Computer-Aided Design. Computer aided clothing pattern design with 3D editing and pattern alteration

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1 Computer-Aded Desgn 44 (2012) Contents lsts avalable at ScVerse ScenceDrect Computer-Aded Desgn journal homepage: Computer aded clothng pattern desgn wth 3D edtng and pattern alteraton Yuwe Meng a,b, P.Y. Mok b,, Xaogang Jn a a State Key Lab of CAD&CG, Zhejang Unversty, Hangzhou, Chna b Insttute of Textle & Clothng, The Hong Kong Polytechnc Unversty, Hong Kong a r t c l e n f o a b s t r a c t Artcle hstory: Receved 25 July 2011 Accepted 15 March 2012 Keywords: Clothng computer aded desgn Cross parameterzaton Mesh edtng/deformaton Pattern alteraton The tradtonal apparel product development process s a typcal teratve optmzaton process that nvolves tral-and-error. In order to confrm the desgn and acheve a satsfactory ft, a number of repeated cycles of sample preparaton, tral fttng and pattern alteraton must be conducted. The process tself s tme-consumng, costly, and dependent on the desgner s sklls and experence. In ths paper, a novel computer aded desgn (CAD) soluton for vrtual try-on, fttng evaluaton and style edtng s proposed to speed up the clothng desgn process. A seres of new technques from cross parameterzaton, geometrcal and physcal ntegrated deformaton, to novel edtng methods are proposed. Frst, a cross parameterzaton technque s employed to map clothng pattern peces on a model surface. The pattern can be precsely postoned to form the ntal shape wth low dstorton. Next, a new deformaton method called hybrd pop-up s proposed to approxmate the vrtual try-on shape. Ths method s an ntegraton of geometrcal reconstructon and physcal based smulaton. In addton, user nteractve operatons are ntroduced for style edtng and pattern alteraton n both 2D and 3D manners. The standard rules regulatng pattern edtng n the fashon ndustry can be ncorporated n the system, so that the resultng clothng patterns are sutable for everyday producton Elsever Ltd. All rghts reserved. 1. Introducton The research n clothng computer aded desgn (CAD) has flourshed snce the poneer work of the MIRALab led by Prof. Magnenat-Thalmann n the late 80s. In the past two decades, computer graphcs communty has made sgnfcant contrbutons to ths area, coverng all aspects of clothng desgn, from desgn automaton, nteractve edtng, vrtual try-on, pattern generaton to custom-desgn clothng Related work of clothng CAD The frst research problem that needs to be solved for any clothng CAD systems s to accurately dsplay a desgn. Most researchers follow two man approaches to vsualze garment models. One approach represents garments as 2D patterns, whch are placed around a human model and then assembled vrtually to form 3D garments. Ths can be named as a 2D-to-3D approach. Fuhrmann [1] used developable surfaces, lke cylnders or cones, to poston clothng patterns around the vrtual human, and then appled the physcally based approach for an automated drape smulaton. McCartney et al. [2] represented a garment as a collecton of panels offset from the body surface, and constructed Correspondng author. Tel.: ; fax: E-mal address: Tracy.Mok@net.polyu.edu.hk (P.Y. Mok). the garment around a statc human model. Volno et al. [3] provded an nteractve desgn envronment to edt patterns n 2D and mmedately vsualzed the garment drapng results n 3D. Meng et al. [4] used physcal-based real-tme smulaton to vsualze desgn effects by vrtually sewng up complex garment patterns on human models. An onlne made-to-measure system was presented by Corder et al. [5], allowng shoppers to vrtually try on garments on the web. Another approach uses parameterzed surfaces and curves to model garments n 3D space drectly. Km et al. [6,7] drew grds on the mannequn and then scanned ths nformaton to construct a 3D garment surface. Lu et al. [8] adopted Bezer s parametrc surface to represent a 3D garment surface. Wang et al. [9] proposed a 3D garment desgn system nvolvng the partcpaton of customers for mass personalzaton, and they employed style surface and curves to represent garments. Other researchers used approxmate surface and offset surface technques, for example, Turqun et al. [10] and Decaudn et al. [11] sketched garment contours drectly onto 3D human models and then generated 3D garments usng a predefned dstance feld around the human model. Wang et al. [12] suggested a system to construct garments around a human model drectly n 3D space by stroke nput. Luo and Yuen [13] represented patterns as loop of curves, so that the pattern szes would change n accordance wth the sze of the human models used. Such a predefned relatonshp between clothng and body embeds the ft n garment modellng. All of /$ see front matter 2012 Elsever Ltd. All rghts reserved. do: /j.cad

2 722 Y. Meng et al. / Computer-Aded Desgn 44 (2012) these are pure geometrcal methods. In other words, the desgns are freeform desgns. Apart from vsualzng a clothng desgn on the computer, t s also mportant to allow desgners to edt the desgn and check the clothng ft. In 2D-to-3D based clothng CAD applcatons, desgn edtng and alteratons are carred out on 2D patterns and then followed by a drape smulaton to examne the results. In applcatons that follow the second approach of modellng garments drectly n 3D space, the desgn edtng can be done by deformng the 3D garments. However, a process must be provded to project the 3D desgn nto 2D space, so as to obtan the pattern peces. The typcal approach s by flattenng the desgned 3D surfaces to 2D planes. Azarads and Aspragathos [14] proposed two optmzaton methods for flattenng 3D surfaces: One wthout takng nto consderaton of the geodesc curvature constrants of the surface soparametrc curves, and the other method uses the constrants to control the local accuracy of the derved planar patterns. Km and Kang [15] proposed a projecton algorthm to flatten surface models by stran mnmzaton and ntroducng darts automatcally. The pattern flattenng methods employed play a crucal part n 3D garment desgn, snce they