衣服のデザイン

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Cloth

Shape

Design

b(ERO

7'ifl

y

Umberto

CUGINI

PolitecnicodiMilano

9)iA<)L

ts

ti

iy

S2"-=

RiYZNX\

This_{paperpresents}a_{physics-based}model forvirtual cloth

simulation speGifically targetedforCAD applications inthe

clothing sector,A di$crete

_{particlebased}

model inNewtonian

formulation

is

considered, inwhich _{particlegrids}definethe

fabric

structure,Grid

_particles

interactwith each other through

forces

describing

Iocaltractionand compression, bendingand

shear

_properties

dependingon thefabricmaterial, lnteractions

with thesurrounding environment are describedinterms of external forces,imposed kinematicgeometricalconstraints, and collisionswith obstacles. Collisiondetectionis

based

on bounding box hierarchiesand region

decomposition.

The

model isimplementedintheframeworkof a 3D

_graphical

en-vironment forvirtual _garment

design,

and

includes

operators

formonitoring thewhole 3D _garmentshape

definition

_process,

e.g. _panelsewing, buttonldart_insertion,mu[ti-layered fabric composition, and other _garment

finishings.

_Asapplications, male and femalecloth shapes simulated on virtual

manne-quinsareshown.

Results

have

been

assessed inthe

frame-work of Europeanand [talian

_projects

forvirtualclothdesign.

1.Introduction

Enhancements inresearch

issues

on shape modelling

have

ledtothedevelopmentof methods thatallow an

increasingly

versatile representation of

3D

complex scenes, from

genera-tionlmodificationof 2D-3D static template _geometries up

todynamic simulatjon of complex-shaped objects moving

inspace, A _particularly$trong

demand

is

addressed to

non-rigid body modelling. Shapes stop beingtime-invariant and

become _propertieschanging withtime,whose staticand

dy-namic behaviourcan berepresented, analysed and predicted,

Handlingdeformableor moving shapes becomes a strategic

capability torvisualization and simu]ation _purposes both in

computer _graphicsand computer aided designforindustrial

purposes.

Modelling

deformableshapes isrequired inmany

applica-tions.Industrialdesignand manufacturing tasksrequire,

for

instance,tomodel flexible_partsthathaveto bemoulded by

NC tools,or movedltransferred byautomated arms of

indus-trialrobots. Examplesare _packscontaining fluidsand _granular materials, sheet metals, wires and cables, and so on, An in-creasing demand of new soft modelling toolscomes alsofrom

thebio-medicalcontext fororganic tissuemanipulation, with virtualsimulation forinspection,surgicaltraining,

_laparoscopic

surgery, etc, Besides,the fieldof computer _{graphicsgreatly}

demands

shape animation tools

for

movies, cartoons, and vid-eogames.

Not

surprisingly,cloth motion has recentlybecome atopic

of

large

investigation.

Virtual

_garments

orvirtual clothdraping

effects are,infact,recurrent visualization elements neces-sary

for

computer

_graphics'

animated scenes, Beyond this,

a strong impulsecomes fromindustrialsectors, e.g,for

ap-parel

and home fabricfurniture

_production:

inthisarea, infact, modelling toolsare widely demanded toassist the_processof

clothdesignand make itfastenUntilnow, indeed,the skilled-labourdependentnature of apparel and upholstery designdid

nothave encouraged toalargeextent of automation and use

ofcomputer programs.AIthougha

_quite

well-established

tech-nology already exists inCADICAM modules for2D

_pattern

editing,nesting and NC cuttinglsewing, textilecompanies still

comp[ain about thelackof more complete clothing-oriented systems, withmodelling toolsspecializedinclothshape draft-ing/designand, _{particular]y,}virtual cloth analysis. Infact,if

such an analysis, bothat afunctionaland aesthetic level,

becomes

po$$ibleat an early stage of apparel design,this

should aliow toreduce thenumber of intermediate

_garment

prototypesand,

definitively,

save timeand cost,

Thiscommon interesttowardsclothmodelling on behalfof

both

computer graphicsresearchers and clothmanufactures

is

dictated

_by

_different

needs. The

former

need torepresent cloth

behaviour

for

visualizationand animation purposes,inwhich

results should bevisually acceptable, _{generallyperformed}with

lowcomputational cost.Atthislevel,geometricalinformation

is

sufficient,as no

importance

is

giventothephysical

reliabil-ityofresults.

On

_theother hand,clothmanufacturers demand

TTifo\mxwle

spedalissueotjapanesesocietyforthescienceofdeslgn

vol.15-4 no.60 2aOB

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11

CAD tools_providinga more accurate and realisticc[othshape

predictionforsimulation and _qualjtyevaluation tasks.

This

deeperlevelof shape representation requires a_{physics-based}

modelling approach

in

which a _physical

framework

supports the _geometricalsubstrate, and constitutive materjal _properties

are considered tocharacterize theshape

behaviour.

Section

2 _presentsa survey on some ofsuch

_geometry-

or

physics-basedmethods used forclothanimation and simulation.

Regardlessofthecontinuous or discretemathematical

rep-resentation used forcloth,what emerges from

_geometry-

or

physics-based

models

_proposed

bythescientific community, isthattheydescribecloth eitheras a _geometricalentity or a mechanical system, butvery rarely theyhandlec[oth as a "construction

process".

Thisisakeyissue,inordertomake a

cloth mode] usable forCAD applications intheclothing indus-try.Althoughwhen themodelling core isinsertedwithin graph-icaluser interfacesor advanced virtual reality environments, most of such systems donot havesufficiently complete CAD functionalities,capable todrivethe_garmentdesignand manu-facturing_processas itisconceived

by

theapparel industryfor

productiontasks.

With the intentof _gettingcloser tocloth manufacturers' needs, we here _presenta _{physics-based}model forvirtual

clothshape simulation,specifically oriented totext"eCAD

ap-plieat[ons.

Such a model hasbeen implementedwithina

sys-tem,named SoftWorld2,O,developedbytheKAEMaRT _group of UniversitbdiParma and PolitecnjcodiMilano,ltaly.

2.

CIoth

Modelling

:

State-of-the-art

Therehavebeen several attempts tomodel clothand

simu-late

its

staticand dynamic response while interactingwith an externa] environment. The most naturalapproach ishandling

fabrics

by

thesame

_{geometricaYmechanical}

standards as other highlyflexiblemateria[ sheets, such as rubber films,

pa-perlayers,etc.Accordingtohighermathematical approaches,

2D models forthin

flexible

objects can be regarded inturnas

degenerategeometriesdirectlyderivedfrom

3D

volume mod-elling.

Ibgether

withthesegeneralapproaches,

further

models

have

been

investigated,specificallyoriented tomodel the

dis-crete

fiber

structureof

fabrics.

Theoreticalstudies about cloth behaviourstarted about sixty_yearsago,

from

E:

Peirce's

first

work _published

in

1

937

[1]

tothemost _promisingmethod of modelling cloth behaviour introducedinthe

`70s

by

S.

De

Jong

and R.Postle

[2].

127ifl)#{IIKe

specialissueefjapanesesocletyferthescleneeefdesign

vol.15-4 no.60 200B

Fig.1

.

