Paper by Erik D. Demaine
- Greg Aloupis, Erik D. Demaine, Henk Meijer, Joseph O'Rourke, Ileana Streinu, and Godfried Toussaint, “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.
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°].
- This paper is also available from the electronic proceedings as http://www.cs.uleth.ca/~wismath/cccg/papers/16.ps.
- The paper is 4 pages.
- The paper is available in PostScript (1005k), gzipped PostScript (303k), and PDF (129k).
- See information on file formats.
- [Google Scholar search]
- Related papers:
- Flat2Flat_ISAAC2002 (Flat-State Connectivity of Linkages under Dihedral Motions)
See also other papers by Erik Demaine.
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Last updated March 9, 2018 by