Paper by Erik D. Demaine

Reference:

Oswin Aichholzer, Erik D. Demaine, Jeff Erickson, Ferran Hurtado, Mark Overmars, Michael A. Soss, and Godfried T. Toussaint, “Reconfiguring Convex Polygons”, Computational Geometry: Theory and Applications, volume 20, number 1–2, October 2001, pages 85–95. Special issue of selected papers from the 12th Annual Canadian Conference on Computational Geometry, 2000.

Abstract:

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. We also demonstrate that there is a motion between any two such polygons using three-dimensional moves known as pivots, although the complexity of the motion cannot be bounded as a function of the number of vertices in the polygon.

Comments:

This paper is also available from ScienceDirect.

Copyright:

The paper is \copyright Elsevier Science B.V.

Length:

The paper is 13 pages.

Availability:

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