2009 | OriginalPaper | Buchkapitel
A Pseudopolynomial Algorithm for Alexandrov’s Theorem
verfasst von : Daniel Kane, Gregory N. Price, Erik D. Demaine
Erschienen in: Algorithms and Data Structures
Verlag: Springer Berlin Heidelberg
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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 to arbitrary precision given the metric, and prove a pseudopolynomial bound on its running time.