Haar Wavelet : A Solution to Global Illumination With General Surface Properties

This paper presents a method for solving the problem of global illumination for general environments, using projection of the radiance function on a set of orthonormal basis functions. Wavelet scaling functions form this basis set. The highlights of the paper are : it (i) points out the di culty associated with the straightforward projection of the integral operator associated with the radiance equation and proposes a method for overcoming this di culty, (ii) gives the data structure and algorithm for illumination solution in environments containing di use and non-di use re ecting surfaces, and (iii) proposes the use of bi-orthogonal wavelet for the radiance function reconstruction at the time of rendering. Actual implementation has been carried out using the Haar wavelet basis. The main reason for using Haar basis is that it makes the projection of the integral operator, as well as the computation of the inner product of the integral kernel with its basis functions much simpler. However, the algorithm and data structures presented are not restricted to the Haar basis alone.