A note on the perimeter of fat objects
type: Item
instance of: scholarly article
title: A note on the perimeter of fat objects
zbMATH Open document ID: 1202.65025
author: Prosenjit Bose
author: Vida Dujmović
author: Otfried Cheong
published in: Computational Geometry
publication date: 2010-10-15T00:00:00Z
review text: A number of realistic models have been studied earlier [see the survey article by \textit{M. de Berg, A. F. van der Stappen, J. Vleugels} and \textit{M. J. Katz}, Algorithmica 34, No.~1, 81--97 (2002; Zbl 1017.68141)]. Four such classes of objects are considered in the paper. The main result of the authors shows that \((\alpha, \beta)\)-covered objects have good perimeter length. Thus each point on the boundary of such an object sees a constant fraction of the length of its boundary. Further, \((\alpha, \beta)\)-covered objects are \(\varepsilon \)-boundary-good for some \(\varepsilon \) that depends only on \(\alpha\) and \(\beta\). It is also shown that a family of curves that converges to the Koch snowflake [see \textit{H. von Koch}, Arkiv f. Mat., Astr. och Fys. 1, 681--702 (1904; JFM 35.0387.02)], defines a family of objects that is locally \(\gamma\)-flat for a specific value of \(\gamma\), has diameter one, but contains objects of arbitrarily large perimeter length.
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 68U05
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 5800752
zbMATH Keywords: realistic inputs
zbMATH Keywords: fat objects
zbMATH Keywords: visibility perimeter
zbMATH Keywords: fractals
zbMATH Keywords: curves
zbMATH Keywords: Koch snowflake
zbMATH Keywords: perimeter length
MaRDI profile type: Publication
full work available at URL: j.comgeo.2010.06.002
OpenAlex ID: W1965013906
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DOI: 10.1016/J.COMGEO.2010.06.002
description: scientific article; zbMATH DE number 5800752