A volume parameterized modeling method based on curve quadrilateral decomposition

Abstract

The present invention discloses a volume parameterized modeling method based on curve quadrilateralization, comprising: using NURBS as the mapping basis function between the parameter domain and the physical domain, first defining features such as contour curves, internal and external connecting lines, and contour polygons, and using an improved ray method to construct a geometric domain inclusion tree. Then, starting from the bottom leaf node of the geometric domain inclusion tree, a series of subdomain partitioning operations are performed, including obtaining and sorting zero-deficient subdomain polygons, searching and sorting feasible partitioning lines, and recursively performing quadrilateral partitioning to obtain a subdomain that is entirely convex quadrilaterals, and avoiding the generation of cusps as much as possible. Finally, COONS interpolation is performed on all non-empty quadrilateral subdomains to generate parameterized surfaces, and a volume parameterized model is obtained by operations such as stretching, scanning, rotating, and lofting. According to the present invention, the two-dimensional and three-dimensional examples provided show that the method can quickly and accurately realize complex two-dimensional quadrilateral partitioning containing genus domains, and further obtain a volume parameterized model.

Description

Technical Field

[0001] The invention relates to the technical field of CAD / CAE, and in particular to a body parameterized modeling method based on curve quadrilateral decomposition. Background Art

[0002] With the rapid development of intelligent manufacturing, the requirements for product design and analysis have also increased. In order to shorten the product design cycle and reduce costs, the integration of design (CAD) and analysis (CAE) has become a general trend. At present, CAD and CAE are still divided into two independent fields, and the expression methods of models are also different. CAD models are mostly expressed in B-Rep and CSG. CAE models are generally expressed in mesh units and are suitable for finite element analysis (FEA). During the entire design process, the design model will be converted back and forth between CAD and CAE, and its consistency and completeness will be destroyed, which will reduce the accuracy of the model and greatly increase the time cost.

[0003] In order to meet the needs of integrated or unified expression of CAD models and CAE models, volume parametric models have emerged as a new model expression method. Volume parametric models can accurately express boundary curves and surfaces, and provide continuous parametric expression of materials and performance inside the model. Volume parametric models do not need to be converted and can be directly used for isogeometric analysis. Compared with other expression models, they require less data storage and can well achieve seamless integration of CAD and CAE.

[0004] To be suitable for isogeometric analysis, the expression of the volume parameterized model must be a zero-genus bivariate tensor surface or a three-variable tensor volume, and adjacent volume parameterized slices must have consistent common surfaces or curves. Therefore, it is necessary to perform regional partitioning on surfaces with genus or non-bivariate tensors to obtain several surfaces whose topological expressions are convex quadrilaterals. The study of convex decomposition of simple polygons expressed in straight lines is relatively mature, but there is still a lot of room for research on quadrilateral partitioning in the form of curves. Most existing algorithms are based on meshing, which can decompose the region into curved quadrilateral meshes, but there are problems such as large computational complexity and failure to meet the needs of volume parameterized modeling. The research object of this paper is curved polygons with genus, and it is required to obtain as few curved quadrilaterals as possible through partitioning.

[0005] At present, the model segmentation algorithms for volume-oriented parameterization can be divided into: 1) simple polygon convex decomposition, the results are mostly a collection of triangles, quadrilaterals and arbitrary convex polygons, and are mostly expressed in the form of straight lines; 2) mesh decomposition, such as finite element mesh or curved quadrilateral mesh, among which the two-dimensional quadrilateral mesh is the basis of the three-dimensional hexahedral mesh, but mesh division can easily lead to problems such as large data volume and large amount of calculation. Summary of the invention

[0006] In view of the shortcomings of the prior art, the purpose of the present invention is to provide a volume parameterized modeling method based on curve quadrilateral decomposition. The two-dimensional and three-dimensional examples given show that the method can quickly and accurately realize the complex two-dimensional quadrilateral decomposition containing the genus domain, and further obtain the volume parameterized model. In order to achieve the above-mentioned purpose and other advantages according to the present invention, a volume parameterized modeling method based on curve quadrilateral decomposition is provided, comprising:

