GPU [16] ( ) GPU [17] GPU GPU Stam [1] 2 [2] Wang [18] Thürey [19] Zhang [20] 2 (smoothed Kim [21] particlehydrodynamicssph) [3] SPH [4] SPH M

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1 Vol25No8 JournalofComputer-AidedDesign & ComputerGraphics Aug2013 1) 1)* 2) 3) 2) 1) ( ) 2) ( ) 3) ( ) (xpzhang@nlpriaaccn) SPH TP391 InteractiveSimulationforWaterDropEffects XuShibiao 1) ZhangXiaopeng 1) * ChenYanyun 2) Yu Haitao 3) and WuEnhua 2) 1) (NationalLaboratoryof Patern RecognitionInstituteof AutomationChinese Academyof SciencesBeijing ) 2) (State Key Laboratoryof ComputerScienceInstituteof SoftwareChinese Academyof SciencesBeijing ) 3) (Science ArtCentreInstituteof AutomationChinese Academyof SciencesBeijing ) AbstractInordertoefectivelysimulatethephenomenonofdynamicwaterdrops withgravityand otherexternalforcesthispaperpresentsaninteractivesimulation methodfor waterdropefects FirstlyanaccurateSPH modelistakentosimulatesmal-scalewaterdropphenomenonthemethod includesaccuratepressurestrengthcalculationandartificialvelocityfieldcorrectiontoensurethe accuracystabilityandconvergenceoffluidequationssecondlyasurfacetensionmodelispresented basedonmeancurvatureandfluiddensityfieldforeficientlysimulatingthesurfacetensionofwater dropsfinalyasimplifiedray-tracing methodbasedonanew shader modelispresentedforthe waterdroprenderingtheray-tracing methodincludessimplifiedfluiddensitydistributionfunction fluidsurfacejudgmentbasedondichotomyandfresnelcalculationforovercomingtheproblemsinthe traditionalfluidrenderingmethodwithlitleconsiderationofcamerasandintensivecalculationsthe resultsshowthatthenewalgorithmisefectiveandeficientsuitabletothesimulationofbothwater bodyandsmal-scalewaterdrops Keywordswaterdropinteractiveray-tracingsurfacetension ( ) ( ) (1986 ) (1963 ) (1971 ) (1981 ) (1947 ) CCF

2 GPU [16] ( ) GPU [17] GPU GPU Stam [1] 2 [2] Wang [18] Thürey [19] Zhang [20] 2 (smoothed Kim [21] particlehydrodynamicssph) [3] SPH [4] SPH MarchingCubes [5-6] Desbrun [11] SPH SPH Müler [4] SPH SPH SPH SPH Sussman [22] 1 MarchingCubes [5-6] Foster [7] [23] MarchingCubes [8-10] [11-12] [13-15] [24]

3 MarchingCubes m A i = A j j W (r i -r j h) j i ρj Wojtan [25] A i h W 2 W (-r)=w (r) W (r)dr=1 Kruger [26] Müler [4] SPH Step1 ρ i = m jw poly6 (ri -r j h) (2) j i Step2 Fi pressure pi +pj =- m ( j Wspiky ri -r j h) j i p = K( ρ -ρ ) 0 Step3 dv dt =Fexternal +F pressure +F viscosity =g- p 2 ρ +μ v ρ (1) 2m j (v j -v i ) v ρ Δv i = j i ρ i + W ρj p μ ε [01] (1) XSPH SPH F viscosity i SPH 2ρj =μ j i m j v j -vi ρj 2 Wviscosity ( ri -r j h) SPH 2 22 [27] SPH [28-29] Monaghan [30] (correctedand dρ dt =- ρ v smoothedparticlehydrodynamicsxsph) dv i dt =vi +εδvi

1162 25 Kruger [26] 075 133 3 n i 133 n t 1 <1 n t 2 1 3 31 SPH 21 SPH SPH 24 c=cos(θi) ni n t =-(I n) ni n t 2 n( ) t [ 1-R(0 )] (1-cosθi) 5 (4) [32] 1 n 1 i 075 n t 2 n 2 i ΔP n t n i ( ) Mathias

