1. Radiosity
Dr. Scott Schaefer

2. Radiosity

3. Radiosity Physically based model for light interaction
View independent lighting
Accounts for indirect
illumination
Color bleeding
Soft shadows

4. The Rendering Equation

5. The Rendering Equation
Outgoing radiance from surface at p in the direction v

6. The Rendering Equation
Emitted radiance from surface at p in the direction v

7. The Rendering Equation
BRDF of surface at p

8. The Rendering Equation
Ray cast from p in the direction of l

9. The Rendering Equation
Output radiance of intersected surface in the direction of -l

10. The Rendering Equation
Angle between l and n

11. The Rendering Equation
Integral about hemisphere centered at p

12. BRDF’s Bidirectional Reflectance Distribution Function
Determines amount of incoming light from direction l reflected from
surface in the direction of v
Image taken from “A Data-Driven Reflectance Model”

13. Discretizing the Rendering Equation
Assume perfectly diffuse surfaces
Discretize space into
patches
Color is constant per
patch
Image taken from “Radiosity on Graphics Hardware”

14. Discretizing the Rendering Equation

15. Discretizing the Rendering Equation

16. Geometric Computation of Form Factors

17. Geometric Computation of Form Factors

18. Geometric Computation of Form Factors

19. Geometric Computation of Form Factors

20. Geometric Computation of Form Factors

21. Geometric Computation of Form Factors

22. Geometric Computation of Form Factors
Project patches onto hemisphere

23. Geometric Computation of Form Factors
Project spherical patches onto tangent plane

24. Geometric Computation of Form Factors
Divide by area of disc in tangent plane ( for surfaces)

25. Geometric Computation of Form Factors
Divide by area of disc in tangent plane ( for surfaces)
Fi,j = form factor

26. Matrix Computation of Radiosity

27. Matrix Computation of Radiosity

28. Matrix Computation of Radiosity
Jacobi iteration

29. Matrix Computation of Radiosity

30. Matrix Computation of Radiosity

31. Matrix Computation of Radiosity

32. Matrix Computation of Radiosity

33. Matrix Computation of Radiosity

34. Radiosity Examples
Image taken from

35. Radiosity Examples

36. Radiosity Examples
Image taken from

37. Advantages of Radiosity
Global illumination method: modeling diffuse inter-reflection
Color bleeding: a red wall next to a white one casts a reddish glow on the white wall
Soft shadows: an area light source casts a soft shadow from a polygon
No ambient hack
View independent: assigns a brightness to every surface

38. Disadvantages of Radiosity
Radiation is uniform in all directions
Radiosity is piecewise constant
No surface is transparent or translucent
Must determine how to subdivide shapes into small enough patches