A Survey of Visibility for Walkthr ough Applicati ons

DanielCohen-Or�

Tel Aviv UniversityYiorgos Chrysanthou†

UCLClaudioT. Silva‡

AT&TFredoDurand§

MIT - LCS

Abstract

Visibility algorithmsfor walkthroughandrelatedapplicationshave grown into a significantarea,spurredby the growth inthe complexity of modelsandthe needfor highly interactivewaysof navigatingthem.

In thissurvey wereview thefundamentalissuesin visibilityand conduct an overview of the visibility culling techniquesdeveloped in the last decade. The taxonomy we usedistin-guishesbetweenpoint-basedandfrom-regionmethods.Point-basedmethodsarefurthersubdivided into object-andimage-precisiontechniques,while from-region approachescan takeadvantageof the cell-and-portalstructureof architecturalen-vironments,or handlegenericscenes.

1 Intr oduction

Visibility determinationhasbeena fundamental problemincomputergraphicssincetheverybeginningof thefield [5,85].A variety of hiddensurfaceremoval (HSR) algorithmsweredevelopedin the1970sto addressthefundamental problemofdeterminingthevisible portionsof thesceneprimitivesin theimage.Thebasicproblemis now believedto bemostlysolved,andfor interactive applications,the HSRalgorithmof choiceis usuallytheZ-buffer [15].

Visibility algorithmshave recently regainedattentionbe-causetheever increasingsizeof 3D datasetsmakesthemim-possibleto displayin realtimewith classicalapproaches.Pio-neeringwork addressingthis issueincludesJones[53], Clark[19] andMeagher[64]. Recently, Airey et al. [2], Teller andSequin[86,89], andGreeneetal. [46] built upontheseseminalpapersandrevisitedvisibility to speedupimagegeneration.Inthis survey, we review recentvisibility algorithmsfor the ac-celerationof walkthrough applications.

Visibility culling aimsat quickly rejectinginvisible geom-etry beforeactualhidden-surfaceremoval is performed.Thiscanbe accomplishedby only drawing the visible set,that is,the subsetof primitiveswhich may contribute to at leastonepixel of thescreen.Muchof visibility-culling researchfocuseson algorithmsfor computing(hopefully tight) estimationsof

�School of Computer Science, Tel Aviv University, Tel Aviv

69978,Israel, dcor@tau.ac.il†Department of Computer Science, University College Lon-

don, Gower Street, London WC1E 6BT, United Kingdom,y.chrysanthou@cs.ucl.ac.uk

‡AT&T Labs-Research, 180 Park Ave., Room D265, FlorhamPark,NJ07932,csilva@research.att.com

§Massachusetts Institute of Technology, Laboratory for ComputerScience,NE43-255,Cambridge, MA 02139,fredo@gfx.lcs.mit.edu

View-frustum culling

Frustum

visible

Back-Face Culling

Occlusion Culling

View

Figure 1: Three types of visibility culling techniques: (i)view-frustumculling, (ii) back-faceculling and(iii) occlusionculling.

the visible set. A Z-buffer algorithmis thenusuallyusedtoobtaincorrectimages.

Visibili ty culling startswith two classicalstrategies: back-faceandview-frustumculling [35]. Back-faceculling algo-rithms avoid renderinggeometry that facesaway from theviewer, while viewing-frustumculling algorithmsavoid ren-deringgeometrythatis outsidetheviewing frustum.Efficienthierarchicaltechniques have beendeveloped [19,39,60], aswell asotheroptimizations[6,82]

In addition, occlusionculling techniquesaim at avoidingrenderingprimitivesthat areoccludedby someotherpart ofthescene.This techniqueis globalasit involvesinterrelation-shipamongpolygonsandis thusfarmorecomplex thanback-faceandview-frustumculling. Thethreekindsof culling canbeseenin Figure1. In this survey, we will focuson occlusionculling andits recentdevelopments.

Sincetestingeachindividual polygon for occlusionis tooslow, almost all the algorithmsthat we will describehere,placea hierarchyon the scene,with the lowest level usuallybeingthe bounding boxesof individual objects,andperformtheocclusiontesttop-down on thathierarchy, asdescribedbyGarlicket al. [39] for view-frustumculling.

A very importantconcept is conservative visibility [1, 89].The conservativevisibility set is the setthat includesat leastall of thevisible setplusmaybesomeadditionalinvisible ob-jects. In it, we mayclassifyanoccludedobjectasvisible, butmay never classify a visible object as occluded. Suchesti-mationneedsto beascloseto thevisible setaspossible,andstill be “easy” to compute. By constructingconservative es-timatesof the visible set,we candefinea potentiallyvisibleset(PVS)[1,89] which includesall thevisible objects,plusa(hopefully small)number of occludedobjects,for thatwhole

region of space. The PVS can be definedwith respectto asingleviewpoint or with respectto a region of space.

It is importantto point out the differencesbetweenocclu-sionculling andHSR.Unlikeocclusionculling methods,HSRalgorithmsinvestcomputational efforts in identifying the ex-act portions of a visible polygon. Occlusionculling algo-rithms needto merely identify which polygons arenot visi-ble, without theneedto dealwith theexpensive sub-polygonlevel. Moreover, occlusionculling can (hopefully conserva-tively) over-estimatethe setof visible objects,sinceclassicalHSR will eventually discardthe invisible primitives. How-ever, thedistinctionis not a clearcut sincein somecases,anHSR algorithm may include an occlusionculling processasan integral part of the algorithm (for example, ray casting),andsincesomemethodsintegrateocclusion-culling andHSRat thesamelevel.

What makes visibility an interestingproblem is that forlarge scenes,the numberof visible fragmentsis often muchsmallerthanthetotal sizeof theinput. For example,in a typ-ical urbanscene,onecanseeonly a very smallportionof theentiremodel,assumingtheviewpoint is situatedator neartheground. Suchscenesaresaid to be denselyoccluded, in thesensethat from any given viewpoint, only a small fractionofthe sceneis visible [2, 86]. Other examplesinclude indoorscenes,wherethewalls of a room occludemostof thescene,andin fact,from any viewpoint insidetheroom,onemayonlyseethe detailsof that room or thosevisible throughthe por-tals, seeFigure 2. A differentexample is a copying machine,shown in Figure 3, wherefrom the outsideonecanonly seeits externalparts. Although intuitive, this information is notavailableaspartof themodelrepresentation,andonly a non-trivial algorithmcandetermineit automatically. (Notethatoneof its doorsmight beopen.)

The goal of visibility culling is to bring the cost of ren-dering a large scenedown to the complexity of the visibleportion of the scene,and mostly independent of the overallsize [19, 44]. Ideally visibility techniques shouldbe outputsensitive; the runningtime shouldbe proportionalto the sizeof the visible set. In openenvironments,the visible set canbequitelarge,but severalcomplex scenesarepartof “denselyoccludedenvironments” [89], wherethe visible set is only asmallsubsetof theoverall environment complexity.

Visibility is not an easyproblem,sincea small change inthe viewpoint might causelargechangesin thevisibility. Anexampleof this canbe seenin Figure 4. The aspectgraph,describedin Section 3, andthe visibility complex (describedin [30]) shedlight on thecomplex characteristicsof visibility.

1.1 Related work and sur veys

Visibility for walkthroughsis relatedto many otherinterestingvisibility problems. In particular, in shadowalgorithms,thepartsof the model that are not visible from the light sourcecorrespond to the shadow. So occlusionculling andshadowalgorithmshave a lot in commonandin many waysarecon-ceptuallysimilar, e.g.[18,97]. It is interestingto notethatcon-servative occlusionculling strategieshave not beenaswidelyusedin shadowalgorithms.

Otherrelatedproblemsincludetheartgalleryproblem[69]and its applicationsto image-basedrendering[34, 83], andgloballighting simulation,e.g.[40,49].

Someothervisibility surveyswhichoverlapin contentwithoursalreadyexist. Durand[30] haswrittenamorecomprehen-sivevisibility survey. For thoseinterestedin thecomputationalgeometryliterature,see[27–29]. Noneof theseworksfocuseson 3D real-timerendering.

Zhang’s thesis[98] containsa short survey of computergraphicsvisibility work, and Moller and Haines[65, Chap-ter 7] cover several aspectsof visibility culling, but with lessdetailthanthepreviouswork, andalsowithoutcoveringmuchof therecentwork.

2 Classification

2.1 A taxonom y of occ lusion culling tech-niques

Theorganizationof thepresentsurvey is basedon thefollow-ing taxonomy:

� Point vs. region.

Our majordistinctionis whetherthealgorithmperformscomputationswith respectto the locationof the currentviewpoint only, or performsbulk computationsthat arevalid anywherein a givenregion of space.Onestrengthof the from-region visibility set is that it is valid for anumberof frames,and thus its cost is amortizedovertime. More importantly, from-region visibility alsohaspredictingcapabiliti es,which is crucial for network ap-plicationsor for disk-to-memorypre-fetching.Usingthevisibility informationfrom adjacentcells, the geometrycanbe prefetchedasit is aboutto be visible. However,from-region algorithmsusually require a long prepro-cessing,significantstoragecost,anddo not handlemov-ing objectsaswell aspoint-based methods.

� Image precisionvs.objectprecision.

For point-based methods,we will usethe classicaldis-tinction betweenobjectand image-precision[85]. Ob-ject precisionmethodsusethe raw objectsin their vis-ibility computations. Imageprecisionmethods on theotherhandoperateon the discreterepresentationof theobjectswhenbrokeninto fragmentsduringtherasteriza-tion process.The distinctionbetweenobjectandimageprecisionis however not definedasclearlyfor occlusionculling as for hiddensurfaceremoval [85], sincemostof thesemethodsareanyway conservative,which meansthattheprecisionis never exact.

� Cell-and-portalvs.genericscenes.

The last criterion is particularlyrelevant to from-regionvisibility. Somealgorithmsexploit thecharacteristicsofarchitecturalinteriorsandothersimilar datasets.Thesescenesarenaturallyorganizedinto cells(rooms)thatarelinkedby portals(doors,windows). A visibility methodcan then be carried out by observingthat other cellsarevisible only throughportals.Thecell-and-portalap-proachcanalsobe seenasthe dual of the occluder ap-proach: cell-and-portaltechniques start with an emptyPVS and add objectsvisible through seriesof portals,

(a) (b)

Figure2: With indoor scenesoftenonly a very smallpartof thegeometry is visible from any given viewpoint. In (b) the hiddenpartof thesceneis drawn. Courtesyof CraigGotsman,Technion.

(a) (b)

Figure3: A copying machine;only a fraction of the geometryis visible from the outside. But behindthe closedshell might behiding a greatdealof geometry(b). Courtesyof CraigGotsman,Technion.

(a) (b)

Figure4: A smallchange in theviewing positioncancauselargechangesin thevisibility.

while otherapproachesfirst assumethat all objectsarevisible andtheneliminateobjectsfoundhidden.

2.2 Additional criteria

In additionto thesethreetaxonomy axes,therearevarious im-portantcriteriato take into accountwhenreviewing avisibilityalgorithm:Thevariousmethodsaresummarizedwith respectto someof thesecriteriain Figure19.

� Conservativevs.approximate.

Most techniques describedin this paperare conserva-tive, that is, they overestimatethe visible set. Only afew approximate the visible set,but arenot guaranteedof finding all the visible polygons. Two classesof ap-proximationtechniquescanbe distinguished:samplingandaggressive strategies.Theformeruseeitherrandomor structuredsampling(ray-castingor sampleviews) toestimatethevisible set,andhopethatthey will not missvisible objects. They tradeconservativenessfor speedandsimplicity of implementation.Ontheotherhand,ag-gressivestrategiesarebasedonmethodsthatcanbecon-servative,butchooseto losethatpropertyin ordertohavea tighter approximation of the visible set. They chooseto declaresomeobjectsas invisible althoughthereis aslight chancethat they arenot, often basedon their ex-pectedcontribution on theimage.

� Tightnessof approximation.

Sincemostalgorithmsareconservative, it would be in-terestingto studythe degreeof over-estimation.Unfor-tunately, few of the paperswe review discussthe ratiobetweenthe sizeof their potentiallyvisible setand thesizeof thevisibleset(theauthorsof theselinesbeingnoexception).Wehope thatthecurrentsurvey will encour-agesubsequentarticlesto provide this measure.

� All vs.subsetof occluders.

Somemethodstreattheocclusionscausedby all objectsin thescene,while othersrequiretheselectionof asubset

of typically big objectsas occluders. The size of thissubsetcanalsovary.

