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. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Kane, D., Price, G. N., & Demaine, E. D. (2009). A pseudopolynomial algorithm for Alexandrov’s theorem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5664 LNCS, pp. 435–446). https://doi.org/10.1007/978-3-642-03367-4_38
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