determne the qualty of the fnal manufactured garments. It s mportant to note that flattenng a freeform desgn has to nvolve some knds of deformaton. In addton, alteratons n desgn very often start from edtng the human models, because the ft gap between the clothng model and the human model s predefned n the 3D garment modellng. If a desgn s changed, t needs to do the 3D garment modellng anew. In summary, the 3D-to-2D approach suffers from the drawbacks of ether lmted style varaton or mpractcal shape of the flattened patterns for apparel manufacturng applcatons. In 2Dto-3D approach, physcal based systems are often used to smulate realstc clothng drape and even catwalk anmaton. However, the computatonal ntensve nature of physcal-based smulaton forces researchers to trade accuracy for speed by usng smplfed models n the smulatons. The smulated results may be good for vrtual characters or flm anmaton, but t cannot reach the requred accuracy n clothng producton Tradtonal fttng process for pattern optmzaton The tradtonal clothng product development s an teratve effort for ft and desgn optmzaton, nvolvng stages lke desgn, sample preparaton, ft evaluaton, and pattern alteratons. In the ndustry, clothng patterns are often constructed n 2D by pattern experts through manpulatng a set of basc blocks, or alterng from the patterns of smlar style. A sample garment s then prepared and put on a mannequn or a lve model to evaluate the ft acheved. In the fttng process, pattern experts vsually examne the sample by lookng at where wrnkles are created, so as to estmate the spatal relatonshp between the sample and the body, namely the clothng gap. Necessary correctons are marked wth pens and pns on the sample, and the 2D patterns are altered accordngly. Another sample garment would then be made. The process s repeated for a number of cycles untl a satsfactory ft s acheved (see [16] for detaled gudelne on tral fttng process). It s mportant to note that although the clothng gap s crtcal for ft evaluaton, the tradtonal sample fttng process s not able to vsualze the gap n any form. Wth reference to ft evaluaton, both geometrcal and physcal based CAD approaches have lmtatons. In geometrcal based CAD systems, the clothng eases for every desgn/style are predefned; but ths concept s obvously very dfferent from the tradtonal practce of the ndustry descrbed above, where 2D patterns are altered to ft the customer s body shape. The concept of predefned ease may be possble only for staple tems where style change s not frequent, lke shrts or trousers. However, for fashonable tems, the predefned ease concept s not practcal because apparel products have dverse ft desgns and people also have vared preferences on ft [17]. In physcal-based systems, drape smulaton could not provde accurate clothng gap for ft evaluaton, but can smulate the clothng stretch and stran. These smulated stretch and stran could only gve desgners lmted nsght on the ft acheved or the ways for ft mprovement. In addton, all clothng desgn and alteratons are done on 2D patterns n physcal-based CAD system, thus another smulaton must be launched to examne the effect of any alteratons made. All n all, true computer-aded desgn s stll absent, because synchronzed 2D and 3D desgn edtng are not possble durng the ft evaluaton. In ths paper, a method s proposed to establsh the spatal relatonshp among 2D patterns, 3D garment and the human model. The man advantage of such assocaton s that any pattern alteratons, ether n 2D or 3D, can be reflected on the human model for ft mprovement and style edtng Research concept and system overvew In ths paper, a novel three-phase framework s proposed to enable vrtual try-on smulaton and ft evaluaton. In contrast to the typcal approach of 2D-to-3D CAD systems, where 2D patterns peces are pulled towards the human model for vrtual sewng smulaton, the proposed method adopts a rather dfferent approach. In the proposed method, 2D pattern peces are frst precsely mapped onto the human model surface by a crossparameterzaton process. Next, a hybrd poston update method ntegratng both geometrcal reconstructon and physcal smulaton s developed. By ths method, the garment pops up from the body surface, based on a few defned contact ponts, to restore ts orgnal sze. After the pop-up process, a gap s formed between the clothng and the body that approxmates the clothng gap n pattern desgn, whch s fundamentally mportant for ft evaluaton. Snce a relatonshp between the clothng and the body has been defned, pattern edtng for ft mprovement or desgn amendment could later be facltated. Fnally, a systematc mult-vew edtng tool s suggested for synchronzed 2D and 3D style edtng and pattern alteraton. A bref outlne of the proposed three-phase method s gven n Fg. 1. Each phase of the method wll be dscussed n separated Sectons 2 4. Phase three of style edtng and pattern alteratons s a large topc n clothng development, nvolvng many steps and operatons. In vew of the substantal contents nvolved, Secton 4 only brefly explans the underlyng concept, and a more detaled dscusson of the topc s gven n [18]. Secton 5 provdes expermental results. The man contrbutons of ths paper are summarzed as follows: A new mesh-to-mesh cross parameterzaton method s suggested for postonng the pattern peces onto the human model that precsely preserves the pattern shapes of the fnal garments. The vrtual try-on s acheved automatcally. A novel hybrd method combnng physcal-based smulaton and geometrcal reconstructon s proposed to deform the garment from ntal form to the desred shape,.e., to resume ts orgnal sze. The hybrd schema enables the local coordnate technque to be used not only for sngle closed mesh deformaton, but also for open mesh surface reconstructon. A unque pattern alteraton method s proposed for garment edtng n both 2D and 3D manners, and such dea has never been reported n the lterature before. The method uses fashon desgn rules to control the style edtng and pattern alteraton, makng t sutable for practcal mplementaton of fashon product development.

