Connecting Polygonizations via Stretches and Twangs

Authors Mirela Damian, Robin Flatland, Joseph O'Rourke, Suneeta Ramaswani

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Mirela Damian
Robin Flatland
Joseph O'Rourke
Suneeta Ramaswani

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Mirela Damian, Robin Flatland, Joseph O'Rourke, and Suneeta Ramaswani. Connecting Polygonizations via Stretches and Twangs. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 217-228, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


We show that the space of polygonizations of a fixed planar point set $S$ of $n$ points is connected by $O(n^2)$ ``moves'' between simple polygons. Each move is composed of a sequence of atomic moves called ``stretches'' and ``twangs''. These atomic moves walk between weakly simple ``polygonal wraps'' of $S$. These moves show promise to serve as a basis for generating random polygons.
  • Polygons
  • polygonization
  • random polygons
  • connected configuration space


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