Paper by Erik D. Demaine

Reference:

Greg Aloupis, Erik D. Demaine, Henk Meijer, Joseph O'Rourke, Ileana Streinu, and Godfried Toussaint, “On Flat-State Connectivity of Chains with Fixed Acute Angles”, in Proceedings of the 14th Canadian Conference on Computational Geometry (CCCG 2002), Lethbridge, Alberta, Canada, August 12–14, 2002, pages 27–30.

BibTeX

@InProceedings{Flat2Flat_CCCG2002,
  AUTHOR        = {Greg Aloupis and Erik D. Demaine and Henk Meijer and Joseph
                   O'Rourke and Ileana Streinu and Godfried Toussaint},
  TITLE         = {On Flat-State Connectivity of Chains with Fixed Acute Angles},
  BOOKTITLE     = {Proceedings of the 14th Canadian Conference on Computational
                   Geometry (CCCG 2002)},
  bookurl       = {http://www.cs.uleth.ca/cccg},
  ADDRESS       = {Lethbridge, Alberta, Canada},
  MONTH         = {August 12--14},
  YEAR          = 2002,
  PAGES         = {27--30},

  LENGTH        = {4 pages},
  PAPERS        = {Flat2Flat_ISAAC2002},
  COMMENTS      = {This paper is also available from the
                   <A HREF="http://www.cs.uleth.ca/~wismath/cccg/proceedings/">
                   electronic proceedings</A> as
                   <A HREF="http://www.cs.uleth.ca/~wismath/cccg/papers/16.ps">http://www.cs.uleth.ca/~wismath/cccg/papers/16.ps</A>.},
  unrefereed    = 1,
  dblp          = {https://dblp.org/rec/conf/cccg/AloupisDMOST02},
  ee            = {http://www.cs.uleth.ca/~wismath/cccg/papers/16.ps},
}

Abstract:

We prove that two classes of fixed-angle, open chains with acute angles are “flat-state connected.” A chain is flat-state connected if it can be reconfigured between any two of its planar realizations without self-crossing. In a companion paper (under preparation) [ADD⁺], several fixed-angle linkages will be proved flat-state connected or disconnected. In particular, all orthogonal or obtuse-angle open chains are flat-state connected. But it remains open whether this holds for acute-angle open chains. In this paper, we prove that two classes of such chains are indeed flat-state connected: those with equal acute angles, and those with equal edge lengths and angles in (60°, 90°].

Comments:

This paper is also available from the electronic proceedings as http://www.cs.uleth.ca/~wismath/cccg/papers/16.ps.

Length:

The paper is 4 pages.

Availability:

The paper is available in PostScript (1005k), gzipped PostScript (303k), and PDF (129k).

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