  The computation of Voronoi Diagrams, or their dual Delauney triangulations is
difficult in high dimensions. In a recent publication Polianskii and Pokorny
propose an iterative randomized algorithm facilitating the approximation of
Voronoi tesselations in high dimensions. In this paper, we provide an improved
vertex search method that is not only exact but even faster than the bisection
method that was previously recommended. Building on this we also provide a
depth-first graph-traversal algorithm which allows us to compute the entire
Voronoi diagram. This enables us to compare the outcomes with those of
classical algorithms like qHull, which we either match or marginally beat in
terms of computation time. We furthermore show how the raycasting algorithm
naturally lends to a Monte Carlo approximation for the volume and boundary
integrals of the Voronoi cells, both of which are of importance for finite
Volume methods. We compare the Monte-Carlo methods to the exact polygonal
integration, as well as a hybrid approximation scheme.
