How do I calculate the Rotation in Radians around Z-axis by giving a CATransform3D struct as the input?
basically what I need is the other way round of CATransform3DMakeRotation.
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It depends on what axis you are doing the rotation on.
Rotation about the z-axis is represented as:
a = angle in radians
x' = x*cos.a - y*sin.a
y' = x*sin.a + y*cos.a
z' = z
( cos.a sin.a 0 0)
(-sin.a cos.a 0 0)
( 0 0 1 0)
( 0 0 0 1)
so angle should be a = atan2(transform.m12, transform.m11);
Rotation about x-axis:
a = angle in radians
y' = y*cos.a - z*sin.a
z' = y*sin.a + z*cos.a
x' = x
(1 0 0 0)
(0 cos.a sin.a 0)
(0 -sin.a cos.a 0)
(0 0 0 1)
Rotation about y-axis:
a = angle in radians
z' = z*cos.a - x*sin.a
x' = z*sin.a + x*cos.a
y' = y
(cos.a 0 -sin.a 0)
(0 1 0 0)
(sin.a 0 cos.a 0)
(0 0 0 1)
Nader Eloshaiker
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1Be sure to use atan2 and not atan as the later will not give an angle in the correct quadrant. – Nader Eloshaiker Oct 15 '10 at 13:02
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Thank you Nader, before your answer, I had resorted back to using CALayer's affineTransform property convert the Transform3D into an AffineTransform and then get the angle out of it from this calculation:http://stackoverflow.com/questions/2051811/iphone-sdk-cgaffinetransform-getting-the-angle-of-rotation-of-an-object Now I know, how to calculate directly from Transform3D. Thanks! – ravinsp Oct 16 '10 at 06:18
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Yeah I learned about this back in first year uni and can remember asking my friend "why the he'll do we need to know this" – Nader Eloshaiker Oct 16 '10 at 12:51
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You can calculate the angle from an affine transform too using atan2(transform.b, transform.a), the maths still holds true for a z-axis rotation – Nader Eloshaiker Oct 16 '10 at 13:00
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If the transform is attached to a layer, then you can get the value of the rotation like follows:
CGFloat angle = [(NSNumber *)[layer valueForKeyPath:@"transform.rotation.z"] floatValue];
From the documentation:
Core Animation extends the key-value coding protocol to allow getting and setting of the common values of a layer's CATransform3D matrix through key paths. Table 4 describes the key paths for which a layer’s transform and sublayerTransform properties are key-value coding and observing compliant
