Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10225738 | Computational Geometry | 2018 | 18 Pages |
Abstract
We investigate folding problems for a class of petal (or star-like) polygons P, which have an n-polygonal base B surrounded by a sequence of triangles for which adjacent pairs of sides have equal length. We give linear time algorithms using constant precision to determine if P can fold to a pyramid with flat base B, and to determine a triangulation of B (crease pattern) that allows folding into a convex (triangulated) polyhedron. By Alexandrov's Theorem, the crease pattern is unique if it exists, but the general algorithm known for this theorem is pseudo-polynomial, with running time O(n456.5); ours is the first efficient algorithm for Alexandrov's Theorem for a special class of polyhedra. We also give a polynomial time algorithm that finds the crease pattern to produce the maximum volume triangulated polyhedron.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Zachary R. Abel, Erik D. Demaine, Martin L. Demaine, Hiro Ito, Jack Snoeyink, Ryuhei Uehara,