[0007] S1. Define multiple geometric features, including geometric domains, contour curves, inner and outer connecting lines, and contour polygons, and the geometric features are used to describe geometric shapes in the process of quadrilateral decomposition algorithm;

[0008] S2. Use NURBS as shape function to express curves, surfaces and bodies, use ray method to determine the positional relationship between any point and any geometric domain, further construct geometric domain inclusion tree, and improve ray method according to the characteristics of NURBS;

[0009] S3. Design a curve quadrilateral decomposition algorithm to divide the geometric domain that does not consist of four sides or has defects into curved quadrilaterals that consist of four sides, and ensure that they are all convex quadrilaterals. The number of quadrilaterals obtained by decomposition is small, and the process does not require meshing;

[0010] S4. Use the curved quadrilateral in step S3 as the cross section, set the path according to the characteristics of the three-dimensional model, use stretching, rotation, sweeping, lofting and other operations to obtain a three-variable tensor NURBS body, combine all NURBS bodies to obtain a body parameterized model, and ensure that all adjacent NURBS bodies have common curves and common surfaces with the same parameters.

[0011] It is preferred to also include a brief introduction to NURBS bodies, demonstrating their advantages in seamlessly integrating CAD / CAE, including defining geometric domains, contour curves, internal and external connecting lines, vertices, contour polygons, and NURBS surfaces.

[0012] Preferably, it also includes defining the inclusion relationship between geometric domains, converting the inclusion relationship judgment between any two geometric domains into whether all the vertices and the midpoints of each curve edge parameter in one of the geometric domains are inside the other geometric domain; according to the characteristics of the NURBS curve, the traditional ray method is improved, and the improved ray method is used to implement the above judgment, thereby further completing the construction of the geometric domain inclusion tree.

[0013] Preferably, the method further includes designing a geometric domain quadrilateral decomposition algorithm, starting from the bottom leaf node of the containing tree, and performing decomposition operations on each node layer by layer upwards.

[0014] Preferably, the geometric domain quadrilateralization algorithm comprises the following steps:

[0015] (1) All contour curves are judged to coincide with each other, and if some of them coincide, the curves need to be truncated;

[0016] (2) Obtain all counterclockwise zero-deficient subdomains and sort them. For each subdomain, find its polygonal feasible partitioning line and sort them.

[0017] (3) Recursively quadrilateralize the subdomain according to the order to obtain a subdomain consisting entirely of convex quadrilaterals.

[0018] Preferably, all subdomain quadrilaterals are subjected to COONS interpolation to obtain NURBS curves, corresponding paths are set according to model characteristics, NURBS bodies are constructed by stretching, rotating, sweeping or lofting operations, and all NURBS bodies are merged to obtain a body parameterized model.

[0019] Compared with the prior art, the present invention has the following beneficial effects: a curve quadrilateralization algorithm is designed based on geometric features, which can divide a geometric domain with defects into a smaller number of zero-defect quadrilateral geometric subdomains. Compared with the existing quadrilateral meshing and mesh-based domain segmentation methods, there is no need to build a pre-model (such as a finite element model), there is no need to divide a large number of meshes, the number of curved quadrilaterals obtained is relatively small, and all edges are expressed by NURBS curves, which has the advantages of small data volume, small amount of calculation, and easy modification. The geometric domain inclusion tree is constructed to guide the partition search, which improves the robustness of the algorithm, and is therefore also applicable to complex geometric models. The quadrilateral subdomain obtained based on the quadrilateralization algorithm can be interpolated into a NURBS surface, and with the help of the path, a volume parameterized model suitable for isogeometric analysis can be further constructed, which makes it possible to achieve CAD / CAE integration. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a mapping relationship diagram between the parameter domain and the entity domain of the NURBS body parameter model;

[0021] Figure 2 is the geometric domain and the contour polygon graph;

[0022] Figure 3 It is a schematic diagram of the geometric domain inclusion relationship;

[0023] Figure 4 For improved ray method diagram;

