CS380: Introduction to Computer Graphics Geometric Modeling...

transcript

18/06/11

MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012

CS380:IntroductiontoComputerGraphicsGeometricModeling

Chapter23

MinH.KimKAISTSchoolofComputing

SUMMARYLightTransport

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Radiantflux•  Abunchofphotonsflyingthroughspaceinadirection.

•  Wehaveasensor(W,X)outinspace– Wisawedgeofdirections– PassthroughthesurfaceX

•  Eachphotoncarriesenergyinunitsofjoules

•  Radiantflux:energymeasuredinseconds,measuredinwatts:

Φ(W ,X)

Irradiance•  Measuredradiantfluxbytheareaofthesensor(measuredinsquaremeters)

•  SmallerandsmallerXaroundasinglepoint(undercontinuityassumptionsabout)àirradiance

•  NoteEatadifferentnormalisdifferent

E(W ,X) := Φ(W ,X)X

En (W , x)

En (W , x) ≠ E′n (W , x)

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Radiance•  In,shrinkWdowntoasinglevector,dividingoutby|W|,thesolidanglemeasureofW(unit:steradians)àradiance

En (W , x)

Ln (W , x) =

En (W , x)W

(thewedgeofalldirectioncovers4πsteradians)

Pathtracing•  Addingonemorebounce•  Geometricpathoflighttransport:•  Notasanestedintegralovertwohemispheres,butasanintegraloveranappropriatespaceofpathsàPathtracing

Le( x, v)+ L1( x, v)+ L2 ( x, v)

( x, ′x , ′′x )

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Renderingequation•  ReflectionequationinshorthandwhereBisthebounceoperatoroflight.

•  Recursivelighttransportis•  Wecansay

•  Therenderingequation(integralequation)is

L1 = BLe

Li+1 = BLi

Lt =Le +L1+L2+L3+ ... =Le +B(Le +L1+L2+L3+ ...) =Le +BLt

Lt( !x , "v)=Le( !x , "v)+ f !x ,"n(

"w , "v)Lt( "w , !x)cos(θ )dwH∫

ANIMATIONChapter23

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Skinning•  Startwithcomplicatedmeshwewanttoanimate•  Rigging:designageometrichierarchicalskeletalstructure

•  Associateeachvertexwithone“bone”(RBTnode)

•  Idea:expressthevertexinitsboneframe

•  Manipulatetheskeleton•  Verticesnowmovealongwiththebones

Details•  Insteadofactuallychangingthevertexcoordinates,•  Arestaccumulatedmatrixrepresentstherelationshipbetweentheobjectandrestboneframe.

•  Anewaccumulatedmatrixrepresentstherelationafterthebonehasbeenmoved.

•  Usethesematrices,inthevertexshadertomovethevertex.

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Details•  Inthiscontext,wecanassociateavectorofbone-weightsanddosoftskinning.– Weusetheweightstoblendtheupdates.

•  Thisisusedextensivelyingamesandwouldmakeaniceproject

Skinning(rigging)example

AlekaMcAdams,YongningZhu,AndrewSelle,MarkEmpey,RasmusTamstorf,JosephTeran,andEftychiosSifakis.2011.Efficientelasticityforcharacterskinningwithcontactandcollisions.InACMSIGGRAPH2011papers(SIGGRAPH'11),HuguesHoppe(Ed.).ACM,NewYork,NY,USA,,Article37,12pages.

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Physicalsimulation•  Physicsusesequationstodescribephysicalprocesses.

•  Wecantrytosimulatetheseprocessescomputationally.

•  Techniques:physicsandcomputationalmathematics.

•  Somemethodsareslowandonlyworkforofflineanimation.

