2 research outputs found
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 a unique convex polyhedron. Recent work by Bobenko and Izmestiev describes a
differential equation whose solution leads to 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. Along the way, we develop
pseudopolynomial algorithms for computing shortest paths and weighted Delaunay
triangulations on a polyhedral surface, even when the surface edges are not
shortest paths.Comment: 25 pages; new Delaunay triangulation algorithm, minor other changes;
an abbreviated v2 was at WADS 200
09111 Abstracts Collection -- Computational Geometry
From March 8 to March 13, 2009, the Dagstuhl Seminar 09111 ``Computational Geometry \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available