The Radiosity Method

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The RadiosityMethod

• Donald Fong
• February 10, 2004

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Why?

• Ray tracing has a visual signature
• Only models perfect specular reflection and
  transmission
• Interaction between diffusely reflecting surfaces
• Interiors, matte surfaces, indirect lighting

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Basic idea

• Divide surfaces into discrete patches
• Object space algorithm
• Model light transfer between patches as system of
  linear equations
• Solve matrix equation for radiosity of each patch
• Do it for R,G,B
• Render patches as colored polygons

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Simplifying assumptions

• All surfaces are perfectly diffuse
• Does not matter which way light enters or leaves
  a surface
• Radiosity is constant over a patch

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Radiosity Equation

• Bi is radiosity of patch i
• energy per unit area leaving a surface patch per
  unit time
• rate energy emitted rate energy reflected
• Ei is non-zero for emitters
• Ri is reflectivity of the patch
• Wavelength dependent
• Fij is the form factor how much light patch j
  contributes to patch i
• Depends on geometric relationship distance and
  relative orientation

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Radiosity solution

• Finding form factors
• Hemicube method
• Meshing strategies
• Solving set of linear equations to get radiosity
  for each patch

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Form factor example

• Almost 100

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Hemicube method

• Efficient
• Fq can be precomputed
• Approximate
• Aliasing

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Gauss-Siedel method

• Iterative
• Generates sequence of vectors that converges to
  the solution
• Slow

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Gathering vs. Shooting

• Gathering
• One iteration updates a single patch by gathering
  contributions from all other patches
• Shooting (and sorting)
• Single iteration updates all receiving patches
  with unshot energy
• Process patches according to amount of energy
  they are likely to radiate

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Progressive radiosity
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Another example
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Problems

• Aliasing from hemicube method
• Uniform pixel size
• Using bilinear interpolation to reconstruct
  radiosity function
• Using meshing of scene independent of variations
  in radiosity function

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Hemicube aliasing

• Limited resolution of the hemicube pixels
• Patches of same size map to different number of
  cells

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Reconstruction artifacts
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Meshing artifacts

• Shadow leakage
• Light leakage

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Meshing strategies

• Discontinuity meshing
• Completed before radiosity solution
• Predict where discontinuities will occur
• Adaptive meshing
• Refine a start mesh as the solution progresses

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Discontinuity meshing

• Mesh around expected discontinuities
• Sharp boundaries from point light source or
  object contact
• Derivative discontinuities from area light
  sources and multi-object shadows

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Hierarchical radiosity

• Use different resolution depending on who is
  emitting and who is receiving

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Remeshing example
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Summary

• Diffuse only
• Costly to add specular
• Not efficient
• Meshing
• Memory intensive

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Two pass solution