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°].

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The paper is 4 pages.

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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 Erik Demaine.