| Flipturning Polygons (Extended abstract) (2009) | |||||||||||||||
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| Figure 1. A flipturn. The pocket is bold (red), and its lid is dashed. A central problem in polymer physics and molecular biology is the reconfiguration of large molecules (modeled as polygons) such as circular DNA. Most of the research in this area involves computer-intensive Monte-Carlo simulations. One efficient method frequently used to generate random chains or polygons is to modify one such object into another using a simple pivot operation. This paper is concerned with a pivot of central concern in polymer physics research called a flipturn, first defined in an unpublished 1973 paper of Joss and Shannon [4] as follows. A pocket of a nonconvex polygon P is a maximal connected sequence of polygon edges disjoint from the convex hull of P except at its endpoints. The line segment joining the endpoints of a pocket is called the lid. A flipturn rotates a pocket 180 | |||||||||||||||
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