Computational topology of spline curves for geometric and molecular approximations

Date of Completion

January 2006


Mathematics|Computer Science




This dissertation provides sufficient conditions and tractable algorithms that guarantee the topological embedding of geometric approximations commonly used by modern geometric design systems. Particular focus is on approximating spline curve geometry via subdivision while using ambient isotopy as the measure of topological equivalence, which is stricter than the more traditional use of homeomorphism. Experimental work is provided to ensure the new methods developed will be rapid enough for graphics animation and robust enough for 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. ^