[0024] Figure 5 To improve the ray method example diagram;

[0025] Figure 6 Include tree graphs for geometry domains;

[0026] Figure 7 Construct a flow chart for the geometry domain inclusion tree;

[0027] Figure 8It is a schematic diagram of the contour curve;

[0028] Fig. 9 It is a schematic diagram of curve truncation;

[0029] Fig.10 It is a schematic diagram of the counterclockwise zero-deficient lattice subdomain;

[0030] Fig.11 Schematic diagram for selecting vertices of the counterclockwise subdomain curved polygon;

[0031] Fig.12 is a schematic diagram of feasible splitting lines;

[0032] Fig.13 It is a schematic diagram of contour curve truncation;

[0033] Fig.14 This is a schematic diagram of concave polygon weight calculation;

[0034] Fig.15 This is a schematic diagram of convex polygon weight calculation;

[0035] Fig.16 It is the flow chart of subdomain quadrilateral decomposition;

[0036] Fig.17 This is an example diagram of quadrilateral decomposition of a two-dimensional geometric domain;

[0037] Fig.18 This is an example diagram of a polygonal hole;

[0038] Fig.19 It is the drawing of the stretching section, path and stretching body;

[0039] Fig. 20 It is the path and cross section of the body of revolution and the diagram of the body of revolution;

[0040] Fig.21 It is the swept volume path, cross section and swept volume diagram;

[0041] Fig. 22 It is the lofted body section and path and lofted body diagram;

[0042] Fig.23 This is a three-dimensional spur gear example diagram;

[0043] Fig.24 This is a three-dimensional box example diagram;

[0044] Fig.25 Schematic diagram of model quality evaluation. DETAILED DESCRIPTION

[0045] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] Reference Figure 1-25 , a volume parameterized modeling method based on curve quadrilateralization, comprising: S1, defining a plurality of geometric features, wherein the geometric features include a geometric domain, a contour curve, inner and outer connecting lines (auxiliary lines), and a contour polygon, wherein the geometric features are used to describe a geometric shape in a quadrilateralization algorithm process;

[0047] S2. Use NURBS as shape function to express curves, surfaces and bodies, use ray method to determine the positional relationship between any point and any geometric domain, further construct geometric domain inclusion tree, and improve ray method according to the characteristics of NURBS;

[0048] S3. Design a curve quadrilateral decomposition algorithm to divide the geometric domain that does not consist of four sides or has defects into curved quadrilaterals that consist of four sides, and ensure that they are all convex quadrilaterals. The number of quadrilaterals obtained by decomposition is small, and the process does not require meshing;

[0049] S4. Use the curved quadrilateral in step S3 as the cross section, set the path according to the characteristics of the three-dimensional model, use stretching, rotation, sweeping, lofting and other operations to obtain a three-variable tensor NURBS body, combine all NURBS bodies to obtain a body parameterized model, and ensure that all adjacent NURBS bodies have common curves and common surfaces with the same parameters.

[0050] Furthermore, it also includes a brief introduction to NURBS bodies, showing their advantages in seamless integration with CAD / CAE, including the definition of geometric domains, contour curves, internal and external connecting lines, vertices, contour polygons and NURBS surfaces.

[0051] Furthermore, it also includes defining the inclusion relationship between geometric domains, and converting the inclusion relationship judgment between any two geometric domains into whether all the vertices and the midpoints of each curve edge parameter in one of the geometric domains are inside the other geometric domain; according to the characteristics of the NURBS curve, the traditional ray method is improved, and the improved ray method is used to realize the above judgment, thereby further completing the construction of the geometric domain inclusion tree.

[0052] Furthermore, it also includes designing a geometric domain quadrilateral decomposition algorithm, starting from the bottom leaf node of the containing tree, and performing a decomposition operation on each node layer by layer upward.

[0053] Furthermore, the geometric domain quadrilateralization algorithm includes the following steps:

[0054] (1) All contour curves are judged to coincide with each other, and if some of them coincide, the curves need to be truncated;

[0055] (2) Obtain all counterclockwise zero-deficient subdomains and sort them. For each subdomain, find its polygonal feasible partitioning line and sort them.

