Locked and unlocked polygonal chains in 3D

T. Biedl, E. Demaine, M. Demaine, S. Lazard, A. Lubiw, J. O'Rourke, M. Overmars, S. Robbins, I. Streinu, Godfried Toussaint, S. Whitesides

Research output: Contribution to conferencePaper

Abstract

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.

Original languageEnglish (US)
StatePublished - Jan 1 1999
EventProceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms - Baltimore, MD, USA
Duration: Jan 17 1999Jan 19 1999

Other

OtherProceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms
CityBaltimore, MD, USA
Period1/17/991/19/99

Fingerprint

Polynomials
Closed
Convexification
Simple Polygon
Convex polygon
Orthogonal Projection
Reconfiguration
Straight
Simplicity
Polynomial

ASJC Scopus subject areas

  • Chemical Health and Safety
  • Software
  • Safety, Risk, Reliability and Quality
  • Discrete Mathematics and Combinatorics

Cite this

Biedl, T., Demaine, E., Demaine, M., Lazard, S., Lubiw, A., O'Rourke, J., ... Whitesides, S. (1999). Locked and unlocked polygonal chains in 3D. Paper presented at Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms, Baltimore, MD, USA, .

Locked and unlocked polygonal chains in 3D. / Biedl, T.; Demaine, E.; Demaine, M.; Lazard, S.; Lubiw, A.; O'Rourke, J.; Overmars, M.; Robbins, S.; Streinu, I.; Toussaint, Godfried; Whitesides, S.

1999. Paper presented at Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms, Baltimore, MD, USA, .

Research output: Contribution to conferencePaper

Biedl, T, Demaine, E, Demaine, M, Lazard, S, Lubiw, A, O'Rourke, J, Overmars, M, Robbins, S, Streinu, I, Toussaint, G & Whitesides, S 1999, 'Locked and unlocked polygonal chains in 3D', Paper presented at Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms, Baltimore, MD, USA, 1/17/99 - 1/19/99.
Biedl T, Demaine E, Demaine M, Lazard S, Lubiw A, O'Rourke J et al. Locked and unlocked polygonal chains in 3D. 1999. Paper presented at Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms, Baltimore, MD, USA, .
Biedl, T. ; Demaine, E. ; Demaine, M. ; Lazard, S. ; Lubiw, A. ; O'Rourke, J. ; Overmars, M. ; Robbins, S. ; Streinu, I. ; Toussaint, Godfried ; Whitesides, S. / Locked and unlocked polygonal chains in 3D. Paper presented at Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms, Baltimore, MD, USA, .
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