� Convex vs.genericoccluders

Convexity of the occluders can be required by somemethods(typically for object-precision methods).

� Individual vs. fusedoccluders.

Given three primitives, A, B, and C, it might happenthat neither A nor B occludeC, but togetherthey dooccludeC. Someocclusion-culling algorithmsareableto perform such an occluder-fusion, while others areonly able to exploit single primitive occlusion. Celland portal methodsare a specialcase,sincethey con-sider the dual of occluders, openings, implicitly fusingtogethermultiple walls. Occluder fusion used to bemostly restrictedto image-precision point-basedmeth-ods. However, from-region visibility methodsperform-ing occluderfusionhave recentlybeendeveloped.

� 2D vs.3D.

Somemethods arerestrictedto 2D floorplansor to 2.5D(heightfields),while othershandle3D scenes.

� Specialhardware requirements.

Severalof the techniquesdescribedcantake furtherad-vantageof hardwareassistancebesidesthefinal Z-bufferpass,either for its precomputationor during the actualrendering.

� Needof precomputation.

Mostfrom-regionmethodsprecomputeandstorethevis-ibility information,but somepoint-based techniquesalsorequirea preprocessingof thedata(e.g. for occluderse-lection).

� Treatmentof dynamicscenes.

A few of thealgorithmsin theliteratureareableto han-dle dynamicscenes.Oneof themaindifficulties is han-dling changesto object hierarchiesthat most visibility

algorithmsuse[84]. Also if thevisibility algorithmusespreprocessing (asdiscussedabove), this informationhasto be updated. Sincefrom-region methodsusuallypre-computeaPVS,it is very hardfor themto treatdynamicscenes.In particular, all theinformationhasto berecom-putedif occludersmove. Moving occludeescanhoweverbe handledby bounding their motion usingmotion vol-umes[31].

2.3 Organization of the sur vey

The organizationof this survey is basedon the above tax-onomy, and on chronological reasons. Before reviewingocclusion-culling techniques,wefirst presenttheaspectgraphdata-structure,whichwill provide areferenceon exactvisibil-ity computationsandanalyticalvisibility properties.

Wethenintroducefrom-regionmethodsexploiting thecell-and-portalstructureof architecturalscenesin Section4. Sec-tion 5 describespoint-basedocclusion culling working atobject-precision,while Section6 is dedicatedto point-basedmethodsusing image-precision.Section7 reviews the morerecentclassof from-region visibility techniquesworking witharbitraryscenes.

3 Exac t visibility and the aspect graph

When dealingwith visibility, it is useful to consider an im-portantdatastructuredeveloped in computervisionandcalledthe aspectgraph [32]. As we will see,the aspectgraphen-codesanalytically all the information necessaryfor efficientdisplay. The principle is to subdivide the viewing spaceintocellswheretheview is qualitatively invariant.Thesecellsareseparatedby visualeventsthatarethelocusof changesin vis-ibility . Thus,for eachsuchcell, thevisible setis constantandchangesonly whentheviewpoint crossesavisualevent.

Let usdefinetheaspectgraphmoreformally andlook atthetwo isomorphic graphsin Figure 5. They areprojectionsofa 3D object;however, we treatthemas2D entities. The Im-age Structure Graph(ISG) is thelabeledplanargraphdefinedby theview of a polyhedral object. Thentwo differentviewsof an objecthave the sameaspect if andonly if their corre-sponding ISGsareisomorphic.Now wecanpartitiontheviewspaceinto maximalconnectedregionsin whichtheviewpointshave thesameaspect.This partitionis theVSP- thevisibilityspacepartition, wheretheboundary of a VSPregion is calledavisualeventasit marksaqualitative changein visibility (seeFigure 6).

The term, aspectgraph,refersto the graphcreatedby as-signinga vertex to eachregion of the VSP, wherethe edgesconnecting adjacentregionscorrespondto visualevents.

Figures6 and 7 show a visibility spacepartition in 2D,which is createdby just two andthreesegments(the2D coun-terpartsof polygons), respectively. Onecanobserve that thenumberof aspectregionsis alreadylarge,andin fact,canbeshown to grow quiterapidly with thenumberof segments.

Theworstcomplexity of aspectgraphs is quitehigh,andinthreedimensions,canbeaslargeasO

�n9 � (becausetriplesof

sceneedgescangive rise to visual events;and triples of vi-sualeventscancauseverticesin thevisibility spacepartition).For a typical numberof segments(saytensof thousands), in

(a) (b) (c)

Figure5: Two differentview directionsof an objecthave thesameaspectif andonly if thecorresponding ImageStructureGraphsare isomorphic. Note that (a) and(b) have the sameaspect,which is differentto (c).

Figure6: 2 polygons- 12 aspectregions.

termsof spaceandtime it turnsout thatcomputing theaspectgraphis computationallyimpractical.Plantinga[73] proposesan early conservative visibility algorithmbasedon his aspectgraphwork. Unfortunately, this algorithmhas,to our knowl-edge,not beenimplemented.

However, as can be seenin Figure8, different aspectre-gionscanhaveequalsetsof visiblepolygons.Thismeansthattherearefar fewer differentregionsof differentvisibility setsthandifferentaspects.

Looking onceagainat the aspectpartition of the two seg-mentsin Figure 9, we can treatoneasan occluder and theotherastheoccludee,definingtheirendpoint connectinglines

Figure7: 3 polygons - “many” aspectregions.

Figure8: Differentaspectregionscanhave equalsetsof visi-ble polygons.

as supporting lines and separating lines. Theselines parti-tion thespaceinto threeregions: (i) theregion from which noportion of the occludee is visible, (ii) the region from whichonly someportion of the occludeeis visible, and(iii) the re-gion from which theoccluderdoesnot occludeany partof theoccludee[24].

In 3D, onehasto considersupportingandseparatingplanesgeneratedby vertex/edgepairs (EV visual events). Visualeventsin 3D scenescanalsobegeneratedby theinteractionofthreeedges (EEE), which corresponds to non-planarquadricsurfaces.

A T

1

2

2

1

3

Supporting

Separating

Separating

Supporting

T − occludeeA − occluder

T is not occluded from region 1T is partially occluded from region 2T is fully occluded from region 3

Figure9: Supportingandseparatingplanes.

The3D visibility complex [30] is anotherwayof describingandstudyingthevisibility of 3D spaceby a dualspaceof 3Dlines, in which all the visibility eventsand their adjacenciesaredescribed.It is morecompact thantheaspectgraph,but itssizeis still O

�n4 � .

4 Cell-and-por tal from-region visibil-ity

We now review from-region visibility for architecturalenvi-ronments.Thework of Airey etal. [1,2] andTellerandSequin[89] startedthetrendtowardsadvancedocclusionculling tech-niques,anddevelopedmuchof thefoundationfor recentwork.Someof thekey conceptsintroducedwerethenotion of “po-tentially visible sets” from a region of space,“conservativevisibility”, and“denselyoccludedenvironments”.

All theseworksarebasedon thecharacteristicsof architec-tural scenes.Namely, that they arenaturallysubdivided intocells,andthatvisibility occursthrough openings,which theycall portals. The potentiallyvisible set is computed for eachcell, andusedduringrun-timewalkthrough.

��

�

�

�

�� ��������������������������

! "

#

$�%�&�'�(�)�*�(�+�,�-�'�.�/

01

23

4

5

Figure10: Cellsandportals:theadjacency graphandstabtree

The work of Airey et al. [1, 2] proposestwo differenttechniquesfor computingthe PVS.A conservative techniquewhich for eachportal, computes whetherit can seea givenpolygon in the model. Their formulation of the algorithmleadsto anO

�n3 � algorithm.Also in Airely’s Ph.D.thesis,he

describesseveral variationsof a “sampling” approach, whichroughly uses“ray shooting” queriesto determinevisible ge-ometryin someuser-specifiedprecision,anddoesnotactuallyguaranteeconservativenessin the computation of the set ofpotentiallyvisible primitives.

Thework of Teller is quitecomprehensive, andcoversdif-ferentaspectsof 2D and 3D visibility computations[86,88,89]. First,we briefly describehis work on 2D visibility com-putations.During preprocessing, themodelis first subdividedinto convex cells using a BSP tree. The main opaque sur-faces,suchas the walls, are usedfor defining the partitionsandthustheboundariesof thecells.Smallerdetailedsceneel-ementsareconsidered’non-occluding’ andareignoredin thisstep.Non-opaqueportals,suchasdoors,areidentifiedon cellboundaries,andusedto form an adjacency graphconnectingthecellsof thesubdivision. Seetheexamplein Figure 10. Thethick black linesarethewalls which areusedfor partitioninginto cells andthe light grey lines arethe portals. On the left,theadjacency graphshows which cellsaredirectly connectedthroughtheportals.

The cell-to-cell visibility is determinedby testingif sight-lines exist that connectsomepoint in onecell to somepointin another. Actually, it is clear that if a line exists from onecell to another, it hasto go througha portalandthuswe onlyneedto determineif theportalsarevisible betweenthem.Foreachcell, theadjacency graphis utilized to generateportalse-quenceswhicharethen’stabbed’with thesightline.For exam-ple, thetreeon theright of Figure 10 shows thecellsthatarevisible from cell A. Thecellsthatarereachedby thesightlinescontainthepotentiallyvisibleset(PVS)for any givencell andis storedwith it.

During aninteractive walkthroughthecell-to-cellvisibilitycanbe further dynamicallyculled using the view volumeofthe observer, producinga supersetof the visible scenedata,theeye-to-cellvisibility [38]. A cell is visible if all of thefol-lowing are true: it is in the view volume,all cells along thestabtreearein theview volume,all portalsalongthestabtreearein theview volume,andasightlinewithin theview volumeexiststhroughtheportals.Althoughwemight decideto applyonly someof thesetests,thegeometry containedin eachvisi-

Figure11: Resultsfrom [89] showing the potentiallyvisiblesetfrom agivencell. Courtesyof SethTeller, UC, Berkeley.

ble cell is neverthelesspasseddown thegraphicspipelineforrendering.

In [86, 88], Teller describestechniques for extendinghisoriginal 2D framework to 3D environments,usinga parame-terizationof line space.Doing soexactly, requiressubstantialmathematicalsophisticationbeyond what is necessaryfor the2D case,andbeyond thescopeof this survey to describe.Werefertheinterestedreaderto his seminalPh.D.thesis[86].

However, Telleralsoproposescomputingaconservativeap-proximation of the visible region [86, 87] through arbitraryportals in 3D. As eachportal is addedto the sequence, theseparatingplanesbounding the visibility region areupdated.Theseseparatingplanesbetweentheportalscorrespond to vi-sual events. For eachedgeof the sequence of portals,onlythe extremalseparatingplaneis considered.It is a conserva-tive approximationbecausesomecomplex non-planar visualeventsarenot considered.

More recently, Jimenezet al. [52] proposedan alternativemethodto computeconservativevisibility throughasetof por-tals.LikeTeller’sexacttechnique [86,88], they performcom-putationsin line space.

5 Point-based object-precis ion meth-ods

In this section,we review several algorithmswhich primarilyperformvisibility computationsin objectprecision.They relyontheidentificationof big occludersor cellsandportals.Theyhave the advantage that all computationscan be performedby theCPU,alleviating theneedfor communicationwith thegraphicshardwarethat image-precisionmethods(surveyed inthenext section)usuallyexhibit. However, largeoccluders orportalsarenotalwayseasyto find, andthesemethodsareusu-ally lesseffective atperformingoccluder fusion.

5.1 Cells and por tals

Luebke and Georges [63] propose a point-based cell-and-portal technique, basedon an earlier ideaof Jones[53] andon the from-region methodsdiscussedin the previous sec-tion [1,86]. Insteadof precomputing for eachcell a setof po-tentiallyvisiblegeometry, LuebkeandGeorgesperformanon-the-fly recursive depth-firsttraversalof thecellsusingscreen-spaceprojectionsof theportalswhich overestimatetheportalsequences, andperformconservativeocclusionculling.

Theiralgorithmworksasfollows. First,thecell whichcon-tainsthevieweris rendered,anditsportalswhichareinsidetheview frustumidentified.Clearly, any remainingvisible geom-etry hasto lie insidetheprojectionof thoseportals.Thealgo-rithm overestimatestheportalsby usingtheaxial2D boundingbox of the projectedverticesof eachportal. Then,the sameprocedureis repeatedfor the cellsadjacentto the portals. Ateachstep,thenew portalsareclippedagainstthepre-existingportals,leadingto smallerandsmallervisible “windows”, un-til no visible portalremains.

