A post-processing method for FEA analysis results

Abstract

This invention belongs to the field of finite element post-processing technology, and particularly relates to a post-processing method for FEA analysis results. The method involves: establishing an element set for all finite element elements in each structure within the finite element structure; identifying the cross-sectional direction of the section body by mapping the 3D section body to the coordinates of the visualization information port through coordinate mapping; determining the orientation of each component facet of the 3D section body; performing inner loop processing, including template testing loop processing at each section layer during volume rendering; multi-section body editing preprocessing; volume rendering processing; and isosurface loop processing. This post-processing method for FEA analysis results is mainly used to further improve the efficiency of data preprocessing and finite element model data generation during finite element analysis, reduce the number of unnecessary data points located on positive surfaces, thereby limiting the total data volume in the finite element model post-processing process and improving post-processing efficiency.

Description

Technical Field

[0001] This invention belongs to the field of finite element post-processing technology, and particularly relates to a post-processing method for FEA analysis results. Background Technology

[0002] Post-processing of FEA analysis results mainly refers to the process of transforming key data from vertices, faces, and configurations within the finite element model into visualized 3D data based on various finite element analysis schemes and volume rendering methods. This improves data readability, allowing various spatial physical parameters, their energies, and spatiotemporal relationships to be expressed in a simple, easy-to-understand, and easily analyzable form, thus enhancing analytical and comprehension efficiency in scientific research and teaching. The design includes finite element model vertex analysis and processing, element model rendering, etc. Because different finite element analysis programs and model structures may employ different data structures and processing schemes, most finite element analysis programs can only perform post-processing analysis for specific fields, and the efficiency and accuracy of post-processing results are greatly affected by variations in the specific processing scheme. Summary of the Invention

[0003] The purpose of this invention is to provide a method for optimizing the finite element analysis process, improving the efficiency of finite element analysis data post-processing, reducing the total data volume, and reducing the consumption of computing power and storage resources during post-processing in the finite element analysis process. This method is specifically for post-processing results of FEA analysis.

[0004] To achieve the above objectives, the present invention adopts the following technical solution.

[0005] A post-processing method for FEA analysis results includes the following steps:

[0006] Step 1: Initialization process. Establish an element set for all finite element elements in each structure within the finite element structure. Define a transformation function based on the transformation function method to control the color and transparency of the finite element elements in the control set. The element set refers to a data structure table used to express the finite element solid element model. In particular, in this embodiment, the element set consists of an array representing the element name, number of element nodes, element edge table, element face table, and number of element face nodes.

[0007] Step 2: Identify the cutting direction of the section body. Map the 3D section body to the coordinates of the visualization information port through coordinate mapping; determine the orientation of each component facet of the 3D section body; perform inner loop processing. In the volume rendering process, perform template test loop processing for each cutting layer.

[0008] Step 3: Multi-section volume editing preprocessing. Multi-section volume editing is only applicable when the finite element set involves multiple sections. For the n sections involved, the pixels in the finite element set will be divided into z-divisions. n Each subset is defined by a different transformation function. These subsets are divided into two categories: Category A is located inside the section volume and is discarded during the carrier drawing process; Category B requires volume drawing operations based on the transformation function corresponding to each section volume. During the drawing process, section markers are established to mark the section processing of each vertex. If a vertex is retained after sectioning, it is marked as 1, otherwise as 0. For each unit, the unit set data structure table is queried to determine whether the vertex marker values ​​of each edge are consistent. If they are inconsistent, it means that the edge intersects with the section surface, and the intersection parameters are calculated.

[0009] Step 4, volume rendering processing, including:

[0010] 4a Node coordinate transformation specifically refers to transforming the coordinates of finite element nodes from the spatial coordinates of the finite element model to the coordinates of the visualization information port;

[0011] 4b Surface data extraction constructs a storage sequence for storing all outer surfaces, where each element stores surface information for a specific outer surface.

[0012] 4c Coincident Outer Surface Filtering: Obtain the vertex sequence of all outer surfaces. For any two surfaces, to determine whether they coincide, compare the first sequence value in the corresponding vertex sequence of the two surfaces. If they are different, they definitely do not coincide. If the first sequence value is the same, compare the second sequence value. If they are different, they definitely do not coincide. Continue to compare the third sequence value... Repeat the above steps until it is determined whether the two surfaces coincide.