3 Y. Meng et al. / Computer-Aded Desgn 44 (2012) Fg. 1. System overvew. 2. Pattern-to-model cross parameterzaton Clothng try-on demands a rgd correspondence between the clothng feature ponts and the human model feature ponts. The proposed computer aded desgn system starts by frst establshng a spatal relatonshp between the 2D clothng patterns and the human model by a surface parameterzaton process. Surface parameterzaton conssts of generatng a planar parameterzaton for a 3D mesh surface. Parameterzaton has varous applcatons n scence and engneerng, ncludng scattered data fttng, re-parameterzaton of splne surfaces, and repar of CAD models. Texture mappng s an mportant applcaton of parameterzaton that commonly used to ncrease the vsual complexty of computer generated mages whle mantanng smplcty n the underlyng geometrc models. Texture mappng algorthms provde parameterzaton by usng an embeddng functon and barycentrc coordnates for each par of mesh trangles that defne a pecewse-affne mappng. An nteractve texture mappng technque was frst proposed by Mallot et al. [19], who obtaned the planar development of a 3D surface by solvng a global optmzaton problem. Sheffer and Hart [20] descrbed a faster technque to lower the vsual dstortons. Haker et al. [21] suggested a sphercal texture doman for seamless mappng of closed surfaces. Sander et al. [22] and Levy et al. [23] subdvded the surface nto multple small patches and texture mapped the patches separately. In summary, nteractve texture mappng methods strve to mnmze the dstorton n the mappng process accordng to dfferent dstorton metrcs. To establsh spatal relatonshp between clothng pattern and human model, a new surface parameterzaton technque s requred because clothng patterns of dfferent desgns vary largely n geometrcal shapes, for nstance, darts and nsde darts may be nvolved. In ths paper, a duplex mappng scheme s proposed, nvolvng the followng three steps: (1) Feature defnton: specfy the correspondng feature ponts on both the human mesh model and the pattern mesh; (2) Mesh segmentaton and regon mappng: trangulate 2D patterns based on defned feature ponts to obtan ancllary patterns, and segment the human body mesh accordngly to match wth the ancllary patterns; and (3) Crossparameterzaton: embed each patch on the body mesh surface to the correspondng clothng pattern mesh to generate parameterzaton coordnates Nomenclature and feature defntons A lst of symbols used n cross parameterzaton process s provded below: F H : feature ponts of the human model F P : feature ponts of the clothng pattern M: Mesh of 2D patterns M : Mesh of ancllary 2D patterns generated based on F P M : 3D confguraton of the pattern M,.e., the mappng result P : patch of the human model T : trangle n M : trangle n M (p k, p l ): vertex n P (v, k v l ): vertex n T (v k, v l ): vertex n T T The planar patterns M and trangulated human model are nputs to the process. The process starts from defnng the feature ponts on both the clothng patterns and the human model. Fgs. 2 and 3 show the human model feature ponts F H and the clothng pattern feature ponts F P, respectvely. The defnton of body feature ponts s avalable n most pattern-makng lterature [24] or body measurement standards [25]. Huang [17] descrbed detal methods to defne feature ponts on a mesh model automatcally. In every pattern pece, the corner ponts, also called grade ponts, are mportant features. If any of the grade ponts do not correspond to the predefned body features F H (for example, pnk crcle ponts n Fg. 3), the system calculates ther relatve postons on the model surface based on known feature ponts (black square ponts) by proporton. The system defnes the relatve poston of a pnk crcle pont on the shortest path between two known feature ponts, F H. The shortest path calculaton wll be explaned n later Secton 3.2. In addton to obtanng the feature pont postons automatcally by proporton, a user nterface s also provded for users to defne the features manually Mesh segmentaton and regon mappng After nputtng the clothng pattern M and the correspondng feature ponts F P, the system adds addtonal auxlary ponts to the feature curves of the pattern peces, as shown n Fg. 4. Ths s done to ensure satsfactory trangulaton results n the later step. The postons of these auxlary ponts are computed as average

4 724 Y. Meng et al. / Computer-Aded Desgn 44 (2012) Fg. 2. Feature ponts on human model, F H. Fg. 3. The correspondng feature ponts on a front and a back pattern peces, F P. splttng between two defned feature ponts. Each boundary curve s dvded nto l /κ segments, where κ s the length of the shortest boundary curve, l s the length of the current boundary curve, and means a round up operaton. Constraned Delaunay trangulaton s then carred out on all pattern peces by usng predefned feature ponts and the auxlary ponts as the vertces. Ths wll obtan a set of ancllary pattern peces, M, whch are the smplfed forms of the pattern peces, M. Fg. 6(b) shows an example of ancllary patterns M, the front pece. After trangulatng the clothng pattern M, the human mesh model s segmented based on the ancllary pattern M by an approxmated shortest path method, as shown n Fg. 6(e). Tradtonal Djkstra shortest path connects two specfc vertces on a mesh wth edges, whch s not the exact shortest path on a mesh surface. A known method to mprove the Djkstra shortest path s to teratvely subdvde the mpact trangle edges and construct new weghted graphs, so that the path s closer to the deal one could by teratons. However, such method costs a consderable amount of memory space and t s rather tme consumng. In ths paper, a smple shortest path method s developed to segment the human model mesh, see Fg. 5. It uses pre-computaton rather than an teratve schema. In the graph constructon stage, the set of mpact edges are subdvded accordng to the edge length of the correspondng trangle T on the ancllary pattern M. Gven a defned length, each edge s nserted wth several ntermedate ponts and the number of ponts nserted s proportonal to the length of the trangle edge, as shown n Fg. 5. Thus, a long edge s dvded nto more segments compared wth a short edge. Another method was also suggested to calculate the shortest path n [26]. It parttoned the mesh nto vald sub-regons after

