Voronoi diagrams have recently received attention as data structures containing significant information about the spatial adjacency of map objects. Despite their theoretical efficiency, batch construction techniques require complete rebuilding after each modification. Incremental Voronoi creation methods use processes such as insert, delete and move for points, and from these derive insertion a...

We present a 2D mesh improvement technique that optimizes Voronoi diagrams for their use in polygonal finite element computations. Starting from a centroidal Voronoi tessellation of the simulation domain we optimize the mesh by minimizing a carefully designed energy functional that effectively removes the major reason for numerical instabilities—short edges in the Voronoi diagram. We evaluate o...

We study Voronoi diagrams of manifolds and varieties with respect to polyhedral norms. provide upper lower bounds on the dimensions cells. For algebraic varieties, we count their full-dimensional As an application, consider Wasserstein distance between discrete probability distributions.