1Chapter 14, Slide 1Copyright © A. Varshney and D. M. MountCMSC 427: Global Illumination ModelsCMSC 427: Global Illumination Models(Guest Lecturer: Dave Mount)(Guest Lecturer: Dave Mount)Reading: Sect. 10.12-10.14 in Hearn & Baker.Overview:– Global Illumination Models–Rendering Equation–Radiosity– Photon MappingChapter 14, Slide 2Copyright © A. Varshney and D. M. MountSummary of Illumination ModelsSummary of Illumination ModelsYou have seen:Local illumination model: Phong•Ambient• Diffuse•Specular• Point light sources• No: shadows, inter-object light reflection.“More global” illumination model: Ray Tracing•Shadows• Area light sources (via distributed ray tracing)• No: inter-object light reflectionTradeoffs:– Improvements in fidelity come at the expense of computational complexity.2Chapter 14, Slide 3Copyright © A. Varshney and D. M. MountRay TracingRay TracingRay tracing: More accurate than Phong, but not without its own limitations.Strengths: – Easy to implement.– General and extensible.– Better handling of global issues (shadows, reflection, etc.).Shortcomings:Optimizing not easy: Involves non-trivial data structures.Not truly global: Relies on the Phong illumination model to compute illumination at each point. Ignores inter-object light reflection.Too “Specular”: Ray-traced images are best for highly specularobjects (glass and metalic balls), but specular reflection is not common in typical real-world scenes.Chapter 14, Slide 4Copyright © A. Varshney and D. M. MountGlobal Illumination and Light TransportGlobal Illumination and Light TransportGlobal Illumination and Light Transport: Describe the flow of light energy in a scene, including inter-object reflections.The Rendering Equation:The theoretical basis for light energy transport.Conservation of Energy:– Global conservation:• Assumes a closed environment.•Energy input = energy output.• Rest is converted to heat.– Local conservation:• Incident energy must be eitherreflected or absorbedImage source: University of Illinois3Chapter 14, Slide 5Copyright © A. Varshney and D. M. MountThe Rendering EquationThe Rendering EquationRendering Equation: (Kajiya 86)– Describes the flow of light energy throughout a scene, assuming that all objects of a scene (not just light sources) may reflect light.– It relates the light energy Lo(x, w) that is reflected outwards from a point x in direction w as a function of:• emitted light energy Le(x, w) (if this object is a light source), and •the total light energy Li(x, w’) received at x from all other directions w’which is then reflected outwards in direction w.– There are a number of variants, depending on the assumptions made. – Radiance form of the rendering equation:We will explain this next.() ()()()()oe r iΩL, L, f,', L,''d'=+ ⋅∫xw xw xw w xw w n wChapter 14, Slide 6Copyright © A. Varshney and D. M. MountThe Rendering EquationThe Rendering EquationRendering Equation: What’s what.– x is a surface point. n is the normal. w is a unit vector (direction).–Lo(x, w) is the light energy reflected outwards from point x in direction w.–Le(x, w) is the light energy emitted at x in direction w.– Ω denotes the hemisphere above the surface patch at x. The integral is taken over all differential directional elements dw’on Ω.–Li(x, w) is the incoming light energy incident on x arriving from direction w’.–fr(x, w’, w) is the fraction of light energyarriving at x from direction w’, that isreflected to direction w. (In general this depends on w and w’.)–The (w’ ⋅ n) term captures the attenuation of arriving light, similar to Lambert’s law. (The bigger the angle, the less the energy per unit area.)() ()()()()oe r iL, L, f,', L,''d'=+ ⋅∫Ωxw xw xw w xw w n wΩdw’nxw4Chapter 14, Slide 7Copyright © A. Varshney and D. M. MountThe Rendering EquationThe Rendering EquationIs this the Holy Grail?–A perfect implementation of this rule would result in accurate lighting.– Virtually all illumination models only provide an approximation.Can we solve the rendering equation? Not practical for real-world scenes:– Need to model the bidirectional reflectance term, fr(x, w’, w). Not hard for pure diffuse and specular reflectors, but harder for real-world materials. (BRDFs)–The incoming light term Li(x, w) requires that we determine what is visible from x in direction w, which would involve hidden surface removal, from every point in the scene.–This is not just one equation. The outgoing light from each point affects the incoming light to all other points. This is a huge system of integral equations, one variable for each point and each direction about that point.Computational Approaches:Path Tracing: Attempts to trace all light rays in a scene.Photon Mapping: Deposits light energy on surfaces for later collection.Radiosity: Simulation of light transport under a steady-state assumption, assuming diffuse reflection.Chapter 14, Slide 8Copyright © A. Varshney and D. M. MountRadiosityRadiosityRadiosity: A method for implementing a global illumination model.– Simulates lighting due to inter-object reflections.– Principally for diffuse surfaces (that is, Lambertian reflectors).–Models view-independent illumination.– Can generate diffuse/soft shadows, color bleeding.Image source: Lightscape Inc.Color bleeding onwalls from floor.5Chapter 14, Slide 9Copyright © A. Varshney and D. M. MountRadiosityRadiosity: Basic Elements: Basic ElementsBasic Elements of Radiosity:– Based on conservation of light energy.– Assumes area light sources.Most light comesfrom baffles inthe ceiling.Image source: Cornell UniversityChapter 14, Slide 10Copyright © A. Varshney and D. M. MountRadiosityRadiosity: Basic Elements: Basic ElementsDefinition: Radiosity is the rate at which energy leaves a surface either through:– Emission or– ReflectionComputational Approach:– Model the scene as a set of small surface patches, each assumed to have constant (but unknown) radiosity.– Set up a linear system (based on a straightforward approximation to the rendering equation) that relates the radiosity of each patch to some function of its surrounding patches.– Solve this linear system (by standard numerical methods) to determine the radiosity of each surface patch.– Render the scene, using these radiosity values.6Chapter 14, Slide 11Copyright © A. Varshney and D. M. MountThe The