Efficient Glossy Global Illumination with Interactive Viewing

Efficient Glossy Global Illumination with Interactive

Viewing

Marc Stamminger, Annette Scheel, Xavier Granier, Frederic Perez-Cazorla,

George Drettakis, Francois X. Sillion

To cite this version:

Marc Stamminger, Annette Scheel, Xavier Granier, Frederic Perez-Cazorla, George Drettakis,et al.. Efficient Glossy Global Illumination with Interactive Viewing. Computer GraphicsForum, Wiley-Blackwell, 2000, 19 (1), pp.13–25. <inria-00509975>

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Volumexxx, (1999) numberyyypp.000–000

Efficient GlossyGlobal Illuminationwith Interacti veViewing

MarcStamminger1, AnnetteScheel1, Xavier Granier2, FredericPerez-Cazorla3, GeorgeDrettakis2, Francois Sillion 2

1 Max-Planck-Institutefor ComputerScience,Saarbrucken,Germany2 iMAGIS-GRAVIR/IMA G-INRIA, Grenoble,France†

3 GGG,Universityof Girona,Spain

AbstractTheability to performinteractivewalkthroughsof global illuminationsolutionsincludingglossyeffectsis a chal-lengingopenproblem.In this paperwe overcomecertain limitations of previousapproaches.We first introducea novel, memory-andcompute-efficient representationof incomingillumination, in thecontext of a hierarchicalradianceclusteringalgorithm.Wethenrepresentoutgoingradiancewith anadaptivehierarchical basis,in a man-nersuitablefor interactivedisplay. Usingappropriaterefinementanddisplaystrategies,weachievewalkthroughsof glossysolutionsat interactiveratesfor non-trivial scenes.In addition,our implementationhasbeendevelopedto be portableand easilyadaptableas an extensionto existing, diffuse-only, hierarchical radiositysystems.Wepresentresultsof theimplementationof glossyglobal illuminationin twoindependentglobal illuminationsystems.

Keywords: globalillumination; glossyreflection;interactive viewing

1. Intr oduction

Real-world scenescontainmaterialswith different reflec-tiveproperties,varyingfrom matte(diffuse)to shiny (glossyor specular).Global illumination researchhasmadegreatadvancesfor the treatmentof diffuse environmentsin re-centyears,in particularwith theadventof theHierarchicalRadiosity(HR) algorithm8 andthesubsequentintroductionof clustering21� 16. It is now possibleto computeglobal il-lumination solutionsof complex diffuse environmentsandperforminteractive walkthroughsof theresult.Interactivityis achieved using the polygonalmodel which is appropri-atelysubdivided into sub-polygonsto captureshadows andlighting variations.Sincethe environmentsare diffuse,noupdatesarenecessaryat eachframe,and the polygonsaredrawn as is. In contrast,scenescontainingglossysurfacescannotyet be treatedin an interactive context. To generateimageswith glossysurfaces,ray-tracingbasedapproachesare typically used,such as the RADIANCE system30 orpath-tracingalgorithms(e.g.,12� 26). Somefinite elementap-proacheshave been presented,but can only treat trivial

† iMAGIS is a joint researchprojectof CNRS/INRIA/UJF/INPG.

scenes(e.g.,14� 1) or require a second,ray-castingpasstogeneratean image3. Otherapproacheshave beenproposedwhicharecapableof interactive viewing17� 18� 28, but they arelimited in theircapacityto treatnon-trivial environmentsandreflectivebehaviours.

We presenta novel solution which allows interactiveviewing of globally illuminated glossyscenes.To achievethis goal,we usea finite elementrepresentationof outgoingradianceatsurfacesor clusters.Thisrepresentationis usedateachframeto evaluatetheradianceleaving a glossysurfaceandreachingtheeye,permittinginteractiveviewing.Theus-ageof afinite elementrepresentationfor exitantlight impliesthatthemethodis bettersuitedfor roughglossysurfaces,butnot for highly specularor evenmirror-like ones.

A novel representationof incomingradiancein the formof a structure called Illumination Samplesis presented,which is efficient both in memoryand computationtime.Thisstructurereplacesanexplicit (andcostly)finite-elementrepresentationof incomingradianceby setsof relevantpointsamples.

Furthermore,wedemonstratetheimportanceandbenefitsof usinganadaptive hierarchicalrepresentationof outgoingradianceimproving on bothcomputationtime andmemory

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The EurographicsAssociation1999.Publishedby Blackwell Publishers,108CowleyRoad,OxfordOX4 1JF, UK and238Main Street,Cambridge,MA 02142,USA.

2 M. Stamminger etal. / EfficientGlossyGlobal Illuminationwith InteractiveViewing

consumptioncomparedto previousapproachessuchasthatof Sillion etal.18 Ouralgorithmproduceshighqualityglossyglobalilluminationsolutionswhichcanbedirectly renderedfor interactive walkthroughs,without theneedfor expensivesecond-passfinal gatherasin thework of Christensenetal.3

2. Previous Work

Most previous work in glossy illumination has beencen-teredaroundray-tracing.Thesestart with distributed ray-tracing31� 5 andtherenderingequation10 in the lateeighties.A large body of researchensuedfocusingon Monte-Carlostochasticalgorithms.The goal of this researchwas to re-ducethe noisein the solutions,introducedby the stochas-tic natureof theMonte-Carlomethods(e.g.,25� 12� 15). Monte-Carlo algorithmsthat proved to be useful in otherresearchareasweresuccessfullytransferredto theglobalilluminationproblem.11� 27

In parallel, several multi-passmethodshave been de-velopedwhich combinethe advantagesof ray-tracingandradiosity-stylecalculations;19 othershave integratedradios-ity calculationsin a stochasticprocess.2 The RADIANCEsystem,30 particletracing13 andphoton-maps9 arealsoin-terestingsincethey collectsamplesof illuminationeitheronsurfacesor in aseparatestructure,andusearay-castor traceto renderthefinal image.

