plot plane through set of 3d point

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?

Answer 1

[Roger Stafford]

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.

[ha ha]

I don't understand your code. Can you perform it by using the attached data "ha.txt"

[Roger Stafford]

I made a mistake on the 'eig' function which I have corrected above. (Chalk it up to old age.)

[ha ha]

Can you help me to perform it by using the attached data "ha.txt"