Modelsfor CharacterAnimation

GordonCollins andAdrian Hilton

Centrefor Vision,SpeechandSignalProcessingUniversityof Surrey, GuildfordGU25XH,UK

g.collins,a.hilton@surrey.ac.ukhttp://www.ee.surrey.ac.uk/Research/VSSP/3DVision

Abstract

We presenta review of methodsfor theconstructionanddeformationofcharactermodels. We considerboth stateof the art researchandcommonpractice. In particularwe review applications,datacapturemethods,man-ualmodelconstruction,polygonal,parametricandimplicit surfacerepresen-tations,basicgeometricdeformations,free form deformations,subdivisionsurfaces,displacementmapschemesandphysicaldeformation.

1 Intr oduction

The scienceof computercharacteranimationaddressesthe problemof buildingmodelsfrom somecaptureddataandsomephysicalknowledgeof the character.Threestagesare involved; staticmodeldesign,deformationschemeandmotionprescription. The staticmodelmay be entirely captured(from a rangescan,forexample)or entirelyuserspecified(usinga commercialmodelbuilding package,for example).Deformationof themodelrequiresat leastsomedegreeof physicalknowledge. If an animatorwantsthedeformationsof his characterto be smooththen in effect he is approximatingthe physicalprocessof skin stretchingby asmoothsurface.On theotherextremeanimatorsmaywantamorephysicallyreal-istic modelwhichcomputesthedeformationsof everymuscleandskinmovement.Motion laws toomaybepainstakinglyappliedby ananimatormoving astick manskeletonor maycomedirectly from motioncapturedata.Theproblemfor theani-matorthenis, givensomecaptureddata,how to bestusehisknowledgeof physicalmovement?

The methodsfor characteranimationare variousand dependenton the ap-plication and the amountandkind of captureddata. The tradeoff involved are

essentiallyrealism,speedandcompactness.Computergamesrequiremodelsthatcanbe renderedvery quickly andmay needsomeform of collision detection;anotoriouslyCPUhungrypractice.As a resultrealismmustoftentake a backseat.At theotherextreme,film animatorsrequireahighdegreeof believability andper-hapsrealismbut theirmodelsdonotneedto berenderedin realtime. Applicationsfor animationarediscussedin Section2.

Theapplicationusuallydeterminesthetypeof datacaptureneededandhencethe representationused. In Section3 we discussthe model building approachwhichrequiresnodatacaptureandthescanningapproachwheremodelsarecopiesof realobjects.In Section4 we outline the representations;polygons,parametricsurfacesandimplicit surfaces.

An importantconceptthat unifiesmostanimationschemesis the layeredap-proach.This is averynaturalapproachsincebodieswhicharelayeredin thesensethatthey have askeleton,amusclelayer, a fat layeranda skin layer. Eachlayeriscontrolledonly by thepreviousone.While someanimationsystemsexactlymirrorthisanatomicalorganisation(seeSection5.7)it is morenormalto haveahierarchythatgoessomethinglike; skeleton,low resolutionlayer, high resolutionlayer. Aswith theanatomicallyaccuratemodel,moving askeleton,in turnmovesthehigherlayers. Unlike the humanbody, it is theskeletonthatmovesthemusclessinceitis easyfor animatorsto move a point on a skeleton.Thepurposeof a layeredap-proachis to gofrom acomplicatedmodelof acharacterto asimpleskeletonwhichcanbeeasilyanimated.As anexample,thelayeredanimationschemein [80, 81]is shown in Figure1.

Low−resolution Control Model Layer

Point−to−line Mapping

Low−resolution Control Model Animation

High−resolution Model Capture & Construction

3D Data Capture (hand−held sensor)

Geometric Fusion & Optimisation

Skeleton Layer

Skeleton Fitting

Motion Control Design

High−resolution Model Layer

Point−to−surface Mapping

High−resolution Model Animation

Model Construction

Layered Animation

Figure1: Systemoverview

The problemthen lies in how to translateskeletonmovementinto renderedsurfacemovement.Here,again,a variabledegreeof physicalrealismis used.InSection5.7 we discussmethodswhich areconcernedwith modelingmusclesandskin with springsandsolving the resultingphysicsbaseddifferential equations.Sucha practiceis clearly time consuming.Wherephysicalrealismis neitherre-quirednor practical,someother, believable, law of deformationis needed.Thislaw is almostalwaysthat deformationsmustbe smooth. Two waysof achievingthis, freeform deformationsandsubdivision surfacesarealsodiscussedin Section5.

