A point array structure conformal filling and fairing method based on equivalent surface extraction

Abstract

This invention discloses a method for conformal filling and smoothing of lattice structures based on isosurface extraction, belonging to the field of lightweight functional structures. The method includes: firstly, establishing an implicit representation model of the lattice cells; then, directly obtaining the coordinates and topological relationships of the triangular facet nodes on the surface by extracting isosurfaces, thus eliminating the need for traditional meshing of the implicit cells. Isoparametric transformation is used to map the cell surface nodes to the target structure mesh, achieving accurate conformal filling. Subsequently, self-intersecting facets between adjacent cells are detected and eliminated to avoid model defects, and the structure is smoothed using Laplacian smoothing. This invention solves the technical problem that implicitly represented lattice cells are difficult to directly use for conformal filling, can universally handle various implicit cells, effectively avoids mesh distortion and STL file self-intersection problems, and finally generates a smooth, high-quality model that can be directly used for additive manufacturing.

Description

Technical Field

[0001] This invention belongs to the field of lightweight functional structures, and particularly relates to a method for conformal filling and smoothing of lattice structures based on isosurface extraction. Background Technology

[0002] With the deep integration of generative design and additive manufacturing, lattice structures are evolving towards "variable density, multi-topological heterogeneity" driven by neural networks, providing a new path to achieve extreme lightweighting and multifunctional integration. This type of data-driven design typically uses implicit functions to describe the complex geometry and spatial distribution of lattice cells. Through flexible combination of implicit models and Boolean operations, high-performance structures spanning macro and micro scales and exhibiting continuous and gradual changes in internal topology can be generated. Compared to traditional explicit modeling, implicit representation has a natural advantage in describing complex surfaces (such as TPMS structures) and implementing gradient functional design, and has become the mainstream paradigm for lattice structure generation.

[0003] However, existing conformal filling techniques still face significant challenges when dealing with large-scale, highly complex implicit lattices. First, there are bottlenecks in computational efficiency and scalability. For variable-density and heterogeneous scenarios generated by neural networks, traditional methods often rely on global high-resolution voxel meshes for field reconstruction. This global discretization strategy not only results in exponentially increasing computational costs with model size, making it difficult to handle large-scale complex structures, but also leads to a huge waste of computational power and the risk of memory overflow due to the forced increase in global resolution to adapt to subtle local changes, severely restricting the engineering application of data-driven design. Second, there are surface quality and geometric defects. Due to the lack of explicit boundaries in implicit cells, traditional voxel-based extraction methods inevitably produce surface staircase effects, disrupting the smoothness of lattice members. Furthermore, when mapping standard cells to complex surface boundaries, severe nonlinear deformation can easily lead to mesh distortion or even self-intersection of triangular facets at the connection points of adjacent cells. These geometric defects not only reduce the accuracy of predicting the mechanical properties of the structure, but may also cause powder placement errors or printing interruptions during additive manufacturing, leading to manufacturing failure. Therefore, there is an urgent need to develop an efficient method that can abandon global voxelization recalculation and adopt a local on-demand extraction strategy to solve the problem of conformal filling under complex surface boundaries. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for conformal filling and smoothing of lattice structures based on isosurface extraction, comprising: Obtain the target structure model to be filled; Establish an implicit expression model for the lattice cell structure to be filled; Based on the implicit expression model, the surface triangular patch information of the lattice cell structure is obtained by extracting isosurfaces. The surface triangular patch information includes the coordinates of the surface nodes and the topological connection relationships between them. The target structure model is meshed to obtain the grid cell node coordinates and cell topology information of the target structure model; Based on the grid cell node coordinates and cell topology information, the surface node coordinates of the lattice cell structure are mapped to the global coordinate system of the target structure model through isoparametric transformation, and the transformed surface nodes are connected according to the topological connection relationship, so as to fill the lattice cell structure into the grid cell of the target structure model to form a conformal filling initial structure. Detect the facets in the regions where adjacent lattice cells meet in the initial structure, and identify and eliminate facets with self-intersection. The structure after eliminating self-intersecting surfaces is subjected to node smoothing to smooth the conformal filling structure.

