A three-dimensional model cutting method for high-quality stamping material arrangement

Abstract

The application discloses a kind of three-dimensional model cutting methods for high-quality stamping material arrangement, belong to computer aided design field.Its steps are as follows:1) fully consider model surface geometric information, generate four symmetry direction field on input surface and extract singular point;2) utilize the number of singular points and cutting line length to carry out correlation analysis, and simplify redundant singular points;3) design a set of mutually perpendicular surface cutting edge, while connecting singular points, input surface is cut into the structure with disc homeomorphism;4) to the surface after cutting, low-torsion parameterization is carried out, and the parameterization result is optimized,5) using plane parameterization optimization result obtains high-quality stamping material arrangement.The method has the advantages that the efficiency of multi-connected square in stamping material arrangement is utilized, and the geometric characteristics of multi-connected square are fully considered, and the operation is simple and robust;The application has very important practical application value for high-quality sheet metal stamping material arrangement.

Description

Technical Field

[0001] This invention belongs to the field of computer-aided design, specifically relating to a three-dimensional model cutting method for high-quality stamping layout. Background Technology

[0002] Parametric methods for achieving high packing efficiency using computer graphics techniques have wide applications in stamping nesting. For high-quality and efficient nesting, industry generally desires stamping nesting to have high packing efficiency (PE), short boundary length (BL), and minimal energy of shape distortion (ED). However, achieving results that satisfy these three indicators often involves complex multi-objective optimization, which is typically difficult to solve efficiently due to its high nonlinearity and nonconvexity.

[0003] For this complex and difficult-to-solve multi-objective optimization problem, existing techniques typically decompose it into a two-step solution: First, considering only the cutting length (BL) and shape distortion (ED), the curved surface model is parameterized to a planar region; then, a packing efficiency (PE) index is introduced into the planar region to further optimize the planar packing efficiency while simultaneously considering both the cutting length (BL) and shape distortion (ED). Clearly, in this two-step optimization strategy, the texture atlas generated in the second step strongly depends on the parameterization in the first step. If the first step introduces a large amount of redundant cutting or significant shape distortion, the final result will fall into a local optimum, thus failing to achieve high-quality stamping layout. Therefore, within the framework of the two-step optimization, a parameterization technique that facilitates the re-optimization of planar textures is crucial.

[0004] Many existing technologies focus on only one of the two optimization steps mentioned above. Although they have made outstanding contributions in the single-step domain, they have all ignored the connection between the two steps. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing methods and provide a three-dimensional model cutting method for high-quality stamping layout, thereby bridging the gap between the two-step optimization strategies in traditional cutting techniques and meeting the application requirements of high quality and high efficiency.

[0006] To achieve the objectives of this invention, the following technical solution is provided:

[0007] A method for cutting a 3D model for high-quality stamping layout includes the following steps:

[0008] S1: Based on the discrete Gaussian curvature of the input model, optimize the smooth discrete four-symmetric direction field on the three-dimensional surface of the input model to obtain the singular points of the discrete direction field.

[0009] S2: Simplify the singular points of the discrete direction field obtained in step S1;

[0010] S3: Connect the singular points obtained in step S1 to obtain a set of mutually perpendicular curved surface cutting edges;

[0011] S4: Cut the input model into a topologically homeomorphic model of the disk along the cutting edge of the surface, and perform isotropic low-twist parameterization on the cut surface model;

[0012] S5: Optimize the parameterized results using planar texture optimization technology to obtain stamping material layout.

