Characterizing and Covering Some Subclasses of Orthogonal Polygons

Abstract

A grid n-ogon is a n-vertex orthogonal polygon that may be placed in a n 2 × n 2 unit square grid and that does not have collinear edges. Given a grid n-ogon P , let |Π(P)| be the number of rectangles that results when we partition P by extending the edges incident to reflex vertices towards its interior. P is called Fat if |Π(P)| is maximal for all grid n-ogons; P is called Thin if |Π(P)| is minimal for all grid n-ogons. Thins with area 2r + 1 are called Min-Area. We will show that n 6 vertex guards are necessary to guard a Min-Area grid n-ogon and present some problems related to Thins. Partially funded by Fundação para Ciência e Tecnologia (FCT) and by CEOC (Univ. of Aveiro) through Programa POCTI, FCT, co-financed by EC fund FEDER.