Covering folded shapes

Covering folded shapes

Can folding a piece of paper flat make it larger? We explore whether a shape <span>S </span><span>must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary folds (continuous piecewise isometries \(S\to\mathbb{R}^2\)). The underlying problem i...

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Main Authors: Oswin Aichholzer, Greg Aloupis, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Michael Hoffmann, Anna Lubiw, Jack Snoeyink, Andrew Winslow
Format: Article
Language:English
Published: Carleton University 2014-05-01
Series:Journal of Computational Geometry
Online Access:http://jocg.org/index.php/jocg/article/view/160
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spelling doaj-4aa7d08e90f144ac8e4b7f8071cb1d8a2020-11-24T22:32:39ZengCarleton UniversityJournal of Computational Geometry1920-180X2014-05-015110.20382/jocg.v5i1a851Covering folded shapesOswin Aichholzer0Greg Aloupis1Erik D. Demaine2Martin L. Demaine3Sándor P. Fekete4Michael Hoffmann5Anna Lubiw6Jack Snoeyink7Andrew Winslow8TU GrazTufts UniversityMITMITTU BraunschweigETH ZurichUniversity of WaterlooUniversity of North CarolinaTufts UniversityCan folding a piece of paper flat make it larger? We explore whether a shape <span>S </span><span>must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary folds (continuous piecewise isometries \(S\to\mathbb{R}^2\)). The underlying problem is motivated by computational origami, and is related to other covering and fixturing problems, such as Lebesgue's universal cover problem and force closure grasps. In addition to considering special shapes (squares, equilateral triangles, polygons and disks), we give upper and lower bounds on scale factors for single folds of convex objects and arbitrary folds of simply connected objects.</span>http://jocg.org/index.php/jocg/article/view/160
collection DOAJ
language English
format Article
sources DOAJ
author Oswin Aichholzer
Greg Aloupis
Erik D. Demaine
Martin L. Demaine
Sándor P. Fekete
Michael Hoffmann
Anna Lubiw
Jack Snoeyink
Andrew Winslow
spellingShingle Oswin Aichholzer
Greg Aloupis
Erik D. Demaine
Martin L. Demaine
Sándor P. Fekete
Michael Hoffmann
Anna Lubiw
Jack Snoeyink
Andrew Winslow
Covering folded shapes
Journal of Computational Geometry
author_facet Oswin Aichholzer
Greg Aloupis
Erik D. Demaine
Martin L. Demaine
Sándor P. Fekete
Michael Hoffmann
Anna Lubiw
Jack Snoeyink
Andrew Winslow
author_sort Oswin Aichholzer
title Covering folded shapes
title_short Covering folded shapes
title_full Covering folded shapes
title_fullStr Covering folded shapes
title_full_unstemmed Covering folded shapes
title_sort covering folded shapes
publisher Carleton University
series Journal of Computational Geometry
issn 1920-180X
publishDate 2014-05-01
description Can folding a piece of paper flat make it larger? We explore whether a shape <span>S </span><span>must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary folds (continuous piecewise isometries \(S\to\mathbb{R}^2\)). The underlying problem is motivated by computational origami, and is related to other covering and fixturing problems, such as Lebesgue's universal cover problem and force closure grasps. In addition to considering special shapes (squares, equilateral triangles, polygons and disks), we give upper and lower bounds on scale factors for single folds of convex objects and arbitrary folds of simply connected objects.</span>
url http://jocg.org/index.php/jocg/article/view/160
work_keys_str_mv AT oswinaichholzer coveringfoldedshapes
AT gregaloupis coveringfoldedshapes
AT erikddemaine coveringfoldedshapes
AT martinldemaine coveringfoldedshapes
AT sandorpfekete coveringfoldedshapes
AT michaelhoffmann coveringfoldedshapes
AT annalubiw coveringfoldedshapes
AT jacksnoeyink coveringfoldedshapes
AT andrewwinslow coveringfoldedshapes
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