Covering Folded Shapes

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

Research output: Contribution to journalConference articlepeer-review


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 languageEnglish
Pages (from-to)150-168
Number of pages6
JournalJournal of Computational Geometry
Issue number1
Publication statusPublished - 2014
Event25th Canadian Conference on Computational Geometry: CCCG 2013 - Waterloo, Canada
Duration: 8 Aug 201310 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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