R. Pollack, M. Sharir, and G. Rote. Computing the geodesic center of a simple polygon . In particular, the space can be discrete for example, a graph or a digital image. They used a different approach and achieved their time bound by a modification of Meggido s technique. 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.
Pollack, R., M. Sharir, and G. Rote, Computing the Geodesic Center of a Simple Polygon . Computing of the geodesic center of a simple polygon .