[0056] (3) Recursively quadrilateralize the subdomain according to the order to obtain a subdomain consisting entirely of convex quadrilaterals.

[0057] Furthermore, all subdomain quadrilaterals are interpolated by COONS to obtain NURBS curves, corresponding paths are set according to model characteristics, NURBS bodies are constructed by stretching, rotating, sweeping or lofting operations, and all NURBS bodies are merged to obtain a volume parameterized model.

[0058] Example 1

[0059] Step 1: Use NURBS as the shape function to establish a mapping relationship from the parameter domain (cube) to the physical domain (3D curved hexahedron) to construct a NURBS body. Multiple NURBS bodies are combined to form a complete body parameterized model, such as Figure 1 Its expression is as follows:

[0060]

[0061] Here {P i,j,k} is the volume control point, {ω i,j,k} is the weight factor, N i,p (u),N j,q (v),N k,r (w) are NURBS basis functions of order p, q, and r respectively defined on the non-periodic (and non-uniform) node vector spaces U, V, and W.

[0062] The node vector space of U, V, W is:

[0063] U=[u0=u1…=u p ,u p+1 ,…,u n-p-1 ,u n-p …=u n ],

[0064] V=[v0=v1…=v q ,v q+1 ,…,v m-q-1 ,v m-q …=v m ],

[0065] W=[w0=w1…=wr ,w p+1 ,…,w l-r-1 ,w l-r …=w l ],

[0066] The following formula is the expression of the NURBS basis function in the U direction. The definition of the basis function in the V and W directions is similar.

[0067]

[0068] NURBS bodies are solid expressions, not surface expressions of traditional CAD software. The coordinates of any point inside can be solved through parameters u, v, and w, so they can be directly applied to isogeometric analysis (IGA), which is expected to achieve the unification of CAD / CAE. However, all NURBS bodies are expressed as curved hexahedrons, so the model needs to be segmented and the corresponding surfaces need to be segmented into curved quadrilaterals.

[0069] To facilitate the subsequent design and description of the segmentation algorithm, the following features are defined (such as Figure 2 ):

[0070] 1) Geometric domain: the area enclosed by the loops connected by several NURBS curves;

[0071] 2) Contour curve: a set of NURBS curves that enclose a single geometric domain. If there are multiple geometric domains, the curve of the largest geometric domain is the outer contour curve, and the rest are inner contour curves;

[0072] 3) Internal and external connecting lines (auxiliary lines): connect the internal and external geometric domains and transform the genus geometric domain into several zero-genus subdomains;

[0073] 4) Vertex: The endpoint of the NURBS curve;

[0074] 5) Contour polygon: A polygon connected by NURBS curves is a curved polygon, a polygon connected by straight lines on the vertices of a single geometric domain is a straight line polygon, and the definition of inner and outer contour polygons is the same as 2);

[0075] 6) NURBS surface: A geometric domain containing only four outer contour curves can be parametrically expressed as a NURBS surface through COONS interpolation;

[0076] Step 2: Define the geometric domain inclusion relationship. Suppose the input geometric domain set is S = {s1, s2, ..., s n}(n≥2), where s i ={l1,l2,…,l m}, li represents the contour curve. Specify any two geometric domains s i ,s j There are only two types of relationships:

[0077] 1)s i Contains j (like Figure 3 a-3c);

[0078] 2)s i With s j No inclusion relationship (such as Figure 3 d-3f);

[0079] Case 1): s i All polygon vertices are in s j On or inside the contour curve; Case 2): There is at least one polygon vertex belonging to s i In s j Therefore, the problem of determining whether there is a containment relationship between two geometric domains can be transformed into the problem of determining whether all the polygon vertices of one geometric domain are inside the other geometric domain. Figure 3 f, just extract s i The coordinates of each curve point at parameter u = 0.5 and determine whether it is in s j Internally.

