A hexahedral mesh model generation method, CAE software, device and medium

Abstract

The application relates to the field of mechanical product structure design and manufacturing, and provides a hexahedral mesh model generation method, CAE software, equipment and medium, which selects candidate cutting surfaces to form a candidate cutting surface set based on geometric data of a geometric model in the CAE software; each candidate cutting surface of the candidate cutting surface set is evaluated; the geometric model is cut according to an evaluation result and based on a preset rule, a swept volume set of the geometric model is obtained, and a hexahedral mesh model of the geometric model is generated according to the swept volume set. The application can automatically evaluate the candidate cutting surfaces in the CAE software, and automatically select the evaluated candidate cutting surfaces for cutting the geometric model. The automatic evaluation and selection of the cutting surfaces improve the efficiency of geometric model cutting and hexahedral mesh generation, reduce the time cost of CAE software simulation pretreatment, improve the simulation efficiency of the mesh model in the CAE, and thus reduce the mechanical product production time cost.

Description

Technical Field

[0001] This application relates to the field of mechanical product structural design and manufacturing, and in particular to a method for generating a hexahedral mesh model, CAE software, equipment, and medium. Background Technology

[0002] In the field of mechanical product structural design and manufacturing, the production of a mechanical part involves key technologies such as computer-aided design (CAD), computer-aided engineering (CAE), computer-aided process planning (CAPP), and computer-aided manufacturing (CAM) systems. Among them, computer-aided engineering (CAE) integrates computer simulation, numerical analysis, and modeling techniques to help engineers predict and optimize product performance, reliability, and safety during the design phase, reducing the need for physical prototype testing and thus lowering development costs and time.

[0003] In fields such as fluid dynamics simulation and mechanical structure simulation, hexahedral meshes offer higher computational accuracy and lower computational cost compared to other mesh types. Therefore, researching hexahedral mesh generation technology is of great significance for simulation solutions in these fields. The sweeping method is a typical hexahedral mesh generation technique, requiring each geometry to be a swept volume. However, a crucial step in generating hexahedral meshes using the sweeping method is selecting suitable cutting surfaces to cut the general geometric model into a set of swept volumes. Currently, however, the cutting surfaces used to cut the geometric model into swept volumes require manual evaluation and selection by the user (i.e., manually evaluating whether the cutting surfaces are suitable for cutting the geometric model, and selecting them manually if the evaluation result is suitable). This manual evaluation and selection of cutting surfaces leads to low efficiency in geometric model cutting and hexahedral mesh generation, reduces the automation level of mesh generation, increases the time cost of pre-processing in CAE software simulation, reduces the simulation solution efficiency of the mesh model in CAE, and thus increases the production time cost of mechanical products. Summary of the Invention

[0004] This application provides a method for generating a hexahedral mesh model, CAE software, equipment, and medium to solve the problem of low efficiency in simulating and solving mesh models in CAE software, which leads to high production time and costs for mechanical products.

[0005] The first aspect of this application provides a method for generating a hexahedral mesh model. This method is applied in CAE software and generates a hexahedral mesh model of the geometric model by performing the following steps:

[0006] Candidate cutting surfaces are selected based on the geometric data of the geometric model to form a candidate cutting surface set;

[0007] Evaluate each candidate cutting face in the candidate cutting face set;

[0008] Based on the evaluation results and according to preset rules, the geometric model is cut to obtain the set of swept volumes corresponding to the geometric model;

[0009] A hexahedral mesh model of the geometric model is generated from the swept body set.

[0010] In some embodiments of this application, the geometric data includes geometric planes, and the step of selecting candidate cutting surfaces to form a candidate cutting surface set based on the geometric data of the geometric model includes:

[0011] Based on geometric data, preset normal vectors and preset geometric vertices are used to construct candidate cutting surfaces, and / or geometric planes are used as candidate cutting surfaces, and all the resulting candidate cutting surfaces are combined into a candidate cutting surface set.

[0012] In some embodiments of this application, the step of evaluating each candidate cutting surface in the candidate cutting surface set includes:

[0013] Based on the geometric data, calculate the geometric factor influence value corresponding to each candidate cutting surface;

[0014] Each candidate cutting surface is scored based on the influence value of geometric factors to obtain the evaluation result of each candidate cutting surface.

[0015] In some embodiments of this application, the geometric factor influence values ​​include: the shortest edge factor influence value, and / or the face intersection factor influence value, and / or the face sinusoidal factor influence value, and / or the face distribution factor influence value, and / or the edge number factor influence value. The geometric data also includes geometric edges and geometric surfaces. The step of calculating the geometric factor influence value corresponding to each candidate cutting surface based on the geometric data includes:

[0016] Select geometric edges to form a geometric edge set, perform intersection detection on the geometric edges and each candidate cutting surface, and calculate the shortest edge factor influence value corresponding to each candidate cutting surface based on the intersection detection results and the shortest geometric edge in the geometric model.

[0017] Select geometric surfaces to form a set of geometric surfaces, perform intersection detection on the geometric surfaces and each candidate cutting surface, and calculate the influence value of the surface intersection factor corresponding to each candidate cutting surface based on the intersection detection results;

[0018] Select geometric planes to form a set of geometric planes, perform intersection detection between the geometric planes and each candidate cutting plane, and calculate the influence value of the surface sinusoidal factor corresponding to each candidate cutting plane based on the intersection detection results and the preset dihedral angle sine value;

[0019] Determine the positional relationship between the geometric plane in the geometric plane set and each candidate cutting surface, and calculate the influence value of the surface distribution factor corresponding to each candidate cutting surface based on the positional relationship;

[0020] The number of geometric edges intersecting with each candidate cutting face in the geometric edge set is counted. Based on the number of geometric edges in the geometric edge set and the number of geometric edges intersecting with each candidate cutting face, the influence value of the edge number factor for each candidate cutting face is calculated.

[0021] In some embodiments of this application, the preset rule is:

[0022] The geometric model is cut sequentially using candidate cutting surfaces corresponding to high to low scores to obtain the geometric body corresponding to the geometric model. The cutting result of the previous candidate cutting surface is used as the cutting object of the next candidate cutting surface.

