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ha ha
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plot plane through set of 3d point

Asked by ha ha
on 28 Feb 2018
Latest activity Edited by ha ha
on 1 Mar 2018
Let's say : I have a set of 3d data (x,y,z) from experiment
data=[x1 y1 z1
x2 y2 z2
x3 y3 z3
x4 y4 z4
...........]
I want to plot the plane contain all points by total least square method. The result as follow. How can I plot like sample illustration?

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1 Answer

Answer by Roger Stafford on 28 Feb 2018
Edited by Roger Stafford on 28 Feb 2018

If X, Y, and Z are vectors of the x,y,z coordinates of your points, do this:
dX = X-mean(X);
dY = Y-mean(Y);
dZ = Z-mean(Z);
XX = sum(dX.^2); YY = sum((dY.^2; ZZ = sum(dZ.^2);
XY = sum(dX.*dY); XZ = sum(dX.*dZ); YZ = sum(dY.*dZ);
A = [XX,XY,XZ;
XY,YY,YZ;
XZ,YZ,ZZ];
[V,D] = eig(A); % <--Corrected
[~,k] = min(diag(D));
Then
V(1,k)*(x-mean(X))+V(2,k)*(y-mean(Y))+V(3,k)*(z-mean(Z)) = 0 % <--Corrected
where V(:,k) is the eigenvector of A with the smallest eigenvalue, and gives the equation for the best fit plane through your points. (Note: The lowercase x, y, and z here refer to coordinates of the equation of the plane.)
You can plot this plane by using an appropriate meshgrid of x,y points along with solving for z in the plane equation making use of the 'surf' command.

  3 Comments

I don't understand your code. Can you perform it by using the attached data "ha.txt"
I made a mistake on the 'eig' function which I have corrected above. (Chalk it up to old age.)
Can you help me to perform it by using the attached data "ha.txt"

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