(Need Help) How to Obtain 2D Interpolation Coefficient?

I have a pre-setup 2D matrix whose size is [N x N].

Using this data, I want to find the each coefficient k in the below specific funtion.

z=k11*x^2+k22*y^2+...

k12*x*y+...

k1*x+k2*y+k0;

What's the simplest way to obtain these coefficients in Matlab?

It seems that the command 'interp2' does not provide these coefficients.

[Matt J]

You have y on both the left and right hand side of the equation. Are they the same y or did you mean

z=k11*x^2+k22*y^2+...

k12*x*y+...

k1*x+k2*y+k0;

[Changwoo Lee]

The equation in reply is correct. I modified the equation in my question.

Answer 1

[Matt J]

If you have the Curve Fitting Toolbox, you can follow this example

https://www.mathworks.com/help/curvefit/polynomial.html#d123e5178

except you would use the 'poly22' model instead of 'poly44'

If you don't have the toolbox, then see one of these FEX submissions.

https://www.mathworks.com/matlabcentral/fileexchange/13719-2d-weighted-polynomial-fitting-and-evaluation?s_tid=srchtitle

https://www.mathworks.com/matlabcentral/fileexchange/34765-polyfitn?s_tid=srchtitle

[Changwoo Lee]

Thank you very much for your kindness.