angularDifference.m

Calculate the difference between two angles

The calculation of the difference between two angles a and b, i.e., subtraction on the circle, is not entirely trivial because the circle is a closed manifold. For this operation to be well defined, a "cut" must be made so that the circle is "opened". One can then require that the interval between b and a cannot cross this cut.
Example 1: a = pi/2, b=0, cut=pi. Then
a-b = pi/2
b-a = -pi/2

Example 2: a = pi/2, b=0, cut=pi/4. Then
a-b = -3*pi/2
b-a = 3*pi/2.

For many applications one is typically concerned about small deviations from 0, and in such cases the obvious cut would be pi. But sometimes the cut must be elsewhere.