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DOI: 10.4230/DagSemProc.09111.2
URN: urn:nbn:de:0030-drops-20328
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Kane, Daniel ; Price, Gregory Nathan ; Demaine, Erik

A Pseudopolynomial Algorithm for Alexandrov's Theorem

09111.DemaineErik.Paper.2032.pdf (0.2 MB)


Alexandrov's Theorem states that every metric with the global topology and local geometry required of a convex polyhedron is in fact the intrinsic metric of some convex polyhedron. Recent work by Bobenko and Izmestiev describes a differential equation whose solution is the polyhedron corresponding to a given metric. We describe an algorithm based on this differential equation to compute the polyhedron given the metric, and prove a pseudopolynomial bound on its running time.

BibTeX - Entry

  author =	{Kane, Daniel and Price, Gregory Nathan and Demaine, Erik},
  title =	{{A Pseudopolynomial Algorithm for Alexandrov's Theorem}},
  booktitle =	{Computational Geometry},
  pages =	{1--22},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9111},
  editor =	{Pankaj Kumar Agarwal and Helmut Alt and Monique Teillaud},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-20328},
  doi =		{10.4230/DagSemProc.09111.2},
  annote =	{Keywords: Folding, metrics, pseudopolynomial, algorithms}

Keywords: Folding, metrics, pseudopolynomial, algorithms
Collection: 09111 - Computational Geometry
Issue Date: 2009
Date of publication: 23.06.2009

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