A manufacturing equipment grid lightweight method considering component importance

Abstract

The present application relates to the technical field of geometry model lightweight, especially to a manufacturing equipment grid lightweight method considering component importance, comprising: S1, obtaining the original assembly body grid model data of the manufacturing equipment; and obtaining the global target simplification rate; S2, constructing half-edge data structure, extracting feature edge set; classifying each vertex into corner point, contour point and smooth point; S3, extracting the geometric feature vector of each component; dividing each component into multiple importance levels by clustering and sorting; S4, determining the local target simplification rate of each component; S5, assigning corresponding weight values to the secondary error measurement matrix of each vertex for weighting, obtaining the weighted error matrix of each vertex; S6, performing edge folding iteration on the triangular grid of each component. This method can greatly reduce the grid data amount of the manufacturing equipment, while accurately retaining the key mechanical geometric features and realizing the optimal configuration of rendering resources according to the importance of components.

Description

Technical Field

[0001] This invention relates to the field of geometric model lightweighting technology, and in particular to a method for lightweighting manufacturing equipment meshes that takes into account the importance of components. Background Technology

[0002] Lightweight geometry model algorithms can reduce mesh complexity while preserving the original visual fidelity and geometric features of the equipment to the greatest extent possible. Among existing lightweight mesh algorithms, edge folding algorithms based on quadratic error metrics (QEM) are widely used due to their balance between efficiency and accuracy.

[0003] However, the traditional QEM algorithm has two limitations when applied to simplify the geometric model of manufacturing equipment: First, the traditional algorithm uses pure geometric error as the single folding criterion, which can easily lead to the degradation or loss of key mechanical geometric features of the equipment (such as right-angled edges, assembly holes, etc.) during the mesh compression process; Second, the entire manufacturing equipment is assembled from many parts of different importance, and if a globally uniform simplification rate is adopted, it will result in a waste of rendering resources and will not be able to achieve the optimal configuration of rendering resources for the geometric model on the Web side.

[0004] Therefore, how to significantly reduce the amount of mesh data in manufacturing equipment while accurately preserving key mechanical geometric features and achieving optimal allocation of rendering resources according to component importance has become an urgent problem to be solved. Summary of the Invention

[0005] To address the aforementioned shortcomings of existing technologies, the present invention aims to provide a lightweight manufacturing equipment mesh method that considers component importance. This method can significantly reduce the amount of manufacturing equipment mesh data while accurately preserving key mechanical geometric features and achieving optimal allocation of rendering resources according to component importance.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A method for lightweighting manufacturing equipment meshes considering component importance includes the following steps:

[0008] S1. Obtain the original assembly mesh model data of the manufacturing equipment, including the triangular mesh of each component and its initial number of faces; and obtain the global target simplification rate;

[0009] S2. For the triangular mesh of each component in S1, construct a half-edge data structure. Based on the adjacency information of each edge in the half-edge data structure, extract the feature edge set through the preset dihedral angle threshold condition and topological boundary judgment condition. Count the number of feature edges belonging to the feature edge set in the one-ring neighborhood of each vertex. According to the number of feature edges, classify each vertex into corner point, contour point and smooth point.

[0010] S3. Based on the triangular mesh of each component in S1 and the feature edge set in S2, extract the geometric feature vector of each component; after standardizing the geometric feature vector of each component, divide each component into multiple importance levels through clustering, and sort the multiple importance levels according to the geometric saliency represented by the centroid of each cluster.

[0011] S4. Based on the global target simplification rate in S1 and the initial number of facets of each component, and combined with the importance level of each component after sorting in S3, determine the local target simplification rate of each component.

[0012] S5. Based on the classification results of corner points, contour points and smooth points described in S2, assign corresponding weight values ​​to the quadratic error metric matrix of each vertex according to the classification to which the vertex belongs, and then weight the matrix to obtain the weighted error matrix of each vertex. The weight of the corner point is greater than the weight of the contour point, and the weight of the contour point is greater than the weight of the smooth point.

[0013] S6. Determine the folding cost of each candidate edge based on the weighted error matrix of each vertex in S5. According to the local target simplification rate of each component in S4, perform edge folding iteration on the triangular mesh of each component based on the folding cost until the number of faces of each component reaches the target number of faces corresponding to the local target simplification rate, and output the lightweight whole mesh model.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] 1. Compared to the traditional QEM algorithm, which relies solely on pure geometric errors leading to the degradation of features such as edges and holes, this method accurately extracts feature edges through dual conditions of dihedral angles and topological boundaries. Based on the number of feature edges in the vertex neighborhood, vertices are further subdivided into three categories: corner points, contour points, and smooth points. On this basis, a hierarchical weighting is applied to the quadratic error metric matrix, giving key feature points a higher priority for preservation during the folding process. This significantly enhances the fidelity of engineering semantic features such as right-angled edges and assembly interfaces of mechanical equipment during the simplification process.

[0016] 2. Unlike existing technologies that use a globally uniform simplification rate, which leads to resource waste or loss of detail, this method automatically classifies importance levels based on cluster analysis of component geometric feature vectors and dynamically allocates the local target simplification rate of each component accordingly. This ensures that core functional components and appearance display components maintain high mesh accuracy, while internal non-critical components are deeply simplified. Under the premise of ensuring the overall visual effect of the machine, it achieves differentiated optimal allocation of limited rendering computing power and storage resources.

[0017] 3. Existing differentiated simplification methods are prone to seam defects due to the accuracy discontinuity of adjacent components. This method determines the local simplification rate by combining the global target simplification rate with the initial number of facets of the component, ensuring a smooth transition between the simplification levels of each component. At the same time, the feature-aware weighted error mechanism avoids structural distortion caused by local oversimplification, so that the lightweight whole model maintains good visual coherence and assembly accuracy on a macro scale.

