EECS487:InteractiveComputerGraphicsLecture27:•  IntroductiontoGlobalIlluminationandRayTracing

RayTracing

Introductionandcontext•  raycasting

Recursiveraytracing•  shadows•  reflection•  refraction

Raytracingimplementation

DistributedRayTracing•  anti-aliasing•  soft-shadows• motionblur• depth-of-field• glossysurface•  translucency

GlobalIlluminationComputesthecoloratapointintermsoflightdirectlyemittedbylightsourcesandoflightindirectlyreflectedbyandtransmittedthroughotherobjects,allowingforcomputationofshadows,reflection,refraction,caustics,andcolorbleedLightpathsarecomplex,notlight�triangle�pixelNaturefindsequilibriumefficientlyComputersstruggleL

Akeley

PipelinedRasterization

PerformprojectionofverticesRasterizetriangle:findwhichpixelsshouldbelitComputeper-pixelcolorTestvisibility,updateframebuffer

Durand

RayTracing

Hanrahan,Yu,Curless,Akeley

Canweproducemorerealisticresultsifwerenderascenebysimulatingphysicallighttransport?TheGreeksquestionedthenatureoflight:dolightraysproceedfromtheeyetothelightorfromthelighttotheeye?Moderntheoriesoflighttreatitasbothawaveandaparticle

image(pixels)

lights(photons)

objects(triangles)

viewer

GeometricOpticsWewilltakeacombinedandsomewhatsimplerviewoflight–theviewofgeometricoptics

Lightsourcessendoffphotonsinalldirections•  modeltheseasparticlesthatbounceoffobjectsinthescene•  eachphotonhasawavelengthandenergy(colorandintensity)•  whenphotonsbounce,someenergyisabsorbed,somereflected,sometransmitted

•  photonsbounceuntil:•  allofitsenergyisabsorbed(aftertoomanybounces)•  itdepartstheknownuniverse(notjusttheviewvolume!)•  itstrikestheimageplaneanditscontributionisaddedtoappropriatepixel

Wecallthepathofthesephotons“lightrays”

Ifwecanmodellightrayswecangenerateimages

Curless,Hodgins

GeometricOpticsLightraysfollowtheserules:•  travelinstraightlinesinfreespace

•  donotinterferewitheachotheriftheycross(lightisinvisible!)

•  travelfromthelightsourcestotheeye,butthephysicsisinvariantunderpathreversal(reciprocity)

•  obeythelawsofreflectionandrefraction

Curless,Hanrahan

WhyTraceRays?Moreelegantthanpipelinedrasterization,especiallyforsophisticatedphysics:• modelinglightreflectance,e.g.,fromskin

• modelinglighttransport,e.g.,inter-reflection,caustics

•  rendering,e.g.,softshadows

Easiestphotorealisticglobalilluminationrenderertoimplement

Jensen,Hart08

Raysemanatefromlightsourcesandbouncearound

Raysthatpassthroughtheimageplaneandentertheeyecontributetothefinalimage

Veryinefficientsinceitcomputesmanyraysthatareneverseen,mostrayswillneverevengetclosetotheeye!

Light-RayTracing

imageplane Merrell08

RayCastingForeachpixelshootaray(a3Dline)fromtheeyeintotheviewvolumethroughapointonthescreen• findthenearestpolygonthatintersectswiththeray•  shadethatintersectionaccordingtolight,e.g.,byusingthePhongilluminationmodel,orotherphysically-basedBRDFs,tocomputepixelcolor

Computesonlyvisiblerays(sincewestartattheeye):moreefficientthanlighttracing

IntroducedbyAppelin1968forlocalillumination(onpenplotter)

Merrell,Curless

Image plane

l

n

RayCastingIlluminationModelSofarit’sstilllight→triangle→pixel

Withraycasting,weadditionallyshootarayfromeachpointtowardeachlightinthesceneandask:•  isthelightvisiblefromtheintersectionpoint?

•  doestherayintersectanyobjectsonthewaytothelight?