5 Y. Meng et al. / Computer-Aded Desgn 44 (2012) Fg. 4. (a) Feature ponts on model F H wth predefned body features (black square ponts) and system generated auxlary ponts (blue crcle ponts) and (b) correspondng features ponts F P on the front and back pattern peces. (For nterpretaton of the references to colour n ths fgure legend, the reader s referred to the web verson of ths artcle.) Fg. 5. The shortest path approxmaton. searchng for the shortest path. Compared wth [26], the method proposed n ths paper for the shortest path approxmaton usng subdvson pre-computaton s robust and effcent for the current applcaton of mesh segmentaton and regon mappng, the reason s because complex computaton of Stener vertces s avoded. To conclude, the method decomposes the body mesh model nto a set of surface patches P. The edges of these patches are paths connectng adjacent feature vertces, whch mantan the same topology as that of ancllary patterns M (see Fg. 6) Cross-parameterzaton After the mesh segmentaton process, a bjectve mappng s constructed between the pattern and the correspondng regon of the human model. Each trangle T on the ancllary patterns M s then matched wth a trangular patch P on the 3D human model mesh. The vertces of each trangle T are three constraned vertces (v k, v l, v m ). The patch P s bounded by paths (p k, p m ), (p l, p m ) and (p k, p l ) between the three mentoned vertces. A cross parameterzaton procedure s carred out to embed every vertex n 2D pattern onto the 3D surface of the human model as follows: 1. In each patch P, place the path (p, p j ) at equal dstances along the correspondng trangle T of the ancllary pattern M. The harmonc coordnates are used to map the rest nteror vertces under the constrant of boundary vertces. Therefore, a mappng functon P = G(T,..., 1 T N ) s constructed mappng vertces of P to M. G s encoded by barycentrc coordnate of a trangle T n M, whch s nsde of P (see Fg. 6(d)). 2. For each vertex v of M, use barycentrc parameterzaton to place ts nteror vertces nsde the trangle T. The barycentrc mappng of a mesh nto a convex doman s known to produce a vald embeddng. Therefore, another mappng functon v = G (T,..., 1 T N ) s thus constructed mappng the vertces n M to M. 3. Combnng the mappng functons G and G, each vertex of the 2D patterns M s mapped around the human model n 3D space. Snce all vertces n M and P have ther correspondng poston n T after the Steps 1 and 2 above, the vertces n M can be encoded by barycentrc coordnate of relatve trangles n P, and vce versa. Therefore, a bjectve mappng between mesh M and patch P s thus constructed. See Fg. 6(e) for detals. It s notced that some pattern peces are of convex shape or nvolved wth curves. It means that no perfect trangulated mesh can cover the full area of these pattern peces. In ths case, the nearest trangle to vertex v s located, and the vertex are encoded by two vectors of the closest trangle v c1 v c2 and v c1 v c3. v c1, v c2, and v c3 are the vertces of the closest trangle. It means the two parameters of the barycentre parameterzaton n the Step 2 mentoned above can be negatve values. Gven that the nput body model s a properly segmented model wth feature ponts F H automatcally defned [27], the cross parameterzaton of dfferent pattern peces are carred out on the relevant body segments only. The result of the procedure s a vald embeddng of the mesh M that satsfes the postonal constrants. The postonal constrants refer to a one-to-one mappng between the featured ponts on patterns and those on the human model Post-procedure Upon the above embeddng process, the clothng patterns are mapped onto the human mesh model. In most cases, a mesh refnement procedure s necessary to optmze the surface for better mappng results. Ths post-procedure s often requred because tradtonal clothng patterns are developed based on some sze standards, whch mples that the clothng can ft well to people wth average buld. If the nput model has an average body fgure, good mappng results would be obtaned because the precsely defned feature ponts can ensure very low dstorton. However, for nput model wth specal body shape such as protrudng abdomen or wde shoulders, the dstorton would be hgh, meanng that the edges of the 3D garment are stretched. In such cases, a post-procedure of mesh refnement s usually carred out to optmze the mesh surface. However, such refnement step s skpped n the current method, because the step has been ntegrated n the later hybrd pop-up process, whch wll be explaned n Secton 3. After the procedure of mappng the clothng patterns onto the human model surface, the pattern peces are sewn up as a complete garment by combnng the correspondng vertces at the seams, as shown n Fg. 7. Such vrtual sewng operaton s almost dstorton-free, because the vertces on the seam lnes are very close to each other. Fg. 8 shows the complete garment results.

6 726 Y. Meng et al. / Computer-Aded Desgn 44 (2012) Fg. 6. (a) Orgnal garment pattern M; (b) ancllary pattern generated by constraned delaunay trangulaton M ; (c) a 3D patch segmented from human model P ; (d) flattened 2D patch by Harmonc map; (e) shortest path graph on human model and the fnal 3D confguraton. Fg. 7. (a) Mappng results of 2D pattern around human model. Usng the pattern M, the seam poston of two seam lne can be mapped to the same coordnate (the red lnes specfy the mesh boundary); (b) mesh after seam operaton; (c) mappng the front and back pattern peces around human model to form a complete garment. (For nterpretaton of the references to colour n ths fgure legend, the reader s referred to the web verson of ths artcle.) Fg. 8. Complete garment after sew operaton (front, sde, back vews). 3. Hybrd pop-up The prevous secton descrbed that spatal relatonshp between the clothng and the human model s developed for attachng the pattern peces onto the body surface. Ths secton presents how the garment s deformed by a hybrd pop-up method nvolvng both geometrcal reconstructon and physcal smulaton, from ts ntal form to the desred shape. The desred shape s defned as a state that the deformed garment surface s at the prescrbed poston, ts boundary lengths (namely, the pattern szes) are restored to that of the orgnal 2D patterns M, and the curvature s remaned the same as the ntal form (3D mappng surface). At the end of the hybrd pop-up, a clothng gap s formed between the garment and the body surface. If the same garment s tred on models wth vared body szes, the clothng gaps formed are dfferent. Ths makes the evaluaton of effectve clothng ft possble Geometrcal reconstructon The purpose of geometrcal reconstructon procedure s to mantan the local curvature of the fnal garment. In ths procedure, the 2D pattern meshes M and the 3D confguraton M generated n Secton 2 are nputs. The output of the process s a mesh that keeps the curvature of 3D confguraton and the sze of the 2D patterns. Many methods have been proposed to preserve the local shape propertes of 3D models durng deformaton or edtng. For example, Sheffer and Kraevoy [28] proposed the use of pyramd coordnates to capture and mantan the local shape propertes,

