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how to find the intersecting curve between the fitted surface (cftool )and a plane ? functions after centering and scaling

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Josh
Josh 2013-9-11
关闭： MATLAB Answer Bot 2021-8-20
I try to work out the function of the intersecting curve of a set of x,y,z points data and a plane, for example z=5. My idea is to fit the data using a polynomial function:z=f(x,y)and solve the equation f(x,y)=5.
The points in XYZ can be fitted into a polynomial function using cftool. However, the cftool ask me to center and scale the data to avoid bad conditioned matrix.
Without the centering and scaling, coefs are:
p00 = 1.357e+04
p10 = -5.287
p01 = -18.78
p20 = 0.002775
p11 = 0.002278
p02 = 0.006697
With the centering and scaling:
p00 = 24.36
p10 = -4.337
p01 = -0.4805
p20 = 0.1175
p11 = 0.09394
p02 = 0.2691
I know the centering and scaling is to replace the x by (x-mean(x))/std(x) and y by (y-mean(y))/std(y). However, I don't know how to construct a sym object after the centering and scaling.
Is anyone can help? thanks in advance.

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