A quadrilateral mesh generation method, system, device, medium and product

Abstract

This application discloses a quadrilateral mesh generation method, system, device, medium, and product, involving the intersection of CAGD, BIM, and digital intelligent manufacturing technologies. The method includes: performing tolerance Boolean stitching on a base surface to generate a physical reference surface; constructing projection rays from each target control point in a spatial target control point set to the physical reference surface along a preset direction, extracting the projection intersection point with the closest Euclidean distance to the target control point to obtain a target projection point array; generating an initial pure quadrilateral base mesh architecture that retains the geometric hard edge characteristics based on an adaptive quadrilateral mesh discretization method; performing topological depth soft decay adsorption based on generalized priority search to generate an adsorbed deformation mesh; performing local Laplacian slight topological relaxation constrained by the physical reference surface; re-recording the algorithm line vectors; and determining the final quadrilateral mesh. This application can output a final quadrilateral mesh that combines extremely high aesthetic quality with engineering practicality.

Description

Technical Field

[0001] This application relates to the intersection of Computer-Aided Geometric Design (CAGD), Building Information Modeling (BIM), and digital intelligent manufacturing technologies, and in particular to a method, system, device, medium, and product for generating quadrilateral meshes. Background Technology

[0002] In the design of modern large-span buildings, irregular curtain wall projects, freeform roofs, and aerospace shells, the digital discretization and panel division of freeform surfaces are core preprocessing steps. Compared to triangular meshes, quadrilateral meshes have become the preferred discretization model in high-end construction and manufacturing industries due to their better mesh flow, easier conversion to T-Spline or NURBS surfaces, and easier flat-panel manufacturing in practical engineering.

[0003] However, existing quadrilateral mesh generation algorithms face extremely serious technical challenges in practical large-span engineering applications: 1. Topological distortion caused by forced attachment of target positioning points (such as the top of support columns): In actual engineering, there are usually specific structural support columns or load-bearing hinge points below the curved surface of the roof. Existing mesh generation algorithms, if they want to force a certain associated node to align with these spatial points, usually use the hard stretching of absolute coordinates. This operation will instantly destroy the local orthogonality and area uniformity of the quadrilateral mesh, resulting in severe self-intersection, creases and extremely distorted elements in the mesh, causing the finite element force transmission matrix to break.

[0004] 2. Lack of a flexible transition mechanism based on mesh topology: Traditional mesh deformation techniques typically rely on attenuation control based on three-dimensional Euclidean distance. However, on highly curved surfaces, the actual mesh topology paths of points with similar Euclidean distances on the surface can be extremely long. Deformation based on spatial distance can lead to "mold-through" or incorrect cross-layer linkage, failing to achieve a smooth and flexible transition along the surface.

[0005] 3. Mesh relaxation and disconnect from the original design intent: When smoothing a mesh that has undergone local deformation, conventional Laplacian smoothing will cause the overall mesh volume to shrink, resulting in the final panel deviating from the initial precise outer contour (Brep Surface) designed by the architect or engineer.

[0006] Therefore, there is an urgent need to develop a quadrilateral mesh generation method that can intelligently identify target positioning points, utilize the mesh's own topological depth for flexible attenuation deformation, and remain absolutely faithful to the original geometric boundaries during the smoothing process. Summary of the Invention

[0007] The purpose of this application is to provide a method, system, device, medium and product for generating quadrilateral meshes, which can output quadrilateral meshes with both high aesthetic quality and engineering practicality while ensuring that the overall flow direction of the high-quality quadrilateral mesh is not disrupted.

[0008] To achieve the above objectives, this application provides the following solution.

[0009] In a first aspect, this application provides a method for generating quadrilateral meshes, comprising the following steps.

[0010] Obtain the multi-parameterized basic surface and spatial target control point set, and perform tolerance Boolean stitching on the basic surface to generate a unique continuous physical reference surface.

[0011] A projection ray is constructed from each target control point in the spatial target control point set along a preset direction to the physical reference plane. The projection intersection point with the closest Euclidean distance to each target control point is calculated and extracted to obtain a target projection point array. The projection intersection point is the spatial intersection point of the projection ray and the physical reference plane.

[0012] Based on the physical reference surface, an initial pure quadrilateral basic mesh architecture that preserves the geometric hard edge characteristics is generated using an adaptive quadrilateral mesh discretization method.

