Determine if angle lies between 2 other angles

Question

I am trying to figure out whether a angle lies between 2 other angles. I have been trying to create a simple function to perform this but none of my techniques will work for

Answer 1

All the top answers here are wrong. As such I feel it is necessary for me to post an answer.

I'm just reposting a portion of an answer which I posted here: https://stackoverflow.com/a/42424631/2642059 That answer also deals with the case where you already know which angle is the lefthand side and righthand side of the reflexive angle. But you also need to determine which side of the angle is which.

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1^st to find the leftmost angle if either of these statements are true angle1 is your leftmost angle:

1. angle1 <= angle2 && angle2 - angle1 <= PI
2. angle1 > angle2 && angle1 - angle2 >= PI

For simplicity let's say that your leftmost angle is l and your rightmost angle is r and you're trying to find if g is between them.

The problem here is the seem. There are essentially 3 positive cases that we're looking for:

1. l ≤ g ≤ r
2. l ≤ g ∧ r < l
3. g ≤ r ∧ r < l

Since you're calculating the lefthand and righthand sides of the angle, you'll notice there is an optimization opportunity here in doing both processes at once. Your function will look like:

if(angle1 <= angle2) {
    if(angle2 - angle1 <= PI) {
        return angle1 <= target && target <= angle2;
    } else {
        return angle2 <= target || target <= angle1;
    }
} else {
    if(angle1 - angle2 <= PI) {
        return angle2 <= target && target <= angle1;
    } else {
        return angle1 <= target || target <= angle2;
    }
}

Or if you need it you could expand into this nightmare condition:

angle1 <= angle2 ?
(angle2 - angle1 <= PI && angle1 <= target && target <= angle2) || (angle2 - angle1 > PI && (angle2 <= target || target <= angle1)) :
(angle1 - angle2 <= PI && angle2 <= target && target <= angle1) || (angle1 - angle2 > PI && (angle1 <= target || target <= angle2))

Note that all this math presumes that your input is in radians and in the range [0 : 2π].

Live Example