Precomputed Radiance Transfer

1. Precomputed Radiance Transfer Peter-Pike Sloan SDE Windows Graphics & Gaming Technologies Microsoft Corporation

2. Challenges in Rendering • Generating realistic images interactively is hard • Many dimensions of complexity • Geometric complexity • Material complexity • Meso-scale complexity • Lighting complexity • Transport complexity • Synergy • This talk focuses on techniques that enable more lighting/transport complexity

3. Material Complexity • Models how light interacts with a surface • Assume the “structure” of the material is below the visible scale • Simple variation • Twist maps

4. Meso-Scale Complexity • Variations at a visible scale - not geometry • Bump/Roughness maps • Parallax Mapping/BTFs extreme examples of this

5. Lighting Complexity • What kind of lighting environment is an object in? • Directional/point lights • Directional + ambient • “Smooth” (low frequency) lighting • Completely general

6. Lighting Complexity • What kind of lighting environment is an object in? • Directional/point lights • Directional + ambient • “Smooth” (low frequency) lighting • Completely general

7. Lighting Complexity • What kind of lighting environment is an object in? • Directional/point lights • Directional + ambient • “Smooth” (low frequency) lighting • Completely general

8. Lighting Complexity • What kind of lighting environment is an object in? • Directional/point lights • Directional + ambient • “Smooth” (low frequency) lighting • Completely general

9. Transport Complexity • How light interacts with objects/scene at a visible scale • Shadows • Inter-reflections • Caustics • Translucency (subsurface scattering)

10. Transport Complexity • How light interacts with objects/scene at a visible scale • Shadows • Inter-reflections • Caustics • Translucency (subsurface scattering)

11. Transport Complexity • How light interacts with objects/scene at a visible scale • Shadows • Inter-reflections • Caustics • Translucency (subsurface scattering)

12. Transport Complexity • How light interacts with objects/scene at a visible scale • Shadows • Inter-reflections • Caustics • Translucency (subsurface scattering)

13. Some of All of This • Real scenes have all of these forms of complexity • Extreme realism in one form of complexity is not necessarily that interesting • Incredible material models that are completely homogenous and lit by a single directional light • Great lighting environments for diffuse surfaces with no shadows

14. What is Precomputed Radiance Transfer (PRT)? • Parameterize an object’s response to lighting, expressed in some basis • Partition into two processes • Offline transport simulator precomputes spatially varying linear operators that map lighting in given basis to exit radiance • Run time render the object using the current viewing/lighting environment using precomputed data

15. PRT Teaser Demo

16. Terminology

17. Terminology

18. Terminology

19. Terminology

20. Rendering Equation

21. Rendering Equation Radiance leaving pointpin directiond

22. Rendering Equation Radiance emitted from pointpin directiond

23. Rendering Equation Integral over directionsson the hemisphere aroundp

24. Rendering Equation BRDF at pointpevaluated for incident directionsin outgoing directiond

25. Rendering Equation Radiance arriving at pointpfrom directions (also LHS)

26. Rendering Equation Lamberts law – cosine between normal and -s=dot(Np, -s)

27. Neumann Expansion Exit radiance expressed as infinite series

28. Neumann Expansion Direct lighting arriving at point p – from distant environment

29. Neumann Expansion Direct lighting arriving at point p – from distant environment

30. Neumann Expansion Source Radiance – distant lighting environment

31. Neumann Expansion Visibility function - binary

32. Neumann Expansion All paths from source that take 1 bounce

33. Neumann Expansion L0 All paths from source that take 1 bounce

34. Neumann Expansion Li-1 All paths from source that take i bounces

35. Diffuse PRT

36. Diffuse PRT

37. Diffuse PRT

38. Diffuse PRT

39. Diffuse PRT

40. Diffuse PRT

41. Diffuse PRT

42. Diffuse PRT

43. Project Light light light • = = • = • Diffuse Self-Transfer 2D example, piecewise constant basis, shadows only Preprocess Rendering

44. . . . . . . Precomputation Basis 16 Basis 17 illuminate result Basis 18

45. Spherical Harmonics • Spherical analog to Fourier transform • Represents complex functions on the sphere, real form used in graphics • Polynomials in R3 • Full basis through O has O2 coeffs • Projection/Evaluation/Rotation are fairly straightforward • Small number of bands implies “low frequency” lighting

46. Spherical Harmonics

47. Spherical Harmonics n=2 n=3 n=5 n=26 original

48. Spherical Harmonics • Rotation invariance • No temporal “wobbling” of projection • Low frequency is also strength • Reduces necessary surface sampling rate • Addresses lighting that is most difficult with traditional techniques • Global support is a limitation

49. PRT Demo

50. PRT Limitations/Extensions • Rigid objects • “Local, Deformable Precomputed Radiance Transfer”, Siggraph 2005 • Raw form unwieldy • 6th order would require 108 coefficients/vertex • Siggraph 2003 paper compresses both data and computation, small number (4-12) coefficiens/vertex, much simpler shaders • This is what makes it work in games…