Minimal roughness property of the Delaunay triangulation: A shorter approach
type: Item
instance of: scholarly article
title: Minimal roughness property of the Delaunay triangulation: A shorter approach
zbMATH Open document ID: 0765.65132
DOI: 10.1016/0167-8396(92)90047-S
author: P. Powar
published in: Computer Aided Geometric Design
publication date: 1993-01-18T00:00:00Z
review text: {S. Rippa} [ibid. 7, No. 6, 489-497 (1990; Zbl 0714.65009)] has shown that the Delaunay triangulation constructed from a set of vertices is of minimial roughness measured by the Euclidean norm of \(\nabla g\) where \(g\) is the piecewise linear function describing the triangulation. A basic tool in the proof was an inequality estimating the difference of the squares of the norms for the two triangulations possible for a quadrilateral in geometric terms. The author gives an inequality yielding the same result but with a much shortened proof.
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 51N20
zbMATH DE Number: 85952
zbMATH Keywords: roughness measure
zbMATH Keywords: piecewise linear interpolating surface
zbMATH Keywords: Sobolev semi- norms
zbMATH Keywords: power of a point
zbMATH Keywords: Delaunay triangulation
zbMATH Keywords: inequality
zbMATH Keywords: shortened proof
reviewed by: Heinrich Guggenheimer
MaRDI profile type: Publication
cites work: Q5341359
cites work: Minimal roughness property of the Delaunay triangulation
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description: scientific article; zbMATH DE number 85952