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

  • Eric Berberich
  • Efi Fogel
  • Dan Halperin
  • Kurt Mehlhorn
  • Ron Wein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4698)

Abstract

We introduce a general framework for sweeping a set of curves embedded on a two-dimensional parametric surface. 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: (i) arrangements of arcs of great circles embedded on a sphere, and (ii) arrangements of intersection curves between quadric surfaces embedded on a quadric.

Keywords

Intersection Curve Arrangement Package Sweep Process Input Curve Event Queue 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Eric Berberich
    • 1
  • Efi Fogel
    • 2
  • Dan Halperin
    • 2
  • Kurt Mehlhorn
    • 1
  • Ron Wein
    • 2
  1. 1.Max-Planck-Institut für Informatik, SaarbrückenGermany
  2. 2.School of Computer Science, Tel-Aviv UniversityIsrael

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