A method for quickly generating overall finite element models based on geometric line and surface information

By automatically generating geometric wireframe models in CAD software and defining attributes, using the interfaces of line-surface grid algorithm and CAE software, an efficient generation of overall finite element models is achieved, solving the problem of inefficiency in the existing technology, and improving the accuracy and efficiency of design analysis.

CN120318463BActive Publication Date: 2025-08-12上海波客实业有限公司
View PDF 2 Cites 0 Cited by

Patent Information

Application Number
CN202510795844.8
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-06-16
Publication Date
2025-08-12
Estimated Expiration
2045-06-16

AI Technical Summary

Technical Problem

The prior art is inefficient in the process of converting geometric line-plane information into an overall finite element model, cumbersome operations, easy to miss and make mistakes, and it is difficult to meet the needs of efficient and rapid design analysis of modern engineering.

Method used

By calling the CAD software interface to import the pneumatic surface and structural skeleton information, the geometric wireframe model is automatically generated, and the material, coordinate system and laying attributes are defined in the CAD software. The intersecting structure is automatically disconnected using the line-surface grid algorithm to generate a geometric line-surface model, and the CAE software is imported for automatic grid division, and the classification, attributes and material data of geometric line-surfaces are extracted and associated.

Benefits of technology

It improves the conversion efficiency from geometric line-plane information to the overall finite element model, reduces omissions and errors, and meets the efficient and rapid design analysis needs of modern engineering.

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure CN120318463B_ABST
    Figure CN120318463B_ABST
Patent Text Reader

Abstract

The present invention provides a method for quickly generating an overall finite element model based on geometric line and surface information. The method of the present invention is based on the open API interface of CAD and CAE software, can quickly complete the layout of the geometric wireframe model in CAD, generate the geometric wireframe model through the line and surface mesh algorithm, and define the corresponding attribute, material and other information data on the geometric line and surface model, automatically divide the grid through the finite element mesh algorithm, extract the classification, attribute and material data of the geometric line and surface, establish an association with the divided grid, and generate a finite element mesh model. The method of quickly generating an overall finite element model based on geometric line and surface information of the present invention improves the efficiency of converting geometric line and surface information into an overall finite element model, reduces omissions and errors, does not require additional time, energy and manpower, and can meet the needs of efficient and rapid design and analysis of modern engineering.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] The present invention relates to the technical field of computer simulation, and in particular to a method for rapidly generating an overall finite element model based on geometric line and surface information. Background Art

[0002] The aircraft scheme design stage mainly involves inputting the overall geometric shape into the CAD software to construct the geometric lines and surfaces of the main structure, and then importing it into the CAE software for finite element mesh division, defining the classification, attributes and material data of the geometric line and surface model, and then establishing attribute and material associations with the divided mesh to obtain the overall finite element model.

[0003] Although existing CAD software defines the classification, attributes, and materials of geometric lines and surfaces, data incompatibilities between different software programs often result in only the geometric model being retained after importing it into CAE. Much of the previously defined geometric line and surface data is lost, requiring manual re-creation and associating with the geometric model in CAE. This process is cumbersome and requires significant manpower, effort, and time. The conversion of geometric line and surface information into an overall finite element model is inefficient, prone to omissions and errors, and fails to meet the demands of modern engineering for efficient and rapid design and analysis. Summary of the Invention

[0004] In response to the technical problems raised in the above background technology, the present invention provides a method for quickly generating an overall finite element model based on geometric line and surface information.

[0005] The present invention solves the above technical problems through the following technical solutions:

[0006] The present invention provides a method for quickly generating an overall finite element model based on geometric line and surface information. The method comprises:

[0007] Calling a CAD software interface to import aerodynamic shape surface and structural skeleton information, automatically generating a geometric wireframe model including a frame, beam, rib, skin and long stringer structure, and completing the classification of curves and surfaces of the geometric wireframe based on the aerodynamic shape surface and the structural skeleton information;

[0008] directly defining the material, coordinate system, cross-section, and layup properties of the geometric wireframe model in the CAD software, wherein the curve geometry is defined as the coordinate system and the cross-section properties, and the surface geometry is defined as the layup properties;

[0009] Automatically disconnecting the intersecting structures between the structures in the geometric wireframe model through a line-surface mesh algorithm to generate a geometric line-surface model, and classifying it into a corresponding structure type;

[0010] Importing the geometric line and surface model into CAE software, and performing automatic meshing according to a preset mesh size and dynamic adjustment strategy;

[0011] Extracting the classification, attributes and material data of the geometric lines and surfaces in the geometric line and surface model through the CAD software, and associating the attributes and materials with the divided grid;

[0012] The obtained finite element model is exported through the CAE software interface.

