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

Painted materials

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

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

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 4x4 matrix, the Mueller matrix: Polarized BRDF, or polarized phase function are represented as Mueller matrices

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 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

Results

Results: Different thicknesses – No base reflection

Results: Polarization Subsurface BRDF exhibits polarization effects

Results: Different materials Titanium dioxide Iron oxideGold Aluminium arsenide

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

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

Results: Different materials – Lambertian base

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

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

Results: Different materials – Metallic base

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

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

Results: Accuracy – Benchmark validation Zenith angle BenchmarkVector Computations Scalar Computations (-2) (-2) (-2) (-2) (-2) (-2) (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1) Benchmark data from Wauben and Hovenier (1992)

Results: Accuracy Taking polarization into accounts yields better precision

Demo BRDF Solver Polarized renderer

Thank you

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

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

VRTE Solution

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

VRTE Solution