4 Kruger [26] n i 133 n t 1 <1 n t SPH 21 SPH SPH 24 c=cos(θi) ni n t =-(I n) ni n t 2 n( ) t [ 1-R(0 )] (1-cosθi) 5 (4) [32] 1 n 1 i 075 n t 2 n 2 i ΔP n t n i ( ) Mathias [31] F pressure pi i =- m j + pj W j i ρ 2 i ρ 2 spiky (r i -r j h) j XSPH F = R(θi)= 1 2 c(g+c)- g-c ( ) n( ) ni 2 2 烄熿燄烌 SPH t 1+ 2 g+ c 烅 c(g-c)+ n( ) ni 2 烍烆燀 t 燅烎 (3) SPH XSPH Fi xsph W poly6 v g= 1+c 2 - 槡 ni = 2m j -v i j j i ρ i + ρj Mathias (3) SPH 32 R(θi) Ra (θi)= R(0)

8 1163 SPH Step4 SPH Step5 SPH 2 Step6 κi=ρ i ρ i ρ i (2) 4 κ - κi +κj i = m j W poly6 (r i -r j h) j i 2ρj F surface i =σκ - i ρ i σ discard (2) 33 GPU

5 SPH Step4 SPH Step5 SPH 2 Step6 κi=ρ i ρ i ρ i (2) 4 κ - κi +κj i = m j W poly6 (r i -r j h) j i 2ρj F surface i =σκ - i ρ i σ discard (2) 33 GPU NVIDIA CUDA SPH 41 GPU (2) 3a CUDA Particles Demo [33] GPU 3b Step1 Step2 Step3 Step4 Step5 GPU [34] 3c I O Step1 A Step2 SPH Step3 SPH ray-casting A I C 3

6 a 4 1 1) r=a+b =ai+bn (5) 5 a=1b=2(n I) 4b 2) t=a+b =ai-bn (6) a=sinθt?sinθi=n i?n t b=1-x-yx=cosθi sinθt?sinθi=-(n I)n i?n t y= -n - 槡 1-sin 2 DirectXCUDA HLSL θt = GPU 1- 槡 1-(n i?n t ) 2 (1-(n I) 2 ) 4c 1 1 GPU 075??s Step2 (5)(6) IntelCorei728GHzCPU 4GB NVIDA GTX460 1GB 700MHz Kinect Step1 SPH 42 Step3 2 2 Step4 (3) 51 5 Step5 Step3~Step4 1 1= 2+ 2 Step6 (4) Step7 Step5~Step ?s = 1+ 1

7 ?s 7 53 Kinect Kinect Kinect

8 Kinect OpenNISDK (OpenNI OpenNIAPI 8 Kinect30?s ) 5000 Kinect 30?s c 9a 7b7c 9b 7d7e [20] 9d 1 [20] 80?s 30?s 9

9 ) New YorkACM Press SPH SPH 2) ) SPH YorkACM Press ) 483 New YorkASMEPress ( ) ( ) (References) 2589) [3]Stam J Fiume E Depicting fire and other gaseous phenomenausingdifusionprocesses[c]?computergraphics ProceedingsAnnualConferenceSeriesACM SIGGRAPH [4]Müler M Charypar D Gross M Particle-based fluid simulationforinteractiveapplications[c]?proceedingsofthe ACM SIGGRAPH?Eurographics Symposium on Computer AnimationAire-la-VileEurographics Association Press [5]Carlson MMuchaPJvan Horn IR BetalMelting andflowing [C]?Proceedings ofthe ACM SIGGRAPH? Eurographics Symposium on Computer Animation New [6]GénevauxOHabibiADischlerJM Simulatingfluid-solid interaction[c]?proceedingsofgraphicsinterfacehalifax Canadian Human-Computer CommunicationsSociety Press ( [J] (12)2581- [7]FosterN Metaxas DRealisticanimation ofliquids [J] GraphicalModelsandImageProcessing199658(5)471- [8]ZhouShizheManJiajuRealtimefluidsimulationbasedon multigridmethod[j]journalofcomputer-aideddesign & ComputerGraphics200719(7) (inchinese) ( [J] (7) ) [9]EnrightDNguyen DGibou FetalUsingtheparticle levelset method and a second order accurate pressure boundaryconditionforfreesurfaceflows[c]?proceedingsof the4th ASME-JSME JointFluidsEngineering Conference [10]LosassoFGibouFFedkiw RSimulatingwaterandsmoke with an octree datastructure [J]ACM Transactions on Graphics200423(3) [11]Desbrun M Gascuel M P Smoothed particlesa new approach for animating highly deformable bodies [C]? Proceedings of the Eurographics Workshop on Computer AnimationandSimulationBerlinSpringer [12]PremozeSTasdizen TBiglerJetalParticles-based simulationoffluids[j]computergraphicsforum (3) [1]StamJStablefluids[C]?ComputerGraphicsProceedings AnnualConferenceSeriesACM SIGGRAPHNew York ACM Press [2]Liu YouquanLiu XuehuiZhu HongbinetalPhysicaly basedfluidsimulationincomputeranimation [J]Journalof Computer-Aided Design & Computer Graphics (12) (inchinese) [13] Wojtan CThürey N Gross MetalPhysics-inspired topology changes for thin fluid features [J] ACM TransactionsonGraphics201029(4)ArticleNo50 [14]LosassoFTaltonJKwatra NetalTwo-waycoupled SPH and particle level set fluid simulation [J]IEEE TransactionsonVisualizationandComputerGraphics (4)

