Pure quadrilateral partitioning intelligent generation method based on diffusion model

Abstract

The pure quadrilateral partition intelligent generation method based on the diffusion model comprises the following steps: S1, a global integer linear programming model containing a plurality of objective functions is constructed, and a quadrilateral grid which is symmetrical and aligned is generated by minimizing the objective function; S2, a two-dimensional contour graph of a CAD model is obtained according to an open source three-dimensional CAD model data set ABC; a triangular mesh model is generated according to the two-dimensional contour graph; S3, boundary fairing treatment is performed on the triangular mesh model, and hole digging and random segmentation are further performed in the interior; S4, a signed distance field is generated according to the triangular mesh model; a pure quadrilateral partition is extracted according to the quadrilateral grid; and a model outer contour image is obtained according to the pure quadrilateral partition; S5, a pure quadrilateral partition generation diffusion model is constructed; and the pure quadrilateral partition generation diffusion model is trained by using the signed distance field and the model outer contour image. The pure quadrilateral partition is rapidly generated, and the training time of the diffusion network model is greatly shortened.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of computer graphics and deep learning, in particular to a structured partition generation method and system for complex geometric models, which is used to improve mesh quality and numerical simulation efficiency. BACKGROUND

[0002] In the field of computer graphics and engineering simulation, quadrilateral mesh is widely used in finite element analysis, geometric modeling, animation production, etc. due to its advantages in boundary alignment, surface direction control, geometric precision and numerical calculation performance.

[0003] In the prior art, partition is a key step in the process of generating quadrilateral mesh. For complex geometric models, it is very difficult to directly generate a global quadrilateral mesh because multiple contradictory optimization objectives need to be met at the same time, such as uniformity of element size, optimization of element quality, rationality of topology structure, and boundary alignment. By dividing the model into multiple smaller partitions, each partition can generate a quadrilateral mesh independently, thus decomposing the complex global problem into multiple relatively simple local problems. After partitioning, each partition can generate mesh in parallel, thus speeding up the mesh generation and significantly improving the efficiency of mesh generation. In addition, quadrilateral mesh usually needs to be aligned with the boundary and direction of the model to ensure the geometric precision and numerical stability of the mesh. Partitioning can better achieve this alignment and direction control, thus generating high-quality quadrilateral mesh. Good partitioning should solve the quadrilateral as much as possible, but the number of partitions should be as small as possible.

[0004] However, generating high-quality pure quadrilateral partitions is a complex and challenging task, and traditional methods such as frame-based methods have the following problems:

[0005] (1) High computational complexity: the calculation of the frame field depends on the background triangular mesh, and needs to iteratively optimize the energy function, which is low in computational efficiency, especially when dealing with complex geometric models, the calculation time increases significantly.

[0006] (2) Unstable partition results: the solution of the frame field is easily affected by the quality of the background triangular mesh and the initial conditions, and the same geometric model may get different results under different mesh partitioning, which reduces the reliability and predictability of the method. SUMMARY

[0007] The present application first proposes a new technical route for pure quadrilateral partition generation by using diffusion model, which fully excavates the rich prior knowledge of the Stable Diffusion network pre-trained on massive data, realizes the rapid generation of pure quadrilateral partition of the model, greatly shortens the training time of the diffusion network model, and shows certain generalization ability.

[0008] The present application obtains a large number of three-dimensional models from an open source dataset ABC and converts them into symmetric plane models, generates symmetric pure quadrilateral partitions, optimizes a quadrilateral mesh algorithm to generate a quadrilateral mesh that is symmetric and aligned with singular points, and extracts Motorcycle Graphs as pure quadrilateral partitions in reverse. Experimental results show that the dataset generated by the present method enables the network to quickly generate pure quadrilateral partitions superior to traditional frame field methods, solves the limitations of existing technologies, and improves the consistency and stability of network output results.