[0013] Based on the target projection point array and the initial pure quadrilateral basic mesh architecture, a topological depth soft decay adsorption based on generalized priority search is performed to generate an adsorption deformation mesh.

[0014] Based on the adsorption deformation mesh, a local Laplacian slight topological relaxation constrained by the physical reference surface is performed, and the algorithmic line vectors are re-evaluated to determine the final quadrilateral mesh.

[0015] Secondly, this application provides a quadrilateral mesh generation system, including the following modules.

[0016] The physical reference surface generation module is used to obtain the multi-parameterized basic surface and the set of spatial target control points, and to perform tolerance Boolean stitching on the basic surface to generate a unique and continuous physical reference surface.

[0017] The target projection point array determination module is used to construct projection rays from each target control point in the spatial target control point set to the physical reference plane along a preset direction, calculate and extract the projection intersection point with the closest Euclidean distance to each target control point, and obtain the target projection point array; the projection intersection point is the spatial intersection point of the projection ray and the physical reference plane.

[0018] The initial pure quadrilateral basic mesh architecture determination module is used to generate an initial pure quadrilateral basic mesh architecture that retains the geometric hard edge characteristics based on the physical reference surface and an adaptive quadrilateral mesh discretization method.

[0019] The adsorption deformation mesh generation module is used to generate an adsorption deformation mesh by performing topological depth soft decay adsorption based on generalized priority search, according to the target projection point array and the initial pure quadrilateral basic mesh architecture.

[0020] The final quadrilateral mesh determination module is used to perform a local Laplacian slight topological relaxation constrained by the physical reference surface based on the adsorbed deformed mesh, and re-recognize the algorithm line vectors to determine the final quadrilateral mesh.

[0021] Thirdly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described quadrilateral mesh generation method.

[0022] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described quadrilateral mesh generation method.

[0023] Fifthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the above-described quadrilateral mesh generation method.

[0024] According to the specific embodiments provided in this application, this application has the following technical effects: Based on the generated physical reference surface, this application determines the target projection point array by constructing projection rays, generates an initial pure quadrilateral basic mesh architecture that retains the geometric hard edge characteristics based on the adaptive quadrilateral mesh discretization method, and introduces topological depth soft decay adsorption based on the target projection point array and the initial pure quadrilateral basic mesh architecture for the first time, generating an adsorbed deformation mesh. Under the premise of ensuring that the overall flow direction of the high-quality quadrilateral mesh is not destroyed, it can smoothly pull the locally related nodes to the target engineering point like a "magnet", and perform local Laplace mild topological relaxation limited by the physical reference surface according to the adsorbed deformation mesh to eliminate internal residual stress, and finally output a final quadrilateral mesh with both extremely high aesthetic quality and engineering practicality (absolute node alignment). Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a schematic diagram of a quadrilateral mesh generation method provided in Embodiment 1 of this application.

[0027] Figure 2 This is a flowchart illustrating another quadrilateral mesh generation method provided in Embodiment 2 of this application.

[0028] Figure 3 This is a schematic diagram of the influence layer provided in Embodiment 2 of this application.

[0029] Figure 4 This is a schematic diagram of the adsorption deformation mesh provided in Embodiment 2 of this application, which is based on traditional Euclidean hard adsorption and the topological depth soft decay adsorption based on generalized priority search of this application; wherein, Figure 4 (a) in the diagram is a schematic diagram of the adsorption deformation grid based on traditional Euclidean space hard adsorption. Figure 4 (b) is a schematic diagram of the adsorption deformation mesh of topological depth soft decay adsorption based on generalized priority search in this application. Detailed Implementation

[0030] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0031] To make the objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0032] Example 1 like Figure 1 As shown in the figure, this application embodiment provides a quadrilateral mesh generation method, including the following steps.

[0033] S1: Obtain the multi-parameterized basic surface and spatial target control point set, and perform tolerance Boolean stitching on the basic surface to generate a unique continuous physical reference surface.

[0034] S2: Construct projection rays from each target control point in the spatial target control point set to the physical reference plane along a preset direction, calculate and extract the projection intersection point with the closest Euclidean distance to each target control point, and obtain the target projection point array; the projection intersection point is the spatial intersection point of the projection ray and the physical reference plane.

