Radiosity Part II Form Factors

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Radiosity Part IIForm Factors

• COMP238

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Goal

• Learn ways of computing form factors.

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Recall

• The Fij are the form factors
• Form factors independent of radiosities

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Form Factor

• Expanding, we get
• where Vij is the visibility

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Alternative

• Area/Hemisphere integral

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Computing the Form Factor
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Computing the Form Factor
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Closed form

• Only feasible for simple cases
• Visibility is hard
• Polygon-to-polygon solution by Schroeder and
  Hanrahan

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Numerical approximation
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Nusselt Analog
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Why?

• Imagine a unit hemisphere centered around patch
  (or node) i.
• Projection onto sphere mechanically computes the
  term
• Projection of solid angle due to patch j.

next
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Solid Angle
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Area on Base
Also, ? is area of unit circle, so division is
appropriate, resulting in
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Hemicube

• Approximation of Nusselts analog

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Hemicube

• For convenience, a cube 1 unit high with a top
  face 2 x 2 is used. Side faces are 2 wide by 1
  high.
•  Decide on a resolution for the cube. Say 512 by
  512 for the top.

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Compute Delta Form Factors

• Store in table.
• Note the symmetry

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Specifically

• Scan convert all primitives onto 5 faces
• Z buffer as usual
• Keep an item buffer

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Aliasing
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Other Problems

• Sampling is not even
• Must render complete dataset
• Should cull
• Could you use levels of detail?

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Monte Carlo

• Sample by casting rays to estimate Nusselts
  analog.
• Distribute the rays to get a good sampling of the
  sphere

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Area
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Area Sampling

• Subdivide the primitive j into small pieces and
  cast a ray to the center of each area to
  determine visibility

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Summary

• Many ways to find form factors
• Hemicube most common
• Hardware acceleration
• Monte Carlo methods also used

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Next

• How do we solve the matrix?
• Shooting
• Progressive Radiosity
• Meshing

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References

• Cohen and Wallace, Radiosity and Realistic Image
  Synthesis, Chapter 4.