Department of Computer Sciences CS354 { Spring 2005Reection and Light Source Mo delsIllumination:Energy physics...Radiance: the ux of light energy in a given directionGeometry/Visibility: how light energy falls up on a surfaceBRDF: the interaction function of a surface p oint with lightEnergy Balance Equation: the lo cal balance of energy in a sceneApproximation:Hacks for interaction at a p oint...Ambient: approximating the global energyLamb ertian: approximating the diuse interactionPhong: approximating the specular interactionThe University of Texas at Austin1Department of Computer Sciences CS354 { Spring 2005Reection VS. IlluminationLight:An electromagneticenergy uxthat hasintensity (p ower per unit area)direction of propagationReection:Alocal lighting modelthat relatesthe prop erties of a surface at a p ointthe incoming direction and energy at the p ointthe outgoing direction and energy at the p ointBRDF:bidirectional reectance distribution functionthe function that emb o dies the surface prop ertiesThe University of Texas at Austin2Department of Computer Sciences CS354 { Spring 2005Illumination:Aglobal lighting modelthat computesoverall light distribution in an environment{from the reection mo dels{from the shap e and lo cation of all objects{from the shap e and lo cation of all light sourcesShading:Alocal interpolation techniqueused toreduce the cost of computing reectionshade p olygons \nicely"The University of Texas at Austin3Department of Computer Sciences CS354 { Spring 2005Energy of IlluminationRadiance:Electromagneticenergy ux, the amount of energytravelingat some p ointxin a sp ecied direction; per unit timeper unit area perp endicular to the directionper unit solid anglefor a sp ecied wavelengthdenoted byL(x;  ; ; )Sp ectral Prop erties:Total energy ux comes from ux at eachwavelengthL(x;  ; ) =RmaxminL(x;  ; ; )dThe University of Texas at Austin4Department of Computer Sciences CS354 { Spring 2005Picture:For the indicated situationL(x;  ; )dxcosd!dtisenergy radiated through dierential solid angled!=sinddthrough/from dierential areadxnot p erp endicular to direction (projected area isdxcos)during dierential unit timedtdωdxnφθPower:Energy per unit time (as in the picture)L(x;  ; )dxcosd!Radiosity:Total power leaving a surface p oint per unit areaRL(x;  ; ) cosd!=R20R20L(x;  ; ) cossin dd(integral is over the hemisphere above the surface p oint)The University of Texas at Austin5Department of Computer Sciences CS354 { Spring 2005Bidirectional Reectance Distribution Function:is a surface prop erty at a p ointrelates energy in to energy outdep ends on incoming and outgoing directionsvaries from wavelength to wavelengthDenition: Ratio{of radiance in the outgoing direction{to radiant ux density for the incoming directionbd(x; i;i;i;o;o;o) =Lo(x; ox;ox;o)Li(x; ix;ix;i) cosixd!ixnL(,x θx,φ,xiiiλi)L(,x θxo,φoo,xλ)oφoxθoxtThe University of Texas at Austin6Department of Computer Sciences CS354 { Spring 2005Energy Balance EquationLo(x; ox;ox;o) =Le(x; ox;ox;o)+R20R20Rmaxminbd(x; ix;ix;i;ox;ox;o)cos(ix)Li(x; ix;ix;i)disin(ix)dixdixLo(x; ox;ox;o)is the radiance{at wavelengtho{leaving p ointx{in directionox;oxLe(x; ox;ox;o)is the radiance emitted by the surface fromthe p ointLi(x; ix;ix;i)is the incident radiance impinging on the p ointbd(x; ix;ix;i;ox;ox;o)is the BRDF at the p oint{describ es the surface's interaction with light at the p ointthe integration is over the hemisphere above the p ointThe University of Texas at Austin7Department of Computer Sciences CS354 { Spring 2005Fast and Dirty ApproximationsRough Approximations:Usered,green, andblueinstead of full sp ectrum{Roughly follows the eye's sensitivity{Forego such complex surface b ehavior as metalsUse nite numb er of point light sources instead of full hemisphere{Integration changes to summation{Forego such eects as soft shadows and color bleedingBRDF b ehaves indep endently on each color{Treat red, green, and blue as three separate computations{Forego such eects as iridescence and refractionBRDF split into three approximate eects{Ambient: constant, nondirectional, background light{Diuse: light reected uniformly in all directions{Sp ecular: light of higher intensityinmirror-reection directionEnergy uxLreplaced by simple \intensity"I{No pretense of b eing physically trueThe University of Texas at Austin8Department of Computer Sciences CS354 { Spring 2005Approximate Intensity Equation:(single light source)Io=Ie+kaIa+kdIlcos(l) +ksIlW(l)S(l)stands for each ofred, green, blueIlis the intensity of the light source (mo died for distance)cos(l)accounts for the projected cross-sectional area of theincoming lightthekare between 0 and 1 and represent absorption factorsW(l)accounts for any highlight eects that dep end on theincoming direction{usecos(l)if there is nothing sp eciallis the mirror reection angle for the light{the angle between the view direction and the mirror reectiondirectionS(l)accounts for highlights in the mirror reection directionthe sup erscriptse,a,d,sstand foremitted, ambient, diuse,specularresp ectivelysum over each lightlif there are more than oneThe University of Texas at Austin9Department of Computer Sciences CS354 { Spring 2005Lamb ertian Reection Mo delDiuse Geometry:iis theunit vectorin the direction of the illumination (lightsource)nis theunit vectornormal to the surfaceris theunit vectorin the mirror reection directionvis theunit vectorin the direction of the eyep ointθθαinrvFormulas:cos() =nirandare not neededThe University of Texas at Austin10Department of Computer Sciences CS354 { Spring 2005Phong Reection Mo delSp ecular Geometry (Phong Mo del):iis theunit vectorin the direction of the illumination (lightsource)nis theunit vectornormal to the surfaceris theunit vectorin the mirror reection directionvis theunit vectorin the direction of the