In this paperwe presenta review of literatureon the modelbuilding andde-formationof characters,wedonotconcentrateon theactualanimationof amodel.This may comefrom a variety of sources,whetherthey be motion capturetech-niques(commonin the computergamesindustry)or if they are in somedegreeautonomous(AVATAR technology).

2 Applications

Thecurrentapplicationsfor characteranimationareroughly, web-basedanimation,computergamesandfilms. Eachapplicationhasdifferentrequirementswhichare;� Web-basedanimation- CompressionandCPUefficiency.� Computergames- CPUefficiency.� Films - Realism.

Web-basedanimationsmustbetransmittedquickly andsocompressionis im-portanthere. It is, also,desirableto transmittheanimationin a coarseform firstand then successively finer forms. For this, web-basedanimationmakes useoflevel of detail(LOD) algorithmsandprogressive transmission[47].

Computergamecharactersneedto beanimatedquickly andrenderedin real-time. Often the detailsof a characterare lessimportant than their motion andtheir interactionwith othercharactersandobjects.Becauseof this,computergamecharactersarenearlyalwaysconstructedwhile thecaptureddatacomesin theformof motioncapture.

In contrast,film charactersarerequiredto be believableandperhapsalsore-alistic. Charactersdo not have to be renderedin real time and so may be verycomplicated.The taskfor the researcheris to automatesomeof the painstakingwork that an animatorhasto put in. A commontechniqueis to build charactersfrom scansof clay sculpturedcharacters.Motion is usuallydictatedby ananima-tor ratherthanby applyingcapturedmotion.Deformationsmustbebelievableand

this is done,aswe will seelater, eitherby applyingphysicallaws or by ensuringsmoothdeformations.

3 Data Capture

Charactermodelsrequiredifferentdegreesof 3 or 4D datacaptureandhencedif-ferentlevelsof manualinput. This rangesfrom a full scanof a charactertogetherwith motioncapturefor animationrules,to amanuallyconstructedmodelwhich isanimatedby manuallymoving controlvertices.

3.1 Model Construction

3D modelconstructionhasbecomea grown up industrywith severalglossymag-azines(digit, 3D world) andwebsites[1, 3] concernedwith theart andtechnol-ogy of constructingmodels.TherearenumerousCAD packagesfor modelbuild-ing with 3D StudioMAX, Maya3DandLightwave beingthestandards.Howeverworkingona2D computerscreento create3D charactersis notaneasilymasteredtaskandthis is oftendiscouragingfor artists.Despitethematurityof 3D softwaretools the processof manualshapeconstructioncanbe highly time consumingtoachieve visualrealismfor detailedcharacterssuchasthoseusedin film animation.

Interactivity is the key hereand Turner et al. have addressedthis problem[85] by augmentingthe desktopwith a headtrackingsensorandspecialglasses.Another, well studied,solutionis haptics[51]. A hapticdevice is a handlewithseveraldegreesof freedom.Thehandlecanreceive forcefeedbackwhena virtualintersectionoccursso that the usercan easily navigate with it arounda virtualenviromentwhichis constrainedby theobjectsin it. Hapticdevicesprovideamorenaturalinterfaceto sculptthesurfaceshapeof a3D computermodelor character.

Figure2: Characterscreatedby RobertKuczerain Mayaand3d StudioMax

Figure3: Characterscreatedby Taronin Lightwave.

