1. Computation of Polarized Subsurface BRDF for Rendering Charly Collin – Sumanta Pattanaik – Patrick LiKamWa Kadi Bouatouch

2. Painted materials

6. Our goal Base layer Binder thickness Particle properties: –Refractive indices –Particle radius –Particle distribution Compute the subsurface BRDF from physical properties:

7. Our goals Compute the diffuse BRDF from physical properties: Accurate light transport simulation: –Accurate BRDF computation –Accurate global illumination Use polarization in our computations: Base layer Binder thickness Particle properties: –Refractive indices –Particle radius –Particle distribution

8. Polarization Light is composed of waves Unpolarized light is composed of waves with random oscillation Light is polarized when composed of waves sharing similar oscillation Polarization of the light can be: –Linear –Circular –Both Polarization properties change the way light interacts with matter

9. Polarization The Stokes vector is a useful representation for polarized light

10. Polarization Each light-matter interaction changes the radiance, but also the polarization state of the light Modifications to a Stokes vector are done through a 4x4 matrix, the Mueller matrix: Polarized BRDF, or polarized phase function are represented as Mueller matrices

11. BRDF Computation

15. ? ? ? To compute the BRDF we need to compute the radiance field for: Each incident and outgoing direction 4 linearly independent incident Stokes vectors The radiance field is computed by solving light transport

16. BRDF Computation ? ? ? Light transport is modeled through the Vector Radiative Transfer Equation:

17. BRDF Computation Our computation makes several assumptions on the material: Plane parallel medium

18. BRDF Computation Our computation makes several assumptions on the material: Plane parallel medium Randomly oriented particles

19. BRDF Computation Our computation makes several assumptions on the material: Plane parallel medium Randomly oriented particles Homogeneous layers

20. Vector Radiative Transfer Equation

22. VRTE Solution VRTE is solved using Discrete Ordinate Method (DOM) Solution is composed of an homogeneous and 4N particular solution The homogeneous solution consists of a 4Nx4N Eigen problem Each particular solution consists of two set of 4N linear equations to solve

23. Results

24. Results: Different thicknesses – No base reflection

27. Results: Polarization Subsurface BRDF exhibits polarization effects

28. Results: Different materials Titanium dioxide Iron oxideGold Aluminium arsenide

29. Results: Different materials – BRDF lobe Titanium dioxide Iron oxideGold Alluminium arsenide

30. Results: Different materials – Degree of polarization Titanium dioxide Iron oxideGold Alluminium arsenide

31. Results: Different materials – Lambertian base

32. Results : Different materials – Diffuse base (BRDF) Titanium dioxide Iron oxideGold Aluminium arsenide

33. Results: Different materials – Diffuse base (DOP) Titanium dioxide Iron oxideGold Aluminium arsenide

34. Results: Different materials – Metallic base

35. Results: Different materials – Metallic base (BRDF) Titanium dioxide Iron oxideGold Aluminium arsenide

36. Results: Different materials – Metallic base (DOP) Titanium dioxide Iron oxideGold Aluminium arsenide

37. Results: Accuracy – Benchmark validation Zenith angle BenchmarkVector Computations Scalar Computations 1.04.26589 (-2)4.49015 (-2)4.48836 (-2) 0.97.94053 (-2)7.94052 (-2)7.94753 (-2) 0.81.16434 (-1)1.16433 (-1)1.16630 (-1) 0.71.64182 (-1) 1.64538 (-1) 0.62.27083 (-1) 2.27612 (-1) 0.53.10078 (-1) 3.10761 (-1) 0.44.18565 (-1) 4.19350 (-1) 0.35.57063 (-1) 5.57858 (-1) 0.27.25362 (-1)7.25361 (-1)7.26032 (-1) 0.19.14221 (-1) 9.14614 (-1) 0.01.111801.108941.10893 Benchmark data from Wauben and Hovenier (1992)

38. Results: Accuracy Taking polarization into accounts yields better precision

39. Demo BRDF Solver Polarized renderer

40. Thank you

41. VRTE Solution Use of the Discrete Ordinate Method (DOM):

42. VRTE Solution The VRTE can be written as: That we reorganize:

43. VRTE Solution

44. Standard solution is the combination of the homogeneous solution...... and one particular solution.

45. VRTE Solution