We describe conditions under which an appropriately-defined anisotropic Voronoi diagram of a set of sites in Euclidean space is guaranteed to be composed of connected cells in any number of dimensions. These conditions are natural for problems in optimization and approximation, and algorithms already exist to produce sets of sites that satisfy them.

An incremental Delaunay triangulation algorithm to generate Voronoi diagrams within the L∞ norm is presented. The main qualities are the preservation of the simplicity of the classical L2 version and its its intrinsic robustness It is then coupled to the well known Lloyd algorithm for computing Centroidal Voronoi Tesselations of point sets. This algorithm is then used to generate well shaped qu...

We consider the Euclidean Voronoi diagram for a set of n parallel halflines in R. A relation of this diagram to planar power diagrams is shown, and is used to analyze its geometric and topological properties. Moreover, a simple plane-sweep algorithm is given that computes the Voronoi diagram for parallel halflines at logarithmic cost per face.

We review the model of the Voronoi Diagrams which allows to reproduce the large-scale structures of our universe as given by the astronomical catalogs. The observed number of galaxies in a given solid angle with a chosen flux/magnitude versus the redshift presents a maximum that is a function of the flux/magnitude ; it can be explained by a detailed analysis of the standard luminosity function ...

We tackle the problem of constructing 2D centroidal Voronoi tessellations with constraints through an efficient and robust construction of bounded Voronoi diagrams, the pseudo-dual of the constrained Delaunay triangulation. We exploit the fact that the cells of the bounded Voronoi diagram can be obtained by clipping the ordinary ones against the constrained Delaunay edges. The clipping itself i...

A new method of benchmarking neural networks based on Voronoi diagrams is introduced. Their complexity is examined and it is shown that data sets of increasing difficulty may be generated. Experiments are conducted examining the performance of five known classification methods on examples of Voronoi data sets.

This paper presents a method for approximating spherical tessellations, the edges of which are geodesic arcs, using spherical Laguerre Voronoi diagrams. The approximation method involves fitting the polyhedron corresponding to the spherical Laguerre Voronoi diagram to the observed tessellation using optimization techniques.

We revisit a new type of a Voronoi diagram, in which distance is measured from a point to a pair of points. We consider a few more such distance functions, and analyze the structure and complexity of the nearestand furthest-neighbor Voronoi diagrams of a point set with respect to these distance functions.

We are given a set of n points moving continuously along given trajectories in d-dimensional Euclid-ean space. At each instant, these sites deene a Voro-noi diagram which changes continuously over time except of certain critical instances, so-called topological events 4]. In this paper, we present an algorithm for maintaining the Voronoi diagram in parallel over time using only O(1) time per ev...

This paper describes how to generate fractal patterns by recursively creating Voronoi diagrams on a set of points. These patterns resemble such things as leaf veins and roadmaps. By varying the degree of subdivision and the distribution of points, different output patterns can be obtained.