Efficiently Evaluating Products of Complex Functions

We present a new technique for importance sampling products of complex functions using wavelets. First, we generalize previous work on wavelet products to higher dimensional spaces and show how this product can be sampled on-thefly without the need of evaluating the full product. This makes it possible to sample products of high-dimensional functions even if the product of the two functions in itself is too memory consuming. Then, we present a novel hierarchical sample warping algorithm that generates high-quality point distributions, which match the wavelet representation exactly. One application of the new sampling technique is rendering of objects with measured BRDFs illuminated by complex distant lighting — our results demonstrate how the new sampling technique is more than an order of magnitude more efficient than the best previous techniques. CR Categories: I.3.7 [Computer Graphics]: ThreeDimensional Graphics and Realism—Shading, G.1.2 [Numerical Analysis]: Approximation—Wavelets, G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation—Multidimensional Quadrature