Weil'sclothmodel bycatenary curves

The researchers and work developed inthose_yearshad been mainly fundedbythetextileindustry;interestjngly,

how-ever, studies on cloth modelling have been abandoned by thetextileindustryforseveral _years.Aroundthe halfE80s,

as

suffjcientlymature computer resources begintobeavailable forcomputer _graphicsand CAD design,the _prob[emof non-rigid bodymodelling becomes aresearch subject ofincreasing

interest.Computer scientists facetheunanswered _questions

proposingcomputable models and

focusing

on

discretization

methods aspects fornumerical simulation.

Among geometry-basedrecent approaches, we

here

men-tionthe wel]-known model from

J,

Weilin1

986

[3],

based

on thedescriptionof

drapes

through suspended catenary curves

(Figure

1).Anothercontribution comes fromT,Agui:swork in '90

[4],

modelling theeffect of abended elbow. ]n'90-'92 _B.K. Hindsand J.McCartney

_[5]

realize one of thefirstCAD tools specialized forclothdesign,basedon surface modelling.

Physics-basedapproaches conceive objects intheir

two-fold_geometricaland _physicalnature. Physicsenters into

geometry through mathematical formulationsderivedfrom

dynamic laws,structuralmechanics, elasticity theories,flu[d dynamics, or other _physicalcontexts. Objectsare dealtas dynamicsystems characterized bymass _properties,with

spe-cificstructuralcharacteristicsdependingon material, They are

subjected tointernalinteractions,and interactwithan external environment throughtheactionofexternalforceslstressesand

theresponse tocollisionswith obstacles. Although

computa-tionallymore hesigent,thesemethods are themost suitable

toperformreliablecloth simulations

for

functional

evaluation

tasks,withmore accurate

_quantitative

results.The underlying mathematical models associa ±ed to

_{physics-based}

formula-tionsare

_generally

systems of ordinary and

_partial

differen-tialequations

(ODE/PDE,

Iinear

or non-linear),which Gan

be

solved byrobust and well-known numerical techniques. These

NII-Electronic Library Service

timediscretizat[onof PDE models fordynamic problems,as well as

finite

element

(FEM),

finite

difference

(FDM)

or

spec-tralmethods

_(SM)

forspace discretizationinPDE models that arise from bothstatic and dynamic

problems.

Basically,

we

distinguishtwomain different

physicsbased

approaches:

con-tinuousand discrete.

(Continuous

models) These interpretthecon$idered object

as a continuous medium subjected tothelawsof

elastic-ity.They _giveraise toa PDE model _generallysolved by FEM, which are accurate methods forsimulations occurring instatic conditions, butare computationally more expensive. The most classical of thecontinuous mode[s is_propo$ed bythe

group

of.

D.

lerzopou[os,

J.

Platt,A.H.Barrand K.Flieischerinthe years'86-'88

_[6],

_{as an extension of thestructural}

mechani-cal approach inwhich the surface deformationisdescribed

by

means of

displacement

functions

with respect to

equilib-rium

_positions.

Another

continuous model is_proposed byJ.

Eischen

in

'96

[7],

based

_{on a non-linear shell}

theory.

Figure

2

shows Eischen:s shellconfigura±iondefiningpositions¢ of

fabric

shellpointsata

distance

E

along a

direction

t,interms

of

fabric

midsurface:s reference

_points

th

.

M,

Aono'smethod in'90

[8]

_{simulates insteadtheeffectof wrinkle and}

drape

propagation,based on theelasticitytheory and D'Alembert principle,lnthiscase, theresultingPDE model

is

a modified

version of thewave equation

_propagating

in

a continuous elasticmedium. L Li,M.Damoran and R.K.

Gay

in

i93-:96

[9]

describe

themodel ofa clo±

h

immersed ina quasi-stationary viscous fluid

by

combining Navier-Stokesequations and

ler-zopoulos' continuous model.

(Discrete

models) These represent objects as discrete

systems composed of a finitenumber of simple mechanical elements interactingwith each other and with theexterior, subjected to Newton:s or Lagrange'slaws.Inthe$o-called

particle-basedmodel, inparticulactheconsMutive mechanical

elements are directly_particles,havingmass, subjected to ln-ternaland external forces

{e.g.

mass-spring models).

fypicaliy,

two main approaches are used among thediscretemode[s:

forcebasedor energy-based. Inthefirstcase, thecontribution of internaland external forcesisestimated foreach

_particle,

with successive numerical solution of thecorresponding

ODE

system, derivedfrom NewtontsIaw.Inthesecond case,

suit-able energy functionsare introduced,and theoverallsystem

dynamics isderivedfrom energy conservation lawsor

La-grangianformulations.

,L.II

r- _t

.v

Fig.2,Eischen'sshellcontiguration

nLaul

vveft

-Fig.3,Particle-basedmodel otaweven fabric

C.R.Feynman in'86

[1

O]isthefirsttouse a _{particlebased}

model torepresent thediscretemicroscopic structureof

fabric

threadswhose _yarniswoven according totheorthogonal

di-rections of weft and warp

(Figure

3).

D,E.

Breen

and

D.

House

since early ]90s

[]

l]have been investigatingindetailwhat they call the"textile

mechanism'', byuslng energy-based

par-ticlemode[s inwhich theinternalinteractionsare describedin

terms of stretchinglrepelling, bendingand trellisingenergies.X, Provotin]95-'97

[1

2]

uses a Newtonian mass-spring model inwhich theelasticforcesactnot onlyalong the weft and warp directions,butalsoalong thetwo

diagonal

directions

of

each cellinthetextile

_grid.

Sincethefirst'90s _{untilnowadays, thecontribution of}

Mi-raLab [aboratoryin

Geneve,

i.e.N.Magnenat-Thalmann, D.

Thalmann, R

Volino

et al,

[13,

141

has

been

fundamental,

lnitiallyinfluenced

by

thecontinuous lerzopoulos]approach,

successively

{and

stillnow) they havebeenworking mainly on discreteparticle-basedmodels, more efficient tostudy

non-lineardeformationsin

dynamic

cases, using non-$tructured triangularmeshes and several techniquesof collision man-agement. Besides,importantcontributions come from M.R

Gascuel-Cani,

C.

Puech,

and M.Desbrunat IMAG inGrenoble

[1

5],

working on structured thindeformablebodiessuch as

fabrics,

and more _generalmodelling aspects re[ated to

2D/3D

deformation,

Recently,

aiming at improvingthecomputational efficiency

T-tf{)-'fimvewfie

specialissueo"apaneseseeletyforthescieneeofdesign vel.15-4 no.60 20e8

NII-Electronic Mbra

13

of cloth modelling methods, new techniques

for

thetime

dis-cretizationof ODE systems for_{particlebased}

_grids

_havebeen particularlyinvestigated.

After

a largeuse ofexplicitlow-order

methods

_(e.g,

explicit EuleOinthe_{previousdecade,the}

inter-est hasbeen recently addressed towardsimplicitschemes, as

proposed

by

the_precursorwork ofA,Witkinand D,Baraffin' 98

_[1

6].Successfulcontributions intheareaof implicit meth-ods for

ODE

systems come

from

YM. Kang at al.in'OO

[1

7], and B,Ebherardt,

O.

_{Etzmuss,M.Hauth}and J,Gross

_[1

8]in' O1

.

The

latter

have

recentlyshown how discretemodels can

be derivedfromcontinuous models when applying space

dis-cretizationby FEM orFDM totheoriginal PDE _problems

[19].

Asemi-implicit BDF _{techniquehasbeen proposedthisyear}

by

K.J.

