Computation of Polarized Subsurface BRDF for Rendering Charly

Computation of Polarized Subsurface BRDF for Rendering Charly Collin – Sumanta Pattanaik – Patrick Li. Kam. Wa Kadi Bouatouch

Painted materials

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

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

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

Polarization The Stokes vector is a useful representation for polarized light

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 4 x 4 matrix, the Mueller matrix: • Polarized BRDF, or polarized phase function are represented as Mueller matrices

BRDF Computation

BRDF Computation 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

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

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

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

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

Vector Radiative Transfer Equation •

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

Results

Results: Different thicknesses – No base reflection

Results: Polarization Subsurface BRDF exhibits polarization effects

Results: Different materials Titanium dioxide Iron oxide Gold Aluminium arsenide

Results: Different materials – BRDF lobe Titanium dioxide Iron oxide Gold Alluminium arsenide

Results: Different materials – Degree of polarization Titanium dioxide Iron oxide Gold Alluminium arsenide

Results: Different materials – Lambertian base

Results : Different materials – Diffuse base (BRDF) Titanium dioxide Iron oxide Gold Aluminium arsenide

Results: Different materials – Diffuse base (DOP) Titanium dioxide Iron oxide Gold Aluminium arsenide

Results: Different materials – Metallic base

Results: Different materials – Metallic base (BRDF) Titanium dioxide Iron oxide Gold Aluminium arsenide

Results: Different materials – Metallic base (DOP) Titanium dioxide Iron oxide Gold Aluminium arsenide

Results: Accuracy – Benchmark validation Zenith angle Benchmark Vector Computations Scalar Computations 1. 0 4. 26589 (-2) 4. 49015 (-2) 4. 48836 (-2) 0. 9 7. 94053 (-2) 7. 94052 (-2) 7. 94753 (-2) 0. 8 1. 16434 (-1) 1. 16433 (-1) 1. 16630 (-1) 0. 7 1. 64182 (-1) 1. 64538 (-1) 0. 6 2. 27083 (-1) 2. 27612 (-1) 0. 5 3. 10078 (-1) 3. 10761 (-1) 0. 4 4. 18565 (-1) 4. 19350 (-1) 0. 3 5. 57063 (-1) 5. 57858 (-1) 0. 2 7. 25362 (-1) 7. 25361 (-1) 7. 26032 (-1) 0. 1 9. 14221 (-1) 9. 14614 (-1) 0. 0 1. 11180 1. 10894 1. 10893 Benchmark data from Wauben and Hovenier (1992)