Suppose you have a group of points of a one-to-one function like so:
I found that you can use what I'm calling a t-curve that for four points looks like:
The same first 3 points as the last but with a fourth point [5,1]...
I'm pretty sure there is always a solution but not positive...
The main drawback is the coefficients can get large, but it has a nice form I think...
This formulation might be better as it seems to keep the coefficients more reasonably sized and nice fractions, the ith term is multiplied by i!: