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Computation of Polarized Subsurface BRDF for Rendering

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

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

  2. Painted materials

  3. Painted materials

  4. Painted materials

  5. Painted materials

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

  7. 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

  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 vectoris a usefulrepresentation 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 donethrough a 4x4 matrix, the Mueller matrix: = • Polarized BRDF, or polarized phase function are represented as Mueller matrices

  11. BRDF Computation

  12. BRDF Computation

  13. BRDF Computation

  14. BRDF Computation

  15. 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

  16. BRDF Computation Light transport ismodeledthrough 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 It has 3 components: • the radiance • corresponding to the light scattering inside the material RTE expresses the change of radiance along optical depth .

  21. 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 .

  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 solutionconsists of two set of 4N linearequations to solve +

  23. Results

  24. Results: Different thicknesses – No base reflection

  25. Results: Different thicknesses – No base reflection

  26. Results: Different thicknesses – No base reflection

  27. Results: Polarization Subsurface BRDF exhibitspolarizationeffects

  28. Results: Different materials Titaniumdioxide Aluminium arsenide Ironoxide Gold

  29. Results: Different materials – BRDF lobe Titaniumdioxide Alluminium arsenide Ironoxide Gold

  30. Results: Different materials – Degree of polarization Titaniumdioxide Alluminium arsenide Ironoxide Gold

  31. Results: Different materials – Lambertian base

  32. Results : Different materials – Diffuse base (BRDF) Titaniumdioxide Aluminium arsenide Ironoxide Gold

  33. Results: Different materials – Diffuse base (DOP) Titaniumdioxide Aluminium arsenide Ironoxide Gold

  34. Results: Different materials – Metallic base

  35. Results: Different materials – Metallic base (BRDF) Titaniumdioxide Aluminium arsenide Ironoxide Gold

  36. Results: Different materials – Metallic base (DOP) Titaniumdioxide Aluminium arsenide Ironoxide Gold

  37. Results: Accuracy – Benchmark validation Benchmark data fromWauben and Hovenier (1992)

  38. Results: Accuracy Takingpolarizationintoaccountsyieldsbetterprecision

  39. Demo • BRDF Solver • Polarizedrenderer

  40. Thank you

  41. VRTE Solution Use of the DiscreteOrdinateMethod (DOM):

  42. VRTE Solution The VRTE can be written as: That we reorganize: Components expressed using Components independant of

  43. VRTE Solution We introduce an differential operator : Needs to be solved for each and

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

  45. 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

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