withInteractiveViewing
MarcStamminger1,AnnetteScheel1,XavierGranier2,
¸oisSillion2FredericPerez-Cazorla3,GeorgeDrettakis2,Franc
1
Max-Planck-InstituteforComputerScience,Saarbr¨ucken,Germany
2iMAGIS-GRAVIR/IMAG-INRIA,Grenoble,France
3GGG,UniversityofGirona,Spain
Abstract
Theabilitytoperforminteractivewalkthroughsofglobalilluminationsolutionsincludingglossyeffectsisachal-lengingopenproblem.Inthispaperweovercomecertainlimitationsofpreviousapproaches.Wefirstintroduceanovel,memory-andcompute-efficientrepresentationofincomingillumination,inthecontextofahierarchicalra-dianceclusteringalgorithm.Wethenrepresentoutgoingradiancewithanadaptivehierarchicalbasis,inamannersuitableforinteractivedisplay.Usingappropriaterefine-mentanddisplaystrategies,weachievewalkthroughsofglossysolutionsatinteractiveratesfornon-trivialscenes.Inaddition,ourimplementationhasbeendevelopedtobeportableandeasilyadaptableasanextensiontoexisting,diffuse-only,hierarchicalradiositysystems.Wepresentresultsoftheimplementationofglossyglobalillumina-tionintwoindependentglobalilluminationsystems.Keywords:globalillumination,glossyreflection,inter-activeviewing
1Introduction
Real-worldscenescontainmaterialswithdifferentre-flectiveproperties,varyingfrommatte(diffuse)toshiny(glossyorspecular).Globalilluminationresearchhasmadegreatadvancesforthetreatmentofdiffuseenvi-ronmentsintherecentyears,inparticularwiththead-ventoftheHierarchicalRadiosity(HR)algorithm[7]andthesubsequentintroductionofclustering[18,15].Itisnowpossibletocomputeglobalilluminationsolu-tionsofcomplexdiffuseenvironmentsandperforminter-activewalkthroughs.Interactivityisachievedusingthepolygonalmodelwhichisappropriatelysubdividedintosub-polygonstocaptureshadowsandlightingvariations.Sincetheenvironmentsarediffuse,noupdatesareneces-saryateachframe,andthepolygonsaredrawnasis.Incontrast,scenescontainingglossysurfacescannotyetbetreatedinaninteractivecontext.Togenerateimageswithglossysurfaces,ray-tracingbasedapproachesaretypi-callyused,suchastheRADIANCEsystem[27]orpath-
tracingalgorithms(e.g.,[11,23]).Somefiniteelementapproacheshavebeenpresented,butcanonlytreattrivialscenes(e.g.,[13,1])orrequireasecond,ray-castingpasstogenerateanimage[3].Twoapproacheshavebeenpro-posedwhicharecapableofinteractiveviewing[16,25],buttheyarelimitedintheircapacitytotreatnon-trivialenvironmentsandreflectivebehaviours.
Wepresentanovelsolutionwhichallowsinteractiveviewingofgloballyilluminatedglossyscenes.Toreachthisgoal,weuseafiniteelementrepresentationofoutgo-ingradianceatsurfacesorclusters.Thisrepresentationisusedateachframetoevaluatetheradianceleavingaglossysurfaceandreachingtheeye,permittinginterac-tiveviewing.
AnovelrepresentationofincomingradianceintheformofastructurecalledIlluminationSamplesispre-sented,whichisefficientbothinmemoryandcomputa-tiontime.Thisstructurereplacesanexplicit(andcostly)finite-elementrepresentationofincomingradiancebysetsofrelevantpointsamples.
Furthermore,wedemonstratetheimportanceandben-efitsofusinganadaptivehierarchicalrepresentationofoutgoingradianceimprovingonbothcomputationtimeandmemoryconsumptioncomparedtopreviousap-proachessuchas[16].Ouralgorithmproduceshighqual-ityglossyglobalilluminationsolutionswhichcanbedi-rectlyrenderedforinteractivewalkthroughs,withouttheneedforexpensivesecond-passfinalgatherasin[3].2
PreviousWork
Mostpreviousworkinglossyilluminationhasbeencen-teredaroundray-tracing.Thesestartwithdistributedray-tracing[28,5]andtherenderingequation[9]inthelateeighties.AlargebodyofresearchensuedfocusingonMonte-Carlostochasticalgorithms.Thegoalofthisre-searchwastoreducethenoiseinthesolutions,introducedbythestochasticnatureoftheMonte-Carlomethods(e.g.[22,11,14]).Monte-Carloalgorithmsthatprovedtobeusefulinotherresearchareasweresuccessfullytrans-
ferredtotheglobalilluminationproblem[10,24].
