Fitting a grid with surface and reconstructing it

Hello,

I have a grid with data points evenly spaced at (x,y), to each point there's a corresponding z. The grid is relatively dense. How can I fit a catmull-rom patch (or other surface function) to it which has a maximum degree of 3 or 4 if I give a maximum allowed error to the algorithm?
Basically the grid represents a set of terrain points. Since there are a lot of points I want to approximate them with some function which I could store instead of the huge amount of data required for the points. When evaluating the calculated spline patches afterwards they should give back the original terrain shape (up to some small error).
Can somebody give me a hint how I can approach this problem? Is this already researched and if yes, which name it have? This seems to be quite difficult to me, for example in flat terrain areas a single spline patch might fit a lot of data points while a single spline patch around a sharp peak will cover just a few points.

Thanks a lot for any help!

-Matthias
.

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