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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2013.269
URN: urn:nbn:de:0030-drops-39407
URL: http://drops.dagstuhl.de/opus/volltexte/2013/3940/
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Abel, Zachary ; Demaine, Erik D. ; Demaine, Martin L. ; Eisenstat, Sarah ; Lubiw, Anna ; Schulz, André ; Souvaine, Diane L. ; Viglietta, Giovanni ; Winslow, Andrew

Algorithms for Designing Pop-Up Cards

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Abstract

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

@InProceedings{abel_et_al:LIPIcs:2013:3940,
  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 =		{http://drops.dagstuhl.de/opus/volltexte/2013/3940},
  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: 18.02.2013


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