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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: https://drops.dagstuhl.de/opus/volltexte/2013/3940/
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
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: |
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geometric folding, linkages, universality |
Collection: |
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30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013) |
Issue Date: |
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2013 |
Date of publication: |
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26.02.2013 |