Paper by Erik D. Demaine

Reference:

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.

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).

See information on file formats.

[Google Scholar search]

Related papers:

Flat2Flat_ISAAC2002 (Flat-State Connectivity of Linkages under Dihedral Motions)