Choi

and H.S.Ko

_[20],

handling_{post-buckling}instabi[ity

and showing significantlyrealistic results of cloth draping.

The

problem

of collisionmanagement has beenconsjdered

in

some oftheabove-mentioned models, inordertotakeinto

account interactionswith external objects and self-collisions.

two

aspects are involved:collision detectionand collision re-sponse. The formecin

_particular,

_playsa significant_part

in

the totalcomputational timeof simulations, as

_proxjmity

_queries

and check$ for_possiblecollisions are required

between

_pairs ofelementary object entities

(points,

edges, triangles).

fech-niques

for

collision

detectien

optimization havebeen studied, such as voxel subdMsion, octree subdivision, bounding box hierarchy,_proximitytracking,and curvature-based methods. Detailsabout collisiondetectiontechniquescan befoundin

[13,12,14].

foconclude, hybridmodels

_propose

a compromise between

thecomputational speed ofpurely

geometric

representations with the higheraccuracy of _{physics-based}methods applied incertain object sub-regions. Among them,we mention I.J.

Rudomin's work

[21]

using

_geometrical

approximations for

modelling cloth draping,and T.L Kuni'sspring-based model

[22]

introducingmetric and curvature energies, both from

'90. _We

also mention E

laillefeurts

study about horizontaland

vertical drapes

[23],

N.

fsopelas'

_garment models builtfrom thin_pipessubjected to_gravity

_[24],

_both

_from

t91,

and S.G. Dhande'stechniquesin

'93

_[25]

_for

modeiling clothas

sweep-ingsurfaces subjected toelastic forces.Theaspirationtoreal timecloth animation hasrecently renewed _{theinteresttowards} hybridapproaches. In'O1, _M.

Oshita

etal.

[26]

model

fabrics

throughvery coarse _particiemeshes subjected _todynamic

laws,

deriving_globalcloth shape motions

by

smoothing and

14T-if{y\ffsckfig

specfalissueetjapanesesocietyferthesclefieeotdesign

ve].15-4 ne.6D 2008

(a)

(b)

Fig,4,Thread_patterns:(a)knitted;(b)woven

interpolation

techniques.A similar ideais_{proposed in}

'Ol

_by

YM.

Kang etal.

_[27]

tofastenaparticle-basedmodel via

cu-bjcsplinejnterpolationwith wrinkle _generation,and in'02 _by Rudomin

_[28]

where mesh _particlesmove accordingly tosets ofellipsoidsdefiningmannequins. Fora

detailed

overview on

physlcs-based

modelling, see

[29,

1

4,

30].

3.

The

Particle-based

Cloth

Model

3.1.

FabricProperties

Fabrics

come ina variety of types,depending on thetype of constitutivefibers,theway fibersare combjned, spun and

twistedtogetherto

_generate

threads,thetype of thread pat-tern,and thedegreeof loosenesslwidthof thread_plots.

Also

possiblechemical or mechanical treatments

_(such

as ironing,

starching, reactiontoenvironment conditions, and so on} con-tributetodjfferentbehaviouroftextiles.

It

is

clear thata _propercloth model should take into ac-count allthese factors.Fabricisnota continuous medium, as threadsare

interlaced

witheach other at afinitedistance,itis highlyflexible,and _presentsanisotropic,non-lineanyhysteretic and time

dependent

characteristics. Differentlyfrom knitted

fabrics,which _presentmore complicated threaci_patterns,

woven textilesare characterized bya regulac structured _plot composed of twosetsof_yarns,thewarp and theweft, as they are interlacedbya weaving loom

(Figure

4}.The most typical woven structure ischaracterized

by

two orthogonal weft and

warp directions.As most _garments are composed of woven

textUes,thiswiH bethestructure mainly considered inour

NII-Electronic Library Service

3.2.

Particleand lnternalForceCharacterization

lncontlnuous formulations fabricsare handled as

'

formablethinshells or _p[atebeams, according tostructural mechanics approaches

(Section

2).Though supported

by

nu-merically robust techniques such as finiteelement methods, nevertheiess, continuous models are more appropriate for

ma-terials$ubjected to

lower

deformability

and smaller

displace-ments, The

discrete

nature of woven textilesas interlaced

sets ofthreadsand the

highly

flexible

behaviour

seem, on the

contrary,tobebetter

de$cribed

interms of discrete represen-tationssuch as particle-basedmodels. Followingtheideaof

Breen,clothisinterpretedas a

"mechanism"

of discrete_parts

{point

masses, or "particles'') _{interactingwith each other and} with an external environment. DifferentlyfromBreen's

energy-basedapproach, more suitableforstaticconditions,we here use a

force-based

representation,

in

order to

include

dynamic

problems,

e.g,tovalidate the cloth model when tested on moving virtual mannequins.

Fabricsareassumed tohavea negligiblethickness, i.e.a2D topologyinwhich flatshapes arecut

from

open connected and

bounded figuresF [ R2with

_piecewise

regular

boundary

OF

(e.g.

a closed Ioopof linearorcurved edges). Similarlyto

Breen'sand Provot'smodels, thechosen

particle

mesh

as-sociated tofabric_panefisisas±ructured

2D

gridwhose

coor-dinatelinesare definedfromwarp and weft directions.

Interior

particlescorrespond to_gridnodes, locatedat warplweft

threadintersections,while

boundary

particlesare

defined

from

intersectionof

_grid

lineswiththe

fabric

borden

Ttiangular

ele-ments are

derived

from

originalrectangu[ar cells byadding diagonals,according toFigure5.

Panel"sgridtopology characterizes the internaldiscrete forcedistribution,

defined

bylinearor torsionalsprings

com-putedfromjnteFparticleconnections. lakingintoaccount the

woven structure ofthreads,

forces

have

been classified into threemain ca±egories

(Figure

5):

-

stretch[nglrepelling

forces,

acting

to

keep particlesat rest

distance

(modelled

as Kelvinvisco-elastic springs directed

along weftand warp) ;

-

bending

forces,acting out-of-plane tokeep objects flat

(derived

by

torsionalmoments normal totheirsupport

tace)l

-

trelfising

_(or

sheari forces,acting tocontrast any _possible

deformationof therectangular ce[ls

_(modelled

again through

torsionalmoments normal tothecells).

Fig.5.Particlegridassociated totabric_panelswith lnternaltorce characterization

The values ofIocalspring, bendingand trellisingconstant$ associated toany

group

oftwo,three,orfour_particleshave

been derivedfrom_globalmechanical dataestimated bythe

Kawabata EvaluationSystem

(KES).

Thisisa well-known sys-tem measuring structural

propedies

of

fabrics

depending

on the type

_[31].

Itowes itsformulationto

S.

Kawabata

in1975,

and isbased on experimental stress and

deformation

tests

performedon rectanguiar fabricsamples with fixed

dimen-sions. Theseare

(gf'=

_gram-force):

1

)

geometryand mass tests,tomeasure thethickness

[mm]

of the sample at _pressureO.5_gf7cm!,and itsmass density

[nag/cmL'];

2) tensHetests,tomeasure thelinearity

[-],

expressed as average _percentageofelongation

in

thesample, its

mation energy

_[

_gf･cm/cm2

]

and tensileresilience

[%];

3) compression test$,measuring the

linearity

[-],

or average

percentage

of shortening inthe sample, itsdeformation energy

[

_gf-cm/cm2

]

and compression resHience

[%l

;

4) bendingtests,which measure thebendingrigidity

[gye･cm2/

cm

]

and itshysteresis

[

gt'･cmi/cm

];

5

)

shear tests,which measure the shear stiffness

[

_gflttm

greel]andtheshear

hysteresis

at O.5eand 5"respectively

[gLlcm];

6) superficial

_property

tests,to measure theaverage friction

coefficlent

[-],

the

corresponding standard deviation

[-]

and the superficial rugosity

[um].