[0080] Step 3: Use the ray method to determine the positional relationship between a point and any geometric domain. Suppose a point P is related to the geometric domain s. i To judge the internal and external relationship, the total number of intersections between the ray and the contour curve is γ, and the initial value is 0. The ray method may produce multiple intersections with a single NURBS curve, and the intersection judgment of the ray method needs to be improved.

[0081] Each intersection point is judged as follows:

[0082] 1) The intersection point is the endpoint of the contour curve, and the tangent vector at the endpoint is solved Located in the first and second quadrants, the γ value remains unchanged. Located in the third and fourth quadrants, γ plus 1 (such as Figure 4 a);

[0083] 2) Collinear with the X-axis, solve the coordinates of a point on the curve at a distance Δu (usually 0.05) from the intersection point, and calculate the direction vector of the two points Located in the first and second quadrants, the γ value remains unchanged. Located in the third and fourth quadrants, γ plus 1 (such as Figure 4 b);

[0084] 3) The intersection point is not the endpoint of the contour curve, solve the tangent vector at the intersection point Not collinear with the X-axis, γ plus 1 (such as Figure 4 a);

[0085] 4) Collinear with the X-axis, solve the coordinates of two points on the curve at u±Δu, and calculate the direction vectors respectively If both are in the first and second quadrants, the γ value remains unchanged. If both are in the third and fourth quadrants, γ increases by 2. Otherwise, γ increases by 1 (e.g. Figure 4 c-4d);

[0086] Each point only needs to be judged separately with each curve, and the γ values ​​of all the judgment results are added together. Odd numbers indicate that it is inside another geometric domain, otherwise it is outside. Figure 5 For example, to determine the inclusion relationship between geometric domains s1, s2, and s3, only vertex P i j And all the points where the contour curve parameter u=0.5 are in another geometric domain, where i is the vertex number and j is the geometric domain number. The figure gives some examples of ray method calculation for some special points. Point P1 2 The ray corresponding to Figure 4 a and Figure 4 In case b, γ=0+1 is an odd number. Rays and curves Tangent, corresponding Figure 4 In case c, γ = 0 is an even number, so s2 is not included in s3. All vertices of s3 are on s1, but the curve The point ray at parameter u=0.5 and γ=0 of s1, so it can be judged that s3 is outside s1.

[0087] Finally, the geometry domain inclusion tree is constructed. Figure 6 a as an example, the constructed geometric domain contains trees such as Figure 6 b. Set the parameter μ value for each node. If μ=1, there is a corresponding path in the geometric domain of the node, and the partitioning operation needs to be performed. If μ=0, there is no corresponding path in the geometric domain of the node, and no partitioning operation is required. If μ=0 for s6, the NURBS surface set and the corresponding path after the partitioning in the domain (s4-s6) can be selected according to the bounding tree to quickly establish the parametric model of the part. The geometric domain contains the tree construction process as shown in Figure 7 .

[0088] Step 4: Based on the geometric domain inclusion tree, starting from the bottom layer, extract the nodes of this layer as the parent node, internal and external connecting lines and child nodes (if any) in turn for quadrilateral splitting. After all nodes of this layer are split, repeat the above operations layer by layer until the parent node is the root node of the tree.

[0089] The angle is used as the evaluation index of the convex quadrilateral obtained by the final segmentation. Each vertex must meet the following conditions:

[0090] 1) The angle between the tangent vectors of the two curve edges corresponding to the point is less than 180°;

[0091] 2) The angle between the direction vectors corresponding to the point and the two adjacent vertices is less than 180°.

[0092] The following definitions are given (such as Figure 8 ):

[0093] Outer contour curve——all contour curves of the parent node;

[0094] Inner contour curve——all contour curves of child nodes;

[0095] Curve truncation - If a contour curve can be truncated from any non-endpoint, its η is defined as 1, otherwise η is 0. Since the partitioning algorithm starts from the leaf node and completes the partitioning layer by layer, for any parent node, the child nodes are all partitioned (the node is not empty, that is, μ=1), and only the contour curves in the child nodes that meet this condition cannot be truncated, corresponding to η=0. For other curves, η=1, if the curves overlap, η=0 shall prevail.