[0013] Further, step S1 includes:

[0014] S11: Define a local coordinate system on each facet of the input model;

[0015] S12: For any common edge e connecting triangles i and j on the mesh of the input model. ij Calculate the smoothing energy of the four-symmetric direction field:

[0016]

[0017] In the formula, θ i and θ j Let κ represent the angles between any component of the four-symmetric direction field on triangles i and j and the x-axis, respectively. ij p represents the angle difference between the parallel x-axis transmissions of triangles i and j. ij This indicates an alignment jump between two triangular direction fields. This represents the four-symmetric direction field from triangle i along the common side e. ij The smooth energy transmitted in parallel to triangle j;

[0018] S13: Integrate the smooth energy of the four-symmetric direction field and find the θ corresponding to the minimum value of the integral. i θ j and p ij ;

[0019] S14: Calculate the corresponding integer basic index based on the angle deficit of each vertex:

[0020]

[0021] Wherein, N(v) i ) represents the vertex v iThe set of triangles surrounding the center, d(v) i ) represents vertex v i angular deficiency, α b (v i ) represents vertex v i The corresponding integer base index; the integer base index α corresponding to all vertices. b (v i ) constitute the basic index set I b ;

[0022] S15: Based on the basic index set I b Calculate v at each vertex in a four-symmetric direction field. i Index:

[0023]

[0024] The indices α(v) of all vertices i ) constitute the index set I(v i Extract set I(v) i The points corresponding to non-zero elements in the equation are considered singular points.

[0025] Furthermore, each vertex v i The formula for calculating the angle deficit is:

[0026]

[0027] in, ∠jik represents vertex v i Discrete Gaussian curvature, Δ ijk Indicates that by vertex v i v j v k The triangle formed by these angles, ∠jik, represents the angle value.

[0028] Further, step S2 includes:

[0029] S21: Based on the index of each singular point, construct an index vector α = [α1, α2, ..., α3] using the index values ​​of the singular points. i ,...,α N ], where α i Let N be the index value corresponding to the i-th singularity, and let N represent the number of singularities in the four-symmetric direction field extracted in step S1.

[0030] S22: Enumerate all integer vector pairs δ i and δ j , i≠j, δ i and δ j The dimension of δ is the same as the dimension of the index vector α, and δ iOnly the i-th element is 1, and all other elements are 0, δ j Only the j-th element is 1, and all other elements are 0;

[0031] S23: Iterative optimization of the index vector α:

[0032]

[0033]

[0034] Where, α k This represents the index vector of the k-th iteration, with the initial value α of the iteration. 0 This is the α obtained in step S21, where ||.||0 represents the L0 norm. S represents the index value of the i-th singular point in the index vector of the k-th iteration. k E represents the simplified energy function value of the k-th iteration. I (α k ) represents the smoothness of the four-symmetric direction field at the k-th iteration; w n It is the weight value;

[0035] S24: When S k ≥S k-1 When the time limit is reached, stop the optimization and set the index vector α in the (k-1)th iteration. k-1 Find all non-zero elements and take the points corresponding to all non-zero elements as the final singular points.

[0036] Furthermore, the formula for calculating the smoothness of the symmetrical direction field is as follows:

[0037]

[0038] Where, α g L is a vector composed of the discrete Gaussian curvatures of all singular points. + It is the pseudo-inverse matrix of the Laplacian operator for a triangular mesh graph, with the superscript T indicating transpose.

[0039] Further, step S3 includes:

[0040] S31: Obtain the initial set of cutting edges C based on the topological features of the input model. 0 ;

[0041] S32: Connect all singular points in the singular point set to the cutting line formed by connecting the beginning and end of several cutting edges in the cutting edge set using an iterative method. The following conditions must be met during the connection of singular points:

[0042] All the singularities fall on the cutting line;

[0043] Cutting lines should intersect each other as perpendicularly as possible;

[0044] After the input model is cut along the cutting line, it should be homologous to the disk.

[0045] The total length of the cutting line should be as short as possible.

[0046] Furthermore, step S31 specifically includes:

[0047] Determine the genus of the input model. If the genus of the input model is greater than 0, first find all n non-shrinkable loop handles on the input model, then recursively perform n-1 connection operations. Each connection uses the shortest path to connect the two currently disconnected loop handles. Finally, use the cut edges at the end of the recursion as the initial cut edge set C. 0 ;

[0048] If the genus of the input model is less than or equal to 0, then for each pair of singularities (σ) i ,σ j The cutting length is evaluated according to the following formula:

[0049]

[0050] Where p(σ) i ,σ j ) represents point σ i Point σ j The shortest path along the grid lines, d(.) represents the distance function, σ k Let d(σ) represent the k-th singularity. k ,p(σ i ,σ j The calculation method for )) is as follows:

[0051]

[0052] stσ m ∈p(σ i ,σ j ).

