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A Note on Reconfiguring Tree Linkages: Trees can Lock

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 $2^{Omega(N)}$ equivalence classes of configurations.
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https://hal.inria.fr/inria-00100889
Contributor : Sylvain Lazard <>
Submitted on : Tuesday, September 26, 2006 - 2:52:42 PM
Last modification on : Friday, February 26, 2021 - 3:28:03 PM

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Thérèse Biedl, Erik Demaine, Martin Demaine, Sylvain Lazard, Anna Lubiw, et al.. A Note on Reconfiguring Tree Linkages: Trees can Lock. Discrete Applied Mathematics, Elsevier, 2002, 117 (1-3), pp.293-297. ⟨10.1016/S0166-218X(01)00229-3⟩. ⟨inria-00100889⟩

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