Calculating the average of two angles (two bearings actually)

I recently needed to find the average of two angles.  I was programmatically creating a irregular polygon. I wanted to draw a small square at the points of the polygon, and I wanted the squares to be rotated to the average of the two lines that met at that point.

The issue is that if you have two bearings, one at 20° and one at 350°, or one at 15° and one at 315°. If you just average the two numbers, you get 185°, but the more appropriate number is 5°.  This is called by some a “Wraparound issue” and if you search the web you will see lots of ways to solve this problem. Unfortunately they mostly try to solve it using a mathematical equation.  Now for people that have read this blog for awhile know that I am not allergic to math, but if we can solve this problem simply with an algorithm, we should … that’s what computers are for, right?

So, here is my algorithm and the thought behind it.

---

(Assumptions: 0 >= bearings < 360)

First if you look at the difference between the two bearings, you will see that there are two possibilities, the actual difference is greater than 180° or less than 180°.  Since we are only concerned about “fixing” the issue when the difference is greater than 180°, that is the first thing we will check.

We will call the smaller value bearing bearingA and the larger value bearing bearingB.

Since we know that bearingB has a larger value and that the difference is greater than 180, so bearingB > 180.

So, if we subtract 360  –  bearingB, then just add bearingA + bearingB and divide the total in half, we are 90% there.

One last check. If the result is less than 0, we need to add 360 back in.

So, example #1 20° & 350° 350 – 20 > 180 350 – 360 = –10 (–10 + 20) / 2 = 5 5 ≥ 0 = 5 °

So, example #2 15° & 315° 315 – 15 > 180 315 – 360 = –45 (-45 + 15) / 2 = –30 –30 < 0–30 + 360 = 354°

And here is the code:

Code Snippet

1. private static double GetAverageBearing(double bearingA, double bearingB)
2.         {
3.             if (bearingA > bearingB)
4.             {


5.                 var temp = bearingA;
6.                 bearingA = bearingB;


7.                 bearingB = temp;
8.             }
9.  
10.             if (bearingB - bearingA > 180) bearingB -= 360;
11.  
12.             var finalBearing = (bearingB + bearingA)/2;
13.  
14.             if (finalBearing < 0) finalBearing += 360;
15.             
16.             return finalBearing;
17.         }