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Every Polygon Can Be Untangled

By Günter Rote Erik D. Demaine Robert Connelly


Main Theorem. We consider a simple polygon in the plane as a system of rigid bars with movable joints at the vertices (a linkage or framework). We show that such a polygon can always be continuously reconfigured into convex position while avoiding self-intersection. Similarly, an open polygonal path (chain) can always be straightened. During this motion, whereas the lengths of the bars remain fixed, all other pairwise distances increase. 1.1. History and Applications; Related Work. This type of problem has been considered in discrete and computational geometry since an early work of Erd""os [5], in knot theory, and in molecular biology and polymer physics. Its applications include wire bending, hydraulic tube folding, and the study of macromolecule folding

Year: 2009
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