“Pure” finite elementapproachesfor glossy illumina-tion have appearedin two main flavours: three-pointap-proaches1� 14 and finite-elementapproachesusing direc-tionaldistributions.18� 3 Weconcentrateonthelasttwo meth-ods in more detail, sincethey are closerto our new algo-rithm.

2.1. Waveletsand Final Gather

Christensenetal.3 extendedthewaveletmethodswhichhavebeenusedfor radiosity32� 7� 4 to a radianceclusteringalgo-rithm. However, it still suffersfrom computationallyexpen-sive stepswhich hinderinteractive viewing. Patchesstorearadiancedistribution which is representedusinga four di-mensionalwavelet basisaccountingfor spatial and direc-tional variations.Clustersmaintaina waveletrepresentationfor an incoming as well as for an outgoing radiancedis-tribution. The doublerepresentationof radianceconsumesadditionalmemory. Computingthetransportcoefficientsin-volvesevaluatinga six-dimensionalintegral which is com-putationally expensive. Importancedriven refinementre-ducesthenumberof interactionsdrastically;but thesolutionbecomesview dependentandconsequentlycannotbe usedfor interactive viewing.

Higherorderwaveletbases(e.g.,6) werealsoinvestigated,which provide a sparsertransportcoefficient matrix andde-liversmootherrepresentations.However, theintegrationsaresocomplex that theauthorsresortedto theHaarbasiswith

asmoothingfinal gatherstep,which is very timeconsumingandview dependent.

2.2. RadianceClustering

The RadianceClusteringapproach(RC) developedby Sil-lion et al.,18 usedsphericalharmonicsto storeexiting ra-diant intensity I on the hierarchicalelementsof a subdivi-sion of the original scene.An “immediate-push”algorithmis used,which, during the gatheroperationof light acrosslinks, “pushes”thecontributionall theway to theleaves.Atthe leaves, radiant intensity I is storedas a sphericalhar-monicfunction; thenew contribution is reflectedandaddedinto this function.

The result can be visualiseddirectly by sampling thesphericalharmonicrepresentationsof I at eachframe.Di-rectvisualisation(i.e., with no acceleration)wasperformedfor simplescenes;sincefor eachframeradianceis evaluatedat eachvertex or leaf element,frameratesarenot optimal.Furthermore,sphericalharmonicsareanon-hierarchicalrep-resentation,andthe numberof coefficientsusedis fixed inadvance.As a result,thereis nocontrolover thelevel of de-tail requiredto representthedirectionallydependentglossyillumination.

Our new algorithmprovidessolutionsto theabove prob-lemsandalsoreducesmemoryand time consumption.Westartwith animprovedrepresentationof incomingradiance,which avoids the memoryoverheadandmultiple hierarchypassesof the“immediate-push”solution.In particularwein-troduceIlluminationSampleswhichareanappropriatepointsampleset representationof incoming light. We then pro-ceedwith an adaptive hierarchicalrepresentationof outgo-ing radianceusingHaarwavelets,andalsopresenta “shoot-ing” solutionfurtherreducingmemoryrequirements.There-sulting glossyglobal algorithmis well-suitedto interactiveviewing, andallows smoothcontrol of the memory/qualitytradeoff. This avoids the problemsof non-adaptive repre-sentationswhich areeithernot sufficiently accurateor toomemory-consuming.Appropriatedirectionalrefinementandsimple heuristics for acceleratedviewing are also intro-duced.

3. The Illumination SamplesAlgorithm

The goal of the new Illumination Samplesalgorithm is toextendanexisting HierarchicalClusteringalgorithmto alsohandlenon-diffusesurfaces.Inter-surfacelight propagationis the samefor diffuseandnon-diffuseenvironments,withthe differencethat in a non-diffuse setupdirectionalinfor-mationaboutincidentlight mustbemaintainedfor a subse-quentglossyreflectionstep.

As in RadianceClustering,18 patchesandclustersareas-sumedto have no spatialextentasfar asthe representationof outgoingradianceis concerned.They storea hierarchi-cal directionaldistribution for outgoingradiancewhich will

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M. Stamminger etal. / EfficientGlossyGlobal Illuminationwith InteractiveViewing 3

be describedseparatelyin Section4. In contrastto Chris-tensenet al.,3 our new algorithmdoesnot differentiatebe-tweenclustersandpatchesconcerningtherepresentationofexitant light.

3.1. BoundedPropagation

Our approachis basedon the radiosity clusteringmethoddescribedby Stammingeret al.,23� 24 which canhandleflatandcurvedsurfacesaswell asclustersin a uniform manner.Boundingboxesaroundtheobjectsareusedto boundthesetof interactingdirections.With this information,boundsonthe form factorandexitant radianceat thesenderarecom-puted,deliveringminimumandmaximumvaluesfor there-ceivedradiosity. Thedifferenceis usedto decidewhethertorefinea link.

