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COMPUTERANIMATIONANDVIRTUALWORLDSComp.
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VirtualWorlds2007;18:259–269PublishedonlineinWileyInterScience(www.
interscience.
wiley.
com)DOI:10.
1002/cav.
190PhysicallybasedanimationofsandstormByShiguangLiu,ZhangyeWang*,ZhengGong,LeiHuangandQunshengPengThispaperdescribesaphysicallybasedmethodformodelingandanimatingsandstorm,atypeofdisastrousnaturalphenomenon.
Themethodadoptsarelativelystableincompressiblemultipleuidmodeltosimulatethemotionofair,sand,anddustparticles.
ThewindeldofsandstormisestablishedbasedonReynold-averageNavier-Stokesequations.
Thesandanddustparticleowisthereforecomputedtakinginteractionamongthewind,sand,anddustparticlesintoaccount.
Toacceleratethemodelingprocessofadynamicsandstormscene,aspecialMulti-FluidSolverisdesignedandimplementedonGPU.
Variousilluminationeffectsofsandstormscenescanbesimulatedbyspectralsamplingscatteringcalculation.
Animationsofrealisticsandstormsoccurringindesertandurbanareasbasedonourmodelaredemonstrated.
Comparedwiththerealsandstormphotos,oursimulatedresultsaresatisfactory.
Copyright2007JohnWiley&Sons,Ltd.
Received:15May2007;Accepted:15May2007KEYWORDS:sandstorm;naturalphenomenasimulation;physicallybasedanimation;Multi-FluidSolver;GPUIntroductionAlthoughmanyworkswereproposedforsimulatingnaturalscenesinthepasttwodecades,relativelittleattentionwaspaidtomodelingandrenderingofdisastrousnaturalphenomenasuchashurricane,tornado,sandstorm,debrisow,etc.
Onereasonmaybethecomplexphysicalmechanismsbehindthesenaturaldisastrousphenomena.
Recently,sandstorm,atypeofdisastrousphenomenarelatedtodesert,attractsmuchattentionofthepeoplearoundtheworld.
Realisticsimulationofdynamicsandstormscenecanbefoundapplicationsinmanydomains.
Forexample,movieandTVplotsoftenincludethedesertscene.
DesertareasarealsothefavoritesitesformanyPCgameasbattlegrounds.
Ecologistscanevaluatetheecologicaldisasterofsandstormbydynamicsimulation.
Mayorsmayfocusonthetrafcjamsduetothelowvisibilitycausedbyheavysandstorm.
Sandanddustparticlesmaycauseseriousrespiratoryillnessforpeoplewhoinhalethem.
Weproposeafast,physicallybased,andeasilyimplementedmethodformodelingandanimatingrealisticsandstormscenes.
*Correspondenceto:Z.
Wang,StateKeyLabofCADCG,ZhejiangUniversity,Hangzhou310027,P.
R.
China.
E-mail:zywang@cad.
zju.
edu.
cnSandstormisaverystrongwindstormwhichfrequentlyhappensinthedesertanditsneighboringarea.
Itcancarryhugeamountofsandanddustintheatmosphere.
Thiswindisusuallycausedbyconvectioncurrentswhicharecreatedbyintenseheatingoftheground.
Airisunstablewhenheatedandthisinstabilitywillcausethemixtureofhigherwindsinthetropospherewithwindsintheloweratmosphere,incurringstrongsurfacewinds.
Therearemanyresearchworksaboutsimulationofsandstormintheeldofphysicsandmeteorology,however,theseworksmainlyfocusonprecisenumericalanalysis,andaretoocomplextobeusedforanimation.
Untilnow,littleworkhasbeenreportedaboutrealisticmodelingandrenderingofsandstorminComputerGraphics.
Inthispaper,weproposeaphysicallybasedmethodformodelingandanimatingsandstorm.
First,weestablishtheunstablewindeldofsandstormbasedonReynold-averageNavier-Stokesequations.
Themotionofsandanddustparticleisregardedasthecontinuousowsandtheycanbeexpressedbythenon-viscosityuidmodeltakingtheinteractionamongthemintoaccount.
Then,weproposeaGPU-basedMulti-FluidSolverfordynamicsandstormscene.
Thevarietyofilluminationeffectofsandstormscenesissimulatedbyspectralsamplingofthescatteringlight.
Finally,Copyright2007JohnWiley&Sons,Ltd.
