计算机图形学RadianceEQ-Anonymous

1RadianceEquation2Outline†Introduction†Light†SimplifyingAssumptions†Radiance†Reflectance†TheRadianceEquation†TraditionalRenderingSolutions†Visibility†Conclusions3Overview†Polygons†Planes†Creatinganobjectfrompolygons4NoMoreSpheres†Mostthingsincomputergraphicsarenotdescribedwithspheres!†Polygonalmeshesarethemostcommonrepresentation†Lookathowpolygonscanbedescribedandhowtheycanusedinray-casting5PolygonalMeshes6Polygons†Apolygon(face)Qisdefinedbyaseriesofpoints†Thepointsaremustbeco-planar†3pointsdefineaplane,buta4thpointneednotlieonthatplane[]()iiiinnzyxpppppp,,,1,...,2,1,0=−7Convex,Concave†Convex†Concave„CGpeopledislikeconcavepolygons„CGpeoplewouldprefertriangles!!†Easytobreakconvexobjectintotriangles,hardforconcave8COP9WhyTriangles?†Ingeneralforanobjectrepresentation(bezier,CSG)isitfarfromeasytofindthe2Dprojectionoftheshape10DifferentialSolidAngledωdω=dxdy={rdθ}{rsin(θdφ}=(r2)sin(θdθdφSphericalCoordinateSystem11Introduction†Lightingisthecentralproblemofreal-timegraphicsrendering„Arbitraryshapedlights„Changesinlightingconditions„Real-timeshadows„Real-timereflections„Mixturesofmanydifferenttypesofsurface12Introduction†Real-timewalkthroughwithglobalillumination„Possibleunderlimitedconditions†Radiosity(diffusesurfacesonly)†Real-timeinteraction„Notpossibleexceptforspecialcaselocalillumination†Whyistheproblemsohard?13Light†Visiblelightiselectromagneticradiationwithwavelengthsapproximatelyintherangefrom400nmto700nm400nm700nm14Light:Photons†Lightcanbeviewedaswaveorparticlephenomenon†Particlesarephotons„packetsofenergywhichtravelinastraightlineinvaccuumwithvelocityc(300,000km.p.s.)†Theproblemofhowlightinteractswithsurfacesinavolumeofspaceisanexampleofatransportproblem.15Light:RadiantPower†ΦdenotestheradiantenergyorfluxinavolumeV.†Thefluxistherateofenergyflowingthroughasurfaceperunittime(watts).†Theenergyisproportionaltotheparticleflow,sinceeachphotoncarriesenergy.†Thefluxmaybethoughtofastheflowofphotonsperunittime.16Light:FluxEquilibrium†Totalfluxinavolumeindynamicequilibrium„Particlesareflowing„Distributionisconstant†Conservationofenergy„Totalenergyinputintothevolume=totalenergythatisoutputbyorabsorbedbymatterwithinthevolume.17Light:FundamentalEquation†Input„Emission–emittedfromwithinvolume„Inscattering–flowsfromoutside†Output„Streaming–withoutinteractionwithmatterinthevolume„Outscattering–reflectedoutfrommatter„Absorption–bymatterwithinthevolume†Input=Output18Light:Equation†Φ(p,ω)denotesfluxatp∈V,indirectionω†ItispossibletowritedownanintegralequationforΦ(p,ω)basedon:„Emission+Inscattering=Streaming+Outscattering+Absorption†CompleteknowledgeofΦ(p,ω)providesacompletesolutiontothegraphicsrenderingproblem.†RenderingisaboutsolvingforΦ(p,ω).19SimplifyingAssumptions†Wavelengthindependence„Nointeractionbetweenwavelengths(nofluorescence)†Timeinvariance„Solutionremainsvalidovertimeunlessscenechanges(nophosphorescence)†Lighttransportsinavacuum(non-participatingmedium)–„‘freespace’–interactiononlyoccursatthesurfacesofobjects20Radiance†Radiance(L)isthefluxthatleavesasurface,perunitprojectedareaofthesurface,perunitsolidangleofdirection.θndALdΦ=LdAcosθdω21Radiance†Forcomputergraphicsthebasicparticleisnotthephotonandtheenergyitcarriesbuttherayanditsassociatedradiance.θndALdωRadianceisconstantalongaray.22Radiance:Radiosity,Irradiance†Radiosity-isthefluxperunitareathatradiatesfromasurface,denotedbyB.„dΦ=BdA†Irradianceisthefluxperunitareathatarrivesatasurface,denotedbyE.„dΦ=EdA23RadiosityandIrradiance†L(p,ω)isradianceatpindirectionω†E(p,ω)isirradianceatpindirectionω†E(p,ω)=(dΦ/dA)=L(p,ω)cosθdω24Reflectance†BRDF„Bi-directional„Reflectance„Distribution„Function†Relates„ReflectedradiancetoincomingirradianceωiωrIncidentrayReflectedrayIlluminationhemispheref(p,ωi,ωr)25Reflectance:BRDF†ReflectedRadiance=BRDF×Irradiance†L(p,ωr)=f(p,ωi,ωr)E(p,ωi)†=f(p,ωi,ωr)L(p,ωi)cosθidωi†InpracticeBRDF’shardtospecify†Relyonidealtypes„Perfectlydiffusereflection„Perfectlyspecularreflection„Glossyreflection†BRDFstakenasadditivemixtureofthese26TheRadianceEquation†RadianceL(p,ω)atapointpindirectionωisthesumof„EmittedradianceLe(p,ω)„TotalreflectedradianceRadiance=EmittedRadiance+TotalReflectedRadiance27TheRadianceEquation:Reflection†Totalreflectedradianceindirectionω:„∫f(p,ωi,ω)L(p,ωi)cosθidωi†RadianceEquation:†L(p,ω)=Le(p,ω)+∫f(p,ωi,ω)L(p,ωi)cosθidωi„(Integrationovertheilluminationhemisphere)28TheRadianceEquation∫∫+=ππφθθθωωωωω2020sincos),(),,(),(),(ddpLpfpLpLiiiie29TheRadianceEquation†pisconsideredtobeonasurface,butcanbeanywhere,sinceradianceisconstantalongaray,tracebackuntilsurfaceisreachedatp’,then„L(p,ωi)=L(p’,ωi)p*ωipL(p,ω)L(p,ω)dependsonallL(p*,ωi)whichinturnarerecursivelydefined.Theradianceequationmodelsglobalillumination.30TraditionalSolutionstotheRadianceEquation†Theradianceequationembodiestotalityofall2Dprojections(view).†Extractionofa2Dprojectiontoformanimageiscalledrendering.31TraditionalSolutionsLocalIlluminationGlobalIlluminationViewDependent‘Realtime’graphics:OpenGLRaytracingPathtracingViewIndependentFlatshadedgraphics(IBR)Radiosity(PhotonTracing