3.2 RangeData

An easierandmorenaturalway for anartistto work in 3D is to sculpta characterout of clay. Thesurfaceshapecanthenbecapturedusingeithera touchprobeoroptical rangesensorto measurethe 3D locationof pointson the surface. Rangesensorshavetheadvantageof requiringnosurfacecontactandallowing rapidmea-surementof thousandsof pointson the surface. The sensorprojectsa structuredlight patternontotheobjectsurfaceandcapturesa cameraimageof theprojectedpattern.Optical triangulationbetweentheprojectorandcamerais usedto recon-structthedistanceof pointson thesurfacefrom thecameraasa 2.5D “rangeim-age”.A numberof establishedtechnologiesexist for rangemeasurementincludinga singlelaserstripewhich is sweptacrossthesurface,grey codeimagesequencesof binary stripepatternsandrandombinary dot patterns. In recentyearshighlyaccuratescannershavebecomecommerciallyavailableandarethenormfor rangedatacapture.

Passivetechniquesfor shapecapturereconstructthesurfaceshapefrom asetofmultiple view images.Shape-from-silhouettes[70, 30] hasbecomeanestablishedtechniquefor recovering the approximatesurfaceshapeof an objectby imagingagainsta known background,suchasa blue-screen.Imagesfrom multiple viewsarecombinedto determinethe spatialvolumeoccupiedby the objectandrecon-struct a surfacemodel. This approachcan be usedto producedhighly realisticobjectmodelsby texture mapping. However, in isololation the silhouettebasedapproachcannot reconstructsurfaceconcavities. Close-rangephotogrammetricapproacheshave beendevelopedwhich reconstruct3D shapefrom matchesbe-tweenimages[4]. Matchesof imagefeaturesbetweenimagesareobtainedeithermanuallyor automaticallyto recover modelsof surfaceshape.Extensive researchin computervision communityhasaddressedtheissueof automaticmatchingbe-

tweenimagesfor structurerecovery [29, 39]. Photogrammetricapproachesresultin accuratestrcturerecovery but sparsefeaturedatadueto therequirementfor vi-sually distinct featureson the object surface. Reconstructionof surfacemodelsfrom suchdataremainsan open-problem.Dencematchingtechniqueshave alsobeenusedto recover dence3D surfacemeasurements[29, 50]. However, duetheproblemsof automaticmatchingthesearerelatively inaccuratecomparedto activesensors.Recentlymodel-basedapproachesfor recovering 3D shapefrom passivemultiple view imageshave beenintroducedwheredomainspecificknowledgeisusedto constrainthereconstrcution.Model-basedapproacheshavebeendevelopedto recover visually realisticmodelsof architecture[20], faces[32] andpeople[40].Thisuseof model-basedapproachestogetherwith photogrammetrictechniquesforrecoveringstructurefrom videoimagesequencesoffersapromisingtechnologyforfuturehighly realisticmodelbuilding.

For example,ahand-heldrangesensorsystem,3DScanners’ModelMaker [2],wasusedby Hilton et al. to build animationmodels[41, 42, 81]. Thesensoris alaserstripebasedrangesensorwith a six degree-of-freedompositionsensor. Theusermaymovefreelyaroundanobjectto capturethedataandusehisknowledgeoftheobjectto positionthesensoreffectively (anadvantageoverautomaticsensors).The result is a densetriangularmeshwhich is structuredin sucha way that notwo pointsareconnectedif they arenotwithin acertainthresholddistanceof eachother. Thusthetopologyis recreated,seeFigure4. A similar systemwasrecentlyusedby FrameStoreto capturethemodelsfor a recentBBC series’Walking withDinosaurs’(http://www.bbc.co.uk/dinosaurs).

Whichevercapturetechniqueis usedtheproblemsinvolvedareintegratingdif-ferentoverlappingviews (for exampledifferentsweepsof the laserscanner)intoonesurface,dealingwith missingdataanddealingwith outlying datapoints.Thisproblemis subdivided into a problemwherethe connectivity of measuredpointsis known (the structuredproblem)and whereit is not known (the unstructuredproblem).Thestructuredproblemhasbeenwell studied[18, 43, 76, 84, 79]. Thesinglesurfacemay be reconstructedby fusing layersthat coincidein a specifiedvolume constructedfrom the surface [18, 44]. The generalproblemof surfacereconstructionof unknown objectsfrom unstructured3D point remainsan open-problem[11, 25, 46, 65, 66]. A recentpaper[73] dealseffectively with outlyingormissingdataby ahybridmethodwhichaugmentsscanneddatawith ahierarchyofuser-specifiedmodels.