[0005] Optionally, in the step of establishing the implicit expression model, the lattice cell structure includes cells defined by a three-period minimal surface function, truss cells defined by a bar component implicit function through Boolean operations, or hybrid cells defined by the three-period minimal surface function and the truss function through Boolean operations.

[0006] Optionally, the three-period minimum surface function is a P-type three-period minimum surface function, whose function value at any point in three-dimensional space is the sum of three cosine functions, the independent variables of the three cosine functions being the product of the coordinate values ​​of the point and the constant 2π, and the P-type three-period minimum surface function includes an adjustable horizontal parameter.

[0007] Optionally, the implicit expression of the truss cell is constructed in the following way: defining implicit functions for multiple rod components, wherein the implicit function of each rod component is defined by its diameter parameter and the coordinate parameters of its two endpoints; and merging the implicit functions of multiple rod components by taking the maximum value operation to obtain the overall implicit function of the truss cell.

[0008] Optionally, the isoparametric transformation is: taking the coordinates of the surface node of the lattice cell in its local coordinate system and performing a transformation matrix composed of shape functions, and then performing a calculation with the coordinates of the mesh unit node of the target structure model in the global coordinate system to obtain the mapped coordinates of the surface node in the global coordinate system.

[0009] Optionally, the transformation matrix consists of eight shape function components, each of which is the product of the linear combination of the coordinate components of the surface node in the local coordinate system, and the sum of all shape function components satisfies the unity decomposition property.

[0010] Optionally, identifying self-intersecting patches includes: calculating the distance or overlap area between each pair of adjacent patches in the initial structure, and marking patches whose distance is less than a preset distance threshold or whose overlap area is greater than a preset area threshold as self-intersecting patches.

[0011] Optionally, the node smoothing process employs Laplace smoothing.

[0012] On the other hand, the present invention also provides an electronic device including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0013] On the other hand, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0014] Compared with the prior art, the present invention has the following advantages and technical effects: This invention directly obtains the node and topological information of the surface triangular facets of implicit expression cells by extracting the isosurfaces of the cells, eliminating the need for traditional meshing of the cells. This enables efficient and universal conformal filling of any implicit expression lattice cells (including TPMS, truss, and hybrid cells). Furthermore, by detecting and eliminating self-intersecting facets in the connection regions of adjacent cells, mesh distortion and STL file defects in the filled structure are effectively avoided. Subsequent Laplacian smoothing significantly improves the smoothness of the structural surface and eliminates node abrupt changes caused by Boolean operations or facet deletion. This method is highly automated, and the final output is a high-quality, self-intersecting STL model that can be directly used for subsequent additive manufacturing. It ensures the freedom of lightweight design for complex irregular structures while guaranteeing the geometric integrity and manufacturability of the final product.

[0015] Meanwhile, this invention addresses the variable density and multi-topological heterogeneous lattice scenarios generated by neural networks by employing an "on-demand extraction, local computation" strategy. It extracts isosurfaces in real-time within the standard space of a single cell, completely eliminating the redundant process of traditional methods that rely on global high-resolution voxel meshes for field reconstruction. This transforms "massive heterogeneity" into "parallel single-cell" computation, significantly overcoming the efficiency bottleneck of data-driven design. Furthermore, by directly extracting high-precision isosurfaces within the standard parameter space, surface staircase effects are avoided. After isoparametric transformation, self-intersecting patches are automatically detected and eliminated, and Laplacian smoothing achieves smooth node transitions, effectively solving the mesh distortion problem. The final output is a high-quality, defect-free STL model that can be directly used in additive manufacturing, significantly improving the manufacturability and engineering applicability of complex lattice structures while ensuring the accuracy of mechanical property prediction. Attached Figure Description

