Cloth Simulation. Simulation in Computer Graphics University of Freiburg WS 05/06

Transcription

1 Clot Smlato Smlato Comptr Grapcs Urst of Frbrg WS 05/06 D. Baraff A. Wtk. Larg stps clot smlato. Sggrap 98 pp

2 Ackoldgmt Ts sld st s basd o t follog sorcs: D. Baraff A. Wtk. Larg stps clot smlato. Sggrap 98 pp D. Macr. Ral-tm clot. Gam dlopr cofrc 000. D. Prtcard. Implmtg Baraff ad Wtk s clot smlato. ttp://frclot.gmat.ca/ 003. sorcforg. frclot proct. ttp://frclot.gmat.ca/ R. Brdso. Comptatoal aspcts of damc srfacs. PD tss Staford Urst 003.

3 Otl gomtr strtc forcs sar forcs bd forcs damc smlato stra lmtg altrat bd forcs dmostratos dscsso

4 Gomtr traglatd ms of mass pots to rprstatos of pot postos 3 orld coordats R pla coordats R orld coordats ar drg t smlato pla coordats rprst tal dformd gomtr maps from pla to orld coordats costat plaar paramtrato tm-arg orld coordats

5 Strtcg rprstd t partal drats matral s strtcd / comprssd drcto ff drcto ff Eampl.

6 Strtc of a Tragl mass pots of a tragl k dgs orld spac - k - dgs t pla s appromatd as lar fcto or a tragl ad ar costat or a tragl

7 Strtc of a Tragl solg for ad ar ot trstd st s ad to rprst ad strtc dos ot ork t dgratd tragls

8 Strtc Codto masrs strtc for a tragl ad drcto qals ro ff t tragl s strtcd / comprssd codto s gtd t t tal tragl ara A

9 Strtc Erg ad Forcs strtc rg of a tragl sr-dfd k st E st >0 f t tragl s strtcd or comprssd strtc forcs F at all mass pots of a tragl forcs ar gat gradt of t rg trms of mass pot postos

10 Strtc Forc strtc forc at pot

11 st st st st A A k C C F rrtg t drats of C trms of Strtc Forc

12 drats of ad t rspct to k 3 3 I Drats of 3 3 I 3 3 k I 3 3 I 3 3 I 3 3 k I

13 Strtc Smmar strtc s rprstd t partal drats of a psdo-mappg fcto c corts from tal plaar coordats to orld coordats strtc s cosdrd dffrt drctos strtc codto s statd pr tragl strtc rg ad strtc forcs ar drd from t cod. strtc forcs for mass pots of a tragl ar comptd sg tr postos orld spac ad tr orgal postos plaar coordats

14 Sarg sar of a tragl s masrd b cosdrg rst stat ts prodct s ro bot ctors ar ortogoal f sar occrs t scalar codto fcto C s qals t cos of t agl bt ad gtd b t tal tragl ara A C s k A T T ad ar ot ormald assmg tr magtds do ot cag sgfcatl d to strtc forcs

15 s s s s s s s s s s s C A k C C C C k C C k F forc s drd from sar rg sr-dfd k s forcs at tr tragl rtcs ar comptd basd o tr postos bot obct rprstatos Sar Forc

16 bd s masrd for pars of adact tragls t o commo dg Bd k k k

17 Bd Codto bd codto s t agl bt a tragl par Cb k θ agl ca b comptd sg sθ cosθ aga ormalato s glctd assmg t magtds do ot cag sgfcatl

18 Bd Forcs forc s drd from bd rg t sr-dfd k b C F b k b C b o gtg t tragl ara C b k b C C mplctl cosdrd b sg ormald ctors. Hor ormald ctors ar sd. b b b C b

19 to compt bot rlatos for t agl ar sd Bd Forcs - Drats C b s cos θ θ θ s θ θ cos s θ θ θ cos θ θ d to sglarts

20 Bd Forcs - Drats ~ ~ ~

21 drats of Bd Forcs - Drats 3 3 I 3 3 I

22 Bd Forcs - Drats [ ] drats of

23 drats of Bd Forcs - Drats k k k

24 drats of t dot ad t ctor prodct Bd Forcs Last Drats + } { k +

25 Smlato Loop talato grato of t tal plaar tragl ms dfto of ad coordats for all rtcs dfto of t tal loct for all rtcs dfto of mass for all rtcs dfto of k st k s for all tragls dfto of k b for all tragl pars forcs loop tragls: compt F st F s for t tr rtcs loop pars of tragls: compt F b for t for rtcs loop rtcs: compt tral forc appl or faort mrcal tgrato scm

26 Eprmtal Rslts Prtcard k st k s k b tm stp 0.0s mplct tgrato mass pots comptg tm 45 s pr smlato stp Ptm 4 3GH Baraff Wtk 4500 mass pots 0 s pr smlato stp bot mplmtatos s mplct tgrato ad cogat gradts t a ko mbr of tratos

27 Stra Lmtg [Proot Brdso] dstac dato of to adact pots lmtd to 0% of t tal dstac largr datos ar prtd b smmtrcall rplacg bot pots rald b loopg trog all pot pars corgt f prformd tratl rplacg ca b trprtd as t rslt of a tral forc global damc baor lar aglar momtm of t modl s ot flcd corrcto tm

28 Stra Lmtg [Brdso Fdk] adstmt of locts stad of postos t smlato loop prdct locts f postos basd o t prdctd locts cd t stra lmt corrct locts accordgl compt postos comptd postos basd o corrctd locts flfll t stra lmt smmtrc cags of locts mata aglar ad lar momtm of t sstm cosstt postos ad locts

29 Altrat Bd Forcs [Brdso Fdk] drato of forcs basd o t bdg agl bt ad forcs sold ot cas rgdbod moto of t for pots ad sold ot cas -pla dformatos compar df. of tral forcs k k ar forc drctos at k as to b paralll to k as to b paralll to a to b t spa of ad k 0 o cag of lar loct k as to b ortogoal to rgd bod rotato

30 Forc Drctos k k + k k

31 Forc Magtd F { k} b kb s + k b s sr-dfd θ / { k} addtoal rstc gtg t tragl aras srs dpdc from msg s s st smpl to compt θ / ± / s

32 Comparso [Baraff Wtk] - [Brdso Fdk] Baraff Wtk df codtos prcpl of rg-dr forcs srs tat rsltg forcs ar tral forcs lgat bt ot stragt-forard to mplmt Brdso Fdk df forcs forcs ar dsgd to rprst rsstac to bdg forcs ar dsgd to b tral forcs lss lgat bt practcal

33 Rlatd Approacs lk lst at t Urst Collg Lodo ttp://.cs.cl.ac.k/ rsarc/r/procts/3dctr/ clot_smlato_lks.tm Volo Talma Ebrardt Wbr Strassr Brdso Fdk Adrso Co Ko

34 Commrcal Clot Smlato.sfl.b Or clot smlator mplmts a compltl orgal tcq. sfl. sfl

35 Bod Skrts - Op Problms ralstc matrals ar rsstacs to sar strtc bdg a approprat paramtrato? stabl collso rspos cas of collsos ad slfcollsos tgt-fttg clot sarp dgs lard matral rkls m