D.S. Johnson, A. Nozaki, T. Nishizeki, H. Willis, Eds, Academic Press, Boston, pp. An edge between two Voronoi vertices is either a straight edge or a hyperbolic arc. Finally , the boundary of a Voronoi cell consists of a concatenation of straight edges and hyperbolic arcs. Finally , the boundary of a Voronoi cell consists of a concatenation of straight edges and hyperbolic arcs.
P lies on the midpoint of the geodesic diameter, it has a special property.
D.S. Johnson, A. Nozaki, T. Nishizeki, H. Willis, Eds, Academic Press, Boston, pp. We need the following definition. Let P be a polygon. The geodesic center of P is the point in P which minimizes the maximum geodesic distance to the boundary of P . Therefore, the geodesic center depends continuously on the boundary of P .