Convexifying monotone polygons while maintaining internal visibility Conference Paper uri icon

abstract

  • Let P be a simple polygon on the plane. Two vertices of P are visible if the open line segment joining them is contained in the interior of P. In this paper we study the following questions posed in [8,9]: (1) Is it true that every non-convex simple polygon has a vertex that can be continuously moved such that during the process no vertex-vertex visibility is lost and some vertex-vertex visibility is gained? (2) Can every simple polygon be convexified by continuously moving only one vertex at a time without losing any internal vertex-vertex visibility during the process? We provide a counterexample to (1). We note that our counterexample uses a monotone polygon. We also show that question (2) has a positive answer for monotone polygons. © 2012 Springer-Verlag.

publication date

  • 2012-01-01