•  iflightisnotvisible,itdoesn’tlitthepoint(pointinshadow)

RayCastingImage

Castrays

Findfirst

intersection

Shading

PipelinedRasterizationCommand

Geometry

Rasterization

Texture

Display

RayCastingvs.PipelinedRasterization

Zwicker06

SceneGraph

OutputImage

ImageOrder

ObjectOrder

RayTracingWhittedintroducedraytracingtothegraphicscommunityin1980:•  recursiveraycasting• firstglobalilluminationmodel:•  anobject’scolorisinfluencedbylightsandotherobjectsinthescene�shadows•  simulatesspecularreflectionandrefractivetransmission

imageplaneMerrell08

Whitted80

RayTracingvs.PipelinedRasterization

RayTracing+ nocomputationforhiddenparts

- usuallyimplementedinsoftware

-  slow,batchrendering- nodominantstandardforscenedescription(RenderManformat,POVray,PBRT,…)

+ photo-realisticimages:morecomplexshadingandlightingeffectspossible

PipelinedRasterization+ implementedinGPU+ standardizedAPIs+ interactiverendering,games-  limitedphoto-realism:hardertogetglobalillumination(butgettingcloser)

Zwicker06

RecursiveRayTracingBasicidea:•  Eachpixelgetslightfromjustonedirection�thelinethroughthescreenandtheeye

• Anyphotoncontributingtothatpixel’scolorhastocomefromthisdirection

•  Soheadinthatdirectionandseewhatissendinglight•  ifwefindnothing—done

•  ifwehitalightsource—done

•  ifwehitasurface—seewherethatsurfaceislitfrom,recurse

imageplaneHodgins,Merrell

Ray:aHalfLine

Anchorpoint:e = (xe, ye, ze, 1)

Ray:r = (e, d)Translatingrays:pointstranslate,directionsdon’tTr = (Te, Td) = (Te, d)

p = r(t) = e + t d,t > 0

Direction: d = s − e = (xd, yd, zd, 0)||d|| = 1preferred,butisnotalwaysso

s:screenintersection

Hart08

RecursiveRayTracingAlgorithm1.  Foreachpixel(s),traceaprimaryrayfromtheeye(e),inthe

directiond = (s – e)tothefirstvisiblesurface

2.  Foreachintersection,tracesecondaryrays,tocollectlight:•  shadowraysindirectionslitolightsourcei•  reflectivesurface:reflectedrayindirectionr,recurse•  transparentsurface:refracted/transmitted/transparencyrayindirectiont,recurse

r n

−dl1

t

l2

shadow rays

ShadowRayAteveryray-objectintersection,weshootashadowraytowardseachlightsource

Iftherayhitsthelightsource(l1),thelightisusedinlightingcalculation,withtheshadowrayasthelightdirection

Iftherayhitsanobject(l2),theintersectionisinshadowandthelightisnotusedinlightingcalculation

Shadowraysdonotspawnadditionalrays(notransparencythroughtransparentobject!)

r n

−dl1

t

l2

shadow rays

RecursiveRayTracingd = primaryrayl = shadowraysr = reflectedrayst = transmittedrays

opaque,reflectiveobject transparent,

reflectiveobject

r1

r2

r3

t1

t2

l3

l1

l2

d

Merrell08

Howdeepdowerecurse?

RayTreeEachintersectionmayspawnsecondaryrays:•  reflectedandtransmittedraysformaraytree•  nodesaretheintersectionpoints

•  edgesarethereflectedandrefractedrays

•  shadowraysaresentfromeveryintersectionpoint(todetermineifpointisinshadow),buttheydonotspawnadditionalrays

Raysarerecursivelyspawneduntil:•  raydoesnotintersectanyobject•  treereachesamaximumdepth•  lightreachessomeminimumvalue(reflected/refractedcontributiontocolorbecomestoosmall)

Merrell08

RayTreeExample

Raytreeisevaluatedbottomup:• depth-firsttraversal(byrecursion)•  thenodecoloriscomputedbasedonitschildren’scolors(BG:background,ambientcolor)• don’tforgettonegatethenormalwheninsideanobject!

