Tutorial T3: Cloth Animation and Rendering

The area of physically-basedmodelingis situatedin the intersectionof computerscience, mathematics,and physics.Theanimationof cloth is a particularly interestingapplicationof physically-basedmodeling, because it aimsat fastanimationsolutionsfor ratherdifficult physicalproblems.Moreover, it addressesoneof themajor difficultiesin creatingrealisticsceneswith virtual actors. Thechallenge of computeranimationis to breakdownphysicalmodelsfor complex structuresastextiles,approximatethemefficiently, andrun fastsimulationswith intelligentnumericalmethods. Furthermore, interactivityand collisionswith otherobjectsin thesceneare challengesthat havemotivatedmuch creativework over therecent years. Therange of methodsproposedin literature is quitelarge. Thetechniquesvary fromsimplifiedmethodsdesigned for real-timeapplicationsto sophisticatedmethodsthatweredesignedto reproducemeasur edmaterialproperties. Renderingcloth is especiallydifficult becauseof its complex material properties.Software renderingcan deal with thesepropertiesfairly easily, oncethey havebeenacquired,but remainstooslowfor interactiveapplications. Hardware acceleratedrenderingoftenprovidesa way to achieve interactiverenderings,unfortunatelycomplex materialsaren’t directly supported.We will demonstr ate how interactiverenderingwith complex materialscan nonethelessbeachieved 1. PhysicalModels (Olaf Etzmuss ) Cloth modelshave beendesignedwith differentobjectives. A commonobjective in computergraphicsis to generate pretty andconvincing picturesandfilms. For that purpose physicsmay be ignoredor simplified significantly. A differentobjective is to preserve physical,measuredproperties in orderto mapreal materialsontoa simulatedcloth. This, for instance,is indispensablein e-commerceapplications,in which a customerselectsclothesbasedon a simulation.In computergraphicsthis alsoshouldleadto ananimationthat is fastandallows interactionwith a complex scene.But the useris preparedto wait abit longerfor theresultsto achieve a physicallysoundsimulation. Accordingto theseconsiderations, we will first startwith amodelhastheformerobjective.After thatwewill describe how discreteandcontinuousmodelsaimto preserverealmaterial properties. All modelshave in commonthatthey discretizethecloth by a polygonalmesh.The verticesof this mesharecalled particlesor (mass)nodes.Themeshtopologydefines,how theparticlesinteractandexert forcesononeanother . 1.1. DiscreteModels Given the meshdescribingthe cloth, forceson eachparticlearecomputeddependingon its positionandvelocityand the positionsand velocitiesof a set of particleswithin its topologicalneighbourhood.When the function F computing the forceshasbeendetermined,Newton’s equationof motion governsthe movementof the particles.The trajectory of eachparticlewith massmi atpositionxi is computed by F x v mi dxi dt2 (1) Here x denotesthe vector containingall particle positions andv the vector of all particle velocities.Note that, since c TheEurographicsAssociation2002. Hauth,Etzmuss, Eberhardt, Daubert,Kautz/ ClothAnimationandRendering s u v deformedsurface r u v (local,partial)reststateof surface d u v displacement xi particlepositions vi particlevelocity ε strain(tensor) σ stress(tensor) C elastictensor D viscoustensor a b scalarproductof vectorsa andb ∆ Laplaciansxx syy szz su partialderivative of s with respecto u Table1: Notationin this section particlesystemsalreadyrepresenta discretizationin space, only a systemof ordinary differential equationshasto be solved. The systemspresentedin literaturediffer by their methodsof computingtheforces. 1.1.1. Mass-springsystems In mass-springsystems,particle interactionis solely modelledby linearsprings.