You only have to remember that the factor between grid and cup (in size terms) always remain constant.
Yes, this makes a lot of sense, and I can see what you're saying, so thank you. I'm just trying to figure out how to use it to help aim, and I'll admit that I'm not the best at math, so let me go over how I'm seeing what you're saying...
The different size grids (207, or 163) also = a different size hole, but no matter what size (or camera angle) we get, the constant is that there are always 7 cups. Correct?
One question... for aiming simplicity, wouldn't it be easier to use 6 since technically there are 6 full cups from one end of the grid to the other. Before your head explodes, let me explain... You say 7, but then you subtract a full cup (17.5 - 17.5) to make your math work, since the two cups on the edge of the grid in your example are split in half. Why not, from an aiming standpoint, just count from the center of the cup to the grid line and make it six and remove the step of having to subtract the two halves that go over the grid lines?
Hole = 35 pixels. Grid = 207 pixels. 35 * 6 = 210 pixels. Six cups. I don't see the reason for counting it as seven holes when you subtract one of them at the end.
But whatever... I'm more interested in what you said about aiming by using half circles not being accurate. How do you aim? If we remove all formulas that get us to our aim point and assume our final aim number is correct, it seems like anything other than counting the exact pixels isn't going to be accurate.
I'm not expecting to find a perfect technique and never two putt again. There are always mistakes, maybe a wrong dot count, etc, but I'd like to find a solid way to aim so that if the putts don't go in, it would be my mistake and not the wrong math or aiming method.
Any pointers, or is this a lost cause?
Right now, I primarily use JC sneed, but I have a couple different techniques that I use at the same time, mostly to confirm what I think a putt is going to do.