Date of Completion
Computational Topology, Numerical Analysis, Scientific Visualization
Professor Thomas J. Peters
Professor Alexander Russell
Professor Robert McCartney
Field of Study
Computer Science and Engineering
Doctor of Philosophy
In Computer Aided Geometric Design (CAGD) B-splines are frequently used to model complex geometric objects. The spline models are smooth structures but piecewise linear (PL) approximations are typically used to render the spline. Aeronautical, automotive and chemical simulations rely on topological algorithms to provide mathematically correct visualization. Topological changes are of significant interest to domain scientists, where self-intersection is a critical event that is often difficult to detect. This research focuses on algorithms that guarantee topology, in terms of ambient isotopic equivalence, between a spline curve and its PL approximations, as used in both static and dynamic visualization. Sufficient conditions for ambient isotopic equivalence for subdivision algorithms and for dynamic perturbations are given. Numerical bounds to ensure ambient isotopic equivalence in the presence of errors from floating point computation are rigorously proved.
Cassidy, Hugh, "Numerical Analysis and Computational Topology for Scientific Visualization" (2014). Doctoral Dissertations. 314.