Formal study of plane delaunay triangulation

Authors:
Jean-François Dufourd;Yves Bertot
Affiliations:
Université de Strasbourg, LSIIT, UMR CNRS-UdS 7005, Illkirch, France;INRIA-Centre de Sophia Antipolis Méditerranée, Sophia-Antipolis Cedex, France
Venue:
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Year:
2010

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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.