Finding Fitting 3d surface

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Mohammad
Mohammad on 15 Mar 2014
Hi, I have a surface which is basically showing stacking fault energy calculated by DFT method, and I want to find the best possible fitting. Beside fitting, I need some way to find the derivative of any points on surface respect to x or y. I used Matlab curve fitting tool box but there are several problems :
1- If I apply some fitting method like cubic or biharmonic, it took too much to find derivative by using differentiate function like this : [dfx,dfy] = differentiate(xfit,x1,y1) Also the result are inorrect.
2- On the other hand, if I use other methods I get wrong result at the end. (not logical, everything is correct because the code working for other surface when we have the equation of surface)
3- Even If I write my own code for numerical derivative like 3 points or 5 points, still at some points the function return NaN and final result are wrong.
I know I might be somehow vague because you obviously don't know what I am trying to do. But from mathematical point of view, how can I find the equation of this surface? I asked some professors and they have strongly advised me :
i) using RBF (radial basis function) method ii) using muffin tin method which basically related to physics and DFT method. iii) using augmented symmetric polynomial function
I would be so grateful if anybody can help me to solve this problem by using either Matlab tool box or other useful mathematical stuff to find fitting equation. Any idea would be really helpful. Thank you.

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