How can I find the difference between two angles?

Question

Given 2 angles in the range -PI -> PI around a coordinate, what is the value of the smallest of the 2 angles between them?

Taking into account that the difference between PI and -PI is not 2 PI but zero.

Example:

Imagine a circle, with 2 lines coming out from the center, there are 2 angles between those lines, the angle they make on the inside aka the smaller angle, and the angle they make on the outside, aka the bigger angle. Both angles when added up make a full circle. Given that each angle can fit within a certain range, what is the smaller angles value, taking into account the rollover

Answer 1

This gives a signed angle for any angles:

a = targetA - sourceA
a = (a + 180) % 360 - 180

Beware in many languages the modulo operation returns a value with the same sign as the dividend (like C, C++, C#, JavaScript, full list here). This requires a custom mod function like so:

mod = (a, n) -> a - floor(a/n) * n

Or so:

mod = (a, n) -> (a % n + n) % n

If angles are within [-180, 180] this also works:

a = targetA - sourceA
a += (a>180) ? -360 : (a<-180) ? 360 : 0

In a more verbose way:

a = targetA - sourceA
a -= 360 if a > 180
a += 360 if a < -180

Answer 2

x is the target angle. y is the source or starting angle:

atan2(sin(x-y), cos(x-y))

It returns the signed delta angle. Note that depending on your API the order of the parameters for the atan2() function might be different.