Inparallel,severalmulti-passmethodshavebeende-velopedwhichcombinetheadvantagesofray-tracingandradiosity-stylecalculations[17];othershaveintegratedradiositycalculationsastochasticprocess[2].TheRA-DIANCEsystem[27],particletracing[12]andphoton-maps[8]arealsointerestingsincetheycollectsamplesofilluminationeitheronsurfacesorinaseparatestructure,andusearay-castortracetorenderthefinalimage.
“Pure”finiteelementapproachesforglossyillumina-tionhaveappearedintwomainflavours:three-pointap-proaches[1,13]andfinite-elementapproachesusingdi-rectionaldistributions[16,3].Weconcentrateonthelasttwomethodsinmoredetail,sincetheyareclosertoournewalgorithm.
2.1WaveletsandFinalGather
Christensenetal.[3]extendedthewaveletmethodswhichhavebeenusedforradiosity[29,6,4]toaradianceclusteringalgorithm.However,itstillsuffersfromsomecomputationallyexpensivestepswhichhinderinteractiveviewing.Patchesstorearadiancedistributionwhichisrepresentedusingafourdimensionalwaveletbasisac-countingforspatialanddirectionalvariations.Comput-ingthetransportcoefficientsinvolvesevaluatingasix-dimensionalintegralwhichiscomputationallyexpensive.Importancedrivenrefinementreducesthenumberofin-teractionsdrastically;butthesolutionbecomesviewde-pendentandconsequentlycannotbeusedforinteractiveviewing.
Higherorderwaveletbaseswerealsoinvestigated,whichprovideasparsertransportcoefficientmatrixanddeliversmootherrepresentations.However,theintegra-tionsaresocomplexthattheauthorsresortedtotheHaarbasiswithasmoothingfinalgatherstep,whichisverytimeconsumingandviewdependent.
2.2RadianceClustering
TheRadianceClusteringapproach(RC)developedbySillionetal.[16],usedsphericalharmonicstostoreex-itingradiantintensityIonthehierarchicalelementsofasubdivisionoftheoriginalscene.An“immediate-push”algorithmisused,which,duringthegatheroperationoflightacrosslinks,“pushes”thecontributionallthewaytotheleaves.Attheleaves,radiantintensityIisstoredasasphericalharmonicfunction;thenewcontributionisreflectedandaddedintothisfunction.
TheresultcanbevisualiseddirectlybysamplingthesphericalharmonicrepresentationsofIateachframe.Directvisualisation(i.e.withnoacceleration)wasper-formedforsimplescenes;sinceforeachframeradianceisevaluatedateachvertexorleafelement,frameratesarenotoptimal.Furthermore,sphericalharmonicsarea
non-hierarchicalrepresentation,andthenumberofcoef-ficientsusedisfixedinadvance.Asaresult,thereisnocontroloverthelevelofdetailrequiredtorepresentthedirectionallydependentglossyillumination.
Ournewalgorithmprovidessolutionstotheaboveproblemsandalsoreducesmemoryandtimeconsump-tion.Westartwithanimprovedrepresentationofin-comingradiance,whichavoidsthememoryoverheadandmultiplehierarchypassesofthe“immediate-push”so-lution.InparticularweintroduceIlluminationSampleswhichareanappropriatepointsamplesetrepresentationofincominglight.Wethenproceedwithanadaptivehi-erarchicalrepresentationofoutgoingradianceusingHaarwavelets,whichiswell-suitedtointeractiveviewing,andallowssmoothcontrolofthememory/qualitytradeoff.Thisavoidstheproblemsofnon-adaptiverepresentationswhichareeithernotsufficientlyaccurateortoomemory-consuming.Appropriatedirectionalrefinementandsim-pleheuristicsforacceleratedviewingarealsointroduced.3
TheIlluminationSamplesAlgorithm
ThegoalofthenewIlluminationSamplesalgorithmistoextendanexistingHierarchicalClusteringalgorithmtoalsohandlenon-diffusesurfaces.Inter-surfacelightprop-agationisthesamefordiffuseandnon-diffuseenviron-ments,withthedifferencethatinanon-diffusesetupdi-rectionalinformationaboutincidentlightmustbemain-tainedforafollowingglossyreflectionstep.
