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1、精品论文http:/Research of Geometric Constraints Modelingand Solving of 3D Interactive Garment Design1Jin Wang*State Key Lab. of CAD & CG, ZhejiangUniversity, Hangzhou 310027, ChinaGuo-dong LuState Key Lab. of CAD & CG, ZhejiangUniversity, Hangzhou 310027, ChinaLong ChenState Key Lab. ofCAD & CG, Zhejian
2、gDengWei-yanYu-lei GengState Key Lab. ofCAD & CG, ZhejiangUniversity, Hangzhou310027,China Collegeof Mechanical Engineering, Universityof Shanghai for Scienceand Technology,Shanghai200093ChinaState Key Lab. of CAD & CG, Zhejiang University, Hangzhou310027, ChinaUniversity, Hangzhou310027, ChinaE-mai
3、l address: (Jin Wang)AbstractGarment CAD mostly adopts freeform operations, and the major constraints are passive ones that described as inequalities equations, compared with the active constraints that described as algebraic equations in solid modeling of mechanical CAD. In this paper we presented
4、 some constraints modeling and solving methods in GCAD. In 3D garment surface modeling, taking the contour spline curves as geometric elements, 13 constraint types include of 7 passive constraint types are proposed. In order to construct the constraint graph conveniently, a hierarchical driven model
5、 of contour curves is also given. Since major constraints are passive ones, three rules, namely priority-ranked solving rules,iterative solving rules, released solving rules，are proposed for graph based constraintssolving. After constraints solving, contour curves are actually deformed, and then the
6、 garment surface is updated via bilinear coons interpolation. For pattern design, taking these style curves as geometric elements, 4 constraints are concluded to satisfy the crafts.1. National Natural Science Foundation of China (No. 60473129) and the Ph.D ProgramsFoundation of the Ministry of Educa
7、tion of China (No. 20060335118)1精品论文Constraint graph is also given to ensure the validity and reasonability of style curves sketching. Finally, the given examples show our approach suits for flexible interactive design of 3D garment, a typical soft product.Key words: 3D garment, constraint modeling,
8、 constraint solving, 3D surface modeling, 3D pattern design1.IntroductionTechnologies of Garment Computer Aided Design (GCAD) have been developed greatly from 2D GCAD1-3 to 3D GCAD. 3D GCAD includes 3D body modeling, surface generation, surface modeling, pattern design, pattern flattening, draping s
9、imulation, animation demonstration and so on. 3D garment surface modeling and pattern design are the key processes for designer interaction, and they are the focus in our paper.Many works have been done on generating garment surface on a 3D body. Hinds and McCartneys 4,5 represented the garment as a
10、 collection of panels offset from the body surface. Kim et al.6,7divided the body model into four panels and adopted a stereovision-based algorithm to generate the garment surface. Based on the body features, Wang 8 specified a garment sketch through a 2D stroke and then used a subdivision method to
11、 refine the garment mesh. Wang9 divided the laser-scanned body into six parts, and connected the human body slice vertices intersected with each part by horizontal cutting plane to reconstruct the body surface. Turquin et al10,11 sketched garment contours directly onto a 3D view of a mannequin and t
12、hen generated a 3D surface according to a distance field around the mannequin.How to model the garment surface effectively is still an open issue. Wang12 adopted FFDmethods to deform the generated garment surfaces. Parametric curves such as sine curves were used to control the bottom garment shape m
13、ore easily in the works of Kim et al7.Wang et al.8,13 proposed four simple modification tools for the generated garment surface by 2D sketches, which were mesh painting, mesh extrusion, mesh cutting and mesh partition.Few works focused on 3D pattern design. Decaudin et al14. added seam lines and dar
14、tsduring sketching garment contours to generate patterns. Wang15 et al gave proper definitions and generation methods for sketching of style curves on 3D triangular surface, and a region searching method is also provided for fast 3D pattern design.Even there are some works having been done on provid
15、ing 3D interactive design tools, it is hard to ensure that the garment surface and pattern are modified validly and reasonably. Constraints modeling and solving is a good solution to solve this problem. It has been widely applied in mechanical CAD, however, how to apply it into 3D GCAD is a new rese
16、arch issue.Geometric Constraint Solving (GCS), namely geometric constraints satisfying problem, is a key technique in parametric CAD. There are four major approaches to GCS: the numerical approach 16-17, the symbolic approach 18-22, the rule-based approach 23-28, and the graph-based approach 29-37.
