Practical product importance sampling for direct illumination

We present a practical algorithm for sampling the product of environment map lighting and surface reflectance. Our method builds on wavelet-based importance sampling, but has a number of important advantages over previous methods. Most importantly, we avoid using precomputed reflectance functions by sampling the BRDF on-the-fly. Hence, all types of materials can be handled, including anisotropic and spatially varying BRDFs, as well as procedural shaders. This also opens up for using very high resolution, uncompressed, environment maps. Our results show that this gives a significant reduction of variance compared to using lower resolution approximations. In addition, we study the wavelet product, and present a faster algorithm geared for sampling purposes. For our application, the computations are reduced to a simple quadtree-based multiplication. We build the BRDF approximation and evaluate the product in a single tree traversal, which makes the algorithm both faster and more flexible than previous methods.