Producing Voronoi diagram in three dimensional

A Voronoi diagram is a kind of tesselation that divided the medium into polygons in 2D and polyhedrons in 3D.

Although there are many algorithms to construct a Voronoi diagram, some of them are faster than others. Based on my knowledge, Fortune’s algorithm is fastest to construct the Voronoi diagram either in two dimensional or three dimensional.

Fortune’s algorithm is based on the sweep-line strategy and balanced binary search tree.

Now, I want to implement Fortune’s algorithm into three dimensional. I want to know which basically variation is made to fit the algorithm to three dimensional?