Asin[16],patchesandclustersareassumedtohavenospatialextent.Theystoreahierarchicaldirectionaldis-tributionforoutgoingradiancewhichwillbedescribedseparatelyinSection4.Incontrastto[3],ournewalgo-rithmdoesnotdifferentiatebetweenclustersandpatchesconcerningtherepresentationofexitantlight.
3.1BoundedPropagation
Ourapproachisbasedontheradiosityclusteringmethoddescribedin[20,21],whichcanhandleflatandcurvedsurfacesaswellasclustersinauniformmanner.Bound-ingboxesaroundtheobjectsareusedtoboundthesetofinteractingdirections.Withthisinformation,boundsontheformfactorandexitantradianceatthesenderarecomputed,deliveringminimumandmaximumvaluesforthereceivedradiosity.Thedifferenceisusedtodecidewhethertorefinealink.
Thisboundedradiosityapproachcanbeappliedtoradiancecomputationseasily,sincethepropagationoflight,i.e.thetransformationofexitanttoincidentlight,isindependentofmaterialproperties.Theonlydiffer-enceliesintheevaluationofboundsontheradianceofthesender,whichiseveneasierifwehaveadirectionaldistributionforthesender’sexitantradiance.However,sincethisexitantradiancerepresentationisonlyapproxi-
mate,theresultingboundsarenolongerconservative.3.2IncidentLight
Onewaytointegratethedirectionalinformationistoexplicitlycomputeafiniteelementrepresentationofit.In[3],eachincidentlightcontributioncomputedduringpropagationisprojectedseparatelyontoabasisforin-cominglight(forclusters).Thisisrathercostly(inmem-oryandtime)andresultsinsignificantblurringofinci-dentlight,whichcanexhibitverystrongvariations.
Analternativeistoreflectincidentlightcontributionsimmediatelyaftertheyhavebeencomputed[16],whiletheirdirectionofincidenceisstillknown.Thereflec-tionresponsesarethenprojectedinfiniteelementbasesseparately.Thismethodcircumventstheneedtostoretheincidentlight,butthestorageconsumptionisnotre-duced:tworepresentationsofexitantradianceareneededforthepush/pullphase.Inaddition,thismethodiscom-putationallyexpensive,becauseofthehighnumberofBRDFevaluations,andthemultiplehierarchytraversalsinvolvedintheimmediateprojection.
Ourproposedsolutionistocombinetheapproachesofincidentlightrepresentationandimmediatereflection.WeattachincidentlighttoareceivingpatchintheformofIlluminationSamples.LightpropagationiscomputedsimilarlytoHRbyrefininglinksuntileachlinkrepre-sentswhatamountstoconstantlightpower.Insteadofsimplysummingtheirradiancevaluesatthereceiver,anIlluminationSamplewiththedirectiontothesenderandthetransportedirradianceisaddedtothereceiverforeachlink.Attheendofthepropagationstep,theilluminationinthesceneisrepresentedasasetofpointsamples,dis-tributedoverthescenehierarchy.
3.3Push/PullandReflection
ApushstepasinHRisneededtocreateaconsistentrepresentationoftheincidentlightattheleaves,i.e.alllightreceivedbyinnernodesispropagatedtothechildrenbypassingitsIlluminationSamplesdownwards.After-wards,eachleafhasalargesetofIlluminationSamplesdescribingitsentireincidentlightfield.NotethatthenumberofhierarchytraversalsismuchsmallerthaninRadianceClustering[16],whereeachsampleispusheddownseparately.
Afterthepushstep,theincidentlighthastobere-flectedaccordingtotheobject’sBRDF.BecauseIllumi-nationSamplescorrespondtoDiracimpulses,thereflec-tionisanimpulseresponseoftheBRDF,i.e.itistheBRDFwithafixedincidentlightdirectionmultipliedbytheirradianceofthesample.ThecompletereflectionisthesumoftheimpulseresponsestoeachIlluminationSample.ThereforetheBRDFmustbeevaluatedonceforeachIlluminationSampletoobtainthereflectedradiance
inaparticulardirection.
