Paper by Erik D. Demaine

Robert Connelly, Erik D. Demaine, and Günter Rote, “Straightening Polygonal Arcs and Convexifying Polygonal Cycles”, in Proceedings of the 41st Annual Symposium on Foundations of Computer Science (FOCS 2000), Redondo Beach, California, November 12–14, 2000, pages 432–442.

Consider a planar linkage, consisting of disjoint polygonal arcs and cycles of rigid bars joined at incident endpoints (polygonal chains), with the property that no cycle surrounds another arc or cycle. We prove that the linkage can be continuously moved so that the arcs become straight, the cycles become convex, and no bars cross while preserving the bar lengths. Furthermore, our motion is piecewise-differentiable, does not decrease the distance between any pair of vertices, and preserves any symmetry present in the initial configuration. In particular, this result settles the well-studied carpenter's rule conjecture.

Ivars Peterson wrote an article describing these results, “Unlocking Puzzling Polygons”, Science News 158(13):200-201, September 23, 2000.

Joseph O'Rourke also wrote an article describing these results, “Computational Geometry Column 39”, International Journal of Computational Geometry and Applications, 10(4):441-444, 2000.

The paper is 11 pages.

The paper is available in PostScript (453k) and gzipped PostScript (114k).
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Related papers:
Linkage (Straightening Polygonal Arcs and Convexifying Polygonal Cycles)
LinkageTR (Straightening Polygonal Arcs and Convexifying Polygonal Cycles)
EuroCG2000 (Every Polygon Can Be Untangled)

Related webpages:
Carpenter's Rule Theorem

See also other papers by Erik Demaine.
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Last updated May 16, 2024 by Erik Demaine.