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arXiv · 1007.3350

Formal study of plane Delaunay triangulation

Jean-François Dufourd·Yves Bertot
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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.

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Jean-François Dufourd, Yves Bertot. 2010-07-20. Formal study of plane Delaunay triangulation. https://arxiv.org/abs/1007.3350

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