[0016] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 The implicit expression model of cell structure in this embodiment of the invention is as follows: (a) is a P-type TPMS structure, (b) is a hybrid truss structure of BCC and FCC, and (c) is a hybrid structure of P-type TPMS structure and truss structure. Figure 2 This is a schematic diagram illustrating how every three nodes in an embodiment of the present invention form a patch through the piling relationship T1; Figure 3 This is a schematic diagram illustrating the process of filling a lattice cell model into a structural model mesh element according to an embodiment of the present invention. Figure 4 The diagrams illustrate the phenomenon of self-intersection at the junction of adjacent cells in this embodiment of the invention and the elimination of self-intersection, wherein (a) is a diagram of the phenomenon of self-intersection and (b) is a diagram of the elimination of self-intersection. Figure 5 The following are schematic diagrams of node mutation and Laplace smoothing in an embodiment of the present invention, wherein (a) is a schematic diagram of node mutation and (b) is a schematic diagram of Laplace smoothing; Figure 6 This is an overall flowchart illustrating an embodiment of the present invention; Figure 7 This is a schematic diagram of a TPMS cell that has been transformed to implicitly express TPMS according to an embodiment of the present invention; Figure 8 This is a schematic diagram of the truss lattice cell for the transformation of implicit expression in an embodiment of the present invention; Figure 9 This is a schematic diagram of a hybrid cell with implicit expression according to an embodiment of the present invention; Figure 10 This is a schematic diagram of a hybrid cell representing the implicit representation of an undevelopable surface in an embodiment of the present invention. Figure 11 This is a schematic diagram of the method flow according to an embodiment of the present invention; Figure 12 This is a schematic diagram illustrating how to handle variable density and multi-topological heterogeneous scenarios generated by neural networks according to an embodiment of the present invention. Detailed Implementation

[0017] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0018] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0019] Example 1 like Figure 6 As shown, this embodiment provides a method for conformal filling and smoothing of lattice structures based on isosurface extraction, including: Obtain the target structure model to be filled; Establish an implicit expression model for the lattice cell structure to be filled; Based on the implicit expression model, the surface triangular patch information of the lattice cell structure is obtained by extracting isosurfaces. The surface triangular patch information includes the coordinates of the surface nodes and the topological connection relationships between them. The target structure model is meshed to obtain the grid cell node coordinates and cell topology information of the target structure model; Based on the grid cell node coordinates and cell topology information, the surface node coordinates of the lattice cell structure are mapped to the global coordinate system of the target structure model through isoparametric transformation, and the transformed surface nodes are connected according to the topological connection relationship, so as to fill the lattice cell structure into the grid cell of the target structure model to form a conformal filling initial structure. Detect the facets in the regions where adjacent lattice cells meet in the initial structure, and identify and eliminate facets with self-intersection. The structure after eliminating self-intersecting surfaces is subjected to node smoothing to smooth the conformal filling structure.

[0020] Furthermore, in the step of establishing the implicit expression model, the lattice cell structure is selected from any of the following or constructed through any combination of the following and Boolean operations: (a) A cell defined by a three-period minimal surface function, wherein the three-period minimal surface function is an implicit function that exhibits periodic fluctuations in three-dimensional space; (b) A truss cell defined by a spatial rod structure, which is obtained by performing a Boolean union operation on multiple implicit functions representing a single rod; (c) A hybrid structure cell is formed by further performing Boolean operations on the implicit functions of the three-period minimal surface function of type (a) and the truss cell of type (b).

[0021] The three-period minimal surface function adopts a P-type function. Its function value at any point in three-dimensional space is composed of the cosine value of the three rectangular coordinate components of the point multiplied by a constant twice pi, the sum of the three cosine values, and finally an independently adjustable horizontal parameter. By adjusting the value of the horizontal parameter, the solid region range and volume fraction of the cell are controlled.

[0022] The specific steps for constructing the truss cell model include: For each member in the truss, an implicit function for the member is defined based on its geometric properties, which include the member's diameter and the position coordinates of its two endpoints in three-dimensional space. Perform a Boolean union operation on the implicit functions of all members in the truss. Specifically, at any point in space, take the maximum value of the implicit functions of all members at that point to form the final implicit function describing the entire truss cell entity region.

