What do I do to fit a surface to given data points in MATLAB?

Does someone here know any command in MATLAB that adjusts a set of points and give me the equation of the surface found?

This is similar to command polyfit but I want for a surface, not a curve.

Answer 1

[Gareth Thomas]

Hi Danilo,

Try using the curve fitting toolbox.

Here is the link to:

Interactive Surface Fitting and Programmatic Surface Fitting

load franke
f = fit( [x, y], z, 'poly23' )
plot(f, [x,y], z)

Gives the nice answer of:

   Linear model Poly23:
       f(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p21*x^2*y +
                       p12*x*y^2 + p03*y^3
       Coefficients (with 95% confidence bounds):
         p00 =       1.118  (0.9149, 1.321)
         p10 =  -0.0002941  (-0.000502, -8.623e-005)
         p01 =       1.533  (0.7032, 2.364)
         p20 = -1.966e-008  (-7.084e-008, 3.152e-008)
         p11 =   0.0003427  (-0.0001009, 0.0007863)
         p02 =      -6.951  (-8.421, -5.481)
         p21 =  9.563e-008  (6.276e-009, 1.85e-007)
         p12 =  -0.0004401  (-0.0007082, -0.0001721)
         p03 =       4.999  (4.082, 5.917)

I hope that this helps you.

Gareth

Answer 2

[dave]

I have the same problem of Danilo. I'm trying your solution, but entering

   load franke

There is this error:

Error using ==> load
 Unable to read file franke: No such file or directory

Maybe it is due to the absence of the file. Where can I find franke's database file or are there other solutions?

Thanks!

Dave

Answer 3

[Image Analyst]

I use John D'Errico's polyfitn: http://www.mathworks.com/matlabcentral/fileexchange/34765-polyfitn

Answer 4

[Kengo Nishi]

It seems that we need to install the curve fitting toolbox.