Other

systems exist, measuring similar structural

fabric

propertieswith differentunit measures

(e.g,

EASZ or UNI-ISO

standard$}, Tnyifiy#ffxksee specialissueofjapanesesocietyforthescieneeofdesign vol,15-4 no,60 200S NII-Electronic Mbrar

15

3.3.

From

FabricstoGarment Models

Garment

shape isthecomplex result ofassembled compo-nents, Basically,itlstheresult ofone- or multHayered fabric

assembly, withfurtherfunctionaland aestheticfinishings.

Re-sortingtoa continuous _geometricalrepresentation, a full

gar-ment shape can

be

formally

approximated as anon-manifold

entity

G=,.L.

!..,F"U,.Y.,,"i'

(])

where Fl･are

fabric

layers

(whose

supports are 2D manifolds inR3)representing _thedeformedspatialconfiguratjon of

origi-nal fabric_panelsF,g RU,fori=1,2,..., nF, and A, are

domains

inR3 forrjgid orsoftaccessorjes, fori=1_,2,,.., ,z,.

When

exist-ing,the

_latter

aregenerallyfewsmall entities, such as

buttons,

hooks,zips,paddings,etc. FabricIayersare sewed witheach

other along

_portions

of theirboundary,or can

be

_partiallyor

totally

attached

in

interiorsub-regions with o±

her

layers

(as

it

occurs _inmultj-layeredfabricfor

_jacket

creation,

by

using

lin-ings,

strengthening adhesives, etc).

Under

these

premjses,

after_particlegrid

discretization

of singlefabriclayers,furthersteps have to

be

considered, to

generate

a complete _{particle-based}model

for

a

full

_garment

shape:a)

sewing of

fabric

panels;

b)dartinsertion; c) fabric

layer

overlapping ;

d)buttoninsertion;

e} _placementofthe

full

garmentmodel ina 3D space ration

{e.g.

on a mannequin).

Algorithm

(a)

dealswith

2D

panelsthathavetobe sewed togetheralong assigned borders,

Tb

_performaseam between existing _{grids,particles}coming fromthetwo

_panels,

located

along each sewing edge, need tobe _properlymerged along theborders.Suppose apanelA _hastobesewed with a _panel B,Foreach $ewing edge,

let

n

be

thenumber of original par-ticlesof theedge inA and m thenumber of originai_particles ofthecorresponding edge inB.

_If

n<m, m-n paniclesare added to

_panel

A bylocatingthem inintermediate

_positions

(analo-gous[y,

intheother case). When n=m, each i-th_particleofA is

merged withthecorresponding i-th_particleofB,_fori=1_,2,...,n,

by

moving

_particle

_pairstoan intermedjate_position,nparticles belongingtoone otthetwo

border

edges are thenremoved,

Correspondingly,mesh topology around each sewed edge is

updated. Internaledges are displaced,and new

internal

edges,

16ftfly#MzakKe

speciaHssueofjapamesesocietyferthes'elenceofdesign

voL15-4 ne.60 200B

edge eiA edge eie

Fig.6.Sewingprocessbetween twofabric_panels /

(1)

$eam definition

as correspondance 1to1between vertices ofpanelborders;

(2)

detaiiofthesewing _processover asingle edge pajnDashed

lines$how theoriginal_particlegridbeforebeingmodified bythe

sewlng process.

forceljnksand trianglesaround added

_particles

areadded

(case

nt m). Internaledges,

force

links

and triangiesaround removed

particles

are removed. Figure

6

shows a sewing _process

be-tween two _{particie-based}models offabric

_panels.

Case

(b}

issimilar to

_(a}

becau$e _dartscan beregarded as

specialseams along a fixedsequence ofedges, inwhich

pan-eiB iscoincident with _panelrf,

_ln

other words, one

(or

more)

vertice(s)is

_(are)

sewed with another

(otheO

vertice(s)

belong-ing

toboundatyloopsof thesame panel.

Case

(c)

models thepossib[epresenceof several fabric

layers

thatmay have tobe_placedon

top

ofeach other,

This

isuseful incase of

_possible

_paddings,linings,etc

(e.g.,

_to

strengthen

jackets).

The ideaisto change physics-based properties

(masses,

springs, bendingand trellisingforces}

in-sidea

fabric

region,substitutjng them with _propervalues that includealleffectsofsingleadded layersthroughtheeffectofa unique equivalentmaterial.

Ca$e

{d)

includestheeffect of buttonswhen two panelsto beconnected are sufficientlyclose toeach other. Each virtual button

is

simulated

by

connecting thetwo _gridpointsclosest

totherequired

button

_positjon,

imposingsignificantly hard spring forceeffectsand mass

jncrement.

Final[y,step e)

defines

the3D configuration of the as-sembled cloth]s _partjclegridafterdefinitionof mannequins or

other rigid objects inthe scene and specificationof mapping laws2D

-,3D.

NII-Electronic Library Service

4.

DynamicSimulation

4.1.

Newtonian

Constrained

Dynamics

Thecomplete

_{particle-based}

model ofa

_garment

is

defined

byasystem S=

{P,

:i= 1_,,,, IV}ofIV

_particles,

each

character-izedbymass m,,

position

r,, velocityy,

=r,

and accelerationa-

--r,, fori=1 _,2,..,IVLParticles'configurationatan initialtime4,is definedbyknown

_positions

{r.}

and velocities

{v,,},

for

i=1,.,, N. Tb

_pertorm

a dynamic analysis of

_garment

movements in

space, we consider Newton's lawsfor_particlesystems,

The

analysis iscarried out intheframeworkofconstrained dynam-ics,totakeintoaccount the_possibleexistence of imposed

constraints,i.e.specific

_geometric

and klnematicconditions

thatobjects must respect.

The dynamic behaviourof thesystem isthusobtained as solution ofthetollowingNewton's_problem

Vi

--

1,2,..,N

,･

ri<to)=rio

(2)

Vi(to)= Vio miii = Fi

(ri

,..rrv

,"i ,..iN

,t)

where

E.

= FiCi"`}+F}(ext)

(3}

is

thetotal

force

actingon thei-th_particle,sum of aH internal

and externalcontributions.Eq.

{2)-{3}

isaCauchy _problemfor

asystem of3N ordinary

differential

equations ofsecond order,

equivalent toa system of 6Nequations of firstorder, Solutions are trajectories

{

r,(t)

},

as well as velocities

{

v,(t)

},

forany par-ticlei= 1,2,,.,ACfortE[4, T].

The motion of thesystem isuniquely determinedunder

hy-potheses

of sufficientlyregulardataF,as functionsof

_particle

positions,velocities and time,allinfactsatisfied inour linear forceestimation method

[32].

The firstaddend inEq.

