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 computation- ally 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.

Zackary Misso, Yining Karl Li, Brent Burley, Daniel Teece, and Wojciech Jarosz. Progressive Null Tracking for Volumetric Rendering. SIGGRAPH '23: ACM SIGGRAPH 2023 Conference Proceedings. Article 31, August 2023.

@inproceedings{misso23progressive,
	author    = {Misso, Zackary and Li, Yining Karl and Burley, Brent and Teece, Daniel and Jarosz, Wojciech},
	title     = {Progressive Null-Tracking for Volumetric Rendering},
	booktitle = {SIGGRAPH '23: ACM SIGGRAPH 2023 Conference Proceedings},
	month     = aug,
	year      = {2023},
	articleno = {31},
	doi       = {10.1145/3588432.3591557},
	keywords  = {participating media, transmittance, null collision, null scattering, stochastic sampling,
	             Monte Carlo integration},
}

The cloud model in Fig. 9 is from Walt Disney Animation Studios. This work was generously supported by NSF award 1844538.

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