Consistent digital line segments
type: Item
instance of: scholarly article
title: Consistent digital line segments
zbMATH Open document ID: 1259.65039
author: Tobias Christ
author: Dömötör Pálvölgyi
author: Miloš Stojaković
published in: Discrete \& Computational Geometry
publication date: 2012-05-22T00:00:00Z
review text: The authors introduce a novel and general approach for digitalization of line segments in the plane that satisfies a set of axioms arising from Euclidean axioms. In particular, it is shown how to derive such a system of digital segments from any total order on the integers. As a consequence, the authors manage to define a system of digital segments such that all digital segments are, in the Hausdorff metric, optimally close to their corresponding Euclidean segments. Thus, an explicit construction is provided that solves the main question of \textit{J. Chun} et al. [Discrete Comput. Geom. 42, No. 3, 359--378 (2009; Zbl 1174.52008)].
Mathematics Subject Classification ID: 65D18
zbMATH DE Number: 6037504
zbMATH Keywords: digitalization
zbMATH Keywords: plane
zbMATH Keywords: integer grid
zbMATH Keywords: line segment
zbMATH Keywords: Hausdorff metric
zbMATH Keywords: Euclidean segments
reviewed by: Sonia Pérez Díaz
MaRDI profile type: Publication
full work available at URL: s00454-012-9411-y
OpenAlex ID: W2950470587
cites work: Consistent digital rays
cites work: Digital straightness -- a review
cites work: Irregularities of distribution, VII
cites work: Q2779282
cites work: Q5759854
DOI: 10.1007/S00454-012-9411-Y
description: scientific article; zbMATH DE number 6037504