cutting grid body as the second sub-mesh.

[0089] The specific topological separation method can refer to the content in step S5, which will not be repeated here.

[0090] S7, stitching the first sub-mesh and the second sub-mesh as the final cut sub-mesh body.

[0091] As a preferred embodiment, in this embodiment, the stitching operation adopts the following scheme:

[0092] Taking the first sub-mesh as the stitched object, adding all the mesh nodes and triangular facets in the second sub-mesh to the first sub-mesh;

[0093] Removing the repeated mesh nodes after addition, and adjusting the normal direction of all triangular facets to be uniform from inside to outside;

[0094] Reconstructing the mesh based on the de-duplicated mesh nodes and the triangular facets with adjusted normal direction as the final cut sub-mesh body.

[0095] The following gives an example of cutting a terrain mesh body by using the method of the present application.

[0096] Referring to Figure 4In this example, the cutting grid body is based on the terrain surface data with an average horizontal grid spacing of 4 meters, and the terrain entity grid model is constructed by stretching vertically downward to a depth of 467.649 meters. The cutting grid is a stratigraphic interface grid with an average horizontal grid spacing of 20m, as shown in (a) and (b) of FIG. 1. Figure 4 Figure 4 The wireframe mode and the smooth mode of the original cutting grid, the cutting grid body, and the cutting grid are shown in (a), (b), and (c) of FIG. 1, respectively.

[0097] The upper surface of the terrain grid body (i.e., the original terrain surface) geometrically fits the stratigraphic interface grid, forming a "thin sheet" spatial relationship. This feature theoretically results in multiple nearly parallel complex intersection lines when intersecting, and this dense and micro-scale intersection line structure greatly increases the difficulty of the intersection algorithm. In this example, a total of 3 intersection lines are generated, of which 1 is the main intersection line on the periphery, and the other 2 are internal intersection lines generated by the local overhang of the stratigraphic interface grid beyond the original terrain surface. Through the independent shearing algorithm steps of the present application, the topological segmentation of the complex terrain grid body can be finally realized, and the volume of the sheared sub-grid body is 2184876.051m³. As shown in (c) and (d) of FIG. 1, the wireframe mode and the smooth mode of the effect of the sheared sub-grid body are shown, respectively. Figure 4 Figure 4 The wireframe mode and the smooth mode of the effect of the sheared sub-grid body are shown in (c) and (d) of FIG. 1, respectively.

[0098] The present application further provides a computer device comprising a memory and a processor, wherein the memory stores computer instructions, and the processor executes the computer instructions to perform the complex grid cutting method disclosed in the foregoing embodiments.

[0099] The present application further provides a computer readable storage medium storing computer instructions, wherein the computer instructions are executed by a computer to perform the complex grid cutting method disclosed in the foregoing embodiments.

[0100] It should be noted that the method of the embodiments of the present application can be executed by a single device, such as a computer or a server. The method of the present embodiment can also be applied to a distributed scenario, and completed by multiple devices cooperating with each other. In this distributed scenario, one of the multiple devices can only execute one or more steps of the method of the present embodiment, and the multiple devices can interact with each other to complete the method.

[0101] ​​It is noted that some embodiments have been described as processes that are depicted as a flow diagram or block diagram. Although each can describe the operations as a sequential process, many of the operations can in fact be performed in parallel or concurrently. In addition, the order of the operations can be rearranged. A process can have additional steps not included in the figure. Furthermore, embodiments of the methods can be implemented by hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When the processes are implemented in software, firmware, middleware or microcode, program code to carry out the processes can be stored in any form of a non-transitory machine-readable medium, such as storage medium. When a process is implemented in hardware, the processes can be implemented with any or a combination of the following technologies: a discrete logic circuit that has a logic for conduction of the processes; an integrated logic circuit, an application specific integrated circuit, a programmable logic device, e.g., a programmable logic array, field programmable gate array, or logic

[0102] It is intended that the embodiments of the present application cover all such modifications and alternatives within the scope of the appended claims as are within the spirit and scope of the embodiments of the present application. Accordingly, any and all modifications, variations or equivalents that fall under the terms of the claims are intended to be embraced within the scope of the present application.