[0013] Preferably, the CAD software is CATIA, and the CATIA automatically generates the geometric wireframe model through its own API interface; the CAE software is Hypermesh software, and the finite element model is output through the interface of the Hypermesh software.

[0014] Preferably, the step of automatically disconnecting the intersecting structures between the structures in the geometric wireframe model by using a line-surface mesh algorithm further comprises:

[0015] identifying intersections between the frame of the geometric wireframe model, the beams, and the rib structure;

[0016] Automatically breaking the wireframe according to the geometric features of the intersecting structure to generate a plurality of independent line and surface units;

[0017] A plurality of the independent line-surface units constitute the geometric line-surface model.

[0018] Preferably, the specific operation of the line-surface mesh algorithm is as follows:

[0019] Extracting and arranging various structures in the geometric wireframe model into a to-be-processed list, extracting one to-be-processed geometric element from the to-be-processed list, and cutting the to-be-processed geometric element;

[0020] Cut the geometric elements to be processed according to the cutting logic to obtain the number of cutting results;

[0021] Perform branch cutting according to the number of cutting results, classify the subunits after the branch cutting into a geometry list, and remove the original geometric elements that have been processed;

[0022] All the to-be-processed geometric elements in the to-be-processed list are cut and classified, the operation is completed, and the independent line and surface units are generated.

[0023] Preferably, the cutting logic is that if the geometric element to be processed has an intersection relationship with other structures, cutting is performed according to the intersection area, sub-geometric units are generated after cutting, and the number of cutting results is output.

[0024] Preferably, the operation of performing branch cutting according to the number of cutting results further includes:

[0025] If the number of the cutting results is 0, no cutting is required, and the to-be-processed geometric element is directly removed from the to-be-processed list;

[0026] If the number of the cutting results is 1, then one sub-geometry unit is generated after cutting, and the sub-geometry unit is added to the geometry list;

[0027] If the number of the cutting results is greater than 1, multiple sub-geometric units are generated after cutting, and it is determined whether to perform combined cutting.

[0028] Preferably, the operation of determining whether to perform combined cutting further includes:

[0029] If the sub-geometric units need to be combined into a composite structure, the sub-geometric units are combined and put into the to-be-processed list.

[0030] If the sub-geometric unit needs to be processed independently, it is directly stored in the to-be-processed list.

[0031] Preferably, the step of automatically dividing the grid according to the preset grid size and the dynamic adjustment strategy further includes:

[0032] Acquire geometric lines and geometric surfaces of the geometric line-surface model, and cut the geometric surfaces along the normals of the geometric surfaces according to the geometric lines to obtain a meshed model;

[0033] Dividing the cut geometric surface into two-dimensional grids according to the preset grid size using the grid division model;

[0034] Cut the geometric line in sections and divide the cut geometric line into one-dimensional grids;

[0035] The two-dimensional grid and the one-dimensional grid are merged to obtain the divided grid.

[0036] Preferably, the one-dimensional grid division includes:

[0037] Obtaining the edge line of each geometric line corresponding to the geometric surface;

[0038] Get the nodes on the edge and save them as a collection;

[0039] cutting the geometric line according to the obtained nodes to segment the geometric line;

[0040] The segmented geometric lines are divided into the one-dimensional grid.

[0041] Preferably, the step of extracting the classification, attributes and material data of the geometric lines and surfaces in the geometric line and surface model by the CAD software and associating the attributes and materials with the divided grids further comprises:

[0042] Reading a predefined attribute file in the CAD software and extracting the part material name and the ply name of each part in the attribute file;

[0043] Reading basic ply information and basic material parameters in the geometric line-surface model;

[0044] Loading the predefined basic materials and basic layers in the CAE software;

[0045] Parsing the cross-sectional parameters output by the CAD software, reading the cross-sectional parameters, and creating cross-sectional properties corresponding to the cross-sectional parameters;

[0046] Binding the cross-sectional properties to the base material to form a reusable primitive;

[0047] Creating a layer attribute with the same name according to the part material name, and simultaneously copying and modifying the name based on the primitive to obtain the part attribute;

[0048] The part properties are associated with the divided grids by property materials.

[0049] The positive progressive effect of the present invention is that the present invention provides a method for quickly generating an overall finite element model based on geometric line and surface information. The method of the present invention is based on the open API interface of CAD and CAE software, and can quickly complete the layout of the geometric wireframe model in CAD, generate the geometric wireframe model through the line and surface mesh algorithm, and define the corresponding attribute, material and other information data on the geometric line and surface model, automatically divide the grid through the finite element mesh algorithm, extract the classification, attribute and material data of the geometric line and surface, establish an association with the divided grid, and generate a finite element mesh model. The method of quickly generating an overall finite element model based on geometric line and surface information of the present invention improves the efficiency of converting geometric line and surface information into an overall finite element model, reduces omissions and errors, does not require additional time, energy and manpower, and can meet the needs of efficient and rapid design and analysis of modern engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a flow chart of a method for rapidly generating an overall finite model based on geometric line and surface information according to Example 1 of the present invention.

[0051] Figure 2 This is a schematic diagram of the line-surface mesh cutting algorithm of Example 1 of the present invention.

[0052] Figure 3Schematic diagram of a specific flow chart of the line-surface mesh cutting algorithm according to embodiment 1 of the present invention.

[0053] Figure 4 Schematic diagram of the process of automatic grid division according to embodiment 1 of the present invention.

[0054] Figure 5 Schematic diagram of the process of one-dimensional meshing in the automated meshing process of embodiment 1 of the present invention.

[0055] Figure 6 This is a schematic diagram of a specific process of associating attribute materials in step S5 of Example 1 of the present invention.

[0056] Figure 7 This is a schematic diagram of a geometric wireframe model created based on an aircraft wing structure according to Example 1 of the present invention.

[0057] Figure 8 This is a schematic diagram of a geometric line and surface model created based on an aircraft wing structure according to Example 1 of the present invention.

[0058] Figure 9 Schematic diagram of a finite element mesh model generated based on an aircraft wing structure according to Example 1 of the present invention. DETAILED DESCRIPTION

[0059] The present invention is further described below by way of examples, but the present invention is not limited to the scope of the examples.

[0060] Example 1

[0061] like Figure 1 As shown, this embodiment provides a method for quickly generating a global finite model based on geometric line and surface information. The method includes:

[0062] Step S1, call the CAD software interface to import aerodynamic shape surface and structural skeleton information, automatically generate a geometric wireframe model including frame, beam, rib, skin and long stringer structure, and complete the classification of curves and surfaces of the geometric wireframe based on the aerodynamic shape surface and structural skeleton information.

[0063] Step S2: directly define the material, coordinate system, section and layup properties of the geometric wireframe model in the CAD software, wherein the curve geometry is defined as the coordinate system and section properties, and the surface geometry is defined as the layup properties.

[0064] Step S3: Automatically disconnect intersecting structures in the geometric wireframe model using a line-surface meshing algorithm to generate a geometric line-surface model, which is then classified into corresponding structural types. In this embodiment, step S3 further includes: identifying intersecting structures between the frame, beam, and rib structures in the geometric wireframe model; automatically disconnecting the wireframe based on the geometric characteristics of the intersecting structures to generate a plurality of independent line-surface units; and the plurality of independent line-surface units forming the geometric line-surface model.

[0065] As an optional embodiment, the specific operation of the line-surface mesh algorithm is as follows: extract and organize each structure (frame, beam, rib, skin, girder) in the geometric wireframe model into a to-be-processed list, extract one of the to-be-processed geometric elements from the to-be-processed list, and cut the to-be-processed geometric element; cut the to-be-processed geometric element according to the cutting logic to obtain the number of cutting results; perform branch cutting according to the number of cutting results, classify the sub-units after branch cutting into the geometric list, and remove the original geometric elements that have been processed; complete the cutting and classification of all the to-be-processed geometric elements in the to-be-processed list, end the operation, and generate independent line-surface units. In this embodiment, the cutting logic is that if the to-be-processed geometric element has an intersection relationship with other structures, it will be cut according to the intersection area, and sub-geometric units will be generated after cutting, and the number of cutting results will be output. Among them, the to-be-processed geometric list is divided into 1D geometric list: storing one-dimensional geometric elements (such as the curves of beams and girder); 2D geometric list: storing two-dimensional geometric elements (such as the curved surface of the skin); component intersection list: recording the intersection lines between each component (such as the intersection point of the beam and the rib), such as Figure 2 shown.

[0066] As an optional embodiment, the operation of performing branch cutting according to the number of cutting results further includes:

[0067] If the number of cutting results is 0, no cutting is required, and the geometric elements to be processed are directly removed from the pending list. If the number of cutting results is 1, only one sub-geometric unit is generated after cutting, and the sub-geometric unit is added to the geometric list. If the number of cutting results is greater than 1, multiple sub-geometric units are generated after cutting, and it is determined whether to perform combined cutting. In this embodiment, the operation of determining whether to perform combined cutting also includes: if the sub-geometric units need to be merged into a composite structure, the sub-geometric units are combined and placed in the pending list; if the sub-geometric units need to be processed independently, they are directly stored in the pending list. Specifically, if Figure 3As shown, a geometric element M to be processed is extracted from the pending list and cut. The number N of cut results for the cut geometric element M is determined. If N = 0, no processing is required and the geometric element M is removed from the list. If N = 1, the cut generates a sub-unit, and the original geometric element M and the generated sub-unit (i.e., the pending geometric element M = M + 1) are added to the pending list. If N > 1, multiple sub-units will be generated after the cut, and further determination is made as to whether to perform combined cutting. The combined cutting conditions are as follows: If the sub-units need to be combined into a composite structure (such as the combined unit of the skin and stringer of an aircraft wing structure), select "Yes" and the combined unit and the original geometric element M (i.e., the pending geometric element M = M + 1) are added to the pending list. If the sub-units need to be processed independently (such as a separated beam segment), select "No" and the original geometric element M and the sub-unit (i.e., the pending geometric element M = M + 1) are added to the pending list.

[0068] Step S4: import the geometric line and surface model into CAE software and perform automatic meshing according to the preset mesh size and dynamic adjustment strategy. As an optional embodiment, step S4 also includes:

[0069] Step S41: obtain geometric lines and geometric surfaces of the geometric line-surface model, cut the geometric surfaces along the normals of the geometric surfaces according to the geometric lines, and obtain a meshed model.

[0070] Step S42: using a meshing model to divide the cut geometric surface into two-dimensional meshes according to a preset mesh size.

[0071] Step S43: segmentally cut the geometric line and divide the cut geometric line into one-dimensional grids. In this embodiment, the one-dimensional grid division includes:

[0072] Step S431: Obtain the edge line of the corresponding geometric surface on each geometric line.

[0073] Step S432: Get the nodes on the edge and save them as a collection.

[0074] Step S433: Cut the geometric line according to the obtained nodes to segment the geometric line.

[0075] Step S434: Divide the segmented geometric lines into one-dimensional grids.

[0076] Step S44: Merge the two-dimensional grid and the one-dimensional grid to obtain a divided grid.

[0077] Step S5: extract the classification, attributes and material data of the geometric lines and surfaces in the geometric line and surface model through CAD software, and associate the attributes and materials with the divided grid.

[0078] As an optional embodiment, step S5 further includes:

[0079] Step S51: Read the attribute file predefined in the CAD software, and extract the part material name and layer name of each part in the attribute file;

[0080] Step S52: Read the basic ply information and basic material parameters in the geometric line-surface model.

[0081] Step S53: Load the basic material and basic ply predefined in the CAE software.

[0082] Step S54: parsing the cross-sectional parameters output by the CAD software, reading the cross-sectional parameters, and creating cross-sectional properties corresponding to the cross-sectional parameters.

[0083] Step S55: Bind the cross-section attributes to the basic material to form a reusable primitive.

[0084] Step S56: Create layer attributes with the same name according to the part material name, and copy and modify the name based on the primitive to obtain the part attributes.

[0085] Step S57: Associating the part attributes with the divided grid attributes and materials.