[0023] The implementation method of the isoparametric transformation is as follows: For each hexahedral element in the target structure mesh, obtain the coordinates of all its nodes in the global coordinate system; For the lattice cell surface nodes that need to be mapped to the interior of the unit, first determine their coordinates in the local parametric coordinate system based on the hexahedral unit. The values ​​of each component of the local coordinates are between negative one and positive one. Using an interpolation function that reflects the shape of a hexahedral element, the local coordinates of the cell node are converted into coordinates in the global coordinate system. The interpolation function is determined by the cell node coordinates and a set of linear shape functions about the local coordinates.

[0024] The shape function set used by the interpolation function consists of eight independent shape function components; each shape function component is the product of linear combination factors of the local coordinate components, specifically, one of each of the three terms (addition and subtraction of local coordinate X component, addition and subtraction of local coordinate Y component, and addition and subtraction of local coordinate Z component) is multiplied together and then multiplied by a constant coefficient; the sum of the function values ​​of all eight shape function components at any local coordinate point is always one.

[0025] Specific methods for identifying self-intersecting patches include: Traverse and examine all adjacent pairs of triangular facets in the initial filled structure; For each pair of pairs, calculate the minimum Euclidean distance between them in three-dimensional space; If the minimum distance is less than a preset positive tolerance threshold, then the opposite face is determined to have self-intersected. Alternatively, calculate the area of ​​the overlapping region of the two faces on a certain projection plane; If the overlapping area is greater than a preset area threshold, then the opposite face is determined to be self-intersecting; Remove the triangular facets that are determined to be self-intersecting from the initial structure.

[0026] The process of performing node smoothing using the Laplace smoothing method is as follows: For each internal node in the structured mesh, find all adjacent nodes that are directly connected to it through mesh edges; Calculate the arithmetic mean of the coordinates of these adjacent nodes; The current position of the internal node is moved a distance along the direction pointing to the arithmetic mean, and this distance is determined by multiplying the vector from the current position to the mean by a smoothing factor between zero and one. Performing the above operation sequentially on all internal nodes in the mesh is denoted as one smooth iteration; Repeat the smoothing iteration multiple times until the overall change in node position is less than the preset convergence criterion or the preset maximum number of iterations is reached.

[0027] The meshing of the target structural model is accomplished using general-purpose computer-aided engineering software. This software can generate a mesh data file containing a list of nodes and a list of element connections. The element types include tetrahedral elements or hexahedral elements.

[0028] The final smoothed conformal filling structure is output as a three-dimensional model file that meets the requirements of the general interface of additive manufacturing equipment. The file format is a standard format that describes the surface geometry using a set of triangular facets.

[0029] Example 2 like Figure 11 As shown, this embodiment provides a method for conformal filling and smoothing of lattice structures based on isosurface extraction, including: Obtain the target structure model to be filled; Establish an implicit expression model for the lattice cell structure to be filled; Based on the implicit expression model, the surface triangular patch information of the lattice cell structure is obtained by extracting isosurfaces. The surface triangular patch information includes the coordinates of the surface nodes and the topological connection relationships between them. The target structure model is meshed to obtain the grid cell node coordinates and cell topology information of the target structure model; Based on the grid cell node coordinates and cell topology information, the surface node coordinates of the lattice cell structure are mapped to the global coordinate system of the target structure model through isoparametric transformation, and the transformed surface nodes are connected according to the topological connection relationship, so as to fill the lattice cell structure into the grid cell of the target structure model to form a conformal filling initial structure. Detect the facets in the regions where adjacent lattice cells meet in the initial structure, and identify and eliminate facets with self-intersection. The structure after eliminating self-intersecting surfaces is subjected to node smoothing to smooth the conformal filling structure.

[0030] Implicitly expressed cellular structure conformal filling includes the following steps: 1. First, a implicit expression model of cell-unit structure is established, taking the P-type TPMS structure as an example. Its implicit formula is: ; Where x, y, and z are three-dimensional physical coordinates, and t is a horizontal parameter used to control the geometry and volume fraction of the cell, such as... Figure 1 As shown in (a) of the diagram.