[0023] The geometric objects form a set of swept bodies corresponding to the geometric model.

[0024] In some embodiments of this application, the step of sequentially cutting the geometric model using candidate cutting surfaces corresponding to high to low scores to obtain the geometric body corresponding to the geometric model includes:

[0025] After cutting the geometric model using each candidate cutting face, it is determined whether the resulting geometry is a swept volume. If it is, the cutting of the geometric model is stopped; otherwise, the cutting of the geometric model is continued using the next candidate cutting face until the resulting geometry is a swept volume, at which point the cutting of the geometric model is stopped.

[0026] In some embodiments of this application, the step of generating a hexahedral mesh model of the geometric model based on the swept volume set includes:

[0027] The source surface, target surface, and side surface of each sweep body in the sweep body set are found according to the preset geometric rules.

[0028] Each sweep body sweeps from the source face to the target face, along the side to generate a hexahedral mesh corresponding to each sweep body;

[0029] Based on all swept bodies in the swept body set, the hexahedral mesh model of the geometric model is calculated.

[0030] The second aspect of this application provides CAE software that performs the following steps to complete the simulation test of a geometric model:

[0031] Using the hexahedral mesh model generation method described in any of the above embodiments, a hexahedral mesh model of the geometric model is calculated based on the geometric data of the geometric model;

[0032] The geometric model was simulated and tested based on the hexahedral mesh model.

[0033] A third aspect of this application provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method described in any of the first aspects of the above embodiments.

[0034] A fourth aspect of this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in any of the first aspects of the above embodiments.

[0035] This application has the following beneficial effects:

[0036] The embodiments described above integrate a hexahedral mesh generation method into CAE software. After the CAE software obtains the geometric data of the geometric model, firstly, candidate cutting surfaces are selected based on the geometric data to form a candidate cutting surface set; secondly, each candidate cutting surface in the candidate cutting surface set is evaluated; then, the geometric model is cut according to the evaluation results and based on preset rules to obtain a sweep volume set corresponding to the geometric model; finally, a hexahedral mesh model of the geometric model is generated based on the sweep volume set. The embodiments described above can automatically evaluate candidate cutting surfaces in CAE software and automatically select the evaluated candidate cutting surfaces for cutting the geometric model. This automated evaluation and selection of cutting surfaces improves the efficiency of geometric model cutting and hexahedral mesh generation, reduces the time cost of CAE software simulation preprocessing, and improves the simulation solution efficiency of the mesh model in CAE, thereby reducing the production time cost of mechanical products. Attached Figure Description

[0037] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with this application and, together with the specification, serve to explain the technical solutions of this application.

[0038] Figure 1 This is a schematic flowchart of an embodiment of the hexahedral mesh model generation method provided in this application;

[0039] Figure 2 This is a schematic flowchart of an embodiment of the candidate cutting surface evaluation method provided in this application;

[0040] Figure 3 This is a schematic flowchart of an embodiment of the method for calculating the geometric influence value of candidate cutting surfaces provided in this application;

[0041] Figure 4 This is a schematic flowchart of an embodiment of the method for calculating the influence value of the shortest side factor of the candidate cutting surface provided in this application;

[0042] Figure 5 This is an example schematic diagram of dividing geometric edges using intersection points, as provided in this application;

[0043] Figure 6 This is a schematic diagram of an example framework of the swept volume and hexahedral mesh provided in this application;

[0044] Figure 7 This is a schematic flowchart of an embodiment of the method for calculating hexahedral meshes based on swept volumes provided in this application;

[0045] Figure 8 This is a schematic flowchart of an embodiment of the CAE software simulation testing method provided in this application;

[0046] Figure 9 This is an example schematic diagram of a connecting rod model on an automobile engine provided in this application;

[0047] Figure 10 This is an example schematic diagram of a hexahedral mesh model of a connecting rod on an automobile engine provided in this application;

[0048] Figure 11 This is a schematic diagram of the framework of an embodiment of the electronic device provided in this application;

[0049] Figure 12 This is a schematic diagram of a framework of an embodiment of the computer-readable storage medium provided in this application. Detailed Implementation

[0050] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0051] In the following description, specific details such as particular system architectures, interfaces, and technologies are presented for illustrative purposes rather than for limiting purposes, in order to provide a thorough understanding of this application.

[0052] In this document, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " generally indicates that the preceding and following related objects have an "or" relationship. Furthermore, "many" in this document means two or more. Moreover, the term "at least one" in this document means any combination of at least two of any one or more of a plurality of objects. For example, including at least one of A, B, and C can mean including any one or more elements selected from the set consisting of A, B, and C.

[0053] As described in the background section, currently, in the process of cutting a geometric model into a swept body, the cutting surface used to cut the geometric model needs to be manually evaluated and selected by the user (i.e., the cutting surface is evaluated manually to determine whether it is suitable for cutting the geometric model, and if the evaluation result is suitable, the cutting surface is selected manually to cut the geometric model). This manual evaluation and selection of the cutting surface makes the cutting of the geometric model and the generation of hexahedral meshes inefficient, reduces the automation of mesh generation, increases the time cost of preprocessing for CAE software simulation, reduces the simulation solution efficiency of the mesh model in CAE, and thus increases the production time cost of mechanical products.

[0054] To address the aforementioned problems, this application proposes a method for generating hexahedral mesh models. This method is applied in CAE software, and as follows... Figure 1 As shown, the method of this application performs the following steps S1-S4 to generate a hexahedral mesh model of the geometric model: S1, select candidate cutting surfaces based on the geometric data of the geometric model to form a candidate cutting surface set; S2, evaluate each candidate cutting surface in the candidate cutting surface set; S3, cut the geometric model according to the evaluation results and based on preset rules to obtain a sweep body set corresponding to the geometric model; S4, generate a hexahedral mesh model of the geometric model based on the sweep body set.

[0055] As described above, the embodiments of this application can automatically evaluate candidate cutting surfaces in CAE software and automatically select the evaluated candidate cutting surfaces for cutting the geometric model. This automated evaluation and selection of cutting surfaces improves the efficiency of geometric model cutting and hexahedral mesh generation, reduces the time cost of CAE software simulation preprocessing, improves the simulation efficiency of mesh models in CAE, and thus reduces the production time cost of mechanical products.

