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The affine transform used for AppKit drawing are represented by a 3 × 3 matrix. This is enough to define transforms between 2D coordinate spaces. With Core Animation, we get a new kind of affine transform. The CATransform3D structure contains a 4 × 4 matrix. This can represent arbitrary transforms in 3D space.
Although transforms are structures, they can be manipulated using KVC key paths. For example, you can set the z-axis rotation in a layer like this: