1. CPSC 641 Computer Graphics: Radiosity Jinxiang Chai

2. Local Illumination I r = k a I a + I i (k d (n.l) + k s (h.n) m ) ambientdiffusespecular

3. Local Illumination I r = k a I a + I i (k d (n.l) + k s (h.n) m ) ambientdiffusespecular

4. Local Illumination I r = k a I a + I i (k d (n.l) + k s (h.n) m ) if there are multiple lights there is a sum of the specular and diffuse components for each light ambientdiffusespecular

5. Local Illumination I r = k a I a + I i (k d (n.l) + k s (h.n) m ) if there are multiple lights there is a sum of the specular and diffuse components for each light ambientdiffusespecular What are limitations of local illumination?

6. Rendering: Illumination Computing Direct (local) illumination Light directly from light sources No shadows

7. Direct and Indirect Light

8. Rendering: Illumination Computing Direct (local) illumination Light directly from light sources No shadows Indirect (global) illumination Hard and soft shadows Diffuse interreflections (radiosity) Glossy interreflections (caustics)

9. Early Radiosity

10. Consolation Room

11. Challenge To evaluate the reflection equation the incoming radiance must be known To evaluate the incoming radiance the reflected radiance must be known

12. Radiosity Only consider inter-reflections between diffuse surfaces!

13. Radiosity: Key Idea #1

14. Diffuse Surface

15. Radiosity: Key Idea #2

16. Constant Surface Approximation

17. Radiosity Equation

19. Radiosity Algorithm

21. Energy Conservation Equation

22. Form factor

23. Compute Form Factors

24. Radiant energy reaching A y from A x Radiant energy leaving A x in all directions

25. Form Factor: Reciprocity

26. Radiosity Equation

27. Linear System

28. Radiosity Algorithm

29. Form Factors

30. Form Factor: How to compute? Closed Form - anlytical Hemicube Monte Carlo

31. Form Factor: Analytical

32. Form Factor: How to compute? Closed Form - anlytical Hemicube Monte Carlo

33. Form Factor: Nusselt Analog

34. Why is it true?

35. Form Factor: Nusselt Analog

36. How can we use this property?

37. Form Factor: Nusselt Analog How can we use this property? - Speed up form-factor evaluation

38. Form Factor: HemiCube

39. Delta Form Factor: Top Face Top of hemicube

40. Delta Form Factors: Side Faces Side of hemicube

41. The Hemicube in Action

42. Form Factor: HemiCube

43. Form Factors

44. Radiosity Algorithm

45. How to Solve Linear System? Matrix conversion Iterative approaches - Jacobian - Gauss-Seidel

46. Matrix Conversion

47. Iterative Approaches

48. Jacobian

49. Successive Approximation

50. Gauss-Seidel

51. Gauss-Seidel (Cont.)

52. Radiosity Algorithm

53. Rendering The final B i 's can be used in place of intensities in a standard renderer (Gouraud) Radiosities are constant over the extent of a patch A standard renderer requires vertex intensities (or radiosities) If the radiosities of surrounding patches are know, vertex radiosities can be estimated using bilinear interpolation

54. Vertex Intensity: Bilinear Interpolation

55. Theatre

56. Steel Mills

57. Radiosity: Benefit 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 near the corner Soft shadows – an “area” light source casts a soft shadow from a polygon No ambient term hack, so when you want to look at your object in low light, you don’t have to adjust parameters of the objects – just the intensities of the lights! View independent: it assigns a brightness to every surface

58. Radiosity: Limitation Radiation is uniform in all directions Radiosity is piecewise constant – usual renderings make this assumption, but then interpolate cheaply to fake a nice-looking answer – this introduces quantifiable errors No surface is transparent or translucent Reflectivity is independent of directions to source and destination