Computer Graphics (Fall 2003)

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Computer Graphics (Fall 2003)

• COMS 4160, Lecture 20 Radiosity
  Ravi Ramamoorthi

http//www.cs.columbia.edu/cs4160
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Radiosity

• Cornell box Goral et al 84

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Rendering Equation
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Radiosity

• Finite Element Method
• Assume Lambertian (polygonal) surfaces
• View Independent
• Classically, capture diffuse interreflection
• Issues
• Meshing (division into small elements)
• Form Factors (Radiosity Matrix)
• Solving Linear equations (Efficient iterative
  solution)

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Earliest Radiosity pictures

• Radiosity was first developed in other fields
• Heat transport, Lighting Design
• In graphics
• Goral et al. 84
  

Parry Moon and Domina Spencer (MIT), Lighting
Design, 1948
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Radiosity Equation

• Simplest case Assume surfaces are diffuse
• Drop angular dependence, f is a constant
• Discretize in constant elements
• Matrix Equation, MB E, with M I-PF
• Solve with iterative numerical techniques

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Form Factors

• Defn of Form Factor
• Intuition
• Bounce energy around until its absorbed
• Like ray tracing except view-independent diffuse
• Form factor controls fraction of energy from i to
  j

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Nusselts Method
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Hemicube
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Hemicubes

• Each small hemicube cell has a precomputed delta
  form factor
• We can render the scene using normal Z-buffer
  scan conversion onto the faces of the hemicube!

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Monte Carlo Ray Tracing

• Can be used to find form factors (slow)
• Can be used directly to shoot energy

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Solution

• Gathering
• Shooting
• Progressive
  Refinement
• Examples (plates)

Constructivist Museum Chen, Feldman, Dorsey,
Cornell 88