A Progressive Algorithm for Three Point Transport

When computing global illumination in environments made up of surfaces with general Bidirectional Reflection Distribution Functions, a three point formulation of the rendering equation can be used. Brute-force algorithms can lead to a linear system of equations whose matrix is cubic, which is expensive in time and space. The hierarchical approach is more efficient. Aupperle et al. proposed a hierarchical three point algorithm to compute global illumination in the presence of glossy reflection. We present in this paper some improvements we brought to this method: shooting, "lazy" push-pull, photometric subdivision criterion, etc. Then we will show how our new method takes into account non-planar surfaces in the hierarchical resolution process.