A cad model simplification and repair method for intelligent decision making
By using reinforcement learning and geometric optimization algorithms, the optimal CAD model cleanup sequence is generated, which solves the problem of improper handling of redundant features in existing technologies, achieves efficient simplification and repair, and improves the efficiency and reliability of simulation analysis.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2026-01-21
- Publication Date
- 2026-05-15
AI Technical Summary
Existing technologies cannot intelligently decide the cleaning order in complex topologies, and cannot balance geometric accuracy and topological effectiveness when removing redundancy, resulting in unstable simulation analysis and wasted computing resources.
A reinforcement learning approach is used to generate the cleanup operation sequence. Combined with geometric deformation and topology optimization algorithms, the agent is trained using a deep reinforcement learning algorithm to generate the optimal cleanup operation sequence. A multi-objective weighted reward mechanism is used to guide the operation, and energy function optimization is used to repair redundant surfaces, ensuring the geometric accuracy and topological integrity of the model.
It achieves the goal of maximizing the preservation of design geometric features while simplifying the model topology, thereby improving the efficiency and reliability of simulation analysis and making it suitable for CAD model processing of high-end manufacturing products.
Smart Images
Figure CN121543373B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of computer-aided design and computer-aided manufacturing systems, and relates to a method for simplifying and repairing CAD models with intelligent decision-making. Background Technology
[0002] Computer-aided design systems have become a primary tool in modern product design, playing a crucial role, especially in the digital design and simulation (CAE) analysis of high-end manufactured products. However, original CAD models in engineering practice often contain redundant features. At the geometric and topological levels, they typically include numerous unnecessary or even harmful micro-features and redundant details for simulation analysis, such as extremely short edges, fragmented surfaces, small holes, small chamfers, and redundant control points. These redundant features can easily lead to mesh quality degradation or even generation failure during the mesh generation stage. They also force excessive mesh refinement, resulting in a sharp increase in computational scale and time, further causing instability in numerical results and distortion of physical meaning, severely restricting the efficiency and reliability of large-scale automated simulation processes.
[0003] To address these issues, engineering practice typically employs geometric cleanup and feature removal techniques to simplify and optimize the original CAD model. Current mainstream methods largely rely on pre-built rule bases and greedy processing strategies, using a series of threshold-based geometric criteria, such as sorting by side length, area, or angle, to progressively delete, merge, or collapse local features. However, these methods heavily depend on local heuristics, lacking a global consideration of the overall topology and the feasibility of subsequent operations. This often results in early local operations locking up the subsequent simplification space, or even introducing new geometric and topological anomalies. Regarding geometric deformation control, traditional feature removal operations often employ only simple projection or interpolation methods, lacking sufficient global error management and precision constraints on key feature regions. This can easily lead to the destruction of design intent and the accidental deletion of important feature boundaries. Furthermore, topological problems such as non-manifold edges, gaps, and degenerate surfaces generated during feature removal can also affect the reliability of subsequent CAE software recognition and simulation.
[0004] Therefore, the problem with existing technologies is that they cannot intelligently decide the cleaning order in complex topologies, and they cannot balance geometric accuracy and topological effectiveness when removing redundancy. Summary of the Invention
[0005] To address the aforementioned technical problems in the existing technology, this invention proposes a method for simplifying and repairing CAD models using intelligent decision-making, the specific technical solution of which is as follows:
[0006] A method for simplifying and repairing CAD models using intelligent decision-making, comprising:
[0007] Step 1: The user inputs CAD model information through the interactive interface of the CAD system, and the original CAD solid model is generated from the CAD model information;
[0008] Step 2: By designing geometric and topological redundancy rules, detect redundant topology in the CAD solid model, including redundant points, edges, and faces;
[0009] Step 3: For all redundant topologies detected in Step 2, use reinforcement learning to generate a cleanup operation sequence;
[0010] Step 4: Clean up the redundant topology of the model according to the cleanup operation sequence obtained in Step 3, use the optimization method based on geometric deformation and geometric feature control to merge the surfaces of the topology, and update the entire model.
[0011] Furthermore, in step 2, the boundary representation data structure of the CAD model is traversed. The geometric and topological redundancy rules are as follows: based on the set geometric threshold, it is determined whether the topological surface is redundant according to the aspect ratio and area; it is determined whether the topological edge is redundant according to the length of the topological edge and whether two adjacent surfaces are based on the same underlying surface; it is determined whether the topological point is redundant according to whether two adjacent edges are based on the same underlying curve.
