Just chiming in since I think (but correct me if I’m wrong) that not everyone picked up on what David was actually suggesting here. It was not, AFAIU, about incorporating the Origin (as currently defined) into the 4x4 matrix that will hold the new direction info, but about having an additional translation in that matrix, one that is in the rotated coord system (the also in the quote above), right @dgobbi?
Sorry if everyone is already on the same page here and I just misunderstood some of the recent responders 