A pseudopolynomial algorithm for Alexandrov's theorem
Author(s)Kane, Daniel; Price, Gregory N.; Demaine, Erik D.
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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.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Algorithms and data structures (Conference)
Kane, Daniel, Gregory N. Price and Erik D. Demaine, "A Pseudopolynomial Algorithm for Alexandrov’s Theorem" Algorithms and data structures (Lecture notes in computer science, v. 5664,2009)435-446. Copyright © 2009, Springer .
Author's final manuscript