This boundedradiosity approachcan be applied to ra-diancecomputationseasily, sincethe propagationof light,i.e., the transformationof exitant to incident light, is in-dependentof materialproperties.The only differenceliesin the evaluationof boundson the radianceof the sender,which is even easierif we have a directional distributionfor the sender’s exitant radiance.However, sincethis exi-tant radiancerepresentationis only approximate,theresult-ing boundsareno longerconservative.

3.2. Incident Light

One way to integrate the directional information is to ex-plicitly computea finite elementrepresentationof it. In thework of Christensenet al.,3 eachincidentlight contributioncomputedduringpropagationis projectedseparatelyontoabasisfor incominglight (for clusters).This is rathercostly(in memoryandtime) andresultsin significantblurring ofincidentlight, which canexhibit very strongvariations.Onthe otherhandthis blurring counteractsto someextent thesharpeningdueto thepoint-representationof clusters.

An alternative is to reflectincidentlight contributionsim-mediatelyafter they have beencomputed,18 while their di-rectionof incidenceis still known. Thereflectionresponsesarethenprojectedontofinite elementbasesseparately. Thismethodcircumventstheneedto storetheincidentlight, butthestorageconsumptionis not reduced:two representationsof exitant radianceare neededfor the push/pullphase.Inaddition,this methodis computationallyexpensive,becauseof the high numberof BRDF evaluations,andthe multiplehierarchytraversalsinvolvedin theimmediateprojection.

Ourproposedsolutionis to combinetheapproachesof in-cidentlight representationandimmediatereflection.We at-tachincidentlight to a receiving patchin theform of Illumi-nationSamples. Light propagationis computedsimilarly toHR by refininglinks until eachlink representswhatamountsto constantlight power. Insteadof simplysummingtheirra-diancevaluesat the receiver, an Illumination Samplewith

thedirectionto thesenderandthe transportedirradianceisaddedto the receiver for eachlink. At the endof the prop-agationstep,the illumination in the sceneis representedasa setof point samples,distributedover the scenehierarchy(seeFigure1, left).

Figure1: IlluminationSamplesin thescenehierarchy. Left:afterpropagationcomputation.Right: after push.

3.3. Push/Pull and Reflection

A push stepasin HR is neededto createa consistentrep-resentationof the incident light at the leaves, i.e., all lightreceived by inner nodesis propagatedto the children bypassingtheir IlluminationSamplesdownwards.Afterwards,eachleaf hasa largesetof Illumination Samplesdescribingits entireincidentlight field (seeFigure1, right). Note thatthe numberof hierarchytraversalsis muchsmallerthan inRadianceClustering,18 whereeachsampleis pusheddownseparately.

After thepush step,theincidentlight hasto bereflectedaccordingto theobject’s BRDF. BecauseIlluminationSam-plescorrespondto Dirac impulses,the reflectionis an im-pulseresponseof theBRDF, i.e., it is theBRDFwith afixedincident light direction multiplied by the irradianceof thesample.The completereflectionis the sumof the impulseresponsesto eachIlluminationSample.ThereforetheBRDFmustbeevaluatedoncefor eachIllumination Sampleto ob-tain thereflectedradiancein a particulardirection.

Using an adaptive directionaldistribution describedbe-low, reflectedlight is projectedonto anadaptive, hierarchi-cal directionalbasisto obtainthenew exitant light for eachpatch.Theserepresentationsarethenaveragedbottom-uptoobtainthedistributionsfor innernodes.

Due to the presenceof the completeillumination infor-mationafter push-pull,coherencein the incident light canbe exploited for reflectioncomputation.Considera glossypatchbeing illuminatedby n nearbyillumination samples,all carryingapproximatlythesameenergy (Figure2). Eachsingle reflection is a sharppeak, but their sum is rathersmooth.

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If eachincominglight transferis reflectedindependently,asit is donein 18, n directionaldistributionsarecreatedandfinally summed.As a resultthedirectionaldistribution willbe subdivided finely over the entirerangeof the reflection.Becausethe Illumination Samplemethoddescribedabovedirectly computesthe summedresponse,it is ableto detectthesmoothregionsof thereflectionandto adaptsubdivisionaccordingly.

Figure2: Reflectionof singleradiancetransfersona highlyglossypatch andsumof reflectiondistributions.

To demonstratethis we appliedthe methodsto the testsceneshown in Figure3. A small glossyreflectoris lit by3 � 7 light sourceswith mutualangleof 3, 15 and30 de-greeswhich causesthe illumination of a large diffuse re-ceiver. Thereflectionis computedby (a)individually reflect-ingeachlight sourceandsummingtheresultingdistributionsand(b) by computinga distribution of theentirereflection.For both methodsthe L1 error norm is usedwith the sameerror threshold.Table1 shows the resultingnumberof ba-sisfunctions,computationtimesandBRDFevaluationsper-formed.

