One step affine transform for rotation around a point?

A rotation of angle a around the point (x,y) corresponds to the affine transformation:

CGAffineTransform transform = CGAffineTransformMake(cos(a),sin(a),-sin(a),cos(a),x-x*cos(a)+y*sin(a),y-x*sin(a)-y*cos(a));

You may need to plug in -a instead of a depending on whether you want the rotation to be clockwise or counterclockwise. Also, you may need to plug in -y instead of y depending on whether or not your coordinate system is upside down.

Also, you can accomplish precisely the same thing in three lines of code using:

CGAffineTransform transform = CGAffineTransformMakeTranslation(x, y);transform = CGAffineTransformRotate(transform, a);transform = CGAffineTransformTranslate(transform,-x,-y);

If you were applying this to a view, you could also simply use a rotation transform via CGAffineTransformMakeRotation(a), provided you set the view's layer's anchorPoint property to reflect the point you want to rotate around. However, is sounds like you aren't interested in applying this to a view.

Finally, if you are applying this to a non-Euclidean 2D space, you may not want an affine transformation at all. Affine transformations are isometries of Euclidean space, meaning that they preserve the standard Euclidean distance, as well as angles. If your space is not Euclidean, then the transformation you want may not actually be affine, or if it is affine, the matrix for the rotation might not be as simple as what I wrote above with sin and cos. For instance, if you were in a hyperbolic space, you might need to use the hyperbolic trig functions sinh and cosh, along with different + and - signs in the formula.

P.S. I also wanted to remind anyone reading this far that "affine" is pronounced with a short "a" as in "ask", not a long "a" as in "able". I have even heard Apple employees mispronouncing it in their WWDC talks.

for Swift 4

print(x, y) // where x,y is the point to rotate aroundlet degrees = 45.0let transform = CGAffineTransform(translationX: x, y: y)    .rotated(by: degrees * .pi / 180)    .translatedBy(x: -x, y: -y)

For those like me, that are struggling in search of a complete solution to rotate an image and scale it properly, in order to fill the containing frame, after a couple of hours this is the most complete and flawless solution that I have obtained.

The trick here is to translate the reference point, before any trasformation involved (both scale and rotation). After that, you have to concatenate the two transform in order to obtain a complete affine transform.

I have packed the whole solution in a CIFilter subclass that you can gist here.

Following the relevant part of code:

CGFloat a = _inputDegree.floatValue;CGFloat x = _inputImage.extent.size.width/2.0;CGFloat y = _inputImage.extent.size.height/2.0;CGFloat scale = [self calculateScaleForAngle:GLKMathRadiansToDegrees(a)];CGAffineTransform transform = CGAffineTransformMakeTranslation(x, y);transform = CGAffineTransformRotate(transform, a);transform = CGAffineTransformTranslate(transform,-x,-y);CGAffineTransform transform2 = CGAffineTransformMakeTranslation(x, y);transform2 = CGAffineTransformScale(transform2, scale, scale);transform2 = CGAffineTransformTranslate(transform2,-x,-y);CGAffineTransform concate   = CGAffineTransformConcat(transform2, transform);