eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-06-23
1
22
10.4230/DagSemProc.09111.2
article
A Pseudopolynomial Algorithm for Alexandrov's Theorem
Kane, Daniel
Price, Gregory Nathan
Demaine, Erik
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09111/DagSemProc.09111.2/DagSemProc.09111.2.pdf
Folding
metrics
pseudopolynomial
algorithms