So, I am aware of how to (both iteratively and using a linear equation) compute the cubic spline of a onevariable function with $m$ control points. However, I am not sure how to do any type of spline on a twovariable 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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There is a nice book by Les A. Piegl and Wayne Tiller, which is intended as an introduction to NURBS, but in the first chapters also provides theoretical background for uni and bivariate Beziers und Splines. The NURBS Book Les A. Piegl, Wayne Tiller Springer ISBN10: 3540615458 ISBN13: 9783540615453 

