Fitting 3-d plot

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Tim Fulcher 2023-8-27

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https://ww2.mathworks.cn/matlabcentral/answers/2013682-fitting-3-d-plot

评论： Tim Fulcher 2023-8-27

Hi all,

I've been plotting a surface plot using surf(x, y, z) where x is a 1 x 8 double, y is a 1 x 11 double and z is an 11 x 8 double and fitting that surface using cftool with no issues. I now need to change my approach slightly and perform the fit programatically (as opposed to using cftool).

However surffit = fit([x,y],z,'poly32','normalize','on') does not accept my current format. How I can I adjust or massage my raw data (x, y and z) for surffit to accept it?

Thanks

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Answer 1

the cyclist 2023-8-27

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Use meshgrid to make a grid out of your x and y vectors:

x = 1:8;

y = 1:11;

z = rand(11,8);

[xx,yy] = meshgrid(x,y);

surf(xx,yy,z)

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the cyclist 2023-8-27

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Sorry, I should have mentioned that the surface fitting function requires you to turn all those matrices into vector again. The key concept being that all the vectors need to be the same length, and specify a series of (x,y,z) coordinates.

You should double-check that my syntax really put the correct z with the corresponding (x,y). It's easy to get the (x,y) swapped.

x = 1:8;

y = 1:11;

z = rand(11,8);

[xx,yy] = meshgrid(x,y);

surf(xx,yy,z)

surffit = fit([xx(:), yy(:)], z(:), 'poly32', 'normalize', 'on')

Linear model Poly32: surffit(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p30*x^3 + p21*x^2*y + p12*x*y^2 where x is normalized by mean 4.5 and std 2.304 and where y is normalized by mean 6 and std 3.18 Coefficients (with 95% confidence bounds): p00 = 0.4901 (0.371, 0.6093) p10 = -0.06547 (-0.2478, 0.1169) p01 = -0.0336 (-0.1297, 0.06249) p20 = -0.02249 (-0.09529, 0.05031) p11 = -0.004547 (-0.06809, 0.059) p02 = 0.03962 (-0.03234, 0.1116) p30 = 0.01978 (-0.06944, 0.109) p21 = 0.01987 (-0.05335, 0.09309) p12 = 0.04835 (-0.02401, 0.1207)

Tim Fulcher 2023-8-27