Elias' Article

Exact Delaunay graph of smooth convex pseudo-circles.
Ioannis Z. Emiris, Elias P. Tsigaridas, and George Tzoumas.
In 25th European Workshop on Computational Geometry (EuroCG), pp. 235–328, Brussels, Belgium, Mar 16--18 2009.

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Abstract:

We examine the problem of computing exactly the Delaunay graph of a set of possibly intersecting smooth convex \pc in the Euclidean plane given in parametric form. The diagram is constructed incrementally. We focus on \kcn, under the exact computation paradigm, and express it by a simple polynomial system, which allows for an efficient implementation by means of iterated resultants and a factorization lemma. Finally, we present examples with certain types of curves.

@InProceedings{ett-eurocg-2009,
  author =       {Ioannis~Z. Emiris and Elias~P. Tsigaridas and George
                  Tzoumas},
  title =        {{Exact Delaunay graph of smooth convex
                  pseudo-circles}},
  booktitle =    {25th European Workshop on Computational Geometry
                  (EuroCG)},
  pages =        {235--328},
  year =         2009,
  month =        {Mar 16--18},
  address =      {Brussels, Belgium},
  abstract =     " We examine the problem of computing exactly the
                  Delaunay graph of a set of possibly intersecting
                  smooth convex \pc in the Euclidean plane given in
                  parametric form. The diagram is constructed
                  incrementally.  We focus on \kcn, under the exact
                  computation paradigm, and express it by a simple
                  polynomial system, which allows for an efficient
                  implementation by means of iterated resultants and a
                  factorization lemma.  Finally, we present examples
                  with certain types of curves.",
}

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