(a)ModelMaker system

(b) Raw data (c)Meshpatches(partial)d) Fusedmodel

Figure4: Model reconstructionfrom hand-heldsensordata

4 Representation

Themethodof modelbuilding usuallydictatestherepresentationof amodel.Con-structedmodelsareusuallyrepresentedby parametricsurfaceswhereascaptureddatausuallycomesin theform of apointcloudwhich lendsitself to polygonalisa-tion. The prosandconsof both representationsanda third representation,meta-balls,arediscussedhereandarewell documentedin WattandWatt [87].

4.1 Polygons

A polygonisedsurfaceis usuallya collectionof verticeswhich areconnectedintotrianglesor quadrilaterals.Besl [10] givesa goodoverview of the advantagesofpolygonalrepresentationsfor variousapplicationsandanalyses.Themostnotableadvantagesaredueto thefactthatpolygonsarea very simplebuilding block. Be-causeof this a wide rangeof topologiescanbe approximatedby polygons.Alsorenderingpolygonsis very simpleandefficient asit is supporteddirectly by cur-rent graphicshardware. The disadvantageis that many verticesmay be needed

to approximatea smoothsurface.Also polygonalsurfacescannotbedeformedinan arbitraryway. For example,if a triangularsurfaceis twisted too much theneventuallytwo edgeswill crosssothattheconnectivity is violated.

4.2 Parametric Surfaces

Parametricsurfacescanbe roughly characterisedascurveswith a predeterminedsmoothness,which fit somegiven control pointsautomatically. They aresimpleto useasthe modelermay specify just a few control points in order to specifyalargesurface.Parametricsurfacesarewidely usedby animatorssincethey canbesmoothlydeformedsimply by moving a singlecontrol point. Parametricsurfacemodelsareusuallybuilt by fitting togetherdifferentpatchesof parametriccurves.The difficulties occur in the manualtask of trimming and fitting togetherthesepatchesso as to maintainsmoothnessover the join. A further difficulty is thatparametricsurfacescannotbedirectly renderedbut mustfirst bediscretised(into apolygonisationfor example)to berendered.

Therearemany parametricsurfaces[28]; Beziersurfaces,B-Splines,�

-Splines,NURBSwhichall differ in termsof easeof rendering,how locally they areaffectedby controlpointsandhow smooththey are.B-Splinesarepopularascontrolpointshave a very local influenceandthey areeasilypatchedtogether. NURBS,Non-Uniform RationalB-Splines,areageneralisationof B-Splineandhavebecomethecomputergraphicsstandard.

4.3 Subdivision Surfaces

Thetraditionaldistinctionbetweensplinesandpolygonshasbeenmuddiedin re-cent yearswith the arrival of robust subdivision surfacetechniqueswhich areapolygonisationbut alsoa smoothsurface. Subdivision surfacesappearto be thebestof bothworldsandhave beenusedextensively in amodernparadigmof char-acteranimation,“Geri’sGame”[21] by Pixaranimationstudios.Theuseof subdi-vision in animationis describedin moredetailin Section5.5.

4.4 Implicit Surfaces

An entirelydifferentapproachis usedby Thalmannet al. [78, 5] andDesbrunandGascuel[22]. They constructimplicit surfaceswhich aremathematicalfield func-tions, ������� constant,giving thedistanceof a surfacefrom a point � . A typicalchoiceof the field function is � ������������� . Thalmannet al. attachan ellipsoidalvolumetricprimitives,“metaballs”, to thejointsof askeletonandthenblendthem

togetherusingB-splines(seeFigure5) As theskeletonmoves,the metaballsde-form accordingly, making this an excellentapproachto musclemodeling. Veryfew primitivesareneededto constructamodel,however renderingandmodelcon-structionis far from straightforward.

