Method for optimizing and designing deployable curved surface and deployable approximation of model fragments

Abstract

The invention relates to a method for optimizing and designing a deployable curved surface and deployable approaching a model fragment, and the method for optimizing the deployable curved surface comprises the steps: flattening a Patch curved surface through employing a curved surface parameterization algorithm, carrying out the UV plane sampling of the Patch curved surface, converting the Patch curved surface into a Grid curved surface with a regular topological structure, taking the Grid curved surface as an agent curved surface, and carrying out the deployable optimization through employing a deep learning method, and finally, performing an inverse sampling method on an optimization result to realize expandability optimization on the original topological curved surface. The design task of the deployable curved surface is converted into a Patch curved surface real-time optimization task under interactive dragging deformation, and the model fragment deployable approximation task is converted into a fragment deployable approximation optimization task under an interactive input condition. According to the method, on the basis of the rapid calculation, a higher optimization freedom degree and a better optimization result are provided.

Description

Technical Field

[0001] The present invention belongs to the field of deep learning and surface optimization technology, and particularly relates to a method for developable surface optimization, design and model segmentation developable approximation. Background Art

[0002] A developable surface is a surface that can be modeled by folding and bending a plane without stretching or compressing it. Due to its manufacturing-friendly properties, it is widely used in industrial design, such as shipbuilding and free-form architecture. The geometric constraints of a discrete developable surface represented by a mesh require that the sum of the angles at each vertex be , while numerical optimization with angle constraints is usually highly nonlinear.

[0003] Existing methods for developable surfaces mainly focus on designing better geometric constraints and use proxy basic surfaces such as cylinders for design, which greatly limits the freedom of developable surface design. In addition, in the piecewise developable approximation task of the model, existing methods pay more attention to objective indicators such as the number of segmentation blocks and segmentation length. However, in actual use, some subjective indicators with semantic meanings are more valuable for practical applications, but it is difficult to measure these indicators using traditional methods. Complex application requirements do not provide enough optimization freedom for existing methods.

[0004] A good method should be able to provide fast computing speed, integrate human prior optimization knowledge, have higher optimization freedom, and not restrict or transform the topological structure in order to meet the complex needs in actual scenarios. Summary of the invention

[0005] In order to solve the above problems, the present disclosure provides a developable surface optimization method based on deep learning, which comprises the following steps: S100: Input the original Patch surface; S200: Flatten the patch surface by performing surface parameterization; S300: Perform UV plane sampling on the flattened Patch surface and convert it into a Grid surface with a regular topological structure; S400: using the Grid surface as a proxy surface and using a deep learning method to perform scalability optimization to obtain an optimization result; S500: optimizing the expandability of the original Patch surface by inverse sampling the optimization result.

[0006] In addition, the present invention also discloses a computer storage medium, wherein the storage medium includes computer instructions, and when the computer instructions are executed on the computer, the computer executes the method.

[0007] In addition, the present invention also discloses an electronic device, wherein the electronic device comprises: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method described is implemented.

[0008] Through the above technical solutions, the core of this method is the data-driven Patch surface optimization method, which can realize the real-time drag optimization design of developable surfaces and the model segmentation developable approximation task under the condition of interactive segmentation input. This method first flattens the Patch surface by using the surface parameterization algorithm, then performs UV plane sampling on the Patch surface, converts it into a Grid surface with a regular topological structure, and uses this as a proxy surface to perform developability optimization using a deep learning method, and finally uses the optimization result to achieve the developability optimization of the original topological surface through the inverse sampling method. This method provides a fast calculation basis for the interactive design and optimization of developable surfaces, and has a wider degree of optimization freedom, and has excellent performance in robustness and generalization. The model segmentation developable approximation results under the condition of human-machine collaborative segmentation input are more reasonable, the overall approximation accuracy is higher, the number of blocks is smaller, and the manufacturing results are lifelike, which provides a high degree of freedom solution for the application requirements of complex actual scenes and provides important research reference for related research. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 is a flow chart of a developable surface optimization method based on deep learning provided in one embodiment of the present disclosure; Figure 2 It is a schematic diagram of the transformation of the UV sampling of the input Patch surface into the Grid surface provided in one embodiment of the present disclosure; Figure 3 It is a schematic diagram of transforming an optimized Grid surface provided in an embodiment of the present disclosure into a Patch surface through UV inverse sampling; Figure 4 is a flow chart of developable surface optimization under interactive input conditions provided in one embodiment of the present disclosure; Figure 5 is a schematic diagram of a developable surface design under drag interactive input in one embodiment of the present disclosure; Figure 6 is a schematic diagram of a 3D model slice developable approximation under interactive segmentation input in one embodiment of the present disclosure; Figure 7 It is a schematic diagram showing the process of model segmentation expandable approximation optimization in one embodiment of the present disclosure; Figure 8 It is a schematic diagram of the model printing and production process in one embodiment of the present disclosure. DETAILED DESCRIPTION

[0010] To further describe the present invention, the following Figures 1 to 8 Further explanation will be given.