It canbeseenthatfor all scenesthenumberof basisfunc-tions for the final result is significantlysmallerthan if thesumis projecteddirectly. Also computationtime is shorter,but the differenceis not aslarge asonewould expect.Thereasoncan be found in the column “BRDF evaluations”,whereweseethattheirnumberis relatively high.This is be-causeby projectingthe sumfor eachexitant radiancesam-ple all Illumination Samplesare reflected,including thosewith neglible contribution.By projectingtheresponsessep-arately, the samplingcanbe focusedto relevant regionsin-dependentlyfor eachIlluminationSample.

3.4. Shooting

With astandardgatheringiterationscheme,thenumberof Il-luminationSamplesandthusthetimefor push/pullincreasesfrom iteration to iteration. With a shootingschemein thespirit of 22 this can be avoided. In sucha scheme,Illumi-nationSamplesarereflectedonceandthenremoved.Thus,in iterationi the light reflectedexactly i timesis consideredonly.

However, this requiresthedistinctionof “unshot”andac-cumulatedlight. If this distinctionis madefor exitant light,thismeansthatfor everypatchtwo memory-intensive direc-tional distributionsare required.With a bit more care,thedistinctionis madewith respectto theincidentlight, avoid-ing theincreasein memoryconsumption.

In particular, every patchgetstwo Illumination Samplesets,ISSetNew andISSetAccum, aswell asonedirec-tionaldistribtionDD. During iterationi (startingwith i � 0),newly computedillumination samplesareappendedto IS-SetNew. In thereflectionstep,ISSetNew is reflectedandthe result is storedin the directionaldistribution DD. Thenthesamplesof ISSetNew areappendedto ISSetAccumandISSetNew is cleared.

This has the following consequences:in iteration i thecostlydirectionaldistributionDD containsthelight reflectedexactly i times.For large i, this light is automaticallyrep-resentedat coarselevels of the hierarchy, so the requirednumberof DDs is small.Therefore,mostmemoryfor DD isrequiredin theinitial iterations,anddecreasescontinuously.

ISSetNew representsthe incident light after exactly ireflections.It is also largest in the beginning and quicklygetssmaller. Only ISSetAccum increasesover time, butit alsorepresentsthefinal result,which shouldbestoredinany case.Illuminationsamplesareprobablyanefficientwayof doingthis.

Thefinal solutionis thusglobal incidentlight only. In or-der to obtainglobal exitant light, e.g.,for interactive view-ing (see below), ISSetAccum has to be reflectedas awholeonefinal time.Thisis notnecessarywith theVISION-renderingarchitecture,whichwasusedfor oneof thetestim-plementations.In VISION, lighting algorithmshaveto com-puteincidentlight only. The last reflectionstepis thenper-formedduringthefinal ray tracingfor rendering.

3.5. Discussion

Note that in our approachpropagationand reflection arecompletelydecoupled.Propagationcomputationdoesnotconsiderthe reflection propertiesof the receiver, e.g. bycomputingthe incidentlight of a highly glossypatchmoreaccuratelythan in the diffusecase.How this glossinessofa patchshouldbe measuredandthenusedto guidethe ac-curacy of thecomputation,is still anopenquestion,though.The spatialrefinementof the patchesis doneduring prop-agation,while the refinementlevel of the directionaldistri-butionsis chosenduringreflection.Thisdistinctiondoesnotimposea problemon convergence,but it resultsin mem-ory/computationsavings.

Illumination Samplescan be interpretedas Dirac-peaksfrom a particulardirectiondescribingincidentlight andarethussomewhatsimilar to thephotonsin thePhotonMapap-proachof Jensenetal.9 However, Photonmapsarenotdeter-

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Figure3: 3 � 7 light sourcesilluminatinga smallglossyreflector, which in turn illuminatesa large diffusereceiver. Theanglesbetweenadjacentlight sourcesare 3, 15and30degrees.

reflectingthesum summingthereflections

light source basis computation BRDF- basis computation BRDF-angle functions time evaluations functions time evaluations

3 4.998 10.05s 457.968 7.140 19.83s 148.17215 3.752 7.56s 342.000 16.390 15.89s 351.55430 3.096 4.86s 251.790 23.574 10.39s 219.372

Table1: Statisticsfor thecomputationof thesimpleexamplescenes.

ministic andtheir usagefor lighting simulationis very dif-ferentfrom ours.

With respectto astandardnorm,with Dirac-peaksnocon-vergentrepresentationcanbe obtained.On the otherhand,theDirac-representationis only usedto computethereflec-tion integral.Fromanotherpointof view, this representationcanbeseenasintermediatedatain a delayednumericalin-tegration,whereeachIllumination Sampleis a temporarilystoredintegrationsample.SoaslongastheBRDFis numer-ically integrable,thecomputedreflectionwill converge.

The artifacts resulting from the Dirac-representationaswell astheconvergenceof thesolutiondueto spatialrefine-mentaredepictedin Figure4. It shows a very simplesceneof anarealight anda highly glossyreflector, renderedwiththreedecreasingerrorthresholdvalues.In orderto make theartifactsmorevisible, no smoothingis performed.It canbeclearly seenhow the arealight is representedby 4, 16 and64 Illumination Samplesandhow thereflectionconverges.

For a morediffusereflector, theartifactswould bemuchlessvisible becauseof the larger splats.This demonstratesthat light propagationtowardsa highly glossypatchshouldbe subdivided finer thantowardsa diffusepatch.However,this requiresan estimationof the glossinessof a patchandanappropriaterefinementstrategy. Wehavenotpursuedthisissuefurther.