[0009] To solve the above technical problems, the technical scheme adopted by the present application is:

[0010] The intelligent pure quadrilateral partition generation method based on a diffusion model comprises the following steps:

[0011] S1. Construct a global integer linear programming model on the basis of existing partitions, wherein the global integer linear programming model comprises multiple objective functions, and a quadrilateral mesh that is symmetric and aligned with singular points is generated by minimizing the objective functions;

[0012] S2. Obtain a two-dimensional contour map of a CAD model according to an open source three-dimensional CAD model dataset ABC; and generate a triangular mesh model according to the two-dimensional contour map;

[0013] S3. Perform boundary fairing processing on the triangular mesh model, and then perform hole digging and random partitioning inside the model;

[0014] S4. Generate a signed distance field according to the triangular mesh model; extract pure quadrilateral partitions according to the quadrilateral mesh; and obtain a model outer contour image according to the pure quadrilateral partitions;

[0015] S5. Construct a pure quadrilateral partition generation diffusion model; and train the pure quadrilateral partition generation diffusion model using the signed distance field and the model outer contour image.

[0016] Preferably, in step S3, 3-7 circular holes are dug inside the triangular mesh model relative to the geometric center position to simulate typical features such as cooling holes and weight reduction holes in the CAD model; and the spacing of the circular holes is limited to satisfy a minimum interval constraint d min ≥L, L is the minimum value of the length and width of the triangular mesh model; and the hole diameter of the circular holes is 0.08L-0.2L.

[0017] Preferably, the random partitioning in step S3 comprises: calculating a symmetry axis of the triangular mesh model, adding a random offset to the symmetry axis of the triangular mesh model in the normal direction of the triangular mesh model to obtain a new symmetry axis of the triangular mesh model; and partitioning the triangular mesh model along the new symmetry axis to obtain a left half, and then mirroring the right half to obtain a complete symmetric triangular mesh model.

[0018] Preferably, the resolution of the signed distance field and the model contour image is 512*512.

[0019] Preferably, the diffusion model for generating the pure quadrilateral partition comprises a variational autoencoder for encoding the pure quadrilateral partition and the signed distance field into a latent space.

[0020] Preferably, the model contour image and the signed distance field are spliced along the channel dimension to form a two-channel input image; and the two-channel input image is input to the variational autoencoder.

[0021] Preferably, the objective function comprises a parity constraint function, a consistency constraint function, a regularity constraint function, a singular point alignment constraint function, and a balance objective function; the balance objective function comprises an equality objective, a regularity objective, and a singular point alignment objective, and is weighted and summed by parameters.

[0022] Preferably, the two-dimensional contour image has multiple two-dimensional contour images; a symmetry detection algorithm is used to screen the two-dimensional contour images according to a preset symmetry threshold; the right half of the two-dimensional contour image is reserved by cutting the two-dimensional contour image along a two-dimensional model symmetry axis; and the triangular mesh model based on image pixels is extracted from the two-dimensional contour image.

[0023] The present application has the following advantages:

[0024] 1. Unlike existing pure quadrilateral partition generation methods, the present application uses an end-to-end mapping technology of a deep learning model to avoid complex frame field calculation and dependence on background triangular meshes, greatly reducing the consumption of computing resources. The present application can generate high-quality structured partitions in a very short time. Experiments show that the pure quadrilateral partition generation method based on the diffusion model takes only about one tenth of the time of the traditional frame field method, significantly improving the processing efficiency.

[0025] 2、 Unlike existing pure quadrilateral partition generation methods, the present application generates diversified training data through operations such as hole digging and random division inside the model. The quadrilateral mesh generation algorithm is improved to effectively generate quadrilateral meshes that are symmetric about singular points and aligned. The technical solution of extracting MotorcycleGraphs from the quadrilateral meshes that are symmetric about singular points and aligned as the model partition standard for network learning is innovatively adopted, so that the generated partition shape is regular, the boundary is clear, and the number is as few as possible. It is significantly better than the traditional frame field method, and exhibits good generalization ability on symmetric and asymmetric models, and can handle various complex geometric features. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 The pure quadrilateral partition generation network structure based on Stable Diffusion of the embodiment 1 of the present application;

[0027] Figure 2 The technical solution flowchart of the embodiment 1 of the present application;

[0028] Figure 3 The singular point alignment constraint example of the embodiment 1 of the present application;

[0029] Figure 4 The main process of obtaining training data of the embodiment 1 of the present application;

[0030] Figure 5 The schematic diagram of forming a plurality of similar models by hole digging in the same model of the embodiment 1 of the present application;

[0031] Figure 6 The model schematic diagram expanded by cutting of the embodiment 1 of the present application;

[0032] Figure 7 The quadrilateral partition result schematic diagram of the embodiment 1 of the present application based on the frame field (left) and network intelligent generation (right) model;

[0033] Figure 8 The generalization ability schematic diagram of the embodiment 1 of the present application of the test network to the CAD model. DETAILED DESCRIPTION

[0034] In order to make the technical means, creative features, purposes and effects realized by the invention easy to understand, the present application will be further described in combination with specific drawings. However, the present application is not limited to the following embodiments.

