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.

Links

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

Contacts

Ron Wein 
@inproceedings{w-hlfca-02,
  author = {Ron Wein},
  title = {High-Level Filtering for Arrangements of Conic Arcs},
  booktitle = {Proceedings of the 10th Annual European Symposium on Algorithms ({ESA})},
  series = {Lecture Notes in Computer Science ({LNCS})},
  volume = {2461},
  publisher = {Springer},
  year = {2002},
  pages = {884--895},
  doi = {10.1007/3-540-45749-6_76}
}

Yair Oz - Webcreator

Contact

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Email. [email protected]

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