Paper by Martin L. Demaine

T. Biedl, E. Demaine, M. Demaine, S. Lazard, A. Lubiw, J. O'Rourke, M. Overmars, S. Robbins, I. Streinu, G. Toussaint, and S. Whitesides, “Locked and Unlocked Polygonal Chains in 3D”, Technical Report 060, Smith College, October 1999.

In this paper, we study movements of simple polygonal chains in 3D. We say that an open, simple polygonal chain can be straightened if it can be continuously reconfigured to a straight sequence of segments in such a manner that both the length of each link and the simplicity of the chain are maintained throughout the movement. The analogous concept for closed chains is convexification: reconfiguration to a planar convex polygon. Chains that cannot be straightened or convexified are called locked. While there are open chains in 3D that are locked, we show that if an open chain has a simple orthogonal projection onto some plane, it can be straightened. For closed chains, we show that there are unknotted but locked closed chains, and we provide an algorithm for convexifying a planar simple polygon in 3D. All our algorithms require only O(n) basic “moves” and run in linear time.

This paper is also available as arXiv:cs.CG/9910009 of the Computing Research Repository (CoRR).

The paper is 29 pages.

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Related papers:
3DChains_DCG2001 (Locked and Unlocked Polygonal Chains in Three Dimensions)
SODA99c (Locked and Unlocked Polygonal Chains in 3D)

See also other papers by Martin Demaine.
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