# On Reconfiguring Tree Linkages: Trees can lock

2 ISA - Models, algorithms and geometry for computer graphics and vision
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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.
Mots-clés :
Type de document :
Rapport
[Intern report] A00-R-388 || biedl00a, 2000, 16 p
Domaine :

https://hal.inria.fr/inria-00099329
Contributeur : Sylvain Lazard <>
Soumis le : mardi 26 septembre 2006 - 08:52:55
Dernière modification le : jeudi 11 janvier 2018 - 06:19:48

### Identifiants

• HAL Id : inria-00099329, version 1

### Citation

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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