situationsolved

Page1of4DanMorris'snoteson:EigenSkin:RealTimeLargeDeformationCharacterSkinninginHardwarePaulKry,DougJames,DineshPaiThebigpictureoWehavesome"skeleton"thatweknowhowtomovearound.
Intheirexample,it'sactuallytheskeletonofahand,butitcouldbeanysetoffixedrigidobjectsthatareattachedtoeachother.
Thewholepaperassumesthatmovingthesethingsaroundisasolvedproblem.
oWehavesome"softtissue"ontopoftheskeleton.
Weknowwhereeachvertexisatrest,butwewanttoputitatanice-lookingplaceasthebonesmovearound.
Notopologychanges,nonewverticesorremovedvertices.
SSD(skeletal-subspacedeformation)oWhat'sthesimplestpossibleapproachtomovingverticesaroundwithanunderlyingskeletonTheabsolutesimplestapproachistosaythateachvertexisjustattachedtoonebone,andwhereverthatbonemoves,thevertexmoveswithit.
Inotherwords,eachvertexstoresitspositionrelativetooneofthebonesandisrenderedinthelocalreferenceframeofthatbone.
I'llcallthis"stupidskeletaldeformation".
What'swrongwiththisTypicallytissuesactuallydeformasanunderlyingbonemovesaround,especiallyneartheintersectionoftwobones.
Thismethoddoesn'tcapturethis(verticesnevermoverelativetotheirneighbors),sotissueneverdeforms,andsometissuewouldjustpenetrateinsideneighboringtissuewhenajointmoved.
Thisisexactlythesameasusingyourfavoriterigidmeshclasstorepresentverticesandskippingthebonealtogether.
JustrotateandtranslateyourCMesh'sinsteadofyourbones.
Figure1:The"Morrisalgorithm"for"stupidskeletaldeformation.
"Eachstraightlineisabone,andeachcurveisasofttissuemesh,inwhicheachvertexis"attached"toexactlyonebone.
Notethatthesofttissuespenetrateeachother.
ThesituationwouldbeevenmessierifIdidn'thavethebigdiscontinuityinthemiddleofthe"surface".
Page2of4oWhat'sthenextstepupfromthisLet'ssayeachvertexstoresacouplepiecesofinformation…ifI'mavertex,Iknowwhichbonesmightaffectmyfinalposition,howfarIamfromeachofthosebonesatrest,andhow"important"eachboneisindecidingmyfinalposition(i.
e.
Istorea"weight"foreachbone).
WhenIgotorendermyself,Ileteachbone"vote"formycurrentposition,likethis://Mypositioninworldspacepositionp=(0,0,0);foreachbonethataffectsme{findthisbone'scurrenttransformation(positionandrotation);findmyownpositionrelativetothisboneatrest;transformthispositionintotheglobalreferenceframe;multiplythisglobalpositionbymy"weight"forthisbone;addthispositiontop;};glVertex3f(p.
x,p.
y,p.
z);This(Ithink)isthe"skeletalsubspacedeformation"algorithm(SSD)It'simportantthatverticesnearajointhaveroughlyequalweightsforbothbonestheylivenear.
Verticesinthemiddleoftheboneareprobablyaffectedonlybythatbone.
Theeffectisthatthere'snofunnyself-collision,sinceverticesnearthejointsareinterpolatedbetweenjoints.
Infact,forthispaper,theirSSDweightsarejustderivedbasedondistancetoabone…ifI'mclosetoaboneinanearest-pointsense,itgetsahighweight.
Asbonesgetfartheraway,theygetlowerweights.
Abovesomethresholddistance,abonedoesn'taffectmeatall.
oSSDisgoodenoughforalotofapplications.
It'seasytoimplementandavoidscertainawkwardself-collisions.
Page3of4oAnothernicepropertyofSSDisthattheonlythingsIhavetodoonlineforeachvertexareadditionsandmultiplicationsofsomeknownconstants.
Theonlythingsthatchangefromvertextovertexarethevertexpositionandtheweight,whichmakesthisreallyeasytodoinavertexshader(Icanfeedtheweightinatextureorwhatever).
Iputtherelevantbonepositionsinglobalmatrices,andsendawholebunchofverticesdownthepipe.