17、Currently GCS approaches are developed from solid modeling techniques in mechanical CAD, and they have some features listed as follows.(1) The major geometric elements are points, straight lines, planes, sphere, and conic surface.Few works has focused on freeform curves and surfaces.(2) The major co
18、nstraint types are dimensional constraints, such as distance, angle, logical constraints, including parallel, perpendicular, concentric, coaxial, and so on. Such constraints are called “active” constraints in paper 38, and they contribute to the shape19generation directly. Correspondingly, “passive”
19、 constraints which denote those do not control shape directly. Active constraints can be described in terms of algebraic equations, while passive constraints may be described as inequalities or in other ways. An example of a passive constraint is INSIDE (Circle1, Point1), where Point1 is constrained
20、 to be inside Circle1.(3) GCS finally turns to solve the groups of nonlinear equations with numerical method. The solving results always are rigid, and in many cases there is no solution if over constraints occurs.Compared to solid modeling, 3D garment design has some differences in GCS, which can b
21、e concluded as follows.(1) Taking the freeform curves or style curves as geometric elements for 3D garment design.(2) Passive constraints play an important role, or even a dominant role, in GCS of GCAD. It emphasizes to hold the correlation between geometric elements more than to maintain the precis
22、e dimensions.(3) The GCS solving result has flexibility. Results which make the geometric elements move in a valid range are regarded as a valid solution, and thus the curves can be sketched more freely.(4) For the 3D pattern design, geometric elements should undergo some special constraints to sati
23、sfy the craft needs.Thus, this paper focused on providing proper constraints description, definition, and solving for 3D interactive garment design. Since graph-based GCS method has high efficiency and can handle over or under constraints, it is applied widely. This approach analyzes the constraint
24、first, and then constructs a graph to express the constraints relation between geometric elements and constraint solving orders. Finally, it solves the constraints based on this graph, and acquires the modification results. So, we adopt this approach to analyze and solve the constraints in GCAD.In 3
25、D garment surface modeling, we take the contour spline curves as basic geometric elements, and summed up 13 constraints. Hierarchical driven model of contour curves is introduced to constraint graph conveniently. Three rules, namely priority-ranked solving rules, iterative solving rules, released so
26、lving rules, are proposed to solve these constraints properly. In3D pattern design, we analyze the crafts demands of style curves, such as seam lines, dart lines, grain lines, notch lines, and propose 4 constraints. Constraint graph is also given for sketching style curves properly.The structure of
27、this paper is as follows: Sect.2, 3, 4, 5 describe the constraints definition, graph construction, solving rules, solving process and surface updating for 3D garment surface modeling. Sect.6 describes the constraint modeling approach for 3D pattern design. In Sect.7, garment designexamples based on
28、GCS are presented, and finally the paper is summarized in Sect.8.2.Constraints definition and classification of 3D garment surface modeling2.1 3D garment surface and contour spline curves generationBased on the recognition of body feature points, 3D garment surface can be quickly generated by piecew
29、ise techniques 9. As shown in Fig.1(a), the body is divided into severalparts, such as the left and the right leg, the torso, the front and the back chest and so on. Fig.1(b) shows the triangular surface generated by piecewise techniques. Fig.1(c) shows the contour curves frame which includes two ca
30、tegories, namely silhouette curves and cross section curves. Silhouette curves, I type as shown in Fig.1(c), are extracted from the boundaries of garment sub-meshes, and are used to control the outline of the surface. Cross section curves, II type as shown in Fig.1(c), are generated from cutting the
31、 garment surface with planes at feature positions, such as breast, waist, hip and so on. The cross section shape can be modeled effectively through these curves. In order to model the surface effectively, silhouette curves andcross section curves are represented as B-Spline curves, as shown in Fig.1