[0035] It is to be understood that the structures, proportions, sizes, etc. shown in the drawings accompanying the present specification are merely intended to facilitate the understanding of the content disclosed in the present specification for those skilled in the art to understand and read, and are not intended to limit the defined conditions under which the present application can be implemented, and therefore do not have technical significance. Any modification of the structure, change of the proportional relationship or adjustment of the size, without affecting the effect and purpose that can be achieved by the present application, should still fall within the scope covered by the disclosed technology content of the present application.

[0036] In recent years, deep learning technology has made significant progress in image processing and model processing. Diffusion models, through the progressive generation paradigm, have shown strong generation capabilities in image generation, video generation, and three-dimensional model generation tasks. The present application innovatively proposes using a diffusion model to intelligently generate partitions for geometric models. By inputting the boundary information and internal features of the geometric model in the form of an image, the diffusion model can learn the mapping relationship from geometric features to partition results, thereby achieving efficient and stable partition generation, providing a new method for automatic partition generation of geometric models.

[0037] Embodiment 1:

[0038] As shown in Figure 1 , the present application proposes a pure quadrilateral partition generation network structure based on Stable Diffusion. This structure makes full use of the rich prior knowledge contained in the latent space of the Stable Diffusion model pre-trained on massive data, effectively recovering clear partition information from noisy data.

[0039] As shown in Figure 2 , a pure quadrilateral partition intelligent generation method based on diffusion model (Stable Diffusion) includes the following steps:

[0040] Step S1, optimize the quadrilateral mesh generation algorithm to generate a quadrilateral mesh that is symmetric about singular points and aligned;

[0041] In order to generate a quadrilateral mesh that is symmetric about singular points and aligned, the present application constructs a global integer linear programming (ILP) model to determine the discrete grid edge number of each partition line based on the partition obtained by the traditional method. The ILP model optimizes the topology of the quadrilateral mesh by defining multiple objective functions and minimizing the objective functions, ensuring the symmetry and alignment of the singular points. The specific objective functions include:

[0042] S1-1, parity constraint: In the process of generating a quadrilateral mesh, the total number of discrete segments of the partition edge must be even to ensure topological closure. Therefore, a forced parity constraint is imposed on each boundary edge group of the partition to ensure that a quadrilateral mesh can be produced subsequently.

[0043] S1-2, consistency constraint: the deviation between the actual number of discrete segments of each partition edge and the preset ideal value is quantified by a weighted penalty term to optimize the regularity of the grid structure:

[0044]

[0045] where e i represents the ideal number of discrete grid segments of the i th edge.

[0046] S1-3, regularity constraint: the definition of the objective function for different edge number partitions is the sum of the absolute values of the edge discrete segment difference.

[0047] The regularity objective function of the three-edge partition:

[0048]

[0049] The regularity objective function of the four-edge partition:

[0050]

[0051] The regularity objective function of the five-edge partition:

[0052]

[0053] For the particularity of the hexagonal partition, the application proposes an additional constraint condition: the sum of the number of three interval edges of the partition needs to meet the parity matching. Specifically, if the sum of the number of three interval edges is odd, then the sum of the number of the remaining three edges also needs to be odd, and vice versa. For this purpose, a binary auxiliary variable 0,1} is introduced, whose value corresponds to the parity state of the sum of the interval edges. By adding the parity constraint term of this variable to the objective function, the regularity condition of the hexagon can be forced to be met. Finally, the regularity objective function of the hexagonal partition can be formalized as:

[0054]

[0055] where ,h∈Z.

[0056] S1-4, singularity alignment objective: this objective requires that the singular points in the generated quadrilateral grid are as aligned as possible with each other, and the objective aims to align the singular points in two adjacent non-quadrilateral partitions with each other, so as to efficiently extract high-quality partitions with symmetry and fewer partitions in the quadrilateral grid in the subsequent process.