[0012] Furthermore, step 3 specifically includes:
[0013] Step 3.1: Extract the topology of the current CAD model into graph structure data and use it as the state input to the agent in the reinforcement learning environment;
[0014] Step 3.2: Dynamic action selection based on mask constraints: The operation of the constraint agent on the CAD model defines the cleanup operation for each redundant topology as an optional action;
[0015] Step 3.3: The agent introduces a multi-objective weighted hybrid reward mechanism;
[0016] Step 3.4: Train the agent using a deep reinforcement learning algorithm, and then use the trained agent to output a cleanup operation sequence that maximizes the cumulative reward based on the current input state.
[0017] Furthermore, step 3.1 specifically includes:
[0018] Step 3.1.1: Traverse the boundary representation data structure of the CAD model, define each face as a node in the boundary representation attribute adjacency graph, and define the adjacent edges between faces as the connecting edges in the boundary representation attribute adjacency graph;
[0019] Step 3.1.2: Input the boundary representation attribute adjacency graph into the agent's graph neural network. Through a multi-layer message passing mechanism, aggregate the feature information of each node and its neighboring nodes, and finally generate a high-dimensional state vector representing the overall topological state and local geometric features of the current CAD model.
[0020] Furthermore, the hybrid reward mechanism in step 3.3 is specifically as follows:
[0021] Construct a reward function based on the quality of the CAD model, perform virtual meshing on the local area after the cleanup operation, calculate the scaling Jacobian determinant and aspect ratio of the mesh cells, and give a positive reward if the average mesh quality index of the local area improves after the cleanup operation.
[0022] If the cleanup operation results in topology errors or excessive geometric deformation, or if the number of operation steps is too high, a negative penalty will be imposed.
[0023] Furthermore, in step 3.4, a parameterized CAD model library containing multiple redundant features is constructed as a dataset input to the agent for training; the deep reinforcement learning algorithm uses the advantage function calculation to guide the agent's policy network update, and calculates a hybrid objective function including a pruning mechanism to achieve the training convergence of the agent.
[0024] Furthermore, the optimization method based on geometric deformation and geometric feature control in step 4 specifically includes:
[0025] Step 4.1: Classify redundant surfaces according to their geometric type, including: complex curved surfaces, planes, or quadratic surfaces;
[0026] Step 4.2: When the redundant surface is a plane or quadratic surface, the analytical method is directly used for fitting to quickly reconstruct the surface; when the redundant surface is a complex surface, the surface merging method based on energy function optimization is adopted, and a surface directly adjacent to the redundant surface is selected as the reference surface. The parameter domains and geometric features of the two are jointly repaired to obtain a new surface.
[0027] Step 4.3: Update the merged topology across the entire model and perform a manifold check.
[0028] Furthermore, the energy function mainly consists of fitting energy, thin plate model bending energy, G1 continuous energy, G2 continuous energy, and tolerance energy;
[0029] The fitting energy is used to maintain the geometry of the original boundary, so that the repaired surface is consistent with the original redundant surface and its adjacent regions in terms of overall shape.
[0030] The bending energy of the thin plate is used to characterize the second-order smoothness of the surface;
[0031] The G1 continuous energy, through normal consistency constraints, ensures the continuity of the repaired surface as it shares a common boundary with the redundant and adjacent surfaces.
[0032] The G2 continuous energy introduces curvature continuity constraints to ensure that the repaired surface and the adjacent surface are consistent in terms of the second derivative.
[0033] The tolerance energy is used to control the deviation between the repaired surface and the original geometry.
[0034] Furthermore, the repair of the complex surface is achieved by iteratively solving with adaptive weights to obtain the optimal new vertex positions and new surface equations, which replace the original redundant topology. In the early stage of repair, the original geometric data is followed, and a large initial value is set for the tolerance energy. The weights of each item are dynamically adjusted according to the energy residual after each iteration. When the repaired surface converges after two consecutive iterations, the surface is considered to have reached a stable state, and the repair is completed.
[0035] Furthermore, the update of the merged topology across the entire model in step 4.3 is achieved by performing Euler operations to modify the underlying topology data structure.