eyed

O1

r2

BG

r3 t2

O1 BG

r1 t1

O1 O2 opaque,reflectiveobject transparent,

reflectiveobject

r3

t2

l3

r1

t1 l1

r2

l2

d

O1

O2

Merrell08

raytrace() raytrace(ray r)

find first intersection color = ambient term for every light

cast shadow ray if (not in shadow)

color += local diffuse+specular terms // Phong illumination model

if reflective surface color += reflectedContrib // constant * raytrace(reflected ray)*local specular term

if transparent object color += refractedContrib // constant * raytrace(refracted ray)*local diffuse term

Durand

edray r

ShadowsIncreaserealismbyaddingspatialrelations•  providecontactpoints,stop“floating”objects•  providedepthcue•  emphasizeilluminationdirection

Provide“atmosphere”

Palmer

Someofitisabsorbed(heat,vibration)Someofitisreflected(bouncesback)Someofitisrefracted(goesinsidethematerial)Theproportionofabsorbed,reflected,andrefractedlightdependonthemedium,thefrequencyoflight,andontheanglebetweenthedirectionofincidentlightandthesurfacenormalLightmayalsobescatteredbythemediumittraverses

Rossignac

LightHittingaSurface

Reflection:arrivingenergyfromonedirectiongoesoutinonlyonereflectiondirection

PerfectSpecularReflection

nd r

θi θr

θi = θr

r = d – 2(d � n)n

RefractionLighttransmitsthroughtransparentobjectsLightenteringanewmediumisrefracted•  itstrajectorybendsinwardswhenenteringadensermedium•  thinkofthewheelononesideofacartslowingdownfirst

•  similarly,soundbendstowardscoolerair

Whydoeshotroadappearwet?•  lightisbent:lighttravelsfasterthroughthehotairneartheground

Rossignac

RefractionAssumethatkicisthespeedoflightinmediumMiandktcisthespeedoflightinmediumMt:•  indexofrefractionofamaterialMis:η = 1/k•  lightbendswhenmovingfromonemediumtoanotheraccordingtoSnell’slaw(1621):ηi sin θi = ηt sin θt

glass

ηiair

ηt

nd

t

θi

θt

Let µ =ηiηt, v = −d

t = µv − µ(n • v) + 1− µ2 (1− (n • v)2 )( )n

Unrefracted (geometrical)line of sight Refracted (optical)

line of sight

Transparentobject

Line of sight

AB

qi

qt

Merrell,Rossignac,FvD

θi

θt

FresnelCoefficientCaptureshowmuchlightreflectsfromasmoothinterfacebetweentwomaterials(F,fractionoflightreflected):

c = F*creflection + (1−F) crefraction

• reflectancedependsonangleofincidence•  notsomuchformetal(conductormaterial)•  butdramaticallyforwater/glass(dielectric/insulatormaterial):

4%atnormal,100%atgrazingangle

Schlick’sapproximationofFresnelcoefficient:F(θ) = F (0) + (1−F (0))(1−(n•v))5

whereistheFresnelcoefficientatnormal(0º)

F(0) = ηt −ηi

ηt +ηi

⎛⎝⎜

⎞⎠⎟

2

Zwicker06,Gillies09

Gold:F(0) = 0.82Silver:F(0) = 0.95Glass:F(0) = 0.04Diamond:F(0) = 0.15

t = µv − µ(n • v)+ 1− µ2 (1− (n • v)2 )( )n

TotalInternalReflectionWhengoingfromadensetoalessdensemedium,theangleofrefractionbecomeslargerthantheangleofincidence(θt > θi)

Iftheangleofincidenceistoolarge(≥ θc),lightcangettrappedinsidethedensematerial• diamond→air:θc = 24.6º• water→air:θc = 48.6º• principlebehindopticalfiber

Canbenegativeforgrazingangleswhenη >1,e.g.,whengoingfromglasstoair,resultingintotalinternalreflection(norefraction)

Hart