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accordingtothestatisticaldistributionofthesizeofsandanddustparticles,fantasticilluminationeffectsofsandstormindifferentareasandatdifferentstagesarerendered.
Therestofthispaperisorganizedasfollows.
TheSectionRelatedWorkgivesabriefsurveyofrelatedworks.
InSectionModelingoftheSandstormweproposeaphysicallybasedmodelofsandstorm.
SectionRenderingofSandstormScenediscussestherenderingmethodsofsandstorm.
ThisisfollowedbyResultsandDiscussionSection.
ConclusionsandFutureWorksaregivenatlast.
RelatedWorkAsasevereglobalnaturaldisaster,sandstormscauseincredibledamageoffacilitieseveryyearintheworld.
Ithasbeenthehotspotinmanyeldsespeciallyforphysicsandmeteorology,etc.
1–4Josephetal.
studiedtherelationshipbetweentheweatherconditionsandvelocityofsandstorm.
5Later,moreandmoreresearchersbegantosimulatethewind-sandmovementusingthemethodofnumericalanalysis.
Alltheaboveworksfocusonstudyingthemotionofsandstormbyexperimentaldataornumericalanalysismethod.
Astheyaimatcalculatingthemovementofsandstormaspreciseaspossible,thesemodelsaretoocomplicatedtobevisualizedinpracticalapplication.
Tosimulatethesandstormscenesrealisticallyandefciently,anapproximatephysicallybasedsandstormmodelshouldbeputforward.
Forsimulationofuid-likenaturalphenomenasuchassmoke,cloud,volcaniccloud,etc.
,mostworksadoptuidmodels.
6–8Multi-uidmodelswerealsoproposedaccountingforgas–liquiduid,gas–gasuid,etc.
Hongsolvedthemultiphaseowthroughthebubblemotioninliquid.
9Andthevolumeofuid(VOF)methodwashiredtotrackthefreesurface,theminimumstresssurfacetensionmethodwasusedtocalculatethesurfacetensiondirectlyfromthematerialeld.
Premozesimulatedthemulti-uidowbasedonmovingparticlesemi-implicit(MPS)withoutreactions.
10Infact,exceptforthesimplemixingofdifferentmaterials,thechemicalreactionmayexist.
Combustionisanexample.
Nguyenetal.
11consideredthegaswaspremixedandthereactiononlyhappenedattheinterfaceofthebluecoretogeneratehotgaseousproducts.
Ihmsimulatedmoregeneralgaschemicalreactions.
Accordingtothechemicalkinetics,theyusedthereactionprocesstodirectlyupdatethetemperaturesofsubstancesandthedivergencecontrolfunction.
12Byextendingtheparticlelevelsetmethod,Losassoetal.
13simulatedinteractionsamongmultipleliquids.
Liuetal.
14simulatedtornadoscenewithaTwo-Fluidmodel.
Zhuetal.
15proposedaTwo-FluidLatticeBoltzmannmodel.
Withthismodel,theycansimulatemisciblebinarymixtureslikepouringhoneyintowater,etc.
Fanetal.
16simulatedmultiphaseowoncurvedsurfacesusingamethodofadaptedunstructuredLBM.
Zhaoetal.
17simulatedthephenomenaofmeltingandowinginmultiphaseenvironment.
Forthegas-solidow,volcaniccloudsweremodeledbyMizunoetal.
Theyassumedthattheowwascomposedoftwotypesofuids:magmaandentrainedgas,andbothwereconveyedbythevelocityeld.
18Explosioncanberegardedasgas-solidorgas-liquidow.
Feldmanetal.
19suggestedthatexplosionwascomposedofsuspendedparticlesandentrainedgas.
Toaccountfortheinteractionsbetweentheparticlesandthegasduringexplosion,theyenforcedthedragforceoneachparticlefromthevelocitydifferenceandtheoppositeforcewasexertedontheuidcells.
Theyalsoemployedparticlesystemwhichincludedhundredsofthousandsparticlesformodelingthemovementofexplosionparticles.
However,inthecaseofsandstorm,airow(windeld),andsandparticlearenotonlyconveyedbythevelocityeld.
Theinteractionbetweensandparticlesandtheairowisalsoanimportantimpetus.
Furthermore,tomodelthedynamicsandstormscene,agreatnumberofsandanddustparticlesshouldbetakenintoaccount.
Soitwouldbequitedifculttosimulatethesceneatfastrenderingratebyparticlesystems.