[0057] Take two opposite T-free partitions as an example (this objective function is not applicable to partitions containing T-type nodes, T-type partitions are a special type of mesh elements, in which one edge is shared by two other edges, forming a shape similar to the letter "T". This type of partition may introduce some discontinuities or irregularities in the mesh, thereby affecting the quality of the mesh and subsequent calculation and analysis.), respectively on the opposite sides of the i-th edge and the j-th edge of the partition, the present application introduces the following penalty term to ensure that the topological lines flowing out of the singular points of the two partitions can be aligned with each other, thereby generating a singular point aligned quadrilateral mesh. Figure 3 An example of this case is shown.

[0058]

[0059] wherein, represents the number of discrete mesh segments of the side edge of the first partition, represents the number of discrete mesh segments of the side edge of the second partition.

[0060] In addition, considering the symmetry of the partition, the partitions on both sides of the symmetry axis are adjacent and have the same number of edges, so the above formula is multiplied by a weight :

[0061]

[0062] wherein Ni represents the number of edges of one of the partitions, and Nj represents the number of edges of the adjacent partition.

[0063] S1-5, balance objective function: the final balance objective function is composed of the equality objective, the regularity objective and the singular point alignment objective, and is weighted and summed by parameters:

[0064]

[0065] wherein in the present application, and The ratio of the two parameters is about 1:50.

[0066] Step S2, based on the open source three-dimensional CAD model dataset ABC (A Big CAD Model Dataset), a plurality of two-dimensional contour maps are obtained, and symmetric contours are screened based on the two-dimensional contour maps to generate a rough triangular mesh model;

[0067] The complex three-dimensional model in the open source dataset ABC is converted into a symmetric two-dimensional model, which prepares for the subsequent generation of symmetric pure quadrilateral partitions, so as to evaluate the quality of the generated partitions, and at the same time improves the consistency and stability of the network output results. As Figure 4 shown, the specific implementation steps of the present application for obtaining a triangular mesh model are as follows:

[0068] S2-1, 3D to 2D projection: Orthogonal projection of the 3D model obtained from the open-source 3D CAD model dataset ABC on three coordinate planes (XOY, XOZ, YOZ) to generate the corresponding 2D contour map.

[0069] S2-2, Symmetry detection: Using a symmetry detection algorithm, according to the preset symmetry threshold, filter out the 2D images with higher symmetry.

[0070] S2-3, Image cropping: Crop the filtered 2D image along the model symmetry axis, and only keep the right half for subsequent symmetry operation.

[0071] S2-4, Extract the jagged rough triangular mesh model based on the image pixel points from the cropped 2D image.

[0072] Step S3, Boundary smoothing of the triangular mesh model, and hole digging and random segmentation inside the triangular mesh model to further enhance the diversity and complexity of the data; remeshing and boundary Laplacian smoothing of the triangular mesh model in step S2 to improve the mesh quality. According to the relative position of the model, some circular holes are dug inside the triangular mesh model, and the triangular mesh model is randomly cut, then symmetrized to form a triangular mesh model with a new outer contour.

[0073] S3-1, Model internal hole generation: By digging N [3,7] (one geometric center is dug, and the remaining holes are symmetrically distributed relative to the geometric center) circular holes in the relative geometric center position of the triangular mesh model, to simulate typical features such as cooling holes, weight reduction holes, etc. in most CAD models, as shown in Figure 5 According to the normalized coordinates of the model geometric center, the hole spacing is limited to satisfy the minimum interval constraint d min ≥ L (L is the minimum value of the length and width of the triangular mesh model), to avoid hole overlap or edge collapse. Randomly set the hole diameter r [0.08L, 0.2L].

[0074] S3-2, Symmetry axis cutting extension: Calculate the symmetry axis A main of the triangular mesh model, and take a random offset ∆A in its normal direction to get a new symmetry axis A cut :

[0075]

[0076] where ∆A (−0.3L, 0.3L), cut the triangular mesh model along the Acut After splitting the left half, the remaining right half is mirrored to form a complete symmetric triangular mesh model, as shown in Figure 6 .