[0036] The beneficial effects of this invention are: the method of this invention introduces reinforcement learning to solve the problem of sequential dependency in geometric cleanup and achieves a globally optimal simplification effect; at the same time, combined with geometric optimization algorithms, it ensures that while greatly simplifying the model topology, the design geometric features of the product are preserved to the greatest extent.
[0037] The method of this invention can effectively use CAD modeling tools for engineering simulation preprocessing and precision manufacturing stages.
[0038] The method of this invention is designed for high-end manufactured products and is a seamless integration of parameterization and direct modeling of high-end manufactured products.
[0039] This invention, guided by the user's input of product CAD model information through the CAD system interface and the hybrid operation of parametric and direct modeling, can intelligently process inconsistent information in the CAD model, ensuring the validity of the CAD model. Attached Figure Description
[0040] Figure 1 This is a flowchart of a method for simplifying and repairing CAD models for intelligent decision-making, according to an embodiment of the present invention.
[0041] Figure 2 This is a flowchart illustrating the intelligent decision-making process for the redundant topology cleanup order in an embodiment of the present invention.
[0042] Figure 3 This is a flowchart of the optimization method based on geometric deformation and geometric feature control according to an embodiment of the present invention;
[0043] Figure 4 This is an example of CAD model simplification and repair according to the present invention. Detailed Implementation
[0044] To make the objectives, technical solutions, and technical effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.
[0045] like Figure 1 As shown, an embodiment of the present invention discloses a method for simplifying and repairing CAD models using intelligent decision-making, comprising:
[0046] Step 1: Generate an entity model based on the input information.
[0047] Users input CAD model information through the interactive interface of the CAD system, and the original CAD solid model is generated from the CAD model information.
[0048] The user interface design is consistent with existing commercial CAD software.
[0049] Step 2: Detect redundant topology in the entity model.
[0050] By designing geometric and topological redundancy rules, redundant topology in CAD entity models is detected, including redundant points, redundant edges, and redundant faces. Then, these are grouped and cached according to different redundancy types to prepare for the subsequent cleanup order decision module.
[0051] This step first iterates through the boundary representation (B-Rep) data structure of the CAD model. Based on the set geometric threshold... For example, if the length of an edge is less than 0.1 mm and the area of a face is less than 0.01 mm², the system automatically identifies all redundant points, edges, and faces that meet the conditions and establishes them as a set of redundant features S to be processed. The specific judgment rules are as follows:
[0052] Determine whether a surface is redundant based on its aspect ratio and area.
[0053] Determine whether a surface edge is redundant based on the length of the topological edge and whether two adjacent surfaces are based on the same underlying surface;
[0054] Whether a point is redundant is determined by whether two adjacent edges of a topological point are based on the same underlying curve.
[0055] Step 3: Design an intelligent decision-making mechanism for the order of redundant topology cleanup.
[0056] For all redundant topologies detected in step 2, reinforcement learning is used to generate the optimal cleanup order, ensuring that the cleaned-up model is optimal. Figure 2As shown, the following four steps are specifically performed:
[0057] Step 3.1: State Definition for High-Dimensional Feature Embedding of Attribute Adjacency Graph: Extract the topology of the current CAD model into graph structure data, which serves as the state input for the reinforcement learning environment. Specifically, this includes:
[0058] Step 3.1.1: Construct the B-Rep boundary representation attribute adjacency graph of the CAD model: Traverse the B-Rep data structure of the CAD model, defining each face as a node in the graph, and defining the adjacent edges between faces as connecting edges. For each node, extract its geometric attributes as node feature vectors. For each connecting edge, extract its topological attributes as edge feature vectors.
[0059] The geometric properties of a surface include: surface area, surface type, average curvature, boundary perimeter, and histogram of normal vector distribution. Surface types include: plane, cylindrical surface, NURBS freeform surface, etc.
[0060] The geometric properties of an edge include: the topological properties include: the length of the edge, the convexity or concavity of the edge, the size of the dihedral angle, and whether the edge is a feature boundary line.
[0061] Step 3.1.2: Graph Embedding Computation: The B-Rep attribute adjacency graph of the CAD model constructed above is input into the graph neural network of the agent. Through a multi-layer message passing mechanism, the feature information of each node and its neighboring nodes is aggregated, and finally a high-dimensional state vector S that can represent the overall topological state and local geometric features of the current CAD model is generated. t .
