Size analysis of nearly regular Delaunay triangulations
type: Item
instance of: scholarly article
title: Size analysis of nearly regular Delaunay triangulations
zbMATH Open document ID: 0944.60016
DOI: 10.1023/A:1010064208174
author: Ian L. Dryden
author: Charles C. Taylor
author: Mohammad Reza Faghihi
published in: Methodology and Computing in Applied Probability
publication date: 1999-12-19T00:00:00Z
review text: Consider a two-dimensional spatial point pattern in which the points are nearly regular. A pattern is nearly regular if the Delaunay triangles formed by points of the pattern are nearly equilateral, and of roughly the same size. Consider \(k\) distinct, labeled points in the complex plane \(\mathbb C\) denoted by \(z = \{z_1,\dots z_k\}^T\). Typically, these \(k\) points to be a subset of \(n\geq k\) points in \(\mathbb C\) are considered. The centroid size is defined by \(S(z) = \{\sum\|z_i -\overline{z}\|^2\}^2\), where \(\overline{z}\) is the center of gravity. The size \(S\) of a triangle with edge lengths \(a\), \(b\) and \(c\) is determined by \(3 S^2 = a^2 + b^2 + c^2\), and it can be seen that the average squared size of a triangle is closely related to the average of three neighboring squared distances (in the case of a nearly regular pattern). The authors propose to model such patterns with Gaussian perturbations about a regular mean configuration.
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 62M30
Mathematics Subject Classification ID: 62P10
zbMATH DE Number: 1367827
zbMATH Keywords: Delaunay muscle
zbMATH Keywords: point pattern
zbMATH Keywords: Procrustes
zbMATH Keywords: shape
reviewed by: Viktor Ohanyan
MaRDI profile type: Publication
full work available at URL: a:1010064208174
OpenAlex ID: W1510121736
description: scientific article; zbMATH DE number 1367827