A multisheet plane figure and its medial axis
Ivan Mekhedov · Russian Mathematics · 2011
A multisheet plane figure is a projection onto the Euclidean plane of a surface whose every point has a neighborhood biuniquely projectable onto the plane. The notion of a multisheet plane figure is a generalization of the usual notion of a plane figure for the case when the boundary contains self-intersecting curves and pairwise intersecting ones. The medial axis of a usual plane figure is the set of points equidistant from the boundary. In this paper we introduce the notion of the medial axis of a multisheet plane figure and study its properties. Medial axes have numerous applications in engineering and computer science.