Bumpy pyramid folding
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Demaine_Bumpy pyramid.pdf
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135.98 KB
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Adobe PDF
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Author(s)
Abel, Zachary Ryan
Demaine, Erik D.
Demaine, Martin L.
Ito, Hiro
Snoeyink, Jack
Uehara, Ryuhei
Date Issued
August 2014
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
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.
MIT 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
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Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
http://www.cccg.ca/proceedings/2014/
