3Loughborough University (Epinal Way, Loughborough, Leicestershire, UK, LE11 3TU - United Kingdom)
Abstract : We show that all star-shaped simple polygons can be transformed, in O(n) steps each of which takes O(n) time to compute in an extended real RAM model, into convex polygons by continuous motions during which the edges remain rigid and the polygon remains star-shaped and simple. For each step, the trajectories of the vertices are given explicitly. In particular, the vertices move along straight lines, circular-arcs, or on the curve traced by an intersection point of two circles whose centers move along straight lines.
https://hal.inria.fr/inria-00442788
Contributor : Sylvain Lazard
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Submitted on : Wednesday, December 23, 2009 - 9:50:02 AM
Last modification on : Thursday, February 7, 2019 - 4:50:27 PM
Long-term archiving on : Friday, June 18, 2010 - 12:04:13 AM
Hazel Everett, Sylvain Lazard, Steve Robbins, H. Schröder, Sue Whitesides. Convexifying Star-Shaped Polygons. 10th Canadian Conference on Computational Geometry (CCCG'98), 1998, Montreal, Canada. pp.10-12. ⟨inria-00442788⟩
