On Reconfiguring Tree Linkages: Trees Can Lock

Authors

Therese Biedl, University of Waterloo
Erik D. Demaine, University of Waterloo
Martin L. Demaine, University of Waterloo
Sylvain Lazard, Institut National de Recherche en Informatique et en Automatique, Lorraine
Anna Lubiw, University of Waterloo
Joseph O'Rourke, Smith CollegeFollow
Steve Robbins, McGill University
Ileana Streinu, Smith CollegeFollow
Godfried Toussaint, McGill University
Sue Whitesides, McGill University

Document Type

Article

Publication Date

9-29-2000

Abstract

It has recently been shown that any simple (i.e. nonintersecting) polygonal chain in the plane can be reconfigured to lie on a straight line, and any simple polygon can be reconfigured to be convex. This result cannot be extended to tree linkages: we show that there are trees with two simple configurations that are not connected by a motion that preserves simplicity throughout the motion. Indeed, we prove that an N-link tree can have 2^Ω(N) equivalence classes of configurations.

Comments

Author’s submitted manuscript.

Recommended Citation

Biedl, Therese; Demaine, Erik D.; Demaine, Martin L.; Lazard, Sylvain; Lubiw, Anna; O'Rourke, Joseph; Robbins, Steve; Streinu, Ileana; Toussaint, Godfried; and Whitesides, Sue, "On Reconfiguring Tree Linkages: Trees Can Lock" (2000). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/72