Given a set of point-sized stones (which we will call ``stones'' for simplicity), a Voronoi diagram is a tesselation of a plane into polygons such (i) that every stone is in the interior of one polygon and (ii) for every point x in the polygon P associated with stone s, x is closer to s than it is to any other stone s'. Distance is based on Euclidean distance.
The Voronoi game is a two person game that works as follows: you and I each start with 7 stones (should be a command line parameter throughout -- no magic numbers in your programs please). Yours are red and mine are blue. The first player places one stone, then the second player places two stones, and play alternates with each player placing one stone until the first player places the last stone. (The second player's first ply consists of two placements to break a symmetry strategy by the second player.)
As the game proceeds, the Voronoi diagram is computed with red polygons surrounding red stones and blue polygons surrounding blue stones. The display should make the stones darker than the other points in the polygon.
It may help you to see this by looking at Chris Poultney's implementation but with strict alternation of moves .