   Principal Component Analysis and OBB generation
  Well, I am using the PCA to compute OBBs. I wanted to test my implementation and decided to do it that way:-first of all, test the correctness of the implementation for a cube that has a unit volume, centered at the origin.-secondly, apply a rotation than a translation to the cube and see if the OBB computed has an orientation equal to the rotation, and a center located at a position equal to the translation vector.When I write "an orientation equal to the rotation", I actually mean that the axes of the box should be equal to the columns of the rotation matrix, or their opposite.Am I right to assume that simply rotating a set of points has no effect on the eigenvectors of the covariance matrix, other than rotating them?   
  if you use some ellipsoid instead of box it should work in a way you wrote.for cube it might give you really ugly results.if you build your covariance matrix just with 6 vertices you might end up with eigenvectors pointing in some weird directions (diagonals of the box or something);  I now remember that using PCA gives quite bad fit with squares...I'll try using a set of points located on an ellipsoid. Thanks for the answer.   