Covering Folded Shapes

Oswin Aichholzer; Greg Aloupis; Erik D. Demaine; Martin L. Demaine; ͆andor P. Fekete; Michael Hoffmann; Anna Lubiw; Jack Snoeyink; Andrew Winslow

doi:10.20382/jocg.v5i1a8

Covering Folded Shapes

Oswin Aichholzer, Greg Aloupis, Erik D. Demaine, Martin L. Demaine, ͆andor P. Fekete, Michael Hoffmann, Anna Lubiw, Jack Snoeyink, Andrew Winslow

Institute of Software Technology (7160)

Research output: Contribution to journal › Conference article › peer-review

Abstract

Can folding a piece of paper flat make it larger? We explore whether a shape S must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary folds (continuous piecewise isometries S ! R2). 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.

Original language	English
Pages (from-to)	150-168
Number of pages	6
Journal	Journal of Computational Geometry
Volume	5
Issue number	1
DOIs	https://doi.org/10.20382/jocg.v5i1a8
Publication status	Published - 2014
Event	25th Canadian Conference on Computational Geometry: CCCG 2013 - Waterloo, Canada Duration: 8 Aug 2013 → 10 Aug 2013

ASJC Scopus subject areas

Geometry and Topology
Computational Mathematics

Fields of Expertise

Information, Communication & Computing

Treatment code (Nähere Zuordnung)

Basic - Fundamental (Grundlagenforschung)

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10.20382/jocg.v5i1a8Licence: CC BY 3.0

Cite this

@article{41affbb7820d47159a392cbdc85ce929,

title = "Covering Folded Shapes",

abstract = "Can folding a piece of paper flat make it larger? We explore whether a shape S must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary folds (continuous piecewise isometries S ! R2). 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.",

author = "Oswin Aichholzer and Greg Aloupis and Demaine, {Erik D.} and Demaine, {Martin L.} and Fekete, {͆andor P.} and Michael Hoffmann and Anna Lubiw and Jack Snoeyink and Andrew Winslow",

year = "2014",

doi = "10.20382/jocg.v5i1a8",

language = "English",

volume = "5",

pages = "150--168",

journal = "Journal of Computational Geometry ",

issn = "1920-180X",

publisher = "Carleton University",

number = "1",

note = "25th Canadian Conference on Computational Geometry : CCCG 2013, CCCG 2013 ; Conference date: 08-08-2013 Through 10-08-2013",

}

TY - JOUR

T1 - Covering Folded Shapes

AU - Aichholzer, Oswin

AU - Aloupis, Greg

AU - Demaine, Erik D.

AU - Demaine, Martin L.

AU - Fekete, ͆andor P.

AU - Hoffmann, Michael

AU - Lubiw, Anna

AU - Snoeyink, Jack

AU - Winslow, Andrew

PY - 2014

Y1 - 2014

N2 - Can folding a piece of paper flat make it larger? We explore whether a shape S must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary folds (continuous piecewise isometries S ! R2). 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.

AB - Can folding a piece of paper flat make it larger? We explore whether a shape S must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary folds (continuous piecewise isometries S ! R2). 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.

U2 - 10.20382/jocg.v5i1a8

DO - 10.20382/jocg.v5i1a8

M3 - Conference article

SN - 1920-180X

VL - 5

SP - 150

EP - 168

JO - Journal of Computational Geometry

JF - Journal of Computational Geometry

IS - 1

T2 - 25th Canadian Conference on Computational Geometry

Y2 - 8 August 2013 through 10 August 2013

ER -

Covering Folded Shapes

Abstract

ASJC Scopus subject areas

Fields of Expertise

Treatment code (Nähere Zuordnung)

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