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Principal Component Analysis and OBB generation

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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?

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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)

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