How to set a custom equation to fit 5 points in space by fitsurface?

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laura bagnale 2021-7-28

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评论： laura bagnale 2021-8-3

Hello everyone,

it would be very nice if someone could help me with this problem.

I have a set of 5 points in space with x, y, z coordinates and I would like to fit them with a surface. Generally I use fitsurf setting the option 'poly22' to get the equation in the secondo order of x and y.

Now I would like to fit them with the equation f(x,y) = ax + by + cxy + d . Is there a way to do it? Can we set the custom equation using fitsurface?

Thank you very much in advance for your answers!

Regards,

Laura

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Answer 1

Matt J 2021-8-2

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https://ww2.mathworks.cn/matlabcentral/answers/887754-how-to-set-a-custom-equation-to-fit-5-points-in-space-by-fitsurface#answer_758957

在 MATLAB Online 中打开

Another way, which would allow you stay within the framework of the Curve Fitting Toolbox, would be to do a poly22 fit with upper and lower bounds,

 lb=-inf(1,6); lb([4,6])=0; ub=-lb; fitsurface=fit([x,y],z, 'poly22','Lower',lb,'Upper',ub)
     Linear model Poly22:
     fitsurface(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2
     Coefficients (with 95% confidence bounds):
       p00 =       1.319  (1.215, 1.423)
       p10 =  -0.0002893  (-0.0003375, -0.0002411)
       p01 =       -1.19  (-1.37, -1.01)
       p20 =           0  (fixed at bound)
       p11 =   0.0002666  (0.0001826, 0.0003507)
       p02 =           0  (fixed at bound)

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Matt J 2021-8-2

This procedure is only necessary for being able to use the Curve Fitting Toolbox but it doesn't affect the fitting procedure, is it correct?

Well, it's a bit less efficient because you have more data to crunch in this case. The most efficient procedure would be the one given in my original answer.

laura bagnale 2021-8-3

Ok thank you very much for your help and for the explanation!

Kind Regards,

Laura

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Answer 2

Matt J 2021-7-28

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https://ww2.mathworks.cn/matlabcentral/answers/887754-how-to-set-a-custom-equation-to-fit-5-points-in-space-by-fitsurface#answer_755754

编辑：Matt J 2021-7-28

在 MATLAB Online 中打开

I can't find "fitsurface" in the Mathworks documentation, but the fit is easy enough to do algebraically.

x=x(:); y=y(:); z=z(:); %ensure column vectors
params=num2cell([x,y,x.*y,x.^0]\z);
[a,b,c,d]=deal(params{:})

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Matt J 2021-7-28

OP's comments moved:

Hi MattJ,

thank you for your answer. Perhaps I wasn't so clear in posting my question, sorry.

Below you can see my code and how I fit the surface:

A = [1; 1.5; 2.0; 7; 2.5; 0.5];

X = normalize(A,'range');

B = [1; 0; 0.5; 2; 1.0; 1.0];

Y = normalize(B,'range');

C = [0.9; 3.2; 4.3; 7.5; 5.5; 0.9];

Z = normalize(C,'range');

%plotting data and fitsurface

plot3(X,Y,Z,'or');

fs=fit([X,Y],Z, 'poly22')

plot(fs, [X,Y],Z)

Linear model Poly22:

fs(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2

Coefficients:

p00 = -1.889

p10 = 13.03

p01 = -0.06061

p20 = 9.816

p11 = -27.58

p02 = 7.677

Now I would like to do the same but replacing the poly22 with my custom equation f(x,y) = ax + by + cxy + d, and I'm not sure how to do it, if there is a way.

Thank you very much!

Laura

Just an additional comment: I already know that through the cftool one can put the custom equation.

My question is referred to the case in which I don't use the cftool but I would like to write the code in my script, as I did in the code above.

Thanks a lot

laura bagnale 2021-7-29

The point is that I would like to have the possibility to fit the points in space with a surface that I can represent in a graph and to have an estimation of the coefficient through the fitting, like what I did using poly22.

I consider your answer very helpful but I would like also to fit the points with a surface.

Thank you for your help.

Laura

Matt J 2021-8-2

在 MATLAB Online 中打开

One you have the coefficients, it is eay to plot the surface.

x=x(:); y=y(:); z=z(:); %ensure column vectors
params=num2cell([x,y,x.*y,x.^0]\z);
[a,b,c,d]=deal(params{:});
fz=@(x,y) ax + by + cxy + d;
fsurf(fz);

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How to set a custom equation to fit 5 points in space by fitsurface?

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