(3),

in fact,iscomputed from

FiCust).FiCsiretcit)+FJrep}+FiCbe,td)+Fi{shettr),

(4)

where

E("'e`'h)

and

ECmp)

aretheresultantstretching and

repel-lingforcesacting on

_particle

i,F,U'""di_{istheresultantbending}

force

on i,and Fi('Se"Dtheshearing

force

on i.

The

approxima-tionmethod forinternalforcecomputation depends,evidently, on thechosen particlediscretizationcriterion

($ection

3.2).

Thesecond term is

_given

_by

E{ext}=E(a)

÷IilC'},

(5)

where F,C")isthe sum of active external forceson i,due to

gravity,wind, viscosity, orimposed constant stresses, and

F,(")thesum of allreactive forcescompensating

possible

con-straints imposed on i,Among theseveral methods for con-straintmanagement

(e,g.,

penaitymethod, Lagrange

multipli-ers, rate-controlled constraints, and dynamic constraints

_[33,

34,

35]),

the dynamicconstraint method hasbeenhere

imple-mented, since

it

permitstoapply multiple constraints tothe

same

_particle

and ensures the respect of alltheconstraints at

each time$tep ofthesimulation,

We

hererefer toequality

(or

bilateral)constraints,i.e.havingthe _generaiform

C(rl,.,rA7,fr,,,.tN,t)=

±

O,

_{6)

beingC a known sufficientlyregularscalaror vector function. Differently

from

themost

_general

rheonomous constraints,

scleronomous constraints do not

depend

explicitelyon time.

Inour model we have imposed,

for

instance,

constraints such

as fixed

positions,

constant distancesbetween

_points,

area or

volume conservation, as well as

fixed

trajectories

for

pointsor

particles.

lermsF,`",tobeincludedintheRHS ofEq,

(2)

for each _particleiinvolvedinsome constraint,are

derived

from

soiutionofacertainlinearalgebraicsystem

[32].

The solution of Eq.

(2)

can benumerically estimated by

us-ing_properexplicitiimp[icit timediscretizationschemes on a

discretesequence to,ti,.., t.oftimesteps.1nour case, a mod-ifiedtwo-stepsEulerscheme hasbeen utilized

[I2],

in

which particles'positionsat k-thtimesteparederivedfromvelocities

already updated atk-thtimestep and corrected with

post-collisionresponse. The modified Euler'smethod turns out to

bestabler thanexplicit

Euler's

and remains computationally cheap, Tbincreasethespeed ofconvergence and manage stiff

equations, however,higher-orderimplicitor semiimplicit time

discretizationschemes are currently under implementationfor thefutureversion ofour

ODE

solver,according to ideas

sug-gested

by

[1

6,

l7,

18,

20].

4.2.

Collision

Management

fo

complete theanalysis of interactlonwith the surround-ingenvironment also theeffect of _possiblecolfiisions with

ob-stacles

has

to

be

taken intoaccount. Co]iisionsoccur, for

in-stance, when _partsofflexibleobjects

(e,g.,

_garments)hitsome

rigidobjects

{e.g,,

mannequins) or _penetratetowards each other

{selfcollisions).

InFigure7,forinstance,collision effects were dominantinsimulating cloth _positioningon a tableor a

sphere, orclothfallon thefloor.

The two aspects of coliision detectionand response are

.-ift)\ffsckese

specialissueofjapamesesocletyforthescieneeofdesign

vol,15-4 mo.60 2eOSNII-Electronic

Mbra

17

Fig.7.Simulationoffabricson rigjdobjects :

(1)

tableclothon atable;

(2)

carpet on asphere ;(3)tableclothfallingon the tloor;

(4)

ribbontallingonthefloor,

analysed jnseparate algorithms. Ateach timestep, _possible

collisionsagainst rigidobjects

{e.g.

_garmentson mannequin$,

fabricson rigidframes)or other soft_parts

(self-collisions)

are

detected,

by

doing

a locaisearch on elementary _grid enti-ties

(points

or

_particles,

edges, triangles).Then,velocities are modified onlyforcoHiding _particles.

From a computational _pointof view, collisjon detection constitutes _{thebottleneck}of simulations, as checks haveto

be

done

in

a

Iarge

numbe4 between _pairsof elementary

enti-ties.Among optimization techniques

_proposed

inSection2, aligned axjs

bounding

box

(AABB)

hierarchieshavebeen here adopted, as a _good compromise between simplicityand

ef-ficiency.

Accordingtothistechnique, objects are

_grouped

hierarchi-caily ciependingon _proximityrules,and thedetec±ioniscarried

out byexploring bounding

box

intersect[ons_{inthehierarchy,} Furthermore,since _garmentfabricscould self-collide,objects

have been split intosub-regions, each

in

turnassociated to an AABB, Otheroptimization _techniquesare currentlyunder

implementationforfutureversions of our model.

When

two

sub-regions are foundtobe intersecting,i.e.candidate for

col-lision,checks are finally

detailed

at

the

Ievel

ofgridelementary entities.Collisionsare detectedwhen _particlesor

_points

are near asurface or edges are clese tootheredges

(i.e.

their dis-tanceisIessthana thresholdvalue},

lnthecollision response _phase,the velocities ofthe

par-ticlesbelongingtocolliding entities are modified _toavoid compenetration. The new velocity vectors are computed

de-18THvrf

v#diveksce

specialissueofiapanesesecietyforthescienceofdesign

vol.15-4 no.60 2eOS

pending

on thecoefficjent of restitution, byimposingthe con-servationoflinearmomentum. AIIcollisions together _giveraise

toa ljnearsystem

{usually

verysparse) whose $olution

_gives

thevelocity variations to beapplied tothe model.

More precisely,lett=

(

r,, r, _{,.., h,)}

be

thesystem

configura-tionat a certain time step, and sbethenumber ofcollisions

detected,havingtheformof unsatisfiedscalarunilateral con-straints

d,(r,t)<O, i=I,2,".s.

(7)

WedefineD(r,t)=(4{gt},.,,4(gt})and

an(r,t)

J:=

o,'

{8)

the sx31V

-sized

Jacobian

matrjxof D with respect tor.First,

we impose theconservation oflinearmomentum. Defining

Av asthe

3N

-sized

vectorofvelocity variations, M as the31Vx 3N

diagonal

matrix whose elements are _particlemasses

(3

vaiues foreach _partjcle),andJ' as thetrasposeof

J,

we can

thus

impose

M･Av+J{A=O,

(9)

where A isas

-sized

auxiliaryvector definedas

A=-F,

{10)

beingI"the

(unknown)

vector ofsLagrangemultipljers as$oci-ated tothe constraints

(7),

The

first

termin

(9}

isthe momen-tum of the_particles.Inthesecond term,matrix

_J'

describes how thevelocity variations must

be

distributedamong the threevelocity components of each colliding_particle.Inother

words,

J'

describes

both

the

direction

ofvelocityvariation vec-torsand the _{proportionality}among thejrmoduli. Ifa

_particle

is not involvedinany collisionthere

is

no velocityvariationand

we can imposedirectly

M･Ay=O.

(ll)

Each collision invoivinga _particley'adds a contribution

_IA,,

which impliesavariation ofthelinearmomentum.

Furthe4we havetoimposetheamount ofvelocityvariation,

dependingon theelasticityof thecol[idingobjects.

