Abstract

Scientific Computing is an exciting and growing area that provides an important link between Computer Science and the Engineering and Physical Sciences. Today, computer graphics and geometric modeling are used routinely in science, engineering, business; and entertainment. In this thesis we develop object-oriented techniques and software for computing and visualizing implicitly defined manifolds ("surfaces") that arise a wide range of applications. The software differs from existing software for computing such manifolds in its software architecture. Furthermore, its algorithms are based on numerical continuation methods, rather than on subdivision techniques, which allows its practical application to the computation of two-dimensional manifolds in high-dimensional Euclidean spaces. The overall software provides a graphical user interface, algorithms for computing two-dimensional manifolds in higher-dimensional spaces, and graphics routines to visualize the manifolds.