基于质点-弹簧模型的布料仿真研究

6640Terzopoulos[1]Carignan[2]Breen[3]EberhardtProvot[4]Choi[5](-)[6](Teng[7])-[8]-1XProvot13,+1,,,+1,[e-mail]-(710025)-RK-4-;;-;;TP23A1000-7024(2007)03-0664-04ResearchonclothmodelingsimulationbasedonmassspringmodelHUIWei-hua,GUANZheng-xi(SecondArtilleryEngineeringCollege,Xi'an710025,China)AbstractThecrucialprobleminclothsimulationbasedonphysicalmodelishowtosolvethemotiondifferentialequations.Thesimu-lationtechnologyofclothmodelingbasedonmassspringmodelispresentedcompletely,fabricmechanicsmodelsareestablishedpre-cisely,andseveralkindsofexplicitnumericalintegrationarecompareddetailedly,especially,usingRK-4methodgreatlyimprovesystem'sstability.Inthesebase,aimingatthemass-springmodelhasthesuperelasticeffectinsimulation.Comparedtothepreviousmethodsofdealingwiththisproblem,superelasticproblemisreasonablysolvedusingofdeformationconstraint.Thisclothsimulationmethodisappliedtoclothsoftware,examplesprovedthatthismethodisadvancedandpractical.Keywordsclothmodeling;physically-basedmodeling;mass-springmodel;deformationconstrain;computeranimation20072Feb.2007283Vol.28No.3ComputerEngineeringandDesign1-P(i+2,j)P(i+2,j+1)P(i+1,j)P(i,j)P(i,j+1)P(i+1,j+1)P(i,j+2)P(i+1,j+2)P(i+2,j+2)665+2,,,+2,+1,+1+1,,+13()[9]1.1.()21.2-(1)+=(1)()(2)(),=,,0,,,=,0,(2),,0,()(3(a)),=,(3),/-(3(b))(2)(3)==1,+,(4)3()(5)=1+2+3(5)123=(6)=(7),=,•,,(8),,=1+(9)--ComputeForce(){for(i=1;in;i++)//{ComputeGravity()//ComputeAirDamping()//ComputeWind()//}for(i=0;in_spring;i++)//{point1point2=1201212=12}}23/-OXZYix,y,ziii()jx,y,zjjj()(a)OXZYij1jk(b)666-=1(10)3×3()2-4Runge-Kutta2.1,+=1,,+=,+,+,+=,+,+(11)2.2+1=++1/2,*+1/2+1/2,*+1/2=+1/2,+2,(12)1*+1/2=+2,*=1*+1/2=+2**+1/2=+2(13)2+1/2()3+1/2=1+1/2+1=++1/2+1=+*+1/2(14)2.3Runge-Kutta4Runge-Kutta(15)++141,2,3,4=,(15)+1=+161+132+133+1641=,2=+12,+23=+22,+24=+32,+(16)111=1=21122=1+212=1+2132233=1+223=1+2243342=1+212=1+21544+=+61+22+23+4+=+61+22+23+42Run-ge-KuttaRK44RK443-53.14210-1-2-2-1012-2-1012-2-1012210-1-2210-1-2ImplicitEulerExplicitEulerExplicitEulerImplicitEuler(a)(b)(c)RK46670=(17)3.2()63.31%15%12121212121274-8(a)-8(b)9:[1]TeschnerM,HeidelbergerB,MüllerM,etal.Aversatileandro-bustmodelforgeometricallycomplexdeformablesolids[C].ProceedingsofComputerGraphicsInternational,2004.312-319.[2]BourguignonD,CaniMP.Controllinganisotropyinmass-springsystems[C].ComputerAnimationandSimulation,2000.113-123.[3]BridsonR,MarinoS,FedkiwR.Simulationofclothingwithfoldsandwrinkles[C].ACMSIGGRAPH/EurographicsSymposiumComputerAnimation,2003.28-36.[4]GrinspunE,HiraniAN,DesbrunM,etal.DiscreteShells[C].ProceedingsoftheACMSIGGRAPH/EurographicsSympo-siumonComputeranimation,2003.62-67.[5]Kwang-JinChoi,Hyeong-SeokKo.Stablebutresponsivecloth[C].ProceedingsofSIGGRAPH2002.604-611.[6]LIL,VolkovV.Clothanimationwithadaptivelyrefinedmeshes[C].ACSC,2005.107-114.[7]TengJG.Afinite-volumemethodfordeformationanalysisofwovenfabrics[J].InternationalJournalforNumericalMethodsinEngineering,1999,46(12):2061-2098.[8],.[J].,2001,13(10):880-885.[9],.[J].,2004,16(5):613-618.56UUC(a)(b)UUUU8(a)-(b)9v1v1nv2nv2v2tp2p17