Is there a fast way to calculate the smallest delta between two rotation values?

Question

There are two views:

viewA and viewB. Both are rotated.

The coordinate system for rotation is weird: It goes from 0 to 179,999999 or -179,99999 degrees. So essentially 179,99999 and -179,99999 are very close together!

I want to calculate how much degrees or radians are between these rotations.

For example:

viewA is rotated at 20 degrees

viewB is rotated at 30 degrees

I could just do: rotationB - rotationA = 10.

But the problem with this formula:

viewA is rotated at 179 degrees viewB is rotated at -179 degrees

that would go wrong: rotationB - rotationA = -179 - 179 = -358

358 is plain wrong, because they are very close together in reality. So one thing I could do maybe is to check if the absolute result value is bigger than 180, and if so, calculate it the other way around to get the short true delta. But I feel this is plain wrong and bad, because of possible floating point errors and unprecision. So if two views are rotated essentially equally at 179,99999999999 degrees I might get a weird 180 or a 0 if I am lucky.

Maybe there's a genius-style math formular with PI, sine or other useful stuff to get around this problem?

Answer 1

Take the difference, add 360, and mod by 360.

Answer 2

EDIT: Original answer (with Mod) was wrong. would have given 180 - right answer in certain circumstances (angles 30 and -20 for example would give answer of 130, not correct answer of 50):

Two correct answers for all scenarios:

If A1 and A2 are two angles (between -179.99999 and 179.99999, and Abs means take the Absolute Value, The angular distance between them, is expressed by:

Angle between = 180 - Abs(Abs(A1 - A2) - 180)

Or, using C-style ternary operator:

Angle between = A1 < 180 + A2? A1 - A2: 360 + A1 - A2

Answer 3

Let's try this again:
There are two angles between A and B. One of them is

θ₁ = A - B

The other is

θ₂ = 360 - θ₁

So just take the minimum of those two.

Answer 4

Judging from the recent questions you've asked, you might want to read up on the unit circle. This is a fundamental concept in trigonometry, and it is how angles are calculated when doing rotations using CGAffineTransforms or CATransform3Ds.

Basically, the unit circle goes from 0 to 360 degrees, or 0 to 2 * pi (M_PI is the constant used on the iPhone) radians. Any angle greater than 360 degrees is the same as that angle minus a multiple of 360 degrees. For example, 740 degrees is the same as 380 degrees, which is the same as 20 degrees, when it comes to the ending position of something rotated by that much.

Likewise, negative degrees are the same as if you'd added a multiple of 360 degrees to them. -20 degrees is the same as 340 degrees.

There's no magic behind any of these calculations, you just have to pay attention to when something crosses the 0 / 360 degree point on the circle. In the case you describe, you can add 360 to any negative values to express them in positive angles. When subtracting angles, if the ending angle is less than the starting angle, you may also need to add 360 to the result to account for crossing the zero point on the unit circle.

Answer 5

In addition to Brad Larson's excellent answer I would add that you can do:

CGFloat adjustAngle(angle) { return fmod(angle + 180.0, 360.0); }
...
CGFloat difference = fmod(adjustAngle(angle1) - adjustAngle(angle2), 360.0);