plot and fit surface

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laura bagnale 2021-5-25

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https://ww2.mathworks.cn/matlabcentral/answers/839275-plot-and-fit-surface

评论： laura bagnale 2021-6-9

采纳的回答： Mahesh Taparia

在 MATLAB Online 中打开

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

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Answer 1

Mahesh Taparia 2021-6-4

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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.

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Walter Roberson 2021-6-7

在 MATLAB Online 中打开

format long g
x = [0; 1; 1; -1; -1; 0.3; 0.6; 0.2; 0.4; 0.3; 0.1; 0.5];
y = [0; 1; -1; -1; 1; 0.5; 0.2; 0.4; 0.7; 0.8; 0.9; 0];
z = [0.9; 0.4; 0; 0.1; 0.3; 0.8; 0.5; 0.4; 0.3; 0.7; 0.2; 0.1];
w = [0.3; 1; 0; -1; 0.5; 0.7; 0.5; 0.6; 0.9; 0.2; 0.3; 0.1];
A = [ones(size(x)), x.^(1:2), y.^(1:2), z.^(1:2), x.*y, x.*z,  y.*z]
A = 12×10
                         1                         0                         0                         0                         0                       0.9                      0.81                         0                         0                         0
                         1                         1                         1                         1                         1                       0.4                      0.16                         1                       0.4                       0.4
                         1                         1                         1                        -1                         1                         0                         0                        -1                         0                         0
                         1                        -1                         1                        -1                         1                       0.1                      0.01                         1                      -0.1                      -0.1
                         1                        -1                         1                         1                         1                       0.3                      0.09                        -1                      -0.3                       0.3
                         1                       0.3                      0.09                       0.5                      0.25                       0.8                      0.64                      0.15                      0.24                       0.4
                         1                       0.6                      0.36                       0.2                      0.04                       0.5                      0.25                      0.12                       0.3                       0.1
                         1                       0.2                      0.04                       0.4                      0.16                       0.4                      0.16                      0.08                      0.08                      0.16
                         1                       0.4                      0.16                       0.7                      0.49                       0.3                      0.09                      0.28                      0.12                      0.21
                         1                       0.3                      0.09                       0.8                      0.64                       0.7                      0.49                      0.24                      0.21                      0.56
b = w;
p = A\b;
pcell = num2cell(p);
[p000, p100, p200, p010, p020, p001, p002, p110, p101, p011] = pcell{:};
f = @(x,y,z) p000 + p001*z + p010*y + p100*x + p002*z.^2 + p020*y.^2 + p200*x.^2 + p011*y.*z + p101*x.*z + p110*x.*y
f = function_handle with value:
    @(x,y,z)p000+p001*z+p010*y+p100*x+p002*z.^2+p020*y.^2+p200*x.^2+p011*y.*z+p101*x.*z+p110*x.*y

and now f is the fitted function. You do not need to do any more fitting on it.

Representing it graphically is more of a challenge.

N = 20;

xvec = linspace(min(x), max(x), N);

yvec = linspace(min(y), max(y), N+1);

zvec = linspace(min(z), max(z), N+2);

[X,Y,Z] = meshgrid(xvec, yvec, zvec);

W = f(X, Y, Z);

L = [-.7, -.5, -.3, 0, .3, .5, .7];

for K = 1 : length(L)

isosurface(X, Y, Z, W, L(K));

end

legend(string(L))

Walter Roberson 2021-6-9

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 2021-6-9

I understand.

Thank you very much for the quick answers, the explanation and the support!

Kind Regards,

Laura

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plot and fit surface

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