Convex Hull and Voronoi Diagram of Additively Weighted Points

We provide a complete description of dynamic algorithms for constructing convex hulls and Voronoi diagrams of additively weighted points of ${\mathbb R}^{d}$. We present simple algorithms and provide a description of the predicates. The algorithms have been implemented in ${\mathbb R}^{3}$ 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.