[0053] Where, σ m This represents the m-th singularity.

[0054] Take the length evaluation value l(σ) i ,σ j The path corresponding to the minimum value p(σ) i ,σ j ) as the initial set of cutting edges C 0 .

[0055] Furthermore, step S32 specifically includes:

[0056] For a set of singular points containing M points, when constructing the t-th cut, it is necessary to use the existing t-1 cuts to find the singular points that minimize the following expression:

[0057]

[0058] C t =p(σ k C t-1 )∪C t-1

[0059] In the formula, σ k Let C represent the k-th singularity. t-1 p(σ) represents the set of cutting edges corresponding to the (t-1)th cut. k C t-1 ) represents point σ k To the set of cutting edges C t-1 The shortest path along the grid lines;

[0060] Obtain the singular point σ corresponding to the minimum value k Then, the shortest path p(σ) will be obtained. k C t-1 The cut edges are then incorporated into the cut edge set to obtain the cut edge set C corresponding to the t-th cut. t .

[0061] The advantages of this invention compared to the prior art are as follows:

[0062] This invention, based on the discovery that "parameterization of polysquare-like structures is beneficial for stamping layout," presents a highly efficient 3D model cutting technique. This technique can map curved surfaces to a polysquare-like parameter domain with low distortion, thereby facilitating subsequent optimization of planar packing efficiency and ultimately achieving high-quality, high-efficiency stamping layout.

[0063] Through observation, this invention discovered that the corners of a multi-connected square have interior angles that are multiples of 90 degrees. When mapped to the cutting points of a curved surface, these angles correspond to angular defects that are multiples of 90 degrees. Since the singular points of a four-symmetric direction field naturally satisfy this angular defect property, this technical solution intends to draw on the technical concept of four-symmetric direction fields to guide the design of parameterization for high-quality and high-efficiency stamping material discharge.

[0064] This invention can efficiently and robustly achieve high-quality and high-efficiency stamping layout on several models, fully demonstrating the practical effect and value of the technology. Compared with existing cutting technologies, this invention can obtain higher quality stamping layout, with improvements in packing efficiency (PE), cutting length (BL), and shape distortion (ED). Attached Figure Description

[0065] Figure 1 A flowchart of a three-dimensional model cutting method for high-quality stamping layout;

[0066] Figure 2 This is a schematic diagram illustrating the process of cutting a 3D model using a specific input model as an example.

[0067] Figure 3 The graph shows the relative improvement of PE, BL, and ED metrics compared to traditional methods on the dataset. Here, af is the distribution graph comparing the present invention and the VarCuts method, and gl is the distribution graph comparing the present invention and the OptCuts method.

[0068] Figure 4 This is a schematic diagram of the material layout results from a 3D model. Detailed Implementation

[0069] The present invention will be further described and illustrated below with reference to the accompanying drawings and specific embodiments.

[0070] like Figure 1-2 The diagram shown is a flowchart of a three-dimensional model cutting method for high-quality stamping layout provided in a preferred embodiment of the present invention. Its main steps include four steps, namely S1 to S4:

[0071] S1: For the three-dimensional geometry of the input model, calculate the discrete Gaussian curvature, optimize to obtain a smooth discrete four-symmetric direction field on the three-dimensional surface, and then extract the singular points of the four-symmetric direction field.

[0072] S2: While fully considering the smoothness of the four-symmetric direction field, the singular points of the four-symmetric direction field extracted in step S1 are merged and simplified.

[0073] S3: For the simplified singularity in step S2, optimize to obtain a set of mutually perpendicular curved cutting edges, and then cut the input model into a model that is topologically homeomorphic to the disk along the curved cutting edges.

