Hi,
If I have the original transform matrix of a rectangular UIImageView and this image is scaled and rotated and by the end I can read the final transform matrix of this same view, how can I calculate how much the image scaled and rotated?
I suppose that somehow these matrix contain these two informations. The problem is how to extract it...
any clues?
thanks for any help.
A little bit of matrix algebra and trigonometric identities can help you solve this.
We'll work forward to generate a matrix that scales and rotates, and then use that to figure out how to extract the scale factors and rotations analytically.
A scaling matrix to scale by Sx (in the X axis) and Sy (in the Y axis) looks like this:
⎡Sx 0 ⎤
⎣0 Sy⎦
A matrix to rotate clockwise by R radians looks like this:
⎡cos(R) sin(R)⎤
⎣-sin(R) cos(R)⎦
Using standard matrix multiplication, the combined scaling and rotation matrix will look like this:
⎡Sx.cos(R) Sx.sin(R)⎤
⎣-Sy.sin(R) Sy.cos(R)⎦
Note that linear transformations could also include shearing or other transformations, but I'll assume for this question that only rotation and scaling have occurred (if a shear transform is in the matrix, you will get inconsistent results from following the algebra here; but the same approach can be used to determine an analytical solution).
A CGAffineTransform has four members a, b, c, d, corresponding to the 2-dimensional matrix:
⎡a b⎤
⎣c d⎦
Now we want to extract from this matrix the values of Sx, Sy, and R. We can use a simple trigonometric identity here:
tan(A) = sin(A) / cos(A)
We can use this with the first row of the matrix to conclude that:
tan(R) = Sx.sin(R) / Sx.cos(R) = b / a and therefore R = atan(b / a)
And now we know R, we can extract the scale factors by using the main diagonal:
a = Sx.cos(R) and therefore Sx = a / cos(R)
d = Sy.cos(R) and therefore Sy = d / cos(R)
So you now know Sx, Sy, and R.