[0018] 4. Enhanced algorithm's ability to automate complex assembly models. Traditional methods often require manual preset of feature protection parameters or manual specification of component priorities, making it difficult to handle manufacturing equipment models containing a massive number of parts. This method, through feature recognition driven by a semi-side data structure and unsupervised clustering and grading, can automatically complete the entire process from feature extraction and importance assessment to differential simplification without manual intervention, significantly improving the processing efficiency and robustness when dealing with large-scale complex assemblies.

[0019] In summary, this method can significantly reduce the amount of mesh data for manufacturing equipment while accurately preserving key mechanical geometric features and achieving optimal allocation of rendering resources according to component importance.

[0020] Preferably, in S2, the step of extracting the feature edge set through a preset dihedral angle threshold condition and a topological boundary determination condition includes:

[0021] For any edge in the triangular mesh, if the number of adjacent faces of the edge is equal to 1, the edge is determined to be a topological boundary edge.

[0022] For an edge with an adjacency count of 2... Calculate the edge The angle between the unit normal vectors of two adjacent triangular facets is called the dihedral angle. When dihedral angle Greater than the preset dihedral threshold When this happens, the edge is determined to be a feature edge;

[0023] Traverse all edges in the triangular mesh, and take the union of the topological boundary edges and the feature edges that satisfy the dihedral angle threshold condition to form the feature edge set.

[0024] This setup can significantly reduce the amount of mesh data for manufacturing equipment while accurately preserving key mechanical geometric features and achieving optimal allocation of rendering resources based on component importance.

[0025] Preferably, in S2, classifying each vertex into corner points, contour points, and smooth points based on the number of feature edges includes:

[0026] Statistical vertices The number of feature edges belonging to the feature edge set within a ring neighborhood ;

[0027] when When ≥3, the vertex Classified as corner points;

[0028] when When =2, this vertex Classified as contour points;

[0029] when When ≤1, the vertex It is classified as a smooth point.

[0030] Preferably, in S3, extracting the geometric feature vectors of each component includes: extracting the following five-dimensional geometric features: bounding box diagonal length. Total surface area Shape complexity Feature edge ratio and grid density ;

[0031] Among them, the shape complexity Calculate according to the following formula:

[0032] ;

[0033] In the formula, Let i be the total surface area of ​​the i-th component; Let be the equivalent volume of the i-th component; when the triangular mesh of the i-th component is a closed mesh, the equivalent volume is... The equivalent volume is calculated by algebraically summing the volumes of the directed tetrahedron formed by each facet and the origin; when the triangular mesh of the i-th component is a non-closed mesh, the equivalent volume is... Take the volume of the enclosure box for this component;

[0034] The feature edge ratio Calculate according to the following formula:

[0035] ;

[0036] In the formula, Let i be the total number of edges of the i-th component; For the i-th component, the dihedral angle is greater than the dihedral angle threshold. The number of internal edges;

[0037] The grid density Calculate according to the following formula:

[0038] ;

[0039] In the formula, Let i be the total number of all facets of the i-th component; Let be the total surface area of ​​the i-th component.

[0040] This setup enables a comprehensive quantitative description of the geometric saliency of components and adaptive calculation under different mesh topologies, ensuring the scientific, accurate, and universal nature of the importance level classification.

[0041] Preferably, in S3, the step of dividing each component into multiple importance levels through clustering, and ranking the multiple importance levels according to the geometric significance represented by the centroid of each cluster, includes:

[0042] The K-Means clustering algorithm is used to determine the optimal number of clusters through clustering evaluation metrics. Divide the components into Each level of importance;

[0043] Calculate the centroid of each cluster. The centroid Given a five-dimensional vector, its geometric significance score is... Calculate according to the following formula:

[0044] ;

[0045] In the formula, Let j be the j-th dimension component of the centroid of the c-th cluster;

[0046] Scoring based on the geometric significance of each cluster. Sort in descending order and map them to importance levels from highest to lowest.

[0047] This setup enables data-driven adaptive classification of component importance levels and objective quantitative ranking based on geometric saliency, ensuring the scientific validity, robustness, and interpretability of the classification results.

[0048] Preferably, in S3, the standardization of the geometric feature vectors of each component includes:

[0049] The geometric feature vectors of each component are combined to form a feature matrix;

[0050] For each feature dimension in the feature matrix, quantile truncation is performed, and feature values ​​that exceed the range of the 1% quantile and 99% quantile of that feature dimension are truncated to the corresponding quantile boundary value.

[0051] Perform a logarithmic transformation on the truncated eigenvalues ​​of each dimension;

[0052] Z-Score standardization is performed on the eigenvalues ​​of each dimension after logarithmic transformation, mapping each dimension of features to a standard space with a mean of 0 and a variance of 1, thus obtaining the standardized feature matrix.

[0053] This setup effectively suppresses the interference of outliers and dimensional differences through cascaded robust standardization, ensuring the stability and accuracy of subsequent clustering and grading results.

[0054] Preferably, in S4, determining the local target simplification rate of each component includes:

[0055] Based on the global target simplification rate and the initial number of facets for each component The number of global target patches is calculated according to the following formula. :

[0056] ;

[0057] ;

[0058] In the formula, m is the total number of parts; This represents the initial total number of facets for the entire machine;

[0059] Based on the importance level of each component, a fidelity weighting factor is assigned to each component according to the following formula. :

[0060] ;

[0061] In the formula, The geometric significance score is given for the cluster to which the i-th component belongs; K is the number of clusters.

[0062] Calculate the overall demand for each component using the following formula. :

[0063] ;

[0064] Based on the comprehensive requirements of each component The proportion of the total demand of all components to the number of global target facets. Assigned to each component, resulting in the theoretical number of reserved facets for each component. :

[0065] .

[0066] This setup, under the hard constraint of global simplification rate, enables the differentiated and on-demand allocation of patch resources based on the geometric saliency of components, balancing the overall data compression target with the high-fidelity requirements of key parts.

[0067] Preferably, in step S4, determining the local target simplification rate of each component further includes:

[0068] Theoretical number of reserved facets for each component Perform out-of-bounds correction: when Greater than the initial number of facets of the component At that time, the theoretical number of retained facets of the component is determined. The numerical value was corrected to The excess budget for the surface piece will be redistributed in multiple iterations according to the overall demand ratio of the remaining components until the budget for the surface piece is fully allocated.