[0011] In one embodiment, Figure 1 As shown, the present disclosure provides a developable surface optimization method based on deep learning, which includes the following steps: S100: Input the original Patch surface; S200: Flatten the patch surface by performing surface parameterization; S300: Perform UV plane sampling on the flattened Patch surface and convert it into a Grid surface with a regular topological structure; S400: using the Grid surface as a proxy surface and using a deep learning method to perform scalability optimization to obtain an optimization result; S500: optimizing the expandability of the original Patch surface by inverse sampling the optimization result.

[0012] As for this embodiment, based on this fast calculation, this method converts the design task of the developable surface into a real-time optimization task of the Patch surface under interactive dragging and deformation, and converts the piecewise developable surface optimization task into a piecewise developable surface optimization task under interactive input conditions, thereby providing higher optimization freedom and better optimization results.

[0013] This method first parameterizes the input Patch surface of arbitrary topology to obtain the corresponding 2D UV plane, and then converts it into a Grid surface with mask information through UV sampling. Then, the data-driven geometric constraint learning method GSO-Net network is used to achieve the expandability optimization of the surface. Finally, the optimized grid surface is subjected to UV sampling inverse transformation based on the relative position relationship of the sampling topology before optimization to obtain the expandability optimization result of the original Patch surface.

[0014] In another embodiment, the surface parameterization formula is:

[0015] where 𝑆 is the original Patch surface, is a parameterized function that maps S to the plane, are vertices on the three-dimensional patch, are the corresponding two-dimensional plane coordinates, Represents two-dimensional real number space.

[0016] In this embodiment, the data of the three-dimensional space is converted into the two-dimensional space by this method, and the topological structure is consistent. represents a two-dimensional real number space. f:S→ Represents a vector from set S to two-dimensional real space The mapping of Figure 2 Input Patch Surface in In the sampling conversion, the input patch surface and the corresponding flat.

[0017] In another embodiment, step S300 further includes: S301: Uniform sampling to obtain sampling points Yohara Relationship between planes:

[0018] in is the triangle index, Each sampling point The coordinates of the center of gravity of the triangle where , Is a function used to obtain the position of the corresponding point from the original Patch surface mesh; S302: Generate a corresponding mask image by judging the position of the sampling point; S303: Apply the triangle index and barycentric coordinates obtained from the two-dimensional UV plane sampling point to the three-dimensional surface to calculate the corresponding position of the corresponding sampling point in the three-dimensional space , get the three-dimensional surface sampling result; S304: Topologically generate the three-dimensional surface sampling result into a Grid surface.

[0019] In this embodiment, Figure 2 As shown, the input Patch surface UV sampling is transformed into a Grid surface. The following is the specific process: 1) Surface parameterization: 2) Uniform sampling: exist Figure 2 In the example, the corresponding parameterized plane is represented by Coordinate collection Definition, the resolution of the grid sampling is The sampling mask is , the value is A two-dimensional array of 0 values. The following is the formula for uniform sampling:

[0020]

[0021] in yes The range of the plane coordinates.

[0022] For each sampling point Find the coordinates of the center of gravity of the triangle in which it is located Position, satisfying the following equation:

[0023] Here, , , is the vertex in the triangle ABC where the sampling point is located Coordinates. For sampling points that are not in any triangle, the nearest triangle is selected to obtain the corresponding centroid coordinates. Through the above process, the sampling point can be obtained. Yohara Relationship between faces:

[0024] in It records the corresponding triangle index relationship.

[0025] 3) Sampling point judgment: In the above sampling coordinates, if the centroid coordinates are greater than or equal to 0, record the mask =1, otherwise = 0. For each cell The data in its field needs to be considered, which can be done by Apply logical operations to achieve expansion, each cell The mask value of needs to consider the union of the 8 points in its surrounding area. The calculation formula is as follows:

[0026] Corresponding to Figure 2 The UV plane is sampled in , and the corresponding mask image is generated by judging the position of the sampling point.

