1. Radiosity Part II Form Factors
COMP238
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2. Goal Learn ways of computing form factors.
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3. Recall The Fij are the form factors
Form factors independent of radiosities
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4. Form Factor Expanding, we get where Vij is the visibility
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5. Alternative
Area/Hemisphere integral
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6. Computing the Form Factor
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7. Computing the Form Factor
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8. Closed form Only feasible for simple cases Visibility is hard
Polygon-to-polygon solution by Schroeder and Hanrahan
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9. Numerical approximation
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10. Nusselt Analog
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11. 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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12. Solid Angle
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13. Area on Base
Also,  is area of unit circle, so division is appropriate, resulting in
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14. Hemicube Approximation of Nusselt’s analog
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15. 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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16. Compute Delta Form Factors
Store in table.
Note the symmetry
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17. Specifically Scan convert all primitives onto 5 faces
Z buffer as usual
Keep an item buffer
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18. Aliasing
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19. Other Problems Sampling is not even Must render complete dataset
Should cull
Could you use levels of detail?
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20. Monte Carlo Sample by casting rays to estimate Nusselt’s analog.
Distribute the rays to get a good sampling of the sphere
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21. Area
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22. 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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23. Summary Many ways to find form factors Hemicube most common
Hardware acceleration
Monte Carlo methods also used
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24. Next How do we solve the matrix? Meshing Shooting
Progressive Radiosity
Meshing
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25. References
Cohen and Wallace, Radiosity and Realistic Image Synthesis, Chapter 4.
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