How many diagonal rectangles are needed to cover an orthogonal polygon?
type: Item
instance of: scholarly article
title: How many diagonal rectangles are needed to cover an orthogonal polygon?
zbMATH Open document ID: 0967.52005
author: Yoshiyas Ishigami
published in: Discrete \& Computational Geometry
publication date: 2001-09-03T00:00:00Z
review text: A polygon whose edges are horizontal and vertical is called ``orthogonal''. A rectangle with a pair of opposite corners at the vertices of an orthogonal polygon is ``diagonal'' (in that polygon). The author finds that any orthogonal polygon with \(n\) vertices can be covered by (the union of) \(\lfloor {3\over 4}n \rfloor-2-\omega\) diagonal rectangles where \(\omega=1\) when \(n=8, 12, 16\) and \(\omega =0\) otherwise. Furthermore this result is sharp and settles a problem proposed by Mamoru Watanabe at the British Combinatorial Conference 1997.
Mathematics Subject Classification ID: 52C10
zbMATH DE Number: 1495784
zbMATH Keywords: covering
zbMATH Keywords: rectangle
zbMATH Keywords: orthogonal polygon
MaRDI profile type: Publication
full work available at URL: s004540010059
OpenAlex ID: W2015894975
DOI: 10.1007/S004540010059
description: scientific article; zbMATH DE number 1495784