•  Somemethodscanbemadereal-time•  Hardtocontroltheoutput

Particlesimulationsystems•  Simplestversionofphysics.•  Alargebunchofnon-interactingparticles.•  Ordinarydifferentialequation(ODE)forthetimeevaluationofapoint:

•  Forcefmightbegravityorwind•  Canmodelflowingfallofwaterparticles,orastreamofsmokeparticlesintheair

•  Typicallyeachparticleisrenderedasasemitransparentlittlebloborsurface

f =ma=m !v =m!!x p=mv

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ODEintegration•  Startingfromaninitialcondition,wecandiscretizethisODEandmarchforwardintimeusingso-calledEulersteps:

•  Stepsmustbesmall(oftenneedmanymorethan30/sec).

•  ThereisawholeliteratureofmoresophisticatedwaystosolveanODE.

xt+h = xt + vthvt+h = vt + athat+h = f (xt+h ,t + h) /m

Particlesimulationexample

TobiasPfaff,NilsThuerey,JonathanCohen,SarahTariq,andMarkusGross.2010.Scalablefluidsimulationusinganisotropicturbulenceparticles.InACMSIGGRAPHAsia2010papers(SIGGRAPHASIA'10).ACM,NewYork,NY,USA,,Article174,8pages.

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RigidBodies•  Upgradefromparticlestosolidhardfiniteobjects(dicerollingonatable)

•  Needtodealwithrotationalissues•  Withtodealwithinteraction:collisiondetection– Boundinghierarchies– Mustundointerpenetration– Musthavetheobjectbounce(thisrequireshackedphysicssincerealobjectsslightlydeformandundeform

•  Mustdealwithobjectsrestingonobjectsandnotendlesslybouncing

Cloth•  Canbemodeledasagridofparticlesconnectedbysprings

•  Canbemodeledasmeshofphysicaltriangularelements

•  Needforcestoavoidstretchingandshearingandoscillation

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ZhiliChen,RenguoFeng,andHuaminWang.2013.Modelingfrictionandaireffectsbetweenclothanddeformablebodies.ACMTrans.Graph.32,4,Article88(July2013),8pages.

Hair•  Hairmodelingisalsooftensimilarlydealtwithasamass-springmodel

AlekaMcAdams,AndrewSelle,KellyWard,EftychiosSifakis,andJosephTeran.2009.Detailpreservingcontinuumsimulationofstraighthair.InACMSIGGRAPH2009papers(SIGGRAPH'09),HuguesHoppe(Ed.).ACM,NewYork,NY,USA,,Article62,6pages.

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Deformablematerials•  Realobjectsaredeformable•  Canbemodeledasvolumetricobjects(meshof3Dtetrahedra)

ChrisWojtan,NilsThürey,MarkusGross,andGregTurk.2009.Deformingmeshesthatsplitandmerge.InACMSIGGRAPH2009papers(SIGGRAPH'09),HuguesHoppe(Ed.).ACM,NewYork,NY,USA,,Article76,10pages.

Fireandwater•  Specialphysicalequations•  Modeledwithcombinationofequations

JeffreyN.ChadwickandDougL.James.2011.Animatingfirewithsound.InACMSIGGRAPH2011papers(SIGGRAPH'11),HuguesHoppe(Ed.).ACM,NewYork,NY,USA,,Article84,8pages.

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Humanlocomotion•  Notpassiveobjects•  Muchharderthanpreviouslydiscussedphenomenon

•  Ideasareusedfromrobotics,control,andoptimization

•  Nowadaysmotioncapturedataisreliedonheavily,andpossiblyalteredorusedaspartoftherocketscience.

Humanlocomotion

JackM.Wang,DavidJ.Fleet,andAaronHertzmann.2010.Optimizingwalkingcontrollersforuncertaininputsandenvironments.InACMSIGGRAPH2010papers(SIGGRAPH'10),HuguesHoppe(Ed.).ACM,NewYork,NY,USA,,Article73,8pages.

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Announcements•  FinalExam:– Roughlyspeaking,afterthemid-termexam

•  Thanksforthissemester!

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