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A Note on Reconfiguring Tree Linkages: Trees can Lock

Thérèse Biedl 1 Erik Demaine 1 Martin Demaine 1 Sylvain Lazard 2 Anna Lubiw 1 Joseph O'Rourke 1 Steve Robbins 3 Ileana Streinu 1 Godfried Toussaint 3 Sue Whitesides 3
1 CPSC - Department of Computer Science [Calgary]
2 ISA - Models, algorithms and geometry for computer graphics and vision
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
3 SCS - School of computer science [Ottawa]
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.
Keywords : distance geometry. motion planning linkage reconfiguration graph embedding tree embedding reconfiguration de mécanismes articulés planification de trajectoires
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https://hal.inria.fr/inria-00100889
Contributor : Sylvain Lazard Connect in order to contact the contributor
Submitted on : Tuesday, September 26, 2006 - 2:52:42 PM
Last modification on : Friday, February 4, 2022 - 3:16:58 AM

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INRIA | CNRS | LORIA | UNIV-LORRAINE | INRIA2

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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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