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High Level Filtering with Conic Arcs

Conic curves are planar curves of degree 2 at most: ellipses, hyperbolas, parabolas and of course lines. A finite conic arc is defined by its underlying conic curve and two end-point on that curve.

Many of the algorithms that appear in the literature involve special cases of planar arrangements of conic arcs:

  • Arrangements of line segments are used to solve a variety of problems, such as motion planning of a polygonal robot in a room with polygonal obstacles, map overlay, etc.
  • Arrangements of line segments and circular arcs are used for motion planning of a disc robot in a room with polygonal obstacles.
  • Arrangements of parabolas can be used for answering dynamic nearest-neighbor queries efficiently.

We aim to deal with all these cases, and many more, using a unified approach that insures efficient and robust constructions of arrangements of conic arcs.


  • Ron Wein
    High level Filtering for Arrangements of Conic Arcs
    In Proceedings of the 10th European Symposium on Algorithms (ESA), 2461: 884-895, Springer-Verlag, LNCS, Rome, 2002 [link] [bibtex


Ron Wein
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