Crystallography - Thermal Ellipsoids from Uij?

I don't know if anyone can help me but here it goes...

I'm trying to write software to display a mollecule by reading in .RES/.INS files used by XP, XShell, etc. to start with. (Though I hope to move on to more formats later.) I've got the conversion from crystal coordinates to reciprocal space and realspace down and can draw simple atoms and bonds. What I'm missing however are the thermal ellipsoids as defined by the Uij values of the atoms.

I don't suppose anyone knows and can explain in simple steps what I have to do in order to convert those Uij values with a 50% probability into either a matrix that defines the ellipsoid's realspace vectors and rotation or a set of realspace vectors angles to use to draw the ellipsoid in realspace?

From what I understand it involves using eigenvectors and should be straight forward, but no matter what I do I just can't seem to get it right.

Help in just understanding the steps needed to get this right would be greatly appreciated. Thanks.

Problem Solved!

In case anyone was wondering, I finally managed to get it working.