4. Adaptive Representationof Outgoing RadianceforInteracti ve Display

To producethefinite-elementsolutionssuitablefor interac-tivedisplay, westoreoutgoinglight in theform of directionaldistributionsattachedto surfacesor clusters.As in RadianceClustering,18 objectsareassumedto have no spatialextent.Insteadof thefour dimensionalradianceonly the2D radiantintensitydistribution is storedwith eachobject.

For therepresentationof directionalradiantintensities,wehave implementedandexaminedtwo options:First, a uni-form subdivision of the directionspace,whereeachdistri-bution is representedby afixednumberof coefficients(non-adaptivebasis). Second,we implementedanadaptive repre-sentationusingHaarWavelets.

Note that theuseof theadaptive basisallows a compari-sonwith RC 18; to becompletewe shouldhave testedwithsphericalharmonics.Sinceno solution for generalsurfaceorientationcurrentlyexists,we usedthe“non-adaptive” ba-sisfor comparison.

The non-adaptive basisis moreuseful for smoothdistri-butions,becauseall operationsonthefixedsubdivisionbasisaresimpleandfast.Theadaptive Haarbasisis bettersuitedfor stronglyvarying functions,becauseit canusemoreba-sis functionsin the interestingregionsandfewer in smoothregions.However, operationssuchas the evaluationof thedistributionor additionof two distributionsaremoreexpen-sive,dueto theunderlyingnon-regularrepresentation.

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Figure4: Convergenceof reflectionsof Dirac-representations.Theerror thresholdis chosensuch that thearealight at thetopis representedby 4, 16 and64 IlluminationSamples.

4.1. “Non-adaptive” Representation

For a non-adaptive basis,we usea uniform subdivision ofthe directionspace.To accomplishthis task,a tetrahedronis subdivided. We thusobtain4n� 1 trianglesif the level ofsubdivison is n. Sincethe numberof verticesis lower thanthe numberof triangles(this is 2 � 4n � 2), we decidedtostore3 floatsfor RGB only at thevertices(seeFigure5).

With Values at VertexDirectional Basis

level 1level 0 level 1level 0

Figure5: Non-adaptivebasissubdivision

If somefunction (e.g.,the reflectedlight of an object)isto be projectedinto the non-adaptive basis,the function issimply evaluatedat theverticesto obtainthecorrespondingcoefficients.As a result,this is in essencea piecewiselinearrepresentation.

4.2. Haar Representation

For theHaarrepresentation,thedomainof directionsis pa-rameterizedby pointson anoctahedron.Theverticesof theoctahedronareselectedto lie on themainaxes,soeachfacecorrespondsto oneoctantof thedirectionaldomain.Simplesignconsiderationsof a directiondeliver thecorrespondingoctahedronface.

A hierarchyof basisfunctionsis built by assigninga firstlevel basisfunctionto eachof theeight facesof theoctahe-dron.Thesearethensubdivided hierarchicallyin the usualmanner(seeFig. 6). In order to allow for linear interpola-tion for laterpointsamples,thehierarchyis alwayskeptbal-anced,i.e., the subdivision levels of two neighboringtrian-glesnever differ by morethanonelevel.

Figure6: Hierarchy on theoctahedron.

In orderto quickly computeanadaptive representation,atop-down approachwaschosen.Assumethatthefunctiontobeprojectedis f . For eachof thefirst eightbasisfunctions,f is sampledat the triangle cornersand at its center. If fis almostconstantover the triangle,the samplevalueswillonly vary slightly. For highly varying f , onecan expect awiderangeof functionsamples.Thusthedifferencebetweenminimum and maximumsampleis considered.If it is toolarge,the four finer basisfunctionspartitioningthedomainareconsideredrecursively.

This top-down approachruns into problemsif f has asharppeakinbetweenthe samples.We alleviate this prob-lem by enforcinga minimum subdivision level in the hopethat theresultingsamplingis denseenoughnot to missanypeaks.

Thereareseveral possibilitiesto decidewhetherthe dif-ferenceis too large.For thealgorithmdescribedin this pa-per, thedifferenceis comparedwith themidpointvalue,i.e.amaximumpercentage deviation ε with respectto thecentervalueis allowed.Thisturnedoutto bebeneficialfor ourcase(especiallyin the context of interactive viewing, seeSec-tion 5.1); for othersettings,differentcriteriacanbeused.

4.3. Comparison

To see the differencesinvolved in using Haar or non-adaptive representations,considerthe following simpleex-

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ample,which is anemptyroom(thegeometryis takenfromtheRADIANCE testscene“SodaShoppe”29).

Thereferenceimagewascomputedwith a path-tracerus-ing next-event estimation.12 The imagesin Figure 7 weregeneratedusingRadianceClustering,with thenon-adaptiveandHaarbasis(seeSection5 for moredetailsonrendering).The “Max Level” parametercorrespondsto the maximumpermittedlevel of subdivision.Clearly, thenon-adaptive ba-sis fails to correctly representthe highlightson the glossyfloor for maximumsubdivision level 3. For maximumlevel4, the result is improved, but at the cost of 4 times morememory(seeTable2). In contrast,the Haarbasisuseslessthan threetimesasmuchmemoryfor an “equivalent” im-provementin quality. However, the Haar basisalso takesmore time. The reasonis that arithmeticoperationson theregularconstantsubdivisionareof coursesimplerandfaster.