[0056] To better understand the technical solutions of the above embodiments of this application, steps S1-S4 will be described in detail below.

[0057] I. Step S1

[0058] According to one embodiment of this application, the geometric data includes: geometric topology objects include: geometric bodies, geometric faces, geometric edges, and geometric vertices; topological relationships include: inclusion relationships and adjacency relationships, wherein the inclusion relationship indicates that a geometric body includes a geometric face, a geometric face includes a geometric edge, and a geometric edge includes a geometric vertices; the adjacency relationship indicates the connection relationship between geometric faces, the connection relationship between geometric edges, and the connection relationship between geometric vertices. It should be noted that geometric topology objects may also include shells, loops, etc., and the inclusion relationship further indicates that a geometric body includes a shell, a shell includes a geometric face, a geometric face includes a loop, etc. Specific geometric topology objects and their corresponding topological relationships can be defined according to the structural characteristics of the geometric model to be processed, and are not specifically limited here.

[0059] As described above, the embodiments of this application generate hexahedral meshes of geometric models based on the aforementioned geometric data. This fully utilizes geometric topological objects (such as geometric bodies, geometric faces, geometric edges, and geometric vertices) and their topological relationships (inclusion and adjacency relationships) to accurately describe the geometric structure and connectivity characteristics of the geometric model, thereby significantly improving the accuracy and efficiency of hexahedral mesh generation. By clarifying the inclusion relationships between geometric bodies and geometric faces, geometric faces and geometric edges, and geometric edges and geometric vertices, as well as the adjacency relationships between geometric faces, geometric edges, and geometric vertices, the integrity and consistency of the geometric model during mesh generation can be improved, avoiding topological errors or mesh distortion. Simultaneously, the simulation and solution efficiency of the mesh model in CAE is improved, thereby reducing the production time cost of mechanical products.

[0060] In one embodiment of this application, the geometric surface includes a geometric plane, and step S1 includes: constructing candidate cutting surfaces by presetting normal vectors and presetting geometric vertices based on geometric data, and / or using the geometric plane as a candidate cutting surface, and forming a candidate cutting surface set by combining all the obtained candidate cutting surfaces.

[0061] According to one embodiment of this application, the geometric topology of the geometric model is determined based on the geometric data of the geometric model. Based on the geometric topology, a normal vector and a geometric vertex are preset to determine a plane, and this plane is used as a candidate cutting surface.

[0062] For example, given a vertex and normal vector Then the point normal equation of the candidate cutting surface is 2(x-1)-1(y-2)+4(z-3)=0. From this, we can see that users can combine the topological properties of the geometric model to design specified normal vector data and specified vertex data to determine a plane.

[0063] As described above, users can determine a plane based on the topology of the geometric model by inputting specific normal vector and vertex data. This plane can then be used as a candidate cutting surface to cut the geometric model. This method of using a plane designed in conjunction with the geometric topology of the geometric model to cut the model improves the quality of subsequent hexahedral mesh generation. Furthermore, this method of designing candidate cutting surfaces based on the topology of the geometric model can adapt to the topologies of different geometric models, providing a foundation for high-quality mesh generation tasks for various geometric models. In addition, using a geometric plane in the geometric model as a candidate cutting surface eliminates the need to reconstruct the candidate cutting surface, simplifying the cutting process and improving the cutting efficiency of the geometric model as well as the generation efficiency of hexahedral meshes.

[0064] II. Step S2

[0065] According to one embodiment of this application, such as Figure 2 As shown, step S2 includes: S21, calculating the geometric factor influence value corresponding to each candidate cutting surface based on the geometric data; S22, scoring each candidate cutting surface based on the geometric factor influence value to obtain the evaluation result of each candidate cutting surface.

[0066] As described above, the embodiments of this application utilize the geometric data of the geometric model to calculate the geometric factor influence values ​​corresponding to the candidate cutting surfaces, and obtain the evaluation results of each candidate cutting surface based on the geometric factor influence values. This method of evaluating candidate cutting surfaces can avoid subsequent invalid or inefficient cutting operations on the geometric model, improve the cutting efficiency of the geometric model and the generation efficiency of the hexahedral mesh, thereby improving the simulation efficiency of the mesh model in CAE.

[0067] Steps S21 and S22 will be explained in detail below.

[0068] (a) Step S21

[0069] According to one embodiment of this application, the geometric factor influence value includes: the shortest edge factor influence value, and / or the surface intersection factor influence value, and / or the surface sinusoidal factor influence value, and / or the surface distribution factor influence value, and / or the edge number factor influence value. The geometric surface also includes a geometric curved surface, and as shown... Figure 3 As shown, this application calculates the geometric factor influence value corresponding to each candidate cutting surface by performing the following steps S211-S215. Steps S211-S215 are explained in detail below.

[0070] 1. Step S211

[0071] According to one embodiment of this application, still referring to Figure 3As shown, this application calculates the shortest side factor influence value corresponding to each candidate cutting surface in the following way: select geometric edges to form a geometric edge set, perform intersection detection between the geometric edges and each candidate cutting surface, and calculate the shortest side factor influence value corresponding to each candidate cutting surface based on the intersection detection results and the shortest geometric edge in the geometric model.

[0072] According to one embodiment of this application, the step of calculating the shortest side factor influence value corresponding to each candidate cutting surface based on the intersection detection results and the shortest geometric side in the geometric model includes: calculating the intersection point of the geometric side and each candidate cutting surface when the geometric side intersects with each candidate cutting surface; dividing the geometric side into two sides using the intersection point; calculating the updated shortest geometric side based on the initialized shortest geometric side and all sides obtained by dividing all geometric sides in the geometric side set that intersect with each candidate cutting surface; and calculating the shortest side factor influence value corresponding to each candidate cutting surface based on the shortest geometric side in the geometric model.

