CSCE 641 Computer Graphics: RadiosityRendering: Illumination ComputingSlide 3Review: Ray Tracing AssumptionSlide 5Slide 6Slide 7Slide 8Ray Tracing AssumptionPros and Cons of Ray TracingRadiosity vs. Local IlluminationRadiosityPhysical Image vs. Radiosity RenderingSlide 14Slide 15Slide 16Slide 17Radiosity: Key Idea #1Diffuse SurfaceRadiosity: Key Idea #2Constant Surface ApproximationRadiosity EquationSlide 23Radiosity AlgorithmEnergy Conservation EquationSlide 26Slide 27Slide 28Slide 29Compute Form FactorsSlide 31Form Factor: ReciprocitySlide 33Linear SystemSlide 35Form Factors for Infinitesimal SurfacesForm Factors for Subdivided PatchesForm Factor: How to compute?Form Factor: AnalyticalSlide 40Form Factor: Nusselt AnalogSlide 42How to speed up the form-factor calculation?Speedup via Precomputation!Slide 45Form Factor: HemiCubeSlide 47Slide 48Slide 49Delta Form Factor: Top FaceDelta Form Factors: Side FacesThe Hemicube in ActionForm Factors: HemiCubeForm FactorsSlide 55How to Solve Linear System?Matrix ConversionIterative ApproachesJacobian IterationsSlide 60Successive ApproximationRenderingVertex Intensity: Bilinear InterpolationConsolation RoomTheatreSteel MillsRadiosity: BenefitRadiosity: LimitationCSCE 641 Computer Graphics: RadiosityJinxiang ChaiRendering: Illumination ComputingDirect (local) illuminationLight directly from light sourcesNo shadowsIndirect (global) illuminationTransparent, reflective surfaces, and hard shadows (Ray tracing)Diffuse interreflections, color bleeding, and soft shadow (radiosity)Rendering: Illumination ComputingDirect (local) illuminationLight directly from light sourcesNo shadowsIndirect (global) illuminationTransparent, reflective surfaces, and hard shadows (Ray tracing)Diffuse interreflections, color bleeding, and soft shadow (radiosity)Review: Ray Tracing AssumptionThe illumination of a point is determined by - illumination/shadow ray (direct lighting from light sources)Review: Ray Tracing AssumptionThe illumination of a point is determined by - illumination/shadow ray (direct lighting from light sources)Review: Ray Tracing AssumptionThe illumination of a point is determined by - illumination/shadow ray (direct lighting from light sources) - reflection ray (light reflected by an object)Review: Ray Tracing AssumptionThe illumination of a point is determined by - illumination/shadow ray (direct lighting from light sources) - reflection ray (light reflected by an object) - transparent ray (light passing through an object)Review: Ray Tracing AssumptionThe illumination of a point is determined by - illumination/shadow ray (direct lighting from light sources) - reflection ray (light reflected by an object) - transparent ray (light passing through an object)Ray Tracing AssumptionThe illumination of a point is determined by - illumination/shadow ray (direct lighting from light sources) - reflection ray (light reflected by an object) - transparent ray (light passing through an object)Pros and Cons of Ray TracingAdvantages of ray tracingAll the advantages of the local illumination modelAlso handles shadows, reflection, and refractionDisadvantages of ray tracingComputational expenseNo diffuse inter-reflection between surfaces (i.e., color bleeding)Not physically accurateRadiosity handles these shortcomings for diffuse surfaces!Radiosity vs. Local IlluminationRadiosityPhysical Image vs. Radiosity RenderingRadiosityThe radiostiy of a surface is the rate at which energy leaves that surface (energy per unit time per unit area). It includes the energy emitted by a surface as well as the energy reflected from other surfaces.RadiosityThe radiostiy of a surface is the rate at which energy leaves that surface (energy per unit time per unit area). It includes the energy emitted by a surface as well as the energy reflected from other surfaces.Techniques of modeling the transfer of energy between surfaces based upon radiosity were first used in analyzing heat transfer between surfaces in an enclosed environment. The same techniques can be used to analyze the transfer of radiant energy between surfaces in computer graphics.RadiosityThe radiostiy of a surface is the rate at which energy leaves that surface (energy per unit time per unit area). It includes the energy emitted by a surface as well as the energy reflected from other surfaces.Techniques of modeling the transfer of energy between surfaces based upon radiosity were first used in analyzing heat transfer between surfaces in an enclosed environment. The same techniques can be used to analyze the transfer of radiant energy between surfaces in computer graphics.Radiosity methods allows the intensity of radiant energy arriving at a surface to be computed. These intensities can then be used to determine the shading of the surface.RadiosityThe radiosity model computes radiant-energy interactions between all the surfaces in a sceneRadiosity: Key Idea #1Diffuse SurfaceRadiosity: Key Idea #2Constant Surface ApproximationRadiosity EquationNjjijiselfiRadiosityaRadiosityRadiosity1,Radiosity EquationNjjjselfRadiosityaRadiosityRadio sity111,1NjjjselfRadiosit yaRadiosit yRadiosity122,2NjjNjNselfNRadiosityaRadiosityRadiosity1,Radiosity AlgorithmEnergy Conservation EquationNjjiieiijF1,)(NjjiieiijF1,)(Energy Conservation EquationThe total rate of radiant energy leaving surface i per unit squareNjjiieiijF1,)(Energy Conservation EquationThe rate of energy emitted from surface i per unit area- zero if surface i is not a light sourceNjjiieiijF1,)(Energy Conservation EquationReflectivity factorPercent of incident light that is reflected in all directionsNjjiieiijF1,)(Energy Conservation EquationForm factorFractional amount of radiant energy from surface j that reaches surface iCompute Form FactorsjiAAxyyxjdAdAyxVrAijFji),(coscos1)(,2The form factor specifies the fraction of the energy leaving one patch and arriving at the other. In other words, it is an expression of radiant exchange between two surface patches!Compute Form FactorsjiAAxyyxjdAdAyxVrAijFji),(coscos1)(,2Radiant energy reaching Ay from AxRadiant energy leaving Ax in all directionsThe form factor specifies the fraction of the energy leaving one patch and arrives at