Locked and Unlocked Polygonal Chains in 3D

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dc.creatorBiedl, T.
dc.creatorDemaine, E.
dc.creatorDemaine, M.
dc.creatorLazard, S.
dc.creatorLubiw, A.
dc.creatorO'Rourke, J.
dc.creatorOvermars, M.
dc.creatorRobbins, S.
dc.creatorStreinu, I.
dc.creatorToussaint, G.
dc.creatorWhitesides, S.
dc.date1998-11-11
dc.date.accessioned2026-07-07T03:23:48Z
dc.date.available2026-07-07T03:23:48Z
dc.descriptionIn 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.
dc.descriptionTo appear in Proc. 10th ACM-SIAM Sympos. Discrete Algorithms, Jan. 1999
dc.identifierhttps://arxiv.org/abs/cs/9811019
dc.identifierhttp://arxiv.org/abs/cs/9811019
dc.identifierProc. 10th ACM-SIAM Sympos. Discrete Algorithms, Jan. 1999, pp. S866-7.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/33090
dc.subjectComputational Geometry
dc.subjectData Structures and Algorithms
dc.subjectRobotics
dc.subjectF.2.2; I.2.9
dc.titleLocked and Unlocked Polygonal Chains in 3D
dc.typetext

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