Toward Optimal Space Partitioning for Unbiased, Adaptive Free Path Sampling of Inhomogeneous Participating Media

Photo-realistic rendering of inhomogeneous participating media with light scattering in consideration is important in computer graphics, and is typically computed using Monte Carlo based methods. The key technique in such methods is the free path sampling, which is used for determining the distance (free path) between successive scattering events. Recently, it has been shown that efficient and unbiased free path sampling methods can be constructed based on Woodcock tracking. The key concept for improving the efficiency is to utilize space partitioning (e.g., kd-tree or uniform grid), and a better space partitioning scheme is important for better sampling efficiency. Thus, an estimation framework for investigating the gain in sampling efficiency is important for determining how to partition the space. However, currently, there is no estimation framework that works in 3D space. In this paper, we propose a new estimation framework to overcome this problem. Using our framework, we can analytically estimate the sampling efficiency for any typical partitioned space. Conversely, we can also use this estimation framework for determining the optimal space partitioning. As an application, we show that new space partitioning schemes can be constructed using our estimation framework. Moreover, we show that the differences in the performances using different schemes can be predicted fairly well using our estimation framework.