The use of the applet is very simple. First, you can add some points to a
Voronoi diagram. The diagram will appear in red.
You can open a context menu by pressing the right mouse button.
Applet start  click here:


Menue item  Meaning 
Clear points  To start all over again. 
Run algorithm  If this is disabled, nothing will happen. 
Show Delaunay circles  A Delaunay circle is defined by three
points of the Voronoi diagram. 
Show Voronoi region  By enabling this item, the regions (green)
which are defined by the intersections of the circles will appear.
You can also see a blue polygon. This is how the red diagram will look like
if you insert the current point to the diagram. You will see that the
neighbourhood within a green region doesn't change.
On the bottom left the size of the area of the blue polygon is shown. 
Show maximum within region  Within the green region, the applet
produces a grid and calculates for every grid point the size of the area of the
blue polygon.
The values are shown from blue (smallest area) to black (biggest area). 
Generate GNUPlot to console  Generaten a output on the console
with x to be xcoordinate of the point, y to be ycoordinate of the point and
z to be the size of the area of the blue polygon. The ouput can be redirected
to a file and plot with e.g. GNUPlot. 
Grid resolution in pixels  You can set the grid resolution in
pixels from 1 to 25. Default is 5. The lower the resolution, the longer the
time of calculation. 

The topological region in Voronoi diagrams are regions which have the same
neighbourhood within the Voronoi diagram. If you move the blue region within
a green one, you can see that the neigbourhood doesn't change within the green
region.
The max region is the one with the maximum area. This area "steals" most of
the area from the other Voronoi regions. For sure infinity is always
the maximum region.
The topological regions are built with a sweep similar to
the line sweep, so the runtime is
O((n+k) log n).
During the sweep a doubly connected edge list (DCEL) is built up
so that we have got a whole arrangment of the circles.