Paper by Erik D. Demaine

Oswin Aichholzer, Erik D. Demaine, Jeff Erickson, Ferran Hurtado, Mark Overmars, Michael A. Soss, and Godfried T. Toussaint, “Reconfiguring Convex Polygons”, in Proceedings of the 12th Annual Canadian Conference on Computational Geometry (CCCG 2000), Fredericton, New Brunswick, Canada, August 16–18, 2000, pages 17–20.

We prove that there is a motion from any convex polygon to any convex polygon with the same counterclockwise sequence of edge lengths, that preserves the lengths of the edges, and keeps the polygon convex at all times. Furthermore, the motion is “direct” (avoiding any intermediate canonical configuration like a subdivided triangle) in the sense that each angle changes monotonically throughout the motion. In contrast, we show that it is impossible to achieve such a result with each vertex-to-vertex distance changing monotonically.

This paper is also available from the electronic proceedings as

The paper is 4 pages and the talk is 25 minutes.

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Related papers:
ConvexPolygonsCGTA (Reconfiguring Convex Polygons)

Related webpages:
Carpenter's Rule Theorem

See also other papers by Erik Demaine.
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Last updated July 21, 2017 by Erik Demaine.