[0073] For example, such as Figure 4 As shown, select the geometric edges in the geometric model. ( And form a geometric edge set And the shortest geometric edge in the geometric model is denoted as and initializing the shortest geometric edge For any candidate cutting surface P, for geometric edges Perform an intersection check with P, if If it does not intersect with candidate cutting plane P, then skip it. Otherwise, calculate The intersection point o with the candidate cutting surface P is used to define the geometric edges. Divided into two sections and (For example, such as) Figure 5 As shown, if If it intersects with the candidate cutting plane P, then the intersection point will be used as the dividing point. Divided into two edges ( ), and will and respectively with the shortest geometric side The comparison is performed to update the shorter edge as the shortest geometric edge. By traversing the geometric edge set Perform the above operation on all geometric edges to obtain the updated shortest geometric edge. And based on the updated shortest geometric edge and the shortest geometric edge in the geometric model The influence value of the shortest side factor is calculated.

[0074] In one embodiment of this application, in step S211, the influence value of the shortest geometric edge factor is calculated based on the shortest geometric edge in the geometric model as follows:

[0075]

[0076] in, The value of the shortest side factor. Represents the updated shortest geometric edge. Let a, b, c, and d be the shortest geometric edge of the geometric model, and let a, b, c, and d be the preset first hyperparameter, second hyperparameter, third hyperparameter, and fourth hyperparameter, respectively. In one embodiment of this application, a = 1.0, b = 0.5, c = 0.25, and d = 0.0. It should be noted that the values ​​of a, b, c, and d in the above embodiment are only one example of this application, and the specific numerical design can be adaptively changed according to the characteristics of the geometric model and the characteristics of the candidate cutting surface; no specific limitation is made here.

[0077] As described above, the embodiments of this application detect the intersection of candidate cutting surfaces with geometric edges in the geometric model, divide the geometric edge into two edges when they intersect, and compare all the edges generated after dividing all geometric edges with the shortest geometric edge of the geometric model to obtain the shortest edge factor influence value corresponding to each candidate cutting surface. This can effectively evaluate the influence of candidate cutting surfaces on the local geometric features of the geometric model. When the updated shortest geometric edge is greater than or equal to the shortest geometric edge of the geometric model, a larger value is assigned, so that subsequent cutting operations on the geometric model will not lead to excessive refinement or degradation of key boundaries in the geometric model. When the updated shortest geometric edge is less than the shortest geometric edge of the geometric model but greater than a preset multiple of the shortest geometric edge of the geometric model, a certain value is also assigned, which can effectively balance the influence of subsequent cutting operations on the local geometric features of the geometric model, thereby maintaining the rationality and stability of mesh generation.

[0078] 2. Step S212

[0079] According to one embodiment of this application, still referring to Figure 3 As shown, this application calculates the influence value of the surface intersection factor corresponding to each candidate cutting surface in the following way: select geometric surfaces to form a set of geometric surfaces, perform intersection detection on the geometric surfaces and each candidate cutting surface, and calculate the influence value of the surface intersection factor corresponding to each candidate cutting surface based on the intersection detection results.

[0080] For example, selecting the geometric surface of the geometric model (j) Constructing a set of geometric surfaces Traversing the set of geometric surfaces All geometric surfaces are subjected to intersection detection with the candidate cutting surface P. If for any geometric surface... , If it intersects with the candidate cutting plane P, then =e, candidate cutting surface P and geometric surface in the geometric model Intersect, otherwise =f, candidate cutting surface P and geometric surface in the geometric model They do not intersect.

[0081] In one embodiment of this application, in step S212, the influence value of the surface intersection factor is calculated based on the intersection detection result in the following manner:

[0082]

[0083] in, Let e ​​and f be the influence values ​​of the surface intersection factor, respectively, and let f be the preset fifth and sixth hyperparameters. In one embodiment of this application, e = 0.0 and f = 1.0. It should be noted that the values ​​of e and f in the above embodiment are only one example of this application, and the specific numerical design can be adaptively changed according to the characteristics of the geometric model and the candidate cutting surface; no specific limitation is made here.

[0084] As described above, the embodiments of this application determine whether the candidate cutting surface intersects with the geometric surface in the geometric model during the cutting process, thereby obtaining the influence value of the surface intersection factor corresponding to the candidate cutting surface. This can effectively evaluate the applicability and potential influence of the candidate cutting surface in complex geometric feature areas. When the candidate cutting surface does not intersect with the geometric surface in the geometric model, a larger value is assigned, which can avoid destroying the continuity of the surface or introducing unnecessary geometric distortion when cutting the geometric model in the future, thereby better maintaining the integrity of the geometric model after cutting.

[0085] 3. Step S213

[0086] According to one embodiment of this application, still referring to Figure 3 As shown, this application calculates the surface sinusoidal factor influence value corresponding to each candidate cutting surface in the following way: select geometric planes to form a set of geometric planes, perform intersection detection between the geometric planes and each candidate cutting surface, and calculate the surface sinusoidal factor influence value corresponding to each candidate cutting surface based on the intersection detection results and the preset dihedral angle sine value.

[0087] According to one embodiment of this application, the step of calculating the surface sinusoidal factor influence value corresponding to each candidate cutting surface based on the intersection detection result and the preset dihedral angle sine value includes: calculating the dihedral angle sine value between the geometric plane and each candidate cutting surface when the geometric plane intersects with each candidate cutting surface; calculating all the dihedral angle sine values ​​calculated based on all geometric planes intersecting with each candidate cutting surface in the geometric plane set; comparing all the dihedral angle sine values ​​with the preset dihedral angle sine value, and selecting the smallest dihedral angle sine value as the surface sinusoidal factor influence value corresponding to each candidate cutting surface.

[0088] For example, selecting a geometric plane in a geometric model (j) Constructing a geometric plane set The sine of the dihedral angle is preset to 1.0 for the geometric plane. Perform intersection detection with candidate cutting surface P, if Intersecting with candidate cutting surface P, calculate The sine of the dihedral angle between P and P If the sine value of the dihedral angle Less than Then the influence value of the sinusoidal factor corresponding to each candidate cutting surface for By traversing the geometric plane set All geometric planes are subjected to intersection detection with the candidate cutting surface P to obtain the final surface sinusoidal factor influence value. .

