1. 1 Radiance Workshop 2004 – Fribourg, Switzerland Radiance Caching for Efficient Global Illumination Computation J. Křivánek P. Gautron S. Pattanaik K. Bouatouch 3 rd International Radiance Workshop 11 - 12 October 2004, Fribourg, Switzerland

2. 2 Radiance Workshop 2004 – Fribourg, Switzerland High Quality GI The Day After Tomorrow, © 2004 20th Century Fox Shrek 2, © 2004 PDI/DreamWorks

3. 3 Radiance Workshop 2004 – Fribourg, Switzerland Global Illumination… How? L o (P, ω o ) ∫ L i (P, ω i ) = * BRDF(ω o, ω i ) *cos(θ)dω i

4. 4 Radiance Workshop 2004 – Fribourg, Switzerland Monte Carlo ShootingGathering L o (P, ω o ) ∫ L i (P, ω i ) = * BRDF(ω o, ω i ) *cos(θ)dω i No analytical solution

5. 5 Radiance Workshop 2004 – Fribourg, Switzerland Shooting

6. 6 Radiance Workshop 2004 – Fribourg, Switzerland Shooting

7. 7 Radiance Workshop 2004 – Fribourg, Switzerland Shooting Final gathering: costly Photon map only for indirect diffuse Distribution ray tracing for non diffuse: noisy

8. 8 Radiance Workshop 2004 – Fribourg, Switzerland Gathering

9. 9 Radiance Workshop 2004 – Fribourg, Switzerland Gathering Random sampling: noisy High quality: many rays Support for glossy GI

10. 10 Radiance Workshop 2004 – Fribourg, Switzerland Irradiance Caching   Sparse computation of indirect diffuse lighting

11. 11 Radiance Workshop 2004 – Fribourg, Switzerland Irradiance Caching Sparse computation of indirect diffuse lighting

12. 12 Radiance Workshop 2004 – Fribourg, Switzerland Irradiance Caching Interpolation  Sparse computation of indirect diffuse lighting

13. 13 Radiance Workshop 2004 – Fribourg, Switzerland Gradients Why? Without gradients With gradients Images from "Irradiance Gradients", Gregory J. Ward, Paul S. Heckbert Eurographics Workshop on Rendering 1992

14. 14 Radiance Workshop 2004 – Fribourg, Switzerland Gradients nini n E = E i + …

15. 15 Radiance Workshop 2004 – Fribourg, Switzerland Rotational gradient nini n nini n θ E = E i + (ni x n) r EiEi E = E i + …

16. 16 Radiance Workshop 2004 – Fribourg, Switzerland Translational gradient nini n D E = E i + (ni x n) r EiEi + D t EiEi

17. 17 Radiance Workshop 2004 – Fribourg, Switzerland Non diffuse surfaces Indirect glossy: distribution ray tracing High quality: many rays Irradiance values: indirect diffuse

18. 18 Radiance Workshop 2004 – Fribourg, Switzerland Contributions BDRF-based selection of record points Novel translational gradient Extension to indirect glossy lighting Low frequency: records High frequency: distribution ray tracing

19. 19 Radiance Workshop 2004 – Fribourg, Switzerland Outline Introduction IC for glossy surfaces Hemispherical data representation Radiance gradients Outgoing radiance computation Results Conclusion

20. 20 Radiance Workshop 2004 – Fribourg, Switzerland Outline Introduction IC for glossy surfaces Hemispherical data representation Radiance gradients Outgoing radiance computation Results Conclusion

21. 21 Radiance Workshop 2004 – Fribourg, Switzerland Caching on glossy surfaces Need hemispherical data representation

22. 22 Radiance Workshop 2004 – Fribourg, Switzerland Caching on glossy surfaces nini n ? Need new gradients

23. 23 Radiance Workshop 2004 – Fribourg, Switzerland Outline Introduction IC for glossy surfaces Hemispherical data representation Radiance gradients Outgoing radiance computation Results Conclusion

24. 24 Radiance Workshop 2004 – Fribourg, Switzerland Hemispherical Functions Original FunctionPiecewise linear approximation  Need a more compact and smooth representation Better fitting Fast computation of integrals

25. 25 Radiance Workshop 2004 – Fribourg, Switzerland Orthogonal Polynomials f i = f(x)b i (x)dx  f(x) = fifi b i (x) g(x) = gigi b i (x)  f(x)g(x)dx = fifi gigi

26. 26 Radiance Workshop 2004 – Fribourg, Switzerland Application to GI Incident RadianceBRDF  dot product 

27. 27 Radiance Workshop 2004 – Fribourg, Switzerland Spherical Harmonics (0,0)(1,-1)(2,-2)(2,-1)(2,0)(2,1)(2,2)(1,0)(1,1)

28. 28 Radiance Workshop 2004 – Fribourg, Switzerland Hemispherical Harmonics (0,0)(1,-1)(2,-2)(2,-1)(2,0)(2,1)(2,2)(1,0)(1,1) A Novel Hemispherical Basis for Accurate and Efficient Rendering P. Gautron, J. Křivànek, S. Pattanaik, K. Bouatouch, EGSR 04

29. 29 Radiance Workshop 2004 – Fribourg, Switzerland Why (Hemi)Spherical harmonics? Ease of use Rotation support

