Convexifying monotone polygons while maintaining internal visibility
Por:
Aichholzer O., Cetina M., Fabila-Monroy R., Leaños J., Salazar G., Urrutia J.
Publicada:
1 ene 2012
Resumen:
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.
Filiaciones:
Aichholzer O.:
Institute for Software Technology, University of Technology, Graz, Austria
Cetina M.:
Instituto de Física, Universidad Autónoma de San Luis Potosí, Mexico
Fabila-Monroy R.:
Departamento de Matemáticas, CINVESTAV, Mexico
Leaños J.:
Unidad Académica de Matemáticas, Universidad Autónoma de Zacatecas, Mexico
Salazar G.:
Instituto de Física, Universidad Autónoma de San Luis Potosí, Mexico
Urrutia J.:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico
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