Usinganadaptivedirectionaldistributiondescribedbelow,reflectedlightisprojectedontoanadaptive,hi-erarchicaldirectionalbasistoobtainthenewexitantlightforeachpatch.Theserepresentationsarethenaveragedbottom-uptoobtainthedistributionsforinnernodes.3.4Shooting
Withagatheringiterationscheme,thenumberofIllumi-nationSamplesandthusthetimeforpush/pullincreasesfromiterationtoiteration.Withashootingschemeinthespiritof[19]thiscanbeavoided.Thisrequiresanaddi-tionaldirectionalrepresentationofunshotradiance,butitalsoavoidsthestorageandreflectionofallIlluminationSamples.
3.5ErrorAnalysis
Notethatinourapproachpropagationandreflectionarecompletelydecoupled.Propagationcomputationdoesnotconsiderthereflectionpropertiesofthereceiver,whichwouldallowthecomputationofincidentlightatahighlyglossypatchmoreaccuratelythaninthediffusecase.Thespatialrefinementofthepatchesisdoneduringpropagation,whiletherefinementlevelofthedirectionaldistributionsischosenduringreflection.Thisdistinctiondoesnotimposeaproblemonconvergence,butitresultsinmemory/computationsavings.
IlluminationSamplescanbeinterpretedasDirac-peaksfromaparticulardirectiondescribingincidentlightandarethussomewhatsimilartothephotonsinthePho-tonMapapproachofJensenetal.[8].However,Photonmapsarenotdeterministicandtheirusageforlightingsimulationisverydifferentfromours.
Withrespecttoastandardnorm,withDirac-peaksnoconvergentrepresentationcanbeobtained.Ontheotherhand,theDirac-representationisonlyusedtocom-putethereflectionintegral.Fromanotherpointofview,thisrepresentationcanbeseenasintermediatedatainadelayednumericalintegration,whereeachIlluminationSampleisatemporarilystoredintegrationsample.SoaslongastheBRDFisnumericallyintegrable,thecom-putedreflectionwillconverge.4
AdaptiveRepresentationofOutgoingRadianceforInteractiveDisplay
Toproducethefinite-elementsolutionssuitableforinter-activedisplay,westoreoutgoinglightintheformofdi-rectionaldistributionsattachedtosurfacesorclusters.AsinRadianceClustering[16],objectsareassumedtohavenospatialextent.Insteadofthefourdimensionalradi-anceonlythe2Dradiantintensitydistributionisstoredwitheachobject.
4.1DirectionalRepresentations
Fortherepresentationofdirectionalradiantintensities,wehaveimplementedandexaminedtwooptions:First,auniformsubdivisionofthedirectionspace,whereeachdistributionisrepresentedbyafixednumberofcoeffi-cients(non-adaptivebasis)1.Second,weimplementedanadaptiverepresentationusingHaarWavelets.
Thenon-adaptivebasisismoreusefulforsmoothdis-tributions,becausealloperationsonthefixedsubdivisionbasisaresimpleandfast.TheadaptiveHaarbasisisbet-tersuitedforstronglyvaryingfunctions,becauseitcanusemorebasisfunctionsintheinterestingregionsandfewerinsmoothregions.However,operationssuchastheevaluationofthedistributionoradditionoftwodis-tributionsaremoreexpensive.
“Non-adaptive”Representation
Foranon-adaptivebasis,weuseauniformsubdivisionofthedirectionspace.Toaccomplishthistask,atetrahe-dronissubdivided.Wethusobtain4n1trianglesifthelevelofsubdivisonisn.Sincethenumberofverticesislowerthanthenumberoftriangles(thisis24n2),wedecidedtostore3floatsforRGBonlyatthevertices.
HaarRepresentation
FortheHaarrepresentation,thedomainofdirectionsisparameterizedbypointsonanoctahedron.Theverticesoftheoctahedronareselectedtolieonthemainaxes,soeachfacecorrespondstooneoctantofthedirectionaldomain.Simplesignconsiderationsofadirectiondeliverthecorrespondingoctahedronface.
Ahierarchyofbasisfunctionsisbuiltbyassigningafirstlevelbasisfunctiontoeachoftheeightfacesoftheoctahedron.Thesearethensubdividedhierarchicallyintheusualmanner.