Apparentlyanapproximatephysicallybasedsandstormmodelaswellasanefcientcalculatingsolverisindemand.
Asthemulti-phaseuidsaremorecomplexthanthesingleuidowduetothedifferentpropertiesofcomponentsandtheinteractionsamongthem,realisticmulti-uidsimulationisachallengetaskforcomputergraphicsresearchers.
Realisticsimulationofsandstormalsoincludesmodelingofsandparticle,renderingofdesertscene,etc.
Belletal.
20proposedamethodofmodelinggranularmaterialssuchassandandgrains.
Theyrepresentedgranularmaterialbyalargecollectionofnon-sphericalparticleswhichmightbeinpersistentcontact.
Thismethodcanbeintegratedtosimulatehighlydynamicphenomenasuchassplashingandavalanchesefciently.
Butasthenumberofparticlesisnotlargeenough,therenderingeffectofthesceneneedtobeimproved.
OnoueandNishita21proposedamethodformodelingandrenderingrealisticdesertscenesincludesanddunesandwindripples.
Theyrenderedtheduneswiththewind-ripplesbybump-mappingusingLevelofDetail(LOD).
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22Nevertheless,theseworksmainlydealwiththestaticdesertandfailtosimulatedynamicsandstorm.
Inthispaper,wepresentanewmethodtosimulatethedynamicsandstormscene.
Belowwewilldescribeitindetail.
ModelingoftheSandstormWeconsidersandstormasamulti-uidcomposedofwind,sand,andsmalldustparticleows.
Belowwewilldiscussthemodelofwindelds,sand,anddustparticleow,respectively.
WindFieldForthestablenear-surfaceairow,wecanestablishitswindeldbasedonclassicalNavier-Stokesequations.
Butsandstormisusuallycausedbyunstableairow,itisnotsuitabletobemodeledwithclassicalNavier-Stokesequations.
Consideringtheeffectsoftheatmosphericturbulence,weestablishthewindeldbyReynold-averageNavier-Stokesequationwhichisexpressedas:ρut=ρ(u·)up+ν2u+·τ+f(1)whereuisthewindvelocity,ρisdensity,pispressure,νdenotesviscosityoftheair,τdenotesReynoldshearstresswhichreectstheunstabilitybyatmosphericturbulence,fdenotesanyexternalforcesactingontheairow.
Theexternalforceconsistsofvorticityconnement,interactionswithsandparticles.
ThersttermisdenedinReference[23].
WewilldescribethesecondterminSubsectionInteractionAmongWind,Sand,andDustParticleFlow.
TheReynoldshearstresscanbeexpressedasthefollowing:τ=ρ|dudy|y2c2k(2)whereyisthedistancefromthesurface,ckistheVonKarmanconstantanditsvalueis0.
4.
ByReynoldshearstress,wecanmodelthevorticityaroundeachsandparticle(Figure1),togenerateamorerealisticsimulationofairowforsandstormscene.
Suppose,sandanddustparticlesarenotbrokenormergedinsandstorm,theairowcanbeconsideredasFigure1.
Thevelocitydistributionaroundasandparticle,(a)notconsideringReynoldshearstress,(b)consideringReynoldshearstress.
incompressibleuid,thatis,·u=0(3)SandandDustParticleFlowModelFordifferenttypesofsandstorm,theratiosofsandparticle(oflargesize)anddustparticle(ofsmallsize)aredifferent.
Sandanddustparticlesarediscretelydistributedinsandstorm.
Ifthenumberofparticlesisnotverylarge,wecantraceeveryparticle'strackaccuratelybyparticlesystem.
Infact,asandstormconsistsofahugenumberofsandsanddustparticles,sotracingeachparticleisnotfeasibleinthiscase.
However,theparticles'movementsobeystatisticaldistribution,andtheyhavethesimilarpropertiesasuid,wecanapproximatethemotionofsandanddustparticleasnon-viscosity,incompressibleuid,whichcanbedescribedasthefollowing:udt=(ud·)udpd+fd(4)·ud=0(5)whereudisthevelocityofsandparticleow,pdispressure,fddenotesanyexternalforcesactingontheCopyright2007JohnWiley&Sons,Ltd.
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Figure2.
Theforceofasandparticleintheairow.
sandparticle.
fdconsistsofthevalidgravityWdofsandparticleinairow,andtheentrainmentforceFdbyairow.
Next,wewillanalyzetheforceofasingleparticleinairow.
