Ways to interpolate 3 dimensional data

Question

I am working to predict an energy production using wind data. We know that power is dependent on wind direction and wind speed, and we have huge sets of data giving us the power function of wind direction and speed.

I also know how to plot those points, and have a first interpolation, but it seems the way the package interpolate is not optimal. I would also like to get the equation of the surface that is interpolated so I can test the remaining data. For now I have tried the gam() function from the mgcv package with different smooth terms, but the result is not optimal, the issue being that it seems to be a quadratic answer, whereas I would try to have polynoms of higher power.

Are there other ways to interpolate a set of 3d points ? to give you an idea of the shape of the data here's what I got from the polar representation (distance from the origin is the wind speed, angle the wind direction, z the power).

Thanks a lot !

to get the most out of stack overflow you should provide a reproducible example and use more precise words and phrases than "result is not optimal" — Cyrus Mohammadian, Aug 16 '16 at 07:46
what do you mean by repoducible example ? my data is quite huge, but I can add the code that I've been using (or more like the functions...) — s.sword333, Aug 16 '16 at 07:50
Read this before posting again: http://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example and update your post accordingly — Cyrus Mohammadian, Aug 16 '16 at 07:58

Ways to interpolate 3 dimensional data

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