Inordertoquicklycomputeanadaptiverepresentation,atop-downapproachwaschosen.Assumethatthefunc-tiontobeprojectedisf.Foreachofthefirsteightbasisfunctions,fissampledatthetrianglecornersandatitscenter.Iffisalmostconstantoverthetriangle,thesam-plevalueswillonlyvaryslightly.Forhighlyvaryingf,onecanexpectawiderangeoffunctionsamples.Thusthedifferencebetweenminimumandmaximumsampleisconsidered.Ifitistoolarge,thefourfinerbasisfunc-tionspartitioningthedomainareconsideredrecursively.Thistop-downapproachrunsintoproblemsiffhasasharppeakinbetweenthesamples.Wealleviatethisproblembyenforcingaminimumsubdivisionlevelinthehopethattheresultingsamplingisdenseenoughtonotmissanypeaks.
3
N/A
Figure1:Comparisonofthenon-adaptive(N/A)vs.Haar.
MaxTrianglesLevelN/AN/A3782K510s4
3127K
731s
theHaarbasisuseslessthanthreetimesasmuchmemoryforan“equivalent”improvementinquality.However,theHaarbasisalsotakesmoretime.Thereasonisthatarith-meticoperationsontheregularconstantsubdivisionareofcoursesimplerandfaster.
Thisexampledemonstratesthatforhighlyglossyscenes,smallhighlightscanonlybecapturedwiththeadaptivebasisoraveryfinenon-adaptivebasisrepre-sentation,whichinturnrequireslargeamountsofmem-ory.Moreimportantly,theuser,whohaslimitedmem-ory,canonlychangethequalityinlarge“quanta”,andoftenwillnotbeabletogetasatisfactoryresultbeforerunningoutofmemory.Adaptivebases,suchasHaar,alleviatethisproblem.However,theuniformityofthenon-adaptivebasisresultsinasmoother,moreregulardistribution,whichbecomesespeciallyvisibleduringin-teractiveviewing.5InteractiveDisplay
AfterthecomputationofaglobalilluminationsolutionusingIlluminationSamples,wehavearepresentationofoutgoingradiantintensity,storedinthedirectionaldistri-butionfunction.Ateachframeduringinteractivedisplay,weneedtoevaluateradianceforeveryglossyhierarchi-calleafelementinthedirectionoftheviewpoint.Thisimpliestworequirements:(i)subdivisionofthedirec-tionaldistributionsappropriatelysothatavisuallypleas-ingrepresentationofglossyeffectsisproducedand(ii)accelerationofthedisplayprocesstoavoidthecostoftheevaluationofradianceateachelementateveryframe.5.1RefinementIssuesforDisplay
Recallthatwehavedecoupleddirectionalsubdivision,intheformoftheHaar-baseddirectionaldistributionfunc-tions,andthespatialsubdivision,intheformofthe“tra-ditional”hierarchicalradiosityelementhierarchy.Todis-playthesolution,weinterpolateradianceintheviewdi-rectionbyevaluatingthedirectionaldistributiononeachelement.Ifsubdivisionindirectionspaceisperformedarbitrarily,thedifferenceinsubdivisionofthedirec-tionalfunctionbetweenneighbouringpatchesmaybetooabrupt.
Thisisthecaseforexampleifwecompareabsolutevaluedifferencesbetweenthecenterandtheverticesofthetrianglesofthedirectionalsubdivisiontodecidewhethertosubdivide.Theuseofrelative(percentage)differencesavoidsthisproblemsinceweapproximatetheformofthefunction,whichvariesmoreslowlyacrossneighbours.TheartifactsduetotheabsoluterefinementcanbeseeninFigure2.
Figure2:Artifactswhenusingthe“absolute”refiner(left),
whichareabsentwhenusingthe“relative”refiner(right).
5.2InteractiveRendering
Forefficientdisplayweseparateobjectsintotwolists,sothatdiffuseobjectscanberenderedonceandredisplayedinefficient,display-listmode.Theotherlist,ofglossyreflectors,isupdatedappropriatelyateachframeanddis-playedinimmediatemode.Theaccelarationachievedobviouslydependsonthepercentageofdiffusesurfacesinthescene.Forthescenestestedweachieveupdateratesvaryingfromafewframespersecondtoafewsecondsperframeformorecomplexscenes.
