Abstract

This dissertation is a presentation of methods for the design of geometric shapes that mimic many forms found in a natural environment. It is argued that a skeleton provides an intuitive and interactive specification for these geometric shapes, and that these shapes are well represented mathematically as implicit surfaces. Substantial portions of the dissertation are devoted to the development of techniques that relate the skeleton to the implicit surface, providing for a geometrically smooth result.

New techniques and presentations are given concerning convolution surfaces and conditions under which they are seamless and bulge-free. New techniques are also given to embed a volume within a surface. Models for the human hand and the botanical leaf illustrate the techniques.