Fowler Angles

If you want a monotonic function of the angle, rather than needing the value of the angle itself, you can avoid the arcsine and arctangent computation by using Fowler angles. These use dx and dy to return a value that can be used for angular comparison routines.

/*
   This function is due to Rob Fowler.  Given dy and dx between 2 points
   A and B, we calculate a number in [0.0, 8.0) which is a monotonic
   function of the direction from A to B. 

   (0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0) correspond to
   (  0,  45,  90, 135, 180, 225, 270, 315, 360) degrees, measured
   counter-clockwise from the positive x axis.
*/
double FowlerAngle(dy,dx)
double dy,dx;
{
    double adx, ady;    /* Absolute Values of Dx and Dy */
    int    code;        /* Angular Region Classification Code */

    adx = (dx < 0) ? -dx : dx;  /* Compute the absolute values. */
    ady = (dy < 0) ? -dy : dy;

    code = (adx < ady) ? 1 : 0;
    if (dx < 0)  code += 2;
    if (dy < 0)  code += 4;

    switch (code)
    {
        case 0: return (dx==0) ? 0 : ady/adx;  /* [  0, 45] */
        case 1: return (2.0 - (adx/ady));      /* ( 45, 90] */
        case 3: return (2.0 + (adx/ady));      /* ( 90,135) */
        case 2: return (4.0 - (ady/adx));      /* [135,180] */
        case 6: return (4.0 + (ady/adx));      /* (180,225] */
        case 7: return (6.0 - (adx/ady));      /* (225,270) */
        case 5: return (6.0 + (adx/ady));      /* [270,315) */
        case 4: return (8.0 - (ady/adx));      /* [315,360) */
    }
}