Convexifying Polygons Without Losing Visibilities
نویسندگان
چکیده
We show that any simple n-vertex polygon can be made convex, without losing internal visibilities between vertices, using n moves. Each move translates a vertex of the current polygon along an edge to a neighbouring vertex. In general, a vertex of the current polygon represents a set of vertices of the original polygon that have become co-incident. We also show how to modify the method so that vertices become very close but not co-incident. The proof involves a new visibility property of polygons, namely that every simple polygon has a visibilityincreasing edge where, as a point travels from one endpoint of the edge to the other, the visibility region of the point increases.
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