Differential Ray Marching

Abstract

Several participating media rendering algorithms are based on ray marching: they integrate the variations of radiance along the volume covered by the participating media by splitting the path of light into segments and sampling light contribution at each of those segments. This paper revisits the concept of ray marching not as an integration technique, but as the application of a numerical method to solve an initial value differential equation. We present how to apply different numerical methods as ray marching techniques, analyze a wide range of them and study their applicability under different scenarios. Furthermore, we show how each of them improves over traditional ray marching. Any participating media rendering algorithm that is based on ray marching will benefit from the application of our technique by reducing the number of needed samples (and therefore, rendering time) and/or increasing accuracy.