Centroidal Voronoi tessellations: Applications and algorithms

A centroidal Voronoi tessellation is a Voronoi tessellation whose generatin g points are the centroids (centers of mass) of the corresponding Voronoi r egions. We give some applications of such tessellations to problems in imag e compression, quadrature, finite difference methods, distribution of resou rces, cellular biology, statistics, and the territorial behavior of animals . We discuss methods for computing these tessellations, provide some analys es concerning both the tessellations and the methods for their determinatio n, and, finally, present the results of some numerical experiments.