This technique is simpleandquiteeffective,andthesourcecode (an SGI Performerlibrary) is available for downloadfrom Luebke’s webpage.1

Hong et al. [50] usean image-based portal techniquesim-ilar to the work of Luebke andGeorges[63] to be ableto flythrougha virtual humancolon in real-time.Thecolon is par-titionedinto cellsatpreprocessingandtheseareusedto accel-eratetheocclusion with thehelpof a Z-buffer at run-time.

5.2 Large convex occ luder s

Thework of Coorg andTeller [24,25] computestheocclusioncausedby a subsetof large convex occluders. Occluderfu-sionis not reallyhandled, but they take advantageof temporalcoherenceby trackinga subsetof visualevents,which allowsthemto checkthe visibility statusof occludeesonly whenitactuallychanges.

They characterizethe occlusionof a convex occludeebya singleconvex occluder usingthe separatingandsupportingplanesbetweenthem(seeFigure8), andthe relative positionof the viewer with respectto thoseplanes.The basicideaisthat if an observer is betweenthe supporting planes,andbe-hind oneof theobjects,thenit is not possibleto seetheotherobject;suchis thecaseif anobserver is in region3 in Figure8.

In [24], a technique is proposedwhich incrementallycom-putesa (small) set of visual events wherevisibility changehappens,effectively trackingvisibility eventsamongobjectsasthe usermovesandthe visual relationshipsamongobjectschange. In effect, the algorithm is implicitly constructingalinearizedportion of the aspectgraphas the usermoves. Inprinciple,a very largenumberof visualeventswould needtobe considered,but in their paperCoorg andTeller show howto drasticallylimit thenumberof visual relationshipsby onlyconsideringa subsetof the silhouetteedgesand verticesoftherelevantprimitives.Theefficiency of thealgorithmis fur-ther improved by usingobjecthierarchies(basedon octrees)to handle thepotentialquadraticcomplexity computational in-crease.Thedynamictrackingof thevisualevents is costlyand(seemsto be)hardto implement.

1Pfportals canbeobtainedat http://pfPortals.cs.virginia.edu.

In [25], Coorg andTeller proposean improved algorithm.Instead of keeping a large number of continuous visibil-ity events, as the usermoves, their algorithm usesa view-dependent set of occluders(which are determinedin a pre-processingstep– seebelow), whichareusedto cull therestofthescene.

For efficiency, thesceneis insertedinto anobjecthierarchy,andtheoccludersareusedto determinewhich portionsof thehierarchycanbepruned,andnot rendered.Theactualvisibil-ity computationis performedhierarchically, andthevisibilitytestsareperformedbetweenthe pre-selectedconvex occlud-ersandthe bounding boxesof the hierarchy. Their occlusiontestis efficient, andusesa conservative estimateof the sepa-ratingandsupportingplanesby only consideringedgesof theoccluderandverticesof theoccludee(i.e. bounding box).

Their algorithmusesa limited form of occlusionfusion inwhich it is ableto fuseconnectedoccluderswhosesilhouettewith respectto theviewpoint is convex. In any case,theirtech-niqueismostsuitablefor usein thepresenceof largeoccludersin thescene.In their preprocessing, they selectobjectswith alargeprojectedareain imagespaceto beoccluders.To dothis,they proposeasimplemetricbasedonapproximatingthesolidanglesubtendedby anobject:

6 A�87N 9 7V �

:;: 7D:;: 2 <

whereA is theareaof theoccluder,7N thenormal,

7V theview-

ing direction,and7D thevectorfrom theviewpoint to thecenter

of theoccluder.

5.3 Culling using shado w frusta

A similar way to look at occlusionrelationships,is to usethefact that a viewer cannot seethe occludeeif it is inside theshadow generatedby theoccluder. Hudson et al. [51] proposeanapproachbasedondynamicallychoosingasetof occluders,andcomputingtheir shadow frusta,which is usedfor cullingthebounding boxesof a hierarchyof objects.

The way Hudsonet al. determinewhich partsof the hi-erarchyareoccluded is different to that of Coorg andTeller.For eachof the n best occluders that fall within the viewfrustum,the authorsbuild a shadow frustumusingthe view-point astheapex andpassingthroughtheoccludersilhouette.The scenehierarchyis testedtop-down againsteachof theseshadow frusta.If a nodeof thehierarchyis foundto betotallyenclosedby oneof thefrustathenit is occludedandhencedis-carded(for this frame). If it is found not to intersectany ofthemthenit totally visible andall theobjectsbelow it areren-dered. If however it partially overlapseven oneof themthenits children needto be further tested. Interferencedetectiontechniquesareusedfor speedingup thetests.

In practice,Hudsonet al. precomputeandstoreinforma-tion for occluderselection.BesidestheCoorg andTellersolid-angleheuristic,they alsoproposetakinginto accountthedepthcomplexity andcoherenceof theoccluders.They useaspatialpartitionof thescene,andfor eachcell, identifyingtheocclud-ersthatwill beusedanytime theviewpoint is insidethatcell,andstorethemfor lateruse.

5.4 BSP tree culling

Themethoddescribedin Hudsonet al. [51] canbe improvedusingBSPtrees.Bittneret al. [13] combinetheshadow frustaof theoccluders into anocclusiontree. This is donein a verysimilarway to theShadow VolumeBSPtree(SVBSP)of ChinandFeiner[16]. Thetreestartsasasinglelit (visible) leafandoccludersareinserted,in turn, into it. If anoccluder reachesalit leaf thenit augmentsthetreewith its shadow frustum;if itreachesashadowed(invisible) leaf thenit is just ignoredsinceit meansit alreadylies in anoccludedregion. Oncethetreeisbuilt, the scenehierarchycanbe comparedwith it. The cuberepresentingthetop of thescenehierarchyis insertedinto thetree.If it is foundto befully visible or fully occluded thenwestopandactappropriately, otherwiseits childrenarecomparedwith theocclusiontreerecursively. Thismethodhasanadvan-tageover Hudsonet al. [51] sinceinsteadof comparingthescenewith eachof the N shadow frusta, it is comparedwithonetreewith an O(logN) expecteddepth(potentiallyO(N)),while takingin into accountoccluderfusion.

The above technique is conservative; an alternative exactmethodwasproposedmuchearlierby Naylor [68]. That in-volveda merging of theocclusiontreewith theBSPtreerep-resentingthescenegeometry.

6 Point-based image-precision tech-niques

As thenamesuggestsimage-precisionalgorithmsperformtheculling at the discreterepresentationof the image. The keyfeaturein thesealgorithmsis thatduringrenderingof thescenethe imagegetsfilled up andsubsequent objectscanbeculledaway quickly by thealready-filledpartsof the images.Sincethey operateon a discretearrayof finite resolutionthey alsotend to be simpler to implementand more robust than theobject-precisionones,which cansometimessuffer numericalprecisionproblems.

Approximatesolutionscanalsobeproducedby someof theimage-precisionalgorithmsby classifyingthem as occludedgeometrypartswhicharevisible throughaninsignificantpixelcount.This invariablyresultsin anincreasein runningspeed.

When the scenesare composed of many small primi-tiveswithoutwell-definedlargeoccluders thenperformingtheculling in image-precisionbecomesmoreattractive. Thepro-jectionsof many smallandindividually insignificantoccluderscanbeaccumulatedon theimageusingstandardgraphicsras-terizing hardware,to cover a significantportion of the imagewhichcanthenbeusedfor culling. Anotheradvantageof thesemethodsis thattheoccludersdonothaveto bepolyhedral;anyobjectthatcanberasterizedcanbeused.

6.1 Ray casting

Oneof thesimplestforms of an imagesynthesisalgorithmisknown asray casting. Herethe imageis generatedby deter-miningwhichobjectof thesceneis visiblefromeachpixel. Bycastinga ray thatemanatesfrom theeye andpassesthroughapixel toward the scene,the closestobject it intersectsdeter-minesthe contentof the pixel. Oneof the nice propertiesofthis simpleconcept is that it never rendersan occluded part

of the scene.The downsideof usingray castingasan imagesynthesistechniqueis its high complexity. A naive implemen-tation requireseachray to apply an intersectioncalculationwith eachof the objectsin the scene.However, whenaccel-erationmethodsare usedthe renderingis in a back-to-frontorder that performsa naturalocclusion. Thus, it canbe ex-tremely fast [7, 8,20,22,71]. In fact, Wald, Slusallek,andcolleagues[91–93] recentlydeveloped an extremely fast raytracerwhich is able to rendervery large scenes,suchas the12.5million trianglePower Plantmodel from the Universityof North Carolinainteractively by usingonly a handful(actu-ally, seven)of PCsat videoresolutions(640by 480).

6.2 Hierar chical Z-buff er

The HierarchicalZ-buffer (HZB) [47,48] is an extensionofthepopularHSRmethod,theZ-buffer. It buildsuponthetech-niqueby Meagher[64] for efficient displayof octrees.It usestwo hierarchies:anoctreein object-precisionandaZ-pyramidin image-precision.The Z-pyramid is a layeredbuffer witha different resolutionat eachlevel. At the finest level it isjust the contentof the Z-buffer; eachcoarserlevel is createdby halvingtheresolutionin eachdimensionandeachelementholdingthefurthestZ-valuein thecorresponding2 = 2 windowof the finer level below. This is doneall the way to the top,wherethereis just onevaluecorresponding to the furthestZ-valuein thebuffer. During scan-conversionof theprimitives,if the contents of the Z-buffer changethenthe new Z-valuesarepropagatedup thepyramidto thecoarserlevels.

In [47] the sceneis arrangedinto an octreewhich is tra-versedtop-down front-to-backandeachnodeis testedfor oc-clusion. If at any point a nodeis found to beoccludedthenitis skipped;otherwiseits childrenarerecursively tested.Anyprimitivesassociatedwith a non-occludedleaf nodeareren-deredandthe Z-pyramid is updated. To determinewhetheranodeis visible,eachof its facesis testedhierarchicallyagainsttheZ-pyramid.Startingfrom thecoarsestlevel, thenearestZ-valueof thefaceis comparedwith thevaluein theZ-pyramid.If thefaceis foundto befurtheraway thenit is occluded; oth-erwiseit recursively descendsdown to finer levelsuntil its vis-ibility canbedetermined.

To allow for real-timeperformance, a modificationof thehardware Z-buffer is suggestedthat allows for much of theculling processingto be donein the hardware. The processcanalsobe somewhat acceleratedthroughthe useof tempo-ral coherence,by first renderingthegeometrythatwasvisiblefrom the previous frameandbuilding the Z-pyramid from itsZ-buffer.

In [42, 43] Greenepresentsseveral optimizationsto theoriginal HZB. An extendedaccountof this work is presentedin [44]. In this laterwork, Greeneproposesa variationof theoriginal techniquesuitablefor hardwareimplementation,thatis shown to be very efficient with respectto the bandwidthnecessaryto updatetheZ-buffer.

In [45], Greeneshows a simple techniquefor supportingnon-conservative culling with a HZB. The basic idea is tochangethe propagationschemefor the Z-buffer bounds,thatis, insteadof propagatingthefarthestz valuethroughthepyra-mid, Greeneproposesto propagatethe eth-to-the-farthestZ-value,wheree is a user-definedparameter.

6.3 Hierar chic al occ lusion map

Thehierarchicalocclusionmapmethod[98] is similar in prin-ciple to theHZB, thoughit wasdesignedto work with currentgraphicshardware. In order to do this, it decouples the vis-ibility test into an overlap test (do the occludersoverlap theoccludeein screenspace?) anda depthtest(arethe occludercloser?). It alsosupports approximatevisibility culling; ob-jectsthat arevisible throughonly a few pixels canbe culledusinganopacity threshold.

The occlusion is arrangedhierarchically in a structurecalledtheHierarchical OcclusionMap (HOM) andthebound-ing volumehierarchyof the sceneis testedagainstit. How-ever, unlike the HZB, the HOM storesonly opacity informa-tion while the distanceof the occluders (Z-values)is storedseparately. Thealgorithmthenneedsto independently testob-jects for overlapwith occluded regionsof the HOM and fordepth.

During preprocessing, a databaseof potentialoccludersisassembled.Thenat run-time, for eachframe, the algorithmperformstwo steps:constructionof the HOM andocclusionculling of thescenegeometry usingtheHOM.

