Abstract
AbstractVoronoi diagrams belong to frequently used structures in computational geometry with application in many fields of science. The properties of Voronoi diagram are already studied in various metric spaces – Euclidean, Manhattan, Minkowski, Hausdorff, or Karlsruhe and also in the hyperbolic metric. In this paper, we focus on the Voronoi diagram and its dual in the Poincaré ball model of the three-dimensional hyperbolic space. We first present some basic tools from the Poincaré ball model needed to construct a Voronoi diagram and for a closer observation of its properties. We have determined certain conditions for the position of the generators controlling the behavior of the hyperbolic Voronoi diagram. In the last section, we demonstrate this effect on the dual graph of a hyperbolic Voronoi diagram, i. e., on hyperbolic Delaunay tessellations.KeywordsPoincaré ball modelhyperbolic spaceVoronoi diagramDelaunay tessellation
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
