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Discrete & Computational Geometry

, Volume 35, Issue 1, pp 131–141 | Cite as

Polygons Needing Many Flipturns

  • Therese BiedlEmail author
Article

Abstract

A flipturn on a polygon consists of reversing the order of edges inside a pocket of the polygon, without changing lengths or slopes. Any polygon with n edges must be convexified after at most (n − 1)! flipturns. A recent paper showed that in fact it will be convex after at most n(n−3)/2 flipturns.We give here lower bounds.We construct a polygon such that if pockets are chosen in a bad way, at least (n − 2)2/4 flipturns are needed to convexify the polygon. In another construction, (n −1)2/8 flipturns are needed, regardless of the order in which pockets are chosen. All our bounds are adaptive to a pre-specified number of distinct slopes of the edges.

Keywords

Computational Mathematic Distinct Slope 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.School of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1Canada

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