[0013] 4D Active Object Processing: A multi-level object storage table structure is established, including a first-level edge storage table structure, a second-level face storage table structure, and a third-level unit storage table structure. The edge storage table structure stores the edge data of a face, and the elements in the storage table are linked lists of edge objects. Each edge in the linked list undergoes data storage twice, storing two vertex sequences of the edge object. The two vertex sequences are filled in sequentially according to their order in the vertex sequence of the finite element model. The face storage structure stores a linked list of the outer surfaces of a finite element unit. The order of each outer surface in the surface sequence of the finite element model is extracted, and the sequence number is filled into each outer surface linked list sequentially. The unit storage structure stores the unit data of the finite element model, and the elements in the storage table are finite element units.

[0014] 4e interactive object activity processing includes cells, surfaces or edges that intersect with the currently analyzed object. Specifically, it means that in each object analysis process, the elements of the object in all the next-level storage structures of the multi-level object storage table structure are analyzed, and the interactivity of the corresponding elements with the current object is determined.

[0015] 4f surface drawing: Extract the active surfaces determined in the previous step, establish an active surface data table consisting of surface number, marking information and intersection data between the surface and the cross section, and determine the drawing method through the intersection information between adjacent cross sections and active surfaces;

[0016] Step 5: Visualization and Isosurface Optimization. To improve the mixed representation of isosurfaces within the volume rendering image and optimize the interference between isosurfaces, the following method is used:

[0017] 5a. Extract vertex data of finite element model elements, establish vertex gradient direction table, and set the buffer value of depth test to the minimum value of Z-axis in finite element mechanism;

[0018] 5b. Isosurface loop processing, the loop steps include: 1. Extracting unit sectional polygon parameters; 2. Pre-drawing sectional polygons, generating isosurface pixels based on the points that pass the test, and assigning the pixel values ​​of the pixels to the template test buffer; using the vertex gradient direction table to perform lighting calculations to draw colors; 3. Using template testing to complete the volume drawing of the remaining pixels, and using the corresponding sectional polygon transformation function to determine the pixel values ​​of each pixel.

[0019] To further improve or specifically implement the aforementioned post-processing method for FEA analysis results, the direction of each component facet of the three-dimensional section body in step 2 is determined based on the following method: generating normal vectors from the inside of the three-dimensional section body outward on each component facet; calculating the dot product of each normal vector with the unit vector of the coordinate axis; if the result is positive, it indicates that the direction of the facet is axially positive, otherwise it is axially negative.

[0020] Further improvements or specific implementations of the aforementioned post-processing method for FEA analysis results include the following steps in step 2: First, clear the contents of the template test buffer and replace the depth information with the current Z-axis coordinates; during the depth test, disable color editing of the volume drawing image; perform incremental depth tests and template tests until the volume drawing parameters for all rear surfaces of the sectioned polyhedron are generated; second, under the current configuration, perform decrementing depth tests and template tests until the drawing parameters for all front surfaces of the sectioned polyhedron are generated; finally, disable the depth test, enable color editing of the volume drawing image, and perform volume drawing.

[0021] In a further improvement or specific implementation of the aforementioned post-processing method for FEA analysis results, step 5 determines the vertex gradient direction table based on the following method:

[0022] Establish a linked list of element nodes for the finite element model. The first node element of the linked list is connected to the remaining node elements through an element variable.

[0023] Establish the relationship between node data values, three-axis coordinate differences, and gradient direction: Where v m ,v n These are the data values ​​for nodes m and n, respectively, where i = x, y, z represent the three coordinate axes, and T... i Let i be the gradient value of the object along the i-axis. m i n Let m and n be the i-axis coordinates of nodes m and n, respectively.

[0024] To find the gradient of a node n in a unit node list, we establish gradient direction relationships by connecting node n to the remaining nodes in the list. The gradient is then calculated using the least squares method, as follows:

[0025]

[0026] Where i≠j and j=x,y,z represent the three coordinate axes; o represents all other nodes in the unit node linked list except node n.

[0027] In a further refinement or specific implementation of the aforementioned post-processing method for FEA analysis results, the surface information in step 4 includes: the finite element unit affiliation of the outer surface, the face sequence of the outer surface in the finite element unit, and the vertex sequence of the outer surface; the finite element unit affiliation refers to which finite element unit the outer surface belongs to; the face sequence refers to the order in which the outer surface is located within all the outer surface sequences of the finite element unit; the vertex sequence refers to a number of vertices that enclose the outer surface and whose surface positions can be determined, and these vertices are selected sequentially according to their order in the vertex sequence of the finite element model.

