1. Advanced Computer Graphics: Radiosity
James Gain
Department of Computer Science University of Cape Town
Advanced Computer GraphicsCollaborative Visual Computing Laboratory

2. Where Ray Tracing Fails
Diffuse inter-reflection: Ray tracing cannot support reflections among diffuse surfaces.
B is in the shadow of L, but it receives reflected illumination from A. If B is a diffuse surface then ray tracing will not account for this.
An ambient component (constant over an entire surface) is added to surface colour to approximate this indirect illumination.
4/07/2019
Advanced Computer Graphics

3. Ambient Lighting Approximation
Ambient Lighting can be visually disturbing and sometimes completely incorrect.
The whiteboards backed by blue and green should cast their colours onto the central diffuse white board.
This does not occur with constant ambient lighting.
4/07/2019
Advanced Computer Graphics

4. Advanced Computer Graphics
Radiosity
A method which takes the diffuse interaction between surface areas into account.
First developed in the context of heat transfer equations. Adopted in CG from 1984.
Surfaces are treated as collectors and radiators of light energy.
Assumes all polygons in the scene are Lambertian (diffuse) reflectors or emmiters.
Light is propagated between surfaces until a stable solution is achieved.
The solution is independent of viewpoint and need only be calculated once for a given scene (fortunately!)
Oven Door Analogy
4/07/2019
Advanced Computer Graphics

5. Advanced Computer Graphics
Radiosity Equation
Radiosity is calculated by:
Dividing surfaces into discrete patches
Solving the radiosity equations for all patches
The Radiosity Equation:
Expresses: the energy leaving a patch is the sum of the light emitted plus the light reflected.
4/07/2019
Advanced Computer Graphics

6. Terms in the Radiosity Equation
Area: the area of patch i
Radiosity: the radiosity of patch i (energy per unit area per unit time)
Energy Emission: the energy emitted by patch i (> 0 iff patch is an emitter, also measured in energy per unit area per unit time)
Reflectivity: the diffuse reflectivity of patch i (in [0,1])
FormFactor: the fraction of light leaving patch j which impacts patch i (in [0,1])
Pi is different for each colour component
Given we find the Radiosity of each patch by solving the system of radiosity equations over all patches.
4/07/2019
Advanced Computer Graphics

7. Simplifying a Radiosity Equation
Reciprocity: the fraction of energy from patch i to j is the same as the fraction of energy from patch j to i:
Simplifying Radiosity:
4/07/2019
Advanced Computer Graphics

8. Advanced Computer Graphics
Radiosity Pipeline
Compute Form Factors:
From the relative position and size of patches in the scene calculate
Solve Radiosity Equations:
Form a system of linear equations and solve.
Render Image:
Convert patch radiosity into diffuse intensity and render using ray tracing or polygon scan conversion. A simple relationship exists between radiance and intensity
4/07/2019
Advanced Computer Graphics

9. Advanced Computer Graphics
Solve Radiosity
The rearranged radiosity equations can be written in matrix form as:
Note, for concave patches, so we can’t cancel these terms.
The are unknown. All the , and are known.
This is a set of n linear equations in n unknowns, solvable by, for instance, Gauss-Seidel Iteration.
This system must be solved for each colour component (red, green, blue) because and will differ.
4/07/2019
Advanced Computer Graphics

10. Advanced Computer Graphics
FormFactors
The formfactors must be determined before the radiosity equations can be solved.
This is very computationally expensive.
However, they depend on the scene geometry and not the viewpoint or patch colouring.
Hence, they only need to be calculated once for a particular static scene.
FormFactors depend on the relative orientation, occlusion and distance between patches and are calculate by subdividing patches into differential elements.
Viewpoint independence makes them useful in games (Unreal)
4/07/2019
Advanced Computer Graphics

11. Advanced Computer Graphics
Summary
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Advanced Computer Graphics

12. Example: Specular and Diffuse Reflections
The environment depicted here was inspired by the painting Lady and Gentleman at the Virginals, by the 17th century Dutch painter, Jan Vermeer. A modified radiosity solution was ray traced to produce the specular highlights on the floor. The image is from the 1987 paper A Two Pass Solution to the Rendering Equation: a Synthesis of Ray Tracing and Radiosity Methods. by John R. Wallace, Michael F. Cohen and Donald P. Greenberg.
4/07/2019
Advanced Computer Graphics