[0035] S3: Based on the physical reference surface, an initial pure quadrilateral basic mesh architecture that preserves the geometric hard edge characteristics is generated using an adaptive quadrilateral mesh discretization method. Here, the geometric hard edge characteristics refer to boundaries or intersections where the normal vectors on the surface undergo abrupt changes.

[0036] S4: Based on the target projection point array and the initial pure quadrilateral basic mesh architecture, perform topological depth soft decay adsorption based on generalized priority search to generate an adsorption deformation mesh.

[0037] S5: Based on the adsorption deformation mesh, perform a local Laplacian slight topological relaxation constrained by the physical reference surface, and re-recalculate the line vectors to determine the final quadrilateral mesh.

[0038] In one exemplary embodiment, S1 specifically includes the following steps.

[0039] S11: Obtain the input multiparameterized base surface and spatial target control point set. The multiparameterized base surface is the set of entities in the multi-boundary representation (Brep).

[0040] S12: Set the geometric tolerance for the input Brep entity set and perform global Boolean merging to generate a unique and continuous physical reference surface.

[0041] In one exemplary embodiment, S2 specifically includes the following steps.

[0042] S21: For each free reference point in the set of spatial target control points, i.e., the target control point, construct a bidirectional infinitely long ray along the local normal or a specific global axis (such as the Z-axis), i.e., the projection ray. Calculate the spatial intersection of the projection ray with the physical reference plane, and extract the projection intersection point with the closest Euclidean distance to the free reference point as the mesh mapping projection point to obtain the target projection point array.

[0043] In one exemplary embodiment, S3 specifically includes the following steps.

[0044] S31: Extract the basic triangular mesh on the physical reference plane and eliminate normal breaks by welding the vertices.

[0045] S32: Invoke the adaptive quadrilateral re-meshing engine. Based on the set target mesh number and adaptive factor, and under the physical constraints of recognizing and preserving the hard edges of the original geometry, generate an initial pure quadrilateral basic mesh architecture with uniform overall flow and reasonable topological distribution.

[0046] In one exemplary embodiment, S4 specifically includes the following steps.

[0047] S41: Lock the anchor node on the initial pure quadrilateral basic mesh architecture that is closest to the target projection point and calculate the displacement compensation vector.

[0048] S42: Using the nearest anchor node as the origin, perform a generalized priority search based on the grid edge connection topology to diffuse outwards to determine the topological level depth of each associated node.

[0049] S43: Calculate the deformation weight based on the topological hierarchy depth, apply the displacement compensation vector to the associated node, and project the node that has generated displacement back onto the physical reference plane to generate an adsorption deformation mesh.

[0050] In one exemplary embodiment, S42 specifically includes the following steps.

[0051] S421: Set the parameter R for the maximum topological influence layer.

[0052] S422: Based on the maximum topological influence layer parameter R, search for connected nodes through the associated node retrieval interface, and record the current search topological layer depth d during the search process.

[0053] S423: When the current search topology level depth d reaches the maximum topology influence circle parameter R, actively truncate and stop the continued traversal search of the current branch, and determine the topology level depth of each associated node.

[0054] In one exemplary embodiment, S43 specifically includes the following steps.

[0055] S431: Based on the current search topology level depth d and the maximum topology influence layer parameter R, calculate the normalized attenuation parameter, and use a nonlinear quadratic attenuation model to calculate the deformation weight W; W=(1-d / R) 2 .

[0056] S432: Based on the deformation weights, when any specific node in the initial pure quadrilateral basic mesh architecture is within the intersection region of the topological influence of multiple anchor nodes, obtain multiple attenuation weights obtained by the specific node from each anchor node; the specific node is an associated node located within the influence range of multiple anchor nodes.

[0057] S433: Based on the comparison results of multiple attenuation weights, apply a displacement compensation vector scaled by the maximum attenuation weight value to the associated node.

[0058] In practical applications, topological depth soft decay adsorption based on generalized priority search specifically includes the following steps.

[0059] Read the generated set of projection points and start the local soft deformation engine.

[0060] 1. Finding anchor nodes: Extract the vertex set of the initial pure quadrilateral basic mesh architecture to construct a point cloud index. Use the nearest point algorithm to find the original mesh node that is closest to the projection point as the anchor node, and calculate the three-dimensional spatial displacement vector of the anchor node to the projection point.