[0069] The local target simplification rate of each component is calculated according to the following formula. :

[0070] .

[0071] This setup, through out-of-bounds correction and iterative redistribution mechanisms, ensures the feasibility, full utilization, and budget conservation of the patch budget allocation, achieving a precise closed loop between the local simplification rate and the global simplification objective.

[0072] Preferably, in S5, the step of assigning corresponding weight values ​​to the quadratic error metric matrix of each vertex according to its category and then weighting the matrix to obtain the weighted error matrix of each vertex includes:

[0073] Based on the vertex classification results, a piecewise weight function is used. As vertices Assign feature protection weights: when the number of feature edges of a vertex... When greater than or equal to 3, = ;when When equal to 2, = ;when When less than or equal to 1, =1; where, and As a feature protection penalty factor;

[0074] and Calculate according to the following formulas respectively:

[0075] ;

[0076] ;

[0077] In the formula, Let $\frac{ ... Standard deviation This represents the cost of folding the maximum edge.

[0078] Vertex The initial quadratic error metric matrix Multiplied by the feature protection weight The weighted error matrix is ​​obtained. :

[0079] ;

[0080] In the formula, As vertices The set of all associated planes; Let be the fundamental error matrix of plane p.

[0081] This setup, through a statistically adaptive segmented feature protection weighting mechanism, effectively protects key geometric features such as corners and edges during the simplification process, significantly suppressing simplification distortion and improving the model's visual fidelity.

[0082] Preferably, in S6, determining the folding cost of each candidate edge based on the weighted error matrix of each vertex in S5, and performing edge folding iteration on the triangular mesh of each component according to the folding cost based on the local objective simplification rate of each component in S4, includes:

[0083] For any candidate edge in the triangular mesh of each component, the weighted error matrices of the two endpoints of the candidate edge are added to obtain a new error matrix after folding. The homogeneous coordinate vector of the new vertex after folding is subjected to a quadratic operation with the new error matrix to obtain the folding cost of the candidate edge. The linear equation system corresponding to the new error matrix is ​​solved to determine the spatial coordinates of the new vertex that minimizes the folding cost. The homogeneous coordinate vector is a four-dimensional vector composed of the three-dimensional spatial coordinates of the new vertex and the constant 1.

[0084] Using the folding cost of each candidate edge as the sorting key, insert all candidate edges into the priority queue in ascending order of folding cost;

[0085] The candidate edges with the lowest folding cost are sequentially selected from the priority queue and the edge folding operation is performed. The two endpoints of the candidate edge are merged into a new vertex. Degenerate patches and degenerate edges caused by folding are deleted. The weighted error matrix of the adjacent vertices connected to the new vertex is updated. The folding cost of the affected candidate edges is recalculated and their positions in the priority queue are updated.

[0086] Determine whether the remaining number of faces in the triangular mesh of the current component is less than or equal to the target number of faces. The target number of faces is equal to 1 minus the local target simplification rate of the component multiplied by the initial number of faces of the component. If the target number of faces has not been reached, continue to perform the edge folding operation. If the target number of faces has been reached, stop the edge folding operation and output the lightweight triangular mesh model of the component.

[0087] This setup, through the greedy folding of the priority queue with optimal error and the termination criterion of the number of local patches, achieves the minimization of cumulative geometric error and precise convergence of the simplified quotas of each component, ensuring the high precision and controllability of the lightweighting results. Attached Figure Description

[0088] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0089] Figure 1 This is a flowchart of the method;

[0090] Figure 2 This is a schematic diagram of the overall framework of this method;

[0091] Figure 3 This is a schematic diagram of a half-side data structure in Example 1;

[0092] Figure 4 , Figure 6 , Figure 8 This is a schematic diagram comparing the rendering models under different algorithms and simplification ratios in Example 2;

[0093] Figure 5 , Figure 7 , Figure 9 They are respectively with Figure 4 , Figure 6 , Figure 8 Comparison of simplified proportional mesh models of corresponding parts using different methods;

[0094] Figure 10 This is a schematic diagram illustrating the determination of the optimal number of clusters in Example 2;

[0095] Figure 11 This is a schematic diagram of the clustering results in Example 2;

[0096] Figure 12, Figure 13 , Figure 14 This is a comparison diagram of the rendering models of different simplification strategies in Example 2. Detailed Implementation

[0097] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0098] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0099] Example 1

[0100] like Figure 1 , Figure 2 As shown, the present invention provides a method for lightweighting manufacturing equipment meshes considering the importance of components, comprising the following steps:

[0101] S1. Obtain the original assembly mesh model data of the manufacturing equipment, including the triangular mesh of each component and its initial number of faces; and obtain the global target simplification rate. .

[0102] S2. For the triangular mesh of each component in S1, construct a half-edge data structure. Based on the adjacent surface information of each edge in the half-edge data structure, extract the feature edge set through the preset dihedral angle threshold condition and topological boundary judgment condition. Count the number of feature edges belonging to the feature edge set in the neighborhood of each vertex. According to the number of feature edges, classify each vertex into corner point, contour point and smooth point.

[0103] This method introduces a half-edge data structure to reconstruct the original OBJ mesh topology, such as... Figure 3 As shown.

[0104] The HalfEdge data structure decomposes a traditional undirected edge into two directed half edges (HalfEdge) with opposite directions. The core class HalfEdge stores four key pointers:

[0105] 1) Vertex pointer (vert): Points to the endpoint vertex of the half-edge. By accessing the vertex pointer of a half-edge, the spatial coordinates and attribute information of its endpoint can be directly obtained, which is the basis for establishing the topological association between edges and vertices.

[0106] 2) Pointer to the dual half: Points to the dual half that is opposite in direction to the original half and shares the same undirected edge. Any undirected edge consists of two dual halfs. The pair pointer allows switching between the two facets of the edge, which is the core mechanism for implementing cross-facet topology queries.

