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On Reconfiguring Tree Linkages: Trees can Lock

By Therese Biedl, Erik Demaine, Martin Demaine, Sylvain Lazard, Anna Lubiw, Joseph O&apos, Steve Robbins, Ileana Streinu, Godfried Toussaint and Sue Whitesides

Abstract

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

Year: 2000
OAI identifier: oai:CiteSeerX.psu:10.1.1.32.2938
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