[0028] Further improvements or specific implementations of the aforementioned post-processing method for FEA analysis results include, in step 4f: during the surface drawing process for each element, analyzing the outer surface linked list of each finite element element; for outer surfaces completely located between two adjacent cut surfaces, directly drawing the surface; for newly added outer surfaces that do not intersect with the previous cut surface, extracting the vertex information of the outer surface. Determining the intersection point between the outer surface and the current cut surface using the active edge data, and judging its positional relationship with the current cut surface by combining the vertex information of the outer surface; drawing the area before the current cut surface, and drawing the area after the current cut surface as the outer surface to be processed by the next cut surface; establishing vertex position markers for finite element elements, the marker content being the relative positional relationship between the vertex and the cutting surface; for any two vertices of the finite element element forming an edge, judging the marker attributes of the two vertices and the cutting surface; if the marker attributes are different, it indicates that the edge intersects the cutting surface as an active edge, generating the intersection point data of the edge and the cutting surface, and generating all the intersection point data of the finite element element and the cutting surface in the order of the vertices to obtain the cutting surface polygon.

[0029] Its beneficial effects are as follows:

[0030] The post-processing method for FEA analysis results in this application is mainly used to further improve the efficiency of data preprocessing and finite element model data generation in the finite element analysis process, reduce the number of unnecessary data points on the positive surface, thereby limiting the total amount of data in the finite element model post-processing process and improving post-processing efficiency. Attached Figure Description

[0031] Figure 1 It is a method for representing the element set of tetrahedral finite element elements;

[0032] Figure 2 This is a schematic diagram illustrating the basic principles of template testing. Detailed Implementation

[0033] The present invention will be described in detail below with reference to specific embodiments.

[0034] This application relates to a post-processing method for FEA analysis results. This method is for the post-processing of basic finite element structural models based on points, edges, and surfaces. It is not limited to a specific finite element program or type of finite element model. It mainly improves the efficiency of post-processing by further optimizing the vertices, edges, surfaces, and section volumes of the finite element model, in conjunction with optimized surface sectioning, volume drawing, and other steps.

[0035] This method designs several consecutive or independent preprocessing or optimization steps. These steps can be performed independently or in conjunction with the current finite element analysis and post-processing workflow. Some of the basic concepts or contents of finite element analysis and processing involved can be obtained by consulting the relevant public algorithms or the corresponding program instructions, and will not be elaborated in this application.

[0036] The following describes the main steps of the post-processing method for FEA analysis results:

[0037] Step 1: Initialization process. Establish the element set of all finite element elements in each structure in the finite element structure; define the transformation function based on the transformation function method to control the color and transparency of the finite element elements in the control set; the element set refers to the data structure table used to express the finite element solid element model. In particular, in this embodiment, the element set is composed of arrays representing the element name, the number of element nodes, the element edge table, the element face table, and the number of element face nodes.

[0038] In this application, a separate data structure table is configured for the optimization of vertices, edges, and unit faces in subsequent processing. Similar to the multidimensional data representation of points, edges, faces, and unit bodies in traditional finite element models, the data structure table stores the index sequence of corresponding units, nodes, edges, and unit faces to facilitate the rapid establishment of their topological relationships and meet the needs of subsequent edge and face sectioning.

[0039] like Figure 1 The figure shows the element set representation method for a common tetrahedral finite element, where A, B, and C represent vertices, edges, and surfaces, respectively, and the surfaces led out by the leaders are the inner surfaces.

[0040] 2. Sectional body cutting direction identification: The 3D sectional body is mapped to the coordinates of the visualization information port through coordinate mapping; the orientation of each component facet of the 3D sectional body is determined; Inner loop processing: In the volume rendering process, template testing loop processing is performed on each cutting layer;

[0041] As a preferred method, the orientation of each component facet of the 3D section body is determined based on the following method: generating normal vectors from the inside of the 3D section body outward on each component facet; calculating the dot product of each normal vector with the unit vector of the coordinate axis; if the result is positive, it indicates that the orientation of the facet is positive axial, otherwise it is negative axial.

