Document Type
Article
Publication Date
11-2001
Publication Title
Computational Geometry
Abstract
We prove that, in all dimensions d ≥ 4, every simple open polygonal chain and every tree may be straightened, and every simple closed polygonal chain may be convexified. These reconfigurations can be achieved by algorithms that use polynomial time in the number of vertices, and result in a polynomial number of “moves.” These results contrast to those known for d = 2, where trees can “lock,” and for d = 3, where open and closed chains can lock.
Keywords
Polygonal chain, Bar framework, Knots, Locked chains
Volume
20
Issue
3
First Page
105
Last Page
129
DOI
dx.doi.org/10.1016/S0925-7721(01)00013-X
ISSN
0925-7721
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Cocan, Roxana and O'Rourke, Joseph, "Polygonal Chains Cannot Lock in 4D" (2001). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/80
Comments
Peer reviewed accepted manuscript. Licensed CC-BY-NC-ND at the request of the publisher.