Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Abel, Zachary; Demaine, Erik D.; Demaine, Martin L.; Eisenstat, Sarah; Lubiw, Anna; Schulz, André; Souvaine, Diane L.; Viglietta, Giovanni; Winslow, Andrew License: Creative Commons Attribution-NoDerivs 3.0 Unported license (CC BY-ND 3.0)
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URN: urn:nbn:de:0030-drops-39407

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Algorithms for Designing Pop-Up Cards



We prove that every simple polygon can be made as a (2D) pop-up card/book that opens to any desired angle between 0 and 360°. More precisely, given a simple polygon attached to the two walls of the open pop-up, our polynomial-time algorithm subdivides the polygon into a single-degree-of-freedom linkage structure, such that closing the pop-up flattens the linkage without collision. This result solves an open problem of Hara and Sugihara from 2009. We also show how to obtain a more efficient construction for the special case of orthogonal polygons, and how to make 3D orthogonal polyhedra, from pop-ups that open to 90°, 180°, 270°, or 360°.

BibTeX - Entry

  author =	{Zachary Abel and Erik D. Demaine and Martin L. Demaine and Sarah Eisenstat and Anna Lubiw and Andr{\'e} Schulz and Diane L. Souvaine and Giovanni Viglietta and Andrew Winslow},
  title =	{{Algorithms for Designing Pop-Up Cards}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{269--280},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Natacha Portier and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-39407},
  doi =		{10.4230/LIPIcs.STACS.2013.269},
  annote =	{Keywords: geometric folding, linkages, universality}

Keywords: geometric folding, linkages, universality
Seminar: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Issue date: 2013
Date of publication: 26.02.2013

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