Toachievesmoothshadingforglossysurfaces,weaddafieldtothedatastructureassociatedwithverticesinthehierarchyofelements.Forplanarsurfaces,thisfieldisupdatedduringpush-pullinamannerslightlydifferenttothatofradiosity;i.e.foravertexbelongingtoaleafele-mentortoanedge,theradiantintensityissummedwiththeradiantintensitystoredatthevertex.Sinceradiantin-tensityisinWatts/sr(see[16]),atdisplaytimewedividebytheareaofthesurroundingelements.
Thespecialcaseofindexedface-setsistreatedsepa-rately.Indexedface-setsarecommonmodellingprimi-tives,andoftenresultfromthetesselationofcurvedob-jectssuchasspheresorcylinders.Theadvantageofsuchaprimitiveisthatverticesaresharedbetweenadjacentelements.Wecanthusavoidthestorageoftheadditionaldirectionaldistributionatthevertices.
Eachvertexstoresthelistofpolygonalelementswhichshareit.Itscoloristhentheaverageradiantintensityofthesepolygons(i.e.Ievaluatedatthecentersoftheele-mentsintheviewingdirection).Formoreefficientdis-play,weevaluatethiscoloroncepervertexforagivendirection.Also,werecomputethecoloronlyifthedirec-tionchanges“sufficiently”i.e.greaterthanauser-definedεthreshold.Thisallowsthecontrolofthequality/updateratetradeoff.
6ImplementationandResults
Onemajorgoalofourapproachwasthedevelopmentofasolutionwhichcanbeconsideredasimple“add-on”toanexistinghierarchicalradiositysystem.Weimplementedthealgorithmontwoverydifferentrenderingarchitec-tures,namelyBRIGHT(iMAGIS)andVISION(Uni-
versityofErlangen).
Wehavetestedourimplementationonseveraltestscenes,showninFigures3and6.ThescenesinFigure3wereusedfortheinteractiveviewingtestinBRIGHT.Thefirstsceneshowsthreelightsourcescoloredred,greenandblue,illuminatingaveryglossy,smallreflec-tor.Thisreflectorinturnindirectlyilluminatesadif-fusewall.Thesecondsceneisaglossysphereillumi-natedbyasmallsourceandaglossyfloor.Theseinturnproduceindirectglossyeffectsonthelowerpartofthesphereandthediffuseceiling.Finally,the“Simplesoda”sceneisasimplifiedversionofthe“SodaShoppe”scene.InBRIGHT,werequiretesselationofallobjectsinitially,whichresultsinahighnumberofinitialobjects;inVISION,objectsarenotinitiallytesselated.Thisex-plainsthelownumberofinitialobjectsinthecomplete“SodaShoppe”scene,usedforFigure6.
6.1RadianceClusteringvs.IlluminationSamplesInBRIGHTwehaveimplementedbothRadianceClus-tering(RC)andtheIlluminationSamples(IS)approach.WehavecomparedrunningtimeandmemoryusagefortheRCandISapproaches.Thethresholdvaluehasthesamemeaningforbothapproaches,sinceweareusinga“relative”refiner.Visualinspectionalsoshowsthattheresultingimagesareequivalentforthesameparametervalues.Alltimingsareona195MhzR10kSGIworksta-tion.
3Lig.3Lig.3Lig.3Lig.Sph.Soda
m/M1/31/31/41/51/31/3RC13866140684351012594435987203339794
ε0.50.10.50.50.50.5ΙΣ44.6σ44.2σ49.3σ58.6σ4167.1σ5207.6σ
50%51%48%44%34%27%
Ταβλε3:ΓαινινcomputationtimefromtheuseoftheIllumi-nationSamplesalgorithm.εistheaccuracythresholdandm/Marethemin/maxlevels.
3LightsSphereS.Soda
Figure3:Testscenesusingilluminationsamples.
6.2MemoryConsumption
InTable2weshowthememorystatisticsforthetestscenesused.Inparticularwelistthedifferentsceneswiththeεaccuracythreshold(seeSection4.1),andthecorre-spondingnumberofdirectionaldistributionbasisfunc-tionsusedforthesolutionbytheRadianceClustering(RC)andIlluminationSamples(IS)approach.Theright-mostcolumnshowsthepercentgainoftheilluminationsamplesapproach.