7 Y. Meng et al. / Computer-Aded Desgn 44 (2012) Fg. 9. Pyramd coordnates of vertex v, n whch v s one of the neghbour vertces of v, and h s the dstance from v to ts projecton plane. The value of h s obtaned by averagng the projecton dstances of v v to the normal of v for all neghbour vertces v 1, v 2,..., v m, and normal component θ s used n computaton of projecton dstances. by usng a set of angles and lengths to relate a vertex to ts mmedate neghbours on a projected plane, as llustrated later n Fg. 9. Pyramd coordnates were extended from the concept of mean value coordnates (MVC) [29]. On a 2D plane, mean value coordnates defne the poston of a vertex v as a convex combnaton of ts one-rng neghbours v 1, v 2,..., v m wth weght parameters λ. The mean value coordnate λ for vertex v wth respect to ts neghbour v s defned by angle parameter α and length parameter l as follows: λ = tan(α /2) + tan(α +1 /2) l = tan(α /2) + tan(α +1 /2) v v whle the mean value coordnates (mean value weghts of all m neghbours) need to be unfed,.e., λ =1 = 1. By extendng the MVC concept from 2D plane to 3D doman, pyramd coordnates nclude both tangental (α and l) and normal (θ) components, as depcted n Fg. 9. In the current applcaton for clothng try-on, the local coordnates encoded n the ntal confguraton s only a rough form of the garment, whch cannot reflect the precse local relatonshp (the desred shape) between the pattern peces. Ths s because dstortons have been ntroduced when the pattern peces are mapped on the human model, and morphng the vertex coordnates s necessary to restore ts sze. In [28], a deformaton technque was ntroduced to deform closed 3D mesh models based on user specfed control vertces. For ths technque, the pyramd coordnates of the source and target meshes, both the angle and length parameters, are defned n 3D doman. In contrast to mesh edtng, n the clothng tryon applcaton, the lengths (garment sze) are defned n the 2D patterns whle the curvature propertes (garment shape) should be preserved from the ntal 3D form. Therefore, a converson from 2D pattern to 3D garment s necessary to update the local coordnates of the 3D garment by geometrcal reconstructon, shown as follows: λ = λ2d (1 cos θ ) (2) where λ s the local coordnate of vertex v on the 3D garment n relaton to ts neghbour v, λ 2d s the correspondng mean value coordnate of the vertex v on the 2D pattern, and θ s the normal angle parameter of the local coordnate (see Fg. 9) from the ntal confguraton. (1) Eq. (2) defnes the target coordnate of the mesh vertces poston of the fnal 3D garment. In ths paper, geometrcal reconstructon s performed by teratvely adjustng the angle parameter θ of the coordnate for relocatng the mesh vertces as follows: θ = arcsn l v v + arcsn l v 2d v 2d 2 (3) where v v s the length between v and v on the 3D shape of the current reconstructon teraton, v 2d v 2d s the correspondng length on the 2D pattern, l s the length parameter value for the local coordnate of the current reconstructon teraton. The Gauss Sedel reconstructon process [28] s used to teratvely deform teratvely the garment vertces postons untl convergence (.e., the local coordnates reach the nterpolated values, whch wll be descrbed n the later morphng step). As shown n Eq. (3), the average angle s used n the calculaton to ensure stable deformaton. Expermental results showed that θ approaches the deal value at the end of the reconstructon process,.e., θ = arcsn l v 2d v 2d. (4) Once the desred local coordnate for the fnal garment s obtaned by Eq. (2), morphng s performed to convert the garment from ntal confguraton to ts desred confguraton. Morphng algorthms create a smooth temporal transton between multple nput models,.e., between nterpolated local coordnates n the current applcaton. A typcal morphng algorthm conssts of three man stages: computng a bjectve mappng between the models; re-meshng the models wth a common connectvty; and computng the trajectory for each vertex n the mesh between ts source and target postons [28]. In ths paper, a method s proposed to generate ntermedate models based on source and target models. The morphng algorthm frst computes the source coordnates and target coordnates, S and T. For each tme frame t, the algorthm computes the local coordnates by lnearly nterpolatng the source and target coordnates as follows: λ = λ S (1 t) + λ T t = λ 3d (1 t) + λ t. (5) In the morphng procedure, the morphng step for t s defned as 10, thus t = 0, 0.1, 0.2,..., 1 n the above Eq. (5). The boundary vertces are controlled by the physcal-based schema, whch wll be ntroduced n the followng secton Two-stage boundary curve teratve update In the geometrcal reconstructon, the local coordnates of the garment are retaned. The ntal confguraton of the garment surface s generated n the mappng process (Secton 2). However, such surface poston s not consdered to be at the desred poston when the garment s tred on. On the other hand, the boundary of the garment surface becomes unstable after geometrcal reconstructon f the boundary s not fxed or under control. In order to restore the garment to the sze defned by ts clothng patterns and solve the boundary nstablty problem n geometrcal reconstructon, a two-stage procedure s performed ncludng a slhouette adjustment and a physcal-based poston update to the boundary vertces of the 3D garment. Ths procedure ams to obtan the geometrc clothng gap between the clothng and the body surfaces. Ths s acheved by defnng a few contact ponts and followed by wdth and length restoraton (Sectons and 3.2.2). The contact ponts are ponts between the garment and the body surface, whch

