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 Three Dimensions”, Discrete & Computational Geometry, volume 26, number 3, October 2001, pages 269–281.
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.”
- This paper is also available from SpringerLink.
- The paper is 29 pages.
- The paper is available in PostScript (491k) and gzipped PostScript (166k).
- See information on file formats.
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- Related papers:
- 3DChainsTR (Locked and Unlocked Polygonal Chains in 3D)
- SODA99c (Locked and Unlocked Polygonal Chains in 3D)
See also other papers by Erik Demaine.
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