[0089] As can be seen from the above description, the embodiments of this application can effectively evaluate the impact of cutting operations on the local smoothness and continuity of the geometric model by calculating the sine value of the dihedral angle between all geometric planes intersecting the candidate cutting surface and taking the smallest dihedral angle sine value as the influence value of the surface sine factor. This avoids introducing too small or sharp angles due to cutting, thereby ensuring that the geometric model maintains reasonable geometric features in key areas.

[0090] 4. Step S214

[0091] According to one embodiment of this application, the influence value of the surface distribution factor corresponding to each candidate cutting surface is calculated in the following manner: the positional relationship between the geometric plane in the geometric plane set and each candidate cutting surface is determined, and the influence value of the surface distribution factor corresponding to each candidate cutting surface is calculated based on the positional relationship.

[0092] According to one embodiment of this application, the step of calculating the influence value of the surface distribution factor corresponding to each candidate cutting surface based on the positional relationship includes: counting the number of geometric planes concentrated on both sides of each candidate cutting surface, and calculating the influence value of the surface distribution factor corresponding to each candidate cutting surface based on the number of geometric planes distributed on both sides of each candidate cutting surface.

[0093] For example, determining geometric plane sets geometric planes in (j) The positional relationship with each candidate cutting surface P (i.e., the candidate cutting surface to be evaluated) is determined, and the initialization is performed. and If it is 0, On one side of the candidate cutting surface, = +1; if On the other side of the candidate cutting surface, = +1; through iteration All geometric planes are used to determine their positional relationship with the candidate cutting surfaces, ultimately yielding the output. and .

[0094] In one embodiment of this application, in step S214, the influence value of the surface distribution factor is calculated based on the number of geometric planes distributed on both sides of each candidate cutting surface in the following manner:

[0095]

[0096] in, The influence value of surface distribution factors, This represents the number of geometric planes that are concentrated on one side of the candidate cutting surface. This represents the number of geometric planes that are concentrated on the other side of the candidate cutting surface. The number of geometric planes in the geometric plane set. This is a preset seventh hyperparameter. According to one embodiment of this application, It should be noted that the above embodiments... The value of is only one embodiment of this application. The specific numerical design can be adaptively changed according to the characteristics of the geometric model and the characteristics of the candidate cutting surface. No specific limitation is made here.

[0097] As described above, the embodiments of this application improve the controllability and adaptability of the calculation results by statistically analyzing the differences in the number of other candidate cutting surfaces on both sides of the candidate cutting surface, and by normalization processing and the introduction of hyperparameters. At the same time, by statistically analyzing the number of geometric planes on both sides, the problem of excessively concentrated or sparse distribution of cutting surfaces in local areas can be avoided when cutting the geometric model in the subsequent process, so that the candidate cutting surfaces can uniformly divide the geometric model, thereby improving the rationality and symmetry of the geometric model cutting.

[0098] 5. Step S215

[0099] According to one embodiment of this application, the influence value of the edge number factor corresponding to each candidate cutting surface is calculated in the following manner: the number of geometric edges intersecting with each candidate cutting surface in the geometric edge set is counted, and the influence value of the edge number factor corresponding to each candidate cutting surface is calculated based on the number of geometric edges in the geometric edge set and the number of geometric edges intersecting with each candidate cutting surface in the geometric edge set.

[0100] For example, statistics The number of geometric edges T intersecting with each candidate cutting face. The total number of geometric edges in the middle is Q.

[0101] In one embodiment of this application, in step S215, the influence value of the edge number factor is obtained based on the number of geometric edges in the geometric edge set and the number of geometric edges in the geometric edge set intersecting with each candidate cutting surface in the following manner:

[0102]

[0103] in, The influence value of the number of edges. This represents the number of geometric edges in the geometric edge set that intersect with each candidate cutting face. The number of geometric edges in the geometric edge set. A second hyperparameter is preset. According to one embodiment of this application, It should be noted that the above embodiments... The value of is only one embodiment of this application. The specific numerical design can be adaptively changed according to the characteristics of the geometric model and the characteristics of the candidate cutting surface. No specific limitation is made here.

[0104] As described above, the embodiments of this application calculate the influence value of the edge number factor based on the number of geometric edges in the geometric edge set and the number of geometric edges in the geometric edge set that intersect with each candidate cutting surface. This can effectively evaluate the degree of cutting of the geometric model boundary by the candidate cutting surface, quantify the impact of the cutting operation on the geometric model boundary, and avoid excessive segmentation or destruction of the geometric model boundary when the candidate cutting surface is used to cut the geometric model, thus maintaining the integrity and rationality of the geometric model.

[0105] (ii) Step S22

[0106] According to one embodiment of this application, in step S22, the evaluation result of each candidate cutting surface is obtained based on the geometric factor influence value in the following manner:

[0107]

[0108] t=1,2,3,4,5

[0109] in, The weight value corresponding to the influence value of the shortest side factor. The weight values ​​corresponding to the influence values ​​of surface intersection factors. The weight values ​​corresponding to the influence values ​​of the sinusoidal factors are: The weight values ​​corresponding to the influence values ​​of the surface distribution factors. This represents the weight corresponding to the influence value of the edge number factor. In one embodiment of this application, =0.2, =0.2, =0.25, =0.25, =0.1. It should be noted that the values ​​of the five weights were adjusted and set according to the experimental results during the experiment. The five weights in this application are not limited to the values ​​in the above embodiment. The specific values ​​can be dynamically adjusted according to the characteristics of the geometric model and the experimental results.

[0110] As described above, the embodiments of this application comprehensively consider the influence values ​​of the shortest side factor, and / or the intersection factor, and / or the sinusoidal factor, and / or the distribution factor, and / or the number of sides factor corresponding to each candidate cutting surface. By weighting the influence values ​​of different factors with preset weight values, it can flexibly adapt to the needs of different geometric models, improve the accuracy and automation of cutting, and improve the simulation solution efficiency of the mesh model in CAE, thereby reducing the production time cost of mechanical products.