This exampledemonstratesthatfor highly glossyscenes,smallhighlightscanonly becapturedwith theadaptive ba-sisor averyfinenon-adaptive basisrepresentation,which inturn requireslarge amountsof memory. More importantly,theuser, whohaslimited memory, canonly changethequal-ity in large“quanta”,andoftenwill notbeableto getasatis-factoryresultbeforerunningoutof memory. Adaptivebases,suchas Haar, alleviate this problem.However, the unifor-mity of the non-adaptive basisresultsin a smoother, moreregular distribution, which becomesespeciallyvisible dur-ing interactiveviewing. NotealsothattheHaarsolutioncap-turessecondaryglossyreflectionfrom thewalls to thefloor,whichareparticularlyhardfor path-tracing.

Max Distr Triangles TimeLevel N/A Haar N/A Haar

3 2878 782K 640K 510s 722s

4 2878 3127K 1829K 731s 1125s

Table 2: Comparisonof Non-adaptive (N/A) andHaarbasisforRadianceClustering,showing the numberof directionalfunctions(Distr) usedandthecomputationtime.Max Level is themaximumlevel of subdivision.

5. Interacti ve Display

After thecomputationof aglobalilluminationsolutionusingIllumination Samples,we have a representationof outgoingradiantintensity, storedin the directionaldistribution func-tion. At eachframeduring interactive display, we needtoevaluateradiancefor every glossyhierarchicalleaf elementin the directionof theviewpoint. This implies two require-ments:(i) subdivision of thedirectionaldistributionsappro-priately so that a visually pleasingrepresentationof glossyeffectsis producedand(ii) accelerationof the displaypro-cessto avoid the costof the evaluationof radianceat eachelementat every frame.

5.1. RefinementIssuesfor Display

Recall that we have decoupleddirectional subdivision, intheform of theHaar-baseddirectionaldistributionfunctions,andthe spatialsubdivision, in the form of the “traditional”hierarchicalradiosityelementhierarchy. To interactively dis-play thesolution,we interpolateradiancein theview direc-tion by evaluatingthe directionaldistribution on eachele-ment.If subdivision in directionspaceis performedarbitrar-ily, the differencein subdivision of thedirectionalfunctionbetweenneighbouringpatchesmaybetooabrupt.

This is thecasefor exampleif wecompareabsolutevaluedifferencesbetweenthecenterandtheverticesof the trian-glesof thedirectionalsubdivision to decidewhetherto sub-divide. The useof relative (percentage)differencesavoidsthisproblemsinceweapproximatetheform of thefunction,which variesmoreslowly acrossneighbours.The artifactsdue to the absoluterefinementcanbe seenin Figure8. Inparticular, notetheringingartifactswhicharevisiblearoundthe highlight using the absoluterefiner. Theseartifactsareremovedwhenusingtherelative (percentage)solution.

5.2. Interacti ve Rendering

For efficient displaywe separatethesceneinto two lists, sothatdiffuseobjectscanberenderedonceandredisplayedinefficient, display-listmode.The otherlist, of glossyreflec-tors,is updatedappropriatelyateachframeanddisplayedinimmediatemode.The accelarationachieved obviously de-pendson thepercentageof diffusesurfacesin thescene.Forthescenestestedweachieveupdateratesvaryingfrom afewframespersecondto afew secondsperframefor morecom-plex scenes.

In theBRIGHT renderingsystem,smoothinteractivedis-playof radiositysolutionsis performedby storingper-vertexradiosityvalues.Thesevaluesareupdatedduring thepush-pull phaseof thesolution,by extrapolatingelementradiosityvaluesto theadjacentvertices.

To achieve smoothshadingfor glossysurfaces,we adda field to the datastructureassociatedwith verticesin thehierarchyof elements.For planarsurfaces,this field is up-datedduringpush-pullin a mannerslightly differentto thatof radiosity;i.e., for a vertex belongingto a leaf elementorto an edge,the radiant intensity is summedwith the radi-antintensitystoredat thevertex. Sinceradiantintensityis inWatts/sr(see18), atdisplaytimewedivideby theareaof thesurroundingelements.

Thespecialcaseof indexedface-setsis treatedseparately.Indexedface-setsarecommonmodellingprimitives,andof-ten result from the tesselationof curved objectssuch asspheresor cylinders.In theBRIGHT renderingsystem,wepre-tesselatesuchobjects,andrepresentthemasanindexedface-set.Theadvantageof sucha representationis thatver-tices are sharedbetweenadjacentelements.We can thus

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Max level 3 4

Non-adaptive

Haar

Reference

Figure7: Comparisonof thenon-adaptive vs.Haarbasis.

Figure8: Artif actswhenusingthe“absolute”refiner(left), whichareabsentwhenusingthe“relative” refiner(right).

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avoid thestorageof theadditionaldirectionaldistributionatthevertices.

Eachvertex storesthe list of polygonalelementswhichshareit. Its color is thentheaverageradiantintensityof thesepolygons(i.e., I evaluatedat the centersof the elementsinthe viewing direction).For moreefficient display, we eval-uatethis color onceper vertex for a given direction.Also,we recomputethe color only if the directionchanges“suf-ficiently” i.e., greaterthana user-definedε threshold.Thisallows thecontrolof thequality/updateratetradeoff.

