Fit and Plot a Polynomial Surface

Allright, the last time i used matlab was two years ago and i almost forgot everything. What i´m trying to do is to plot a x y z matrix and fit it so i get an mathematical formular. So basically what´s done here : https://de.mathworks.com/help/curvefit/polynomial.html#bt9ykh7 "Fit and Plot a Polynomial Surface"

I tried it like this, as i said i haven´t done this in a while so don´t execute me

 y1=[1 2 3 4];
x1=[100 200 300 400]';
[x,y]=meshgrid(x,y1);
z=[1.0  1.6  2.0  2.460; 1.0  1.5...
    1.8  2.2; 1.0  1.5  1.931  2.2;...
    1.1  1.6  2.1  2.4];
fitsurface=fit([x,y],z, 'poly21');
plot(fitsurface, [x,y],z);

And that´s what i get :

Error using fit>iFit (line 135)
X must be a matrix with one or two columns.
Error in fit (line 116)
[fitobj, goodness, output, convmsg] = iFit( xdatain, ydatain, fittypeobj, ...
Error in Matlab_Versuch (line 7)
fitsurface=fit([x,y],z, 'poly21');

I basically know what´s wrong but i can´t fix it.

Thanks

Answer 1

[dpb]

Check spelling... :)

x1=[100 200 300 400]';
[x,y]=meshgrid(x,y1);

You defined x1 but used x as argument instead...

fitsurface=fit([x,y],z, 'poly21')

fit wants vectors, not arrays. Use the Matlab idiom (:) to return all elements of matrix/array as column vector:

x=x(:); y=y(:); z=z(:);
fitsurface=fit([x,y],z, 'poly21')

Somehow the builtin plot doesn't recognize it's a surface and only plots on 2D axis; I had to use scatter3 to show...

Also, it appears the real curvature is in Y but you fit the quadratic in X; looks like should either reverse role of X,Y or use 'poly12' instead of 'poly21'

[dpb]

[Maruius Gratzi Answer moved to comment -- dpb]

That was incredibly helpful, thank you so much.

[dpb]

If it solves the problem, go ahead and Accept the answer to indicate so others don't take time to try to add...