How to wrap around a range

Angles in my program are expressed in 0 to 2pi. I want a way to add two angles and have it wrap around the 2pi to 0 if the result is higher than 2pi. Or if I subtracted an angle from an angle and it was below 0 it would wrap around 2pi.

Is there a way to do this?



  • What you are looking for is the modulus. The fmod function will not work because it calculates the remainder and not the arithmetic modulus. Something like this should work:

    inline double wrapAngle( double angle )
        double twoPi = 2.0 * 3.141592865358979;
        return angle - twoPi * floor( angle / twoPi );


    The remainder is commonly defined as what is left over after long division (eg. the remainder of 18/4 is 2, because 18 = 4 * 4 + 2). This gets hairy when you have negative numbers. The common way to find the remainder of a signed division is for the remainder to have the same sign as the result (eg. the remainder of -18/4 is -2, because -18 = -4 * 4 + -2).

    The definition of x modulus y is the smallest positive value of m in the equation x=y*c+m, given c is an integer. So 18 mod 4 would be 2 (where c=4), however -18 mod 4 would also be 2 (where c=-5).

    The simplest calculation of x mod y is x-y*floor(x/y), where floor is the largest integer that is less than or equal to the input.