1. Interreflections and Radiosity : The Forward Problem Lecture #11 Thanks to Kavita Bala, Pat Hanrahan, Doug James, Ledah Casburn

3. Cornell Box blue hue red hue

6. Phong Shading no shadows no object interactions Plastic looking scene

7. Ray Tracing Scene doesn’t look realistic enough. where is the corner of room? is the carpet and wood supposed to be this dark? is window flush with wall?

8. Radiosity – today’s topic carpet and wood on table is lighter Indirect lighting affects realism. window has depth walls look more pink room has a corner

9. The Rendering Equation – Graph Style p p’ p’’ Visibility (shadows) Emission (light source) Reflectance from Surfaces source viewer

11. Diffuse Interreflections - Radiosity Consider lambertian surfaces and sources. Radiance independent of viewing direction. Consider total power leaving per unit area of a surface. Can simulate soft shadows and color bleeding from diffuse surfaces. Used abundantly in heat transfer literature

12. Irradiance, Radiosity Irradiance E is the power received per unit surface area –Units: W/m 2 Radiosity –Power per unit area leaving the surface (like irradiance)

13. Planar piecewise constancy assumption Subdivide scene into small “uniform” polygons

14. Power Equation Power from each polygon: Linear System of Equations:

17. Form Factors Invariant

18. Form Factor Computation Schroeder and Hanrahan derived an analytic expression for polygonal surfaces. In general, computing double integral is hard. Use Monte Carlo Integration.

19. Form Factor Computation

22. Linear System of Radiosity Equations Known Unknown Matrix Inversion to Solve for Radiosities.

24. Doug James

25. Wireframe

26. Classical Approach No Interpolation

27. Wireframe

28. Classical Approach Low Res

29. Classical Approach High Res More accurate

30. Classical Approach High Res Interpolated

32. Sample Scenes

37. Summary

38. Doug James

39. Two Pass Solution First Pass: Diffuse Interreflections View independent, global diffuse illumination computed with radiosity. Second Pass: Specular Interreflections View dependent, global specular illumination computed with ray-tracing. Combine strengths of radiosity and ray-tracing.

40. Interreflections : The Inverse Problem Lecture #12