Hi Ilian - The real problem I have is somewhat less complicated. I have an unstructured {xa,ya} and I want to calculate the corresponding {x,y} which is structured; it has equal increments in x and y. That means I can use Interpolation[ ] to interpolate from {x,y} to {xa,ya}, but not from {xa,ya} to {x,y}, which is what I want.

What I guess I will have to do is use the F[{x,y}]={xa,ya} interpolation, and then use FindMinimum[ ] to find the {x,y} that minimizes [ F[{x,y}] - {xa,ya} ]^2

Does that sound like the best way to do it?

Hmm - that's not doing it. If I use p (no random added), the above gives {6.5,6.5}, not the {6.25,6.25) that I need, because it's using InterpolationOrder->1, but if I remove the InterpolationOrder->1, it gives me the unstructured grid problem again, and forces the interpolation order to 1.