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100406 |
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|a Abel, Zachary Ryan
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|a Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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|a Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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|a Massachusetts Institute of Technology. Department of Mathematics
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|a Abel, Zachary Ryan
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|a Demaine, Erik D.
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|a Demaine, Martin L.
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|a Demaine, Erik D.
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|a Demaine, Martin L.
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|a Ito, Hiro
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|a Snoeyink, Jack
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|a Uehara, Ryuhei
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|a Bumpy pyramid folding
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|c 2015-12-17T01:55:59Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/100406
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|a 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.
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|a Article
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|t Proceedings of the 26th Canadian Conference on Computational Geometry
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