plot and fit surface

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laura bagnale
laura bagnale on 25 May 2021
Commented: laura bagnale on 9 Jun 2021
Hello everyone,
I hope that someone can help me.
I'm trying to plot several points in the space and to fit them so I can get an mathematical formula like this topic https://de.mathworks.com/help/curvefit/polynomial.html#bt9ykh7 "Fit and Plot a Polynomial Surface"
I want to get a quadratic polynomial so I'm trying to use 'poly22' function. This is my code:
X = [0; 1; 1; -1; -1; 0.3]
Y = [0; 1 ; -1; -1; 1; 0.5]
Z = [0.9; 0.3; 0; 0.2; 0.6; 1]
plot3(X,Y,Z,'or')
z = Z;
fitsurface=fit([X,Y],z, 'poly22','Normalize','on')
plot(fitsurface, [X,Y],z)
I obtained this results:
Linear model Poly22:
fitsurface(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2
where x is normalized by mean 0.05 and std 0.9028
and where y is normalized by mean 0.08333 and std 0.9174
Coefficients:
p00 = 0.9097
p10 = -0.2332
p01 = 0.2645
p20 = -1.07
p11 = -0.02071
p02 = 0.5786
But I am not sure about them and the syntax.
Could you help me please?
Thank you a lot!
Laura

Accepted Answer

Mahesh Taparia
Mahesh Taparia on 4 Jun 2021
Hi
The syntax and code which you have used is correct. The above code will fit a 2nd degree polynomial to the given data points and this is what you need.
  17 Comments
Walter Roberson
Walter Roberson on 9 Jun 2021
When you have a minimization problem, analytic solutions are best unless they would take an undue amount of time.
(There are some minimization problems that can be approached probabilisticly to get a likely solution in a relatively short time, but proving that the answer is the best possible might take a long time. There is a famous mathematical problem involving one of the largest numbers ever invented, literally too large to write down in this universe... for a situation where it is suspected that the real minimum is 6. So sometimes it really does not pay to do a complete analysis. But in a situation like the function you have, you might as well go for the analysis and so be sure that you have the right solution.
laura bagnale
laura bagnale on 9 Jun 2021
I understand.
Thank you very much for the quick answers, the explanation and the support!
Kind Regards,
Laura

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