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)


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.


Intersection Curve Arrangement Package Sweep Process Input Curve Event Queue 
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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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