1MIT EECS 6.837, Durand and CutlerGlobal Illumination:RadiosityAn early application of radiative heat transfer in stables.MIT EECS 6.837, Durand and CutlerLast Time?Shadow Volumes (Stencil Buffer)Shadow MapsProjective Texture Shadows (Texture Mapping)Planar ShadowsMIT EECS 6.837, Durand and CutlerSchedule• Review Session: Monday Oct. 25 , 7:30 - 9 pm, Room 1-150bring lots of questions!• Quiz 2: Tuesday October 26th, in class80 minutes, closed books, 1 page of notes allowed• No assignment due next week• Ray tracing acceleration due Nov 3MIT EECS 6.837, Durand and CutlerToday• Why Radiosity– The Cornell Box – Radiosity vs. Ray Tracing• Global Illumination: The Rendering Equation• Radiosity Equation/Matrix• Calculating the Form Factors• Progressive Radiosity• Advanced RadiosityMIT EECS 6.837, Durand and CutlerRendering Recap• Ray-tracing– For each pixel, for each object• Graphics pipeline, scan conversion– For each object, for each pixel• Local lighting models– Diffuse, Phong• Shadows– Ray casting, shadow maps, shadow volumes• Reflection, refractionMIT EECS 6.837, Durand and CutlerWhy global illumination?• Simulate all light inter-reflections(indirect lighting)– e.g. in a room, a lot of the light is indirect: it is reflected by walls. • How have we dealt with this so far?– Ambient term to fake some uniform indirect light2MIT EECS 6.837, Durand and CutlerDirect illuminationMIT EECS 6.837, Durand and CutlerGlobal IlluminationMIT EECS 6.837, Durand and CutlerWhy Radiosity?eye• Sculpture by John Ferren• Diffuse panelsdiagram from above:photograph:MIT EECS 6.837, Durand and CutlerRadiosity vs. Ray TracingOriginal sculpture by John Ferren lit by daylight from behind.Image rendered with radiosity. note color bleeding effects.Ray traced image. A standardray tracer cannot simulate theinterreflection of light between diffuse surfaces.MIT EECS 6.837, Durand and CutlerThe Cornell Boximages by Micheal Callahan http://www.cs.utah.edu/~shirley/classes/cs684_98/students/callahan/bounce/direct illumination (0 bounces)1 bounce2 bouncesMIT EECS 6.837, Durand and CutlerThe Cornell BoxGoral, Torrance, Greenberg & BattaileModeling the Interaction of Light Between Diffuse SurfacesSIGGRAPH '84photographsimulation3MIT EECS 6.837, Durand and CutlerLight Measurement LaboratoryCornell University, Program for Computer GraphicsThe Cornell Box• Careful calibration and measurement allows forcomparison between physical scene & simulationphotograph simulationMIT EECS 6.837, Durand and CutlerCornell box pun• Cornell university: leading lab in radiosity research in the 80s and 90s• Joseph Cornell 1903-1973artist famous for his “boxes” MIT EECS 6.837, Durand and CutlerTwo approaches for global illumination• Radiosity–View-independent– Diffuse only• Monte-Carlo Ray-tracing– Send tons of indirect raysMIT EECS 6.837, Durand and CutlerRadiosity vs. Ray Tracing• Ray tracing is an image-space algorithm– If the camera is moved, we have to start over• Radiosity is computed in object-space–View- independent (just don't move the light)– Can pre-compute complex lighting to allow interactive walkthroughsMIT EECS 6.837, Durand and CutlerQuestions?Lightscape http://www.lightscape.comMIT EECS 6.837, Durand and CutlerToday• Why Radiosity– The Cornell Box – Radiosity vs. Ray Tracing• Global Illumination: The Rendering Equation• Radiosity Equation/Matrix• Calculating the Form Factors• Progressive Radiosity• Advanced Radiosity4MIT EECS 6.837, Durand and CutlerThe Rendering EquationL (x',ω') is the radiance from a point on a surface in a given direction ω'x'ω'L(x',ω') = E(x',ω') + ∫ρx'(ω,ω')L(x,ω)G(x,x')V(x,x') dAMIT EECS 6.837, Durand and CutlerThe Rendering EquationE(x',ω') is the emitted radiance from a point: E is non-zero only if x' is emissive (a light source)x'ω'L(x',ω') = E(x',ω') + ∫ρx'(ω,ω')L(x,ω)G(x,x')V(x,x') dAMIT EECS 6.837, Durand and CutlerThe Rendering EquationSum the contribution from all of the other surfaces in the scenex'ω'L(x',ω') = E(x',ω') + ∫ρx'(ω,ω')L(x,ω)G(x,x')V(x,x') dAMIT EECS 6.837, Durand and CutlerThe Rendering EquationFor each x, compute L(x, ω), the radiance at point x in the direction ω (from x to x') x'ω'ωxL(x',ω') = E(x',ω') + ∫ρx'(ω,ω')L(x,ω)G(x,x')V(x,x') dAMIT EECS 6.837, Durand and CutlerThe Rendering Equationscale the contribution by ρx'(ω,ω'), the reflectivity (BRDF) of the surface at x'x'ω'ωxL(x',ω') = E(x',ω') + ∫ρx'(ω,ω')L(x,ω)G(x,x')V(x,x') dAMIT EECS 6.837, Durand and CutlerThe Rendering EquationFor each x, compute V(x,x'), the visibility between x and x': 1 when the surfaces are unobstructed along the direction ω, 0 otherwise x'ω'ωxL(x',ω') = E(x',ω') + ∫ρx'(ω,ω')L(x,ω)G(x,x')V(x,x') dA5MIT EECS 6.837, Durand and CutlerThe Rendering EquationFor each x, compute G(x, x'), which describes the on the geometric relationship between the two surfaces at x and x’x'ω'ωxL(x',ω') = E(x',ω') + ∫ρx'(ω,ω')L(x,ω)G(x,x')V(x,x') dAMIT EECS 6.837, Durand and CutlerIntuition about G(x,x')? • Which arrangement of two surfaces will yield the greatest transfer of light energy? Why?MIT EECS 6.837, Durand and CutlerMuseum simulation. Program of Computer Graphics, Cornell University.50,000 patches. Note indirect lighting from ceiling.Questions?MIT EECS 6.837, Durand and CutlerToday• Why Radiosity– The Cornell Box – Radiosity vs. Ray Tracing• Global Illumination: The Rendering Equation• Radiosity Equation/Matrix• Calculating the Form Factors• Progressive Radiosity• Advanced RadiosityMIT EECS 6.837, Durand and CutlerRadiosity Overview• Surfaces are assumed to be perfectly Lambertian (diffuse)– reflect incident light in all directions with equal intensity• The scene is divided into a set of small areas, or patches. • The radiosity, Bi, of patch i is the total rate of energy leaving a surface. The radiosity over a patch is constant. • Units for radiosity: Watts / steradian * meter2x'ω'MIT EECS 6.837, Durand and CutlerRadiosity EquationL(x',ω') = E(x',ω') + ∫ρx'(ω,ω')L(x,ω)G(x,x')V(x,x') dABx'= Ex'+ ρx'∫ BxG(x,x')V(x,x')Radiosity assumption: perfectly diffuse surfaces (not directional)6MIT EECS 6.837, Durand and CutlerContinuous Radiosity Equationxx’form factorG: geometry termV: visibility termNo analytical solution, even for simple configurationsreflectivityBx'= Ex'+ ρx'∫
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