To build theHOM, a largesetof occludersis selectedfromthe occluder databaseandrenderedinto the frame-buffer. Atthis point only occupancy information is required;thereforetexturing, lighting andZ-buffering areall turnedoff. Theoc-cludersarerenderedaspurewhiteonablackbackground.Theresultis readfrom thebuffer andformsthehighestresolutionin the occlusionmap hierarchy. The coarserlevels are cre-atedby averagingsquaresof 2 = 2 pixelsto form a mapwhichhashalf theresolutiononeachdimension.Texturinghardwarecanprovide someaccelerationof the averagingif the sizeofthemapis largeenough to warranttheset-upcostof thehard-ware. As we proceedto coarserlevels the pixels arenot justblackor white (occluded or visible) but canbeshadesof grey.Theintensityof apixel atsucha level shows theopacityof thecorresponding region.

Figure12: A hierarchyof occlusionmapscreatedby recur-sivelyaveragingblocksof pixels.Courtesyof HansongZhang,UNC.

An object is testedfor occlusion by first projecting itsbounding box onto the screenandfinding the level in the hi-erarchywherethepixelshave approximatelythesamesizeasthe extent of the projectedbox. If the box overlapspixels ofthe HOM which are not opaque, it meansthat the box can-not beculled. If thepixelsareopaque(or have opacityabovethespecifiedthresholdwhenapproximatevisibility is enabled)thentheobjectisprojectedonaregionof theimagethatiscov-

ered. In this casea depthtestis neededto determinewhethertheobjectis behindtheoccluders.

In paper[98] anumberof methodsareproposedfor testingthedepthof theobjectsagainstthatof theoccluders. Thesim-plesttestmakesuseof aplaneplacedbehindall theoccluders;any objectthat passesthe opacity test is compared with this.Although this is fastandsimple it canbe over-conservative.An alternative is thedepthestimationbuffer wherethescreenspaceis partitionedinto a setof regionsanda separateplaneis usedfor eachregion of thepartition.

For efficiency reasons,thefinestlevel of theocclusionmapis usually coarserthan the image. This could result in sam-pling artifactsalongsilhouettes,andthusin non-conservativeresults.However, theauthorsreportthatthis usuallydoesnotoccurin practice.

6.4 Directional discretiz ed occ luder s

Thedirectionaldiscretizedoccluders(DDOs)approach is sim-ilar to the HZB and HOM methodsin that it alsousesbothobject-andimage-space hierarchies.Bernardiniet al. [12] in-troducea methodto generateefficient occludersfor a givenviewpoint. Theseoccludersarethenusedto recursively culloctreenodesduringrenderingsimilarly to HZB andHOM.

In thepreprocessing stage,theinputmodelis approximatedwith anoctreeandsimple,view-dependentpolygonalocclud-ers are computedto replacethe complex input geometryinsubsequent visibility queries. Eachfaceof every cell of theoctreeis regardedasa potentialoccluder andthesolid anglesspanningeachof the two halfspaceson the two sidesof thefacearepartitionedinto regions. For eachregion, a flag indi-cateswhetherthat faceis a valid occluder for any viewpointcontainedin that region. Eachsquare,axis-alignedfaceis aview-dependentpolygonal occluder thatcanbe usedin placeof theoriginal geometryin subsequent visibility queries.

Figure13 is a two-dimensional illustrationof theDDO ap-proach. The grid is a discretizationof the spacesurroundingthe scene;it representsour octreenodes. The input geome-try, A andB, is shown usingdashedlines. For thepurposeofocclusionculling, the geometryA canbe replacedby a sim-plerobject(shown usingthick solid lines)which is asubsetofthegrid edges,that is, theoctreefaces.Thetwo figuresshowthesamescenefrom differentviewpointsandview directions.Notethatthesubsetof grid edgesthatcanactasoccluders(inplaceof geometryA) changesastheviewpoint changes.

The preprocessingstageis expensive, andmay take in theorderof hoursfor modelscontaininghundredsof thousandsof polygons. However, the computedoccludersareall axis-alignedsquares,a factthatcanbeexploitedto designefficientdatastructuresfor visibility queries. The memoryoverheadof the methodis only six bitmasksper octreenode. Cullingmethodswhich needto pre-selectlargeoccluders,(e.g.CoorgandTeller [25]), or whichpre-renderoccludersto computeoc-clusionmaps,(e.g. Zhanget al. [99]), could benefitfrom theDDO preprocessingstepto reducethe overheadof visibilitytests.

6.5 OpenGL-assisted occ lusion culling

Bartz et al. in [10,11] describea different image-precisionculling method.Thehierarchicalrepresentationof thesceneis

BAA

B

Figure13: Illustrationof theDDO approach. Theinputgeom-etry, A andB, is drawn asdashedlines.Thevalid occludersforthetwo viewpointsareshown asthick solid lines.CourtesyofJamesKlosowski, IBM.

testedagainsttheoccludedpartof theimage,whichresemblestheHZB andtheHOM. However, in contrastto thesemethods,thereis no hierarchicalrepresentationof theocclusion, ratherOpenGLcallsareusedto do thetesting.

To test for occlusion,a separatebuffer, the virtual occlu-sion buffer, is associatedwith the frame-buffer to detectthepossiblecontribution of any object to the frame-buffer. Thisis implementedwith a stencilbuffer. The bounding boxesofthe scenearehierarchicallysentdown the graphicspipeline.As they arerasterized,thecorresponding pixels aresetin thevirtual occlusion buffer whenever the Z-buffer testsucceeds.The frame-buffer andthe Z-buffer remainunalteredthrough-out this process,sincetherenderingof thebounding boxesisusedjust to querythehardwarefor visibility information.

The virtual occlusionbuffer is then readand any bound-ing box that hasa footprint in it is consideredto be (at leastpartially) visible andtheprimitiveswithin it canberendered.Sincetheoperationof readingthevirtual occlusionbuffer canbeveryexpensive,it wasproposedto sampleit by readingonlyspansfrom it. Thesamplinginevitably makesthealgorithmanon-conservative test.

The performanceof the algorithmdepends on the relativecostof readingthevirtual occlusionbuffer. With commonad-vancedgraphicsboards the set-upfor readingthe buffer is asignificantportionof theoverall time,reducingtheusefulnessof themethod.

6.6 Hardware-assisted occ lusion culling

Hardwarevendorshavestartedadoptingocclusion-cullingfea-turesinto theirdesigns. Thesearebasedon a feedbackloop tothe hardware which is able to checkwhetherany change ismadeto theZ-buffer whenscan-convertinga givenprimitive.Using this hardwarefeaturecanavoid renderinga very com-plex setmodelby first checkingwhetherit is potentiallyvisi-ble, for example,by checking whetheranenclosingprimitive(e.g.,a bounding box or an enclosingk-dop [55]) is visible,

andonly renderingthe actualobject if the simplerenclosingobjectis indeedvisible. Othervendorsprovide a similar func-tionality by simply addinginstrumentationcapabilitiesto thehardwarewhich is ableto countthefragmentswhich passthedepthtest(e.g.,[77–79]).

Severson[78] estimatesthatperforminganocclusion-querywith a boundingbox of an object using feedbacksfrom thegraphicscardis equivalentto renderingabout19025-pixel tri-angles.This indicatesthata naive approach whereobjectsareconstantlychecked for occlusionmight actuallyhurt perfor-mance,andnotachievethefull potentialof thegraphicsboard.In fact,it is possibleto slow down thefx6 considerably if oneis unlucky enough to project the polygons in a back-to-frontorder(becausenoneof theprimitiveswould beoccluded).

Researchers[9, 54] have exploredways to minimize suchvisibility queries. In general,by renderingprimitives in afront-to-backorder, onecanpotentiallyminimize thenumberof necessaryhardware queries.Bartzet al. [9] studiestheuseof k-DOPs[55] for speedingup occlusion-culling queriesinsucharchitectures.

In their recent offerings, vendors have improved theocclusion-culling featuresby performing several occlusionculling queriesin parallel[26], or loweringthememoryband-width required for updating the Z-values [66] (which theyclaim is the largestuserof bandwidthon their cardswith tex-turefetching).Therearealsoreportson thepartial implemen-tationof thehierarchicalZ-buffer of Greeneetal. [47] in hard-ware.

6.7 Appr oximate volumetric visibility

Oneapproach toapproximatevisibility isbasedonusingavol-umetricrepresentation,that is, insteadof performinggeomet-ric visibility computations,onecancomputea volumewhichhasintrinsic propertiesrelatedto the“density” of geometryinthe environment, and approximatethe visibility betweenre-gionsby computing thevolumeopacitybetweenregions.Thisapproachwasfirst proposed by Sillion [80] in the context ofspeedingupvisibility computationsfor aradiositysystem,andextendedin [81] into a multi-resolutionframework. Volumet-ric visibility wasindependently developed by Klosowski andSilva [56,57] in theirPLPsystem(seebelow), whereit is usedto roughly estimatethe order of projectionof the geometry.ThePrioritized-LayeredProjection(PLP)algorithm [56,57],is an approximateocclusion-culling technique. Ratherthanperforminganexpensiveconservativevisibility determination,PLPis an aggressive culling algorithmthatestimatesthevis-ible primitivesfor a given viewpoint, andonly rendersthoseprimitivesthat it determinesto bemostlikely visible, up to auser-specifiedbudget.

Consequently, PLPis suitablefor generating partially cor-rect imagesfor usein a time-critical renderingsystem. PLPworks by initially creatinga partition of the spaceoccupiedby the geometricprimitives. Eachcell in thepartition is thenassigned,duringtherenderingloop,aprobabilistic valueindi-catinghow likely it is thatthecell is visible,giventhecurrentviewpoint, view direction, and geometry in the neighboringcells.Theintuitiveideabehindthealgorithmis thatacell con-taining much geometryis likely to occludethe cells behindit. At eachpoint of the algorithm,PLP maintainsa priorityqueue,also called the front, which determineswhich cell is

mostlikely to bevisibleandthereforeprojectednext by theal-gorithm. As cellsareprojected,thegeometryassociatedwiththosecells is rendered,until thealgorithmrunsout of time orreachesits limit of renderedprimitives.At thesametime, theneighboringcellsof therenderedcell areinsertedinto thefrontwith appropriateprobabilistic values.PLPperformseffectivevisibility estimationby schedulingthe projectionof cells asthey areinsertedin thefront.

In [54], Klosowski andSilva extendtheir work into a con-servative techniqueby usingimage-precisiontechniques.Thenew algorithmprovidesanefficientwayof findingtheremain-ing visible primitivesby addinga secondphaseto PLPwhichusesimage-precisiontechniques for determiningthe visibil-ity statusof the remaininggeometry. Anothercontribution ofthatwork is to show how to efficiently implementsuchimage-precisionvisibility queriesusingcurrentlyavailableOpenGLhardwareandextensions.

El-Sanaetal. [33] presentanapproach thatintegratesocclu-sionculling within theview-dependentrenderingframework.View-dependentrenderingprovides the ability to changethelevel of detail over the surfaceseamlesslyand smoothly inreal-time. The exclusive useof view-parametersto performlevel-of-detail selectioncauseseven occludedregions to berenderedwith a high level of detail. The authorsovercomethis drawback by integratingocclusionculling into the levelselectionmechanism. Becausecomputingexact visibility isexpensive andit is currentlynot possibleto performthiscom-putationin real time, they usean approximatevisibility esti-mationtechniqueinstead.

6.8 Occluder shado w footprints

Many 3D sceneshave in factonly two anda half dimensions.Sucha sceneis calleda terrain or heightfield, i.e.,a functionz > f

�x < y� . WonkaandSchmalstieg [94] exploit this charac-

teristic to compute occlusionswith respectto a point usingaZ-buffer with a top parallelview of a scene.

Considerthe situationdepictedin Figure 14 (side view).They call the part of the scenehiddenby the occluderfromthe viewpoint the occludershadow (asif the viewpoint werea light source).This occludershadowis delimitedby wedges.Theprojectionof sucha wedgeon thefloor is calledthefoot-print,andanoccludeeis hidden by theoccluderif it liesontheshadow footprint andif it is below theedge.

The Z-buffer is usedto scan-convert and storethe heightof theshadow footprints,usinganorthographictop view (seeFigure14). An object is hiddenif its projectionfrom aboveis on a shadowfootprint andif it is belowtheshadow wedgesi.e., if it is occludedby thefootprintsin thetop view.

