This project is in the area of computational topology, which is the application of topological algorithms to problems traditionally in the domain of computational geometry. The project will employ topological methods to develop and implement algorithms for various applications in the areas of 1) geometric modeling, 2) robot motion planning, and 3) computer graphics. Algorithms will be coded on graphics workstations. Particular effort will be put on algorithms for geometric objects that are modeled as simplicial complexes in low- dimensional Euclidean space. Further, the underlying theory of computational topology will be systematically investigated in the context of applications.
