The natural-constraint representation of the path space for efficient light transport simulation

The path integral formulation of light transport is the basis for (Markov chain) Monte Carlo global illumination methods. In this paper we present half vector space light transport (HSLT), a novel approach to sampling and integrating light transport paths on surfaces. The key is a partitioning of the path space into subspaces in which a path is represented by its start and end point constraints and a sequence of generalized half vectors. We show that this representation has several benefits. It enables importance sampling of all interactions along paths in between two endpoints. Based on this, we propose a new mutation strategy, to be used with Markov chain Monte Carlo methods such as Metropolis light transport (MLT), which is well-suited for all types of surface transport paths (diffuse/glossy/specular interaction). One important characteristic of our approach is that the Fourier-domain properties of the path integral can be easily estimated. These can be used to achieve optimal correlation of the samples due to well-chosen mutation step sizes, leading to more efficient exploration of light transport features. We also propose a novel approach to control stratification in MLT with our mutation strategy.