Paper by Erik D. Demaine

Reference:

Greg Aloupis, Erik D. Demaine, Vida Dujmović, Jeff Erickson, Stefan Langerman, Henk Meijer, Joseph O'Rourke, Mark Overmars, Michael Soss, Ileana Streinu, and Godfried Toussaint, “Flat-State Connectivity of Linkages under Dihedral Motions”, in Proceedings of the 13th Annual International Symposium on Algorithms and Computation (ISAAC 2002), Lecture Notes in Computer Science, volume 2518, Vancouver, British Columbia, Canada, November 20–23, 2002, pages 369–380.

BibTeX

@InProceedings{Flat2Flat_ISAAC2002,
  AUTHOR        = {Greg Aloupis and Erik D. Demaine and Vida Dujmovi\'c and
                   Jeff Erickson and Stefan Langerman and Henk Meijer and
                   Joseph O'Rourke and Mark Overmars and Michael Soss and
                   Ileana Streinu and Godfried Toussaint},
  TITLE         = {Flat-State Connectivity of Linkages under Dihedral Motions},
  BOOKTITLE     = {Proceedings of the 13th Annual International Symposium on
                   Algorithms and Computation (ISAAC 2002)},
  bookurl       = {http://cg.scs.carleton.ca/~isaac02/},
  ADDRESS       = {Vancouver, British Columbia, Canada},
  MONTH         = {November 20--23},
  YEAR          = 2002,
  PAGES         = {369--380},
  SERIES        = {Lecture Notes in Computer Science},
  SERIESURL     = {http://www.springer.de/comp/lncs/},
  VOLUME        = 2518,

  COPYRIGHT     = {The paper is \copyright Springer-Verlag.},
  LENGTH        = {12 pages},
  PAPERS        = {Flat2Flat_CCCG2002},
  COMMENTS      = {This paper is also available from <A HREF="https://doi.org/10.1007/3-540-36136-7_33">SpringerLink</A>.},
}

Abstract:

We explore which classes of linkages have the property that each pair of their flat states—that is, their embeddings in R² without self-intersection—can be connected by a continuous dihedral motion that avoids self-intersection throughout. Dihedral motions preserve all angles between pairs of incident edges, which is most natural for protein models. Our positive results include proofs that open chains with nonacute angles are flat-state connected, as are closed orthogonal unit-length chains. Among our negative results is an example of an orthogonal graph linkage that is flat-state disconnected. Several additional results are obtained for other restricted classes of linkages. Many open problems are posed.

Comments:

This paper is also available from SpringerLink.

Copyright:

The paper is \copyright Springer-Verlag.

Length:

The paper is 12 pages.

Availability:

The paper is available in PostScript (966k), gzipped PostScript (276k), and PDF (178k).

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Flat2Flat_CCCG2002 (Flat-State Connectivity of Chains with Fixed Acute Angles)