# Cubic spline of a two-variable function

So, I am aware of how to (both iteratively and using a linear equation) compute the cubic spline of a one-variable function with $m$ control points. However, I am not sure how to do any type of spline on a two-variable function with $mn$ control points in a square grid. Is this even possible? Is there a simple algorithm? I've tried to see if the process is separable, but so far I can't seem to prove it one way or the other.

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Carl de Boor has elaborated on the theory of multivariable splines. See here: pages.cs.wisc.edu/~deboor/ftpreadme.html –  Steve Huntsman Dec 18 '09 at 21:04