A Pseudopolynomial Algorithm for Alexandrov's Theorem
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.
Folding
metrics
pseudopolynomial
algorithms
1-22
Regular Paper
Daniel
Kane
Daniel Kane
Gregory Nathan
Price
Gregory Nathan Price
Erik
Demaine
Erik Demaine
10.4230/DagSemProc.09111.2
Creative Commons Attribution 4.0 International license
https://creativecommons.org/licenses/by/4.0/legalcode