[0061] 2. Topology Depth Probing: Centered on the anchor node, the BFS algorithm is used to traverse the grid layer by layer based on the topological edge connections of the mesh objects. The number of traversed layers is recorded as the current topological depth d. The branch traversal terminates when d reaches the user-defined maximum topological influence layer parameter R.

[0062] 3. Quadratic Weight Decay: For any neighboring node visited, calculate its normalized decay parameter t = d / R. Apply a nonlinear quadratic decay model to allocate deformation weights: W = (1-t) 2 .

[0063] 4. Multi-source weight fusion and spatial displacement: If a certain associated node is simultaneously affected by multiple projected anchor nodes, the maximum attenuation weight value is extracted by comparison. The current coordinates of the associated node are then superimposed with a displacement compensation vector scaled by this maximum attenuation weight value.

[0064] 5. Deformation springback: After displacement occurs, the nearest point between the new node's spatial position and the physical reference plane is immediately calculated, and the node is forcibly snapped back to the original surface, thereby achieving compliant local deformation without detaching from the surface.

[0065] In one exemplary embodiment, S5 specifically includes the following steps.

[0066] S51: Based on the topological exposed edge state of the adsorption deformation mesh, extract all outer boundary nodes and merge all outer boundary nodes together with all initial anchoring nodes to generate an absolutely fixed constraint set.

[0067] S52: Based on the absolutely fixed constraint set, mark the nodes in the adsorption deformation mesh other than those in the absolutely fixed constraint set as free nodes.

[0068] S53: Based on the free node, calculate the spatial geometric center of the topological neighbor node to obtain the sliding vector.

[0069] S54: According to the sliding vector, the free node is allowed to slide towards the spatial geometric center of the corresponding topological neighbor node, and the spatial coordinates of the absolutely fixed constraint set remain unchanged in the sliding iteration loop.

[0070] In one exemplary embodiment, S54 specifically includes the following steps.

[0071] S541: After completing a single sliding calculation based on the sliding vector, the sliding transient point is obtained.

[0072] S542: Based on the physical reference plane, forcibly extract the closest point of the sliding transient point relative to the physical reference plane using Euclidean distance.

[0073] S543: Overwrite the coordinates of the sliding transient point with the coordinates of the nearest point in Euclidean distance, so as to realize the free node sliding towards the spatial geometric center of the corresponding topological neighbor node.

[0074] In practical applications, a local Laplacian mild topological relaxation is performed on the adsorbed deformed mesh that has undergone soft decay adsorption.

[0075] Extract the topologically exposed edge points and the anchored adsorption center points of the adsorption deformation mesh, and mark these two types of points as absolutely fixed constraint nodes.

[0076] For a free node outside the absolutely fixed constraint set, calculate the average centroid, i.e. the spatial geometric center, based on the spatial position of its first-order topological neighbor nodes, and make a small slip towards the centroid to obtain the slip vector.

[0077] After the glide, the nearest point projection function is called again to re-attach the free nodes to the physical reference plane surface. The global vertex normals are recalculated, and the final engineered mesh is output.

[0078] Example 2 To further clarify the mathematical and physical logic and practical engineering application value of this application, the following section, using the engineering scenario of "large-span spatial structure curved surface meshing combined with lower support columns" as an example, and comparing it with the core technical steps of this application, provides a detailed analysis of the underlying complete algorithm flow mechanism, such as... Figure 2 As shown.

[0079] Project Scenario Definition: A large exhibition center adopts a large-span single-layer freeform reticulated shell roof. The architect provided a complex hyperboloid appearance for the roof, which includes multiple spliced ​​Brep surfaces, i.e., multiple parametric base surfaces; at the same time, the structural engineer arranged dozens of independent support columns under the roof.

[0080] In finite element analysis and subsequent detailed fabrication of the nodes, the associated nodes of the roof must be precisely aligned with the center position of the column tops of these supporting columns. If there is a deviation between the associated nodes and the column positions, the support constraints will be suspended during structural analysis, and the mechanical transmission matrix will be broken.

[0081] Input: Geometry to be meshed.

[0082] Step 101: Geometric datum merging and spatial ray projection calculation.

[0083] Step 101 corresponds to the process of establishing a unified physical reference plane and capturing the structural column mapping points.