8 728 Y. Meng et al. / Computer-Aded Desgn 44 (2012) the postons would not change n the sze restoraton process. Ths s acheved by addng poston constrants to these contact ponts n the mplementaton. These contact ponts are usually defned as the feature ponts on shoulder lne for top garments lke shrts, and on the wast grth for bottom garments lke trousers. The ratonale behnd ths sze restoraton procedure s that f the boundary curves of the pattern that defne the garment sze can be transformed from ts ntal state to the desred lengths by teratve morphng, the nteror vertces of the garment can be transformed accordngly by the geometrcal reconstructon procedure descrbed n Secton 3.1. It s later proved by experments that ths approach s vald and effectve Slhouette adjustment To restore the garment to ts orgnal sze, the adjustment s done by frst extendng the garment wdth n a pre-computaton step, called slhouette adjustment. It s then followed by updatng the garment vertcal lengths usng a physcal-based method. For the slhouette adjustment, t s noted that each garment s composed of a set of pattern peces. For example, the front and back panels wrap around the body to form a top garment, such as blouse or t-shrt, or wrap around the legs to form a skrt or trousers. Therefore, the fnal garment s grth measurement at the hem level s known from the pattern peces, whch s the total length of the bottom boundary curves of the front and back peces. Assume that the length of the correspondng boundary curve on the ntal form, after the cross parameterzaton, s c, whch s equal to the grth measurement of a feature curve on the body model. If the length of the boundary curve on the fnal garment should be adjusted to c (c > c), whch s the sze of the pattern peces, then the length adjustment for ths boundary curve s c c. It later creates the clothng gap at the hem level. The slhouette adjustment s done by frst computng a geometrcal centre of the closed boundary curve. To ensure stable transformaton, the adjustment of c c s acheved teratvely by a number of steps. The vertces postons on ths closed boundary curve s adjusted usng the geometrcal centre of the curve as ther average poston. For specal cases of tght-ft garments, n whch the clothng grth s smaller than the crcumference of the human body (c > c), the process of sze restoraton s omtted and ths wll be dscussed further later Physcal-based poston update Upon every step of slhouette adjustment, a physcal-based smulaton s performed n the normal drecton, so as to update the 3D garment length teratvely. Force defnton Physcal smulaton s wdely researched n the area of clothng smulaton. The purpose of the proposed physcal smulaton procedure s not to obtan a drape result, but to stretch the garment to ts orgnal length. It s found that a system of nteractng partcles s well sutable for ths smulaton applcaton. The method presented here s nspred by the work of Breen et al. [30], who frst appled the partcle model to the smulaton of textle fabrcs. Compared wth Breen et al. [30], a smplfed partcle model s used n ths paper. Fg. 10 presents the connectvty of the mass partcles of the cloth surface. The green partcle (green crcle) s one of the boundary partcles, where the forces actng on t are llustrated. The red partcles (red squares) are boundary partcles connectng to the green one. The blue partcles (blue trangles) are nteror partcles. In contrast to the general methods that apply three dfferent knds of force on a sngle partcle, only the stretchng and the bendng forces are employed n the smulaton. It s because shearng force s necessary for anmaton, but the current Fg. 10. Forces actng on partcles. smulaton does not nvolve any anmaton. It s found that the twoforce model works well n ths applcaton. Gravty force s also omtted n the calculaton, because t has lttle effect on the partcle. As shown n Fg. 10, every nteror partcle s fully connected, wth the excepton of partcles at the boundares. Therefore, the partcle nteracton model employed nvolves two types of partcles, the blue trangle ones as the centre partcles and the boundary vertces (red squares and green crcle). The physcal smulaton s appled only to the boundary vertces of the surface n order to acheve real-tme speed. Numercal smulaton In clothng smulaton, the computaton of dfferental equatons s usually one domnant part of the total computatonal costs. Upon decdng the physcal model, a sutable numercal ntegraton method must be selected. The Stoermer Verlet ntegraton scheme [31] s selected, because t s especally effcent f the mechancal systems are represented as second order ordnary dfferental equatons. In the smulaton, the velocty s omtted n the dynamc equatons. As a result of ths, t may not be precse enough for dynamc anmaton, but s suffcent for obtanng accurate deformaton results of garment sze restoraton. To ensure stable sze restoraton, the physcal smulaton procedure updates the vertex poston by constranng ts dsplacement along the normal drecton by: x = N (x N) (6) N where x s the dsplacement calculated by physcal module, N s the thrd drecton obtaned by prncpal component analyss on the set of boundary vertces Hybrd schema The steps of the deformaton algorthm are: Step 1. Compute the local coordnates of the nput mesh model,.e., the source coordnates, S. Set the current coordnates as S. Defne the contact ponts on the nput mesh. Step 2. Use Eq. (5) to compute local coordnates n the current teraton. The number of teratons for morphng the garment from ts ntal form to the desred shape s set as 10. If the teraton ndex reaches the defned value, end the procedure. Step 3. Adjust the clothng slhouette of the 3D garment boundary curve by the pre-adjustment algorthm descrbed n Secton Ths ensures that the garment wdth gradually reaches the dmensons defned n the pattern peces. Step 4. Use physcal-based poston update procedure (Secton 3.2.2) to change the postons of the boundary vertces.

