CS-184: Computer GraphicsLecture #15: Radiometry Prof. James O’BrienUniversity of California, BerkeleyV2008-S-15-1.012TodayRadiometry: measuring lightLocal Illumination and Raytracing were discussed in an ad hoc fashionProper discussion requires proper unitsNot just pretty pictures... but correct pictures23Matching RealityUnknown34Matching RealityPhotoRenderedCornell Box ComparisonCornell Program of Computer Graphics44Matching RealityPhotoRenderedCornell Box ComparisonCornell Program of Computer Graphics45UnitsLight energy Really power not energy is what we measureJoules / second ( J/s ) = Watts ( W )Spectral energy density power per unit spectrum intervalWatts / nano-meter ( W/nm )Properly done as function over spectrumOften just sampled for RGBOften we assume people know we’re talking about S.E.D. and just say E...56IrradianceTotal light striking surface from all directionsOnly meaningful w.r.t. a surfacePower per square meter ( )Really S.E.D. per square meter ( )Not all directions sum the same because of foreshorteningW/m2W/m2/nm66IrradianceTotal light striking surface from all directionsOnly meaningful w.r.t. a surfacePower per square meter ( )Really S.E.D. per square meter ( )Not all directions sum the same because of foreshorteningW/m2W/m2/nm67W/m2/nmRadiant ExitanceTotal light leaving surface over all directionsOnly meaningful w.r.t. a surfacePower per square meter ( )Really S.E.D. per square meter ( )Also called RadiositySum over all directions ⇏ same in all directionsW/m278Solid AnglesRegular angles measured in radiansMeasured by arc-length on unit circle Solid angles measured in steradiansMeasured by area on unit sphereNot necessarily little round pieces...[0..2π][0..4π]89RadianceLight energy passing though a point in space in a given directionEnergy per steradian per square meter ( )S.E.D. per steradian per square meter ( )Constant along straight lines in free spaceW/m2/sr /nmW/m2/srdkdarea=DΑσd2area=DΑσ(kd)2910RadianceNear surfaces, differentiate between Radiance from the surface ( surface radiance )Radiance from other things ( field radiance )LfLs1011Light FieldsThe radiance at every point in space, direction, and frequency: 6D functionCollapse frequency to RGB, and assume free space: 4D functionSample and record it over some volume1112Light FieldsLevoy and Hanrahan, SIGGRAPH 19961213Light FieldsLevoy and Hanrahan, SIGGRAPH 19961314Light FieldsMichelangelo’s Statue of NightFrom the Digital Michelangelo Project1415Computing IrradianceIntegrate incoming radiance (field radiance) over all directionTake into account foreshorteningH =ZΩLf(k)cos(θ)dσθndσk!H =Z2π0Zπ/20Lf(θ,φ)cos(θ)sin(θ) dθ dφ1516Revisiting The BRDFHow much light from direction A goes out in direction BNow we can talk about units:BRDF is ratio of foreshortened field radiance to surface radianceρ(θi, θo) =Ls(θo)Lf(θi)cos(∠ˆnθ)lightdetectorkikoWe left out frequency dependance here...Also note for perfect Lambertian reflector with constant BRDF ρ = 1/π1617The Rendering EquationTotal light going out in some direction is given by an integral over all incoming directions: Note, this is recursive ( my is another’s )Ls(ko) =ZΩρ(ko, ki)Lf(ki)cos(θ)dσLfLs1718The Rendering EquationWe can rewrite explicitly in terms of Ls(ko) =ZΩρ(ko, ki)Lf(ki)cos(θ)dσLsLs(ko, x) =ZSρ(ko, ki)Ls(x − x", x")cos(θi)cos(∠ˆn"(x − x"))δ(x, x")||x − x"||2dx"Consider what ray tracing was doing....i1819Light PathsMany paths from light to eyeCharacterize by the types of bouncesBegin at lightEnd at eye“Specular” bounces“Diffuse” bounces1920Light PathsDescribe paths using stringsLDE, LDSE, LSE, etc.Describe types of paths with regular expressionsL{D|S}*EL{D|S}S*EL{D|S}ELD*EVisible pathsStandard raytracingLocal illuminationRadiosity method(have not talked about
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