EigenskinoButtheauthorsarenothappywithSSD…ithasnophysicalbasisandgivesstrange"bulging"deformationsnearjoints.
oSoI'mgoingtoproposeanewapproach,called"theMorrisalgorithmforstupidvertexsuperposition".
ForgetSSDentirely,andtrytodothis:Runasuper-fancyFEMsimulationofyourskeletonoffline,andtrackthepositionofeachvertexinawholebunchofdifferenthandpositions.
Trytolearnsomesetofweightsateachvertexthattellsyouthepositionofthatvertexasalinearfunctionofeverybonepositionandrotation.
Whenyourenderinreal-time,justmultiplytheweightsbythebonepositions/rotationsandvoila,youhavevertexpositions.
oConceptually,thisisokay.
Inpractice,it'sjusttoomuchinformationtorepresentwithlinearsuperpositionandsimpleweights,andthelearningproblemisjusttoohard.
oInstead,theauthorsrealizethatSSDis"prettyclose".
Soinsteadoftryingtogoofflineandbuildalinearmapfrombonepositiontovertexposition,theyjustplantorunSSDonline,anduseafancyofflinesimulatortobuildalinearmapfrombonepositiontoSSDerror.
Soooooooclever.
oThenwhenwerunitonline,wejusthaveafewmoremultiplicationstodo,butwestillbasicallyhaveasimplelinearfunctionwithlimitedper-vertexdatathatwecanruninavertexshaderprogram.
oInfact,usingofflinesimulationtolearnSSDerrorinsteadofabsolutepositionisthekeyinsightinthispaper.
ThelearningitselfisbasicallyjustSVD:Foreachjoint,collectabunchofsample"poses"(boneconfigurations)andalltheassociatedvertexpositionsfromyourfancyFEMprogram(theycleverlyonlyusetheverticesthatareaffectednoticeablybymovingagivenjoint).
RemembertowritevertexpositionsasoffsetsfromwhatyouwouldgetifyouusedSSD.
PutallthevertexpositionsforeachposeinabigmatrixTaketheSVDofthatmatrix.
Nowyouhaveasetof"eigendisplacements"(fundamentaldisplacementscausedbymovingthisjoint)and–foreachPage4of4vertex–itsexactdisplacementineachposeintermsoftheseeigendisplacements.
Again,rememberthatdisplacementsareallrelativetotheSSD-basedpositions.
AswealwaysdowithSVD,throwoutthelowsingularvaluesandalltheirassociateddisplacements.
Weusuallydoittosavespace,butherewedoitbecausewehavealimitednumberofmultiplicationswecanperforminthegraphicshardwarethatwe'reultimatelygoingtouseforrendering.
Afootnote…notethatIsay"foreachjoint"atthebeginningofthisbulletedlist.
Theychoosetorepresenteachvertex'sdisplacementduetoeachjointindependently,sothismethodwouldn'tworkiftherewerecomplexornon-lineareffectsinvolvingmultiplejoints.
oWhenwerendereachvertex,we'llloaduptheeigendisplacementbasis(whichwegotfromourSVD)forthatvertexandthecurrentboneconfigurationforrelevantbones,andletthehardwaredothelinearsuperposition.
Thenwe'llrunSSDandaddtheresulttowhatwegotfromoureigenstuff.
oOneinterestingpointcomesupthat'srelatedspecificallytotheimplementationingraphicshardware.
Foreachvertex,Icanonlyfit64floats(atthetime)ofper-vertexdata,plussomeglobaldatathatdoesn'tchangefromvertextovertex(likematrixtransformations).
TheyconcludethatIcanfitroughly10eigendisplacementspervertex.
SohowdoIallocatethatspaceIfavertexwasaffectedbyjustonesinglebone,Iwoulduseall10spotstostoredisplacementsrelatedtothatbone(meaningIcouldusethefirst10singularvaluesfrommySVD).
Ifavertexisaffectedbytwobones,doItakefivesingularvalues(eigendisplacements)fromeachboneIcould,orIcoulddofourandsix,basedonthemagnitudeoftherelevantdisplacementsorsingularvalues.
Theydon'treallyspeculateonthatmuch,buttheydoimplyintheirconclusionthattheyendupusingjustoneortwosingularvaluesfromeachjointforagivenvertexinsomecases(probablybecausethatvertexwasaffectedbyfiveortendifferentjoints).