Rendering Multiple Scattering In Hair And Other Discrete Random Media

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Discrete random media are collections of explicitly-defined scatterers distributed according to an underlying random process. Examples include blond hair assemblies, piles of soap bubbles, sand, and snow. High albedo discrete random media exhibit smooth high-order scattered radiance that depends not on the specific instance of scattering geometry but instead on the statistical properties of that geometry. This dissertation proposes three new techniques for rendering discrete random media that accelerate the computation of high-order scattering by assuming its smoothness and by limiting the computation done using explicit geometry. The first technique precomputes bulk scattering properties for spatially and directionally homogeneous discrete random media, then uses them in a path tracing method to take large steps through the core of a medium. The other two methods focus on rendering multiple scattering in hair assemblies, although the methods can be applied to other discrete random media as well. One method is a two pass photon mapping approach that uses a 5D data structure to estimate scattered radiance values while preserving their directionality. The other method is also a two pass method, but instead of a particle map it uses a grid of spherical harmonic coefficients to store radiance and to efficiently calculate scattering integrals. These new methods are among the first to render discrete random media accurately and efficiently, with the third technique being able to estimate multiple scattering in blond hair several orders of magnitude faster than a Monte Carlo path tracer, in roughly the time it takes to render the single scattering component.
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