[0077] This method can generate a series of new triangular mesh models with similar but not identical geometric features, not only significantly increasing the size of the dataset, but also providing more diverse training samples for the neural network, effectively increasing the diversity of the dataset, helping to improve the model's generalization ability for different geometric characteristics, and thus improving the robustness of the model's intelligent partition generation. It is worth noting that the singular structures around the holes often exhibit certain regularity and repeatability. These features are valuable learning materials for deep learning, as they provide explicit spatial relationships and geometric constraints, helping the model to learn more accurate and robust representations, and thus better understand and represent the distribution of complex singular structures;

[0078] Step S4, based on the triangular mesh generation model Symbol distance field map and singular point symmetric and aligned quadrilateral mesh, construct pure quadrilateral partition from the quadrilateral mesh;

[0079] Based on the triangular mesh model obtained in step S3, generate a triangular mesh-based signed distance field and a 512*512 image as input for the subsequent network;

[0080] The triangular mesh model-based signed distance field generation step of the present application is as follows:

[0081] Input: closed two-dimensional triangular mesh model Output: signed distance field with image resolution of

[0082] S4-1, the specific implementation process of the triangular mesh-based signed distance field generation algorithm is as follows:

[0083] 1. Based on the bounding box calculation of the triangular mesh vertex:

[0084] , , ,

[0085] Where V is the set of triangular mesh vertices

[0086] 2. Define pixel coordinates , and scale the coordinates of the vertices in the bounding box to the plane, where:

[0087] 3. Nearest triangular face search:

[0088] ​Traverse the triangle facets, if inside the model (determined by the triangle normal direction: ) calculate the projection distance to ; if outside the model, directly set the distance to

[0089] 4. Triangle projection distance calculation (for triangle and point ), calculation steps:

[0090] Calculate the vector formed by the three edges of the triangle:

[0091] Calculate the barycentric coordinates :

[0092]

[0093] If :

[0094] Otherwise, calculate the shortest distance from to the three edges according to the next step.

[0095] 5. Edge projection distance calculation (for edge and point ) the projection of point is:

[0096]

[0097] where,

[0098]

[0099]

[0100] ​​S4-2, according to step S1 optimized quadrilateral mesh algorithm, the generation of singular point symmetry and alignment of quadrilateral mesh, from the quadrilateral mesh extraction Motorcycle Graphs as the model of pure quadrilateral partition. Motorcycle Graphs with traditional frame field of pure quadrilateral partition is basically the same, and from the quadrilateral mesh extraction partition, naturally have the advantage of close to quadrilateral, meet the basic requirements of partition. Motorcycle Graphs is based on quadrilateral mesh construction. Its core idea is to use the singular points and boundary concave points in quadrilateral mesh as starting point, from these key positions, along the edge of quadrilateral mesh launch “motorcycle”. These “motorcycle” in the grid along the pre-defined path movement, the choice of path based on the topological structure and geometric characteristics of quadrilateral mesh. In the process of movement, “motorcycle” will continue to track the boundary and internal structure of the grid, until they encounter the boundary of the model or with other “motorcycle” path collision. These closed path will divide the whole model into several sub regions. The boundary of each sub region is defined by the path of “motorcycle”, since these paths are based on quadrilateral mesh, therefore ensure that the shape of the partition as close to quadrilateral as possible.

[0101] Based on quadrilateral mesh Motorcycle Graphs construction steps as follows:

[0102] Input: singular point symmetry and alignment of quadrilateral mesh

[0103] Output: the model Motorcycle Graphs with image resolution

[0104] 1. System initialization to establish the visited quadrilateral mesh vertex set Vvisited, initially all the singular points (degree is not 4 vertex) and concave points (degree greater than 2 boundary point) join; to establish the visited quadrilateral edge set Evisited, initially all the boundary edge join; to establish the current processing of extended edge queue Qcurrent, all the singular point issued edge as the initial element; to establish the next round of processing of extended queue Qnext, initialization is empty set ∅;

[0105] 2. Loop processing extended edge to determine whether the current processing queue Qcurrent is empty: if Qcurrent is not empty, then execute steps 3 to 11 of the loop processing;

[0106] 3. Edge element traversal from Qcurrent in turn take each edge e=(u,v) for processing;