32、(d).L1L2S1L3S2 L4 L5 L6L10S3S4(a)(b)(c)(d) Fig.1 Generation of the 3D garment surface and contour spline curves2.2 Constraints description and definitionL8L9The definitions of constraints are multiple. Paper 38 described the derivation of a consistent and comprehensive set of geometrical constraints
33、 for shape definition in CAD. However, how to describe the curve constraints in GCAD is still under research. In this paper, we summed up 13 constraints according to the interactive features of garment contour curves, as shown in Fig.2 and listed in Table 1.Define a constraint as Ci=Tp,(e1,e2,ei),Hd
34、. Where Tp denotes the constraint type, (e1,e2,ei) denotes the set of the Constrained Geometric Elements, CGE for short, Hd denotes constraint solving methods or rules.Fig.2 Constraints definition of editing contour curvesTable1. Definition and description of 13 constraints of editing contour curves
35、TpNameCGE(e1,ei,)Description (Hd)C1Same point(A1,A2)All the CGE have the same coordinate valuesC2Same plane(N1,N2,N3,N4)All the CGE are on a same plane.C3Symmetric(Hl0,Hr0)The CGE are symmetric about one plane and belong todifferent entitiesC4Selfsymmetric(S5,S7)The CGE are symmetric about one plane
36、 and belong to a sameentityC5Follow-up(S1, S2, S3, S4, S5)When a main element is moving, other CGE follow the movement by scale. As shown in Fig.2, in order to move the cross section evenly, when a point V3 is moving, points V1, V2,V4, V5 moves along with V3 by scale.C6Precise dimension(Hfi)The CGE
37、should not move out of range in x,y,z direction precisely. As shown in Fig.4, the control point Hfi should not exceed a maximum z coordinate and also can not bring on the garment sizes out of range after the garment surface isdeformed by Hfi moving.C7Relative dimension(B1)The CGE should not exceed a
38、 specified relative range. As shown in Fig.2, the control point B1 should not be moved below the middle of the bust and waist, such range is a relative value, so we call it a fuzzy size constraint.C8Mutual orientation(Hri-1,Hri,Hri+1)Each CGE should not be over each other in one or several direction
39、s. As shown in Fig.2, control points Hri-1, Hri, Hri+1 should be monotone in y directionC9Tangent(P3,L3)The CGE has tangent relation with each other. As shown inFig.2, the point V6 in the cross section Lc3 is tangent with contour curve L3C10Orientation(V0, V3, V6, V9)The CGE move in a specified dire
40、ction. As shown in Fig.2, points V0, V6 and V3, V9 are constrained to move in z or x axisdirection.C11Inside(Rgn, V1, V2)The CGE move inside a specified region Rgn. As shown inFig.2, points on Lc3 are constrained in a box composed by thefour extreme points V0, V3, V6, V8. Points on L10 move insideth
41、e specified loop R2.C12Outside( V3, V4)The CGE should be outside the reference objects, such asbody mesh, body cross section curves, or body silhouette curves.C13No selfintersection(Spl)The CGE can not intersect with itself. As shown in Fig.2, thegarment cross section Spl intersects at the shade reg
42、ion Rg, such cases should be avoided.2.3 Constraint classificationSince there are many constraints in 3D garment surface modeling, we have to classify them for easy constructing constraints graph and solving. First, we take the traditional approach to classify them into geometric constraints, topolo
43、gic constraints, and dimension constraints, as listed in Table 2. Based on this, these constraints are further classified into active and passive constraints.Table 2 constraints classification in contour curve editingConstraintsclassificationTopologic constraintsGeometric constraintsDimension constr
44、aintsActive constraintsC1, C2, C9C3, C4, C5Passive constraintsC8, C10, C11, C12, C13C6, C73.The constraint graph construction of 3D garment surface modeling3.1 Geometric constraint system and constraint graphBased on the constraints description, the linkage relation of the contour curves is essentia
45、lly a constraint system, and can be expressed by a binary function, GCS=(E,C). Where GCS denotes geometric constraints system, E denotes geometric elements, C=Ci denotes constraint sets. In our paper, E=(Spli,BLni,Fpi,Szi), the geometric elements meaning and their related constraints are listed in T
46、able 3.Table 3 the geometric elements meaning and their related constraints in ENameMeaningRelated constraintsSpliContour spline curves of 3D Garment surfaceC1,C2,C3,C4,C5,C8,C9,C10,C13BLjBody silhouette lines, cross section lines or specifiedreference linesC11,C12FpiBody feature pointsC7SziThe range set of garment siz