Voronoi Diagram of Lines in 3D

Let $n\in\mathbb{N}$ be the number of input objects, where the input consists either of $n$ lines or of $n$ line segments in three-dimensional Euclidean space. Determine the combinatorial complexity of the resulting Voronoi diagram as a function of $n$. In particular, close the gap between the known lower bound of $\Omega(n^2)$ and the essentially cubic upper bound, and decide whether the conjectured nearly quadratic complexity holds.