[0111] III. Step S3

[0112] According to one embodiment of this application, in step S3, the preset rule is: the geometric model is cut sequentially using candidate cutting surfaces corresponding to high to low scores to obtain the geometric body corresponding to the geometric model, wherein the cutting result of the previous candidate cutting surface is used as the cutting object of the next candidate cutting surface; the geometric bodies are used to form a sweep body set corresponding to the geometric model.

[0113] As described above, the embodiments of this application utilize candidate cutting surfaces with scores ranging from high to low to sequentially cut the geometric model. This improves the efficiency and rationality of the cutting operation, avoids redundant calculations on low-quality cutting surfaces, and significantly enhances the cutting efficiency of the geometric model, enabling the rapid acquisition of a high-quality mesh model. Simultaneously, it reduces the consumption of computational resources and lowers the simulation solution efficiency of the mesh model in CAE software, thereby reducing the production time cost of mechanical products.

[0114] In one embodiment of this application, in step S3, after cutting the geometric model using each candidate cutting surface, it is determined whether the resulting geometric bodies are all swept bodies. If they are all swept bodies, the cutting of the geometric model is stopped; otherwise, the cutting of the geometric model is continued using the next candidate cutting surface until the resulting geometric bodies are all swept bodies, at which point the cutting of the geometric model is stopped.

[0115] As described above, the embodiments of this application use candidate cutting surfaces with scores from high to low to cut the geometric model sequentially, and determine whether the resulting geometry is a swept body after each cut. Cutting the geometric model is stopped when all the resulting geometry is a swept body. This method can divide the geometric model into a set of geometry that meets the swept body condition in the shortest number of cuts, avoid over-cutting or invalid operations, and improve the generation efficiency of the hexahedral mesh model.

[0116] IV. Step S4

[0117] According to one embodiment of this application, such as Figure 6 and Figure 7 As shown, step S4 includes: S41, finding the source face, target face, and side face of each sweep body in the sweep body set according to preset geometric rules; S42, each sweep body sweeps from the source face to the target face and along the side face to generate a hexahedral mesh corresponding to each sweep body; S43, calculating the hexahedral mesh model of the geometric model based on all sweep bodies in the sweep body set, that is, performing the above steps S41-S42 on all sweep bodies in the sweep body set to obtain the hexahedral mesh model of the geometric model.

[0118] According to one embodiment of this application, in step S41, the preset geometric rule is as follows: based on the geometric topology of the swept volume, find two faces in the swept volume whose vertices coincide after an affine transformation, and designate one face as the source face and the other face as the target face; find the face connecting the source face and the target face and designate it as the side face. According to one embodiment of this application, the affine transformation includes transformations such as rotation, and / or translation, and / or scaling. That is, after a rotation transformation, the vertices of the two faces can completely coincide; or after a translation transformation, the vertices of the two faces can completely coincide; or after a scaling transformation, the vertices of the two faces can completely coincide.

[0119] It should be noted that rotation, translation, and scaling are only some of the affine transformations exemplified in this application. This application can also use other types of affine transformations to determine the source and target surfaces in the swept volume, without making specific limitations here.

[0120] As described above, defining the source and target surfaces in the swept volume through affine transformations (such as rotation, translation, and scaling) improves the continuity and smoothness of mesh generation during the sweeping process. The lateral faces are used to connect the source and target surfaces, enhancing the smooth transition and geometric integrity of the mesh during the sweeping process. This method of defining the source, target, and lateral faces improves the quality of the mesh.

[0121] In one embodiment of this application, step S42 includes: identifying the source surface and target surface of the sweep body, and generating a quadrilateral mesh on the source surface; sweeping the quadrilateral mesh of the source surface layer by layer along the sweep path on the side to the target surface to generate a hexahedral mesh corresponding to the sweep body.

[0122] As described above, the embodiments of this application define the source surface, target surface, and side surface of the swept volume, and generate a hexahedral mesh layer by layer along the swept path based on the quadrilateral mesh of the source surface. Through a systematic sweeping process, the structural rationality and uniformity of the hexahedral mesh are improved, significantly enhancing the quality and efficiency of mesh generation. At the same time, geometric distortion and calculation errors are reduced, enabling efficient and accurate conversion of the swept volume into a high-quality hexahedral mesh.

[0123] Furthermore, according to one embodiment of this application, this application proposes a CAE software, such as... Figure 8 As shown, the CAE software performs the following steps T1-T2 to complete the simulation test of the geometric model: T1, using the hexahedral mesh model generation method described in any of the above embodiments, calculates the hexahedral mesh model of the geometric model based on the geometric data; T2, performs simulation test on the geometric model based on the hexahedral mesh model.

[0124] According to one embodiment of this application, a hexahedral mesh model generation method is used to process different components constituting a car model to generate a hexahedral mesh model corresponding to the car model. The car model components include parts such as an engine, tires, transmission, and body; the engine includes connecting rods. Figure 9 and 10 The figures shown are schematic diagrams of a connecting rod model and a hexahedral mesh model in a car engine, respectively. Figure 9 This is a model of a connecting rod in a car engine. Figure 10 A hexahedral mesh model of a connecting rod in an automobile engine, obtained by implementing the hexahedral mesh generation method of this application. Figure 10 As can be seen, by importing the linkage model into CAE software, the CAE software applies the hexahedral mesh generation method proposed in this application to the linkage, resulting in a uniformly distributed hexahedral mesh of the linkage with consistent mesh size. Simultaneously, the hexahedral mesh generation method of this application effectively improves the efficiency of generating linkage mesh models on automotive engines and enhances the simulation solution efficiency of automotive mesh models in CAE, thereby significantly improving the efficiency of automotive design, optimization, and performance analysis.

[0125] It should be noted that the solutions of the above embodiments of this application can be applied to all mechanical parts that need to be simulated and tested. The method of generating a hexahedral mesh model of this application for the connecting rod on the automobile engine is only one embodiment, and no specific limitation is made here.

