I want to draw a Voronoi diagram with 9 sites and with no vertex, 1 vertex, 4 vertices, and7 vertices.How do I approach this question. The one with no vertex is easy, it can be done by collinear points. What about the others.A figure for each would be appreciated.
Voronoi diagram with given number of vertices and sites
computational geometry
Conceptually, it is maybe easier to construct a Delaunay triangulation tessalation. The DT is the dual to the Voronoi diagramm, so you want to limit the number of faces to $0,1,4,7$. This can be achieved by placing some of the vertices of the DT on a circle, or by picking the right number of vertices on the convex hull.Here is a picture for the 4 vertex case (black DT, red Voronoi diagramm). Play around to get the solutions of 2. and 4. (You already solved 1.)