On Reconfiguring Tree Linkages: Trees can lock

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 $2^{\Omega(N)}$ equivalence classes of configurations.
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https://hal.inria.fr/inria-00099329
Contributor : Sylvain Lazard <>
Submitted on : Tuesday, September 26, 2006 - 8:52:55 AM
Last modification on : Thursday, January 11, 2018 - 6:19:48 AM

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  • HAL Id : inria-00099329, version 1

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Thérèse Biedl, Erik Demaine, Martin Demaine, Sylvain Lazard, Anna Lubiw, et al.. On Reconfiguring Tree Linkages: Trees can lock. [Intern report] A00-R-388 || biedl00a, 2000, 16 p. ⟨inria-00099329⟩

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