Using Voronoi triangulation

I am hoping someone can help me get started on creating a Voronoi tessellation of a set of discrete points. I would like to accomplish the following:

1. Create an initial set of x-y (and possibly z if necessary) points that lie within a given rectangle of width W and length L.

2. Create the corresponding Voronoi tessellation.

3. Find the centroid of each Voronoi polygon. For this I would need something like lists of the vertices of each polygon.

4. Move each vertex corresponding to each polygon to the centroid point.

5. Loop to step 2 and repeat until stable.

This scheme is called Lloyd's algorithm and one use (the one I want) is to find the arrangement of points within a rectangle that are as evenly distributed as possible, in a certain sense. There is a nice visualization of this technique here. Note how the edges of the enclosing rectangle are included in the edge polygons.

So mostly I'd like some advice on performing steps 2 (mainly) and step 3 (at least as far as getting the polygon vertices). I have read the documentation but it's a bit hard to understand how to get going.