Figure5: a) Sphericalimplicit surfaces b) Surfaceblendedtogether

5 Deformation

Onceastaticmodelis built, specifyinghow regionsdeformrequiressomeextra in-put. For mostanimatorsthemanipulationsaredonein astraightforwardgeometricway, suchasdirectly manipulatingthemodel,interpolatingbetweenknown posesor usinga simpleskeletonmodel. More sophisticatedmodelsusesmoothdefor-mationmethodssuchas free form deformations(FFDs)or subdivision surfaces.Physicallyrealisticmodelsareusuallytoo computationallyexpensive for today’scomputersbut area very active areaof research.Thesemethodsareall discussedherein orderof complexity.

5.1 Dir ect Methods

All the representationsmentionedabove can, to a certainextent, be directly an-imatedby moving control pointsor vertices. In the caseof parametriccurves asinglecontrolpointcanbemovedto locally effect theshapeof awholeregion. Forpolygonisationsdirect animationof individual verticesis a painstakingbut com-monpractice.Furthermore,polygonalverticesmayonly bemovedwith regardtotheir connectivity or elseedgecrossingmayoccur.

Onestepup from directmethodsaretheglobaldeformationsof Barr [8]. Hegeneralisesthestandardmatrix transformations(translation,rotationetc.) so thatthematricesmaychangedependingonwherethey areapplied.In thiswayawiderrangeof shapesanddeformationsis possiblethanwith thestandarddeformations.ChangandRockwood [15] generalisefurther by allowing the axeson which the

transformationsactto change,for examplethetransformationsmayacton anaxiswhich is a B-spline. Although a wide rangeof deformationsarepossiblein thisway, thesemethodscannotperformall the deformationsthat animatorsmay re-quire.

5.2 BasicSkeletonMethods

Theproblemof moving many polygonalverticesor parametriccontrolpointsmaybesolvedby imposingasimplerlayerwithin themodelandanimatingthat.Maestri[62] givesa review of the technicaldetailsof this processaswell assomeof thepackagesavailablefor it. A basicform of this layeredapproachis widely usedandinvolvesfitting asimple“stick-man”typeskeletonmaybeplacedinsidethemodel.Figure 6 shows a genericavatar model animationsequencewhich is deformedusingaskeleton.

ThestandardH-animformat [75] for animatingvirtual humanshasa joint hi-erarchywhichis reviewedin [6]. Similarily MPEG-4is astandardformatfor faceswhichusesa similarparametricdeformationmethod[71].

The problemis one of how to attachsurfaceverticesor control points to askeletalsurface.A poorattachmentmayleadto surfacecollapses,bulging andthewrong segmentbeingmappedafter the skeletonis animated. For example,if askeletalsegmentinfluencesall its nearestvertices,then,whenit is animated,partsof oneleg maymove astheotherleg. Researchers[63, 81] have looked into thisproblemandproducedautomaticattachmentwhich counterall theseproblemsforsimpleone-chainjoints. Complicatedjoints suchasthepelvisandespeciallytheshoulderareopenproblemswhich arecurrentlytackledwith physicallymodelledconstraints[64].

5.3 ShapeInter polation

Shapeinterpolationis a commonmethodfor animatingfaces,which is closelyre-latedto thetechniqueof morphing.Essentiallya library of expressionsis built andan animatormay move betweenexpressionsin the library by interpolating. Themethodis clearlylimited by thesizeof thelibrary andalsoby theexactmethodofinterpolation.Maestri[62] givesthetechnicaldetailsof this method,somepracti-caltipsandpresentsthepackagesthatperformit. Lewis etal. [59] presentastateoftheartmethodof shapeinterpolationandalsounify thiswith skeletaldeformations.They show thatwhereskeletaldeformationsbreakdown, thefaceandshoulderforexample,shapedeformationmaytake overandgive a realisticdeformation.

Figure6: Skeletonbasedanimationsequencefor anavatarmodel.

5.4 FreeForm Deformations

FreeFormDeformation(FFD) is aclassof methodswhichareindependentof rep-resentation.They werefirst developedby Sederburg andParry [77] for deformingsoft objects. Sederburg usesthe analogyof embeddingthe object in deformableplastic.Whentheplasticis deformed,theobject,which is alsoto beconsideredasflexible, is deformedaccordingly. An objectis enclosedwithin a four dimensionalparametriccurve, for examplea Bezierhyperpatch,which is a volume(usuallyacube). The control pointsof the hyperpatcharedeformedand,sincethe hyper-patchis a smoothfunction,theobjectis deformedin a smoothway (seeFigure7)If the hyperpatchweresimply a volume, insteadof a parametriccurve, thenthedeformationwouldbeequivalentto simply moving controlpointson theobject.