[0107] ​4. Find the next unvisited grid vertex w along the edge e direction, i.e. w is not in Vvisited; if there is no vertex w that meets the condition, skip the current edge processing, return to step 3 to process the next edge;

[0108] 5. Find the next extended edge according to the adjacent quadrilateral face of the edge Find the adjacent face of the edge e according to the edge e So that , ; determine the next edge e' = (w, x) according to the topological relationship of the face;

[0109] 6. Queue update Add the successor edge e' to the next round processing queue Qnext;

[0110] 7. Access state marking Add the vertex w to the visited vertex set Vvisited; add the current edge e to the visited edge set Evisited;

[0111] 8. Motorcycle edge record Store the ordered edge pair (e, e') in the output edge set Emotor;

[0112] 9. Single edge processing Complete the current edge e processing, return to step S103 to continue processing the next edge in the queue;

[0113] 10. Processing round update Assign Qnext queue to Qcurrent; reset Qnext to empty set ∅;

[0114] 11. Algorithm termination When Qcurrent is empty, the algorithm ends; output the final Emotor as the edge set constituting the Motorcycle Graphs, and the Motorcycle Graphs and the boundary edge of the model divide the entire model into multiple closed quadrilateral regions, which are the final model quadrilateral partitions. After obtaining the edge set of the Motorcycle Graphs, according to the first two steps of the symbolic distance field method, draw the Motorcycle Graphs into an image with a resolution of .

[0115] The Motorcycle Graphs obtained through the above steps can efficiently extract the partition boundaries from the quadrilateral mesh. These partition boundaries not only have a clear geometric meaning, but also are closely related to the singular points and boundary concave points of the quadrilateral mesh, thereby ensuring the rationality and effectiveness of the partition.

[0116] Step S5, construct and train the pure quadrilateral partition generation diffusion model proposed in the application.

[0117] The application converts the discretized triangular mesh model into a fixed 512x512 resolution model signed distance field (SDF) image and a model outer contour image suitable for network input of the diffusion model, fundamentally eliminating the expression uncertainty caused by the difference in triangular mesh discretization of the same model. The entire topological and boundary information of the geometry is encoded in the form of an image, so that mature high-performance image diffusion networks can be directly used for training and reasoning. The GPU parallel acceleration capability is fully utilized, and the data augmentation (rotation, scaling, cropping) cost is almost zero.

[0118] A pre-trained text-to-image latent diffusion model (LDM) is used, and it is fine-tuned to adapt to the partition intelligent generation task. The architecture includes a frozen variational autoencoder (VAE) that encodes the model contour map (after extracting the model boundary edges, the model is scaled to the image in the same way as the MotorcycleGraphs image is generated) and the signed distance field map into the latent space to train the conditional denoising diffusion model. Since the VAE encoder is originally designed for single-channel input, and the input data of the application includes two single-channel images (i.e., the boundary map and the signed distance field map), the application concatenates the two single-channel images along the channel dimension to form a double-channel input.

[0119] During the denoising process, the application modifies the U-Net structure to realize conditional encoding of the image, thereby significantly improving the training efficiency and maintaining the ability to generate high-resolution images. Specifically, this improvement enables the model to better handle complex geometric information and speeds up the convergence rate while ensuring the generation quality, as shown in Figure 7 Fig. 4. The average time for generating quadrilateral partitions is 43 seconds (about 10,000 triangular mesh units) for the traditional frame field, while the application method tested on an Inteli9-12900K+RTX 4090 takes only about 2.3 seconds on average. This method not only simplifies the processing flow of input data, but also enhances the adaptability and robustness of the model to different geometric structures, as shown in Figure 8 Fig. 5, providing strong support for generating quadrilateral partitions.

