Scalings must always be positive. Scaling refers to a change in length, and length is always a positive quantity. I noted this in class and at one or more points in the notes such as:
Clearly this requires a scaling of: S1per = S(|URW'''3/URW'''1|, |URW'''3/URW'''2|, 1) where the absolute values are used to protect against negative scalings.
However there are other points in the notes where the issue is not revisited but just left to common sense. For example, at one point I refer to:
Sper = (URW'''3 / URW'''1 / L3''', URW'''3 / URW'''2 / L3''', 1 / L3''')
If any of the three parameters here is negative, what we want is its absolute value.
The consequence of scaling by negative amounts can be to reverse a direction completely since it can turn x into -x.
So please check anywhere you do scaling to make sure its always a positive scaling. --