Does this matrix make me look sheared?
A customer recently had a problem with the way we were drawing his circles. They were coming out looking like weird wankel rotator things.
The problem turned out to be a spline thing: stress management and periodicity. But before sorting that out I went down this long rabbit hole about transformation matrices, and figuring out whether a given matrix contains a shear component.
You can go down the rabbit hole yourself if you want to: just pull out your linear algebra textbook, and spend some quality time at Wikipedia’s extensive math pages, but it all comes back to a very simple question: if I take two vectors that are perpendicular before I transform them, will they still be perpendicular after I transform them? Check for each pair of vectors in a basis set, and you’re done.
So I think the check for shear is (T * x) dot (T * y) != 0 => implies shear. Seem sensible enough?
Why does this matter? Tune in another time.