RAY INTERPOLANTS FOR FAST RAY-TRACING REFLECTIONS AND REFRAC

To render an object by ray tracing, one or more rays are shot from the viewpoint through every pixel of the image plane. For reflective and refractive objects, especially for multiple levels of reflections and/or refractions, this requires many expensive i

RAYINTERPOLANTSFORFASTRAY-TRACINGREFLECTIONS

ANDREFRACTIONS1

FatmaBetulAtalay

DavidM.Mount

DepartmentofComputerScienceUniversityofMaryland,CollegePark

betul,mount@cs.umd.edu

ABSTRACT

Torenderanobjectbyraytracing,oneormoreraysareshotfromtheviewpointthrougheverypixeloftheimageplane.Forre ectiveandrefractiveobjects,especiallyformultiplelevelsofre ectionsand/orrefractions,thisrequiresmanyexpensiveintersectioncalculations.Thispaperpresentsanewmethodforacceleratingray-tracingofre ectiveandrefractiveobjectsbysubstitutingaccurate-but-slowintersectioncalculationswithapproximate-but-fastinterpolationcomputations.Ourapproachisbasedonmodelingthere ective/refractiveobjectasafunctionthatmapsinputraysenteringtheobjecttooutputraysexitingtheobject.Weareinterestedincomputingtheoutputraywithoutactuallytracingtheinputraythroughtheobject.Thisisachievedbyadaptivelysamplingraysfrommultipleviewpointsinvariousdirections,asapreprocessingphase,andtheninterpolatingthecollectionofnearbysamplestocomputeanapproximateoutputrayforanyinputray.Inmostcases,objectboundariesandotherdiscontinuitiesarehandledbyap-plyingvariousheuristics.Incaseswherewecannot ndsuf cientevidencetointerpolate,weperformraytracingasalastresort.Weprovideperformancestudiestodemonstratetheef ciencyofthismethod.Keywords:raytracing,renderingre ectionsandrefractions,interpolation1

INTRODUCTION

Highquality,physicallyaccuraterenderingofcomplexilluminationeffectssuchasre ection,refraction,andspecularhighlightsishighlydesirableincomputer-generatedimagery.Themostpopulartechniqueforgeneratingtheseeffectsisraytracing[Whitt80].However,raytracingremainsacomputa-tionallyexpensivetechnique.Theprimaryexpenseinraytracingliesinintersectioncalculations,especiallyforscenesthatcontaincomplexobjects,suchasBezierorNURBSsurfaces,andincaseofmultiplelevelsofre ectionsand/orrefractions.

Inthispaper,wepresentamethodtoaccelerateraytracingofre ectiveandrefractiveobjectsbyelimi-natingintersectioncalculations.Ouralgorithmfacil-itatesfast,approximaterenderingoftheobjectfromanyviewpoint,andwouldbemostusefulwhenthesameobjectisrenderedfrommultipleviewpointsinasequenceofframes.Thekeyinsighttoourmethodisthatarayintersectingare ectiveorrefractiveobjectgoesthroughasetofre ectionsand/orrefractions,and nallyexitstheobjectasanoutputray.There-fore,wecanmodeltheobjectasafunctionthatmapsinputraystooutputrays.Formanyrealworld

To render an object by ray tracing, one or more rays are shot from the viewpoint through every pixel of the image plane. For reflective and refractive objects, especially for multiple levels of reflections and/or refractions, this requires many expensive i

tion3,weexplaintheconstructionofourdatastruc-ture.Section4outlinestherenderingphaseandtheheuristicsusedforhandlingdiscontinuities.InSec-tion5,wedescribecomputinglocalillumination.TheexperimentsarepresentedinSection6.Finally,weconcludewithSection7.2

PREVIOUSWORK

Earlyresearchconcentratedonacceleratingraytrac-ingbyreducingthecostofintersectioncomputationsusingboundingvolumehierarchies[Rubin80],spacepartitioningstructures[Glass84,Kapla85],andmeth-odsexploitingraycoherence[Arvo87,Heckb84].Recentresearchhasfocusedonfastgenerationofray-tracedimagesfrommultipleviewpoints.Thesesys-temsexploitframe-to-framecoherenceandreusepix-elsfromthepreviousframebyreprojectionandonlyrecomputeorpossiblyre nethepotentiallyincorrectpixels[Adels95,Walte99].

TheInterpolantRayTracersystemdescribedbyBala,DorseyandTellerintroducedtheradianceinterpolanttoaccelerateshadingbyquadrilinearlyinterpolatingradiancesamplescachedinanadaptive4Ddatastruc-turewhileconservativelyboundingtheerror[Bala99].Wedifferinthatweareprimarilyinterestedinfastrenderingofre ectiveandrefractiveobjects.Ourdatastructuremapsraystoraysratherthanraystoradiance,andweinterpolateamongrays.Bythismethod,wedecouplelocalgeometryoftheobjectfromtheenvironment,andmuchlesssamplingofraysissuf cientthansamplingofradiancetorenderre ec-tive/refractiveobjects.Torenderre ectedtextures,theInterpolantRayTracersystemshootsadditionalre ectionrays,whichisexpensive,especiallyformul-tiplere ections.Theirinterpolationrequiresthattheraytreesofallsamplesusedforinterpolationbeiden-ticaltoconstituteavalidinterpolant.Forre ec-tive/refractiveobjectsthisstrongrequirementsignif-icantlyreducesthecaseswhereinterpolationcouldbesubstitutedforraytracing.Instead,weapplyheuris-ticsthatwouldallowustouseinterpolationsinmorecaseswhiletradingoffqualitytosomeextent.Image-BasedRenderingmethodsconstituteanotherlineofresearchtosupportfastrenderingofscenes.Amongthem,themostrelevanttoourworkistheLumigraph[Gortl96]andLightFieldRendering[Levoy96]techniques.Botharebasedondensesam-plingoftheplenopticfunction[Adels91].Thesesys-temshaveapreprocessingphasewherethe4Dplenop-ticfunctionissampledbyuniformlysubdividinginallfourdimensions.Theradiancealonganyrayfromanyviewpointcanthenbeapproximatedbyquadri-linearlyinterpolatingtheradiancevaluesforthenear-estsixteenraysamples.Tohavereasonablequalityofcomplexeffectssuchasre ection,refractionandspecularhighlights,thesemethodsshouldsampleverydensely.Schirmacher,etal.[Schir99]andSloan,etal.[Sloan97]proposedextensionstotheLumigraph.

Thereexistapproachesotherthanraytracingtoren-derfastapproximationsofre ective/refractiveob-jects.Theoldestsuchmethodisenvironmentmap-ping[Blinn76].Itassumesthattheenvironmentissuf- cientlyfarawayfromthere ectiveobject.Anothermethodexplainedin[Ofek98]isbasedonmirroringthesceneobjectswithrespecttoare ector.Itworksforcurvedre ectorsrelyingonhighresolutiontessel-lationofboththere ectorandthere ectedobjectsandfocusesonasinglelevelofre ection.Heidrich,etal.proposedalight eldmethodforrenderingrefractiveobjects[Heid …… 此处隐藏：28980字，全部文档内容请下载后查看。喜欢就下载吧 ……