Optimality of the Delaunay triangulation in \(\mathbb{R}^ d\)
type: Item
instance of: scholarly article
title: Optimality of the Delaunay triangulation in \(\mathbb{R}^ d\)
zbMATH Open document ID: 0808.52012
DOI: 10.1007/BF02574375
author: V. T. Rajan
published in: Discrete \& Computational Geometry
publication date: 1994-09-26T00:00:00Z
full work available at URL: https://eudml.org/doc/131326
review text: The author defines a power function for a triangulation of a finite point set in \(\mathbb{R}^ d\) and shows that it is minimized by the Delaunay triangulation. From this he obtains a number of new optimality results for Delaunay triangulations and generalizes some results previously known for the plane to \(\mathbb{R}^ d\). E.g. it is shown that a triangulation in \(\mathbb{R}^ d\) is the Delaunay triangulation iff each simplex is self- centered, i.e. contains the center of its circumsphere.
Mathematics Subject Classification ID: 52B55
Mathematics Subject Classification ID: 68U05
zbMATH DE Number: 644706
zbMATH Keywords: Voronoi diagram
zbMATH Keywords: Delaunay triangulation
reviewed by: Christoph Schulz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 644706