Preferred directions for resolving the non-uniqueness of Delaunay triangulations

Authors:
Christopher Dyken;Michael S. Floater
Affiliations:
Centre of Mathematics for Applications, Department of Informatics, University of Oslo, Blindern, Oslo, Norway;Centre of Mathematics for Applications, Department of Informatics, University of Oslo, Blindern, Oslo, Norway
Venue:
Computational Geometry: Theory and Applications
Year:
2006

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Abstract

This note proposes a simple rule to determine a unique triangulation among all Delaunay triangulations of a planar point set, based on two preferred directions. We show that the triangulation can be generated by extending Lawson's edge-swapping algorithm and that point deletion is a local procedure. The rule can be implemented exactly when the points have integer coordinates and can be used to improve image compression methods.