# GPU accelerated computation of Polarized Subsurface BRDF for Flat Particulate Layers

BRDF of most real world materials has two components, the surface BRDF due to the light reflecting at the surface of the material and the subsurface BRDF due to the light entering and going through many scattering events inside the material. Each of these events modifies light's path, power, polarization state. Computing polarized subsurface BRDF of a material requires simulating the light transport inside the material. The transport of polarized light is modeled by the Vector Radiative Transfer Equation (VRTE), an integro-differential equation. Computing solution to that equation is expensive. The Discrete Ordinate Method (DOM) is a common approach to solving the VRTE. Such solvers are very time consuming for complex uses such as BRDF computation, where one must solve VRTE for surface radiance distribution due to light incident from every direction of the hemisphere above the surface. In this paper, we present a GPU based DOM solution of the VRTE to expedite the subsurface BRDF computation. As in other DOM based solutions, our solution is based on Fourier expansions of the phase function and the radiance function. This allows us to independently solve the VRTE for each order of expansion. We take advantage of those repetitions and of the repetitions in each of the sub-steps of the solution process. Our solver is implemented to run mainly on graphics hardware using the OpenCL library and runs up to seven times faster than its CPU equivalent, allowing the computation of subsurface BRDF in a matter of minutes. We compute and present the subsurface BRDF lobes due to powders and paints of a few materials. We also show the rendering of objects with the computed BRDF. The solver is available for public use through the authors' web site.

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