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Computing Form Factors: Methods and Techniques

Learn various methods and techniques for computing form factors in Radiosity. Explore closed-form solutions, numerical approximations, and the use of hemicubes for accurate form factor calculations. Discover the benefits and challenges of Monte Carlo methods and area sampling. References included.

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Computing Form Factors: Methods and Techniques

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  1. Radiosity Part IIForm Factors COMP238

  2. Goal • Learn ways of computing form factors.

  3. Recall • The Fij are the form factors • Form factors independent of radiosities

  4. Form Factor Expanding, we get where Vij is the visibility

  5. Alternative • Area/Hemisphere integral

  6. Computing the Form Factor

  7. Computing the Form Factor

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

  9. Numerical approximation

  10. Nusselt Analog

  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…

  12. Solid Angle

  13. Area on Base Also,  is area of unit circle, so division is appropriate, resulting in

  14. Hemicube • Approximation of Nusselt’s analog

  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.

  16. Compute Delta Form Factors • Store in table. • Note the symmetry

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

  18. Aliasing

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

  20. Monte Carlo • Sample by casting rays to estimate Nusselt’s analog. • Distribute the rays to get a good sampling of the sphere

  21. Area

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

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

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

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

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