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: [applet could not be started]

Menue itemMeaning
Clear pointsTo start all over again.
Run algorithmIf this is disabled, nothing will happen.
Show Delaunay circlesA Delaunay circle is defined by three points of the Voronoi diagram.
Show Voronoi regionBy 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 regionWithin 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 consoleGeneraten a output on the console with x to be x-coordinate of the point, y to be y-coordinate 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 pixelsYou 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.