[0107] 3) Next pointer: Points to the next half-edge within the same facet, following the direction of traversal along the facet boundary. By repeatedly accessing the next pointer, all boundary half-edges of a triangular facet can be completely traversed, thus achieving local topological traversal at the facet level.

[0108] 4) Face pointer: Points to the triangular face to which the half-side belongs. The face pointer can be used to obtain the geometric properties of the face, such as its normal vector and area.

[0109] For the central vertex Each connection to adjacent vertices Each edge consists of a pair of dual halves. and The algorithm can traverse the entire neighborhood of a given vertex in a clockwise or counterclockwise direction by starting from any radiating half-edge and alternately accessing the pair and next pointers. This avoids global search and significantly improves the iteration efficiency of the algorithm on large-scale grids.

[0110] In specific implementation, the extraction of the feature edge set through preset dihedral angle threshold conditions and topological boundary determination conditions includes:

[0111] For any edge in the triangular mesh, if the number of adjacent faces of the edge is equal to 1, the edge is determined to be a topological boundary edge.

[0112] For an edge with an adjacency count of 2... Its two adjacent triangular facets are respectively and Let the unit normal vectors of these two faces be respectively... and The included angle (i.e., the dihedral angle) It can be obtained by calculating the dot product of the two: ;

[0113] If this dihedral angle greater than the threshold angle ,Right now ( When an edge is considered to have a significant geometric abrupt change between adjacent facets, it is determined that there is no edge. These are characteristic edges.

[0114] The set of features is formed by taking the union of the topological boundary edges and the feature edges that satisfy the dihedral angle threshold condition.

[0115] In specific implementation, classifying each vertex into corner points, contour points, and smooth points based on the number of feature edges includes:

[0116] Statistical vertices The number of feature edges belonging to the feature edge set within a ring neighborhood ;

[0117] In a triangular mesh model, arbitrary vertices are defined. A ring neighborhood is the set of all adjacent vertices directly connected to a given vertex by a single edge. Then with the vertex The set of adjacent edges that have direct topological associations As shown in the following formula.

[0118] ;

[0119] To count at the vertex The set of characteristic edges in a ring of adjacent edges. To determine the quantity, first define the characteristic indicator function. As shown in the following formula.

[0120] ;

[0121] make Represents vertices The number of characteristic edges in a ring of adjacent edges is expressed mathematically as follows:

[0122] .

[0123] when When ≥3, the vertex These vertices are classified as corner points; they are typically located at the intersection of three or more non-coplanar planes, corresponding to the intersection center of multiple intersection lines in the geometric model of the manufacturing equipment.

[0124] when When =2, this vertex These are classified as contour points; topologically, these vertices lie on a continuous geometric boundary. In the geometric model of manufacturing equipment, contour points are abundantly and continuously distributed on right-angled stepped surfaces, the opening edges of assembly voids, and the edges of regularly chamfered corners.

[0125] when When ≤1, the vertex These vertices are classified as smooth points. They are typically located within a continuous geometric surface with gently changing curvature, indicating that there are no significant abrupt changes in geometry around the vertex.

[0126] S3. Based on the triangular mesh of each component in S1 and the feature edge set in S2, extract the geometric feature vector of each component; after standardizing the geometric feature vector of each component, divide each component into multiple importance levels through clustering, and sort the multiple importance levels according to the geometric saliency represented by the centroid of each cluster.

[0127] In specific implementation, the extraction of geometric feature vectors for each component includes: extracting the following five-dimensional geometric features: bounding box diagonal length. Total surface area Shape complexity Feature edge ratio and grid density ;

[0128] Among them, the shape complexity Calculate according to the following formula:

[0129] ;

[0130] In the formula, Let i be the total surface area of ​​the i-th component; Let be the equivalent volume of the i-th component; when the triangular mesh of the i-th component is a closed mesh, the equivalent volume is... The equivalent volume is calculated by algebraically summing the volumes of the directed tetrahedron formed by each facet and the origin; when the triangular mesh of the i-th component is a non-closed mesh, the equivalent volume is... Take the volume of the enclosure box for this component;

[0131] The feature edge ratio Calculate according to the following formula:

[0132] ;

[0133] In the formula, Let i be the total number of edges of the i-th component; For the i-th component, the dihedral angle is greater than the dihedral angle threshold. The number of internal edges;

[0134] The grid density Calculate according to the following formula:

[0135] ;

[0136] In the formula, Let i be the total number of all facets of the i-th component; Let be the total surface area of ​​the i-th component.

[0137] In specific implementation, the standardization of the geometric feature vectors of each component includes:

[0138] The geometric feature vectors of each component are combined to form a feature matrix. As shown below:

[0139] .

[0140] Outlier truncation

[0141] For the eigenmatrix, the th For each feature, calculate its 1% and 99th percentiles, denoted as . and Quantile truncation is used to reduce the impact of extreme samples on mean and variance estimation, resulting in truncated eigenvalues, as shown below:

[0142] ;

[0143] Logarithmic transformation

[0144] For the diagonal length of the bounding box Total surface area Shape complexity and grid density Given the non-negative and typically right-skewed distribution characteristics, a logarithmic compression transformation is applied, as shown in the following equation, to reduce the order-of-magnitude range and alleviate the dominant role of large numerical samples in Euclidean distance calculations:

[0145] .

[0146] Z-Score Standardization

[0147] To eliminate the influence of differences in the dimensions of different features on the clustering results, Z-Score standardization is applied to each dimension of the preprocessed features. Let the first feature be... The mean and standard deviation of the 3D features are respectively and The standardized eigenvalues ​​are shown in the following formula:

[0148] ;

[0149] in, This represents the eigenvalues ​​after truncation and necessary logarithmic transformation. After this processing, all features are mapped to a unified standard space with a mean of 0 and a variance of 1, resulting in the standardized feature matrix. .

