Computational Topology for Geometric and Molecular Approximations

The goal of this research will be to provide sufficient conditions and tractable algorithms that guarantee the topological embedding of geometric approximations commonly used by modern geometric design systems. Particular focus is on the use of ambient isotopy as the measure of topological equivalence, which is stricter than the more traditional use of homeomorphism. Such topological guarantees will be made within a user-specified tolerance for applications specific to future Computer-Aided Geometric Design (CAGD) and Computer-Aided Molecular Design (CAMD) systems. The results of this work contribute to the emerging field of computational topology, while providing more accurate and efficient modeling methods to the geometric and molecular design communities.