On Thu, Jun 13, 2019 at 3:01 PM Richard Copley <address@hidden
> Yes, but our transformation includes translation, rotation, and
> another translation. Not just one translation. IOW, it isn't the
> transformation matrix that is given; it's the operation on the image.
There's a miscommunication here. I was speaking to Alan's question about how
to geometrically interpret the components of a transformation matrix.
If the question is what translations to use in order to generate a rotation
around an arbitrary point p, then there's no question: the sequence of
operations is translation by -p, then rotation, then translation by p.
> The origin is at the top left so a pure rotation clockwise about the origin
> through angle a goes like this:
> [cos(a) -sin(a) 0] [X] [cos(a) * X - sin(a) * Y]
> [sin(a) cos(a) 0] [Y] = [sin(a) * X + cos(a) * Y]
> [ 0 0 1]  [ 1]
That is a counter-clockwise rotation.