Accurate and efficient strategies for the appearance filtering of complex materials
Realistic computer generated images and simulations require physically-based models to properly capture and reproduce light-material interactions. The underlying mathematical formulations are complex and mandate the use of efficient numerical methods, since analytic solutions are not available. Monte Carlo integration is one such commonly used numerical method, although, alternative approaches leveraging, e.g., basis expansions, may be suitable to solve these challenging problems. In this thesis by articles, we present two works where we efficiently devise numerical integration strategies for the rendering of complex materials. First, we propose a method to compute a spatial-angular multi-dimensional integration problem present when rendering materials with high-frequency normal variation under large, angularly varying illumination. By computing and manipulating a novel spherical histogram data representation, we are able to use spherical harmonics to efficiently solve the integral, outperforming the state-of-the-art by a factor of roughly 30×. Our second work describes a high-performance Monte Carlo integration strategy for rendering layered materials. By identifying the best path sampling strategies in the micro-scale light transport context, we are able to tailor an unbiased and efficient path construction method to evaluate high throughput, low variance paths through an arbitrary number of layers.
BSDF Monte Carlo Rendering normal maps glints summed-area tables spherical harmonics layered materials Monte Carlo integration