A Comparison of Volumetric Illumination Methods by Considering their Underlying Mathematical Models

In this paper, we study and analyze seven state-of-the-art volumetric illumination methods, in order to determine their differences with respect to the underlying theoretical mathematical models and numerical problems potentially arising during implementation. The chosen models are half angle slicing, directional occlusion shading, multidirectional occlusion shading, shadow volume propagation, spherical harmonic lighting, dynamic ambient occlusion and progressive photon mapping. We put these models into a unified mathematical framework, which allows them to be compared among each other as well as to the global volume rendering equation. We will discuss the mathematical differences of the compared models and describe the numerical implications of the simplifications made by each method.