9 Y. Meng et al. / Computer-Aded Desgn 44 (2012) provdes crucal nformaton for desgners to evaluate the clothng ft acheved. Cross-secton vews for ft evaluaton can be easly extracted, as shown n Fg. 12. Tradtonally, the local coordnates can only handle sngle closed mesh deformaton. If t s appled to open mesh surface, the surface boundary would be unstable. Usng the proposed hybrd schema, local coordnates can now be appled n open mesh surface reconstructon. 4. Interactve edtng and pattern alteraton Fg. 11. Pop-up results. The clothng gap obtaned from the above process provdes desgners wth excellent nformaton about clothng ft acheved. A unque pattern alteraton method s proposed to allow real-tme nteractve style edtng based on the try-on results, n both 2D and 3D operaton manners. Snce the topc of pattern alteraton and style edtng nvolves many complex operatons, t s not n the scope of ths paper. Therefore, only the underlyng concept for 2D-based and 3D-based nteractve pattern alteraton s brefly explaned n ths paper. A more detaled dscusson of the topc s shown n [18] D pattern alteraton Fg. 12. Cross-secton extracton from the fnal pop-up result. (The outer green lne s the cross-secton of the garment and the nner blue lne s the cross-secton of the human model.) (For nterpretaton of the references to colour n ths fgure legend, the reader s referred to the web verson of ths artcle.) Step 5. Update the rest vertces by geometrcal reconstructon wth desred local coordnates obtaned from Eq. (5) of the current state. Step 6. Update the teraton ndex, and go back to Step 2. In order to evaluate the effectveness of the proposed hybrd pop-up process for sze restoraton, a performance measure s defned: χ = L3d L 2d (7) where L 3d s the length of an edge n the 3D garment mesh model, and L 2d s the correspondng edge length of the 2D pattern mesh model. In deal sze restoraton, the parameter value of χ of all edges approach to 1 at the end of the smulaton. Table 1 shows the error measurement of each smulaton step, n whch E(χ) s the expected value of χ,.e., the mean value of the parameter (Eq. (7)) for all edges on the mesh, and σ 2 s the varance of χ devated from hs expected value. It can be shown from the table that the proposed hybrd schema s effectve for sze restoraton. Fg. 11 shows the fnal result from the hybrd pop-up schema. As shown n the result after the pop-up step, a clothng gap s formed between the clothng and the body. The garment has been restored to ts orgnal sze, as defned by the clothng patterns. Ths gap In the tradtonal fashon product development cycle, desgners often adjust 2D patterns to produce clothng wth better ft for ndvdual customers, who often do not have deal body shape and possess a few abnormaltes n one or two areas of the body, for example n the areas of the neck lne, shoulder and armhole [16]. Based on the establshed spatal relatonshp between the clothng and the human model, tools are developed for users to alter 2D patterns nteractvely by modfyng the poston of the pattern feature curves, whlst vsualzng the synchronzed edtng effects n 3D space. For pattern alteraton, t s mportant to mantan the topology of the pattern mesh, as well as the neghbourng relatonshp of the feature ponts n 2D pattern alteratons. Ths corresponds to a 2D case of Laplacan edtng. Nevertheless, the method proposed n ths paper for 2D-based edtng s to calculate the relatve vertex postons by a smple lnear nterpolaton to ts neghbourng features. Users frst mpose constrants on the pattern feature curves by nalng down feature ponts on the boundary. Users then deform the pattern by draggng a feature pont to the desred poston. By keepng the relatve poston of the edted feature pont and ts neghbourng feature ponts, the postons of other vertces on the feature curve can be calculated as follows. v f = v f1 + α A + βr 90 A (8) where v f1 s the updated vertex poston of edtng feature f 1, vector A s the relatve poston of feature f 1 and ts neghbour feature f 2, A = v f2 v f1, n whch the vertex poston of f 2 s fxed by user. In Eq. (8), R 90 s the rotaton matrx for a 90 counter-clockwse rotaton. As shown n Eq. (8), the poston of any vertex, v f, on the boundary curve can be updated by a smple lnear nterpolaton of ts two neghbour features v f1 and v f2. The remanng nteror vertces are then updated teratvely wth reference to the deformed boundary poston constrants by mean value coordnates. The geometrcal topology of the orgnal pattern mesh s mantaned. In Eq. (8), α, β and R 90 are known from the prevous calculaton. Comparng wth Laplacan edtng, whch has order at least N squared tme complexty O(N 2 ), Eq. (8) has order 1 tme complexty O(1). Thus, the mplementaton of ths formulaton s much smpler, yet suffcent for the 2D-based pattern edtng.

10 730 Y. Meng et al. / Computer-Aded Desgn 44 (2012) Table 1 Error measures of each smulaton step. Step E(χ) σ Fg. 13. Illustraton of 2D edtng: (a) 2D patterns and (b) 3D armhole shape before edtng; (c) lftng up the armpt pont on 2D patterns and (d) the resulted 3D armhole s reduced; (e) lowerng the armpt pont on 2D patterns and (f) the resulted 3D armhole s enlarged. Fg. 13 demonstrates the pattern alteraton results of lftng up and lowerng the armpt feature pont [APpsx1] on the armhole curve. Snce the assocatons and dependences between pattern peces have been defned n the mappng process, any modfcatons made to one pattern pece can be automatcally transferred to all dependent peces. It speeds up the product development process sgnfcantly. It s mportant to note that the rules governng fashon desgn are used to gude the edtng process, so that the altered patterns fulfl the textle materal propertes and clothng manufacturng constrants, and can be used for apparel manufacturng. More detals are gven n [18] D-based edtng for style and ft mprovement In addton to 2D pattern alteraton, tools are developed for 3Dbased nteractve style edtng. Users can drag the feature curve or boundary of the 3D garment drectly to alter the garment sze. In most CAD applcaton, freeform deformaton s used for 3D garment edtng, the edted results cannot be accurately reflected on 2D patterns, because dstorton free flattenng method s stll not yet avalable. Wth the known spatal relatonshp between clothng features and body features n the current method, 3Dbased desgn edtng becomes possble because the necessary 2D pattern alteraton used to acheve the requred 3D effects can be easly calculated. In ths paper, 3D-based edtng s used to alter the grth measurements of the garment, as well as to change the garment style lnes n 3D,.e., the poston of the pattern grade ponts. These functons satsfy most style edtng requrements for ft mprovement n the fashon product development process. To edt a 3D desgn, the area to be edted s frst specfed by a sketch tool, see green lne n Fg. 14(a). It can select to alter a grth measurement of the garment or ndvdual style lne, such as the necklne shape. The system wll automatcally calculate the pattern peces beng affected by the selecton and ther feature ponts. To edt the garment, users specfy the control vectors for deformng the selected feature ponts on the 3D garments. For example, f the bust grth measurement s to ncrease by 4 cm ease, the system wll share the ease to the pattern peces affected, whch s 1 cm on the two front peces and 1 cm at each sde of the back pece, as shown n Fg. 14(b). Fg. 14 demonstrates a 3D-based edtng for addng ease to the bust level. The feature ponts beng affected n the edtng operaton are shown as blue ponts on the 2D patterns n the fgure. If the control vector of the edtng operaton s parallel to the selected feature curve, eases are added to the grth of the feature curve. If the control vector of the edtng operaton s perpendcular to the selected feature curve (see Fg. 15), the correspondng level of the feature lne wll drop. In other words, the length of the garment wll be extended, refer to Fg. 19(d) n Secton 5 for an llustraton. The proposed method for 3D-based edtng s a novel dea. To the best knowledge of the authors, smlar methods have not been reported before. It allows drect style edtng for ft mprovement n 3D space, and results are drectly projected on the pattern alteraton n 2D plane. The edtng results are vsualzed through the hybrd pop-up process. The 3D edtng functons fulfl the needs of most pattern edtng requrements n the fashon ndustry. Most mportantly, the edted pattern peces fulfl the requrement of the clothng ndustry n terms of lne, gran, balance and set [32]. Therefore, dfferent from free-form edtng, the proposed 3D edtng s sutable for ndustral applcaton, whch can drastcally shorten the product development cycle. 5. Expermental results and dscussons In ths secton, two garments ncludng a par of trousers and a blouse are used to demonstrate the proposed clothng CAD system.

