Within the image it comprises of 3 curves, therefore 6 points. The highlighted areas comprises 4 points in total, where each pair is a few millimetres from one another.
I sit possible to have potentially many of these placeholders, extract their curves and start/end points, then repair or handle the ‘close vicinity’ points and return new curves?
Can you label what you mean by 3 curves? I see a LOT more than that here.
Yes, I agree with @jacob.small - the question is not clear
It probably more of a simple geometry problem.
If the question is what I think it is:
If the red and green lines are not quite cotangent (and you have 2 intersection points) it is probably easier to project a line from the centre of green circles perpendicular to the red.
Then intersect that black line with either the red or green- to get either blue or purple dots respectively
Is red a circle or a spline ?