[0062] Step 3.2: Dynamic Action Selection Based on Mask Constraints: Define how the agent operates on the model, defining cleanup operations for each redundant topological feature, such as edge collapse and face merging, as optional actions. The specific steps are as follows:
[0063] Step 3.2.1: The action space is set as a discrete action space, including two main categories of atomic operations: edge collapse and face merging;
[0064] Step 3.2.2: At each time step t, the system first runs a geometric validity pre-checker to generate a binary mask vector of the same length as the action space;
[0065] Step 3.2.3: Force the probability of all illegal actions that would result in self-intersection, non-manifold structure, or excessive deformation to 0, ensuring that the agent only samples from the valid action subset.
[0066] Step 3.3: Multi-objective weighted hybrid reward mechanism: Constructing a reward function r based on model quality tIf the mesh quality improves and the geometric error is small after the cleanup operation, a positive reward is given; if the operation involves many steps and causes topological errors or excessive geometric deformation, a negative penalty is given.
[0067] Specifically, the setting for the grid quality reward is as follows: after the cleanup operation, the local area is divided into virtual grids, and the scaling Jacobian determinant and aspect ratio of the grid cells are calculated. If the cleanup operation improves the average grid quality index of the local area, a positive reward is given.
[0068] The specific settings for topology errors and step penalties are as follows: if the cleanup operation causes geometric calculation failure or generates an invalid topology, a large negative penalty is given; to encourage the agent to complete the cleanup in the fewest steps, a small negative penalty is given for each step.
[0069] Step 3.4: Training and Inference Based on Proximal Policy Optimization: Train the agent using a deep reinforcement learning algorithm, and then use the trained agent to output the cleanup operation sequence that maximizes the cumulative reward based on the current state. The specific sub-steps are as follows:
[0070] Step 3.4.1: Initialization and Interactive Sampling: Construct a parametric CAD model library containing various redundant features. The agent interacts with the environment, recording the current state S. t Input the agent and sample action a using the action mask generated in step 3.2.2. t A reward of r is received after performing the cleanup operation. t and the new state S t+1 The trajectory data is stored in the experience buffer.
[0071] Step 3.4.2: Dominance Function Calculation (GAE): First, calculate the time series difference residuals. Then calculate the advantage value. ,in For the Critic value network, the estimation of state value, As a discount factor, For smoothing parameters.
[0072] Step 3.4.3: Loss Function Construction and Parameter Update: Construct a hybrid objective function that includes a pruning mechanism. First, calculate the target of the clipping strategy. ,in, The clipping hyperparameter is set to 0.2. The function is to limit the ratio to Within the interval, The ratio of the old to the new strategies is then calculated. Finally, calculate the entropy regularization term. .
[0073] Step 3.4.4: Reasoning and Execution: Using the trained agent, the CAD model to be processed is converted into a B-Rep attribute map and input into the Actor network. The action with the highest probability that satisfies the mask constraint is directly selected: The system executes the action sequence sequentially until no more features satisfying the redundancy definition exist in the CAD model, thus completing the automatic cleanup.
[0074] Finally, the above processing solutions are sorted and cleaned up in a list, which can be left to the user to decide whether to modify the order or skip them. In the default mode, the cleanup order is the optimal result.
[0075] Step 4: Perform redundant topology removal and geometric reconstruction.
[0076] Redundancy cleanup is performed according to the cleanup operation obtained in step 3. An optimization method based on geometric deformation and geometric feature control is used to merge the two geometric surfaces that need to be merged. Finally, the merged topology is updated on the entire model to ensure the manifoldness and topological correctness of the final model.
[0077] like Figure 3 As shown, the optimization method based on geometric deformation and geometric feature control performs the following four steps for each operation in the cleanup sequence queue Q:
[0078] Step 4.1: Classify redundant surfaces according to their geometric type, including: complex curved surfaces, planar or quadratic surfaces. Planar or quadratic surfaces include, for example, spheres, cylindrical surfaces, conical surfaces, etc.
[0079] Step 4.2: When the redundant surface is a plane or quadratic surface, the analytical method is directly used for fitting to quickly reconstruct the surface of the region; when the redundant surface is a complex surface, the surface merging method based on energy function optimization is adopted, and a surface directly adjacent to the redundant surface is selected as the reference surface. The parameter domain and geometric features of the two are jointly repaired to obtain a new surface.