11 Y. Meng et al. / Computer-Aded Desgn 44 (2012) Fg D-based edtng for addng ease to the bust grth: (a) 3D garment before edtng, where bust lne s selected; (b) the correspondng pattern alteraton for ncreasng ease to the bust level; and (c) the edted result. Table 2 Pattern and seam nformaton of garment types. Garment styles Pattern nformaton Number of seams Trousers 4 peces: 2 front panels and 2 back panels 13 seams Standng collar blouse 9 peces: a front panel, 2 sde front panels, 2 back panels, 2 sde back panels and 2 sleeves. 13 seams Fg. 15. Two scenaros of 3D-based edtng control vectors. The system reads n dxf fles of the producton patterns, whch were developed by standard pattern desgn systems (PDS). Fg. 16 shows the pattern peces of the blouse and the trousers. Table 2 lsts the pattern and seam nformaton of the garments. The results of pattern mappng and hybrd pop-up procedures of the blouse and trousers are shown n Fgs. 17 and 18, respectvely. Fg. 19 shows the results of ft evaluaton for the trousers and the pattern alteraton for wdenng and lowerng the hem lne of the blouse. Table 3 shows that the proposed method s very effcent. Usng the smple blouse as an example, the shortest path generaton procedure used about s to calculate a path, wth an average of 0.77 s for one path, a total of s and MB memory for 112 paths. The tme consumpton of mappng procedure can be omtted, because t s very fast. The pop-up smulaton procedure took 0.23 s for one teraton, and the whole procedure usually nvolved 10 teratons. It has been demonstrated that the proposed system estmates the try-on results of clothng, provdng desgners wth useful nformaton for ft evaluaton. The proposed method obtans the try-on results by mappng clothng patterns on the body and then poppng up the clothng from the body surface. Ths unque approach mantans the szes and shape of the clothng patterns, allowng effectve ft evaluaton. Besdes, tools are developed to facltate pattern alteratons on the computer. It s an mportant tool for the fashon ndustry. It s beleved that the current method works well for just-ft garments and tght-ft garments. For tght-ft clothng, such as undergarment and jeans, the clothng patterns would be smaller than the body sze. The try-on process s completed after the pattern-to-model cross parameterzaton step, and the stretchng of the garment can be easly obtaned for ft evaluaton. For just-ft and most loose ft styles, lke most ready-to-wear top garments and trousers, accurate try-on results can be obtaned after the process of hybrd pop-up, whch provdes detaled nformaton of the clothng gap. The clothng gap nformaton s very useful for pattern alteratons and ft mprovement. Currently, the method may not handle skrts or some very loose ft styles wth a lot of drape and many rregular shapes, because the garments keep the form of the ntal mappng step. It s beleved that the current method can be used to try on skrts by computng the approxmated boundng volume of the lower body before the mappng process. Ths wll be dscussed n detal n [18]. The system currently allows mmedate vsualzaton on edtng results, so that desgners can check f the necessary clothng and textle requrements are fulflled. The rules governng style edtng can be ncorporated to the system, so that the resulted patterns automatcally fulfl the requrements and thus sutable for ndustral applcaton. More detaled dscusson s found n [18]. On the other hand, a physcal-based drape smulaton wll be ntroduced at the end of the try-on process, allowng better ft evaluaton results for more complex styles wth a lot of folds and gathers, and ths wll be tackled n the future work [18].

12 732 Y. Meng et al. / Computer-Aded Desgn 44 (2012) Fg. 16. Patterns of (a) blouse and (b) trousers. Fg. 17. (a) Mappng and (b) hybrd pop-up results of the blouse (front, sde, and back vews). Table 3 Computatonal speed of the system. Garment Number of vertces/trangles (garment) Number of vertces/trangles (human model) Number of the shortest paths n the segmentaton process Average computaton tme for each path (s) Total memory cost (MB) Smple blouse (Fg. 14) 1049/ / Standng collar blouse 2855/ / (Fg. 17) Trousers (Fg. 18) 3322/ / System confguraton: Intel Core GHz, 4 GB RAM. Tme for each teraton n pop-up stage (s) 6. Conclusons In ths paper, a novel clothng computer aded desgn soluton has been proposed for vrtual try-on, fttng evaluaton and style edtng. The system helps the fashon ndustry to speed up the clothng desgn and development process. Dfferent from tradtonal CAD approach, the proposed system frst maps the garment pattern peces on the model surface wth a novel cross parameterzaton technque. Next, a hybrd pop-up procedure, ntegratng both geometrcal reconstructon and physcal-based smulaton, s used to restore the garment to ts orgnal sze defned by the pattern peces. It vsualzes the clothng gap n the vrtual try-on results, whch provde useful nformaton for ft evaluaton. In addton, tools have been developed for users