I think I go over it in week 7 actually, and I know you do have it already so not like I'm peddling :p
But in terms of shape animation, you have three modes in Softimage.
Global and Object are fairly self explanatory in how the displacement vector that moves one base point to its target shape is oriented. If shapes happen before other deformations, those are fine.
However, if you save a displacement vector moving a point on the top of a head by one unit in Y, oriented to the object, when the envelope bends that head forward and you apply the shape AFTER the envelope, you are left with a stray point still moving in object Y.
Local relative shapes in Soft still save a displacement vector like the other modes, but instead of using one transform for the whole set, those vectors are saved after a local transform for each point is obtained, so that if you move a set of points, that vector multiplied by the transform of each point will still produce a displacement similar to the one intended.
Now, points don't have a full transform, they have a position, and possibly a normal and a set of edges coming off it, so you have to figure out a coherent, repeatable (after points move) transform with those.
AFAIK Soft uses a simple system, Normal = Y axis, first edge projected on the normal plane then normalized = X axis, the cross product between the two (with the right handedness and normalized again for good measure) produces the Z. You can then transform your displacement in object space by the inverse of that transform, and it will become "point neutral" in a way, at least for storage.
When time comes to re-apply it, after the mesh has deformed, you re-derive that point's transform the same way, and multiply that vector by it, and it will be "mesh relative".
Of course it comes with fringe cases (IE: first edge aligned to the normal, resulting in a 0 vector for X), but those fringe cases would normally imply someone who modelled, or subsequently deformed the mesh needs to be chemically castrated ASAP, lest they have kids just as stupid.