In this report we concentrate on exact construction and maintenance of arrangements induced by arcs of great circles embedded on the sphere, also known as geodesic arcs, and exact computation of Voronoi diagrams on the sphere, the bisectors of which are geodesic arcs. This class of Voronoi diagrams includes the subclass of Voronoi diagrams of points and its generalization, power diagrams, also ...

This paper considers the interpolation for multi-dimensional data using Voronoi diagrams. Sibson's interpolant is well-known as an interpolation method using Voronoi diagrams for discretely distributed data, and it is extended to continuously distributed data by Gross. On the other hand, the authors studied another interpolation method using Voronoi diagrams recently. This paper outlines the au...

A set of points in the plane induces a Voronoi diagram, a division of the plane based on proximity to points in the set. Voronoi diagrams have been used extensively in engineering and scientific disciplines, but the possibility of using them for creating abstract ornamental designs is largely unexplored. I present some techniques for creating attractive ornamental designs using Voronoi diagrams...

In this paper we initiate the study of tropical Voronoi diagrams. We start out with investigating bisectors finitely many points respect to arbitrary polyhedral norms. For more general scenario show that three are homeomorphic a non-empty open subset Euclidean space, provided certain degenerate cases excluded. Specializing our results then yields structural and algorithms for