1. 1 Dr. Scott Schaefer Radiosity

2. 2/38 Radiosity

3. 3/38 Radiosity Physically based model for light interaction View independent lighting Accounts for indirect illumination  Color bleeding  Soft shadows

4. 4/38 The Rendering Equation

5. 5/38 The Rendering Equation Outgoing radiance from surface at p in the direction v

6. 6/38 The Rendering Equation Emitted radiance from surface at p in the direction v

7. 7/38 The Rendering Equation BRDF of surface at p

8. 8/38 The Rendering Equation Ray cast from p in the direction of l

9. 9/38 The Rendering Equation Output radiance of intersected surface in the direction of -l

10. 10/38 The Rendering Equation Angle between l and n

11. 11/38 The Rendering Equation Integral about hemisphere centered at p

12. 12/38 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. 13/38 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. 14/38 Discretizing the Rendering Equation

15. 15/38 Discretizing the Rendering Equation

16. 16/38 Geometric Computation of Form Factors

17. 17/38 Geometric Computation of Form Factors

18. 18/38 Geometric Computation of Form Factors

19. 19/38 Geometric Computation of Form Factors

20. 20/38 Geometric Computation of Form Factors

21. 21/38 Geometric Computation of Form Factors

22. 22/38 Geometric Computation of Form Factors Project patches onto hemisphere

23. 23/38 Geometric Computation of Form Factors Project spherical patches onto tangent plane

24. 24/38 Geometric Computation of Form Factors Divide by area of disc in tangent plane ( for surfaces)

25. 25/38 Geometric Computation of Form Factors Divide by area of disc in tangent plane ( for surfaces) F i,j = form factor

26. 26/38 Matrix Computation of Radiosity

27. 27/38 Matrix Computation of Radiosity

28. 28/38 Matrix Computation of Radiosity Jacobi iteration

29. 29/38 Matrix Computation of Radiosity

30. 30/38 Matrix Computation of Radiosity

31. 31/38 Matrix Computation of Radiosity

32. 32/38 Matrix Computation of Radiosity

33. 33/38 Matrix Computation of Radiosity

34. 34/38 Radiosity Examples Image taken from http://www.9jcg.com/tutorials/jason_jacobs/radiosity_01.jpg

35. 35/38 Radiosity Examples

36. 36/38 Radiosity Examples Image taken from www.cs.dartmouth.edu/~spl/Academic/ComputerGraphics/Fall2004/radiosityExample.jpg

37. 37/38 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. 38/38 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