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Computation of Polarized Subsurface BRDF for Rendering. Charly Collin – Sumanta Pattanaik – Patrick LiKamWa Kadi Bouatouch. Painted materials. Painted materials. Painted materials. Painted materials. Our goal. Compute the subsurface BRDF from physical properties:. Base layer

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computation of polarized subsurface brdf for rendering

Computation of Polarized Subsurface BRDF for Rendering

Charly Collin – SumantaPattanaik – Patrick LiKamWa Kadi Bouatouch

our goal
Our goal

Compute the subsurface BRDF from physical properties:

  • Base layer
  • Binder thickness
  • Particle properties:
    • Refractive indices
    • Particle radius
    • Particle distribution
our goals
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
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
polarization1
Polarization

The Stokes vectoris a usefulrepresentation for polarized light

polarization2
Polarization
  • Each light-matter interaction changes the radiance, but also the polarization state of the light
  • Modifications to a Stokes vector are donethrough a 4x4 matrix, the Mueller matrix:

=

  • Polarized BRDF, or polarized phase function are represented as Mueller matrices
brdf computation4
BRDF Computation

To compute the BRDF weneed to compute the radiance field for:

  • Each incident and outgoing direction
  • 4 linearlyindependent incident Stokes vectors

? ? ?

The radiance fieldiscomputed by solving light transport

brdf computation5
BRDF Computation

Light transport ismodeledthrough the Vector Radiative Transfer Equation:

? ? ?

brdf computation6
BRDF Computation

Our computation makes several assumptions on the material:

  • Plane parallel medium
brdf computation7
BRDF Computation

Our computation makes several assumptions on the material:

  • Plane parallel medium
  • Randomly oriented particles
brdf computation8
BRDF Computation

Our computation makes several assumptions on the material:

  • Plane parallel medium
  • Randomly oriented particles
  • Homogeneous layers
vector radiative transfer equation
Vector Radiative Transfer Equation

It has 3 components:

  • the radiance
  • corresponding to the light scattering inside the material

RTE expresses the change of radiance along optical depth .

vector radiative transfer equation1
Vector Radiative Transfer Equation

It has 3 components:

  • the radiance
  • corresponding to the light scattering inside the material
  • accounting for attenuated incident radiance

RTE expresses the change of radiance along optical depth .

vrte solution
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 solutionconsists of two set of 4N linearequations to solve

+

results polarization
Results: Polarization

Subsurface BRDF exhibitspolarizationeffects

results different materials
Results: Different materials

Titaniumdioxide

Aluminium arsenide

Ironoxide

Gold

results different materials brdf lobe
Results: Different materials – BRDF lobe

Titaniumdioxide

Alluminium arsenide

Ironoxide

Gold

results different materials degree of polarization
Results: Different materials – Degree of polarization

Titaniumdioxide

Alluminium arsenide

Ironoxide

Gold

results different materials diffuse base brdf
Results : Different materials – Diffuse base (BRDF)

Titaniumdioxide

Aluminium arsenide

Ironoxide

Gold

results different materials diffuse base dop
Results: Different materials – Diffuse base (DOP)

Titaniumdioxide

Aluminium arsenide

Ironoxide

Gold

results different materials metallic base brdf
Results: Different materials – Metallic base (BRDF)

Titaniumdioxide

Aluminium arsenide

Ironoxide

Gold

results different materials metallic base dop
Results: Different materials – Metallic base (DOP)

Titaniumdioxide

Aluminium arsenide

Ironoxide

Gold

results accuracy benchmark validation
Results: Accuracy – Benchmark validation

Benchmark data fromWauben and Hovenier (1992)

results accuracy
Results: Accuracy

Takingpolarizationintoaccountsyieldsbetterprecision

slide39
Demo
  • BRDF Solver
  • Polarizedrenderer
vrte solution1
VRTE Solution

Use of the DiscreteOrdinateMethod (DOM):

vrte solution2
VRTE Solution

The VRTE can be written as:

That we reorganize:

Components expressed using

Components independant of

vrte solution3
VRTE Solution

We introduce an differential operator :

Needs to be solved for each and

vrte solution4
VRTE Solution

Standard solution is the combination of the homogeneous solution...

... and one particular solution.

+

vrte solution5
VRTE Solution
  • The homogeneous solution consists of an 4N x 4N Eigen problem
  • The particular solutionconsists of a set of 4N linearequations to solve
  • It needs to besolved for each