Constructing polygons from the edges in a Voronoi diagram
To improve the speed of your code, you'd really have to profile it, and know what the bottleneck is (use a profiler, and find out in what methods most of the time is spent).

Here's what I would have a look at (no promise it will yield significant improvements).


polygonsList.get(n) is evaluated twice per iteration.
The polygon class you're using (I assume java.awt.Polygon) takes ints as coordinates, while the library calculates them in doubles. Yo may want to consider writing a custom Polygon class that takes doubles, in order to avoid the casts.
if you only need the Polygon class for drawing, you may even forego that entirely and make a class that can draw a line given a GraphEdge. This will avoid creating Polygon objects, and you can reuse the same drawing instance.