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

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Comments

Peer reviewed post-print. Licensed CC-BY-NC-ND at the request of the publisher.

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