Constructing Centroidal Voronoi Tessellations on Surface Meshes

Centroidal Voronoi tessellations can be constructed using iterative improvement methods such as Lloyd’s method. Using iterative improvement methods implies that the convergence speed and the quality of the results depend on the initialization methods. In this chapter, we briefly describe how to construct centroidal Voronoi tessellations on surface meshes and propose efficient initialization methods. The proposed methods try to make initial tessellations mimic the properties of the centroidal Voronoi tessellations. We compare our methods with other initialization methods: random sampling and farthest point sampling. The experimental results show that our methods have the faster convergence speed than farthest point sampling and outperform random sampling.