Spectral and Decomposition Tracking for Rendering Heterogeneous Volumes

We present two novel unbiased techniques for sampling free paths in heterogeneous participating media.

Our decomposition tracking accelerates free-path construction by splitting the medium into a control component and a residual component and sampling each of them separately.To minimize expensive evaluations of spatially varying collision coefficients, we define the control component such that it allows constructing free paths in closed form. The heterogeneous residual component is then homogenized by adding a fictitious medium and handled using weighted delta tracking.We also describe how to avoid the burden of computing strict majorants of the extinction function.Our second contribution, spectral tracking, enables efficient light transport simulation in chromatic media and further reduces the estimation variance by appropriately biasing the free-path distribution. To demonstrate the correctness of our algorithms, we derive them directly from the radiative transfer equation by extending an integral formulation of null-collision algorithms recently developed in reactor physics.This mathematical framework, which we thoroughly review, encompasses existing trackers and postulates an entire family of new estimators for solving transport problems; our algorithms are examples of such.We analyze the proposed methods in canonical settings and on production scenes, and compare to the current state of the art in simulating light transport in heterogeneous participating media.