Chapter

Algorithms and Data Structures

Volume 5664 of the series Lecture Notes in Computer Science pp 435-446

A Pseudopolynomial Algorithm for Alexandrov’s Theorem

  • Daniel KaneAffiliated withDepartment of Mathematics, Harvard University
  • , Gregory N. PriceAffiliated withMIT Computer Science and Artificial Intelligence Laboratory
  • , Erik D. DemaineAffiliated withMIT Computer Science and Artificial Intelligence Laboratory

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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 to arbitrary precision given the metric, and prove a pseudopolynomial bound on its running time.