Progressive null-tracking for volumetric rendering

Null-collision approaches for estimating transmittance and sampling free-flight distances are the current state-of-the-art for unbiased rendering of general heterogeneous participating media. However, null-collision approaches have a strict requirement for specifying a tightly bounding total extinction in order to remain both robust and performant; in practice this requirement restricts the use of null-collision techniques to only participating media where the density of the medium at every possible point in space is known a-priori. In production rendering, a common case is a medium in which density is defined by a black-box procedural function for which a bounding extinction cannot be determined beforehand. Typically in this case, a bounding extinction must be approximated by using an overly loose and therefore computationally inefficient conservative estimate. We present an analysis of how null-collision techniques degrade when a more aggressive initial guess for a bounding extinction underestimates the true maximum density and turns out to be non-bounding. We then build upon this analysis to arrive at two new techniques: first, a practical, efficient, consistent progressive algorithm that allows us to robustly adapt null-collision techniques for use with procedural media with unknown bounding extinctions, and second, a new importance sampling technique that improves ratio-tracking based on zero-variance sampling.