نمودار ورونوي دايره ها در فضاي هذلولوي

Hyperbolic Voronoi Diagram of Circles

In this paper the positions of vertices and equations of edges of the hyperbolic Voronoi diagram of a hyperbolic circle set on the Poincare upper half-plane is computed, where the radii of the hyperbolic circles are not necessary equal and disjoint. The Poincare upper half-plane is considered as a complex upper half-plane. By using a Mobius transformation this complex upper half-plane is transformed into another complex upper half-plane in order to formulate the problem of finding the position of the hyperbolic Voronoi vertex of three given hyperbolic circles as a point location problem. Finally the equations of edge are computed in a rational quadratic Bezier curve form.