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    Fast Approximation of Multiple Scattering in Inhomogeneous Participating Media
    (The Eurographics Association, 2009) Szirmay-Kalos, László; Liktor, Gábor; Umenhoffer, Tamás; Tóth, Balázs; P. Alliez and M. Magnor
    This paper presents a fast approximation for the solution of the radiative transfer equation in inhomogeneous participating media. This scheme traces rays from the point light creating spherical wavefronts. While we march on a particular ray, we assume that other rays find similar material properties, which allows the solution of the diffusion equation for this ray. The proposed approximation of the scattered component can be computed in parallel with obtaining the direct term at practically no additional cost. The approximation may be used for direct visualization, an initial guess for an iterative solution, or for the main part of a Monte Carlo solution.
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    Importance Sampling with Floyd-Steinberg Halftoning
    (The Eurographics Association, 2009) Szirmay-Kalos, László; Szécsi, László; Penzov, Anton; P. Alliez and M. Magnor
    This paper proposes a deterministic importance sampling algorithm for complex integrands. The idea is based on the recognition that halftoning algorithms are equivalent to importance sampling if the gray-scale image and a resulting white pixel are considered as the target importance function and the sampling position, respectively. We adopt the Floyd-Steinberg halftoning algorithm, extend it to higher dimensions, and rephrase it as a sampling method. As the Floyd-Steinberg halftoning places a sample also considering where other samples are located, our sampling algorithm distributes samples in a stratified way. In order to demonstrate the power of the method, we present an environment mapping application where the sampling mimics the product of the cosine weighted BRDF, environment radiance, and the environment visibility.