1. Computer Graphics (Fall 2003) COMS 4160, Lecture 20: Radiosity Ravi Ramamoorthi http://www.cs.columbia.edu/~cs4160

2. Radiosity Cornell box [Goral et al 84]

3. Rendering Equation

4. Radiosity Finite Element Method Assume Lambertian (polygonal) surfaces View Independent Classically, capture diffuse interreflection Issues –Meshing (division into small elements) –Form Factors (Radiosity Matrix) –Solving Linear equations (Efficient iterative solution)

5. Earliest Radiosity pictures Radiosity was first developed in other fields –Heat transport, Lighting Design –In graphics: Goral et al. 84 Parry Moon and Domina Spencer (MIT), Lighting Design, 1948

6. Radiosity Equation Simplest case: Assume surfaces are diffuse –Drop angular dependence, f is a constant –Discretize in constant elements –Matrix Equation, MB = E, with M = I-PF –Solve with iterative numerical techniques

7. Form Factors Defn of Form Factor Intuition –Bounce energy around until it’s absorbed –Like ray tracing except view-independent diffuse –Form factor controls fraction of energy from i to j

8. Nusselt’s Method

9. Hemicube

10. Hemicubes Each small hemicube cell has a precomputed delta form factor: We can render the scene using normal Z-buffer scan conversion onto the faces of the hemicube!

11. Monte Carlo Ray Tracing Can be used to find form factors (slow) Can be used directly to shoot energy

12. Solution Gathering Shooting Progressive Refinement Examples (plates) Constructivist Museum: Chen, Feldman, Dorsey, Cornell 88