Most probable number of clusters

Question

I have a set S of N 2D points, each point P is associated with a doubly infinite cone Cone(P) with vertical axis, apex in P and angle a.

Cluster(A, S):
    union all
        (
          {A, B} union Cluster(B, S excluding A)
          where {A, B} belongs to S and A intersects with Cone(B)
        )

I know the bounding box of the set S, the number of points N and the cone angle.

h = height of the bounding box w = width of the bounding box

I need to find the most probable number of unique clusters in a set S.

M = F(w,h,N,a) ?

Actually this will be used as a means of choosing a maximum cone angle a small enough for the points to form at least M clusters.

This way the problem could be stated as:

a = Y(w,h,N,M) ?

Just to help you imagine, it could be illustrated as the shadows of a set of parallel strings with sun moving by the angle a. If a line shadows another one at any time - they both belong to same cluster.