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

25 8 2013 8 Vol25No8 JournalofComputer-AidedDesign & ComputerGraphics Aug2013 1) 1)* 2) 3) 2) 1) ( 100190) 2) ( 100190) 3) ( 100190) (xpzhang@nlpriaaccn) SPH TP391 InteractiveSimulationforWaterDropEffects XuShibiao 1) ZhangXiaopeng 1) * ChenYanyun 2) Yu Haitao 3) and WuEnhua 2) 1) (NationalLaboratoryof Patern RecognitionInstituteof AutomationChinese Academyof SciencesBeijing 100190) 2) (State Key Laboratoryof ComputerScienceInstituteof SoftwareChinese Academyof SciencesBeijing 100190) 3) (Science ArtCentreInstituteof AutomationChinese Academyof SciencesBeijing 100190) 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 2012-08-27 2012-11-06 (608330076090207861172104) (4112061) (1986 ) (1963 ) (1971 ) (1981 ) (1947 ) CCF

1160 25 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]

8 1161 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 23 21 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 [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)+ 31 1 2

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 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

1164 25 42 4a 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 133 10000 100 Step2 (5)(6) 1 2 1 2 IntelCorei728GHzCPU 4GB NVIDA GTX460 1GB 700MHz 10000 80 Kinect 5000 30 Step1 SPH 42 Step3 2 2 Step4 (3) 51 5 Step5 Step3~Step4 1 1= 2+ 2 Step6 (4) Step7 Step5~Step6 1 100?s = 1+ 1

8 1165 6 52 1 7 80?s 7 53 Kinect Kinect Kinect

1166 25 2 Kinect OpenNISDK (OpenNI OpenNIAPI 8 Kinect30?s ) 5000 Kinect 30?s 8 54 9c 9a 7b7c 9b 7d7e [20] 9d 1 [20] 80?s 30?s 9

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