6. Implementation and Results

One major goal of our approachwas the developmentofa solution which can be considereda simple “add-on” toan existing hierarchicalradiositysystem.We implementedthealgorithmon two very differentrenderingarchitectures,namely BRIGHT (iMAGIS) and VISION (University ofErlangen).20

Wehavetestedour implementationonseveraltestscenes,shown in Figures9 and 13. The scenesin Figure 9 wereusedfor the interactive viewing test in BRIGHT. The firstsceneshows threelight sourcescoloredred,greenandblue,illuminating a very glossy, small reflector. This reflectorinturn indirectly illuminatesa diffusewall. Thesecondsceneis aglossysphereilluminatedby asmallsourceandaglossyfloor. Thesein turn produceindirect glossyeffects on thelower partof thesphereandthediffuseceiling. Finally, the“Simple soda” sceneis a simplified version of the “SodaShoppe”scene.In BRIGHT, we require tesselationof allobjectsinitially, whichresultsin ahighnumberof initial ob-jects; in VISION, objectsare not initially tesselated.Thisexplains the low numberof initial objectsin the complete“SodaShoppe”scene,usedfor Figure13.

6.1. RadianceClustering vs. Illumination Samples

In BRIGHT wehaveimplementedbothRadianceClustering(RC) andthe Illumination Samples(IS) approach.We havecomparedrunningtime andmemoryusagefor the RC andIS approaches.The thresholdvalue hasthe samemeaningfor bothapproaches,sincewe areusinga “relative” refiner.Visual inspectionalso shows that the resultingimagesareequivalentfor thesameparametervalues.All timingsareona 195MhzR10kSGIworkstation.

6.2. Memory Consumption

In Table3 we show thememorystatisticsfor thetestscenesused.In particularwe list thedifferentsceneswith theε ac-curacy threshold(seeSection4.2), and the correspondingnumberof directionaldistribution basisfunctionsusedforthesolutionby theRadianceClustering(RC) andIllumina-tion Samples(IS) approach.The rightmostcolumn showsthepercentgainof theilluminationsamplesapproach.

ε m/M IS RC

3 Lights 0.5 1/3 8618 13866 38%

3 Lights 0.1 1/3 8820 14068 37%

3 Lights 0.5 1/4 27306 43510 37%

3 Lights 0.5 1/5 79218 125944 37%

Sphere 0.5 1/3 2114324 3598720 41%

Soda 0.5 1/3 2097534 3339794 37%

Table 3: Gain in memoryusagefrom the useof the IlluminationSamples(IS) algorithm.ε is the accuracy thresholdand m/M themin/maxpermittedlevels.

Memoryusageis clearlyreducedusingIlluminationSam-plescomparedto the RadianceClusteringapproachfor allscenes.Thegainvariesfrom 37 % to 41%in thebestcase.This is mainly dueto the fact that RadianceClusteringre-quires the additional intermediatedirectional distributionfunctionsto be able to correctlyperformthe push-pullop-eration(seeSection2.2).

6.3. Computation Time

In Table4 we show the computationtime statisticsfor thetest scenesused.In particularwe list the different sceneswith the ε threshold,and the correspondingcomputationtime for the solution by the two approaches(RC and IS).The rightmostcolumn shows the percenttime gain of theilluminationsamplesapproach.

ε m/M IS RC

3 Lights 0.5 1/3 44.6s 90.1s 50%

3 Lights 0.1 1/3 44.2s 90.0s 51%

3 Lights 0.5 1/4 49.3s 95.5s 48%

3 Lights 0.5 1/5 58.6s 105.3s 44%

Sphere 0.5 1/3 4167.1s 6492.9s 34%

Soda 0.5 1/3 5207.6s 7117.4s 27%

Table4: Gainin computationtimefrom theuseof theIlluminationSamplesalgorithm(IS). ε is theaccuracy thresholdandm/M arethemin/maxpermittedlevels.

For all scenestheilluminationsamplesapproachprovidesaspeedupof atleast27%.Thisis mainlydueto thereductionin thenumberof hierarchytraversals,andalsothereductionin the numberof trianglesusedto representthe directionaldistributionsasdiscussedabove.

As expectedandconfirmedby the experimentalresults,

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the Illumination Samplesapproachreducesboth memoryandcomputationtime with respectto RadianceClustering.Theimagesproducedby bothapproachesareessentiallyin-distinguishable.

6.4. Visual Quality/Comparisons

We qualitatively comparethe visual quality of the imagesof RadianceClusteringandIlluminationSampleswith thosefrom a path-traceror the RADIANCE system.The path-tracertestsarerenderedusingan in-houseimplementationof the next-event estimation.12 In Fig. 10 and11 we showthereferencepath-traceror RADIANCE imagesandthecor-respondingIllumination Samplesimagestogetherwith thecomputationtimesfor thetestscenes.

Thereareseveral interestingobservationsthatwe canin-fer from theseexamples:

� In thecaseof thethreelight scene,RADIANCE runsintosamplingproblems.Even after more than an hour anda half of computationit doesnot converge. In contrast,illumination samplesachieves a solution in less than aminute,which is in additionviewablefrom any directioninteractively. A bi-directionalpath-tracer, or photon-mapwhich would considerthe reflectionas a causticwouldprobablygeneratebetterresults.

