This thesis explores wavelet based multiresolution representation schemes. We survey existing research in this area, describe implementation issues that arise, and, in general, attempt to provide a unified discussion of past work. Since the computer graphics community uses images, curves, and surfaces as its three primary primi­tives, we have used that as the ordering for our investigations into wavelet based representation schemes.

We begin by constructing a general purpose wavelet transformer and building the related mathematical background. Some common properties and basis functions are then examined. The framework is then extended to two dimensional image data, following which we extend the results to three dimensions. We then develop and instantiate a framework for an implementation of multi-resolution B-splines.

Lastly we present a preprocessing step to convert arbitrary unstructured mesh­ing into a structured scheme. A wavelet basis for the structured spaces is introduced followed by an implementation of a multiresolution surface.