[0042] The template test loop process refers to the following steps: First, clear the contents of the template test buffer and replace the depth information with the current Z-axis coordinates; during the depth test, disable color editing of the volume rendering image; execute incremental depth tests and template tests until the volume rendering parameters for all rear surfaces of the sectioned polyhedron are generated; second, under the current configuration, execute decrementing depth tests and template tests until the rendering parameters for all front surfaces of the sectioned polyhedron are generated; finally, disable depth tests, enable color editing of the volume rendering image, and execute volume rendering.

[0043] 3. Multi-section volume editing preprocessing: Multi-section volume editing only applies to cases where the finite element set involves multiple sections. For the n sections involved, the pixels in the finite element set will be divided into z-divisions. n Each subset is defined by a different transformation function. These subsets are divided into two categories: Category A is located inside the section volume and is the part discarded during the carrier drawing process; Category B requires volume drawing operations for each section volume corresponding to the transformation function.

[0044] During the drawing process, a sectioning marker is established to mark the sectioning process of each vertex. If a vertex is retained after sectioning, it is marked as 1, otherwise it is marked as 0. For each cell, the cell set data structure table is queried to determine whether the vertex marker values ​​of each edge are consistent. If they are inconsistent, it means that the edge intersects with the sectioning surface, and the intersection parameters are calculated.

[0045] 4. Volume rendering process:

[0046] 4a Node coordinate transformation specifically refers to transforming the coordinates of finite element nodes from the spatial coordinates of the finite element model to the coordinates of the visualization information port;

[0047] 4b Surface data extraction constructs a storage sequence for all outer surfaces. Each element in the outer surface storage sequence stores surface information for a specific outer surface. This surface information includes: the finite element unit affiliation of the outer surface, the face sequence of the outer surface within the finite element unit, and the vertex sequence of the outer surface. The finite element unit affiliation refers to which finite element unit the outer surface belongs to. The face sequence refers to the order in which the outer surface is located within all outer surface sequences of the finite element unit. The vertex sequence refers to a number of vertices that enclose the outer surface and whose surface position can be determined, and these vertices are selected sequentially according to their order in the vertex sequence of the finite element model.

[0048] 4c Coincident Outer Surface Filtering: Obtain the vertex sequence of all outer surfaces. For any two surfaces, to determine whether they coincide, compare the first sequence value in the corresponding vertex sequence of the two surfaces. If they are different, they definitely do not coincide. If the first sequence value is the same, compare the second sequence value. If they are different, they definitely do not coincide. Continue to compare the third sequence value... Repeat the above steps until it is determined whether the two surfaces coincide.

[0049] 4D Active Object Processing: A multi-level object storage table structure is established, including a first-level edge storage table structure, a second-level face storage table structure, and a third-level unit storage table structure. The edge storage table structure stores the edge data of a face, and the elements in the storage table are linked lists of edge objects. Each edge in the linked list undergoes data storage twice, storing two vertex sequences of the edge object. The two vertex sequences are filled in sequentially according to their order in the vertex sequence of the finite element model. The face storage structure stores a linked list of the outer surfaces of a finite element unit. The order of each outer surface in the surface sequence of the finite element model is extracted, and the sequence number is filled into each outer surface linked list sequentially. The unit storage structure stores the unit data of the finite element model, and the elements in the storage table are finite element units.

[0050] 4e interactive object activity processing includes cells, surfaces or edges that intersect with the currently analyzed object. Specifically, it means that in each object analysis process, the elements of the object in all the next-level storage structures of the multi-level object storage table structure are analyzed, and the interactivity of the corresponding elements with the current object is determined.

[0051] 4f Surface Drawing: Extract the active surfaces determined in the previous step and establish an active surface data table consisting of surface number, marking information, and intersection data between the surface and the cross-section. The drawing method is determined by the intersection information between adjacent cross-sections and active surfaces. Specifically: during the surface drawing process of each element, analyze the outer surface linked list of each finite element element. For outer surfaces that are completely between two adjacent cross-sections, draw the surface directly. For newly added outer surfaces that do not intersect with the previous cross-section, extract the vertex information of the outer surface. The intersection points of the outer surface and the current cut surface are determined by the active edge data. The positional relationship between the outer surface vertex information and the current cut surface is determined. The area before the current cut surface is drawn, and the area after the current cut surface is drawn as the outer surface to be processed for the next cut surface. The vertex position markers of the finite element elements are established. The marker content is the relative positional relationship between the vertex and the cutting surface. For any two vertices of the finite element elements, the marker attributes of the two vertices and the cutting surface are determined. If the marker attributes are different, it indicates that the edge intersects the cutting surface as an active edge. The intersection point data of the edge and the cutting surface are generated. All the intersection point data of the finite element elements and the cutting surface are generated in sequence according to the vertex order to obtain the cutting surface polygon.