Claims

1. A method for cutting complex meshes based on an autonomous shearing algorithm, characterized in that, Includes the following steps: Preprocessing is performed on the cutting mesh and the mesh volume to be cut, where the mesh volume to be cut is a terrain entity mesh model and the cutting mesh is a stratigraphic interface mesh. Collision detection is performed on the pre-processed cutting mesh and the mesh body to be cut; Based on the detection results, the intersection of the intersecting triangles is calculated to obtain the intersection line; The obtained intersection lines are embedded into the cutting mesh and the mesh body to be cut, respectively; The mesh to be cut is topologically separated based on the intersection line, and the part located in the positive direction of the cutting mesh is denoted as the first sub-mesh; The cutting mesh is topologically separated based on the intersection line, and the part located inside the mesh volume to be cut is denoted as the second sub-mesh; The first and second sub-mesh are stitched together to form the final cut sub-mesh body, including: Using the first submesh as the object to be stitched, add all the mesh nodes and triangular faces of the second submesh to the first submesh; Remove duplicate mesh nodes after addition, and adjust the normal orientation of all triangles to be uniformly from the inside out; The mesh is reconstructed based on the deduplicated mesh nodes and the triangular facets after adjusting the normal orientation, resulting in the final cut sub-mesh.

2. The complex mesh cutting method based on the autonomous shearing algorithm as described in claim 1, characterized in that, The preprocessing of the cut mesh and the mesh volume to be cut includes at least triangulation, removal of duplicate vertices and / or repair of non-manifold geometry.

3. The complex mesh cutting method based on the autonomous shearing algorithm as described in claim 2, characterized in that, The collision detection of the pre-processed cut mesh and the mesh body to be cut includes: Calculate whether the bounding boxes of any triangle in the cutting mesh and any triangle in the mesh body to be cut overlap; If the two triangles overlap, proceed to the next step of finding their intersection; otherwise, skip the intersection calculation.

4. The complex mesh cutting method based on the autonomous shearing algorithm as described in claim 3, characterized in that, The method of performing intersection calculations on intersecting triangles based on the detection results to obtain the intersection line includes: Find the intersections of the three sides of the first triangle with the second triangle, and then find the intersections of the three sides of the second triangle with the first triangle to obtain the set of intersection points; If there is only one intersection point in the set of intersection points, then it is determined that there are no intersecting line segments; If the set of intersection points contains only two intersection points and the two intersection points do not coincide, then the line connecting the two intersection points is determined to be an intersection line segment; If there are more than two intersection points in the set of intersection points, then the duplicate intersection points are removed. If there are only two intersection points after removing duplicate intersection points, then the line connecting the two intersection points is determined to be an intersection segment. If there are still more than two intersection points after removing duplicate intersection points, then there is no intersection segment. All the obtained intersection segments are deduplicated, and the remaining intersection segments are connected end to end to form an intersection line.

5. The complex mesh cutting method based on the autonomous shearing algorithm as described in claim 4, characterized in that, The step of embedding the acquired intersection lines into the cutting mesh and the mesh volume to be cut includes: Determine which triangular facet of the mesh to be cut the intersection point is located on one by one; Delaunay triangulation with constraints is performed on each triangular facet containing intersection points, using valid triangles as units. The valid triangles contain both intersection points and intersection line segment constraints. Determine whether all intersection segments on the intersection line have been embedded. If not, embed the unembedded intersection segments into the mesh body to be cut, until all intersection segments have been embedded.

6. The complex mesh cutting method based on the autonomous shearing algorithm as described in claim 5, characterized in that, The aforementioned topology separation of the mesh to be cut based on intersection lines includes: Divide the mesh to be cut into two or more sub-triangles using the intersection line as the boundary; The set of subtriangles located in the positive direction of the cutting mesh is taken as the result of Boolean intersection, and the set of subtriangles located in the opposite direction of the cutting mesh is taken as the result of Boolean subtraction; The set of sub-triangulated meshes obtained by Boolean intersection is reconstructed into a triangulated mesh and used as the first sub-mesh.

7. A computer device, characterized in that, It includes a memory and a processor, wherein the memory stores computer instructions, and the processor executes the computer instructions to perform the complex mesh cutting method as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, The storage medium stores computer instructions that are executed by a computer during runtime using the complex mesh cutting method as described in any one of claims 1-6.

Images