[0086] Step S6: Export the obtained finite element model through the CAE software interface.

[0087] In this embodiment, the CAD software is CATIA, which automatically generates a geometric wireframe model through its own API interface; the CAE software is Hypermesh software, which outputs a finite element model through the interface of Hypermesh software.

[0088] In this embodiment, the entire method is described using an aircraft wing structure as an example. Assume that there is an aircraft wing structure aerodynamic surface created by CATIA software. The surface includes the geometric shape of the skin and the positions of the framework such as beams, ribs, and stringers. Using the method of this embodiment, first, a layout model is created by calling the CATIA software interface, the wing aerodynamic shape and framework data are read, and a geometric wireframe model of the wing structure is generated in CATIA, such as Figure 7 As shown in the figure, its structural classification includes wing spars, wing ribs, long stringers, skins, leading edge ribs, etc.; and according to the geometric data of the geometric wireframe model (including 1D and 2D geometry), line and surface mesh cutting is performed to generate a geometric line and surface model, such as Figure 8As shown. The properties, materials and other data of geometric lines and surfaces are quickly defined through the program interface. Then, by calling the interface of Hypermesh software, the geometric line and surface model is imported and the line and surface mesh algorithm is used for preliminary mesh division. Then, a structural classification corresponding to the geometric line and surface model is established in CAE, and each part mesh is given properties (such as the cross-sectional size of the 1D edge strip, the thickness and layup of the 2D web), and materials (such as the elastic modulus of steel, etc.), and the overall finite element mesh model for mechanical analysis is successfully generated, as shown in the figure. Figure 9 Through actual testing, compared with the traditional method, the method of this embodiment shortens the time from establishing geometric lines and surfaces to generating the overall finite element mesh model by 90%, and the analysis results are more accurate.

[0089] In the present embodiment, a method for quickly generating an overall finite model based on geometric line and surface information is provided. The method is based on the open API interface of CAD and CAE software, and can quickly complete the layout of the geometric wireframe model in CAD, generate the geometric wireframe model through the line and surface mesh algorithm, and define the corresponding attribute, material and other information data on the geometric line and surface model, automatically divide the grid through the finite element mesh algorithm, extract the classification, attribute and material data of the geometric line and surface, establish an association with the divided grid, and generate a finite element mesh model. The method of quickly generating an overall finite element model based on geometric line and surface information of the present invention improves the efficiency of converting geometric line and surface information into an overall finite element model, reduces omissions and errors, does not require additional time, energy and manpower, and can meet the needs of efficient and rapid design and analysis of modern engineering.

[0090] Although specific embodiments of the present invention have been described above, those skilled in the art will appreciate that these are merely illustrative and that the scope of the present invention is defined by the appended claims. Those skilled in the art may make various changes or modifications to these embodiments without departing from the principles and essence of the present invention, and such changes and modifications are intended to fall within the scope of the present invention.

Claims

1. A method for rapidly generating an overall finite element model based on geometric line and surface information, characterized in that: The method comprises: Calling a CAD software interface to import aerodynamic shape surface and structural skeleton information, automatically generating a geometric wireframe model including a frame, beam, rib, skin and long stringer structure, and completing the classification of curves and surfaces of the geometric wireframe based on the aerodynamic shape surface and the structural skeleton information; directly defining the material, coordinate system, cross-section, and layup properties of the geometric wireframe model in the CAD software, wherein the curve geometry is defined as the coordinate system and the cross-section properties, and the surface geometry is defined as the layup properties; Automatically disconnecting the intersecting structures between the structures in the geometric wireframe model through a line-surface mesh algorithm to generate a geometric line-surface model, and classifying it into a corresponding structure type; Importing the geometric line and surface model into CAE software, and performing automatic meshing according to a preset mesh size and dynamic adjustment strategy; Extracting the classification, attributes and material data of the geometric lines and surfaces in the geometric line and surface model through the CAD software, and associating the attributes and materials with the divided grid; Exporting the obtained finite element model through the CAE software interface; The step of automatically disconnecting the intersecting structures between the structures in the geometric wireframe model by using the line-surface mesh algorithm further comprises: identifying intersections between the frame of the geometric wireframe model, the beams, and the rib structure; Automatically breaking the wireframe according to the geometric features of the intersecting structure to generate a plurality of independent line and surface units; A plurality of the independent line-surface units constitute the geometric line-surface model; The specific operation of the line-surface mesh algorithm is as follows: Extracting and arranging various structures in the geometric wireframe model into a to-be-processed list, extracting one to-be-processed geometric element from the to-be-processed list, and cutting the to-be-processed geometric element; Cut the geometric elements to be processed according to the cutting logic to obtain the number of cutting results; Perform branch cutting according to the number of cutting results, classify the subunits after the branch cutting into a geometry list, and remove the original geometric elements that have been processed; All the to-be-processed geometric elements in the to-be-processed list are cut and classified, the operation is completed, and the independent line and surface units are generated.