MemoryusageisclearlyreducedusingIlluminationSamplescomparedtotheRadianceClusteringapproachforallscenes.Thegainvariesfrom37%to41%inthebestcase.ThisismainlyduetothefactthatRadi-anceClusteringrequirestheadditionalintermediatedi-rectionaldistributionfunctionstobeabletocorrectlyper-
Forallscenestheilluminationsamplesapproachpro-videsaspeedupofatleast27%.Thisismainlyduetothereductioninthenumberofhierarchytraversals,andalsothereductioninthenumberoftrianglesusedtorepresentthedirectionaldistributionsasdiscussedabove.
Asexpectedandconfirmedbytheexperimentalre-sults,theIlluminationSamplesapproachreducesbothmemoryandcomputationtimewithrespecttoRadianceClustering.Theimagesproducedbybothapproachesareessentiallyindistinguishable.
6.4VisualQuality/Comparisons
WequalitativelycomparethevisualqualityoftheimagesofRadianceClusteringandIlluminationSampleswiththosefromapath-tracerortheRADIANCEsystem.Thepath-tracertestsarerenderedusinganin-houseimple-mentationofthenext-eventestimation[11].InFig.4and5weshowthereferencepath-tracerorRADIANCEim-agesandthecorrespondingIlluminationSamplesimagestogetherwiththecomputationtimesforthetestscenes.Thereareseveralinterestingobservationsthatwecaninferfromtheseexamples:
1)Inthecaseofthethreelightscene,RADIANCEruns
Reference
Radiance6537s
Radiance1303s
IlluminationSamples
5208s
Figure5:SimpleSodareferencesolution(path-tracerat
455x364resolution)comparedtoISsolution.
intosamplingproblems.Evenaftermorethananhourandahalfofcomputationitdoesnotconverge.Incon-trast,illuminationsamplesachievesasolutioninlessthanaminute,whichisinadditionviewablefromanydirec-tioninteractively2.
2)ThecomputationtimesofISareeitherlowerorinthesameorderofmagnitudeasthoseofthereferencesolutions.TheimportantthingtorememberisthattheISsolutionscanbeviewedinteractively,whiletherefer-ence(path-tracerorRadiance)requirethesameamountoftime(tensofminutesorevenhours)foreveryimage.3)Path-tracingimagesareverynoisy.The“smooth-shaded”solutionsproducedbyISdonotsufferfromthisproblem.Despitebeingapproximate,thesmooth-shadedimagesarethereforemuchbettersuitedtointeractiveap-plications,wherenoiseandflickeringareverydistracting.Wethusbelievethatourapproachhasgreatpromise,sinceitcanbeusedtogeneratelowtomoderatequalitysolutionsforglossyenvironments,aswellasproduceso-lutionssuitableforinteractiveviewing.
isanimportantsteptowardsinteractivewalkthroughsofgloballyilluminatedglossyscenes:(i)WeintroducedtheIlluminationSamplesalgorithmwhichrepresentsincom-inglightmoreaccuratelyandefficiently,bothinmemoryandcomputationtime.(ii)Wehaveusedanadaptivehi-erarchicalfinite-elementbasistostoreoutgoinglight,inamannersuitableforinteractiveviewing.Thisallowsfinecontrolofthememory/qualitytradeoff,whichwasnotpossibleinprevioussolutions.(iii)Thesealgorithmscanbeimplementedwithmarginaleffortoveranexist-inghierarchicalradiositysystem,byconfiningthemodi-ficationstoasmallnumberofphasesanddatastructures.(iv)Interactiveviewingoftheglossyglobalilluminationsolutionsisachievedbysuitablyrefiningthedirectionalrepresentationofoutgoinglightandacceleratingthedis-playprocess.
Oursolutionhoweverisstillquitememory-consumingrequiringintheorderoftensofMbytesforthesmallestscenesandhundredsofMbytesforthemorecomplex.Toremedytheseproblemsweneedtogeneralisethemulti-resolutionnatureofoursolution.Notablywewillintroduceamulti-resolutionrepresentationofoutgoinglight,whichwillallowsignificantsavingsinmemoryatthecostoflowervisualquality.Thisapproachwillre-quireanovelrepresentationaswellasanovelrefinementalgorithm.Thisrepresentationcanbeusedbothfortheactuallightingsimulationaswellasfordisplay.Acknowledgements
ThisresearchwasfundedbytheESPRITOpenLTRSIMULGEN(#25772)ThankstoCyrilSoler(iMAGIS)andIgnacioMartin(GGG)forcodinghelp,andtoBruceWalterforproofreading.iMAGISisajointprojectofCNRS/INRIA/UJF/INPG.
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