I wish I could remove my previous question, 2 seconds on google pointed me to Matlab's interp2 which I'm using now on the output of your excellent gridfit. Thanks for sharing!

I found that it is very straightforward to fit a nice looking surface to some 55 data-points using gridfit. I was wondering though, is there a way to get values of the surface that are not on the nodes? I wish to interpolate between my 55 samples using the surface.

For those of you who don't appreciate why Felon's comment is silly, think of it like this. Gridfit fits a surface of the form f(x,y), over a rectangular grid. It does so quite well, as many people have found over the years.
While you may think of the surface of a sphere as a surface, it is not of the form that gridfit can fit. It is multi-valued, so for any single (x,y) pair, there will be zero, one, or two values of z that would apply. As well, that "surface" (better to call it a manifold) has derivative singularities, if we were to look at it as a function of x and y. So even a hemisphere will be problematic for this tool.
You would not use gridfit to fit something that is not representable as a function of two variables over a rectangular grid, any more than you would expect it to do numerical integration, numerical optimization, or compute an FFT. Nor would you expect it to cook dinner for you, do your laundry, etc. Use the right tool to solve your problem, but if you try to force the wrong tool to solve a random problem, expect poor results and don't complain about what you get.

Felon -
So you are using a tool that builds a single valued function to fit something that is obviously not. What did you expect? Magic?
Software does what it is programmed to do. It does not magically rewrite itself when you give it a problem of a completely different sort. In fact, I fail to understand why you would downrate a tool for not solving a class of problem it is explicitly not designed to solve.
If you have a closed manifold, like a ball or some other multivalued form, then don't use this tool. I have NEVER claimed it would solve that problem. Instead, you might look into tools like convex hulls, alpha shapes, CRUST, etc. Or, you might choose to convert the problem into spherical coordinates, at which point gridfit would be able to build a viable surface.
Or maybe you just wanted to complain with no good reason.

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