Peter Schröder, Steven J. Gortler, Michael Cohen, and Pat Hanrahan. Fourth Eurographics Workshop on Rendering, June 1993
Wavelet theory, which explores the space of hierarchical basis functions, offers an elegant framework that unites these two concepts and allows us to more formally understand the hierarchical radiosity method.
Wavelet expansions of the radiosity kernel have negligible entries in regions where high frequency/fine detail information is not needed. A sparse system remains if these entries are ignored. This is similar to applying a lossy compression scheme to the form factor matrix. The sparseness of the system allows for asymptotically faster radiosity algorithms by limiting the number of matrix terms that need to be computed. The application of these methods to 3D environments is described in [Gortler 93]. Due to space limitations in that paper many of the subtleties of the construction could not be explored there. In this paper we discuss some of the mathematical details of wavelet projections and investigate the application of these methods to the radiosity kernel of a flatland environment, where many aspect are easier to visualize.