The Voronoi diagram is a fundamental geometric structure widely used in various fields, especially in

computer graphics and geometry computing. For a set of points in a compact domain (i.e. a bounded and

closed 2D region or a 3D volume), some Voronoi cells of their Voronoi diagram are infinite or partially

outside of the domain, but in practice only the parts of the cells inside the domain are needed, as when

computing the centroidal Voronoi tessellation. Such a Voronoi diagram confined to a compact domain

is called a clipped Voronoi diagram. We present an efficient algorithm to compute the clipped Voronoi

diagram for a set of sites with respect to a compact 2D region or a 3D volume. We also apply the proposed

method to optimal mesh generation based on the centroidal Voronoi tessellation.