[0150] In specific implementation, the step of dividing each component into multiple importance levels through clustering, and ranking the multiple importance levels according to the geometric significance represented by the centroid of each cluster, includes:

[0151] The K-Means clustering algorithm is used to determine the optimal number of clusters through clustering evaluation metrics. Divide the components into Each level of importance;

[0152] Calculate the centroid of each cluster. The centroid Given a five-dimensional vector, its geometric significance score is... Calculate according to the following formula:

[0153] ;

[0154] In the formula, Let j be the j-th dimension component of the centroid of the c-th cluster;

[0155] Scoring based on the geometric significance of each cluster. Sort in descending order and map them to importance levels from highest to lowest.

[0156] S4. Based on the global objective simplification rate in S1 Based on the initial number of faces of each component and the importance level of each component after sorting in S3, the local target simplification rate of each component is determined.

[0157] In specific implementation, determining the local target simplification rate of each component includes:

[0158] Based on the global target simplification rate and the initial number of facets for each component The number of global target patches is calculated according to the following formula. :

[0159] ;

[0160] ;

[0161] In the formula, m is the total number of parts; This represents the initial total number of facets for the entire machine;

[0162] Based on the importance level of each component, a fidelity weighting factor is assigned to each component according to the following formula. :

[0163] ;

[0164] In the formula, The geometric significance score is given for the cluster to which the i-th component belongs; K is the number of clusters.

[0165] Calculate the overall demand for each component using the following formula. :

[0166] ;

[0167] Based on the comprehensive requirements of each component The proportion of the total demand of all components to the number of global target facets. Assigned to each component, resulting in the theoretical number of reserved facets for each component. :

[0168] .

[0169] In this way, under the hard constraint of global simplification rate, the patch resources are allocated on demand according to the geometric saliency of the components, taking into account both the data compression target of the whole machine and the high-fidelity requirements of key parts.

[0170] In specific implementation, determining the local target simplification rate of each component also includes:

[0171] Theoretical number of reserved facets for each component Perform out-of-bounds correction: when Greater than the initial number of facets of the component At that time, the theoretical number of retained facets of the component is determined. The numerical value was corrected to The excess budget for the surface piece will be redistributed in multiple iterations according to the overall demand ratio of the remaining components until the budget for the surface piece is fully allocated.

[0172] The local target simplification rate of each component is calculated according to the following formula. :

[0173] .

[0174] The mechanism of out-of-bounds correction and iterative redistribution ensures the feasibility, full utilization and budget conservation of the patch budget allocation, and achieves a precise closed loop between the local simplification rate and the global simplification target.

[0175] S5. Based on the classification results of corner points, contour points and smooth points described in S2, assign corresponding weight values ​​to the quadratic error metric matrix of each vertex according to the classification to which the vertex belongs, and then weight the matrix to obtain the weighted error matrix of each vertex. The weight of the corner point is greater than the weight of the contour point, and the weight of the contour point is greater than the weight of the smooth point.

[0176] In specific implementation, the step of assigning corresponding weight values ​​to the quadratic error metric matrix of each vertex according to its category and then weighting them to obtain the weighted error matrix of each vertex includes:

[0177] Based on the vertex classification results, a piecewise weight function is used. As vertices Assign feature protection weights:

[0178] ;

[0179] in, and As a feature protection penalty factor;

[0180] and Calculate according to the following formulas respectively:

[0181] ;

[0182] ;

[0183] In the formula, Let $\frac{ ... Standard deviation This represents the cost of folding the maximum edge.

[0184] Vertex The initial quadratic error metric matrix Multiplied by the feature protection weight The weighted error matrix is ​​obtained. :

[0185] ;

[0186] In the formula, As vertices The set of all associated planes; Let be the fundamental error matrix of plane p.

[0187] S6. Determine the folding cost of each candidate edge based on the weighted error matrix of each vertex in S5. According to the local target simplification rate of each component in S4, perform edge folding iteration on the triangular mesh of each component based on the folding cost until the number of faces of each component reaches the target number of faces corresponding to the local target simplification rate, and output the lightweight whole mesh model.

[0188] In specific implementation, the step of determining the folding cost of each candidate edge based on the weighted error matrix of each vertex in S5, and performing edge folding iteration on the triangular mesh of each component according to the local objective simplification rate of each component in S4 based on the folding cost, includes:

[0189] For any candidate edge in the triangular mesh of each component, the weighted error matrices of the two endpoints of the candidate edge are added to obtain a new error matrix after folding. The homogeneous coordinate vector of the new vertex after folding is subjected to a quadratic operation with the new error matrix to obtain the folding cost of the candidate edge. The linear equation system corresponding to the new error matrix is ​​solved to determine the spatial coordinates of the new vertex that minimizes the folding cost. The homogeneous coordinate vector is a four-dimensional vector composed of the three-dimensional spatial coordinates of the new vertex and the constant 1.

[0190] Using the folding cost of each candidate edge as the sorting key, insert all candidate edges into the priority queue in ascending order of folding cost;

[0191] The candidate edges with the lowest folding cost are sequentially selected from the priority queue and the edge folding operation is performed. The two endpoints of the candidate edge are merged into a new vertex. Degenerate patches and degenerate edges caused by folding are deleted. The weighted error matrix of the adjacent vertices connected to the new vertex is updated. The folding cost of the affected candidate edges is recalculated and their positions in the priority queue are updated.

[0192] Determine whether the remaining number of faces in the triangular mesh of the current component is less than or equal to the target number of faces. The target number of faces is equal to 1 minus the local target simplification rate of the component multiplied by the initial number of faces of the component. If the target number of faces has not been reached, continue to perform the edge folding operation. If the target number of faces has been reached, stop the edge folding operation and output the lightweight triangular mesh model of the component.

