MIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Algorithms for Designing Pop-Up Cards

Author(s)
Abel, Zachary Ryan; Demaine, Erik D.; Demaine, Martin L.; Eisenstat, Sarah Charmian; Lubiw, Anna; Schulz, Andre; Souvaine, Diane L.; Viglietta, Giovanni; Winslow, Andrew; ... Show more Show less
Thumbnail
DownloadDemaine_Algorithms for.pdf (1.207Mb)
PUBLISHER_CC

Publisher with Creative Commons License

Creative Commons Attribution

Terms of use
Creative Commons Attribution http://creativecommons.org/
Metadata
Show full item record
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°.
Date issued
2013-02
URI
http://hdl.handle.net/1721.1/87552
Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Mathematics
Journal
Proceedings of the 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Publisher
Schloss Dagstuhl Publishing
Citation
Abel, Zachary, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Anna Lubiw, Andre Schulz, Diane L. Souvaine, Giovanni Viglietta, and Andrew Winslow. "Algorithms for Designing Pop-Up Cards." Natacha Portier and Thomas Wilke (Eds.) 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013), February 27-March 2, 2013, Kiel, Germany (Leibniz International Proceedings in Informatics (LIPIcs) ; Volume 20). p.269-280.
Version: Final published version
ISBN
978-3-939897-50-7
ISSN
868-8969

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries
PrivacyPermissionsAccessibilityContact us
MIT
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.