10 [15]Xu S B Mei X Dong W MetalInteractive visual simulationofdynamicinkdifusionefects[c]?proceedings ofthe 10th International Conference on Virtual Reality Continuum and Its Applicationsin Industry New York ACM Press ) [18] WangH MMilerGTurkGSolvinggeneralshalow wave equations on surface [C]?Proceedings of the ACM SIGGRAPH?Eurographics Symposium on Computer AnimationAire-la-VileEurographics Association Press [19]ThüreyNWojtanCGrossMetalA multiscaleapproach tomesh-basedsurfacetensionflows[j]acm Transactions ongraphics201029(4)articleno48 [20]ZhangY ZWang H MWangS AetalA deformable surfacemodelforreal-timewaterdropanimation [J]IEEE TransactionsonVisualizationandComputerGraphics (8) [21]Kim BMulti-phasefluidsimulationsusingregionallevelsets [J]ACM TransactionsonGraphics201029(6)Article No175 [16]LiuYouquanLiu XuehuiWu EnhuaReal-time3Dfluid [J]Monthly Noticesofthe Royal AstronomicalSociety simulationon GPU withcomplexobstacles [J]Journalof (1) Software200617(3) (inchinese) [25] WojtanCMüler-Fischer MBrochu TLiquidsimulation ( GPU with mesh-basedsurfacetracking [C]?Computer Graphics [J] (3) ) ProceedingsAnnualConferenceSeriesACM SIGGRAPH [17]Chen Xi Wang Zhangye HeJianetalAnintegrated New YorkACM Press2011ArticleNo8 algorithmofreal-timefluidsimulationongpu [J]Journalof [26]Kruger J Westermann R Acceleration techniques for Computer-AidedDesign & ComputerGraphics201022(3) GPU-basedvolumerendering [C]?Proceedingsofthe14th (inchinese) IEEE Visualization Washington D C IEEE Computer ( GPU SocietyPress2003Page38 [J] (3)396- [27]Liu DaozhiComputationalfluid dynamics [M]Beijing [22]Sussman MOhta M A stableand eficient methodfor treatingsurfacetensioninincompressibletwo-phaseflow [J] SIAMJournalonScientificComputing200931(4) [23]FosterNFedkiw RPracticalanimationofliquids [C]? ComputerGraphicsProceedingsAnnualConferenceSeries ACM SIGGRAPHNew YorkACM Press [24]Gingold R A Monaghan J J Smoothed particles hydrodynamics theoryandapplicationtonon-sphericalstars BeihangUniversityPress1989 (inchinese) ( [M] 1989) [28]Monaghan J J An introduction to SPH [J] Computer PhysicsCommunications198848(1)89-96 [29]MonaghanJJLatanzioJCArefinedparticlemethodfor astrophysicalproblems [J] Astronomy and Astrophysics (1) [30]MonaghanJJSimulatingfreesurfaceflowswithSPH [J] JournalofComputationalPhysics (2) [31]Mathias W Fresnel reflection technical report [R] ShanghaiNVIDIA Corporation2002 [32]Enright D Marschner S Fedkiw R Animation and renderingofcomplexwatersurfaces[j]acm Transactions ongraphics200221(3) [33]GreenSParticlesimulation using CUDA [R]Shanghai NVIDIA Corporation2010 [34]MilerGPearceAGlobulardynamicsaconnectedparticle system for animating viscous fluids [J] Computers and Graphics198913(3)

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