Supposethatthesandanddustparticlesarespherical,withmassmd,diameterDd,anddensityρd.
Forsimplicity,wesupposethattheparticlesmoveinXOYplane.
Theforceconsistsofthevalidgravityofsandparticlesandtheentrainmentforcebyairow.
Theentrainmentforceisproducedbythevelocitydifferencebetweentheairowandthesandparticleow,anditisthemostimportantdrivingforceofsandparticles.
Figure2isthesketchofforcesofasandparticleintheairow.
Thevalidgravityofasandordustparticleintheairowisexpressedas:24Wd=16πDd3(ρdρ)g(6)wherethesubtractionpartisbuoyancyofthesandparticleintheairow,ρandgarethedensityandaccelerationofgravity,respectively.
Theentrainmentforceisexpressedas:Fd=CDπνDd(udu)(7)whereudisthevelocityofthesandparticle,νtheviscosityoftheatmosphere,CDthecoefcientofresistanceandwecalculateitbythefollowingempiricalformula:CD=24Re+6(1+Re)1/2+0.
4(8)whereReistheReynoldnumbercorrespondingtodifferentairowmotion.
Theaboveanalysisisforasingleparticle.
Asweconsiderthemotionofparticlesasanincompressibleuid,theEulermethodcanbeusedtosolveit.
Inthiscase,eachsandordustparticleactuallybelongstoagroupofparticlesinavoxel.
Inthisway,wecansimulatethemotionandinteractionamongthewind,sand,anddustparticlesbasedonvoxel,whichismoreefcientcomparedwithparticlesystem.
InteractionAmongWind,Sand,andDustParticleFlowFollowingthetheoryofuiddynamics,sandstormisdifferentfromothernaturalphenomenasuchassmoke,re,etc.
duetotheobviousinteractionamongthesand,dustparticleowsandthewindeld.
Whenthesandanddustparticlesareblownintotheair,itwillbeentrainedbythewind.
Onthecontrary,thevelocityofthewindwillbeaffectedbythecounterforceofthesandanddustparticleow.
Infact,forsandstorm,itsexternalforceismainlytheinteractionforcebetweensandparticleowandairow,whichiscausedbythevelocitydifferencebetweenthem.
Herewewilldiscussthemodelingofinteractionforceforsandstorm.
Thewindeld,sand,anddustparticleowscanberegardedascontinuousuid.
Sotheinteractionamongthemcanbemodeledasthatbetweenwindeldandagroupoftheseparticles.
Weaccountthesandanddustparticlesinaunitvolumeasawhole,andthecounterforcetothewindeldbythesandanddustparticleowisequivalenttoaddingabodyforcetothewindeldmodel.
AccordingtoSubsectionSandandDustParticleFlowModel,theforceexertedbyasingleparticlemovingthroughthegasisCDπDd(udu).
WedescribethediameterdistributionofsandanddustparticlesinsandstormsbyEquation(9):n(Dp)=N01√2πηDpexp(lnDpδ)22η2(9)whereη,δismeanvalueandstandardvarianceoflnDp,N0isthetotalnumberofsandparticlesintheunitvolume.
Figure3showsthedistributionofsandparticleinsandstormsofdifferentvisibility.
Here,L,M,Sarethedifferenttypesofsandstormunderlow,moderateandhighvisibilities,respectively.
Duetothediameterofsandanddustparticleistenstohundredsmicrons,theinteractionforcebetweenthemcanbeignored.
Sotheinteractionforcebetweensandparticlesinaunitvolumeandtheairowcanbeexpressedas:FDP=n(Dp)·CDπDp(udu)dDp(10)Copyright2007JohnWiley&Sons,Ltd.
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1002/cavANIMATIONOFSANDSTORMFigure3.
Diameterdistributionofsandparticlesindifferenttypesofsandstorm.
Multi-FluidSolveronGPUOursandstormmodeldistinguishesfrompreviousuidmodelinthatourmodeldescribesamultipleuidsystem,oneisairowandtheothersaresandanddustparticleows.
Ifweusethepreviousmethodssuchas25tosolvemultipleNavier-Stokesequationsseperatelyformultiplevelocitytextureinonerenderingpass,thecalculatingtimecostwillbeincreasedseveraltimes.
Toavoidthis,wesolvethemultipleNavier-Stokesequationsinparallelinonerenderingpassbycombiningmultipleelddatatextureintoonetexture.