[0084] First, multiple roof surfaces are received from upstream. The geometric stitching tolerance is set to 0.01 mm. Then, the underlying surface topology merging interface (Brep.JoinBreps interface) is called to seamlessly stitch all discrete surfaces into a single watertight roof physical reference surface.

[0085] The system reads the set of three-dimensional coordinates (base_points) of the tops of dozens of supporting columns provided by the structural engineer. Since the column top coordinates may not perfectly fit the roof surface, the system constructs an infinitely long ray through the roof along the vertical Z-axis (or the direction of the main structural force) for each column top coordinate pt.

[0086] The spatial intersection engine (Intersection.CurveBrep) is invoked to calculate the intersection point of the ray with the overall roof physical reference plane. The system rigorously calculates the Euclidean distance from all intersection points to the original column top, extracts the spatial intersection point with the shortest distance as the "target projection point" of the column position on the roof, and stores it in the target projection point array.

[0087] Step 102: Adaptive construction of the base quadrilateral topology mesh.

[0088] Step 102 corresponds to generating an initial mesh architecture with a good overall flow direction.

[0089] The basic triangular mesh is extracted on the physical reference surface of the overall roof and vertex welding is performed. Then, the quad remesh engine is called, the expected number of roof panel divisions is set to target_count=5000, and the adaptive size parameter (AdaptiveSize=50) and hard edge detection (DetectHardEdges=True) are enabled.

[0090] Output an initial pure quadrilateral basic mesh architecture with uniform overall flow and good orthogonality. However, in this initial state, the vertices of the roof mesh are freely distributed according to geometric equal distribution logic, and the vast majority of associated nodes are not aligned with the "target projection points" (column positions) extracted in step 101.

[0091] Step 103: Topological depth soft decay adsorption based on BFS.

[0092] Step 103 involves flexibly pulling the associated nodes to the support column positions like a "magnet" without compromising the overall quality of the mesh.

[0093] 1. Finding Anchor Points: Traverse the array of cylindrical projection points generated in step 101, i.e., the target projection point array. For a given cylindrical projection point, quickly retrieve the original mesh node with the closest spatial distance from the vertex library of the basic mesh, lock it as the "anchor node", and calculate the three-dimensional spatial displacement compensation vector from this associated node to the cylindrical projection point.

[0094] 2. Topology Depth Detection: The influence ring number for local deformation of the column is set to influence_ring=4. The system uses the anchor node as the seismic source (current search topology depth d=0) and performs a generalized priority search based on the physical connectivity of the grid edges. It expands outward to first-order neighbors (d=1), second-order neighbors (d=2), until it reaches the set 4th ring, at which point the search for that branch is actively truncated, such as... Figure 3 As shown, the number of the influencing layers is represented by layer 1 to layer 4.

[0095] 3. Quadratic weight decay, and multi-source weight fusion and spatial displacement: For any surrounding related node affected by the search, based on the current search topology level depth d, the quadratic weight decay function W=(1-d / 4) is applied. 2 Assign centripetal deformation weights. Superimpose the attenuated displacement compensation vector onto the current coordinates of the associated node.

[0096] 4. Deformation Springback: After soft displacement, the mesh will be stretched locally in space. Immediately call the ClosestPoint function on the reference plane to force all nodes that have been displaced back to the overall roof physical reference plane determined in step 101.

[0097] Step 103 shows an extremely smooth geometric transition in the roof grid near the column location, and the center anchor point is absolutely aligned with the structural column location.

[0098] Step 104: Geometrically constrained topological relaxation and residual crease elimination.

[0099] Step 104 can release the local residual stress in the mesh caused by the traction deformation of the column and eliminate the micro-creases.

[0100] Set the number of Laplace relaxation cycles to smooth_steps=10.

[0101] Extract all topologically exposed outer boundary points (Naked Edges) of the roof mesh, along with the anchor nodes that have been accurately pulled to the support column positions in step 103, and add them all to the absolutely fixed constraint set. The coordinates of these points are completely locked during subsequent relaxation.

[0102] For freely associated nodes affected by the surrounding environment, the algorithm calculates the geometric centroid of its neighboring topological vertices and generates a small slip. After each slip, conformal projection (ClosestPoint) is performed again to unconditionally snap the transient node back onto the roof surface.