[0193] Compared to traditional QEM algorithms that rely solely on pure geometric errors, leading to feature degradation such as edges and holes, this method accurately extracts feature edges using dual conditions of dihedral angles and topological boundaries. It further subdivides vertices into three categories—corner points, contour points, and smooth points—based on the number of feature edges in their neighborhoods. On this basis, a hierarchical weighting of the quadratic error metric matrix is ​​applied, giving key feature points a higher retention priority during the folding process. This significantly enhances the fidelity of engineering semantic features such as right-angled edges and assembly interfaces in mechanical equipment during simplification. In addition, this method automatically classifies importance levels based on cluster analysis of component geometric feature vectors and dynamically allocates the local target simplification rate for each component accordingly. This ensures that core functional components and appearance display components maintain high mesh accuracy, while internal non-critical components are deeply simplified. This achieves differentiated optimal allocation of limited rendering computing power and storage resources while maintaining the overall visual effect of the machine. In addition, this method determines the local simplification rate by combining the global target simplification rate with the initial number of facets of the component, ensuring a smooth transition between the simplification levels of each component. Simultaneously, the feature-aware weighted error mechanism avoids structural distortion caused by local oversimplification, enabling the lightweight overall model to maintain good visual coherence and assembly accuracy at a macro scale. Furthermore, this method, through feature recognition driven by a half-side data structure and unsupervised clustering grading, automatically completes the entire process from feature extraction and importance assessment to differential simplification without manual intervention, significantly improving the processing efficiency and robustness when dealing with large-scale complex assemblies.

[0194] This method can significantly reduce the amount of mesh data for manufacturing equipment while accurately preserving key mechanical geometric features and achieving optimal allocation of rendering resources according to component importance.

[0195] Example 2

[0196] To better illustrate the effectiveness of this method, the following experimental verification was conducted.

[0197] To verify the effectiveness of this method, comparative experiments were conducted. Using components (frame structure parts, connecting rods, and slides) of a certain type of die forging press, as well as a complete die forging press model, as verification objects, the effectiveness of this method was verified by comparing the visual effects and geometric errors of the QEM algorithm, literature algorithms, and this method on the components. Furthermore, the effectiveness of the hierarchical simplification strategy of this method was verified by comparing the visual effects and geometric errors of the unified simplification strategy and the hierarchical simplification strategy of this method on the complete machine assembly.

[0198] 1 Evaluation Indicators

[0199] Geometric error is a direct measure of the shape difference between the simplified model and the original model. To objectively reflect the algorithm's ability to preserve the geometric features of the components in the geometric model of the manufacturing equipment, three indicators are selected for measurement: Hausdorff distance, average error, and root mean square error. Weighted normalized Hausdorff distance is introduced as an evaluation index for the overall machine hierarchical lightweighting strategy.

[0200] Comparative Experiment of Component Lightweighting Algorithms

[0201] The bed, large column, and small column models were used as test objects. The number of their facets was simplified to 80%, 40%, and 20% of the original number using the traditional QEM algorithm, the algorithm in the literature, and the method of this paper, respectively.

[0202] (1) Comparison of visual effects of lightweight model algorithms

[0203] A comparison chart of the simplification effects of the three algorithms, as shown below. Figures 4-9 As shown. Among them, Figure 4 , Figure 6 , Figure 8 A comparison of rendering models under different algorithms and simplification ratios. Figure 4 Lightweight renderings of the connecting rod Figure 6 Lightweight renderings of frame structural components Figure 8 The images show the effect of the slider lightweighting process; (a) is the original model; (b) to (d) are the models after the QEM algorithm, the literature algorithm, and the method in this paper, which simplify the number of triangle faces to 80%, respectively; (e) to (g) are the models after simplification to 40%; and (h) to (j) are the models after simplification to 20%.

[0204] from Figure 4 , Figure 6 , Figure 8 The results clearly demonstrate that our proposed method significantly outperforms the QEM algorithm and the algorithms in the literature in preserving geometric features. When the model is simplified to 80%, the QEM algorithm loses some features in the simplified model; the geometric features of the simplified model obtained from the literature algorithm remain clearly discernible, and its detailed features are preserved relatively well. When the model is simplified to 40%, most of the detailed features of the simplified models obtained from the QEM algorithm and the literature algorithm are lost, and severe surface damage occurs. When the model is simplified to 20%, almost all the detailed features of the simplified models obtained from the QEM algorithm and the literature algorithm are lost, making it impossible to recognize the original outline of the model; while the geometric features of the simplified model obtained by our proposed method remain clearly discernible, and its detailed features are preserved relatively well, with no surface damage or feature loss observed in the simplified model.

[0205] Figure 5 , Figure 7 , Figure 9 They are respectively with Figure 4 , Figure 6 , Figure 8 By comparing the simplified mesh models of the corresponding parts with different simplification ratios using this method, it can be clearly seen that the simplified model of this method can maintain the geometric features well. The mesh density decreases significantly as the simplification ratio increases, and the number of mesh vertices and triangular faces is significantly reduced.

[0206] (2) Comparison of geometric errors of lightweight model algorithms

[0207] To quantitatively evaluate the simplification quality, the Hausdorff distance, average error, and root mean square error between the component models with different simplification ratios and the original models were calculated. The comparison results of the lightweight geometric errors of the three algorithms are shown in the table below.

[0208] Table 1. Comparison of geometric errors of connecting rods with different simplification ratios.

[0209]

[0210] Table 2 Comparison of geometric errors of frame structural components with different simplification ratios

[0211]

[0212] Table 3 Comparison of geometric errors of sliders with different simplification ratios

[0213]

[0214] The comparison results in the table show that at an 80% simplification ratio, the Hausdorff distance, mean error, and root mean square error of the proposed algorithm and the literature algorithm are similar, indicating that all three algorithms preserve the geometric features of the model well. As the simplification ratio decreases, the Hausdorff distance, mean error, and root mean square error of the proposed method are significantly lower than those of the traditional QEM algorithm and the literature algorithm. Particularly at a 20% simplification ratio, the errors of the traditional QEM algorithm and the literature algorithm increase sharply, indicating severe model deformation; while the Hausdorff distance of the proposed method remains at a low level, indicating that the geometric features of the model are well preserved.

[0215] 3. Comparative Experiment of Overall Machine Tiered Lightweighting Strategy

[0216] Using the complete assembly model of the die forging press as the test object, the components of the complete machine are first clustered and classified, and then a graded lightweighting experiment is carried out on the complete machine model to verify the effectiveness of the proposed strategy.

