Average of two angles with wrap around

Question

Possible Duplicate:
How do you calculate the average of a set of circular data?

I have two angles, a=20 degrees and b=350 degrees. The average of those two angles are 185 degrees. However, if we consider that the maximum angle is 360 degrees and allows for wrap around, one could see that 5 degrees is a closer average.

I'm having troubles coming up with a good formula to handle that wrap around when calculating average. Anyone got any hints?

Or am I shooting myself in the foot here? Is this considered "bad practice" in math?

Answer 1

if you have a look at the angular circle, you will see that there are 2 opposite "angles" that corresponds to your "average".

So both 185° and 5° are correct.

But you mentionned the closer average. So in that case, you may choose the angle that is closer.

Usually, the "average" of angles concerns the counterclockwise direction. The "average" is not the same if you switch your two angles (or if you use the clockwise direction).

For example, with a=20° and b=350°, you are looking for the angle that comes after a and before b in the counterclockwise direction, 185° is the answer. If you are looking for the angle that comes before a and after b in the counterclockwise direction (or after a and before b in the counterclock wise direction), 5° is the answer.

The answer of this post is the right way to do.

So the pseudo-code for the solution is

if (a+180)mod 360 == b then
  return (a+b)/2 mod 360 and ((a+b)/2 mod 360) + 180 (they are both the solution, so you may choose one depending if you prefer counterclockwise or clockwise direction)
else
  return arctan(  (sin(a)+sin(b)) / (cos(a)+cos(b) )