6.9 Discussion

Onedrawbackcommonto mostof thetechniquesdescribedinthis sectionis thatthey rely on beingableto readinformationfrom thegraphicshardware.Unfortunately, in mostcurrentar-chitectures,usingany sortof feedback from thegraphicshard-wareis quiteslow andplacesa limit on theachievable framerateof suchtechniques. As Bartzet al. [10] show, thesemeth-ods areusually only effective when the scenecomplexity isabove a largethreshold.

?A@�@CB DAEGFCHJI KGLCEG?GMN OGOGP QGR S TGP

UGVCVCW XGYGZC[

\G]�]C^ _G`GaCbc dGeCfGgGhikj�lAmGj

nGoCo�p qGrGsCstGu vCwkxGyGu zG{

| } ~G���G} ��� � �G���G� ���

�G�C�C� �G�G�C�J� �G�C�G�G�� �G�G� �A� � �G�

�G�C�C�  G¡A¢�¢£G¤C¤C¥ ¦G§G¨C©

Figure14: Occludershadow footprints.A projectionfrom above is usedto detectocclusion.Objectsarehiddenif they arebelowtheoccludershadows.Thefootprints(with height)of theoccluded regionsarerasterizedusinga Z-buffer. Depthis representedasgrey levels.Notethegradient in thefootprint dueto theslopeof thewedge.

An oftenoverlooked problemis thatof latency andrender-ing pipeline. Indeed, mostof thesemethodsassumethat thedrawing andculling stagesaresynchronous,thatis, thegraph-ics hardware andthe applicationwork simultaneouslyon thesameframe. Unfortunately, this is not necessarilythecaseinmodernreal-timeAPIs [74], wherethreepipelinestagescanberun in parallelon threedifferentframes:applicationscenemanagement,cull anddraw. In this case,readingfrom theZ-buffer for culling would usetheinformationfrom thepreviousframe.

7 Generic from-region visibility

In a typical visibility culling algorithmtheocclusionis testedfrom a point [25,51]. Thus, thesealgorithmsareappliedineachframeduring the interactive walkthrough. A promisingalternative is to find thePVSfrom aregionor view cell, ratherthan from a point. The computationcostof the PVS from aview cell would thenbe amortizedover all the framesgener-atedfrom the given view cell. As aforementioned, the pre-dictivecapabilitiesof from-regionmethodsarecrucialfor pre-fetching.

Effective methodshave beendeveloped for indoor scenes[37,89], but for general scenes,the computationof the visi-bility set from a region is more involved than from a point.Samplingthe visibility from a numberof view pointswithintheregion [41] yieldsanapproximatedPVS,which may thencauseunacceptableflickeringartifactsduringthewalkthrough.Conservative methodswere introduced in [21,75] which arebasedon theocclusionof individual largeconvex objects.

In thesemethodsa given objector collectionof objectsisculled away if andonly if they arefully occluded by a singleconvex occluder. It wasshown thataconvex occluder is effec-tive only if it is larger thanthe view cell [67]. However, thisconditionis rarely met in real applications.For example,theobjectsin Figure 15 aresmallerthanthe view cell, andtheirumbrae(with respectto theview cell) arerathersmall. Theirunion doesnot occludea significantportionof thescene(seein (a)),while theiraggregateumbrais large(seein (b)).

Recently, new techniquesweredevelopedin whichthevisi-bility culling from aregionis basedonthecombinedocclusionof a collectionof objects(occluderfusion). Thecollectionorclusterof objectsthat contributesto the aggregateocclusionhasto be neitherconnectednor convex. The effective from-region culling of thesetechniques is significantly larger thanprevious from-region visibility methods. Below, five tech-niquesaredescribedfollowedby a discussion.

7.1 Conser vative volumetric visibility with oc-cluder fusion

Schaufleretal. [76] introduceaconservative techniquefor thecomputationof view cell visibility. Themethodoperateson adiscreterepresentationof spaceandusestheopaqueinteriorofobjectsasoccluders.This choiceof occludersfacilitatestheirextensioninto adjacentopaque regionsof space,in essence,maximizingtheir sizeandimpact.

Themethodefficiently detectsandrepresentstheregionsofspacehiddenby occludersandis the first to usethe propertythatoccluderscanalsobeextendedinto emptyspaceprovidedthis spaceitself is occludedfrom theview cell. This is provedto beeffective for computingtheocclusionby a setof occlud-ers,successfullyrealizingoccluder fusion.

Initially, the boundary of objectsis rasterizedinto the dis-cretizationof spaceand the interior of theseboundaries isfilled with opaquevoxels.Foreachview cell, theocclusionde-tectionalgorithmiteratesovertheseopaquevoxels,andgroupsthemwith adjacentopaquevoxelsinto effectiveblockers.Sub-sequently, a shaftis constructedaroundthe view cell andtheblocker to delimit the region of spacehiddenby the blocker.Thecorresponding voxelsaremarkedasoccluded. As regionsof spacehave alreadybeenfound to behiddenfrom theviewcell, extensionof blockers into neighboring voxels can alsoproceedinto thesehidden regions realizing occluderfusionwith all theoccluderswhich causedthis region to behidden.

As an optimization, opaquevoxels are usedin the orderfrom largeto smallandfrom front to back. Occludedopaquevoxelsarenot consideredfurtherasblockers.

umbraindividual

(a)

umbraaggregate

occludervirtual

(b)

1

3

2

(c)

Figure15: (a) Theunionof theumbraeof theindividual objectsis insignificant.(b) But their aggregateumbrais largeandcanberepresentedby a singlevirtual occluder. (c) The individual umbrae(with respectto theyellow view cell) of objects1, 2 and3 donot intersect,but yet their occlusioncanbeaggregatedinto a largerumbra.)

To recover the visibility statusof objectsin the originalscenedescription,the spacethey occupy is looked up in thespatialdatastructureand, if all the voxels intersectedby theobjectareclassifiedashidden, the object is guaranteedto behiddenaswell.

Theauthorspresentspecializedversionsfor thecasesof 2Dand2.5D visibility, andmotivatetheeaseof extensionto 3D:becauseonly two convex objectsat a time areconsideredinthevisibility classification(theview cell andtheoccluder),theusualdifficultiesof extendingvisibility algorithmsfrom 2D to3D, causedby triple-edgeevents,areavoided. Exampleap-plicationsdescribedin thepaper includevisibility preprocess-ing for real-timewalkthroughsandreductionin thenumberofshadow raysrequiredby a ray-tracer(see[76] for details).

7.2 Conser vative visibility prepr ocessing us-ing extended projections

Durandetal. [31] (seealso[62]) presentanextensionof point-basedimage-precisionmethodssuchasthe HierarchicalOc-clusionMaps [99] or the HierarchicalZ-buffer [47] to volu-metricvisibility from aview cell, in thecontext of preprocess-ing PVScomputation. Occludersandoccludeesareprojectedontoa plane,andanoccludeeis declaredhiddenif its projec-tion is completelycoveredby thecumulative projectionof oc-cluders(andif it lies behind).Theprojectionis however moreinvolvedin thecaseof volumetricvisibility: to ensureconser-vativeness,theExtendedProjectionof anoccluder underesti-matesits projectionfrom any point in theviewcell, while theextendedprojectionof an occludeeis an overestimation(seeFigure 16(a)). A discrete(but conservative) pixel-basedrep-resentationof extended projectionsis used,calledanextendeddepthmap. Extendedprojectionsof multiple occluders ag-

gregate,allowing occluder-fusion. For convex viewcells, theextendedprojectionof aconvex occluderis theintersectionofits projectionsfrom theverticesof thecell. This canbecom-putedefficiently using the graphicshardware(stencilbuffer)anda conservative rasterization.Concave occludersintersect-ing theprojectionplanearesliced(see[31] for details).

A singlesetof six projectionplanescanbeused,asdemon-stratedby anexampleinvolving a city database.Thepositionof theprojectionplaneis howevercrucialfor theeffectivenessof extendedprojections. This is why a reprojectionoperatorwasdeveloped for hard-to-treatcases.It permitsa group ofoccludersto be projectedonto one planewherethey aggre-gate,andthenreprojectsthis aggregatedrepresentationontoanew projectionplane(seeFigure 16(b)). This reprojectionisusedto defineanocclusion-sweepwherethesceneis sweptbyparallelplanesleaving thecell. Thecumulative occlusionob-tainedon the currentplaneis reprojectedonto the next planeaswell asnew occluders.Thisallowsthehandlingof verydif-ferentcasessuchastheocclusioncausedby leavesin a forest.

7.3 Vir tual occ luder s

Koltun et al. [58] introducethe notion of from-region virtualoccluders,andproposea 2.5Dimplementation.Givena sceneandaview cell,avirtual occluderisaview-dependent(simple)convex object,which is guaranteedto be fully occludedfromany given point within the view cell andwhich servesasaneffective occluderfrom thegivenview cell. Virtual occluderscompactlyrepresent the aggregateocclusionfor a given cell.Theintroductionof suchview-dependentvirtual occludersen-ablesapplyinganeffective from-region culling technique andefficiently computingapotentialvisibility setfrom acell. Thepaperpresentsan object-precisiontechniquethat synthesizes

ª¬«®­ ­¯C° ±C² ³�´�µ ¶ ±C·¸C¹ º�»C¼8½

¾C¿ ÀCÁ Â�Ã�Ä Å ÀCÆÇCÈ É�ÊCË�Ì

ÍÏÎCÐ�Ñ Ò�ÓÏÔÍÏÕCÖ×CØ ØÏÙ ÚCÛ�Ü�Ý

Þ�ßÏà�á�âäã

å�æÏç�è�éëê

ì íÏî ì ïCð í�ñÏò ó ïCô

õ®ö�÷8ø

ùÏú®û

ü¬ý¬þ þ

ÿ�� ��� ������

� �� ���� � ������ �����

��� ��� ���� �

�! #" �!$#%#�!%&#')(#* +!,!- . (#/0#132 4#56#7!7!8 9#:#;!<

=!>#? =!@#A#=!AB#C)D#E F!G!H I D#JK#LNM O#PQ#R!RTS U#V#W!WX

Y)Z#[

Figure16: (a)Principleof ExtendedProjections.TheExtendedProjectionof theoccluderis theintersectionof its projectionsfromall thepointsin theviewing cell, while theextendedprojectionof theoccludeeis theunionof its projections.(b) If plane2 is usedfor projection,theocclusionof group1 is not takeninto account.Theshadow coneof thecubeshows thatits ExtendedProjectionwould bevoid, sinceit vanishesin front of theplane.Thesameconstraintappliesfor group2 andplane1. Wethusprojectgroup1ontoplane1, thenreprojectthis aggregateprojectionontoplane2.

suchvirtual occludersby aggregatingthevisibility of a setofindividualoccluders.It is shown thatonly asmallsetof virtualoccludersis requiredto computethePVSefficiently on-the-flyduringthereal-timewalkthrough.

In the preprocessing stageseveral objectsareidentifiedasseedobjects.For eachseedobject,a clusterof nearbyobjectsis constructedsothatasinglevirtual occluder faithfully repre-sentstheocclusionof this clusterof objects.At first, theclus-ter is definedto includeonly theseedobject.Then,iteratively,at eachstep,moreobjectswhich satisfya geometriccriterionareaddedto theclusterof occluders,thusaugmentingtheag-gregateumbraof the cluster. The virtual occluderis placedjustbehindthefurthestobjectin thecluster, andis completelycontainedin theaggregateumbraof thecluster(seeFigures15and17).

Onevirtual occluderis storedat eachstepof the iteration.As aresult,attheendof theprocess,thereis alargeandhighlyredundant groupof virtual occluders.This groupcanbewellrepresentedby a smallsubsetof themosteffective virtual oc-cluders.

In the real-timerenderingstage,the PVS of a view cell iscomputedjust beforethewalkthroughenterstheview cell. Itis doneby hierarchicallytestingthescene-graphnodesagainstthevirtual occluders.Sinceonly a very smallnumberof themareused,this testis extremelyfast.

The3D problemis solvedby a2.5Dimplementation,whichproves to be effective for most typical scenes,suchasurbanandarchitecturalwalkthroughs. The2.5Dimplementationper-forms a seriesof slicesin the heightdimension, andusesthe2D algorithmto construct2D virtual occludersin eachslice.Theseoccludersarethenextendedto 3D by giving themthe

heightof their respective slices.