A

constraint violationmeans thatD

_{g

₄

changes froma _posjtiveor zero va[ue toanegative value, thereforeD

(;

4

must benegative.

fo

pushthesystem toan acceptable state we must vary D

(g

4

in

such away thatD

_tr,

₄

results _positiveor zero. Thus,ifEi$the

NII-Electronic Library Service

AD(r,t)=-(1+s)D(r,t).

₍₁

2)

SubstitutingAD

_(g

₄

=J･Av, we obtain

J･Ay=-(1+a)D(r,t).

(13)

Eqs.

_(9)-(1

1}

and

(1

3)

constitutea non-singular

linear

system with3N+ sequations and 3AJ+sunknowns, i.e.

[Y

el

l"AY]=:[-a+e9･D(r,t>]'

(1

4) whose solution

{e,g,

bya conjugate _gradientmethod) returns

thevelocity variations thatavoid compenetration. Pre-collision velocity _y

{

4

}

foreach _particleJ'involvedincollisions during thetimestep ₄can befinallycorrected with the_{post-collision} velocity _y･

(

tn

)

+ Ay･

A _particularsituation fora collis]onsolver arises when there isacontinued contact

(e.g.,

a cloth resting on a rigid object) :

our sy$tem has

been

tested

alsoforthesecase$ with a _good response bothin_precisionand stability.

Generally,

thesimulationstep

is

so smallthatitisnot neces-sary tosearch fornew col]isions at each time step. Duringthe

ODE

step,the veiocity ofthe fa$test_particleiscomputed. In

the worst case, this_particleisclose tocollision with atriangle, the

_distance

_between

_thetwo

_being

onlya littlelargerthan

thethresholdvalue, say

6.

By

computing thetime4needed

forthis_particletocover halfofO,we can

be

surethatno un-detectedcollisions willleadtoa _penetrationinthenext ₄ sec-onds. Itis_possibletomake a more conservative computation of t.,basedon a _quarteror lessof dor tobemore aggressive using biggerfractions.Accordingtothisideaithasbeen pos-sible toreduce thecomputational timeforcollision detection.

5.

Implementation lssues

The

_{particle-based}

model describedinSections3 and 4 hasbeenimplementedina system named Softworld2.0,

run-ning on Windows, Unix/Linux,SGI-IRIX_platforms.Thesystem iscomposed oftwo fundamentalmodules :

･

_2D13D

_{Modeller,creating the}

_{particle-based}

_model

associ-ated to3D

_garment

models ;

-

_3D

_Simulator,

_genera

_±

_ing

_simulation

_frames

_at

_discrete

_time

steps4,ti,..,t.,

The

system

is

_providedwith a

Graphical

User

lnterface

to

create a unique environment

from

which

both

the Modeller

and the

Simulator

are executed. Figure

8

displaystheoverali

Fig.8.lable,1Ba$icSoftworld:sarchitecture

,

Datastructure ofthe2D13DModeller

lable.2.Mainalgorithm ofthe3D Simulator

Softworld

architecture,

lable

1

displays

inputand output data

ofthe

2D/3D

Modellec

while

lable

2describesthemain algo-rithm inthe3D

Simulator.

Paretleiversion.

Some

_partsof thesimuiation algorithm al-[owdatato besplitintoindependentsets, suitable for_parallel processing.Beowulfclusters, networks ot workstations using

rifify#ffxtsseg

speclalissueefjapanesesocietytorthescienceotdesign

val.15-4 ne.60 2e08

NII-ElectronicMbra

19

MPI

libraries,

have

been used with thatintent.Ibdecreasethe

computational _time,in

_particulany

_thecollision

detection

algo-rithmhas been

_{parallelized.}

The approach basedon

bounding

box hierarchywith sub-region subdivision,

in

fact,

allows man-agement ofeach region as an independentdata$et.

When two regions are checked to

find

co[lisionstheir

data

are sent toa separate _processorthat

_performs

thecheck,

Each _processorcan work

in

_parallelusing only itslocaldata and itsresults

(a

listof

data

representing detectedcollisions) can beeasily merged withtheones fromother_processors.

6.

Applications

Several

tests

have

been

done

toeva[uate Softworld2.0,

Fjgure7 already showed

frames

of simulated fabricsfalling

overrigidobjects such as atable,a sphere, or thefloor. Actu-ally,forour

design

intents,theseexamples arenot so

signffi-cant because theyhand[esimp[e-shaped one-layered fabric

wjthout any ofthosedesigncomplexities

(seams,

complex

borders,

djfferentmaterials,etc,)encountered while designing

and manufacturing real cloth. Forour _purposes,testson

com-plete

garment

shapes havebeen more interesting,

The

next

Sections

show how thesystem hasbeenapplied in

the design _processofmen's and women]s _garments.Results have

been

obtained

in

thecontext of Europeanand ltalian re-search _projects,incooperation with industrial

_partners

from

the clothing industry.Althoughbasedon thesame modelling and simulation algorithms, the two ways of _proceedingwhile definingma[e and

female

clothshavebeendifferent,

6.1.

Women

Cloth

Design

Theactivity on women _garmentdesignhasbeencarriedout

byKAEMaRT _group

in

the

framework

of

MASCOT

Brjte-Euram

Project.Here,we havestarted from

3D

dressmodels, directly chosen froma libraryof templatecloth shapes

(skirt,

blouse,

etc.), thatare modified by3D surface model[ing toolsbased

on NURBS representation, acting on characteristic lines.

Seams, _pences,and other textilecharacterizatjons aredefined on the3D model, fromwhich 2D _panelsare extracted with allnecessary intormation

_(e,g.,

sewing lines)necessary tothe

simulator fortheircorrect locationon virtual mannequins,

The modelling algorithm _generatesthe_{padicle-basedgrid}

of each 2D

_panel

composing the cloth, associating _proper KES datacorresponding tothechosen fabricmateriai, By

us-inginformation

_provided

bythemodeller, 2D _panelsare semted

and located

_properly

on themannequin forthe finalsimulation

207ifl)\Mvek#g

speclalissueofjapenesesocietyforthesclemceotdesign

vol.15-4 no.60 200S

Fig,9,Particle-basedmodels otwomenis garments placedon

quinsbeforesimulation

Fig,1O,Simulationof women's _garments:initialconfiguration and simulated resultofaskirtand tunic

of itsbehaviourinstatic conditions

[36].

Here,

_themodelling and sjmu[ation algorithms developedbyKAEMaRT _group

have

been accompanied by a CAD intenfacefor

3D

_geometrical

modeiling,

_provided

bytheUniversityofValenciennes.

In

Fig-ure 9,we display_{particle-based}modeis of a skirt, atop and

a woman's dressbeforesimulation. Figure1O _presentsthe simulated resultsofaskirtand a linentunic.Detailsabout the modelling and simulation _phases,results on testmodels, and

a

_performance

analysisarereported in

_[37].

6.2.

Men

Cloth

Design

laskstormen's

_garment

designhave been developed in

the

framework

oftheNationai

_project

IA2000

_[38],

Differently

fromfemale

fashion,

the

_production

of men:s

_garments

NII-Electronic Library Service

thatonly slightlydifferfromone season and theother,Here, therefore,we havechosen towork bymodification of existing appare[articles.

