Cengiz Öztireli, Gurprit Singh

Point patterns and stochastic structures lie at the heart of Monte Carlo based numerical integration schemes. Physically based rendering algorithms have largely benefited from these Monte Carlo based schemes that inherently solve very high dimensional light transport integrals. However, due to the underlying stochastic nature of the samples, the resultant images are corrupted with noise (unstructured aliasing or variance). This also results in bad convergence rates that prohibit using these techniques in more interactive environments (eg games, virtual reality). With the advent of smart rendering techniques and powerful computing units (CPUs/GPUs), it is now possible to perform physically based rendering at interactive rates. However, much is left to understand regarding the underlying sampling structures and patterns which are the primary cause of error in rendering.

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