CGAffineTransform rotation goes the wrong way

Question

In my experiment, i conclude these:

YourView.transform = CGAffineTransformMakeRotation( positive value ); 

will rotate the view clockwise, and

YourView.transform = CGAffineTransformMakeRotation( Negative value ); 

will rotate the view counterclockwise,

But the document says:

The angle, in radians, by which to rotate the affine transform. In iOS, a positive value specifies counterclockwise rotation and a negative value specifies clockwise rotation.

does those contradict with each other?

Answer 1

Your confusion is quite understandable.

In truth, a positive angle represents a rotation from the positive X axis toward the positive Y axis. A negative angle represents a rotation from the positive X axis toward the negative Y axis.

The “native” Core Graphics coordinate system is modeled after the standard Cartesian coordinate system, in which the Y axis increases upward on the page. In this system, a positive angle represents a counter-clockwise rotation:

So if you create your own CGContext (for example, by using CGBitmapContextCreate or CGPDFContextCreate), rotations will work as you expect.

However, computer systems have historically used a coordinate system in which the Y axis increases downward on the page. In a flipped coordinate system like this, a positive angle represents a clockwise rotation:

Notice that in both coordinate systems, a positive angle rotates from the positive X axis toward the positive Y axis.

It turns out that UIKit flips the coordinate system of the graphics contexts that it creates for you. This includes the graphics context it sets up before sending you drawRect: and the graphics context it sets up in UIGraphicsBeginImageContext. (The Quartz 2D Programming Guide explains this.) You can check this by looking at the current transform matrix (using CGContextGetCTM). You will find that it has a -1 in its d element, meaning that the Y axis is flipped.

A UIView also uses a flipped coordinate system for laying out its subviews, which affects the meaning of the UIView transform property.