[0027] 4) Sampling point mapping: The triangle index and barycentric coordinate relationship obtained from the two-dimensional UV plane sampling point is applied to the three-dimensional surface to calculate the corresponding position of the corresponding sampling point in the three-dimensional space. :

[0028] This process is carried out through Figure 2 The corresponding UV plane sampling results and the input Patch surface are mapped to the sampling points, and the corresponding sampling points are displayed on the surface.

[0029] 5) Mesh topology generation: exist Figure 2In the process, the three-dimensional surface sampling results are topologically generated into a Grid surface.

[0030] The surface relationship and vertex position information of the Grid surface are as follows: The quadrilateral surface information at is:

[0031] The vertex information is obtained by arranging it in the order of expanding the two-dimensional N*N array.

[0032] In another embodiment, after the above surface sampling, the irregular Patch surface can be converted into a Grid surface with a regular topological connection relationship, and then encoded into a geometric image to design a surface optimization network GSO-Net network. The network input is the geometric image before optimization, and the output is the geometric image after optimization. The scalability optimization is performed through an end-to-end data-driven method. Figure 1 The upper part of the figure shows the end-to-end optimization process of geometric images using a learning-based method.

[0033] In another embodiment, step S500 further includes: S501: In UV plane sampling, obtain the position relationship of the original Patch surface mesh in the sampling triangle, and record the position relationship between the corresponding triangle mesh vertices and the sampling triangle:

[0034] S502: According to the above positional relationship, the optimized surface is inversely transformed to obtain a surface optimization result of the original Patch surface.

[0035] In this embodiment, Figure 3 As shown in the figure, the optimized Grid surface is transformed into a Patch surface through UV inverse sampling. The sampled Grid surface is used as an optimization medium, and after optimization, it is transformed into the optimized surface of the corresponding original input topology structure through inverse sampling transformation. The following is the specific process: 1) Topology conversion: exist Figure 3 In the example, the UV plane sampling result is first converted into an inverse sampling result, where the sampling points become the UV vertices corresponding to the original Patch surface vertices, and the sampling mesh topology is Figure 2 The generated Grid surface UV plane is then used to calculate the position relationship of the sampled vertices in the sampled triangle.

[0036] 2) Sampling point mapping: The triangle index and barycentric coordinate relationship obtained from the above two-dimensional UV plane sampling points are applied to the three-dimensional surface to calculate the corresponding position of the corresponding sampling point in the three-dimensional space. ,and Figure 2 The sampling point mapping operation in Figure 3 Displayed in.

[0037] 3) Mesh topology generation: Through the above process, the vertex position information of the optimized Patch surface can be obtained, and the corresponding surface information is consistent with the input Patch surface.

[0038] The sampling triangle is defined as the triangulated patch of the Grid surface obtained by the previous sampling. middle is a point, representing the corresponding Patch surface vertex on the UV plane. . : Represents the index of a triangle in the original Patch surface mesh. This index is used to identify a specific triangle in the original mesh. : These are the barycentric coordinates. : This is a function used to get the position of the corresponding point from the original Patch surface mesh.

[0039] In another embodiment, an interactive design method for a developable surface comprises the following steps: S601: according to the input patch surface, add control points to perform interactive dragging deformation to obtain the deformed surface; S602: Performing scalability optimization on the deformed surface using the method described in claim 1 to obtain a rough optimization result; S603: fine-tuning and optimizing the obtained rough optimization result using a traditional numerical optimization algorithm to obtain a fine optimization result.

[0040] In this embodiment, Figure 4 As shown in the figure, in the interactive design of developable surfaces, control points are first added to the input Patch surface for interactive dragging and deformation, and then developability optimization is performed according to the previously designed Patch surface optimization method. In this case, the rough optimization result is obtained. Figure 4 The curvature optimization of the dotted line part is to select secondary optimization after the interactive design is completed to obtain the optimized result. Figure 5 The developable surface design process under drag-and-drop interactive input is demonstrated in Figure 2.

[0041] Interactive control point dragging deformation surface module: In the design task of developable surface, the dragging deformation of the surface is used to optimize the surface in real time instead of the previous design of specific types of surfaces. By adding control points to the input Patch surface bounding box, the deformation of the surface area can be achieved by dragging the position of the control points. The specific process is as follows: Figure 5As shown, row (A) is the deformation of the surface achieved by dragging after adding control points, and row (B) is the optimization result of the corresponding deformed surface using the Patch surface optimization method.

[0042] Curvature optimization module: After obtaining the rough optimization results above, when considering the strict requirements of curvature in the application scenario, traditional numerical optimization algorithms can be used for fine-tuning optimization. In another embodiment, the optimization loss function of the traditional numerical optimization algorithm is as follows:

[0043] in is the discrete Gaussian curvature of all non-boundary vertices in the Patch surface, Represents the tangent plane distance calculated from the vertex to the closest point on the original model. , are the corresponding weight coefficients respectively.

