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

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 adaptations 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.