Anisotropic centroidal voronoi tessellations and their applications
Date of Issue2005
School of Physical and Mathematical Sciences
In this paper, we introduce a novel definition of the anisotropic centroidal Voronoi tessellation (ACVT) corresponding to a given Riemann metric tensor. A directional distance function is used in the definition to simplify the computation. We provide algorithms to approximate the ACVT using the Lloyd iteration and the construction of anisotropic Delaunay triangulation under the given Riemannian metric. The ACVT is applied to the optimization of two-dimensional anisotropic Delaunay triangulation, to the generation of surface CVT, and high-quality triangular mesh on general surfaces. Various numerical examples demonstrating the effectiveness of the proposed method are presented.
DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis
Siam journal on scientific computing
Siam Journal on Scientific Computing © copyright 2005 Society for Industrial and Applied Mathematics. The journal's website is located at http://www.siam.org/journals/sisc.php