[0052] 5. Visualized isosurface optimization processing

[0053] Isosurfaces are a means of visualizing the three-dimensional data field of a finite element model, used to represent regions or spaces with specific values. In this application, to improve the mixed representation effect of isosurfaces within the volume rendering image and optimize the interference problem between isosurfaces, the following method is adopted:

[0054] 5a. Vertex gradient analysis: Extract vertex data of finite element model elements, establish vertex gradient direction table, and set the buffer value of depth test to the minimum value of Z-axis in finite element mechanism;

[0055] Specifically, the vertex gradient direction table is determined as follows: 1. Establish a linked list of element nodes for the finite element model, where the first node element is connected to the remaining node elements through an element variable; 2. Establish the relationship between node data values, triaxial coordinate differences, and gradient directions: Where v m ,v n These are the data values ​​for nodes m and n, respectively, where i = x, y, z represent the three coordinate axes, and T... i Let i be the gradient value of the object along the i-axis. m i n Let m and n be the i-axis coordinates of nodes m and n, respectively. 3. To solve for the gradient of a node n in the unit node list, establish gradient direction relationships by connecting node n to the remaining nodes in the unit node list, and solve for the gradient based on the least squares method. The calculation method is as follows:

[0056]

[0057] Where i≠j and j=x,y,z represent the three coordinate axes; o represents all other nodes in the unit node linked list except node n;

[0058] 5b. Isosurface iterative processing, the iterative steps include:

[0059] 1. Extract the parameters of the unit sectional polygon;

[0060] 2. Pre-draw the cross-sectional polygon, generate isosurface pixels based on the points that pass the test, and assign the pixel values ​​of the pixels to the template test buffer; use the vertex gradient direction table to perform lighting calculations to draw the color;

[0061] 3. Use template testing to complete the volume rendering of the remaining pixels, and determine the pixel value of each pixel using the corresponding section polygon transformation function. The template testing may differ depending on the graphics API or rendering mode used for different finite element models, but it is based on the same testing principle. The basic principle of template testing is as follows: Figure 2 As shown.

[0062] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the essence and scope of the technical solutions of the present invention.

Claims

1. A method for post-processing results of FEA analysis, characterized by, It comprises the following steps: Step 1, initialization processing, establishing element set of all finite element units in the finite element structure in the finite element structure; defining transformation function; element set refers to data structure table for expressing finite element entity unit model; Step 2, section body section direction identification, mapping three-dimensional section body to visualization information port coordinates through coordinate mapping; judging the direction of each component face sheet of three-dimensional section body; inner loop processing, in the process of volume rendering processing, template test loop processing is carried out in each section layer; Step 3, multi-section editing preprocessing, for the involved section, the pixels in the finite element unit set are divided into subsets, each subset is defined by a different transformation function, the subsets are divided into two categories, A category is located inside the section, which is discarded in the volume rendering process, and B category is subjected to volume rendering processing for each section corresponding to the transformation function; Step 4, volume rendering processing, comprising: 4a node coordinate conversion: converting finite element unit node coordinates from space coordinates where finite element unit model is located to visualization information port coordinates; 4b surface data extraction: constructing outer surface storage sequence, each element in outer surface storage sequence stores surface information of an outer surface; 4c coincident outer surface screening: obtaining vertex sequence of all outer surfaces, comparing first sequence value in corresponding vertex sequence of any two surfaces, if different, it must not coincide; if same, comparing next sequence value, repeating the above steps until determining whether two surfaces coincide; 4d active object processing: establishing multi-level object storage table structure, including first-level edge storage table structure, second-level surface storage table structure and third-level unit storage table structure; edge storage table structure stores edge data of a section; surface storage table structure stores active surface data of a finite element unit; unit table storage structure stores unit data of finite element model; 4f surface rendering: extracting active surface determined in step 4d, establishing active surface data table composed of surface serial number, mark information and intersection data of the surface and section, determining rendering method through intersection information of adjacent section and active surface; Step 5, visualization isosurface optimization processing, which is processed in the following way: 5a, extracting finite element model unit vertex data, establishing vertex gradient direction table, setting depth test buffer value as minimum value of Z axis in finite element structure; In the vertex gradient direction table, the gradient of the node is established in the gradient direction relationship with the other nodes in the unit node linked list, and the least square method is used for solving; 5b, isosurface loop processing, the loop steps include: 1, extracting unit section polygon parameters; 2, pre-rendering section polygon, generating isosurface pixel points according to the points passing through the test, and assigning pixel values to the template test buffer; using the vertex gradient direction table to calculate the color for rendering; 3, using template test to complete the volume rendering of the remaining pixel points, and using the corresponding section polygon transformation function to determine the pixel value of each pixel point.

