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# Locked and Unlocked Polygonal Chains in Three Dimensions

2 ISA - Models, algorithms and geometry for computer graphics and vision
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : This paper studies movements of polygonal chains in three dimensions whose links are not allowed to cross or change length. Our main result is an algorithmic proof that any simple closed chain that initially takes the form of a planar polygon can be made convex in three dimensions. Other results include an algorithm for straightening open chains having a simple orthogonal projection onto some plane, and an algorithm for making convex any open chain initially configured on the surface of a polytope. All our algorithms require only O(n) basic moves.''
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Document type :
Journal articles
Domain :

https://hal.inria.fr/inria-00100521
Contributor : Sylvain Lazard Connect in order to contact the contributor
Submitted on : Tuesday, September 26, 2006 - 2:46:27 PM
Last modification on : Friday, February 4, 2022 - 3:15:31 AM

### Citation

Thérèse Biedl, Erik Demaine, Martin Demaine, Sylvain Lazard, Anna Lubiw, et al.. Locked and Unlocked Polygonal Chains in Three Dimensions. Discrete and Computational Geometry, Springer Verlag, 2001, 26 (3), pp.269-281. ⟨10.1007/s00454-001-0038-7⟩. ⟨inria-00100521⟩

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