I want to support sheer transforms to deform objects (see picture of a sheered cube, with matrix on the right).
But i'm unsure how to enable this for a transform gizmo an any intuitive way.
Til yet i had avoided to expose this as it usually causes lots of issues and confusion, especially if within a hierarchy of transformations. On the other hand it seems a pretty useful option to have.

I can not remember any tool to support this (Max, XSI, Modo…). They do so only with something like a deformation modifier, but i'd like to enable it just for any transform.

Current idea is to use SVD to orthonormalize and keep the gizmo unaffected as in the picture. Seems promising but i'd like to look at some reference of how others do this.