[0074] S4: Perform isotropic low-twist parameterization on the cut surface model;

[0075] S5: Utilize planar texture optimization technology to optimize the parameterized results, thereby obtaining high-quality stamping material layout.

[0076] The specific implementation methods of S1 to S4 in this embodiment and their effects are described in detail below.

[0077] First, while four-symmetric orientation field generation techniques are relatively mature, existing techniques often consider factors such as feature alignment and mesh density. Such redundant constraints not only lead to slow solution speeds but also cause the solver to get stuck in local optima instead of obtaining the global optimum. Therefore, the goal of step S1 should be the optimization of the four-symmetric orientation field under the intrinsic geometric features of the model, i.e., considering only the Gaussian curvature of the model without considering other irrelevant factors such as feature line alignment. To achieve this, this invention introduces an evaluation energy for the smoothness of the four-symmetric orientation field in relation to Gaussian curvature, thereby obtaining a four-symmetric orientation field and singularities that meet the application objectives.

[0078] For the discrete representation of a four-symmetric directional field, this invention adopts a piecewise constant form, meaning that the directional field has a fixed direction on each facet of the triangular mesh. Since any two triangles in a spatial triangular mesh are often non-coplanar, a local coordinate system is needed to account for the angular difference after parallel transmission of the directional field between different facests.

[0079] In this embodiment, a smooth four-symmetric directional field is designed according to S11 to S15 for the Gaussian curvature information at each point of the model:

[0080] S11: Define a local coordinate system on each facet of the input model, where the x-axis is the unit vector of any side of the triangle, the y-axis is obtained by rotating the x-axis counterclockwise by 90° in the triangle plane, and the z-axis is obtained by the cross product of the x-axis and the y-axis.

[0081] S12: For any common edge e connecting triangles i and j on the grid ij The smooth energy of the four-symmetric direction field is expressed as

[0082]

[0083] In the formula, θ i and θ j κ represents the angle between any component of the four symmetric direction fields on triangles i and j and the x-axis. ij p represents the angular difference between the parallel x-axis transmissions of triangles i and j, and is an integer. ij This represents the alignment jump between two triangular direction fields. This represents the four-symmetric direction field from triangle i along the common side e. ij The smooth energy transmitted in parallel to triangle j;

[0084] S13: Integrate the smoothing energy of the four-symmetric direction field over the entire input model. Where A ij Let E be the average area of ​​triangles i and j, and obtain E using a mixed integer solver.s All θ corresponding to the minimum value i θ j and p ij ;

[0085] S14: For each vertex v on the triangular mesh i Calculate its angle deficiency in, ∠jik represents vertex v i Discrete Gaussian curvature, N(v) i ) represents the vertex v i The set of triangles surrounding the center, Δ ijk Indicates that by vertex v i v j v k The triangle formed is ∠jik, where ∠jik represents the angle value; then, based on the value of each vertex v... i The angle defect, further calculate v i Corresponding integer basic index All vertices are represented by their corresponding integer base indices α. b (v i ) constitute the basic index set I b ;

[0086] S15: Based on the basic index set I b Calculate v at each vertex in a four-symmetric direction field. i index The indices α(v) of all vertices i ) constitute the index set I(v i Extract set I(v) i Points that are not equal to 0 in the equation are taken as singular points extracted in step S1.

[0087] When the surface geometry of the input model has many undulations, the number of singular points obtained in step S1 is often enormous, posing a significant computational challenge to subsequent cutting processes. Furthermore, redundant neighboring singular points not only result in numerous jagged edges on the cutting lines but also lead to excessively long cutting lines and fragmented packing in the final layout. Inspired by the Gauss-Bonnet theorem, this invention proposes a method to merge and simplify neighboring singular point pairs with indices (-1, +1) while maintaining a global topology for the four-symmetric direction field. However, simply merging the nearest (-1, +1) point pairs has two major drawbacks: firstly, due to the geometric specificity of the model, a unified merging termination condition is difficult to determine; secondly, it is difficult to assess the degree of distortion after subsequent cutting solely based on the number of singular points. Therefore, this invention presents a singular point simplification method that fully considers the intrinsic geometry of the model. Specifically, the singular point merging and simplification process in this embodiment is mainly implemented through step S2, and its specific method is described in detail below:

[0088] S21: Based on the index of each singular point, construct an index vector α = [α1, α2, ..., α3] using the index values ​​of the singular points. i ,...,α N ], where α i Let N be the index value corresponding to the i-th singularity, and let N represent the number of singularities in the four-symmetric direction field extracted in step S1.