[0080] Step 4.3: Update the merged topology across the entire model, specifically by performing Euler operations to modify the underlying topology data structure and performing a manifold check.
[0081] The energy function is specifically defined as: for the new surface to be solved... Using their control points or coefficients as optimization variables, an energy function is constructed. ,
[0082] in For each weight, The expression for the new surface, defined in the parameter domain. The descriptions of each energy item are as follows:
[0083] Fitting energy To ensure that the repaired surface maintains the same overall shape as the original redundant surface and its adjacent regions, a point set is obtained by sampling from the redundant surface and its adjacent surfaces. And construct fitting terms ,in The spatial coordinates of the sampling points from the redundant surface and adjacent surfaces; to further constrain the boundary positions, the boundary set... Increase weight : It is used to maintain the original boundary geometry so that the repaired surface does not drift.
[0084] Thin plate bending energy To prevent folding, collapse, or local distortion of the repaired surface, bending energy from a thin-plate model is introduced to characterize the second-order smoothness of the surface. ,in For the surface parameter domain region, , , It represents the second-order partial derivative of the surface; in practical implementation, it is discretized into a second-order difference with respect to the control points, which facilitates calculation.
[0085] G1 Continuous Energy Redundant surfaces typically share a common boundary with adjacent surfaces. By applying a normal consistency constraint, the repaired surface achieves G1 continuity at this boundary. Let the normal of the original surface be... The normal of the repaired surface is ,in For public boundaries For sampling points on the above, the continuous energy is This is to ensure that the new surface has a smooth normal change at the transition.
[0086] G2 Continuous Energy When users require higher smoothness, a curvature continuity constraint is introduced to ensure that the repaired surface and adjacent surfaces maintain consistency on their second derivatives. The curvature continuity energy is: If the user has not enabled this feature, the weight of this item is zero by default.
[0087] Tolerance Energy To ensure that the deviation between the repaired surface and the original geometry is controlled, tolerance constraint energy is introduced to strictly control the repair area within tolerances, avoiding the generation of surfaces that do not meet accuracy requirements. Let the maximum permissible deviation be *f*, then the tolerance energy is: .
[0088] The repair of the complex surface is achieved by iteratively solving with adaptive weights to obtain the optimal new vertex positions and new surface equations, thereby replacing the original redundant topology.
[0089] To ensure the overall shape remains intact, the initial repair process strictly adheres to the original geometric data, setting relatively large initial values for tolerance constraints. The weights of each constraint are dynamically adjusted based on the energy residual after each iteration. When the changes in the repaired surface satisfy the following conditions after two consecutive iterations: ,in For the surface in the k-th iteration, If the convergence threshold is set by default or specified by the user, the surface is considered to have reached a stable state, and the repair is complete.
[0090] Finally, the CAD model obtained in step 4 can be used for actual production and manufacturing. Specifically, it can be processed using CNC machine tools or imported into finite element analysis software for simulation calculation.
[0091] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Although the implementation process of the present invention has been described in detail above, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for simplifying and repairing CAD models using intelligent decision-making, characterized in that, include: Step 1: The user inputs CAD model information through the interactive interface of the CAD system, and the original CAD solid model is generated from the CAD model information; Step 2: By designing geometric and topological redundancy rules, detect redundant topology in the CAD solid model, including redundant points, edges, and faces; Step 3: For all redundant topologies detected in Step 2, use reinforcement learning to generate a cleanup operation sequence; Step 4: Clean up the redundant topology of the model according to the cleanup operation sequence obtained in Step 3, use the optimization method based on geometric deformation and geometric feature control to merge the surfaces of the topology, and update the entire model. In step 2, the boundary representation data structure of the CAD model is traversed. The geometric and topological redundancy rules are as follows: based on the set geometric threshold, it is determined whether the topological surface is redundant based on the aspect ratio and area; it is determined whether the topological edge is redundant based on the length of the topological edge and whether two adjacent surfaces are based on the same underlying surface; it is determined whether the topological point is redundant based on whether two adjacent edges are based on the same underlying curve. In step 3, the generation of the cleanup operation sequence using reinforcement learning is based on training and inference of proximal policy optimization: the intelligence is trained using a deep reinforcement learning algorithm, and then the trained intelligence is used to output the cleanup operation sequence that maximizes the cumulative reward based on the current state. The deep reinforcement learning algorithm uses the advantage function calculation to guide the agent's policy network update, and calculates a hybrid objective function including a pruning mechanism to achieve the training convergence of the agent.