[0096] Step 5: The input inner and outer contour curves may have overlapping segments. If there are two partially overlapping curves, the curve truncation operation is required, and finally the curve duplication is removed ( Fig. 9 for Figure 8 Partial contour curve), if the coincident curve contains an inner contour curve, this curve will be kept first.

[0097] Step 6: To facilitate subsequent calculations, it is necessary to obtain all zero-deficient subdomains and sort the polygon vertices counterclockwise. Fig.10 , connect all vertices with straight lines to obtain several subdomain curved polygons. Construct a directed graph G = (V, E) based on the vertex adjacency relationship. V represents the set of all vertices, and each vertex is a node of the graph, set as node i (i=1,2,…,n), E represents the set of all edges. To ensure that all subdomain polygon vertices are sorted counterclockwise, the edge where the outer contour curve is located has only one direction, and the edges where the other curves are located have two directions. Fig.10 b. The outer contour curve only has edges in the direction of node1→node2, while other curves have edges in both directions such as node1→node3 and node3→node1.

[0098] The algorithm for obtaining the subdomain curved polygon (including concave polygon) is as follows:

[0099] Input: directed graph G.

[0100] Output: The set of zero-deficient subdomains POL.

[0101] Step 1: Randomly select a node with an edge i As the current node now , and select the node corresponding to the edge jAs the next node next , delete the edge to prevent repeated searches.

[0102] Step 2: Calculate the node now To node next Direction Vector The node next Set as node now , and extract all the edges corresponding to the nodes, calculate the node now Direction vectors to these nodes

[0103] Step 3: Calculation relatively The rotation direction and angle of rotation are used to select the best node as the node of the counterclockwise subdomain polygon. next , delete the edge (such as Fig.11 ).

[0104] Step4: Repeat Step2 to Step3 until node next =node i , store the corresponding vertex subdomain into the set POL.

[0105] Step 5: Go back to Step 1. If there are no edges between all nodes, the process ends.

[0106] Step 7: For the set POL=(pol1,pol2,…,pol n ) Perform the following operations to make the splitting order as inner-outer as possible (splitting starts from the end of POL and traverses to the beginning in sequence):

[0107] 1) Remove the subdomains corresponding to all child nodes;

[0108] 2) Calculate the contour polygon uniform surface gravity center O of the current parent node and the uniform surface gravity centers of all polygons in POL and store them in the set Weigth = (O1, O2, ..., O n );

[0109] 3) Calculation |OO i |, and sort POL from large to small by value. If there are subdomains with the same value, these subdomains are randomly sorted.

[0110] The curve added by the subdomain division first connects two vertices, and secondly, one end is a vertex and the other end cuts off a contour curve. This division line does not intersect with the original curve. Find two points that are visible to each other. For any two vertices P of any subdomain straight line polygon i and P j (i<j), first determine whether the line connecting the two points meets the angle requirement (such as Fig.12a), if it meets the requirements, then intersect with other edges. If there is no intersection, then P i and P j is a set of visible point pairs.

[0111] Assuming the number of polygon vertices is n, the steps for finding feasible segmentation lines are as follows:

[0112] Input: Subdomain pol.

[0113] Output: feasible segmentation line set Visbp, Cusp, Cutlp.

[0114] Step 1: Find the first type of visible point pair P in the straight polygon i With P j (like Fig.12 b), since the subdivision result is at least a quadrilateral, it must satisfy |ij|≥3 and |i+nj|≥3 and be stored in the set Visbp.

[0115] Step 2: If there is at least one cusp in the two straight line polygons generated by connecting the visible point pairs in the set Visbp (such as Fig.12 d, θ≤20°), remove this case and store it in the set Cusp.

[0116] Step 3: Find the second type of visible point pairs in the straight polygon, requiring |ij|≥2 and |i+nj|≥2, such as Fig.12 c, if P i With P j , P i With P k Each is a pair of visible points, and |jk|=1, P j With P k For the corresponding contour curve η=1, the contour curve can be truncated and the situation is stored in the set Cutlp.