[0089] S22: Enumerate all integer vector pairs δ i and δ j (i≠j) is used in the calculation of step S23, where δ i and δ j The dimension of δ is the same as the dimension of the index vector α, and δ i Only the i-th element is 1, and all other elements are 0, δ j Similarly, only the j-th element is 1;

[0090] S23: Iteratively optimize the index vector α according to the following model:

[0091]

[0092]

[0093] Where, α k This represents the index vector of the k-th iteration, with the initial value α of the iteration. 0 This is the α obtained in step S21, where ||.||0 represents the L0 norm. S represents the index value of the i-th singular point in the index vector of the k-th iteration. k This represents the simplified energy function value for the k-th iteration; here EI (α k The symbol represents the smoothness of the four-symmetric direction field at the k-th iteration. The specific calculation method is as follows:

[0094]

[0095] Where, α g It is a vector composed of the discrete Gaussian curvatures of all singular points. It is the pseudo-inverse matrix of the Laplacian operator for a triangular mesh graph, with the superscript T indicating transpose;

[0096] Additionally, w n It is a weight value, calculated as follows:

[0097]

[0098] Here, ||α 0 ||0 represents the vector α 0 The number of non-zero elements, where λ is a parameter controlling the number of singularities;

[0099] S24: When S k ≥S k-1 When the time limit is reached, stop the optimization and set the index vector α in the (k-1)th iteration. k-1 Find all non-zero elements and take the points corresponding to all non-zero elements as the final singular points.

[0100] After step S2 above, the simplified set of singularities can be determined. To meet the requirements of high-efficiency and high-quality stamping layout, this invention needs to connect the simplified singularities through cutting lines, thereby flattening the curved surface model with low distortion into a planar region resembling a multi-connected square. To achieve this, the following conditions must be met during the connection of singularities: First, all singularities must fall on the cutting lines; second, the cutting lines should intersect each other as perpendicularly as possible; third, the model should be homogeneous with the disk after being cut along the cutting lines; fourth, the total length of the cutting lines should be as short as possible. In this embodiment, to simultaneously meet the above four conditions, the specific method for perpendicular cutting in step S3 is as follows:

[0101] S31: Obtain the initial cut based on the topological features of the input model: Determine the genus of the input model. If the genus of the input model is greater than 0, proceed to step S32 after executing step S311; otherwise, proceed to step S32 after executing step S312.

[0102] S311: First, find all n non-shrinkable handles in the input model. Then, recursively perform n-1 connection operations, using the shortest path to connect the two currently disconnected handles in each connection. Finally, use the cut edges at the end of the recursion as the initial cut edge set C.0 ;

[0103] In this embodiment, the connecting lines in each triangular grid are called cutting edges, and several tangent edges connected end to end form a cutting line.

[0104] S312: For each pair of singular points (σ) i ,σ j The cutting length is evaluated according to the following formula:

[0105]

[0106] Where p(σ) i ,σ j ) represents point σ i Point σ j The shortest path along the grid lines, d(.) represents the distance function, σ k Let d(σ) represent the k-th singularity. k ,p(σ i ,σ j The calculation method for )) is as follows:

[0107]

[0108] stσ m ∈p(σ i ,σ j ).

[0109] Where, σ m This represents the m-th singularity.