[0103] After 10 short-term relaxation cycles, all normals are recalculated. The final output roof quadrilateral mesh not only perfectly fits the complex hyperboloid designed by the architect, but also achieves precise topological alignment between the core mesh nodes and the bottom support columns. A comparison of the local orthogonality of the adsorption deformation mesh based on traditional Euclidean hard adsorption and the soft attenuation adsorption based on topological depth of this application is shown below. Figure 4 As shown in (a)-(b) in the figure.

[0104] Output: Final quadrilateral mesh.

[0105] Example 3 This application provides a quadrilateral mesh generation system, which includes the following modules.

[0106] The physical reference surface generation module is used to obtain the multi-parameterized basic surface and the set of spatial target control points, and to perform tolerance Boolean stitching on the basic surface to generate a unique and continuous physical reference surface.

[0107] The target projection point array determination module is used to construct projection rays from each target control point in the spatial target control point set to the physical reference plane along a preset direction, calculate and extract the projection intersection point with the closest Euclidean distance to each target control point, and obtain the target projection point array; the projection intersection point is the spatial intersection point of the projection ray and the physical reference plane.

[0108] The initial pure quadrilateral basic mesh architecture determination module is used to generate an initial pure quadrilateral basic mesh architecture that retains the geometric hard edge characteristics based on the physical reference surface and an adaptive quadrilateral mesh discretization method.

[0109] The adsorption deformation mesh generation module is used to generate an adsorption deformation mesh by performing topological depth soft decay adsorption based on generalized priority search, according to the target projection point array and the initial pure quadrilateral basic mesh architecture.

[0110] The final quadrilateral mesh determination module is used to perform a local Laplacian slight topological relaxation constrained by the physical reference surface based on the adsorbed deformed mesh, and re-recognize the algorithm line vectors to determine the final quadrilateral mesh.

[0111] Example 4 In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments. The computer device can be a server or a terminal. The computer device includes a processor, a memory, an input / output interface (I / O), and a communication interface. The processor, memory, and I / O interface are connected via a system bus, and the communication interface is connected to the system bus via the I / O interface. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The database of the computer device stores data to be processed. The I / O interface of the computer device is used for exchanging information between the processor and external devices. The communication interface of the computer device is used for communicating with an external terminal via a network connection. When the computer program is executed by the processor, it implements the above-described methods.

[0112] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0113] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0114] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0115] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by hardware related to computer program instructions. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0116] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0117] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0118] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for generating quadrilateral meshes, characterized in that, include: Obtain the multi-parameterized basic surface and spatial target control point set, and perform tolerance Boolean stitching on the basic surface to generate a unique continuous physical reference surface; Projection rays are constructed from each target control point in the spatial target control point set along a preset direction to the physical reference plane. The projection intersection points with the closest Euclidean distance to each target control point are calculated and extracted to obtain a target projection point array. The projection intersection point is the spatial intersection point of the projection ray and the physical reference plane. Based on the physical reference surface, an initial pure quadrilateral basic mesh architecture that retains the geometric hard edge characteristics is generated using an adaptive quadrilateral mesh discretization method. Based on the target projection point array and the initial pure quadrilateral basic mesh architecture, perform topological depth soft decay adsorption based on generalized priority search to generate an adsorption deformation mesh. Based on the adsorption deformation mesh, a local Laplacian slight topological relaxation constrained by the physical reference surface is performed, and the algorithmic line vectors are re-evaluated to determine the final quadrilateral mesh.

2. The quadrilateral mesh generation method according to claim 1, characterized in that, Based on the target projection point array and the initial pure quadrilateral basic mesh architecture, a topological depth soft decay adsorption based on generalized priority search is performed to generate an adsorption deformation mesh, specifically including: Lock the anchor node on the initial pure quadrilateral basic mesh architecture that is closest to the target projection point and calculate the displacement compensation vector; Using the nearest anchor node as the origin, a generalized priority search is performed based on the grid edge connection topology to diffuse outwards to determine the topological level depth of each associated node; The deformation weight is calculated based on the topological hierarchy depth, a displacement compensation vector is applied to the associated nodes, and the nodes that have generated displacement are projected back onto the physical reference plane to generate an adsorption deformation mesh.

