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In their recent article (2010), Levy and Liu introduced a generalization ofCentroidal Voronoi Tessellation (CVT) - namely the Lp-CVT - that allows thecomputation of an anisotropic CVT over a sound mathematical framework. In thisarticle a new objective function is defined, and both this function and itsgradient are derived in closed-form for surfaces and volumes. This method opensa wide range of possibilities, also described in the paper, such asquad-dominant surface remeshing, hex-dominant volume meshing or fully-automatedcapturing of sharp features. However, in the same paper, the derivations of thegradient and of the new objective function are only partially expanded in theappendices, and some relevant requisites on the anisotropy field are leftimplicit. In order to better harness the possibilities described there, in thiswork the entire derivation process is made explicit. In the authors' opinion,this also helps understanding the working conditions of the method and itspossible applications.

Gradient of the Objective Function for an Anisotropic Centroidal Voronoi Tessellation (CVT) - A revised, detailed derivation