Maximum Points in the paralleogram

Dear Friends,
I want to write logic for finding what are the different ways of placing Maximum number of points in the given paralleogram with a limitation saying that distance between any 2 points should not be less then the given distance.

I tried in many ways but I didnt get the perfect logic. Is there any specified logic for it. If any one worked on it please help me in sorting out this problem.

Iam giving my requirement in more detail:

I have to place Maximum number of points in the given paralleogram.
Paralleogram's four coordinates will be given as an array.
a real value for the Minimum distance allowed is given.

Thankyou
Vamsi.