7.4 Occluder fusion for urban walkthr oughs

Wonkaetal. [95] presentanapproachbasedontheobservationthat it is possibleto computea conservative approximationofthe umbra for a view cell from a set of discretepoint sam-plesplacedon theview cell’s boundary. A necessary, thoughnot sufficient condition that an object is occludedis that it iscompletelycontained in the intersectionof all samplepoints’umbrae. Obviously, this condition is not sufficient as theremay be viewing positionsbetweenthe samplepoints wheretheconsideredobjectis visible.

However, shrinkinganoccluderby ε providesasmallerum-brawith auniqueproperty:anobjectclassifiedasoccludedbythe shrunkoccluder will remainoccludedwith respectto theoriginal larger occluderwhenmoving the viewpoint no morethanε from its original position.

Consequently, a point sampleusedtogetherwith a shrunkoccluderis a conservativeapproximationfor asmallview cellwith radiusε centeredat thesamplepoint. If theoriginal viewcell is coveredwith samplepointsso that every point on theboundary is containedin an ε -neighborhood of at leastonesamplepoint, then an object lying in the intersectionof theumbraefrom all samplepoints is occludedfor the originalview cell. A too small ε would requireapplying too manyredundant samplings, while a too largeε would shrinktheob-ject too muchcausingthevisibility to beoverly conservative.Using this idea,multiple occluders canbe consideredsimul-taneously. If theobject is occludedby the joint umbraof theshrunkoccludersfor every samplepoint of theview cell, it is

1

3

2

4

S

(a)

1

3

2

4

S

(b)

3

2

4

1

S

(c)

1

3

2

4

S

(d)

Figure17: Growing thevirtual occludersby intersectingobjectswith theactive separatingandsupportinglines.

occludedfor thewholeview cell. In thatway, occluder fusionfor an arbitrarynumberof occludersis implicitly performed(seeFigure18).

They recentlyextended this methodto onlinecomputation[72]. They proposedanasynchroneousscheme,wherea visi-bility servercomputesvisibility for aregionaroundthecurrentviewpoint andtransmitsit to thedrawing client. Theirmethodis in factquitegeneric,it canuseoccludershrinkingwith anypoint-basedocclusionculling method.

7.5 Hardware-accelerated using a dual rayspace

Koltunetal. [59] introduceamethodthatdrasticallyimprovesfrom-region techniquesfor scenesrepresentedby 2.5D mod-els, both in termsof accuracy and speed. It utilizes a dualspacetransform,enablingvisibility to berepresentedin anal-ternative two-dimensionalspace,which allows usinggraphicshardwarefor rapidly performingvisibility computation.

The algorithm’s speedand accuracy aims at computingfrom-regionvisibility on-line, eliminatingtheneedfor prepro-cessingandstoringprohibitive amountsof visibility informa-tion on the walkthrough server. A notableadvantageof thealgorithmis that it retainsits speedandaccuracy even whenappliedto largeviewcells.

The algorithmprocessesa model that is representedby akd-tree.For a givenviewcell, thealgorithmhierarchicallytra-versesthe treein a top-down fashion. For eachnode,the al-gorithm determineswhetherthe bounding box of the nodeisvisible from theviewcell. Whenanoccludednodeis reached,the recursionterminates.The fastcell-to-cell visibility deter-minationis thecoreof thealgorithm.

The visibility betweentwo cells is conservatively reducedto a problemof visibility betweentwo segmentson a plane:the sourcesegment,representingthe viewcell, and the targetsegment, representingthe bounding box of a kd-tree node.Every ray originatingin the sourcesegment,andintersectingthetargetsegment,correspondsto a singlepoint in a boundedtwo-dimensional dual ray space. All theraysemanatingfromthe sourcesegmentandpassingthrougha segmentthat rep-resentsoneoccluder form a polygon, which is eithera trape-zoid or a double-triangle. This polygon representsthe raysthat are blocked by the occluder. If the occluderstogether

block all theraysthatemanatefrom thesourcesegment,thenthereis no singlevisibility raybetweenthesourceandthetar-getsegments. This canbe determinedby testingwhethertheunion of the polygons (that correspondto occluders) coversthebounded dualray space.

This testcanbe accomplished conservatively by discretiz-ing the union of the polygons into a bitmap using graphicshardware. All the polygons are drawn in white, without Z-buffering or shading, onto an initially black background. Ifa black pixel remains,the sourceandtarget segmentsarere-portedto be mutually visible. The discretizationavoids thecomplex analyticcomputationof the union andalleviatesro-bustnessproblemscommonin geometricalgorithms.Relatedapproachescanbefoundin [17,70].

7.6 Discussion

When the visibility from a region is concerned, occlusioncausedby individual occludersin a generalsettingis insignif-icant. Thus,it is essentialto take advantageof aggregateoc-clusioncausedby groupsof nearbyobjects.Theabovepapersaddresstheproblemof occlusionaggregationalsoreferredtoasoccluderfusion.

All five techniques areconservative; they aggregateocclu-sion in mostcases,but not in all possibleones.In sometech-niques,thecriterionto fusetwo occludersor to aggregatetheirocclusionsis basedon the intersectionof two umbrae.How-ever, in [58,59,96], moreelaboratecriteria are used,whichpermitaggregationof occlusionsevenin caseswheretheum-braearenotnecessarilyintersected.Thesecasesareillustratedin Figure15(c). Unfortunately, thesemethods do not handlethe3D case.

To copewith thecomplexity of thevisibility in 3D scenes,all thetechniquesusesomediscretization.

Thefirst methoddiscretizesthespaceinto voxels,andop-eratesonly on voxels. This leadsto the underestimationofocclusionwhentheumbraof occluders is relatively smallandpartially overlapssomelargevoxels,but doesnot completelycontainany. Theadvantageof this approach is its generality:it canbe appliedto any representationof 3D scenes, andnotnecessarilypolygonal.

Thesecondmethoddiscretizesthespacein two ways.First,it projectsall objectsonto a discretesetof projectionplanes,

(a) (b)

Figure18: (a) Samplingof theocclusionfrom five samplingpoints.(b) Thefusedumbrafrom thefive pointsis theintersectionoftheindividual umbrae.It is largerthantheunionof umbraeof theoriginal view cell. Courtesyof PeterWonka,ViennaUniversityof Technology.

and second,the representationof objectsin thoseplanesisalsodiscrete. Moreover, 3D projectionsarereplacedby two2D projections(seeFigure16), to avoid performinganalyticaloperationson objectsin 3D space.The advantageof this al-gorithmis that,sincemostoperationsareperformedat image-precision,they canbehardware-assistedto shortentheprepro-cessingtime.

The third methodis object-precisionanalytical in the 2Dcase.It treatsthe 3D caseasa 2.5D sceneandsolvesit by aseriesof 2D casesby discretizingthe heightdimension.It isshown that in practicethe visibility of 2.5D entitiesapproxi-mateswell thevisibility of theoriginal 3D models.

The forth methodsamplesthe visibility from a view cellfrom adiscretenumberof samplepoints.Althoughit underes-timatesocclusion,it is alsoa conservative method.This maybe insignificantin the caseof closeand large occluders,butin caseswherethe occlusionis createdby a large numberofsmall occluders,the approximationmight be too crude. Themethodof Koltun et al. [59] is a significantsteptowardsthecomputationof from-region visibility in real-time. However,it only dealswith 2.5D scenesandseemsapplicableto urbanandarchitecturalmodelsonly.

Somethingthatcouldproveusefulwhencomputingvisibil-ity from a region is a methodfor depth-orderingobjectswithrespectto theregion. Findingsuchanorderingcanbea chal-lengingtask,if at all possible,sinceit might vary at differentsamplepointsin thegiven region. Chrysanthou in [18] (Sec-tion 3.2)suggestsa hybrid methodbasedon graphtheoryandBSPtreeswhich will sorta setof polygons asfar aspossibleandreportunbreakable cycleswherethey arefound.

7.7 Appr oximate from-region visibility

In [4] a schemeto combine approximate occlusioncullingwith level-of-detail (LOD) techniquesis presented.The ideais to identify partially-occluded objectsin addition to fully-occludedones.Theassumptionis thatpartially-occludedob-jectstake lessspaceon the screen,andthereforecanbe ren-deredusinga lower LOD. The authorsusethe term Hardly-VisibleSet(HVS) to describeasetconsistingof bothfully andpartiallyvisible objects.

A setof occludersis selectedandsimplifiedto a collectionof partially-overlappingboxes.Occlusionculling is performedfrom the view cell usingtheseboxesasoccluders to find the”fully-visible” part of the HVS. It is performedconsideringonly occlusionby individualboxes[21,75]. Thereis noocclu-sionfusion,but a singlebox mayrepresentseveralconnectedoccluderobjects.

To compute partially-visible objects, all the occluders(boxes)areenlargedby a certainsmalldegree,andocclusionculling is performedagainusing thesemagnifiedoccluders.The objectsthat areoccluded by the enlargedoccludersandnotby theoriginalonesareconsideredto bepartiallyoccludedfrom theview cell, andarethuscandidatesto berenderedat alower LOD.

Several partsof the HVS are computedby enlarging theoccludersseveral times,eachtime by a differentdegree,thus,classifyingobjectswith adifferentdegreeof visibility. Duringreal-timerendering,the LOD is selectedwith respectto thedegreeof visibility of theobjects.

It shouldbenotedthatthisbasicassumptionof thedegreeofvisibility is solelyheuristic,sinceanobjectpartially occludedfrom a region doesnot meanit is partially occluded from anypoint within the region. It could be fully visible at onepoint

andpartiallyvisible or occluded atanother.In [41] anotherapproximatefrom-region visibility tech-

niqueis proposed. Castingraysfrom afive-dimensionalspacesamplesthe visibility. The paper discusseshow to minimizethe number of rayscastto achieve a reliableestimateof thevisibility from a region.

7.8 The PVS stora ge space problem

PrecomputingthePVSfrom aregionrequiressolvingapromi-nentspaceproblem. The sceneis partitionedinto view cellsandfor eachcell a PVSis precomputedandstoredreadilyforthe online renderingstage. Sincethe numberof view cellsis inherently large, the total size of all the visibility setsismuch larger than the original sizeof the scene. Aside for afew exceptionsthis problemhasnot received enoughatten-tion yet. VandePanneandStewart [90] presenta techniquetocompressprecomputedvisibility setsby clusteringobjectsandview cells of similar behavior. Gotsmanet al. [41] presentahierarchicalschemeto encodethevisibility efficiently. Cohen-Or et al. [21,23] dealwith the transmissionof visibility setsfrom theserver to theclient andin [21,67] discusstheselec-tion of thebestview cell sizein termsof thesizeof thePVS.

A completelydifferentapproachis taken by Koltun et al.[58]. The PVS of eachview cell doesnot needto be storedexplicitly. An intermediaterepresentationthat requiresmuchlessstoragespacethan the PVS is createdand usedto gen-eratethe PVS on-the-flyduring rendering. In [59] they takeit onestepfurther by attemptingto compute the PVS on thefly during the walkthrough avoiding any precomputation andstorage.

8 Conc lusion

In summary, this survey is our attemptto cover the visibilityliteratureas it relatesto walkthrough applications.Our goalin writing this paperwasto producea studyguidefor bothre-searchersandpractitionersinvolved in writing real-timeren-dering systems(e.g., computer games),covering the issuesinvolved, and the available literature. For this, we surveyedmostof therelevantvisibility literatureavailable,andprovideda classificationframework. Figure19 lists andcomparesthevariousmethods.Weseethataconsiderableamountof knowl-edgehasbeenassembledin thelastdecade,andthenumberofpapersin theareahasincreasedsubstantially in thelastcoupleof years.

Despitethetremendousprogressin thearea,muchinterest-ing work remains:

Quantita tive comparis on of exis ting appr oaches.At thispoint in timevery little work hasbeendonein perform-ing directcomparisonsof differenttechniques.Severalfactorscomplicatethis, including the fact that very few researchersmake their codeanddataavailable.

Hardware-ass isted cullin g. As aforementioned, hard-ware manufacturers integrate more and more occlusion-culling capabilitiesin thegraphicscards.We seethe interac-tion betweenthehardwareandtheCPUfor efficienthigh-level

culling as an important issue,especiallybecauseof latencyproblems.

From-re gion visib ility . More researchis neededto de-velop a 3D from-region algorithmthat computesa tight PVSfor largeviewing cells.

