Rendering participating media is still a challenging and time consuming task. In such media light interacts at every differential point of its path. Several rendering algorithms are based on ray marching: dividing the path of light into segments and calculating interactions at each of them. In this work, we revisit and analyze ray marching both as a quadrature integrator and as an initial value problem solver, and apply higher order adaptive solvers that ensure several interesting properties, such as faster convergence, adaptiveness to the mathematical definition of light transport and robustness to singularities. We compare several numerical methods, including standard ray marching and Monte Carlo integration, and illustrate the benefits of different solvers for a variety of scenes. Any participating media rendering algorithm that is based on ray marching may benefit from the application of our approach by reducing the number of needed samples (and therefore, rendering time) and increasing accuracy.
Parts of the source code for this paper have been released to the public domain.