[0110] Take the length evaluation value l(σ) i ,σ j The path corresponding to the minimum value p(σ) i ,σ j ) as the initial set of cutting edges C 0 ;

[0111] S32: An iterative approach is used to connect all singular points in the singular point set to the cutting line. Specifically, for a singular point set containing M points, when constructing the t-th cut, it is necessary to use the existing t-1 cuts to find the singular point that minimizes the following expression:

[0112]

[0113] C t =p(σ k C t-1 )∪C t-1

[0114] In the formula, C t-1p(σ) represents the set of cutting edges corresponding to the (t-1)th cut. k C t-1 ) represents point σ k To the set of cutting edges C t-1 Find the shortest path along the grid lines; obtain the singular point σ corresponding to the minimum value. k Then, the shortest path p(σ) will be obtained. k C t-1 The cut edges are then incorporated into the cut edge set to obtain the cut edge set C corresponding to the t-th cut. t .

[0115] Thus, through the aforementioned S1 to S3, a complete vertical cut of the three-dimensional model has been obtained, meaning that a three-dimensional surface with any topological shape can be cut into a surface that is homeomorphic to the disk along the cutting line.

[0116] The specific parameterization method for step S4 is briefly described below:

[0117] S41: Cut the model along the cutting line obtained in step S3, and use the Tutte graph embedding algorithm to deform the cut surface model into planar space;

[0118] S42: Optimizing the symmetric Dirichlet energy in planar space:

[0119]

[0120] Among them, a i f represents the i-th triangle i The area, J i This represents the Jacobian deformation of a curved triangle under a plane mapping. This represents the square of the F-norm.

[0121] Thus, the present invention has constructed a low-twist mapping from a three-dimensional curved surface to a shape resembling a multi-connected square, in order to achieve a high-quality and high-efficiency stamping material discharge effect.

[0122] Next, the parameterization results are further optimized using a planar parameterization optimization method:

[0123] S5: Using the planar parametric optimization method (Liu HY, Fu XM, Ye C, et al. Atlas refinement with bounded packing efficiency[J]. ACM Transactions on Graphics(TOG),2019,38(4):1-13.), and setting the lower bound of packing efficiency to 0.8, the final stamping discharge is obtained.

[0124] The following demonstrates the effect of applying the methods described in the above embodiments to specific examples. The specific process is as described above and will not be repeated here; the following mainly shows the specific parameter settings and the achieved results.

[0125] The following describes the invention in detail using a model based on a publicly available dataset as an example. The specific steps are as follows:

[0126] 1) Using the publicly available dataset from a top international journal paper (Liu HY, Fu XM, Ye C, et al. Atlas refinement with bounded packing efficiency[J]. ACM Transactions on Graphics(TOG),2019,38(4):1-13.), for each model in the dataset, the Blender software was used to stitch up the cracks, and non-manifolds and edge-degenerate triangular meshes were removed from the stitched models. Among them, there are a total of 5588 models in the publicly available dataset, and 53 models have non-manifolds or edge-degenerate meshes during the stitching process, for a total of 5588-53=5519 valid data.

[0127] 2) Following step S1 above, for each model in the effective dataset, establish an optimization model based on the smooth energy described above, and solve it using the mixed integer optimization solver in the libitl code library to obtain a smooth four-symmetric direction field, and extract singular points according to the method mentioned above.

[0128] 3) Following step S2 above, iteratively simplify the singular points. In each iteration, find the optimal (-1, +1) singular point pair to merge, reducing the number of singular points while considering the degree of deformation of the model after cutting. In this embodiment, the weight ratio of the model's shape distortion energy to the number of singular points is 1:0.5, that is, λ is set to 0.5. The iteration stops when the total optimization energy no longer decreases.

[0129] 4) Connect the simplified singular points according to the aforementioned step S3. First, classify them according to the topological features of the input model. If they are not homeomorphic to the sphere, perform the initial cutting process according to the aforementioned S311. If they are homeomorphic to the sphere, perform the processing according to S312. Then, perform the subsequent cutting design according to step S32.

[0130] 5) Following the aforementioned step S4, the model is cut into a disk-homeomorphic surface using the cutting line in step S3, and then low-twist planar parametric mapping is performed.