Recentdevelopmentsin themethodhave concentratedon fitting FFDsto ob-jects[9, 38, 68, 72]. TheExtendedFreeForm Deformationmethodof Coquillart[16, 17] weldstogetherstandardFFD blocksto createa toolkit of new primitiveswhich canbebetterfitted to anarbitrarytopology. MacCrackenandJoy [61] sub-divideanFFDlatticeinto asequenceof latticeswhichconvergeto theshapeof theobject.

Figure7: Freeform deformationappliedto a teapot

Comprehensive animationsystemswith heavy useof FFDsaredescribedbyFaloutsoset al. [27]. Chadwick[14] presentsa systemin which a skeletonmovesthecontrolpointsof FFDsto deformmusclesandphysicalspringlaws move con-trol pointsonfattyareassuchascheeks.Otherwork is concernedwith maintainingphysicalpropertiesthroughFFDssuchasvolumepreservingmethods[45, 74].

5.5 Subdivision

A growth areain computergraphicsof recentyearshasbeensubdivision surfaces.Subdivision surfacesarea way of obtaininga smoothsurfacewith a polygonalrepresentation.Startingwith a coarsepolygonalmesh,new verticesare addedand, in someschemes,old verticesaremoved. The resultingrefinedmeshis asmoothsurfacein thesensethat,if this processis repeatedadinfinitum, the“limitsurface”would bea splinesurface.Figure10 shows a headmodelafter2,3and6subdivisionsof thewholemesh.

Themethodsto performsubdivision arecategorisedinto interpolatingandap-proximatingschemes.Approximatingschemesinsertnew verticesandmove ex-isting ones.Thenew pointsaregenerallyinsertedin a geometricallysimpleman-ner (in the centreof a triangleor splitting the sideof a triangle). Smoothnessisachieved by “relaxing” the old pointsby repositioningthemat an averageof thesurroundingpoints. Interpolatingschemeshave the desirablepropertythat theiroriginal controlpointsarenotmoved. In orderto ensuresmoothness,thetemplateof controlpointsneededto computethepositionof thenew vertex mustbelarger.

CharlesLoop [60] describedthearchetypalapproximatingschemefor triangu-lar meshes.In his schemeeachedgeof a triangleis split in half andtheresultingthreepointsareconnectedto form four triangles.Theold verticesarethenrelaxed.Dyn et al. [24] proposedthe interpolatingButterfly schemewhich wasextendedto arbitrarymeshesby Zorin etal. [90]. OtherseminalschemesareCatmull-Clark[13] andDoo-Sabin[23] for quadrilateralmeshes.Also worthy of noteis the � � -

subdivision schemeof Kobbelt[52] in which a vertex is placedin the middle ofa triangleandthenconnectedto eachvertex, creatingthreetriangles. The edgesof theoriginal trianglearethenswappedto connecteachnew vertex, in this wayundesirablethin trianglesareavoided.Theadvantageof this novel schemeis that,unlike many schemes,refinementmaybelocalisedandthereforeit is ausefultoolfor adaptivity.

a)Original Mesh b) New VerticesInserted c) Verticesrelaxed

Figure8: Representationof Loop Subdivision

a)New VerticesInserted b) EdgesSwapped c) Verticesrelaxed

Figure9: Representationof � � -Subdivision

DeRoseet al. [21] make extensive useof Catmull-Clarktypesubdivision sur-facesfor a sophisticatedcommercialanimatedcartoon. They favour subdivisionsurfacesover parametricsurfacesbecauseof the“considerablemanualeffort” in-volvedin fitting thesetoeachotherandin keepingthemfittedwithoutvisibleseamsappearing.They alsouseavariantof subdivision surfacesdueto Hoppeetal. [48]whichallows sharpedgesto bepresentin thesurface.