[0126] In summary, compared to existing hexahedral mesh generation methods where the cutting surfaces used to cut the geometric model require manual evaluation and selection by the user, the embodiments described above in this application can automatically evaluate candidate cutting surfaces in CAE software and automatically select the evaluated candidate cutting surfaces for cutting the geometric model. This automated evaluation and selection of cutting surfaces improves the efficiency of geometric model cutting and hexahedral mesh generation, reduces the time cost of CAE software simulation preprocessing, improves the simulation efficiency of the mesh model in CAE, and thus reduces the production time cost of mechanical products.

[0127] Based on the inventive concept of the above embodiments, this application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the method described in the above embodiments. The following is in conjunction with... Figure 11 Please provide a detailed explanation.

[0128] like Figure 11 As shown, it illustrates the electronic device 100 of this application, which may specifically include a processor 110 and a memory 120. The memory 120 is coupled to the processor 110.

[0129] Processor 110 is used to control the operation of electronic devices. Processor 110 may also be referred to as a CPU (Central Processing Unit). Processor 110 may be an integrated circuit chip with signal processing capabilities. Processor 110 may also be a general-purpose processor, digital signal processor (DSP), application-specific integrated circuit (ASIC), field-programmable gate array (FPGA), or other programmable logic device, discrete gate or transistor logic device, or discrete hardware component. The general-purpose processor may be a microprocessor, or processor 110 may be any conventional processor.

[0130] The memory 120 is used to store computer programs and may be RAM, ROM, or other types of storage terminals. Specifically, the memory 120 may include one or more computer-readable storage media, which may be non-transitory or transient. The memory 120 may also include high-speed random access memory and non-volatile memory, such as one or more disk storage terminals or flash memory terminals. In some embodiments, the non-transitory computer-readable storage media in the memory 120 is used to store at least one line of program code.

[0131] The processor 110 is used to execute computer programs stored in the memory 120 to implement the methods described in the various method embodiments of this application.

[0132] In some embodiments, the electronic device may further include a peripheral terminal interface 130 and at least one peripheral terminal. The processor 110, memory 120, and peripheral terminal interface 130 may be connected via a bus or signal line. Each peripheral terminal may be connected to the peripheral terminal interface 130 via a bus, signal line, or circuit board. Specifically, the peripheral terminal includes at least one of a radio frequency circuit 140, a display screen 150, an audio circuit 160, and a power supply 170.

[0133] The peripheral terminal interface 130 can be used to connect at least one I / O (Input / Output) related peripheral terminal to the processor 110 and the memory 120. In some embodiments, the processor 110, memory 120 and peripheral terminal interface 130 are integrated on the same chip or circuit board; in some other embodiments, any one or two of the processor 110, memory 120 and peripheral terminal interface 130 can be implemented on separate chips or circuit boards, which is not limited in this embodiment.

[0134] The radio frequency (RF) circuit 140 is used to receive and transmit RF (Radio Frequency) signals, also known as electromagnetic signals. The RF circuit 140 communicates with communication networks and other IoT devices via electromagnetic signals; it is the communication circuit of the electronic device. The RF circuit 140 converts electrical signals into electromagnetic signals for transmission, or converts received electromagnetic signals back into electrical signals. Optionally, the RF circuit 140 includes: an antenna system, an RF transceiver, one or more amplifiers, a tuner, an oscillator, a digital signal processor, a codec chipset, an operator identification module card, etc. The RF circuit 140 can communicate with other terminals through at least one wireless communication protocol. This wireless communication protocol includes, but is not limited to: the World Wide Web, metropolitan area networks, intranets, various generations of mobile communication networks (2G, 3G, 4G, and 5G), wireless local area networks, and / or WiFi (Wireless Fidelity) networks. In some embodiments, the RF circuit 140 may also include circuitry related to NFC (Near Field Communication), which is not limited in this application.

[0135] Display screen 150 is used to display a UI (User Interface). This UI may include graphics, text, icons, videos, and any combination thereof. When display screen 150 is a touch display screen, it also has the ability to collect touch signals on or above its surface. These touch signals can be input as control signals to processor 110 for processing. In this case, display screen 150 can also be used to provide virtual buttons and / or a virtual keyboard, also known as soft buttons and / or a soft keyboard. In some embodiments, there may be one display screen 150, located on the front panel of the electronic device; in other embodiments, there may be at least two display screens, located on different surfaces of the electronic device or in a folded design; in still other embodiments, display screen 150 may be a flexible display screen, located on a curved or folded surface of the electronic device. Furthermore, display screen 150 may be configured as a non-rectangular, irregular shape, i.e., a non-rectangular screen. Display screen 150 may be made of materials such as LCD (Liquid Crystal Display) or OLED (Organic Light-Emitting Diode).

[0136] The audio circuit 160 may include a microphone and a speaker. The microphone is used to collect sound waves from the operator and the environment, converting the sound waves into electrical signals that are input to the processor 110 for processing, or input to the radio frequency circuit 140 for voice communication. For stereo sound acquisition or noise reduction purposes, multiple microphones may be used, each positioned in a different part of the electronic device. The microphone may also be an array microphone or an omnidirectional microphone. The speaker is used to convert electrical signals from the processor 110 or the radio frequency circuit 140 into sound waves. The speaker may be a conventional film speaker or a piezoelectric ceramic speaker. When the speaker is a piezoelectric ceramic speaker, it can convert electrical signals not only into audible sound waves but also into inaudible sound waves for purposes such as distance measurement. In some embodiments, the audio circuit 160 may also include a headphone jack.

[0137] Power supply 170 is used to supply power to various components in an electronic device. Power supply 170 can be alternating current, direct current, a disposable battery, or a rechargeable battery. When power supply 170 includes a rechargeable battery, the rechargeable battery can be a wired rechargeable battery or a wireless rechargeable battery. A wired rechargeable battery is a battery that is charged via a wired line, while a wireless rechargeable battery is a battery that is charged via a wireless coil. The rechargeable battery can also be used to support fast charging technology.

[0138] For a detailed description of the functions and execution processes of each functional module or component in the electronic device embodiments of this application, please refer to the descriptions in the above-described method embodiments of this application, which will not be repeated here.

