Geometry, Graphics, and Numerical Analysis (thesis)

Abstract:

Geometric computations (e.g. polygon/line intersections and detection, etc.), like all numerical procedures, are extremely prone to roundoff error. However, virtually none of the numerical analysis literature directly applies to geometric calculations. As a result, most of these applications resort to ad hoc methods to overcome the numerical difficulties. The goal of this research is to present and analyze systematic approaches to handle unreliability and enable more robust solutions to problems in applied computational geometry.