Claims

1. A method for pure quadrilateral partitioning intelligent generation based on diffusion model, characterized in that, The method comprises the following steps: S1, constructing a global integer linear programming model on the basis of existing partitions, the global integer linear programming model containing multiple objective functions, and generating a quadrilateral grid with symmetrical singular points and alignment by minimizing the objective functions; S2, obtaining a two-dimensional contour graph of a CAD model according to an open source three-dimensional CAD model dataset ABC; generating a triangular mesh model according to the two-dimensional contour graph; The objective functions include: S1-1, parity constraint: the total number of discrete segments of each partition edge is even; S1-2, consistency constraint: quantifying the deviation between the actual number of discrete segments of each partition edge and the preset ideal value by a weighted penalty term, and formalized as: ； wherein, represents the ideal number of discrete mesh segments of the ith edge, represents the actual number of discrete meshes of the ith edge; S1-3, regularity constraint: defining the sum of the absolute values of the differences in the number of discrete segments of different edges for each partition; ； ； E reg3 a regularity constraint function representing a three-edge partition, where, , respectively represent the actual discrete grid numbers of the two edges adjacent to the i-th edge. E reg5 a regularity constraint function representing a pentagonal partition, where, , , , respectively represent the actual discrete grid numbers of the four edges adjacent to the ith edge. In a hexagonal partition, if the total number of the three interval edges is odd, then the total number of the remaining three edges is also odd, and vice versa, formalized as: ； E reg6 regularity constraint function representing the hexagonal partition, where, , respectively represent the actual discrete grid numbers of the two edges adjacent to the ith edge, and α, β are weight coefficients; , is an integer set; S1-4, singular point alignment objective: the singular points in two adjacent non-quadrilateral partitions in the quadrilateral grid are aligned with each other; ； wherein E s , respectively represent the number of side discrete mesh segments of the i-th edge, the i+2-th edge of the first partition, respectively represent the number of side discrete mesh segments of the j-th edge, the j+1-th edge of the second partition; S1-5, balanced objective function: composed of the consistency constraint, the regularity constraint, and the singular point alignment objective, and weighted and summed by parameters: ； wherein, , is a weight coefficient for adjusting the regularity constraint function E reg +E s the degree of influence in balancing the objective function, is a weight coefficient for adjusting the equidistance objective function E iso the degree of influence in balancing the objective function; S3, performing boundary fairing processing on the triangular mesh model, and then performing hole digging and random segmentation in the interior thereof; S4, generating a signed distance field according to the triangular mesh model, extracting a pure quadrilateral partition according to the quadrilateral grid, and obtaining a model outer contour image according to the pure quadrilateral partition; S5, constructing a pure quadrilateral partition generation diffusion model, and training the pure quadrilateral partition generation diffusion model by using the signed distance field and the model outer contour image.

2. The method of claim 1, wherein, In the step S3, 3-7 circular holes are dug in the relative geometric center position inside the triangular mesh model to simulate the typical features of the cooling holes and weight-reducing holes in the CAD model; the interval of the circular holes is limited to meet the minimum interval constraint d min The minimum value L of the length and width of the triangular mesh model; the aperture of the circular hole is 0.08L-0.2L.

3. The method of claim 2, wherein, The random segmentation in the step S3 comprises: calculating a symmetry axis of the triangular mesh model, adding a random offset in the normal direction of the triangular mesh model to the symmetry axis of the triangular mesh model to obtain a new symmetry axis of the triangular mesh model, and segmenting the left half of the triangular mesh model along the new symmetry axis of the triangular mesh model, and then mirroring the remaining right half to obtain a complete symmetrical triangular mesh model.

4. The method of claim 1, wherein, The resolution of the signed distance field and the model outer contour image is 512*512.

5. The method of claim 4, wherein, The pure quadrilateral partition generation diffusion model comprises a variational autoencoder for encoding the pure quadrilateral partition and the signed distance field into a latent space.

6. The method of claim 5, wherein, The model outer contour image and the signed distance field are spliced along the channel dimension to form a two-channel input image; and the two-channel input image is input into the variational autoencoder.

7. The method of claim 1, wherein, The objective functions include a parity constraint function, a consistency constraint function, a regularity constraint function, a singular point alignment constraint function, and a balanced objective function; the balanced objective function is composed of an equality objective, a regularity objective, and a singular point alignment objective, and is weighted and summed by parameters.

8. The method of claim 1, wherein, The two-dimensional contour maps are multiple; a symmetry detection algorithm is used to screen the two-dimensional contour maps according to a preset symmetry threshold; the two-dimensional contour maps after screening are cut along a two-dimensional model symmetry axis, and only the right half of the two-dimensional contour maps is reserved; The triangular mesh model based on image pixels is extracted from the two-dimensional contour maps after cutting.

Images