Get just the scaling transformation out of CGAffineTransform

Question

I found a similar question about getting just the rotation, but as I understand scaling and rotating work different in the transform matrix.

Matrixes are not my strength

Answer 1

Assuming that the transformation is a scaling followed by a rotation (possibly with a translation in there, but no skewing) the horizontal scale factor is sqrt(a^2+c^2), the vertical scale factor is sqrt(b^2+d^2), and the ratio of the horizontal scale factor to the vertical scale factor should be a/d = -c/b, where a, b, c, and d are four of the six members of the CGAffineTransform, per the documentation (tx and ty only represent translation, which does not affect the scale factors).

|  a  b 0 |
|  c  d 0 |
| tx ty 1 |