Sweeping and Maintaining Two-Dimensional Arrangements on Surfaces: A First Step

We introduce a general framework for processing a set of curves defined on a continuous two-dimensional parametric surface, while sweeping the parameter space. We can handle planes, cylinders, spheres, tori, and surfaces homeomorphic to them. A major goal of our work is to maximize code reuse by generalizing the prevalent sweep-line paradigm and its implementation so that it can be employed on a large class of surfaces and curves embedded on them. We have realized our approach as a prototypical Cgal package. We present experimental results for two concrete adaptions of the framework for: (i) arrangements of arcs of great circles embedded on a sphere, and (ii) arrangements of intersection curves between quadric surfaces embedded on a quadric.

• Type: Conference
• Year: 2007
• Where: ESA
• Authors: Eric Berberich, Efi Fogel, Dan Halperin, Kurt Mehlhorn, Ron Wein
• Keywords: ESA 2007, Prevalent Sweep-line Paradigm, Surfaces, Two-dimensional Parametric Surface