DagSemProc.09111.2.pdf
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A Pseudopolynomial Algorithm for Alexandrov's Theorem
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Dagstuhl Seminar Proceedings, Volume 9111
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2009-06-23
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Daniel Kane, Gregory Nathan Price, and Erik Demaine. A Pseudopolynomial Algorithm for Alexandrov's Theorem. In Computational Geometry. Dagstuhl Seminar Proceedings, Volume 9111, pp. 1-22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/DagSemProc.09111.2
Abstract
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.
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Keywords
- Folding
- metrics
- pseudopolynomial
- algorithms
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