Convex hull and Voronoi diagram of additively weighted points

Abstract

We provide a complete description of dynamic algorithms for constructing convex hulls and Voronoi diagrams of additively weighted points of ℝd. We present simple algorithms and provide a description of the predicates. The algorithms have been implemented in ℝ3 and experimental results are reported. Our implementation follows the CGAL design and, in particular, is made both robust and efficient through the use of filtered exact arithmetic. © Springer-Verlag Berlin Heidelberg 2005.