Thetechniqueofat3Dtextureisalsousedtostorethe3Dtexturedata.
Differentfromthepreviousmethods,westoretheairow(wind)velocitytextureandthesandanddustparticleowvelocitytextureinoneat3Dtextureratherthaninseveralat3Dtextures,asshowninFigure4.
Inthisgure,thegreenpartisforthesandparticleow,andthebluepartisfortheairow.
ItisconvenienttoFigure4.
Datatextureinoursandstormmodel.
Figure5.
FlowchartofMulti-FluidSolver.
readandstorevelocitydatabytheYcoordinate.
IftheYcoordinateisabove0.
5,itrepresentsthedataofthesandanddustparticleow.
Ifnot,itrepresentsthedataoftheairow.
Itissimilarforotherelddatasuchaspressuresandsoon.
Thecalculationowcanbedescribedasfollows.
First,weinitializetheairowandsandparticleow,settheinitialconditionandboundarycondition.
Then,wesolvetheNavier-StokesequationsonGPUbytheSemi-Lagrangemethods.
25Thereareseveralvelocitytexturedatainoneat3Dtexture.
Theycanbebothupdatedoronlyoneisupdatedduringonestep.
WeshowthisowinFigure5.
Inthisgure,theyellowpartincludestextureoperation,andthewhitepartinvolvesnotextureoperation.
Bythismethod,wecansolvemultipleNavier-Stokesequationsinparallelinonerenderingpass.
Nowonder,thesizeofourat3Dtextureisseveraltimesaslargeasthatofthepreviousmethod,butitdoesnotaffectthecalculationefciencyverymuchforthelinearcalculationfunctionofGPU.
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RenderingofSandstormSceneTogeneraterealisticimagesofsandstorms,wemustconsidertheinteractionofvarioustypesofcomponentsofsandstormwithnaturallight.
Sandstormappearswithdifferentcoloratdifferentareasandstages.
Thisismainlyduetoscatteringandabsorptioneffectofparticlesinsandstorm.
OurrenderingmodelofsandstormsceneisbasedonmultipleMiescatteringtheory.
26Andweadoptpre-computationtechniquetoacceleratetherenderingrate.
BelowwewillsimplydescribeMiescatteringmodelanddiscussourrenderingmethod.
MieScatteringModelforNaturalLightMiescatteringmodelisaclassicaltheoryforexplainingscatteringofsphericalparticles.
SupposeaparticleisofdiameterDd,refractiveindexm.
Mie'smodelofscatteringcanbeexpressedas:I(λ)=I0(λ)i1+i22k2Dd2(11)whereλisthewavelengthofincidentlight,themeaningofotherparametersinEquation(11)canbefoundinReference[27].
CalculationofScatteringinSandstormAccordingtothedataofexperimentandmeasurement,wendthattheshapeofthemajorityofsandanddustparticlesisspherical.
AccordingtotheIsometric-Spheretheory,sand,anddustparticlesinsandstormcanthusberegardedassphericalforsimplicity.
28Figure6.
Theincidentradianceofavoxel.
Figure7.
Renderingsandstorminhardware.
TheeffectofscatteringcanbedeterminedbymeasuringtheintensityIscaofalightrayaftertravelingldistanceinascatteringmedia.
IfI0istheintensityofthelightsource,accordingtoBougureLaw,26theFigure8.
Comparisonbetweenourrenderingresultandtherealphotoindesert,(a)ourrenderingresult,(b)therealphoto.
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Comparisonbetweenourrenderingresultandtherealphotoinanurbanroad,(a)ourrenderingresult,(b)therealphoto.
ratioisIsca/I0=exp(Qsca(λ)·l)(12)whereQsca(λ)isthescatteringsectionofaparticle.
Consideringthedistributionofsandparticlesinsandstorm(SeeSectionModelingoftheSandstorm),wedenethescatteringcoefcientofsandparticlesinaunitvolumeasσ(λ)=∞0πDp24Qscan(Dp)dDp(13)AsthecomputationoftheMiescatteringisverycomplicated,whichincludecalculationofscatteringsectionandscatteringcoefcient,hereweuseanewmethodtopre-computethesetermsofsandparticleswithdifferentdiameterandstoretheresultsasalook-uptable.
Whilerendering,wecaninterpolatedatafromthistable.
Thespectralsamplingintervalofincidentlightis5nmfrom380to780nm,andsamplingintervalofscatteringangleis1degreefrom0to180.
