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.

Bumpy pyramid folding

Author(s)
Abel, Zachary Ryan; Demaine, Erik D.; Demaine, Martin L.; Ito, Hiro; Snoeyink, Jack; Uehara, Ryuhei; ... Show more Show less
Thumbnail
DownloadDemaine_Bumpy pyramid.pdf (135.9Kb)
OPEN_ACCESS_POLICY

Open Access Policy

Creative Commons Attribution-Noncommercial-Share Alike

Terms of use
Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
Metadata
Show full item record
Abstract
We investigate folding problems for a class of petal polygons P, which have an n-polygonal base B surrounded by a sequence of triangles. We give linear time algorithms using constant precision to determine if P can fold to a pyramid with flat base B, and to determine a triangulation of B (crease pattern) that allows folding into a convex (triangulated) polyhedron. By Alexandrov’s theorem, the crease pattern is unique if it exists, but the general algorithm known for this theorem is pseudo-polynomial, with very large running time; ours is the first efficient algorithm for Alexandrov’s theorem for a special class of polyhedra. We also give a polynomial time algorithm that finds the crease pattern to produce the maximum volume triangulated polyhedron.
Date issued
2014-08
URI
http://hdl.handle.net/1721.1/100406
Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Department of Mathematics
Journal
Proceedings of the 26th Canadian Conference on Computational Geometry
Citation
Abel, Zachary R., Erik D. Demaine, Martin L. Demaine, Hiro Ito, Jack Snoeyink, Ryuhei Uehara. "Bumpy pyramid folding." 26th Canadian Conference on Computational Geometry (August 2014).
Version: Author's final manuscript

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.