Radiosity Part II Form Factors COMP 238 1

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Radiosity Part II Form Factors COMP 238 1 Anselmo Lastra, October 2000

Radiosity Part II Form Factors COMP 238 1 Anselmo Lastra, October 2000

Goal • Learn ways of computing form factors. 2 Anselmo Lastra, October 2000

Goal • Learn ways of computing form factors. 2 Anselmo Lastra, October 2000

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

Recall • The Fij are the form factors • Form factors independent of radiosities 3 Anselmo Lastra, October 2000

Form Factor Expanding, we get where Vij is the visibility 4 Anselmo Lastra, October

Form Factor Expanding, we get where Vij is the visibility 4 Anselmo Lastra, October 2000

Alternative • Area/Hemisphere integral 5 Anselmo Lastra, October 2000

Alternative • Area/Hemisphere integral 5 Anselmo Lastra, October 2000

Computing the Form Factor 6 Anselmo Lastra, October 2000

Computing the Form Factor 6 Anselmo Lastra, October 2000

Computing the Form Factor 7 Anselmo Lastra, October 2000

Computing the Form Factor 7 Anselmo Lastra, October 2000

Closed form • Only feasible for simple cases • Visibility is hard • Polygon-to-polygon

Closed form • Only feasible for simple cases • Visibility is hard • Polygon-to-polygon solution by Schroeder and Hanrahan 8 Anselmo Lastra, October 2000

Numerical approximation 9 Anselmo Lastra, October 2000

Numerical approximation 9 Anselmo Lastra, October 2000

Nusselt Analog 10 Anselmo Lastra, October 2000

Nusselt Analog 10 Anselmo Lastra, October 2000

Why? • Imagine a unit hemisphere centered around patch (or node) i. Projection onto

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. Anselmo Lastra, October 2000 next… 11

Solid Angle 12 Anselmo Lastra, October 2000

Solid Angle 12 Anselmo Lastra, October 2000

Area on Base Also, is area of unit circle, so division is appropriate, resulting

Area on Base Also, is area of unit circle, so division is appropriate, resulting in 13 Anselmo Lastra, October 2000

Hemicube • Approximation of Nusselt’s analog 14 Anselmo Lastra, October 2000

Hemicube • Approximation of Nusselt’s analog 14 Anselmo Lastra, October 2000

Hemicube • For convenience, a cube 1 unit high with a top face 2

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. 15 Anselmo Lastra, October 2000

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

Compute Delta Form Factors • Store in table. • Note the symmetry 16 Anselmo Lastra, October 2000

Specifically • Scan convert all primitives onto 5 faces • Z buffer as usual

Specifically • Scan convert all primitives onto 5 faces • Z buffer as usual • Keep an item buffer 17 Anselmo Lastra, October 2000

Aliasing 18 Anselmo Lastra, October 2000

Aliasing 18 Anselmo Lastra, October 2000

Other Problems • Sampling is not even • Must render complete dataset – Should

Other Problems • Sampling is not even • Must render complete dataset – Should cull – Could you use levels of detail? 19 Anselmo Lastra, October 2000

Monte Carlo • Sample by casting rays to estimate Nusselt’s analog. • Distribute the

Monte Carlo • Sample by casting rays to estimate Nusselt’s analog. • Distribute the rays to get a good sampling of the sphere 20 Anselmo Lastra, October 2000

Area 21 Anselmo Lastra, October 2000

Area 21 Anselmo Lastra, October 2000

Area Sampling • Subdivide the primitive j into small pieces and cast a ray

Area Sampling • Subdivide the primitive j into small pieces and cast a ray to the center of each area to determine visibility 22 Anselmo Lastra, October 2000

Summary • Many ways to find form factors • Hemicube most common – Hardware

Summary • Many ways to find form factors • Hemicube most common – Hardware acceleration • Monte Carlo methods also used 23 Anselmo Lastra, October 2000

Next • How do we solve the matrix? – Shooting – Progressive Radiosity •

Next • How do we solve the matrix? – Shooting – Progressive Radiosity • Meshing 24 Anselmo Lastra, October 2000

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

References • Cohen and Wallace, Radiosity and Realistic Image Synthesis, Chapter 4. 25 Anselmo Lastra, October 2000

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