� The computationtimes of IS are either lower or in thesameorderof magnitudeas thoseof the referencesolu-tions.The importantthing to rememberis that the IS so-lutions can be viewed interactively, while the reference(path-traceror RADIANCE ) requirethesameamountoftime(tensof minutesor evenhours)for every image.

� Path-tracingimagesareverynoisy. The“smooth-shaded”solutionsproducedby IS do not suffer from this prob-lem. Despitebeingapproximate,the smooth-shadedim-agesarethereforemuchbettersuitedto interactive appli-cations,wherenoiseandflickeringarevery distracting.

Wethusbelievethatourapproachhasgreatpromise,sinceit canbeusedto generatelow to moderatequality solutionsfor glossyenvironments,aswell asproducesolutionssuit-ablefor interactive viewing.

6.5. A Mor e ComplexScene

As a last test we appliedthe Illumination Samplemethodto a more complex scene,the Soda Shoppe,one of theRADIANCE test scenes.Our version consistsof 1,644initial patches,several of which are non-planar, includingthe sphericallight sources.About one third of the patchesarenon-diffuse.Sinceboundedform factorcomputationisused,23 no initial tessellationof theseobjectswasnecessary,which would have increasedthe initial complexity signifi-cantly. Thesceneis notyet reallycomplex in thesenseof anindustrial-sizemodel,but sufficiently non-trivial to imposesevereproblemson previous finite-elementradiancemeth-ods.

Thesolutionshown in Figure13 wascomputedwith theimplementationof VISION, which incorporatesthe“shoot-ing” solutiondescribedpreviously (Section3.5). It wasob-tainedin 8,488secondsandcontains29,138final patches.91% of the computationtime was spenton propagation,which in turn is dominatedby visibility (97%), only 9%was used for push/pull including the reflection. 743,284links werecomputed,resultingin 29,138patches.Notethatthe usedVISION implementationdoesnot yet incorporatesmoothreconstructioncapabilities,sothat thepatchbound-ariesareclearlyvisible.

By far mostof the computationis spenton visibility, aswith diffuse radiosity computation.This indicatesthat wewere able to reducethe overheadintroducedby explicitlystoring directional illumination information to reasonablelevels.The morecostly push/pullstepwasexpected,but itis interestingto noticethatit still requiresonly about10%ofthe overall computationfor this particularscene.For othersceneswith more glossyobjects,this percentageis some-what larger, althoughalways“reasonablysmall”. Note thatthis is only truefor usingshootinginsteadof gathering!Forgatheringthepush/pulltimescanincreasesignificantly.

7. Conclusions

We have presenteda novel solution to global illuminationsimulationfor glossyenvironments.Our new algorithm isanimportantsteptowardsinteractive walkthroughsof glob-ally illuminatedglossyscenes:(i) We introducedtheIllumi-nation Samplesalgorithmwhich representsincoming lightmoreaccuratelyandefficiently, both in memoryandcom-putation time. (ii) We have usedan adaptive hierarchicalfinite-elementbasisto storeoutgoinglight, in amannersuit-ablefor interactive viewing. This allows fine control of thememory/qualitytradeoff, whichwasnotpossiblein previoussolutions.(iii) Thesealgorithmscan be implementedwithmarginal effort over an existing hierarchicalradiosity sys-tem, by confining the modificationsto a small numberofphasesand datastructures.(iv) Interactive viewing of theglossyglobal illumination solutionsis achieved by suitablyrefining thedirectionalrepresentationof outgoinglight andacceleratingthedisplayprocess.

Oursolutionhowever is still quitememory-consumingre-quiringin theorderof tensof Mbytesfor thesmallestscenesandhundredsof Mbytesfor themorecomplex.

An obviousweaknessof theproposedmethodis thesepa-rate refinementof the patchesand the directionalintensityfunctions.We hope to achieve a more efficient algorithmby coordinatingthesetwo typesof refinement.Suchan im-proved refiner shouldalso better take into accountthe re-quirementsof interactive viewing, in orderto provide asub-division of directionswhich is both efficient andamenableto smoothinterpolationfor interactive viewing.

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Figure9: Testscenesusingilluminationsamples

.

Reference(Radiance) IlluminationSamples

6537s 59s

1303s 4167s

Figure10: Referencesolutions(RADIANCE) comparedto IS solutionsfor threelightsandspherescenes.

Reference(path-tracer) IlluminationSamples

51873s 5208s

Figure11: SimpleSodareferencesolution(path-tracerat 455x364resolution)comparedto IS solution.

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12 M. Stamminger et al. / EfficientGlossyGlobal Illuminationwith InteractiveViewing

Figure 12: A solution to the glossysodashoppe,computedin8,488seconds.

Acknowledgements

This researchwasfundedby theESPRITOpenLTR ProjectSIMULGEN (#25772) ”Simulation of Light for GeneralEnvironments”, (http://www-imagis.imag.fr/SIMULGEN).Thanksto Cyril Soler(iMAGIS) andIgnacioMartin (GGG)for coding help, and to Bruce Walter for proofreading.iMAGIS is a joint projectof CNRS/INRIA/UJF/INPG.

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