Paper by Erik D. Demaine

Therese C. Biedl, Erik D. Demaine, Sylvain Lazard, Steven M. Robbins, and Michael A. Soss, “Convexifying Monotone Polygons”, Technical Report CS-99-03, Department of Computer Science, University of Waterloo, March 1999.

This paper considers reconfigurations of polygons, where each polygon edge is a rigid link, no two of which can cross during the motion. We prove that one can reconfigure any monotone polygon into a convex polygon; a polygon is monotone if any vertical line intersects the interior at a (possibly empty) interval. Our algorithm computes in O(n2) time a sequence of O(n2) moves, each of which rotates just four joints at once.

The paper is 12 pages.

The paper is available in PostScript (242k).
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Related papers:
ISAAC99 (Convexifying Monotone Polygons)

Related webpages:
Carpenter's Rule Theorem

See also other papers by Erik Demaine.
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Last updated January 15, 2021 by Erik Demaine.