(b) Reconstructedheadmodelsat threeLOD ( ����������� )Figure10: Reconstructedsubdivision headmodelat threelevels-of-detail

Subdivision surfacesprovide an easily implementedrepresentationwhich iscompatiblewith polygonalmeshes.They shareall the advantagesof parametricrepresentations(smoothness,few controlpoints)but areeasilyrenderedanddonothave to bepatchedtogether. Adaptive methodsareneededto countertheproblemof overly densemeshes.

5.6 DisplacementMaps

In orderto displaydetailon amodel(suchasdetailedscanneddata)anextra layerin the hierarchyis needed.This may be representedby a displacementmap. Adisplacementmapis generatedfrom adetailedpoint !#" by computinganormal $ ,adistance% andapoint of intersectionon thecontrollayer !'& suchthat

!#"()!'&+*,%�$.-Thedetailedlayercanthenbereconstructedby subdividing thecontrolmeshandrenderingthemodelat thecorrespondingdisplacedpoint. Thenormalsusedmustbecontinuouson thecontrolmodelto ensureall detailpointscanbemappedandthatthedetailedlayervariessmoothlyasthelow resolutionmeshis deformed.

Krishnamurthyand Levoy [56] ensureda continuousnormal by calculatingdisplacementsoff a B-Splinesurface.Hilton et al. [80, 81] reconstructa captureddetailedsurfacefrom a coarsecontrol modelby computinga displacementmapfor eachdetailedpoint alonga normalto the coarsemesh(seeFigure11). Oncethe meshis deformedthe detailedlayer canbe reconstructedby subdividing andremapping. The map is calculatedin sucha way as to precludedetailedlayerintersectionsandseams.A similar approachis followed by Lee et al. [57]. The

differencehereis thatthedisplacementmapis calculatedon a subdivision surfacegeneratedfrom thecontrolmesh.

Displacementmapsallow multiple level of detail representationssimply byspecifyinghow many timesthecontrolmodelshouldbesubdivided.This is averyuseful tool for web basedanimationsinceit allows progressive transmissionoflevelsof detailandeffective compressionof themodel.

a) High-resolutionModel b) Controlmesh c) Colourcodedmapping

d) Displacementmapwith colourrepresentationof height

Figure11: Headmodelmappedontoacube

5.7 Physically BasedAnimation

Physicalanimationmethodsareasdiverseastheir applications.Researchershavetackledproblemsin everything from finger nails andclothesto breastsandbut-tocks. In fact,modelingmuscleandskin layersis now a maturesubject.Usuallysomespringmodelis setupconnectingmuscles,skinandskeleton.Newton’s lawsof motion andHook’s law of springscanbe usedto derive differentialequationsfor the skin andmusclemotion. A simplemodel for a particle, � with mass/ ,dampingcoefficient 0 , gravitationalconstantvector 1 andcoefficient of elasticity

2might bestatedas,

/ %3�%54 � ���647�. 2 �����648���9����:;�7�<�=/>1?�@0 %%;4 ���648�A-Thetermsontheright handsideareduetoelastic,gravitationalanddampingforcesrespectively. Often elasticpropertiesbetweenparticlesareconsideredandthenaconnectivity matrixof forcesis addedto themodel.A furthersophisticationis thenonlineareffectof allowing thecoefficientof elasticity

2to varywith its extention.

This leadsto a systemof ordinarydifferentialequationswhich aresolvednumeri-cally. Theproblemis constrainedby collisionsbetweenskinandskinandbetweenskin andobject.

An exampleof afully intergatedphysicalsystemis thatof GrobbettiandTurner[85]. They presentaninteractive systemcalledLEMAN. Themodelhasskeleton,boneandmuscle,fatandskinlayers.Theskeletonlayeris astickFigurewhichcanbemovedandin turndeformsaboneandmusclelayer. Fat is modeledsimplyasalayerof constantthicknesswith connective tissuein betweentheskin andmuscle.Theskin is thendeformedby consideringforcesfrom themusclesvia connectivetissueaswell aselastic,dampingandgravitational forces. This requiressolvinga systemof differential equationsusing a finite differencenumericaltechnique.Figure12 depictsasimilar framework.

