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I wish I could answer, but I have no clear and general solution. For instance, I browsed OGL doc yesterday and I still don't know if scale and shear can be done in only one operation using F and glMultMatrixd. Actually, I don't even understand how the current 4x4 matrix can shear the box correctly... Do you know a good web page about this? http://www.songho.ca/opengl/gl_transform.html#matrix doesn't work.But I get in trouble there is no easy way to separate scaling and (rotation+shear), right? Setting 1s on the diagonal is clearly nonsense, although that is what we (I) do now.
For display, at least, one solution would be to draw the 12 edges one by one (origin->Hsize[0],origin->Hsize[1],etc.). (note : there is commented code in periController to recompute Hsize with refSize and F.)
Perhaps list the precise problems here, so we can think about them. For the most general answer on scaling/rotation split, I would think in terms of R.U polar factorisation(http://en.wikipedia.org/wiki/Finite_strain_theory), but I'm not sure we really need that.
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