Is angle in between two angles

Question

I have 3 angles a b c

a=315 b=20 c=45

ok so would like to know giving all three if b is in between a and c

i have the long way of doing this adding a

Answer 1

1^st off, every angle is between 2 other angles, what you're really asking is:

For given angles: a, b, and g, is g outside the reflex angle between a and b?

You can just go ahead and define a as the leftmost angle and b as the rightmost angle or you can solve for that, for example if either of these statements are true a is your leftmost angle:

1. a ≤ b ∧ b - a ≤ π
2. a > b ∧ a - b ≥ π

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

If you're just defining a to be leftmost and b to be rightmost you're done here and your condition will look like:

a <= g && g <= b ||
a <= g && b < a ||
g <= b && b < a

If however you calculated the l and r you'll notice there is an optimization opportunity here in doing both processes at once. Your function will look like:

if(a <= b) {
    if(b - a <= PI) {
        return a <= g && g <= b;
    } else {
        return b <= g || g <= a;
    }
} else {
    if(a - b <= PI) {
        return b <= g && g <= a;
    } else {
        return a <= g || g <= b;
    }
}

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

a <= b ?
(b - a <= PI && a <= g && g <= b) || (b - a > PI && (b <= g || g <= a)) :
(a - b <= PI && b <= g && g <= a) || (a - b > PI && (a <= g || g <= b))

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

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