Interconnective

Skin Layer

Particle

Skeleton

Spring

Muscle Layer

Surface Spring

Figure12: Layeredmodelwith springs

AmongtheearlierphysicallyrealisticlayeredmodelswereKomatsu[55] whoadjustedparametricsurfacecontrol points accordingto joint angleson a skele-ton. Forsey [31] follows this approachbut addsa hierarchyof control for detailed

movements.Chadwicket al. [14] arealsopioneersin this field (seeSection5.4)asis Gascuel[33] who useda simplifiedandcomputationallyfastermethod.Sheattachesoneendof a springto a muscleandthe other to the control pointsof aB-Splineskin layer. This alsoallows springsto affect nearbysprings.Terzopou-los [82] inventeddynamicNURBSwherebydifferentialequationsfor Lagrangiandynamicsaresolvedwith a finite elementmethodto move thecontrolpointsof astandardNURBS.

Thalmannetal. [5, 69] usemetaballsin a layeredphysicalapproachto muscledeformationsThey usea realisticskeletonandusedesignersto modeleachindi-vidual muscle. Wilhelms andGelderalsoproposea working anatomicalmodelwhich with a minimunof computation[88]. Physicalmodelinghasbeenstronglyfocusedon facialanimationby Leeetal. [58], Magnenat-Thalmannetal. [26] andKochetal. [53, 54]

An alternative to the massspringmodel, is to considerthe skin asan elasticsurfacewhoseshapeis dictatedby minimisingits elasticenergy. Kochetal [53, 54]write thetotalenergy as,

B C�DFEHG 4I�KJ�4��MLONQPSRT* �VU J�PW%3NQPSRF%3XY-if weconsiderasurface Z[��\]�8^�� andno externalforces,thenEHG 4���JM4I�ML_NQPSR� E<` Z �a * E � Z �b * Edc Z a Z b and�VU J�PW%3NQPSRe � ` Z �a�a * � � Z �b8b * � c Z �a�b -The energy is minimisedover the surface %3X which gives the shapeof the sur-face. Theminimisationis usuallydoneusingtheFinite ElementMethod(FEM),wherebypiecewisepolynomialfunctionsaredefinedonatriangulatedsurfacesuchthatthefunctionsfit togetherat their boundariesandthis constructedsurfacemin-imisestheenergy functionabove. JamesandPai [49] presentthesubjectwell andusea novel solver for theminimisation.Gourretet al. usethis modelfor grasping[34].

In mostsystems,physicallyrealisticdetail is patchedon to anexisting model.Examplesof this kind of modelingarenumerous.Magnenat-Thalmannetal. haveresearchedclothes[83, 36, 86], hair [19, 37] andwrinkles [89]. Fingernails andclothesarealsodiscussedin DeRoseet al. [21]. Baraff andWitkin [7] studythenumericalstabilityproblemfor amass-springmodelof clothes.

Researchin this areaalsooverlapswith medicalapplications[53, 12, 67]. In-teractivesystemsthatusesoft tissuemodelsandcollisiondetectionarerequiredbyboth applications.Most physicallybasedmodelingmentionedabove requiressomuchcomputationthat it is suitableonly for nonrealtimeapplications.Thethree

major problemspersist;solving large systemsof differential equationsquickly,maintainingstability in thesolvingof theseequationsanddetectingcollisions.

6 Conclusion

Characteranimationis still a youngsubjectandmuchwork remainsin developingnew technologies,aswell asin understandingold onesbetter. Thedrivesin com-puteranimationresearchwould seemto be towardsgreaterinteractivity, realismandmorerobustrepresentations(suchasfully adaptivepolygonalrepresentations).It seemslikely thatwith greatercomputingpowerandnew renderinghardwarethegoalsof all thesefieldswill bemet.

7 Acknowledgements

We thankRobertKruczera(www.3dcharacters.de)andTaron(www.taron.de)fortheir characterart in Figures2 and3 andJonathonStarckfor Figure5. We alsothank the supportof the EPSRC(grantnumberGR/L89518). Finally we wouldlike to acknowledgethehelpof theSiggraph’s graphbib[35].

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