Problems fitting a plane using cftool
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I'm having an issue fitting a plane to a 3d data set using the cftool. I have lots of these data sets, and every once and a while, the plane fit it gives me is clearly way off, and I have no idea why.
Here is the piece of code I'm using, its pretty basic:
X = data(:,1);
Y = data(:,2);
Z = data(:,3);
fitobject = fit( [ X, Y], Z, fittype('poly11'));
Fitted_plane = [ fitobject.p00 , fitobject.p10 , fitobject.p01 ];
And to give you an idea of what the fit looks like:
And the fit is clearly not correct, but I cannot for the life of me figure out how to fix it. This happens for maybe 1/10 of the fits I'm doing, and I was wondering if maybe there is a problem with the toolbox? I can definitely send out the data set, I just didnt want to post the whole thing here.
Thanks in advance.
采纳的回答
From your plots, it looks like the 3D plane containing your data could be of the form
a*X + b*Y + c*Z = d
but with c=0. Obviously, when c=0, this cannot be rewritten as a function Z(X,Y), as you are trying to do.
The following is a way to fit the plane without CFTOOL and it works for all plane orientations,
m=mean(data,1);
[~,~,v]=svd( bsxfun(@minus, data, m) ,0);
abc=v(:,end); %plane normal vector
d=dot(abc,m); %distance from origin
a=abc(1); b=abc(2); c=abc(3);
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If you have the Symbolic Toolbox, this
seems to work well. And even if you don't, it's not too hard to modify the file.
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