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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

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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 ISBN-10: 3540615458 ISBN-13: 978-3540615453

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Thanks, will see if I can get my hands on it. –  rlbond Dec 26 '09 at 1:49

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