30. 30 Radiance Workshop 2004 – Fribourg, Switzerland Representation Limitations Bandlimited: "ringing" artifacts Limit to low-frequency BRDFs

31. 31 Radiance Workshop 2004 – Fribourg, Switzerland Adaptive BRDF Representation Low frequency "(H)SH-Friendly" High frequency Why? Ward BRDF with same parameters

32. 32 Radiance Workshop 2004 – Fribourg, Switzerland Adaptive BRDF Representation How? BRDF = 4D Function Parabolic Parameterization

33. 33 Radiance Workshop 2004 – Fribourg, Switzerland Incoming Radiance λ l m (P) = L i (P, ω i )B l m (ω i ) d ω i ∫ Same principle as Irradiance Caching

34. 34 Radiance Workshop 2004 – Fribourg, Switzerland Incoming Radiance λ l m (P) = L i (P, ω i )B l m (ω i ) d ω i ∫ Same principle as Irradiance Caching (H)SH

35. 35 Radiance Workshop 2004 – Fribourg, Switzerland Outline Introduction IC for glossy surfaces Hemispherical data representation Radiance gradients Outgoing radiance computation Results Conclusion

36. 36 Radiance Workshop 2004 – Fribourg, Switzerland Radiance Gradients nini n (H)SH

37. 37 Radiance Workshop 2004 – Fribourg, Switzerland Rotational gradient nini n Rotation Matrix (H)SH = R nini n θ

38. 38 Radiance Workshop 2004 – Fribourg, Switzerland Translational gradient D nini n (H)SH Goal (H)SH = ∂ ∂ x, ∂ (H)SH ∂ y, 0

39. 39 Radiance Workshop 2004 – Fribourg, Switzerland Translational Gradient Numerical Method p

40. 40 Radiance Workshop 2004 – Fribourg, Switzerland Translational Gradient Numerical Method p ΔxΔx p'

41. 41 Radiance Workshop 2004 – Fribourg, Switzerland Translational Gradient Numerical Method p ΔxΔx p' ∂ λ l m ∂ x = λ'lm - λlmλ'lm - λlm ΔxΔx λlm =λlm = *Li( )*B l m ( ) λ'lm =λ'lm = θ k, Φ k ΩkΩk Σ k=1 N λlm =λlm = λ'lm =λ'lm = *L i ( )*B l m ( ) Ω'kΩ'k Σ k=1 N θ k, Φ k θ' k, Φ' k

42. 42 Radiance Workshop 2004 – Fribourg, Switzerland Translational Gradient Analytical Method *L i ( )*B l m ( ) θ k, Φ k ΩkΩk Σ k=1 N λ l m = θ k, Φ k = ∂ ∂ x, ∂ ∂ y, 0 Σ k=1 N ∂ λ l m = ∂ x L i ( θ k, Φ k )* +Ωk+Ωk ∂ x ∂ B l m ( θ k, Φ k ) ∂ Ω k ∂ x B l m ( θ k, Φ k )

43. 43 Radiance Workshop 2004 – Fribourg, Switzerland Outline Introduction IC for glossy surfaces Hemispherical data representation Radiance gradients Outgoing radiance computation Results Conclusion

44. 44 Radiance Workshop 2004 – Fribourg, Switzerland Outgoing Radiance nini n (H)SH RiRi = dxdx + ∂ ∂ x (H)SH + ∂ ∂ y (H)SH dydy

45. 45 Radiance Workshop 2004 – Fribourg, Switzerland Outgoing Radiance nini n = Λ(P) RiRi dxdx + ∂ Λ i ∂ x Σ i S ΛiΛi dydy ∂ Λ i ∂ y + w i (P) Σ i S w i (P)

46. 46 Radiance Workshop 2004 – Fribourg, Switzerland Outgoing Radiance Incident RadianceBRDF  dot product 

47. 47 Radiance Workshop 2004 – Fribourg, Switzerland Outline Introduction IC for glossy surfaces Hemispherical data representation Radiance gradients Outgoing radiance computation Results Conclusion

48. 48 Radiance Workshop 2004 – Fribourg, Switzerland Stills comparison P4 2.2GHz, 512MB RAM Monte Carlo Path Tracing Radiance Caching Rendering time: 155s

49. 49 Radiance Workshop 2004 – Fribourg, Switzerland Stills comparison Monte Carlo Path Tracing Radiance Caching

50. 50 Radiance Workshop 2004 – Fribourg, Switzerland Video: Cornell Box

51. 51 Radiance Workshop 2004 – Fribourg, Switzerland Video: Flamingo

52. 52 Radiance Workshop 2004 – Fribourg, Switzerland Outline Introduction IC for glossy surfaces Hemispherical data representation Radiance gradients Outgoing radiance computation Results Conclusion

53. 53 Radiance Workshop 2004 – Fribourg, Switzerland Conclusion Extension of irradiance caching to radiance caching Definition of new translational gradient Quality improvementEfficiency improvementIndependent from distributionIndependent from basis functions

54. 54 Radiance Workshop 2004 – Fribourg, Switzerland Future Work "All-frequency" hemispherical representation Hardware support

55. 55 Radiance Workshop 2004 – Fribourg, Switzerland Any Questions ? Rendered using Radiance Caching