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Formal Study of Plane Delaunay Triangulation

  • Jean-François Dufourd
  • Yves Bertot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6172)

Abstract

This article presents the formal proof of correctness for a plane Delaunay triangulation algorithm. It consists in repeating a sequence of edge flippings from an initial triangulation until the Delaunay property is achieved. To describe triangulations, we rely on a combinatorial hypermap specification framework we have been developing for years. We embed hypermaps in the plane by attaching coordinates to elements in a consistent way. We then describe what are legal and illegal Delaunay edges and a flipping operation which we show preserves hypermap, triangulation, and embedding invariants. To prove the termination of the algorithm, we use a generic approach expressing that any non-cyclic relation is well-founded when working on a finite set.

Keywords

Computational Geometry Delaunay Triangulation Naive Algorithm Adjacent Triangle Delaunay Edge 
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 2010

Authors and Affiliations

  • Jean-François Dufourd
    • 1
  • Yves Bertot
    • 2
  1. 1.Université de Strasbourg, LSIIT, UMR CNRS-UdS 7005IllkirchFrance
  2. 2.INRIA-Centre de Sophia Antipolis MéditerranéeSophia-Antipolis CedexFrance

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