Delaunay triangulations approximate anchor hulls

Authors:
Tamal K. Dey;Joachim Giesen;Samrat Goswami
Affiliations:
The Ohio State U., Columbus, Ohio;Theoretische Informatik, ETH Zürich, Switzerland;The Ohio State U., Columbus, Ohio
Venue:
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2005

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Abstract

Recent results establish that a subset of the Voronoi diagram of a point set that is sampled from the smooth boundary of a shape approximates the medial axis. The corresponding question for the dual Delaunay triangulation is not addressed in the literature. We show that, for two dimensional shapes, the Delaunay triangulation approximates a specific structure which we call anchor hulls. As an application we demonstrate that our approximation result is useful for the problem of shape matching.