[0044] In another embodiment, a method for interactive piecewise expandable approximation of a model comprises the following steps: S701: Interactively segment the model according to the input model to divide the model into blocks, each block is a separate Patch surface; S702: Optimize each patch surface individually using the method as claimed in claim 1; S703: merging the optimized patches using a boundary merging and smoothing method to obtain a rough optimized result; S704: performing post-processing operations on the rough optimization result to obtain a fine optimization result; S705: Printing and manufacturing the optimized detailed results.

[0045] In this embodiment, Figure 4 As shown, firstly, interactive segmentation is performed according to the input model to divide the model into blocks. Each block is a separate Patch surface. Then, the previous Patch surface optimization method is used for individual optimization. The designed boundary merging and smoothing method is used to merge the patches to obtain the optimized rough result. This process is real-time and interactive multiple times. Figure 6 This process is demonstrated, in which Figure 6 The (A) row in the figure is the interactive input segmentation to divide the model into blocks, and the (B) row is the corresponding optimization result. Finally, after the optimization, post-processing is performed to obtain the optimized result and then print it.

[0046] In another embodiment, the step S701 further includes: S7011: Perform initial semantic segmentation on the model according to the component segmentation method; S7012: Add segmentation paths to areas where the optimization result has a large approximation error, divide the area into more blocks, or fine-tune the segmentation paths.

[0047] In this embodiment, interactive segmentation input model blocks: the model is divided through interactive segmentation, and then optimized. Through the optimization, timely optimization result feedback is given, the segmentation path is increased or the segmentation path is fine-tuned to achieve better optimization results. The specific interactive process is as follows: First, the model is initially semantically segmented according to the component segmentation method, as follows: Figure 6 The initial segmentation column (A) is shown. Then, the segmentation path is increased where the optimization result has a large approximation error, and more blocks are divided. The segmentation path is fine-tuned through multiple interactions to achieve a better optimization result. Figure 6 shown.

[0048] In another embodiment, the step S703 further includes: S7031: For the vertices at the cut, the number of patches involved is calculated, and the average value of the corresponding vertex coordinates is obtained; S7032: Fine-tune the position of the vertices on the cutting edge so that the vertices on the edge and within one ring of the edge can be smoothly connected naturally.

[0049] In this embodiment, the boundary merging and smoothing processing module: under the interactive segmentation input condition, the entire three-dimensional model is divided into multiple patch surfaces, and then each patch surface is individually optimized for scalability and then merged and connected. The cut seam represents the boundary vertices left when the model is segmented previously. The average value is the position of the cut seam boundary vertex obtained in step S7032, which is used as a rough connection result and then smoothed. In mesh processing, a ring domain includes all vertices connected to the vertex through an edge.

[0050] In another embodiment, the post-processing operations include boundary optimization, curvature optimization, and block merging.

[0051] In this embodiment, the rough optimization of the model is performed in the previous step. In order to meet the curvature requirements of manufacturing and reduce the difficulty of manufacturing, post-processing operations are performed here, which mainly include boundary optimization, curvature optimization, and block number merging. Figure 7 This optimization process is demonstrated. Figure 7 The (B) row is the results of different stages of model processing, the (A) row is the Gaussian curvature distribution diagram of the corresponding (B) model, and the (C) row is the error distribution diagram from the input model to the corresponding (B) model.

[0052] Boundary optimization: By optimizing the position of the vertex at the slit boundary, three main factors are considered: ensuring the smoothness of the slit boundary to meet manufacturing requirements, minimizing the approximation error, and satisfying the Gaussian curvature optimization of non-boundary points within a ring around the slit. The specific calculation formula is as follows:

[0053] In the formula is the expandable energy based on discrete Gaussian curvature:

[0054] represents the smoothing energy associated with all the cut edges, which can be calculated by the average value of adjacent boundary vertices, Represents the tangent plane distance calculated from the vertex to the closest point on the original model. , , are the corresponding weight coefficients respectively.

[0055] Curvature optimization: After the above optimization, the next stage involves the optimization of internal vertices. Due to the independence of each internal vertex, parallel optimization is adopted, and local and global optimization techniques are used for each block. The Gaussian curvature threshold of all vertices inside the region is lower than the specified threshold. We set the threshold to 5e-4. The specific optimization steps are as follows: Evaluation of global optimization or local optimization in the initial stage: Determine the proportion of vertices in the block that meet the curvature threshold condition. If most of them meet the condition, which is set to 80% here, local optimization of the Gaussian curvature of the area around the maximum point is performed, otherwise global optimization is performed.

