Simple: Angle Between Two Angles of Circle

Question

I want to be able to define a start and an end angle in a circle and then be able to come up with an algorithm that allows me to test if an angle is between the two angles (clockwise from start to end). Note that this has to work if the start point is 300deg and the end point is 45degrees. So for example,

start=10, end=50, test=20 (inside) start=270, end=90, test=350 (inside) start=270, end=90, test=180 (outside) start=310, end=20, test=0 (inside) start=310, end=20, test=200 (outside)

Thanks so much!

Answer 1

• Start by subtracting the start angle from all angles.
• If any angles are now negative, add $360^\circ$ to them.
• Now check to see if the middle angle is smaller than the end angle.

Example $1$: Is $180^\circ$ between $270^\circ$ and $90^\circ$?

• Subtract to get start and end angles $0^\circ$, $-180^\circ$, with midpoint $-90^\circ$
• Add $360^\circ$ to get $0^\circ$, $180^\circ$, with midpoint $270^\circ$
• Since $270^\circ > 180^\circ$, $180^\circ$ is not between $270^\circ$ and $90^\circ$.

Example $2$: Is $0^\circ$ between $310^\circ$ and $20^\circ$?

• Subtract to get start and end angles $0^\circ$, $-290^\circ$, with midpoint $-310^\circ$
• Add $360^\circ$ to get $0^\circ$, $70^\circ$, with midpoint $50^\circ$
• Since $50^\circ < 70^\circ$, $0^\circ$ is between $310^\circ$ and $20^\circ$.

And in C / C++:

bool isBetween(float start, float end, float mid) {     
    end = (end - start) < 0.0f ? end - start + 360.0f : end - start;    
    mid = (mid - start) < 0.0f ? mid - start + 360.0f : mid - start; 
    return (mid < end); 
}