[0031] A truss structure composed of columnar members can be expressed by the following implicit formula: ; Where i is the rod assembly number. The diameter of the rod assembly, ( (), Using ) as the endpoint, multiple groups of members form a typical truss structure through Boolean operations, such as Figure 1 As shown in (b) of the diagram.

[0032] A hybrid cell structure can be obtained by performing Boolean operations on both the TPMS structure and the truss structure. For example... Figure 1 As shown in (c) in the figure.

[0033] 2. Secondly, by extracting isosurfaces, the surface of the implicitly expressed cell is obtained. This surface consists of several nodes N, such as... Figure 2 As shown, the method for extracting isosurfaces outputs both the coordinates of the nodes and the topological relationships T1 (connection relationships) between the nodes. Every three nodes form a patch through the connection relationship T1.

[0034] 3. Mesh the structural model to be filled (using software such as ANSYS, Abaqus, or HyperMesh) to obtain the node information M and the element topology information T2. ​​Transform the coordinates of the cell surface nodes N in the local coordinate system of the lattice cell model to their coordinates in the global coordinate system of the structural model using isoparametric transformation (this can be implemented using MATLAB, Python, etc.). Connect the nodes N through the topological relationship T1, thereby filling the lattice cell model into the structural model's mesh elements, as shown below. Figure 3 As shown.

[0035] The isoparametric changes are calculated in the following way: ; Where N is the shape function matrix, expressed as follows: ; X, Y, Z are the interpolated coordinates of cell node N in the global coordinate system, and x, y, z are the coordinates of node M in the global coordinate system mesh element. , , Let N be the coordinates of the cell surface node N in the local coordinate system, ranging from [-1, 1].

[0036] 4. Self-intersection will occur at the junction of adjacent cells, such as... Figure 4 As shown in (a), the distance between each pair of adjacent faces is calculated. If the distance is less than a certain threshold (or the overlapping area is greater than the threshold), it is marked as self-intersecting, and these self-intersecting faces are eliminated, as shown in (a). Figure 4 As shown in (b) above, this method avoids mesh distortion and self-intersection in the final output STL file.

[0037] 5. Eliminating self-intersecting patches can lead to abrupt node mutations, such as... Figure 5 As shown in (a) above. Using Laplacian smoothing, smooth transitions between nodes and the smoothness of the entire cell can be achieved, as shown in [example]. Figure 5 As shown in (b) of the diagram.

[0038] Figure 7 , Figure 8 , Figure 9 They respectively showed the Figure 1 Examples of three typical implicit expression cell structures shown in (a), (b), and (c) of the paper, which conformally fill circular surfaces, verify that the method of the present invention can accurately conform the above typical structures onto circular surfaces.

[0039] Figure 10 An example of applying the method of the present invention to conformal filling of irregular curved surfaces is shown, demonstrating that the method is also well applicable to complex irregular curved surfaces.

[0040] like Figure 12 As shown, in this embodiment, an implicit mathematical model of the lattice cell is first constructed, and a high-precision isosurface is directly extracted in the standard parameter space to obtain the node coordinates and topological connectivity of the initial surface triangular mesh. This process does not require traditional volume meshing of the cell entity, nor does it require establishing a global voxel field in the target space for resampling calculations.

[0041] Specifically, for variable-density and multi-topological heterogeneous scenarios generated by neural networks, this embodiment adopts an "on-demand extraction, local computation" strategy: based on the implicit function output by the neural network, isosurface extraction is completed in real time within the standard space of a single cell. This approach strictly limits the costly isosurface extraction process to a local scale, avoiding the need for traditional methods to establish a global high-resolution voxel grid and the corresponding field reconstruction process to adapt to complex changes across the entire field. This transforms the "massive heterogeneous" global computation problem into a parallelizable "single-cell" computation task, effectively reducing computational complexity and improving the processing efficiency of data-driven design.

