[vtkusers] RE: plane approximation

[CPBuid: ljvanruijven]

Hi Ebner,

For every point x,y,z calculate xx, xy, xz, yy, yz and zz. Add all terms, and 
put the sums in a symmetric 3 by 3 matrix (xx,xy,xz; xy,yy,yz; xz,yz,zz). 
This matrix represents an ellipsoid whose shape corresponds with the shape of 
your points. From this matrix you can calculate the eigenvalues and 
eigenvectors (see vtkMath). These eigenvectors and eigenvalues define the 
directions and lengths of the main axes of this ellipsoid. The vectors 
belonging to the largest eigenvalues give you the orientation of the 
requested plane.

The position of the plane is determined by the centriod of your points.

Leo van Ruijven