We introduce a class of systems of Hamilton-Jacobi equations that
characterize critical points of functionals associated to centroidal
tessellations of domains, i.e. tessellations where generators and centroids
coincide,
such as centroidal Voronoi tessellations and centroidal power diagrams. An
appropriate version of the Lloyd algorithm, combined with a Fast Marching
method on unstructured grids for the Hamilton-Jacobi equation, allows computing
the solution of the system. We propose various numerical examples to illustrate
the features of the technique