[0117] Step 4: Solve the feasible segmentation line under the Cutlp condition. The best segmentation result is the orthogonal intersection of the common edges of adjacent quadrilaterals. Fig.13 , first find P i To the foot of the corresponding side, if it does not exist, find the intersection of the angle bisector and the corresponding side, otherwise take the midpoint of the corresponding side. In the actual segmentation, calculate the position ratio u of the point on the opposite side, and split the corresponding contour curve at the parameter u, and the split point is used as the vertex of the new polygon.

[0118] Step 5: Calculate the feasible segmentation line weight ω of the set Visbp, Cusp, Cutlp ij , and sort the dividing lines of the three sets according to the values ​​from large to small.

[0119] The calculation method of the feasible segmentation line weight is as follows:

[0120] 1) There are at least concave points in the subdomain polygon. If the set Cutlp is not empty, there must be a concave point. Fig.14 a,P i is the concave point (∠P i-1 P i P i+1 ≥180°), ω i Calculate as formula 3. Fig.14 b, P i is a convex point, ω i Calculate as formula 4, ω ij The calculation is as in formula 5.

[0121]

[0122]

[0123] 2) All vertices of the subdomain polygon are convex points (such as Fig.15 ),ω ij Calculation is as in formula 6:

[0124] ω ij =α×S+β×T (6)

[0125] Among them, θ ij =min{θ1,θ2,θ3,θ4},L ij =||P i -P j ||, α=1, β=0.5.

[0126] Step 8: Perform the subdomain quadrilateralization operation. The set POL has been sorted, and all the curved polygons are traversed from back to front and divided into quadrilaterals until POL is empty and the quadrilateralization is completed. The algorithm steps are as follows:

[0127] Input: subdomain set POL.

[0128] Output: quadrilateral set Quad.

[0129] Step 1: If POL is not empty, take pol max As pol now .

[0130] Step 2: Solve pol now The feasible splitting line set Visbp, Cutlp, Cusp is sorted in this order. Assume that the number of splitting connection methods is m, and the initial selected splitting line n=1.

[0131] Step 3: m = 0, indicating that the subdomain does not meet any partitioning conditions; n> m, indicating that all partitioning connection methods have been traversed but the results do not meet the conditions, and backtracking to the previous partitioned subdomain pol front , set as pol now , n=n+1.

[0132] Step 4: Create a new NURBS curve based on the currently selected segmentation and connection method, and obtain two new subdomains pol temp1 ,pol temp2 , delete the currently split subdomain pol now .

[0133] Step 5: poll temp For a convex quadrilateral, store it in the set Quad, pol temp If it is a pentagon or larger, it is stored in the tail of the set POL. If none of them meet the requirements, it will backtrack to the last subdivided subdomain, n=n+1.

[0134] Step 6: Recursively execute Step 1 to Step 5. If the set POL is empty, end.

[0135] The specific process is as follows Fig.16 . Fig.17 This is an example of quadrilateral decomposition of a two-dimensional geometric domain, which represents the contour curve expression, the addition of internal and external connection line expression, the NURBS surface expression after decomposition, and the mesh expression in turn. In this model, all the child nodes of the root node μ=0. In this case, all the outer contour curves of the child nodes η=1. After decomposition, the number of outer contour curves of the child nodes can be different from 4 to obtain a better decomposition effect. At the same time, this model example can quickly subdivide the NURBS surface into a surface mesh according to the needs of isogeometric analysis. Fig.18 This is an example of quadrilateral decomposition of a polygonal hole. The root node's child nodes μ=0 and μ=1 are distinguished to obtain different decomposition results. The μ=1 case can be applied to the construction of non-through hole NURBS body models.