[0042] This embodiment addresses the computational efficiency and scalability challenges in scenarios involving variable density and multi-topological heterogeneous lattices generated by neural networks, while overcoming the self-intersection defect in the mapping process. This method can efficiently process various complex implicit cells and rapidly generate defect-free STL models that can be directly used for additive manufacturing, while ensuring high model accuracy and surface smoothness.

[0043] Through the above methods, this invention successfully achieves "decoupling" on two levels: first, it completely separates the geometric generation of cells from their spatial positioning in the target structure; second, it transforms complex global geometric reconstruction into a large number of independent and simple local calculations. Thus, it not only completely avoids the preprocessing step of meshing cell entities in traditional methods, but also eliminates the need to establish a global voxel field for resampling in the target space, significantly reducing computational complexity and memory consumption. This lays an efficient technical foundation for the rapid conformal filling of large-scale, heterogeneous lattice structures.

[0044] On the other hand, this embodiment also provides an electronic device, including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0045] On the other hand, this embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0046] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for conformal filling and smoothing of lattice structures based on isosurface extraction, characterized in that, include: Obtain the target structure model to be filled; Establish an implicit expression model for the lattice cell structure to be filled; Based on the implicit expression model, the surface triangular patch information of the lattice cell structure is obtained by extracting isosurfaces. The surface triangular patch information includes the coordinates of the surface nodes and the topological connection relationships between them. The target structure model is meshed to obtain the grid cell node coordinates and cell topology information of the target structure model; Based on the grid cell node coordinates and cell topology information, the surface node coordinates of the lattice cell structure are mapped to the global coordinate system of the target structure model through isoparametric transformation, and the transformed surface nodes are connected according to the topological connection relationship, so as to fill the lattice cell structure into the grid cell of the target structure model to form a conformal filling initial structure. Detect the facets in the regions where adjacent lattice cells meet in the initial structure, and identify and eliminate facets with self-intersection. The structure after eliminating self-intersecting surfaces is subjected to node smoothing to smooth the conformal filling structure.

2. The method according to claim 1, characterized in that, In the step of establishing the implicit expression model, the lattice cell structure includes cells defined by a three-period minimal surface function, truss cells defined by a bar component implicit function through Boolean operations, or hybrid cells defined by the three-period minimal surface function and the truss function through Boolean operations.

3. The method according to claim 2, characterized in that, The three-period minimum surface function is a P-type three-period minimum surface function, whose function value at any point in three-dimensional space is the sum of three cosine functions. The independent variables of the three cosine functions are the product of the coordinate values ​​of the point and the constant 2π, respectively. The P-type three-period minimum surface function includes an adjustable horizontal parameter.

4. The method according to claim 2, characterized in that, The implicit expression of the truss cell is constructed in the following way: an implicit function is defined for each of the multiple rod components, and the implicit function of each rod component is defined by its diameter parameter and the coordinate parameters of its two endpoints; the implicit functions of the multiple rod components are merged by taking the maximum value operation through Boolean merging to obtain the overall implicit function of the truss cell.

5. The method according to claim 1, characterized in that, The isoparametric transformation is as follows: the coordinates of the surface nodes of the lattice cell in its local coordinate system are transformed by a transformation matrix composed of shape functions and then compared with the coordinates of the mesh unit nodes of the target structure model in the global coordinate system to obtain the mapped coordinates of the surface nodes in the global coordinate system.

6. The method according to claim 5, characterized in that, The transformation matrix consists of eight shape function components. Each shape function component is the product of the linear combination of the coordinate components of the surface node in the local coordinate system, and the sum of all shape function components satisfies the unity decomposition property.

7. The method according to claim 1, characterized in that, Identifying self-intersecting facets includes: calculating the distance or overlap area between each pair of adjacent facets in the initial structure, and marking facets with a distance less than a preset distance threshold or an overlap area greater than a preset area threshold as self-intersecting facets.

8. The method according to claim 1, characterized in that, The node smoothing process employs the Laplace smoothing method.

9. An electronic device comprising a memory, a processor, and a computing program stored in the memory and executable on the processor, characterized in that, When the processor executes the computing program, it implements the method of any one of claims 1-8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1-8.

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