The

3D

modeller has been implemented byu$ing Maya

Deformers(htrp:/C'tvww.afiaswavof-ont.comfezarebroductimaya/1'ndex. shtm4. An interface

{modification

module) iscreated inMayats

owner languageallowing interactivemodification of sizes in

jacket

parts

(sleeves,

shoulders, breast,waist, etc.}, with free form deformation

driven

by

characteri$tic lines.An export

module automatically _generatesafifieinCEX

{Cloth

EXchange} format,containing informationabout themodified 3D mode[, tobeused as inputfor2D _pane]extraction. Generationof 2D panelsisdone bymeans of an owner textile

_CAD

software used at Cornelianiclothing industry.A _program,called cexlblV

creates the IVformats

for

the

3D

clothmodel and its

2D

pan-els.

Softworld's

modeller

_generates

_{theparticie-based}

_grids

of

thepanels,thenassembled togetheron thevirtualmannequin thanks ±othe

_2D13D

mapping rulesstored

from

the

3D

mod-eller.

Once

theparticle-basedmodel

has

been

created

in

3D,

simulationcan

be

performed.

Figure

1

1

displays

themain modelling $±eps. Figure12 shows several

_points

ofview ofthe simulated effect of the

jacket

leaned

on the

bust

ofa mannequin

in

staticconditions,

The man

_jacket

example was computationally expensive, due toa fine

_particle

discretization

necessary

for

_guaranteeing

good

accuracy foracomplex model composed ofatleast12

panels.Detailsabout the

jacket

model and simulationresu[ts,

as well as _performance

(for

bothserial and _parallelSoftworld:s versions), can be read again in

[37],

Parallelsimulations have been executed on thecluster Feronia,40 APIbi-processor nodes, locatedatEnea-Casaccia,Rome.

7.

Conclusions

and FutureWork

Physics-basedmodels show their_potentialinrealistically

simulating cloth shapes, as the _geometricalsubstrate is en-riched with informationderivedfromstructural fabric proper-tiesand

dynamic

laws.

In

thiswork,

the

physics-basedcloth shape simulation is

derived

from a discrete_{particle-based}

approach, with

dynamic

analysisexpressed

by

Newton]s

law,

Fig.11.Virtuaidesignofmale _garments.Main modelling steps :

(1)

Smoothed geometricalmodel fromdigitalizationofareal

et,

{2)

ModMcation module.

(3)

Extractionof2D _patterns,

₍₄₎

Particlebasedmodel ofeach _panel,

(5)

Panelassembly with

finalparticle-basedmodel readytor 3D simulation.

Fig.12.Some views otasimulated _jacket

7on)7Mverekg specialissueo"apanesesocietyforthescienceofdesigm vol.15-4 no.60 200S NII-Electronic Mbra

21

y

involving

internal

and external forcecomputation, constraint management and collisiondetectionand response. The

sys-tem includesspecificalgorithms fortextileoperations such as

sewing, buttonand dartinsertion,etc. and has

been

included

inCAD environments forcloth design,Applicationsand

ex-amples on simulated testcases were shown formen:s and

women's _garmentdesign.

Modellingand simu[ation module$ of

Softworld

have been

assessed byend-users _{participating}to European _projects,

in-volving bothacademic and jndus±rial_partners,The modelling

module has

been

evaluated _positively

by

end-users,

because

itdoes not require specific

knowledge

on

_geometric

model-lingor _professionalskillson apparel

design,

On

theother

hand,simulation re$ults arereliable.A significantaccuracy is reached forsimple- or complexshaped

fabric

models, when designedthrough simple seams, one-layered fabric,e.g.for

tunics and nonaccessoried _garments composed of Iight fab-ric. Models such as male

_jackets

_providegood simulation

results as well,although theseturnout tobe computation-al[ymore

hesigent,

due the

_presence

of multi-layered fabrics,

abundance ofseams between constitutive

_panels,

and use of

heaviermaterials.

New featureswillbe added, to expand thesystem

capabili-tiesforvirtual cloth

design

and _generateshapes thatare

clos-er totheones conceived by stylists.These are,

for

instance, parametricsewing algorithms _givingspecial aesthetic effects

(collars,

puffedsleves, closefitting sewings,

jacket

rollers, etc,),

multi-layered fabricmodelling

(such

as liningsand _paddings), ormodelljng effects

due

to

manufacturing _proces$es,e.g.,

producingpermanent deformations

(as

jtoccurs

by

ironing,

starching, etc.), Alltheseissuescorrespond to_geometrical tricksapplied on associated _particlemeshes.

The most critical issueisthecalcu]ation time,_particulariy duetothecollisiondetection_phase,as _possiblecollisions at

each timestep are searched among _pairsof elementary

enti-ties

_{particies

or

_points,

edges and triangles).New optimization techniquescan beintroducedtoreduce the number of

neces-sarychecks. Higher-orderimplicitand semi-implicitODE

solv-ersfortheassocia ±e Newtonian _problem and adaptive time

discretization

criteriaare also currentiy under development toreduce thecomputational time.Besides,furthereffortsare

under way

for

parallel

implementation

ofthecollision detection phase,and othersimulationmodules.

Many

questionsstillremain open.

Cloth

modelling is

some-22T-if{>\ffftksug

speclaiissueetjapamesesecietyforthescienceotdesign

vei.15-4 no.60 200e

how a challenge forcomputer graphic$community. At

pres-ent,our _group

is

working on thesemodelling issues:

-

geometrical

modelling aspects

(e.g.,

grid

generation

for

complex-shaped objects,

_grid

assembly, 2D-3D

ping)i

-

materialmechanjcs issues

(e.g,,

fabricmaterial _properties,

extension of KES data,otherfabricmeasure systems);

-

specifictextileoperators

(e,g.,

sewing, multi-layered

rics,small accessory insertion,manufacturing _processes),

Concerningthe3D Simulator,arguments come from:

-

_dynamic analysis _problems

(such

as internalforce

tationand collision detectionand response);

-

numerical aspeots

{e.g.,

stabi[ity and convergence of

ODE

solvers,ill-conditioningof algebraic solvers}.

Despitetheseopen issues,simulation results obtained on complete _garmentshapes are realistic and encouraging.

They

pointout _{potentialities}of _{physics-based}approaches in

model-linga complex matter such as cloth,

for

CAD

applications

in

clothing, home fabricfurnitureand upholstety

industry,

Acknowledgements

Thiswork has

been

carried out intheframework ofthe

Brite-EuramProjectMASCOZ fundedbythe European

com-mission, and theItalianProjectIA2000, fundedbyMIUR.The

authors are

_gratefui

toDrs.A.Galimbertiand

G.

Frugoli,

for

contributions with implementationcode, and students from theDjpartimentodilngegnerialndustriale,Universita

di

Parma,

developingtheGUIinterface.

References

1

ET.

Peirce,"The

geometry

ofclo±hstructure",Journalof

fextile

lnstitute,

Vol.28,]937,

pp.45-97.

2

S.

De

Jong

and R.Postle,"An _{energy analysis of} woven

fabric

mechanics by means of optimal control theory.

Parts1and ll",Journalof lextilelnsMute,Vol.68,1977,

pp.350-369.

3

J,

Weil,

"The _{synthesis of}

_Cloth

_Objects",

_Computer

Graphics

(Proc.

SIGGRAPH

'86),

Vdl.20(4},1986,

54.4

T Agui,Y Nagao and M.Nakajma,

"An

Expression

od of Cy[indrical

Cloth

Objects-An

Expression

of

Folds

of

a Sleeveusing Computer Graphics",frans,

Soc.

of

NII-Electronic Library Service

1990,

pp,1

095-1097,

5 B.K.Hinds,J.McCartney and

G.