[0217] (1) Clustering and grading results of components

[0218] Based on the constructed five-dimensional feature vectors of the components, the K-Means algorithm was used to perform cluster analysis on all components in the entire machine. For each candidate cluster, three evaluation indicators—DBI index, CHI index, and SC index—were calculated, and the results are as follows: Figure 10 As shown in the figure. A smaller DBI value indicates more compact clusters and more dispersed inter-cluster clusters; a larger CHI value indicates higher inter-cluster dispersion compared to intra-cluster dispersion; and a larger SC value (maximum 1) indicates clearer sample affiliation. Based on these three evaluation metrics, the optimal number of clusters was determined to be... .

[0219] Based on the comprehensive geometric significance score of the centroids of each cluster, the components are divided into six importance levels. The clustering results are as follows: Figure 11 As shown.

[0220] (2) Comparison of whole machine graded lightweighting experiments

[0221] After obtaining the component classification results, a local target simplification rate is generated for each component based on the simplification rate allocation method oriented towards global constraints. The improved QEM algorithm is then called to perform overall system lightweighting. The overall system hierarchical lightweighting strategy is compared with a unified simplification rate strategy, reducing the number of facets in the overall model to 40%, 20%, and 10% of the original number, respectively.

[0222] 1) Visual effect comparison of model lightweighting strategies

[0223] Figure 12 , Figure 13 , Figure 14 A comparison of rendering models using different simplification strategies is provided, among which... Figure 12 To simplify to 40%, Figure 13 To simplify to 20%, Figure 14 To simplify to 10%, it can be seen that at simplification ratios of 40% and 20%, there is no significant difference in the visual rendering effect of the models using the two simplification strategies; at a simplification ratio of 10%, the visual effect of the model using the hierarchical simplification strategy is better than that using the uniform simplification strategy, and the appearance features of important supporting components such as the bed frame, large columns, and small columns are complete and clear.

[0224] 2) Comparison of geometric errors of lightweight model strategies

[0225] To quantitatively evaluate the simplification quality, the weighted normalized Hausdorff distance between the complete model and the original model at different simplification ratios was calculated. The geometric error comparison results for the two strategies at different simplification ratios are shown in Table 4.

[0226] Table 4. Comparison of geometric errors of different simplification ratios for the two simplification strategies.

[0227]

[0228] As shown in Table 4, the geometric errors of the proposed hierarchical simplification strategy and the uniform simplification rate strategy are similar at a 40% simplification ratio. However, as the simplification ratio decreases, the geometric error generated by the proposed hierarchical simplification strategy is lower than that of the uniform simplification rate strategy. This indicates that the proposed hierarchical simplification strategy can achieve a better configuration of the overall machine mesh rendering resources.

[0229] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A method for lightweighting manufacturing equipment meshes considering component importance, characterized in that, Includes the following steps: S1. Obtain the original assembly mesh model data of the manufacturing equipment, including the triangular mesh of each component and its initial number of faces; and obtain the global target simplification rate; S2. For the triangular mesh of each component in S1, construct a half-side data structure. Based on the adjacent surface information of each side in the half-side data structure, extract the feature edge set through the preset dihedral angle threshold condition and topological boundary determination condition. Count the number of feature edges belonging to the feature edge set within the one-ring neighborhood of each vertex, and classify each vertex into corner points, contour points, and smooth points based on the number of feature edges. S3. Based on the triangular mesh of each component in S1 and the feature edge set in S2, extract the geometric feature vector of each component; after standardizing the geometric feature vector of each component, divide each component into multiple importance levels through clustering, and sort the multiple importance levels according to the geometric saliency represented by the centroid of each cluster. S4. Based on the global target simplification rate in S1 and the initial number of facets of each component, and combined with the importance level of each component after sorting in S3, determine the local target simplification rate of each component. S5. Based on the classification results of corner points, contour points and smooth points described in S2, assign corresponding weight values ​​to the quadratic error metric matrix of each vertex according to the classification to which the vertex belongs, and then weight the matrix to obtain the weighted error matrix of each vertex. The weight of the corner point is greater than the weight of the contour point, and the weight of the contour point is greater than the weight of the smooth point. S6. Determine the folding cost of each candidate edge based on the weighted error matrix of each vertex in S5. According to the local target simplification rate of each component in S4, perform edge folding iteration on the triangular mesh of each component based on the folding cost until the number of faces of each component reaches the target number of faces corresponding to the local target simplification rate, and output the lightweight whole mesh model.

2. The manufacturing equipment mesh lightweighting method considering component importance according to claim 1, characterized in that, In S2, the extraction of the feature edge set through preset dihedral angle threshold conditions and topological boundary determination conditions includes: For any edge in the triangular mesh, if the number of adjacent faces of the edge is equal to 1, the edge is determined to be a topological boundary edge. For an edge with an adjacency count of 2... Calculate the edge The angle between the unit normal vectors of two adjacent triangular facets is called the dihedral angle. When dihedral angle Greater than the preset dihedral threshold When this happens, the edge is determined to be a feature edge; Traverse all edges in the triangular mesh, and take the union of the topological boundary edges and the feature edges that satisfy the dihedral angle threshold condition to form the feature edge set.

3. The manufacturing equipment mesh lightweighting method considering component importance according to claim 2, characterized in that, In S2, classifying each vertex into corner points, contour points, and smooth points based on the number of feature edges includes: Statistical vertices The number of feature edges belonging to the feature edge set within a ring neighborhood ; when When ≥3, the vertex Classified as corner points; when When =2, this vertex Classified as contour points; when When ≤1, the vertex It is classified as a smooth point.