Prepr ocess ing time; PVS stora ge. Most from-regiontechniquesperforma considerableamountof preprocessing,whichgeneratesquiteabit of storageoverhead. Reducingthisoverheadis an importantareaof research.Moreover, furtherresearchis necessaryinto techniqueswhich lower theamountof preprocessingrequired(andnot only for from-region tech-niques,but for visibility culling algorithmsin general).Also,memoryis a big issuefor largescenes,especiallyin thecon-text of from-region techniques.

Occluder simplific ation and syn thesis . Despiterecentwork in the area[12, 14,58,61,98], most methodsuse theraw objectsof thesceneasoccluders.Simplifying thesemod-elsmight speed-upvisibility calculations,but that shouldnotcome at the cost of conservativeness. Moreover, more ap-propriaterepresentation might yield simplercomputations ormoreeffective culling.

Integration with other acceleratio n techniques . Vis-ibility culling is only oneof a setof real-timerenderingtech-niques. The issue of integrating a visibility-culling algo-rithm with other forms of accelerationis an important one(see[3, 4, 33,36]), which we believe is an areastill rich ininterestingproblems.

Dynamic object s. Anotherlargely under-exploredareaisthehandlingof dynamicobjects[84].

Ackno wledgments

We would like to thank all the authorswho have helpeduswith materialfrom theirwork. In particular, we thankVladlenKoltun, PereBrunet, Seth Teller, JamesKlosowski, CraigGotsman,GernotSchauflerandPeterWonka, for helpinguswith text andfiguresfrom their papers,andJoseph Mitchellfor usefulcommentson this survey.

This researchwaspartially supportedby theIsraelScienceFoundationfoundedby the IsraelAcademyof SciencesandHumanities(Centerfor GeometricComputingandits Appli-cations),andby agrantof theIsraelMinistry of Science.

References

[1] John Airey. Increasing Update Ratesin the Building Walk-through Systemwith Automatic Model-Space Subdivision andPotentially Visible SetCalculations. PhD thesis, University ofNorth Carolina,Chappel Hill , 1991.

[2] JohnM. Airey, JohnH. Rohlf, andFrederick P. Brooks,Jr. To-wards imagerealism with interactive update rates in complexvirtual building environments.Computer Graphics (1990Sym-posiumon Interactive 3D Graphics), 24(2):41–50,March 1990.

Method 2D/3D Conservative Occluders Fusion Precomputation Hardware DynamicFrom-region cell-portalsAirey 2D & 3D yesor no portals PVS no noTeller 2D & 3D yes portals PVS no noObject-precision point-basedLuebke & Georges 3D yes portals cell no needupdate

connectivity hierarchyCoorg & Teller 3D yes large if convex occluders no needupdate

convex silhouette selection hierarchyHudsonet al. 3D yes large no occluders no needupdate

convex selection hierarchyBittneret al. 3D yes large yes occluder no needupdate

selection hierarchyImage-precision point-basedGreeneet al. 3D yes all yes no needs yes,temporal

z readback coherenceZhanget al. 3D yesor big yes occluder current needupdate

aggressive subset database graphics hierarchyhardware

Bernardiniet al. 3D yes preprocessed yes occluders no noBartzet al. 3D no all yes no secondary needupdate

buffer hierarchyKlosowski & Silva ’00 3D no all yes volumetric no needupdate

hierarchyKlosowski & Silva ’01 3D yes all yes volumetric yes needupdate

hierarchyWonkaet al. ’99 2.5D yes large yes no Z-buffer yes

subsetGeneric from-region visibilityCohen-Oret al. 3D yes all no PVS no motionvolume

for occludeesSchaufleretal. 2D or 3D yes all yes PVS no motionvolume

watertight for occludeesDurandetal. 3D yes largesubset yes PVS yes motionvolume

for occludeesKoltun et al. ’00 2D & 2.5D yes largesubset yes virtual occluders no motionvolume

for occludeesWonkaet al. ’00 2.D yes largesubset yes PVS yes motionvolume

for occludeesKoltun et al. ’01 2.5D yes all yes no yes needupdate

hierarchy

Figure19: Comparisonof thevariousmethods.

[3] D. Aliaga,J.Cohen,A. Wilson, Eric Baker, H. Zhang,C. Erik-son,K. Hoff, T. Hudson,W. Stuerzlinger, R. Bastos,M. Whit-ton,F. Brooks,andD. Manocha. MMR: An interactive massivemodel rendering systemusing geometric and image-basedac-celeration. In ACM Symp.on Interactive 3D Graphics, 1999.

[4] Carlos Andujar, Carlos Saona-Vazquez, Isable Navazo, andPereBrunet. Integrating occlusion culling andlevelsof detailsthrough hardly-visible sets. Computer Graphics Forum, 19(3),2000.

[5] Arthur Appel. Sometechniquesfor shadingmachine renderingsof solids. In AFIPS 1968 Spring Joint Computer Conf., vol-ume32,pages37–45,1968.

[6] Ulf Assarssonand TomasMoller. Optimized view frustumculling algorithms for bounding boxes. Journal of GraphicsTools, 5(1),2000.

[7] Kavita Bala,JulieDorsey, andSethTeller. Radianceinterpolantsfor acceleratedbounded-errorray tracing. ACM TransactionsonGraphics, 18(3):213–256,July 1999. ISSN0730-0301.

[8] Kavita Bala,JulieDorsey, andSethTeller. Ray-tracedinteractivesceneediting usingray segmenttrees. Eurographics RenderingWorkshop1999, June1999.Held in Granada, Spain.

[9] D. Bartz, J. Klosowski, and D. Staneker. k-dops as tighterbounding volumesfor better occlusion performance. In ACMSIGGRAPHVisual Proceedings2001, 2001.

[10] Dirk Bartz, MichaelMeiner, andTobiasHttner. Opengl-assistedocclusion culling for large polygonal models. Computer &Graphics, 23(5):667–679,1999.

[11] Dirk Bartz, Michael Messner, and Tobias Httner. Extendinggraphics hardware for occlusion queries in opengl. In Proc.Workshopon GraphicsHardware ’98, pages97–104,1998.

[12] F. Bernardini, J. T. Klosowski, andJ. El-Sana.Directional dis-cretized occludersfor accelerated occlusion culling. ComputerGraphicsForum, 19(3),2000.

[13] J. Bittner, V. Havran, and P. Slavik. Hierarchical visibil-ity culling with occlusion trees. In Proceedings of ComputerGraphics International ’98, pages207–219,June1998.

[14] PereBrunet,IsabelNavazo, JarekRossignac, andCarlosSaona-Vazquez. Hoops: 3d curves asconservative occludersfor cell-visibility. In A. ChalmersandT.-M. Rhyne,editors,ComputerGraphics Forum (Proc. of Eurographics ’01), volume 20(3),Manchester, UK, September 2001.

[15] E. Catmull. A Subdivision Algorithm for ComputerDisplay ofCurvedSurfaces. Ph.D. thesis, University of Utah, December1974.

[16] N. Chin andS.Feiner. Nearreal-time shadow generation usingBSPtrees.ACM ComputerGraphics, 23(3):99–106,1989.

[17] Franklin S.ChoandDavid Forsyth. Interactive ray tracing withthe visibility complex. Computer & Graphics, 23(5):703–717,1999.

[18] Y. Chrysanthou. ShadowComputation for 3D Interaction andAnimation. PhDthesis,QueenMary andWestfieldCollege,Uni-versity of London,February 1996.

[19] J. H. Clark. Hierarchical geometric modelsfor visible surfacealgorithms. Communicationsof theACM, 19(10):547–554,Oc-tober 1976.

[20] D. Cohen-Or andA. Shaked. Visibility anddead-zonesin digitalterrain maps. ComputerGraphicsForum, 14(3):C/171–C/180,September1995.

[21] Daniel Cohen-Or, Gadi Fibich, Dan Halperin, and Eyal Zadi-cario. Conservativevisibil ity andstrongocclusionfor viewspacepartitioning of densely occludedscenes.Computer GraphicsFo-rum, 17(3):243–254,1998.

[22] Daniel Cohen-Or, EranRich, Uri Lerner, and Victor Shenkar.A real-time photo-realistic visual flythrough. IEEE Transac-tions on Visualization and Computer Graphics, 2(3):255–264,September 1996.

[23] Daniel Cohen-OrandEyal Zadicario. Visibil ity streaming fornetwork-basedwalkthroughs. Graphics Interface’98, pages1–7, June1998.

[24] SatyanCoorg andSethTeller. Temporally coherentconservativevisibil ity. In Proc. 12th Annu.ACM Sympos.Comput.Geom.,pages78–87,1996.

[25] SatyanCoorg andSethTeller. Real-time occlusionculling formodelswith large occluders. 1997 Symposium on Interactive3D Graphics, pages83–90,April 1997.

[26] RossCunniff. Visualize fx graphics scalable architecture. Inpresentation at Hot3D Proceedings,part of GraphicsHardwareWorkshop, 2000.

[27] Mark deBerg, Marc vanKreveld, Mark Overmars, andOtfriedSchwarzkopf. Computational Geometry: AlgorithmsandAppli-cations. Springer-Verlag,Berlin, 1997.

[28] D. P. Dobkin and S. Teller. Computer graphics. In JacobE.GoodmanandJosephO’Rourke, editors,Handbookof DiscreteandComputational Geometry, chapter 42,pages779–796. CRCPressLLC, BocaRaton,FL, 1997.

[29] S.E.Dorward.A survey of object-spacehidden surfaceremoval.Internat. J. Comput.Geom.Appl., 4:325–362, 1994.

[30] F. Durand.3D Visibili ty: Analytical studyandApplications. PhDthesis,UniversiteJosephFourier, Grenoble, France,July 1999.

[31] Fredo Durand, George Drettakis, Joelle Thollot, and ClaudePuech. Conservative visibil ity preprocessingusing extendedprojections. Proceedingsof SIGGRAPH2000, pages239–248,July 2000.

[32] David W. Eggert,Kevin W. Bowyer, andCharles R. Dyer. As-pect graphs: State-of-the-art and applications in digital pho-togrammetry. In Proc. ISPRS17th Cong.: Int. ArchivesPho-togrammetry RemoteSensing, pages633–645, 1992.

[33] J. El-Sana, N. Sokolovsky, andC. Silva. Integrating occlusionculling with view-dependent rendering. In Proc. IEEE Visual-ization2001, 2001.

[34] S.Fleishman, D. Cohen-Or, andD. Lischinski. Automatic cam-eraplacementfor image-basedmodeling. In Proceedingsof Pa-cific Graphics99, pages12–20,October1999.

[35] JamesD. Foley, AndriesvanDam,Steven K. Feiner, andJohnF.Hughes. Computer Graphics, Principles and Practice, Sec-ond Edition. Addison-Wesley, Reading, Massachusetts, 1990.Overviewof research to date.

[36] T. Funkhouser andC. Sequin. Adaptive display algorithm forinteractive frame rates during visualization of complex virtualenvironments.In Computer Graphics (Proc.Siggraph), 1993.

[37] T.A. Funkhouser. Databasemanagementfor interactive displayof large architectural models. GraphicsInterface, pages1–8,May 1996.

[38] ThomasA. Funkhouser, Carlo H. Sequin, and Seth J. Teller.Management of large amounts of data in interactive buildingwalkthroughs. 1992 Symposium on Interactive 3D Graphics,25(2):11–20,March 1992. ISBN 0-89791-467-8.

[39] B. Garlick, D. Baum,andJ.Winget.Parallel AlgorithmsandAr-chitecturesfor 3D Image Generation, volumeSIGGRAPH’90CourseNotes,Vol 28,chapterInteractiveViewingof LargeGeo-metricDataBasesUsingMultiprocessorGraphicsWorkstations,pages239–245.ACM SIGGRAPH,1990.

[40] CindyM. Goral,Kenneth E.Torrance,DonaldP. Greenberg,andBennett Battaile. Modelling theinteractionof light betweendif-fusesurfaces.In Computer Graphics(SIGGRAPH’84 Proceed-ings), volume18(3),pages212–22,July 1984.

[41] Craig Gotsman,OdedSudarsky, andJeffry Fayman.Optimizedocclusionculling. Computer & Graphics, 23(5):645–654,1999.

[42] N. Greene. Occlusion culling with optimized hierachical z-buffering. In ACM SIGGRAPHVisual Proceedings1999, 1999.

[43] N. Greene. Occlusion culling with optimized hierachical z-buffering(cdromonly). In ACM SIGGRAPHVisualProceedings1999, 1999.