[0139] In the embodiments provided in this application, it should be understood that the disclosed electronic devices and methods can be implemented in other ways. For example, the embodiments of the electronic devices described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some data may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0140] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0141] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0142] Based on the inventive concept of the above embodiments, this application also provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, performs the steps of the method described in any of the above embodiments. The following is in conjunction with... Figure 12 This describes the execution process of the above embodiments on a computer-readable storage medium.

[0143] like Figure 12 As shown, it illustrates the computer-readable storage medium of this application. The integrated units described above, if implemented as software functional units and sold or used as independent products, can be stored in the computer-readable storage medium 200. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions / computer programs to cause an Internet of Things device (which may be a personal computer, server, or network terminal, etc.) or processor to execute all or part of the steps of the methods of various embodiments of this application. The aforementioned storage medium includes various media such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks, as well as electronic terminals such as computers, mobile phones, laptops, tablets, and cameras that have the aforementioned storage media.

[0144] The execution process of program data in a computer-readable storage medium can be described with reference to the above-described method embodiments of this application, and will not be repeated here.

[0145] The above description is merely an embodiment of this application and does not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

[0146] Those skilled in the art will understand that, in the above-described method of the specific implementation, the order in which each step is written does not imply a strict execution order and does not constitute any limitation on the implementation process. The specific execution order of each step should be determined by its function and possible internal logic.

Claims

1. A method for generating a hexahedral mesh model, characterized in that, The method is applied to CAE software, and the method includes: Candidate cutting surfaces are selected based on geometric data from a geometric model to form a candidate cutting surface set, wherein the geometric data includes geometric edges, geometric surfaces, and geometric planes; Based on the geometric data, the geometric factor influence value corresponding to each candidate cutting surface is calculated, wherein the geometric factor influence value includes: surface intersection factor influence value, edge number factor influence value, and surface sine factor influence value, and: The geometric surfaces are selected to form a set of geometric surfaces. Intersection detection is performed between the geometric surfaces and each candidate cutting surface. When the candidate cutting surface does not intersect with the geometric surfaces in the geometric model, a larger value is assigned to obtain the surface intersection factor influence value corresponding to each candidate cutting surface. The geometric edges are selected to form a geometric edge set. The number of geometric edges in the geometric edge set that intersect with each candidate cutting face is counted. The influence value of the edge number factor corresponding to each candidate cutting face is calculated in the following way: in, Let T be the number of geometric edges in the geometric edge set that intersect with each candidate cutting face, and Q be the number of geometric edges in the geometric edge set. β This is a preset second hyperparameter; The geometric planes are selected to form a set of geometric planes. Intersection detection is performed between the geometric planes and each candidate cutting surface. Based on the intersection detection results and the preset dihedral angle sine value, the surface sine factor influence value corresponding to each candidate cutting surface is calculated. Each candidate cutting surface is scored based on the influence values ​​of the surface intersection factor, the number of edges factor, and the surface sine factor to obtain the evaluation result of each candidate cutting surface; The geometric model is cut sequentially using the candidate cutting surfaces corresponding to the high to low scores in the evaluation results to obtain the set of swept volumes corresponding to the geometric model; A hexahedral mesh model of the geometric model is generated based on the swept body set.

2. The method for generating a hexahedral mesh model according to claim 1, characterized in that, The step of selecting candidate cutting surfaces based on geometric model data to form a candidate cutting surface set includes: Based on the geometric data, preset normal vectors and preset geometric vertices are used to construct the candidate cutting surfaces, and / or the geometric planes are used as the candidate cutting surfaces, the candidate cutting surfaces constituting the candidate cutting surface set.

3. The method for generating a hexahedral mesh model according to claim 2, characterized in that, The geometric factor influence value further includes: the shortest side factor influence value, and / or the surface distribution factor influence value, and the step of calculating the geometric factor influence value corresponding to each candidate cutting surface based on the geometric data includes: Intersection detection is performed between the geometric edge and each candidate cutting surface, and based on the intersection detection results and the shortest geometric edge in the geometric model, the influence value of the shortest edge factor corresponding to each candidate cutting surface is calculated. Determine the positional relationship between the geometric planes in the geometric plane set and each candidate cutting surface, and calculate the influence value of the surface distribution factor corresponding to each candidate cutting surface based on the positional relationship.

4. The method for generating a hexahedral mesh model according to claim 1, characterized in that, The step of sequentially cutting the geometric model using the candidate cutting surfaces corresponding to the evaluation results from high to low, to obtain the set of swept volumes corresponding to the geometric model, includes: The geometric model is cut sequentially using the candidate cutting surfaces corresponding to the scores from high to low to obtain the geometric body corresponding to the geometric model, wherein the cutting result of the previous candidate cutting surface is used as the cutting object of the next candidate cutting surface; The geometric bodies constitute the sweep body set corresponding to the geometric model.

5. The method for generating a hexahedral mesh model according to claim 4, characterized in that, The step of sequentially cutting the geometric model using the candidate cutting surfaces corresponding to the scores from high to low to obtain the geometric body corresponding to the geometric model includes: After cutting the geometric model using each candidate cutting surface, it is determined whether the resulting geometric bodies are all swept bodies. If they are all swept bodies, the cutting of the geometric model is stopped; otherwise, the next candidate cutting surface is used to cut the geometric model until the resulting geometric bodies are all swept bodies, at which point the cutting of the geometric model is stopped.

6. The method for generating a hexahedral mesh model according to claim 5, characterized in that, The step of generating the hexahedral mesh model of the geometric model based on the swept body set includes: The source surface, target surface, and side surface of each sweep body in the sweep body set are found according to the preset geometric rules; Each of the sweep bodies sweeps from the source face to the target face along the side to generate a hexahedral mesh corresponding to each of the sweep bodies; Based on all swept bodies in the swept body set, the hexahedral mesh model of the geometric model is calculated.

7. A CAE software, characterized in that, The CAE software performs the following steps to complete the simulation test of the geometric model: Using the hexahedral mesh model generation method as described in any one of claims 1-6, a hexahedral mesh model of the geometric model is calculated based on the geometric data of the geometric model; The geometric model is simulated and tested based on the hexahedral mesh model.

8. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the method as described in any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-6.

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