Understanding Akima Bivariate Interpolation: A Missing Piece in the Puzzle?

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Anyone familiar with the bivariate interpolation method developed by Akima?

I've been reading H. Akima, Commun. ACM 17, 18 (1974) and trying to implement his method, but he actually doesn't describe how to do the interpolation! The formulas for calculating the derivatives at each point are given, but not the polynomial that uses them for the interpolation.

I've been trying to reverse engineer his code, but it's starting to take too much of my time. Any help welcome.
 
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