Adaptive Numerical Cumulative Distribution Functions for Efficient Importance Sampling
As image-based surface reflectance and illumination gain wider use in physically-based rendering systems, it is becoming more critical to provide representations that allow sampling light paths according to the distribution of energy in these high-dimensional measured functions. In this paper, we apply algorithms traditionally used for curve approximation to reduce the size of a multidimensional tabulated Cumulative Distribution Function (CDF) by one to three orders of magnitude without compromising its fidelity. These adaptive representations enable new algorithms for sampling environment maps according to the local orientation of the surface and for multiple importance sampling of image-based lighting and measured BRDFs.
Jason Lawrence, Szymon Rusinkiewicz, and Ravi Ramamoorthi. "Adaptive Numerical Cumulative Distribution Functions for Efficient Importance Sampling". In Eurographics Symposium on Rendering, pages 11–20, June 2005.