[0131] The cutting method of this invention is named OrthoCuts. Compared with the original classic VarCuts method (Sharp N, Crane K. Variational surface cutting[J]. ACM Transactions on Graphics(TOG),2018,37(4):1-13.) and OptCuts method (Li M, Kaufman DM, Kim VG, et al. Optcuts: Joint optimization of surface cuts and parameterization[J]. ACM Transactions on Graphics(TOG),2018,37(6):1-13.), it improves in bin packing efficiency (PE), cutting length (BL), and shape distortion (ED). On the entire dataset, the relative improvements in bin packing efficiency, cutting length, and shape distortion were statistically analyzed:

[0132]

[0133]

[0134]

[0135] Wherein, the superscript "our" represents the quantitative index value in this invention, and the superscript "cmp" represents the index value in the comparison. The percentage statistics on the entire dataset are shown in Table 1 below:

[0136] Table 1

[0137]

[0138] To further analyze the number of results for each category compared to the classical methods in the comparative analysis, all results in the dataset were divided into four categories: A) All three indicators of the proposed OrthoCuts method are superior to the comparative method; B) Two indicators of the proposed OrthoCuts method are superior to the comparative method, and one indicator is inferior to the comparative method; C) One indicator of the proposed OrthoCuts method is superior to the comparative method, and two indicators are inferior to the comparative method; D) All three indicators of the proposed OrthoCuts method are inferior to the comparative method. The specific statistical results are shown in Table 2.

[0139] Table 2

[0140]

[0141] To more intuitively demonstrate the performance comparison of methods under various indicators, this invention provides relative improvement values ​​(r) for packing efficiency, cutting length, and shape distortion. PE ,r BL ,rED The discrete frequency distribution plot of ), and the two-dimensional discrete distribution plot of pairwise combinations of relative boost values. For example... Figure 3 As shown, af is a comparison distribution plot with VarCuts, gl is a comparison distribution plot with OptCuts, and a and g represent the r... PE The distribution of r, b and h represent r BL The distribution of r, c and i represent r ED The distribution. From Figure 3 As can be seen, compared to the classic techniques VarCuts and OptCuts, most of the results in the data satisfy r. PE ≥0,r BL ≥0,r ED ≥0, therefore, this invention achieves a material layout effect that simultaneously possesses higher packing efficiency, shorter cutting length, and less twisting. Furthermore, to demonstrate the material layout effect on specific models, this invention also presents several example results, such as... Figure 4 As shown, the present invention can flatten the model into a polysquare structure with low distortion by cutting perpendicularly to each other, thereby obtaining a high-efficiency and high-quality material layout result.

[0142] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A three-dimensional model cutting method for high-quality stamping layout, characterized in that, Includes the following steps: S1: Based on the discrete Gaussian curvature of the input model, optimize the smooth discrete four-symmetric direction field on the three-dimensional surface of the input model to obtain the singular points of the discrete direction field. Step S1 includes: S11: Define a local coordinate system on each facet of the input model; S12: For any common edge connecting triangle i and triangle j on the mesh of the input model. Calculate the smoothing energy of the four-symmetric direction field: ； In the formula, and Let represent the angles between any component of the four symmetric direction fields on triangles i and j and the x-axis, respectively. This represents the angular difference between the parallel transmission along the x-axis of triangles i and j. This indicates an alignment jump between two triangular direction fields. This represents the four-symmetric direction field from triangle i along the common edge. The smooth energy transmitted in parallel to triangle j; S13: Integrate the smooth energy of the four-symmetric direction field and find the point corresponding to the minimum value of the integral. , as well as ; S14: Calculate the corresponding integer basic index based on the angle deficit of each vertex: ； in, Representing vertices A set of triangles surrounding the center. Represents vertices The corner is missing, Represents vertices Corresponding integer base index; the integer base index corresponding to all vertices. Constructing the basic index set ; S15: Based on the basic index set Calculate the field at each vertex in the four-symmetric direction. Index: ； Indices of all vertices Construct an index set Extract the set Points corresponding to non-zero elements are considered singular points; S2: Simplify the singular points of the discrete direction field obtained in step S1; Step S2 includes: S21: Based on the index of each singular point, construct an index vector from the index values ​​of the singular points. ,in, Let N be the index value corresponding to the i-th singularity, and let N represent the number of singularities in the four-symmetric direction field extracted in step S1. S22: Enumerate all integer vector pairs and , , and Dimensions and index vectors The dimensions are the same, and Only the i-th element is 1, and all other elements are 0. Only the j-th element is 1, and all other elements are 0; S23: For index vectors Iterative optimization will be carried out accordingly: ； in, This represents the index vector of the k-th iteration, and the initial value of the iteration. This is what was obtained in step S21. , Describing the L0 norm, Let represent the index value of the i-th singularity in the index vector of the k-th iteration. This represents the simplified energy function value for the k-th iteration; This indicates the smoothness of the four-symmetric direction field at the k-th iteration. It is the weight value; S24: When When the time limit is reached, stop the optimization and use the index vector in the (k-1)th iteration. Find all non-zero elements and take the points corresponding to all non-zero elements as the final singular points; S3: Connect the singular points obtained in step S2 to obtain a set of mutually perpendicular curved surface cutting edges; S4: Cut the input model into a topologically homeomorphic model of the disk along the cutting edge of the surface, and perform isotropic low-twist parameterization on the cut surface model; S5: Optimize the parameterized results using planar texture optimization technology to obtain stamping material layout.