Figure10.
Sandstormsceneswithdifferentvisibilityinurbanarea,(a)highvisibility,(b)moderatevisibility,(c)lowvisibility.
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Figure11.
Seriesofsandstormscenesindesert,(a)–(d)showthatsandstormisdrawingneartheviewpoint.
RenderingofSandstormSceneToproducetherealisticappearanceofsandstormscene,multiplescatteringeffectofsandsmustbeconsidered.
Herewediscretethespacelledwithsandstormintovoxels.
ForeachvoxelPi,j,itsincidentradiancefromdirectionωincludesthedirectlightfromthelightsourceindirectionωandmultiplescatteredlightfromothervoxels(SeeFigure6).
Themultiplescatteringmodelisexpressedas:IPi,j=I0·Nj=1σj(λ)+Nj=1ImNk=j+1σk(λ)(14)whereImisthemultiplescatteringintodirectionωatarbitraryvoxelX.
In-scatteringfromthesixneighboringvoxelsaresampled,soImcanbeexpressedas:Im=6s=1IPs·p(θ)·σs(λ)(15)wherep(θ)isphasefunction.
Forscatteringofsandparticlesisalmostisotropic,weconsiderthephasefunctionasconstant.
Ourrenderingmethodisatwo-passalgorithm.
AsshowninFigure7,wepre-computetheshadingofsandstormsceneaccordingtothepositionofeachvoxelandtheincidentdirectionoflightsourceintherstpass.
Then,weusetheshadingresulttorenderthesceneunderxedviewpointinthesecondpass.
ResultsandDiscussionWiththeproposedmethods,wesuccessfullygeneratedvarioustypesofrealisticsandstormscenesonaPCwithFigure12.
Sandstormsceneswithmoderatevisibilityinacornerofurbanarea.
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8GHZ,PentiumIVprocessor,2GBmemoryandanNVIDIA'sGeForceFX6800GTgraphicscard.
Figure8showsthecontrastofourrenderingresultsofsandstormindesertandtherealphoto.
Fromthegures,wecanseethatoursimulatedresultisquitesatisfactory.
Figure9isthecomparisonbetweenourrenderingresultsofsandstorminanurbanroadatnightwiththerealphoto.
Figure10showsthesandstormsceneswithdifferentvisibilityatnightinurbanarea.
Withtheincreaseofthedensityofsandanddustparticles,thescatteringcolorischanginggraduallyfromlightyellowtoyellow,thentored,andthevisibilitydecreasescorrespondingly.
Thiscolorchangeismainlycausedbythechangeofdensitydistributionofsandparticles.
Asourmethodisbasedonphysicaltheory,theappearanceofsandstormandscatteringeffectsoftheroadlamplooksrealistic.
Figure11showsseriesofdynamicsandstormscenesindesert.
From(a)to(d),sandstormisrollingneartheviewpoint.
Thedynamicseriesofsandstormscenecanbeseenfromtheaccompanyinganimationvideo.
Wecanalsoseetheilluminationeffectsofsandstormsceneatdifferentstagescausedbymultiplescatteringofsandparticles.
Figure12showsacornerofurbanareainsand-stormwithmoderatevisibility.
Thesimulationdomainis64*64*64.
Theaveragerenderingrateofourmethodfordynamicsandstormisabout6framespersecond.
ConclusionandFutureWorksWehaveproposedanovelphysicallybasedmethodformodelingandanimatingsandstormscenes.
Ourmethodadoptsmulti-phaseuidmodelstosimulatethemotionofair,sand,anddustparticlesinthesandstorm.
ThewindeldisestablishedbyReynold-averageNavier-Stokesequationsandthesandanddustparticleowisbuiltwiththenon-viscosityuidmodeltakingthestatisticaldistributionofparticlesofvariedsizeintoaccount.
Toefcientlycomputethedynamicsandstormscene,wedesignaMulti-FluidSolverandimplementitonGPUtoachievehighrenderingrates.
Byspectralsamplingofthelightscattering,thepeculiarilluminationeffectofdynamicsandstormscenesisrevealed.
Comparedwithrealsandstormdisplays,oursimulatedresultsarequitesatisfactory.
Thecontributionsofthispapercanbesummarizedasfollows.
(1)Asfarasweknow,itisthersttimetosimulatedynamicsandstormscenerealisticallybasedonphysicalprinciples.