[44] N. Greene. Occlusion culling with optimized hierachical z-buffering. In In ACM SIGGRAPH CourseNotes#30, 2001.

[45] N. Greene. A quality knob for non-conservative culling withhierarchical z-buffering. In In ACM SIGGRAPHCourseNotes#30, 2001.

[46] Ned Greene, M. Kass,andGary Mill er. Hierarchical Z-buffervisibility. In Computer GraphicsProceedings,AnnualConfer-enceSeries,1993, pages231–240,1993.

[47] Ned Greene, M. Kass,andGary Mille r. Hierarchical z-buffervisibility. Proceedingsof SIGGRAPH93, pages231–240, 1993.

[48] Ned GreeneandMichael Kass. Error-bounded antialiasedren-dering of complex environments. In Andrew Glassner, editor,Proceedingsof SIGGRAPH’94 (Orlando,Florida, July 24–29,1994), ComputerGraphicsProceedings,Annual ConferenceSe-ries,pages59–66.ACM SIGGRAPH,ACM Press,July 1994.

[49] P. Hanrahan,D. Salzman,andL. Aupperle. A rapid hierarchi-cal radiosity algorithm. In ThomasW. Sederberg, editor, ACMComputer Graphics, volume25,pages197–206,July 1991.

[50] Lichan Hong, ShigeruMuraki, Arie Kaufman,Dirk Bartz, andTaosongHe. Virtual voyage: Interactive navigation in the hu-man colon. In Turner Whitted, editor, SIGGRAPH97 Con-ference Proceedings, Annual Conference Series,pages27–34.ACM SIGGRAPH,AddisonWesley, August1997.

[51] T. Hudson, D. Manocha, J. Cohen, M. Lin, K. Hoff, andH. Zhang. Accelerated occlusion culling usingshadow frustra.In Proc.13thAnnu.ACM Sympos.Comput.Geom., pages1–10,1997.

[52] W.F.H. Jimenez, C. Esperana,andA.A.F. Oliveira. Efficient al-gorithms for computing conservative portal visibilit y informa-tion. Computer GraphicsForum, 19(3),2000.

[53] C. B. Jones.A new approachto the‘hidden line’ problem.Com-puter Journal, 14(3):232–237,August1971.

[54] J.T. Klosowski andC. T. Silva. Efficient conservative visibilityculling usingtheprioritized-layeredprojection algorithm. IEEETransactions on Visualization and Computer Graphics, to ap-pear.

[55] JamesT. Klosowski, Martin Held,JosephS.B. Mitchell, HenrySowizral, and Karel Zikan. Efficient collision detection usingbounding volume hierarchies of k-dops. IEEE Transactionson Visualization andComputer Graphics, 4(1):21–36, January-March1998.

[56] JamesT. Klosowski and Claudio T. Silva. The prioritized-layered projection algorithm for visible set estimation.IEEE Transactions on Visualization and Computer Graphics,6(2):108–123,April - June2000. ISSN1077-2626.

[57] JamesT. Klosowski andClaudio T. Silva. Rendering on a bud-get:A framework for time-critical rendering. IEEEVisualization’99, pages115–122, October 1999.

[58] Vladlen Koltun, Yiorgos Chrysanthou, and Daniel Cohen-Or.Virtual occluders:An efficient intermediate pvs representation.RenderingTechniques 2000: 11th EurographicsWorkshoponRendering, pages59–70,June2000. ISBN 3-211-83535-0.

[59] Vladlen Koltun, Daniel Cohen-Or, and Yiorgos Chrysanthou.Hardware-accelerated from-region visibility using a dual rayspace. RenderingTechniques2001: 12th EurographicsWork-shopon Rendering, June2001.

[60] SubodhKumar, DineshManocha, Will iam Garrett, and MingLin. Hierarchical back-face computation. Computers andGraphics, 23(5):681–692,October 1999.

[61] Fei-Ah Law andTiow-SengTan. Preprocessingocclusion forreal-timeselectiverefinement(colorplateS.221).In StephenN.Spencer, editor, Proceedingsof theConferenceonthe1999Sym-posiumon interactive 3D Graphics, pages 47–54,New York,April 26–281999.ACM Press.

[62] Hong Lip Lim. Toward a fuzzy hidden surface algorithm. InComputer GraphicsInternational, Tokyo, 1992.

[63] David Luebke andChrisGeorges. Portals andmirrors: Simple,fastevaluation of potentially visible sets. In Pat Hanrahan andJimWinget, editors,1995Symposiumon Interactive 3D Graph-ics, pages105–106.ACM SIGGRAPH,April 1995.

[64] D. Meagher. Efficient synthetic imagegeneration of arbitrary3D objects. In IEEE Computer Society Conference on PatternRecognition andImage Processing, pages473–478, 1982.

[65] TomasMoller and Eric Haines. Real-TimeRendering. A.K.PetersLtd., 1999.

[66] Steve Morein. Ati radeon hyper-z technology. In presentationat Hot3D Proceedings, part of GraphicsHardware Workshop,2000.

[67] Boaz Nadler, Gadi Fibich, Shuly Lev-Yehudi, and DanielCohen-Or. A qualitative andquantitative visibilit y analysis inurbanscenes.Computer & Graphics, 23(5):655–666,1999.

[68] BruceF. Naylor. Partitioning treeimagerepresentationandgen-eration from 3D geometric models.In Proceedings of GraphicsInterface’92, pages201–212,1992.

[69] J. O’Rourke. Art Gallery Theoremsand Algorithms. The In-ternational Seriesof Monographson ComputerScience.OxfordUniversity Press,New York, NY, 1987.

[70] Rachel Orti, Stephane Riviere, Fredo Durand, and ClaudePuech. Radiosity for dynamicscenesin flatlandwith the visi-bilit y complex. In JarekRossignac andFrancoisSilli on,editors,Computer GraphicsForum(Proc.of Eurographics’96), volume16(3),pages237–249,Poitiers,France,September1996.

[71] Steven Parker, Will iam Martin, Peter-Pike J. Sloan, Peter S.Shirley, Brian Smits,andCharlesHansen. Interactive ray trac-ing. 1999ACM Symposiumon Interactive 3D Graphics, pages119–126,April 1999. ISBN 1-58113-082-1.

[72] Michael WimmerPeterWonkaandFrancois X. Silli on. Instantvisibil ity. In A. Chalmers andT.-M. Rhyne,editors,ComputerGraphics Forum (Proc. of Eurographics ’01), volume 20(3),Manchester, UK, September2001.

[73] Harry Plantinga. Conservative visibilit y preprocessingfor effi-cient walkthroughsof 3D scenes. In Proceedings of GraphicsInterface ’93, pages 166–173,Toronto, Ontario, Canada, May1993.CanadianInformation ProcessingSociety.

[74] JohnRohlf andJamesHelman. IRIS performer:A high perfor-mancemultiprocessingtoolkit for real–time3D graphics.In An-drew Glassner, editor, Proceedingsof SIGGRAPH’94 (Orlando,Florida, July 24–29, 1994), ComputerGraphics Proceedings,Annual Conference Series,pages 381–395. ACM SIGGRAPH,ACM Press,July 1994. ISBN 0-89791-667-0.

[75] Carlos Saona-Vazquez,IsabelNavazo, and PereBrunet. Thevisibility octree: A datastructurefor 3d navigation. Computer& Graphics, 23(5):635–644,1999.

[76] GernotSchaufler, JulieDorsey, Xavier Decoret, andFrancoisX.Silli on. Conservative volumetric visibility with occluder fusion.Proceedings of SIGGRAPH2000, pages229–238,July 2000.ISBN 1-58113-208-5.

[77] N. Scott, D. Olsen,andE. Gannet.An overviewof thevisualizefx graphicsaccelerator hardware. TheHewlett-Packard Journal,May:28–34,1998.

[78] K. Severson. VISUALIZE Workstation Graphics for WindowsNT. HP productlit erature.

[79] Inc. Silicon Graphics. Sgi visual workstation opengl program-ming guidefor windows nt. Technical report,DocumentNum-ber007-3876-001, ??

[80] Francois X. Sill ion. A unified hierarchical algorithm forglobal illuminationwith scattering volumesandobject clusters.IEEE Transactions on Visualization and Computer Graphics,1(3):240–254,September1995. ISSN1077-2626.

[81] Francois X. Silli onandGeorgeDrettakis. Feature-basedcontrolof visibility error: A multi-resolution clustering algorithm forglobal illumination. Proceedingsof SIGGRAPH95, pages145–152,August1995. ISBN 0-201-84776-0.Held in Los Angeles,California.

[82] M. Slater and Y. Chrysanthou. View volume culling using aprobabilisti c cashingscheme.In S.Wilbur andM. Bergamasco,editors,Proceedingsof Framework for ImmersiveVirtual Envi-ronmentsFIVE, December 1996.

[83] WolfgangStuerzlinger. Imagingall visible surfaces. GraphicsInterface’99, pages115–122, June1999.ISBN 1-55860-632-7.

[84] Oded Sudarsky and Craig Gotsman. Dynamic sceneocclu-sionculling. IEEETransactionson VisualizationandComputerGraphics, 5(1):13–29, January- March1999.

[85] I. E. Sutherland,R. F. Sproull, andR. A. Schumaker. A char-acterization of ten hidden surface algorithms. ACM ComputerSurveys, 6(1):1–55, March1974.

[86] SethTeller. Visibil ity Computations in DenselyOccludedEnvi-ronments. PhDthesis,University of California, Berkeley, 1992.

[87] SethTellerandPatHanrahan.Global visibility algorithmsfor il-lumination computations.Proceedingsof SIGGRAPH93, pages239–246, August1993.

[88] Seth J. Teller. Computingthe antipenumbraof an arealightsource. ComputerGraphics (Proceedings of SIGGRAPH92),26(2):139–148, July 1992. ISBN 0-201-51585-7. Held inChicago,Illino is.

[89] SethJ.Teller andCarloH. Sequin. Visibility preprocessingforinteractive walkthroughs. Computer Graphics(ProceedingsofSIGGRAPH91), 25(4):61–69,July 1991.

[90] Michiel van dePanneandJamesStewart. Efficient compressiontechniquesfor precomputedvisibil ity. In Proceedingsof Euro-graphicsWorkshopon Rendering’99, 1999.

[91] I. Wald andP. Slusallek. State-of-the-art in interactive ray trac-ing, 2001.

[92] I. Wald, P. Slusallek, and C. Benthin. Interactive distributedray tracing of highly complex models.In Rendering Techniques2001- Proceedingsof the12thEUROGRAPHICSWorkshoponRendering, pages274–285,2001.

[93] I. Wald, P. Slusallek, C. Benthin, and M. Wagner. Interactiverendering with coherentraytracing. Computer GraphicsForum,20(3):153–164,2001.

[94] PeterWonka and Dieter Schmalstieg. Occluder shadows forfastwalkthroughsof urbanenvironments.In Hans-Peter SeidelandSabineCoquillart, editors,Computer Graphics Forum, vol-ume18, pagesC51–C60.Eurographics Association andBlack-well PublishersLtd 1999,1999.

[95] PeterWonka,Michael Wimmer, andDieter Schmalstieg. Vis-ibili ty preprocessing with occluder fusion for urban walk-throughs. RenderingTechniques 2000: 11th EurographicsWorkshopon Rendering, pages71–82,June2000. ISBN 3-211-83535-0.

[96] PeterWonka,Michael Wimmer, andDieter Schmalstieg. Vis-ibili ty preprocessing with occluder fusion for urban walk-throughs.Technical ReportTR-186-2-00-06, Institute of Com-puter Graphics, Vienna University of Technology, Karlsplatz13/186,A-1040 Vienna, Austria, March 2000. humancontact:technical-report@cg.tuwien.ac.at.

[97] A. Woo, P. Poulin, andA. Fourier. A survey of shadow algo-rithms. IEEE Computer Graphics and Applications, 10(6):13–31,1990.

[98] HansongZhang.Effective OcclusionCulling for theInteractiveDisplayof Arbitrary Models. Ph.D.thesis,Departmentof Com-puterScience,UNC-Chapel Hill, 1998.

[99] HansongZhang,DineshManocha, ThomasHudson,andKen-nethE. Hoff III. Visibil ity culling usinghierarchical occlusionmaps. In Turner Whitted, editor, SIGGRAPH97 ConferenceProceedings, Annual Conference Series,pages77–88. ACMSIGGRAPH,AddisonWesley, August1997.