3. The quadrilateral mesh generation method according to claim 2, characterized in that, Using the nearest anchor node as the origin, a generalized priority search is performed based on the grid edge connection topology to propagate outwards, determining the topological hierarchy depth of each associated node, specifically including: Establish the parameter R for the maximum topological influence layer; Based on the maximum topological influence layer parameter R, the connected nodes are searched through the associated node retrieval interface, and the current search topological layer depth d is recorded during the search process; When the current search topology level depth d reaches the maximum topology influence circle parameter R, the current branch is actively truncated and the traversal search is stopped to determine the topology level depth of each associated node.

4. The quadrilateral mesh generation method according to claim 2, characterized in that, Based on the aforementioned topological hierarchy depth, deformation weights are calculated, and displacement compensation vectors are applied to the associated nodes, specifically including: According to the current search topology level depth d and the maximum topology influence circle layer parameter R, the normalized attenuation parameter is calculated, and the deformation weight W is calculated by using a nonlinear quadratic attenuation model; W=(1-d / R) 2 ; Based on the deformation weights, when any specific node in the initial pure quadrilateral basic mesh architecture is located within the intersection region of the topological influence of multiple anchor nodes, multiple attenuation weights obtained by the specific node from each anchor node are acquired; the specific node is an associated node located within the influence range of multiple anchor nodes. Based on the comparison results of multiple attenuation weights, a displacement compensation vector scaled by the maximum attenuation weight value is applied to the associated node.

5. The quadrilateral mesh generation method according to claim 1, characterized in that, Based on the adsorption-deformed mesh, a local Laplacian slight topological relaxation constrained by the physical reference surface is performed, specifically including: Based on the topological exposed edge state of the adsorption deformation mesh, all outer boundary nodes are extracted, and all outer boundary nodes are merged together with all initial anchoring nodes to generate an absolutely fixed constraint set. Based on the absolutely fixed constraint set, nodes in the adsorption deformation mesh other than those in the absolutely fixed constraint set are marked as free nodes; Based on the free node, calculate the spatial geometric center of the topological neighbor node to obtain the sliding vector; According to the sliding vector, the free node is allowed to slide toward the spatial geometric center of the corresponding topological neighbor node, and the spatial coordinates of the absolutely fixed constraint set remain unchanged in the sliding iteration loop.

6. The quadrilateral mesh generation method according to claim 5, characterized in that, Based on the sliding vector, the free node is allowed to slide towards the spatial geometric center of its corresponding topological neighbor node, specifically including: After performing a single sliding calculation based on the sliding vector, the transient sliding point is obtained; Based on the physical reference plane, forcibly extract the closest point of the sliding transient point relative to the physical reference plane using Euclidean distance; The coordinates of the sliding transient point are overwritten with the coordinates of the Euclidean nearest point to enable the free node to slide toward the spatial geometric center of the corresponding topological neighbor node.

7. A quadrilateral mesh generation system, characterized in that, The quadrilateral mesh generation method according to any one of claims 1-6 includes: The physical reference surface generation module is used to obtain the multi-parameterized basic surface and the set of spatial target control points, and to perform tolerance Boolean stitching on the basic surface to generate a unique and continuous physical reference surface. The target projection point array determination module is used to construct projection rays from each target control point in the spatial target control point set to the physical reference plane along a preset direction, calculate and extract the projection intersection point with the closest Euclidean distance to each target control point, and obtain the target projection point array; the projection intersection point is the spatial intersection point of the projection ray and the physical reference plane. The initial pure quadrilateral basic mesh architecture determination module is used to generate an initial pure quadrilateral basic mesh architecture that retains the geometric hard edge characteristics based on the physical reference surface and an adaptive quadrilateral mesh discretization method. The adsorption deformation mesh generation module is used to perform topological depth soft decay adsorption based on generalized priority search to generate an adsorption deformation mesh according to the target projection point array and the initial pure quadrilateral basic mesh architecture. The final quadrilateral mesh determination module is used to perform a local Laplacian slight topological relaxation constrained by the physical reference surface based on the adsorbed deformed mesh, and re-recognize the algorithm line vectors to determine the final quadrilateral mesh.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the quadrilateral mesh generation method according to any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the quadrilateral mesh generation method as described in any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the quadrilateral mesh generation method as described in any one of claims 1-6.

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