2. The CAD model simplification and repair method as described in claim 1, characterized in that, Step 3 specifically includes: Step 3.1: Extract the topology of the current CAD model into graph structure data and use it as the state input to the agent in the reinforcement learning environment; Step 3.2: Dynamic action selection based on mask constraints: The operation of the constraint agent on the CAD model defines the cleanup operation for each redundant topology as an optional action; Step 3.3: The agent introduces a multi-objective weighted hybrid reward mechanism; Step 3.4: Train the agent using a deep reinforcement learning algorithm, and then use the trained agent to output a cleanup operation sequence that maximizes the cumulative reward based on the current input state.
3. The CAD model simplification and repair method as described in claim 2, characterized in that, Step 3.1 specifically includes: Step 3.1.1: Traverse the boundary representation data structure of the CAD model, define each face as a node in the boundary representation attribute adjacency graph, and define the adjacent edges between faces as the connecting edges in the boundary representation attribute adjacency graph; Step 3.1.2: Input the boundary representation attribute adjacency graph into the agent's graph neural network. Through a multi-layer message passing mechanism, aggregate the feature information of each node and its neighboring nodes, and finally generate a high-dimensional state vector representing the overall topological state and local geometric features of the current CAD model.
4. The CAD model simplification and repair method as described in claim 2, characterized in that, The hybrid reward mechanism in step 3.3 is as follows: Construct a reward function based on the quality of the CAD model, perform virtual meshing on the local area after the cleanup operation, calculate the scaling Jacobian determinant and aspect ratio of the mesh cells, and give a positive reward if the average mesh quality index of the local area improves after the cleanup operation. If the cleanup operation results in topology errors or excessive geometric deformation, or if the number of operation steps is too high, a negative penalty will be imposed.
5. The CAD model simplification and repair method as described in claim 2, characterized in that, In step 3.4, a parametric CAD model library containing multiple redundant features is constructed as a dataset input to the agent for training.
6. The CAD model simplification and repair method as described in claim 1, characterized in that, The optimization method based on geometric deformation and geometric feature control in step 4 specifically includes: Step 4.1: Classify redundant surfaces according to their geometric type, including: complex curved surfaces, planes, or quadratic surfaces; Step 4.2: When the redundant surface is a plane or quadratic surface, the analytical method is directly used for fitting to quickly reconstruct the surface; when the redundant surface is a complex surface, the surface merging method based on energy function optimization is adopted, and a surface directly adjacent to the redundant surface is selected as the reference surface. The parameter domains and geometric features of the two are jointly repaired to obtain a new surface. Step 4.3: Update the merged topology across the entire model and perform a manifold check.
7. The CAD model simplification and repair method as described in claim 6, characterized in that, The energy function mainly consists of fitting energy, thin plate model bending energy, G1 continuous energy, G2 continuous energy, and tolerance energy. The fitting energy is used to maintain the geometry of the original boundary, so that the repaired surface is consistent with the original redundant surface and its adjacent regions in terms of overall shape. The bending energy of the thin plate model is used to characterize the second-order smoothness of the surface; The G1 continuous energy, through normal consistency constraints, ensures the continuity of the repaired surface in sharing a common boundary with the redundant surface and the adjacent surface. The G2 continuous energy introduces curvature continuity constraints to ensure that the repaired surface and the adjacent surface are consistent in terms of the second derivative. The tolerance energy is used to control the deviation between the repaired surface and the original geometry.
8. The CAD model simplification and repair method as described in claim 7, characterized in that, The repair of the complex surface is achieved by iteratively solving with adaptive weights to obtain the optimal new vertex positions and new surface equations to replace the original redundant topology. In the early stage of repair, the original geometric data is followed and a large initial value is set for the tolerance energy. The weights of each item are dynamically adjusted according to the energy residual after each iteration. When the repaired surface converges after two consecutive iterations, the surface is considered to have reached a stable state, and the repair is completed.
9. The CAD model simplification and repair method as described in claim 6, characterized in that, The update of the merged topology across the entire model in step 4.3 is achieved by performing Euler operations to modify the underlying topology data structure.