  In their recent article (2010), Levy and Liu introduced a generalization of
Centroidal Voronoi Tessellation (CVT) - namely the Lp-CVT - that allows the
computation of an anisotropic CVT over a sound mathematical framework. In this
article a new objective function is defined, and both this function and its
gradient are derived in closed-form for surfaces and volumes. This method opens
a wide range of possibilities, also described in the paper, such as
quad-dominant surface remeshing, hex-dominant volume meshing or fully-automated
capturing of sharp features. However, in the same paper, the derivations of the
gradient and of the new objective function are only partially expanded in the
appendices, and some relevant requisites on the anisotropy field are left
implicit. In order to better harness the possibilities described there, in this
work the entire derivation process is made explicit. In the authors' opinion,
this also helps understanding the working conditions of the method and its
possible applications.
