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https://hdl.handle.net/10119/14769
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| Title: | Bumpy Pyramid Folding |
| Authors: | Abel, Zachary R.
Demaine, Erik D.
Demaine, Martin L.
Ito, Hiro
Snoeyink, Jack
Uehara, Ryuhei |
| Keywords: | folding problem
pyramid
petal polygon
Alexandrov's theorem |
| Issue Date: | 2014-08 |
| Publisher: | CCCG 2014 |
| Magazine name: | The 26th Canadian Conference on Computational Geometry (CCCG 2014) |
| Start page: | 258 |
| End page: | 266 |
| 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. |
| Rights: | Copyright (C) 2014 Authors. Zachary R. Abel, Erik D. Demaine, Martin L. Demaine, Hiro Ito, Jack Snoeyink and Ryuhei Uehara, The 26th Canadian Conference on Computational Geometry (CCCG 2014), 2014, 258-266. |
| URI: | https://hdl.handle.net/10119/14769 |
| Material Type: | publisher |
| Appears in Collections: | b11-1. 会議発表論文・発表資料 (Conference Papers)
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| 20453.pdf | | 177Kb | Adobe PDF | View/Open |
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