[0136] Step 9: According to the model requirements, the path curve is stretched, rotated, swept, and lofted to obtain a three-variable tensor NURBS body. Figure 19-22 shown. Fig.23 This is an example of a three-dimensional spur gear model, which includes half-tooth contour curve expression, half-tooth NURBS surface expression, single full-tooth NURBS surface expression after mirroring, single full-tooth mesh expression, gear overall expression and gear overall mesh expression. Fig.24 It is an example of a three-dimensional box model, which is the curve and surface expression before and after the geometric domain of the partial section is divided, and the three-dimensional model expression of the box. The Jacobian distribution of the calculation model is required to be greater than zero. The result is as follows Fig.25 shown.

[0137] The number of devices and processing scales described here are used to simplify the description of the present invention, and the application, modification and variation of the present invention are obvious to those skilled in the art. Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and the implementation mode, and they can be fully applied to various fields suitable for the present invention. For those familiar with the art, other modifications can be easily realized, so without departing from the general concept defined by the claims and the equivalent scope, the present invention is not limited to the specific details and the legends shown and described here.

Claims

1. A volume parameterized modeling method based on curve quadrilateral decomposition, characterized in that: The following steps are involved: S1. Define multiple geometric features, including a geometric domain, a contour curve, an inner and outer connecting line, and a contour polygon, and the geometric features are used to describe the geometric shape in the process of the geometric domain quadrilateral decomposition algorithm; S2. Use NURBS as shape function to express curves, surfaces and bodies, use ray method to determine the positional relationship between any point and any geometric domain, further construct geometric domain inclusion tree, and improve ray method according to the characteristics of NURBS; S3. Design a geometric domain quadrilateralization algorithm to split the geometric domain that does not consist of four sides or has defects into curved quadrilaterals that consist of four sides, and ensure that they are all convex quadrilaterals. The number of quadrilaterals obtained by the splitting is small, and the process does not require meshing; The geometric domain quadrilateralization algorithm consists of the following steps: (1) All contour curves are judged to coincide with each other. If some of them coincide, the curves need to be truncated; (2) Obtain all counterclockwise zero-deficient subdomains and sort them. For each subdomain, find its polygonal feasible partitioning line and sort them. (3) Recursively divide the subdomain into quadrilaterals according to the order to obtain a subdomain that is entirely convex quadrilaterals; S4, taking the curved quadrilateral in step S3 as a cross section, setting a path according to the characteristics of the three-dimensional model, obtaining a three-variable tensor NURBS body by stretching, rotating, sweeping, or lofting operations, combining all NURBS bodies to obtain a body parameterized model, and ensuring that all adjacent NURBS bodies have common curves and common surfaces with the same parameters; The modeling method is applied to the process of modeling a three-dimensional spur gear model or a three-dimensional box model through CAD or CAE simulation.

2. A volume parameterized modeling method based on curve quadrilateral decomposition as claimed in claim 1, characterized in that: It also includes a brief introduction to NURBS bodies, showing their advantages in seamlessly integrating CAD / CAE, including defining geometric domains, contour curves, internal and external connecting lines, vertices, contour polygons, and NURBS surfaces.

3. A volume parameterized modeling method based on curve quadrilateral decomposition as claimed in claim 1, characterized in that: It also includes defining the inclusion relationship between geometric domains, converting the inclusion relationship judgment between any two geometric domains into whether all the vertices and the midpoints of each curve edge parameter in one of the geometric domains are inside the other geometric domain; according to the characteristics of the NURBS curve, the traditional ray method is improved, and the improved ray method is used to realize the above judgment, further completing the construction of the geometric domain inclusion tree.

4. The method for volume parameterization modeling based on curve quadrilateral decomposition according to claim 1, characterized in that: It also includes a quadrilateral decomposition algorithm for the design geometry domain, starting from the bottom-level leaf node of the containing tree and performing decomposition operations on each node layer by layer upward.

5. The method for volume parameterization based on curve quadrilateral decomposition according to claim 1, characterized in that: All subdomain quadrilaterals are interpolated by COONS to obtain NURBS curves, the corresponding paths are set according to the model characteristics, and NURBS bodies are constructed by stretching, rotating, sweeping or lofting operations. All NURBS bodies are merged to obtain a volume parameterized model.

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