[0056] A numerical optimization method is used to perform a fixed number of optimizations. If the threshold condition of the maximum area value in the current block is met, the ongoing optimization process is terminated and the resulting deformation is generated.

[0057] If the maximum curvature of the new mesh decreases less than a certain proportion of the maximum curvature compared to the previous iteration, the current optimization state is evaluated. In the state of global optimization, it is converted to local optimization. For local optimization, re-meshing is performed in the local area based on the previous step.

[0058] Block merging: In order to reduce the number of final blocks, you can merge the segmentation boundaries with lower curvature, and then perform local optimization of the curvature to meet the curvature requirements. Figure 7 (d) to Figure 7 The process in (e) demonstrates this strategy, which greatly reduces the number of blocks.

[0059] In another embodiment, printing is performed. After the above optimization is completed, the optimized model is manufactured. Figure 8 The process of model making is shown in the figure. The specific processing steps are as follows: The first step is to use a parametric algorithm to perform block-by-block planar unfolding on the optimized model.

[0060] The unfolded plane is then processed to generate annotation lines corresponding to the boundaries.

[0061] Print onto paper, then use tools to cut the blocks.

[0062] Perform splicing and gluing to form a model.

[0063] In addition, the present invention also discloses a computer storage medium, wherein the storage medium includes computer instructions, and when the computer is run on the computer, the computer executes any of the methods described above.

[0064] In addition, the present invention also discloses an electronic device, wherein the electronic device comprises: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, any of the methods described above is implemented.

[0065] Although the embodiments of the present invention are described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments and application fields, and the above specific embodiments are only illustrative and instructive, rather than restrictive. A person of ordinary skill in the art can also make many forms under the guidance of this specification and without departing from the scope of protection of the claims of the present invention, all of which belong to the protection of the present invention.

Claims

1. A developable surface optimization method based on deep learning, comprising the following steps: S100: Input the original Patch surface; S200: Flatten the patch surface by performing surface parameterization; S300: Perform UV plane sampling on the flattened Patch surface and convert it into a Grid surface with a regular topological structure; S400: using the Grid surface as a proxy surface and using a deep learning method to perform scalability optimization to obtain an optimization result; S500: optimizing the expandability of the original Patch surface by inverse sampling the optimization result.

2. According to the method of claim 1, preferably, the formula for parameterizing the surface is: ； in is the original Patch surface, is a parameterized function that maps S to the plane, are vertices on the three-dimensional patch, are the corresponding two-dimensional plane coordinates, Represents two-dimensional real number space.

3. A computer storage medium, wherein: The storage medium includes computer instructions, and when the computer instructions are executed on the computer, the computer executes the method according to any one of claims 1 to 2.

4. An electronic device, wherein: The electronic device comprises: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method according to any one of claims 1 to 2 is implemented.

5. An interactive design method for a developable surface, the method comprising the following steps: S601: according to the input patch surface, add control points to perform interactive dragging deformation to obtain the deformed surface; S602: Performing scalability optimization on the deformed surface using the method described in claim 1 to obtain a rough optimization result; S603: fine-tuning and optimizing the obtained rough optimization result using a traditional numerical optimization algorithm to obtain a fine optimization result.

6. According to the method of claim 5, the optimization loss function of the traditional numerical optimization algorithm is as follows: ； in is the discrete Gaussian curvature of all non-boundary vertices in the Patch surface, Represents the tangent plane distance calculated from the vertex to the closest point on the original model. , are the corresponding weight coefficients respectively.

7. A computer storage medium, wherein: The storage medium includes computer instructions, which, when executed on a computer, enable the computer to execute the method according to any one of claims 5 to 6.

8. An electronic device, wherein: The electronic device comprises: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method according to any one of claims 5 to 6 is implemented.

9. An interactive piecewise expandable approximation method for a model, the method comprising the following steps: S701: Interactively segment the model according to the input model to divide the model into blocks, each block is a separate Patch surface; S702: Optimize each patch surface individually using the method as claimed in claim 1; S703: merging the optimized patches using a boundary merging and smoothing method to obtain a rough optimized result; S704: performing post-processing operations on the rough optimization result to obtain a fine optimization result; S705: Printing and manufacturing the optimized detailed results.

10. The method according to claim 9, wherein the post-processing operation comprises boundary optimization, curvature optimization and block number merging.

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