The CSM lab at the University of Utah is actively developing the Material Point Method (MPM). Like other particle methods, the MPM discretizes a body into a set of points at which problem data (velocity, stress, temperature, etc.) are stored.  Centroidal Voronoi Tesselation is a promising way to distribute points within a domain in a way that is favorable to the MPM, where using a distribution of particles conforming to the boundary is highly desired.  For a thorough overview, see Max Gunzburger’s website,  http://people.sc.fsu.edu/~mgunzburger/cvt/cvt.html.  Some excerpts from his site are shown below,

Other interesting images from Gunzburger’s website (each illustrating various benefits to MPM) are shown below…