A weak characterisation of the Delaunay triangulation
type: Item
instance of: scholarly article
title: A weak characterisation of the Delaunay triangulation
zbMATH Open document ID: 1165.52014
published in: Geometriae Dedicata
publication date: 2008-07-30T00:00:00Z
review text: The author introduces a variant of the well-known Delaunay triangulation of a finite point set in a metric space, the so-called weak Delaunay triangulation, which in general contains additional simplices. The two simplicial complexes turn out to be equal for point sets in Euclidean space, as well as in spherical and hyperbolic space and certain other geometries. There are weighted and approximate versions of the weak and strong complexes in all these geometries, and the author proves equality theorems in those cases also. On the other hand, for discrete metric spaces the weak and strong complexes are decidedly different. Finally, the application which motivated these ideas is discussed: how to recover the topology of a manifold (or simplicial complex) from a finite sample of points.
reviewed by: Johann Linhart
Mathematics Subject Classification ID: 52B55
Mathematics Subject Classification ID: 68U05
zbMATH DE Number: 5306121
zbMATH Keywords: Delaunay triangulation
zbMATH Keywords: Voronoi diagram
zbMATH Keywords: witness complex
zbMATH Keywords: manifold reconstruction
zbMATH Keywords: topological approximation
author: Vin de Silva
MaRDI profile type: Publication
full work available at URL: s10711-008-9261-1
OpenAlex ID: W2013613854
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DOI: 10.1007/S10711-008-9261-1
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description: scientific article; zbMATH DE number 5306121