2. The three-dimensional model cutting method for high-quality stamping layout according to claim 1, characterized in that, Each vertex The formula for calculating the angle deficit is: ； in, Represents vertices Discrete Gaussian curvature, Indicates the origin of the vertex , , The triangle formed Indicates the angle value.

3. The three-dimensional model cutting method for high-quality stamping layout according to claim 1, characterized in that, The formula for calculating the smoothness of the symmetrical direction field is as follows: ； in, It is a vector composed of the discrete Gaussian curvatures of all singular points. It is the pseudo-inverse matrix of the Laplacian operator for a triangular mesh graph, with the superscript T indicating transpose.

4. The three-dimensional model cutting method for high-quality stamping layout according to claim 1, characterized in that, Step S3 includes: S31: Obtain the initial set of cutting edges based on the topological features of the input model. ; S32: Connect all singular points in the singular point set to the cutting line formed by connecting the beginning and end of several cutting edges in the cutting edge set using an iterative method. The following conditions must be met during the connection of singular points: All the singularities fall on the cutting line; Cutting lines should intersect each other as perpendicularly as possible; After the input model is cut along the cutting line, it should be homologous to the disk. The total length of the cutting line should be as short as possible.

5. The three-dimensional model cutting method for high-quality stamping layout according to claim 4, characterized in that, The specific steps of S31 are as follows: Determine the genus of the input model. If the genus of the input model is greater than 0, first find all n non-shrinkable handle loops in the input model, then recursively perform n-1 connection operations. Each connection uses the shortest path to connect the two currently disconnected handle loops. Finally, use the cut edges at the end of the recursion as the initial cut edge set. ; If the genus of the input model is less than or equal to 0, then for each pair of singularities... The cutting length is evaluated according to the following formula: ； in, Point Time The shortest path along the grid lines, Represents the distance function. This represents the k-th singularity. The calculation method is as follows: ； in, This represents the m-th singularity. Take the length evaluation value The path corresponding to the minimum As the initial set of cutting edges .

6. The three-dimensional model cutting method for high-quality stamping layout according to claim 5, characterized in that, The specific steps of S32 are as follows: For a set of singular points containing M points, when constructing the t-th cut, it is necessary to use the existing t-1 cuts to find the singular points that minimize the following expression: ； ； In the formula, This represents the k-th singularity. This represents the set of cutting edges corresponding to the (t-1)th cut. Point To the cutting edge collection The shortest path along the grid lines; Represents the distance function; Find the singularity corresponding to the minimum value Then, the shortest path will be obtained. By incorporating the cut edges into the cut edge set, we obtain the cut edge set corresponding to the t-th cut. .

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