I've been studying the closest pair algorithm lately and I found this to be an extremely good and intuitive resource: http://serverbob.3x.ro/IA/DDU0221.html. It is also explained in section 33.4, "Finding the closest pair of points" of introduction to algorithms, third edition by CLRS.
I understand why I'd need 7 comparisons for a non pairwise distinct set of points and only 5 otherwise (33.4-2). Both of them follow from the fact that I can fit only 4 points, at least Delta away from each other, on a Delta x Delta box.
What I've been wondering though, is if I could trim the number of comparisons down to 3 if I included only points strictly less than Delta away from the middle line, in the middle Delta x 2 Delta strip. The reasoning is that I already have a pair of points Delta away from each other from the recursive calls, I only need points less than Delta and I can only fit 2 points Delta away from each other AND less than Delta from the middle line on each side.
Have I missed something or can I really just compare the 3 following points of every point in a middle strip only containing points strictly less than Delta from the center?
Edit: I have started a bounty for a very similar question on stack overflow also and we have come up with a very interesting discussion there. So I'm linking it here. We've also started a very insightful chat here.