Woods,

"Pattern

velopment for3D surfaces",

Computer

Aided

Design,

Vol,23(8},1991,

pp.583-592.

6 D.ferzopoulos,J.Platt,A.Barrand K.Fleischer,

cally Deformable Models",

Computer

Graphics

(Proc.

SIGGRAPH ･87}, _Vol,21

{4),

1

987,

_pp,205-21

4.

7 J.W.Eischen,S,Deng,and 11G.Clapp,"Finite _Element

Modelingand Controlof FIexibleFabricParts",Computer

Graphicsinlextilesand Apparel,IEEEComputer

ics,Vol.l6(5),l996, pp,71

-80.

8 M.Aono,'`A _{WrinklePropagationModel forCloth",Proc.}

Computer

Graphicslnternational,1990, pp.95-105.

9 L.Li,M. Damoran and R,K.Gay, [`Aerodynamic _force

models foranimating cloth motion inairflow'',The Visual

Computer,

Vol.12,

1

996,

pp.84-104.

1

O

C,R.

Feynman,

"Modelling

theAppearanceof Cloth",MSc

thesis,

Dept,

of

Electrical

Engineeringand Computer

ence, Massachussetts]n$tituteoffechnology,US,1986,

11

D.H.

House

and

D,E.

Breen,

"Representation

of Woven

Fabrics",

SIGGRAPH

"98

Course

Notes,N.31,l998. I2 ×

,

Provot,"CoHision _{and self-collision}handlingin_cloth

model dedicatedto

design

garments",Proc.Graphics

terface'97,1997,pp.177-189,

13

R Volinoand N,

Magnenat

Thalmann,

"CoHislon _and

Co[lisionDetectlon:Robustand

Efficient

fechniques

for

Highly

Deformable

Surfacesi',

EurographicsWorkshop on

Animationand Simulation,1995.

14 R Volinoand N,Magnenat-Thalmann, "Virtual _Clothing,

Theoryand Practise",Springer-Verlag,Heidelberg,

many, 2000.

15 M.Desbrun,R Schroederand A.H.Barr,`tlnteractive

mation of structured deformableobjects", Graphicsjntee

face,1999,pp.1-8.

16 D.Baraffand A.Witkin,"Large _{Steps inCloth} tion",Computer Graphics

{Proc.

SIGGRAPH '98), 1998,

pp,43-54.

I7 M Kang,J.Choiand C.RH.Cho,"Fast _{and stable} tionof cloth with an approximated implicitmethod:',

Proc.

Computer Graphicslnternational

(CGI

'OO),

2000.

18 M.Hauthand O.EtzmuB,"A _{HighPerformance}

Solver

for

theAnimationof Deformable

Objects

using

Advanced

merical Methods",Proc,Eurographics

'Ol

, 200I

.

19 O.EtzmuB,J.Grossand W.

StraBer,

`'Deriving

a Particle

System

from

Continuum

Mechanics

fortheAnimationof

DeformableObjects",IEEE

fransactions

on Visualization

and Computer Graphics,

2002.

20 K-J.Choiand H-S. Ko,"Stable

but

ResponsiveC)oth",

Computer Graphics

(Proc,

SIGGRAPH

:02),

2002,

21 l.J.Rudomin, "Simulating _{clothusing a mixed}

physicalmethod", Ph.DThesis,Dept.of

Computer

ence, Universityof Pennsylvania,US,

1990,

22 T.L Kuniiand H,Godota, "Modelling _{and animation of} garment wrinkle formation_processes",Proc.

Computer

Animation,

Springer-Verlag,

Berlin,1990,

pp,1

31

-1

47,

23

F.Taiilefer,

"Mixed

modeling", Proc.Compugraphics,

1991,pp.467-478.

24

N.isopelas,

"Animating

thecrump[ing behaviourof

ments'',

Proc,

2nd

Eurographics

Workshop on Animation

and

Simulation,

Blackwekk

UK, 1991 , pp.11

-24.

25 S.G,Dhande, RNLM, Rao,

S.

lavakkoiiand C.L Moore.,

"Geometric _{modeling of}drapedfabric_surface", Proc.IFIP

lnt.ConferenceOn Computer

Graphics,

North-Ho]land, Amsterdam, 1993, pp.349-356.

26 M.Oshitaand A.Makinouchi,

"Real-Time

Cloth

tionmtithSparseParticles",

SIGGRAPH

:Ol

Sketches

And

Applications,2001.

27 Y,M. Kang,J.H.

Choi,

H.

G,

Cho

and

D.H.

Lee,"An

ficientanimation ofwrinkled clothwith approximate

plicitintegration",The VisualComputer,Vol.17(3),2001, pp,147-157,

28 1.J,Rudomin and J.

Castilio,

"Real-Time

Clothing: etry and Physics",

WSCG

Posters

'02, _2002.

29 Eds.IEEE

Computer

Graphicsand Applications,special

issueon

Computer

_graphicsinfextilesand Apparel,IEEE Computer

Graphics,

Vbl.16(5),1996,

30

Eds.

D,H,

House

and D.E.Breen,"Cloth

modelling and

Animationi',

A KPetersLtd.,Natick,MA

(US),

2000.

31 S.Kawabata,

``The

Standardizationand Analysisof Hand

Eva[uation"',ThefextileMachinerySocietyofJapan,

ka,

1980,

32

G.

Frugoli,

A.

Galimberti,

C,Rizziand M.Bordegoni,

crete element approach fornon-rigid materlal modelling",

Robot

Manipulationof DeformableObjects,Eds.

D,

rich &H,Worn,Advanced ManufacturingSeries,Springer,

2000, pp.29-42.

33 K.Fleisher,A.Witkinand A.Barr,"Energy _constraints on _parametrizedmodeis",

Computer

Graphics,

Vo[.21

,

7if{y#anvekEt

specialissueetjapanesesocietyferthescienceatdesign vel.15-4 no.60 2008

NII-Electronic Mbrar

l987,

pp.225-232.

34

J.Plattand A.H. Barr,"Constraint

Methods

for

ible

Models",

Computer

Graphjcs,

Vol,22(4),1988,

pp.279-288.

35

A.Witkin,"lnteractive

Dynamic$",

Computer Graphics,

Voi.24,Proc.

Symposium

on

3D

lnteractiveGraphics,

1990,pp.l1-20

36 r Bonte,

A.

Galimberti

and

C.

Rizzi,[`A _3D

graphic ronment to design

_garments",

From GeometricModeljng to

Shape

Modeling,

Eds.

U.Cugini& M.Wozny, Kluwer Academic Publishers,

2000,

pp,137-1

50

_{also

Proc,7th

IFIP

Workshop

on GeometricModeling :Fundamentals

and Appljcatjons

-

GE07,

_Parma,2-4 ottobre 2000}, 37 A.

Galimberti,

"Sviluppo _dj

un sistema disimulazione _per

]a

progettazjonedicapi diabbigliamento", Ph.D.

Thesis,

Dipartlmentodilngegnerialndustriale,Universita

di

ma,

ltaly,

2001,

38

U.

Cugini

and O.Rizzi,"3D _Design

and Simulationofmen

garments",

Proc.

Wdrkshop WSCG '02, _2002.

24T'･ifl)#ffSkseX

specialissueefjapanesesocietyfortheseienceotdesign