Paper by Erik D. 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.
- The paper is available in PostScript (957k) and gzipped PostScript (256k).
- See information on file formats.
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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 Erik Demaine.
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