(2)Ratherthanusingsingleuidmodel,weadoptmultipleuidmodeltodealwiththemotionandthecomplexinteractionofvariouscomponentsinthesandstorm.
AspecialMulti-FluidSolverisdesignedandimplementedonGPU,whichgreatlyacceleratestherenderingspeedofthescene.
(3)Oursystemiseasytoimplement.
Withdifferentinitialparameters,thewind,sand,anddustparticleowswillblowautomaticallyanduserscangeneratevariousrealisticsandstormsceneswithdifferentvisibilityatdifferentstages.
Furthermore,thismodelcanbeextendedtosimulateotherphenomenaofmultiplegas-solidmixtures.
However,itisnotsuitableforsimulatingphenomenawithobviousinterface,suchasoil-water,etc.
Simulatingthesephenomenainvolvesreconstructingthedynamicfreesurface,whichisournextgoal.
Ontheotherhand,ourdynamicsandstormmodelisstillfarfromperfect.
Forexample,thoughwecansimulaterealisticdynamicsandstormscenewhichisfarfromtheviewpoint,westillsufferfromfog-likeappearanceofsandparticleswhenitisclosetotheviewpoint.
Euler-basedmethodcombiningwithparticlesystemsuggestsapotentialwayforovercomingthislimitation.
Ourfutureworksalsoincludesimulationofothernaturaldisastrousphenomenasuchasdebrisow,avalanche,etc.
ACKNOWLEDGEMENTSThisresearchwassupportedby973ProgramofChinaunderGrantNo.
2002CB312101,theNationalHighTechnologyRe-searchandDevelopmentProgramofChina(863Program)underGrantNo.
2006AA01Z314andNaturalScienceFoundationofChinaunderGrantNo.
60475013andNo.
60603076.
Wearedeeplygratefultothereviewersfortheirprecisecomments,whichhaveimprovedthequalityofthispaperandwillbenetourfuturework.
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Authors'biographies:ShiguangLiuisassistantprofessoratSchoolofComputerScienceandTechnology,TianjinUniversityP.
R.
China.
HegraduatedfromZhejiangUniversityandin2007hereceivedaPhDfromStateKeyLabofCAD&CG.
Hisresearchinterestsincludenaturalphenomenasimulation,uidsimulationandcomputeranimation.
ZhangyeWangisassociateprofessorattheStateKeyLaboratoryofCAD&CG,ZhejiangUniversity,P.
R.
China.
HereceivedhisBSdegreeinPhysicsin1987andMScdegreeinOpticsin1990,respectively,bothfromEastChinaNormalUniversity.
In2002,hereceivedhisPhDincomputergraphicsfromZhejiangUniversity.
Hisresearchnterestsincluderealisticimagesynthesis,computeranimationandvirtualreality.
ZhengGongisaMScandidateattheStateKeyLabofCAD&CG,ZhejiangUniversity,P.
R.
China.
HereceivedhisBSdegreeinDepartmentofComputerScience,Xi'anCopyright2007JohnWiley&Sons,Ltd.
268Comp.
Anim.
VirtualWorlds2007;18:259–269DOI:10.
1002/cavANIMATIONOFSANDSTORMJiaotongUniversity,P.
R.
China.
Hisresearchinterestsincluderealisticimagesynthesisandsimulationofmultiplescattering.
LeiHuangisaMScandidateattheStateKeyLabofCAD&CG,ZhejiangUniversity,P.
R.
China.
HereceivedhisBSdegreeinDepartmentofComputerScience,HunanUniversity,P.
R.
China.
Hisresearchinterestsincluderealisticimagesynthesisandnaturalphenomenasimulation.
QunshengPengisprofessorattheStateKeyLabofCAD&CG,ZhejiangUniversity.
Hisresearchinterestsincluderealisticimagesynthesis,virtualreality,infraredimagesynthesis,point-basedrendering,scienticvisu-alization,andbiologicalcalculation,etc.
HegraduatedfromBeijingMechanicalCollegein1970andreceivedaPhDfromtheDepartmentofComputingStudies,UniversityofEastAnglia,in1983.
HeiscurrentlytheViceChairmanoftheAcademicCommittee,StateKeyLabofCAD&CG,ZhejiangUniversityandisservingasamem-beroftheeditorialboardsofseveralChinesejournals.
Copyright2007JohnWiley&Sons,Ltd.
269Comp.
Anim.
VirtualWorlds2007;18:259–269DOI:10.
1002/cav