Averaging angles

Question

I looked at some solutions here but none provide what I need, so:

I need to average an array of angles(0 to 359.9, no negatives) (A1 + A2 + A3 + An) / n

The issue is when you get an array {1, 359, 2, 358} the average if you use the formula above is 180, but actually it is supposed to be 0.

Any thoughts?

Answer 1

Add unit vectors of each angle, and convert the resulting vector back into an angle. If the result vector is of zero length, the inputs cancelled each other out and the result is indeterminate.

A unit vector has a length of 1, and its x and y lengths are given by the cosine and sine of the angle. Thus you average your examples as in the following pseudo-code:

x = cos(radians(1)) + cos(radians(359)) + cos(radians(2)) + cos(radians(358));
y = sin(radians(1)) + sin(radians(359)) + sin(radians(2)) + sin(radians(358));
angle = degrees(atan2(y, x));