Delaunay triangulations approximate anchor hulls

Authors:
Tamal K. Dey;Joachim Giesen;Samrat Goswami
Affiliations:
Department of CSE, The Ohio State University, Columbus, OH 43210, USA;Institute for Theoretical Computer Science, ETH Zürich, CH-8092 Zürich, Switzerland;Department of CSE, The Ohio State University, Columbus, OH 43210, USA
Venue:
Computational Geometry: Theory and Applications
Year:
2007

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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.