2. The method for post-processing results of FEA analysis according to claim 1, characterized in that, The direction of each component face sheet of three-dimensional section body in step 2 is realized based on the following method: generating normal vector from inside to outside of each component face sheet of three-dimensional section body; calculating the dot product of each normal vector and unit vector of coordinate axis, if the result is positive, it indicates that the direction of the face sheet is axis positive, otherwise it is axis negative.

3. The method for post-processing results of FEA analysis according to claim 1, characterized in that, The template test loop processing in step 2 includes: firstly, clearing the content of the template test buffer, replacing the depth information with the current Z-axis coordinate; shielding the color editing processing of the volume rendering image during the execution of the depth test; executing the depth test and the template test in turn until the volume rendering parameter generation of all back surfaces of the cut polyhedron is completed; secondly, executing the depth test and the template test in turn under the current configuration until the rendering parameter generation of all front surfaces of the cut polyhedron is completed; and finally, closing the depth test, opening the color editing processing of the volume rendering image, and executing the volume rendering.

4. The method for post-processing results of FEA analysis according to claim 1, characterized in that, In step 5, the vertex gradient direction table is determined based on the following manner: The unit node linked list of the finite element model is established, and the first node element of the unit node linked list is connected with the remaining node elements through a unit edge; Establish the relationship of node data value, three-axis coordinate difference and gradient direction: ; to solve the gradient of node in the node chain table of the solution unit, connect the remaining other nodes in the node chain table of the solution unit with node , respectively establish the gradient direction relationship, solve the gradient based on the least square method, and the calculation method is as follows: ; wherein are data values of the nodes , i and j respectively refer to two different coordinate axes among the three coordinate axes x, y, z, are gradient values of the axis objects, are gradient values of the axis objects, are axis coordinate values of the nodes m and n respectively; represent all other nodes in the unit node linked list except the node .

5. The method for post-processing results of FEA analysis according to claim 1, wherein, The surface information in step 4 includes: the finite element unit attribution of the outer surface, the face sequence of the outer surface in the finite element unit, and the vertex sequence of the outer surface; the finite element unit attribution refers to which finite element unit the outer surface belongs to; the face sequence refers to the order of the outer surface in the sequence of all outer surfaces in the finite element unit; and the vertex sequence refers to a plurality of vertices that enclose the outer surface and can determine the position of the surface, which are sequentially selected according to their order in the sequence of vertices of the finite element model.

6. The method for post-processing results of FEA analysis according to claim 1, wherein, Step 4f specifically includes: during the surface rendering process of each unit, analyzing the outer surface linked list of each finite element unit, directly rendering the outer surface that is completely between two adjacent cutting surfaces, extracting the vertex information of the newly added outer surface that has no intersection with the previous cutting surface, determining the intersection point of the outer surface and the current cutting surface from the active edge data, judging the position relationship of the outer surface and the current cutting surface according to the vertex information of the outer surface, rendering the region before the current cutting surface, and taking the region after the current cutting surface as the outer surface to be rendered for the next cutting surface; establishing a vertex position marker of the finite element unit, and the marker content is the relative position relationship of the vertex and the cutting surface; for the edge formed by any two vertices of the finite element unit, judging the marker attributes of the two vertices and the cutting surface, if the marker attributes are different, it indicates that the edge is an active edge intersecting with the cutting surface, generating the intersection point data of the edge and the cutting surface, and generating all intersection point data of the finite element unit and the cutting surface in turn according to the vertex order to obtain the cutting surface polygon.

Images