4. The manufacturing equipment mesh lightweighting method considering component importance according to claim 1, characterized in that, In S3, the extraction of geometric feature vectors for each component includes: extracting the following five-dimensional geometric features: bounding box diagonal length. Total surface area Shape complexity Feature edge ratio and grid density ; Among them, the shape complexity Calculate according to the following formula: ； In the formula, Let i be the total surface area of ​​the i-th component; Let be the equivalent volume of the i-th component; when the triangular mesh of the i-th component is a closed mesh, the equivalent volume is... The equivalent volume is calculated by algebraically summing the volumes of the directed tetrahedron formed by each facet and the origin; when the triangular mesh of the i-th component is a non-closed mesh, the equivalent volume is... Take the volume of the enclosure box for this component; The feature edge ratio Calculate according to the following formula: ； In the formula, Let i be the total number of edges of the i-th component; For the i-th component, the dihedral angle is greater than the dihedral angle threshold. The number of internal edges; The grid density Calculate according to the following formula: ； In the formula, Let i be the total number of all facets of the i-th component; Let be the total surface area of ​​the i-th component.

5. The manufacturing equipment mesh lightweighting method considering component importance according to claim 4, characterized in that, In S3, the process of dividing each component into multiple importance levels through clustering and ranking these importance levels according to the geometric significance represented by the centroid of each cluster includes: The K-Means clustering algorithm is used to determine the optimal number of clusters through clustering evaluation metrics. Divide the components into Each level of importance; Calculate the centroid of each cluster. The centroid Given a five-dimensional vector, its geometric significance score is... Calculate according to the following formula: ； In the formula, Let j be the j-th dimension component of the centroid of the c-th cluster; Scoring based on the geometric significance of each cluster. Sort in descending order and map them to importance levels from highest to lowest.

6. The manufacturing equipment mesh lightweighting method considering component importance according to claim 1, characterized in that, In S3, the standardization of the geometric feature vectors of each component includes: The geometric feature vectors of each component are combined to form a feature matrix; For each feature dimension in the feature matrix, quantile truncation is performed, and feature values ​​that exceed the range of the 1% quantile and 99% quantile of that feature dimension are truncated to the corresponding quantile boundary value. Perform a logarithmic transformation on the truncated eigenvalues ​​of each dimension; Z-Score standardization is performed on the eigenvalues ​​of each dimension after logarithmic transformation, mapping each dimension of features to a standard space with a mean of 0 and a variance of 1, thus obtaining the standardized feature matrix.

7. The manufacturing equipment mesh lightweighting method considering component importance according to claim 1, characterized in that, In S4, determining the local target simplification rate of each component includes: Based on the global target simplification rate and the initial number of facets for each component The number of global target patches is calculated according to the following formula. : ； ； In the formula, m is the total number of parts; This represents the initial total number of facets for the entire machine; Based on the importance level of each component, a fidelity weighting factor is assigned to each component according to the following formula. : ； In the formula, The geometric significance score is given for the cluster to which the i-th component belongs; K is the number of clusters. Calculate the overall demand for each component using the following formula. : ； Based on the comprehensive requirements of each component The proportion of the total demand of all components to the number of global target facets. Assigned to each component, resulting in the theoretical number of reserved facets for each component. : 。 8. The manufacturing equipment mesh lightweighting method considering component importance according to claim 7, characterized in that, In S4, determining the local target simplification rate of each component further includes: Theoretical number of reserved facets for each component Perform out-of-bounds correction: when Greater than the initial number of facets of the component At that time, the theoretical number of retained facets of the component is determined. The numerical value was corrected to The excess budget for the surface piece will be redistributed in multiple iterations according to the overall demand ratio of the remaining components until the budget for the surface piece is fully allocated. The local target simplification rate of each component is calculated according to the following formula. : 。 9. The manufacturing equipment mesh lightweighting method considering component importance according to claim 1, characterized in that, In S5, the step of assigning corresponding weight values ​​to the quadratic error metric matrix of each vertex according to its category and then weighting them to obtain the weighted error matrix of each vertex includes: Based on the vertex classification results, a piecewise weight function is used. As vertices Assign feature protection weights: when the number of feature edges of a vertex... When greater than or equal to 3, = ;when When equal to 2, = ;when When less than or equal to 1, =1; where, and As a feature protection penalty factor; and Calculate according to the following formulas respectively: ； ； In the formula, Let $\frac{ ... Standard deviation This represents the cost of folding the maximum edge. Vertex The initial quadratic error metric matrix Multiplied by the feature protection weight The weighted error matrix is ​​obtained. : ； In the formula, As vertices The set of all associated planes; Let be the fundamental error matrix of plane p.

10. The manufacturing equipment mesh lightweighting method considering component importance according to claim 1, characterized in that, In S6, determining the folding cost of each candidate edge based on the weighted error matrix of each vertex in S5, and performing edge folding iteration on the triangular mesh of each component according to the local objective simplification rate of each component in S4 based on the folding cost, includes: For any candidate edge in the triangular mesh of each component, the weighted error matrices of the two endpoints of the candidate edge are added to obtain a new error matrix after folding. The homogeneous coordinate vector of the new vertex after folding is subjected to a quadratic operation with the new error matrix to obtain the folding cost of the candidate edge. The linear equation system corresponding to the new error matrix is ​​solved to determine the spatial coordinates of the new vertex that minimizes the folding cost. The homogeneous coordinate vector is a four-dimensional vector composed of the three-dimensional spatial coordinates of the new vertex and the constant 1. Using the folding cost of each candidate edge as the sorting key, insert all candidate edges into the priority queue in ascending order of folding cost; The candidate edges with the lowest folding cost are sequentially selected from the priority queue and the edge folding operation is performed. The two endpoints of the candidate edge are merged into a new vertex. Degenerate patches and degenerate edges caused by folding are deleted. The weighted error matrix of the adjacent vertices connected to the new vertex is updated. The folding cost of the affected candidate edges is recalculated and their positions in the priority queue are updated. Determine whether the remaining number of faces in the triangular mesh of the current component is less than or equal to the target number of faces. The target number of faces is equal to 1 minus the local target simplification rate of the component multiplied by the initial number of faces of the component. If the target number of faces has not been reached, continue to perform the edge folding operation. If the target number of faces has been reached, stop the edge folding operation and output the lightweight triangular mesh model of the component.

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