Computer Science – Computational Geometry
Scientific paper
1998-11-11
Proc. 10th ACM-SIAM Sympos. Discrete Algorithms, Jan. 1999, pp. S866-7.
Computer Science
Computational Geometry
To appear in Proc. 10th ACM-SIAM Sympos. Discrete Algorithms, Jan. 1999
Scientific paper
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 with a polynomial number of moves.
Biedl Therese
Demaine Erik
Demaine M.
Lazard Sylvain
Lubiw Anna
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