2. The method for rapidly generating an overall finite element model based on geometric line and surface information according to claim 1, characterized in that: The CAD software is CATIA, which automatically generates the geometric wireframe model through its own API interface; the CAE software is Hypermesh software, which outputs the finite element model through the interface of the Hypermesh software.

3. The method for rapidly generating an overall finite element model based on geometric line and surface information according to claim 1, wherein: The cutting logic is that if the geometric element to be processed has an intersection relationship with other structures, cutting is performed according to the intersection area, sub-geometric units are generated after cutting, and the number of cutting results is output.

4. The method for rapidly generating an overall finite element model based on geometric line and surface information according to claim 3, wherein: The operation of performing branch cutting according to the number of cutting results further includes: If the number of the cutting results is 0, no cutting is required, and the to-be-processed geometric element is directly removed from the to-be-processed list; If the number of the cutting results is 1, then one sub-geometry unit is generated after cutting, and the sub-geometry unit is added to the geometry list; If the number of the cutting results is greater than 1, multiple sub-geometric units are generated after cutting, and it is determined whether to perform combined cutting.

5. The method for rapidly generating an overall finite element model based on geometric line and surface information according to claim 4, characterized in that: The operation of determining whether to perform combined cutting further includes: If the sub-geometric units need to be combined into a composite structure, the sub-geometric units are combined and put into the to-be-processed list; If the sub-geometric unit needs to be processed independently, it is directly stored in the to-be-processed list.

6. The method for rapidly generating an overall finite element model based on geometric line and surface information according to claim 1, wherein: The steps of automatic meshing based on preset mesh size and dynamic adjustment strategy also include: Acquire geometric lines and geometric surfaces of the geometric line-surface model, and cut the geometric surfaces along the normals of the geometric surfaces according to the geometric lines to obtain a meshed model; Dividing the cut geometric surface into two-dimensional grids according to the preset grid size using a grid division model; Cut the geometric line in sections and divide the cut geometric line into one-dimensional grids; The two-dimensional grid and the one-dimensional grid are merged to obtain a divided grid.

7. The method for rapidly generating an overall finite element model based on geometric line and surface information according to claim 6, characterized in that: The one-dimensional grid division comprises: Obtaining the edge line of each geometric line corresponding to the geometric surface; Get the nodes on the edge and save them as a collection; cutting the geometric line according to the obtained nodes to segment the geometric line; The segmented geometric lines are divided into the one-dimensional grid.

8. The method for rapidly generating an overall finite element model based on geometric line and surface information according to claim 1, wherein: The step of extracting the classification, attributes and material data of the geometric lines and surfaces in the geometric line and surface model by the CAD software and associating the attributes and materials with the divided grids further includes: Reading a predefined attribute file in the CAD software and extracting the part material name and the ply name of each part in the attribute file; Reading basic ply information and basic material parameters in the geometric line-surface model; Loading the predefined basic materials and basic layers in the CAE software; Parsing the cross-sectional parameters output by the CAD software, reading the cross-sectional parameters, and creating cross-sectional properties corresponding to the cross-sectional parameters; Binding the cross-sectional properties to the base material to form a reusable primitive; Creating a layer attribute with the same name according to the part material name, and simultaneously copying and modifying the name based on the primitive to obtain the part attribute; The part properties are associated with the divided grids by property materials.

Citation Information

Patent Citations

  • Rapid generation method for fine finite element model of complex structure

    CN113536617A

  • Geometric modeling and grid generation integrated method based on quadratic analysis curve surface

    CN119004699A