Circle Sort Comparator

circle_sort_comparator.js

/**
 * This is a comparator for two points to position them along the circle around C(x,y)
 *
 * @example
 * points.sort(function (a, b) {
 *   return comparator(a.x, a.y, bx, b.y, c.x, c.y);
 * });
 * 
 * @param {number} ax
 * @param {number} ay
 * @param {number} bx
 * @param {number} by
 * @param {number} cx Center x
 * @param {number} cy Center y
 * @return {number} -1 if a is before b on the circle
 */
function compare (ax, ay, bx, by, cx, cy) {
  if (ax - cx >= 0 && bx - cx < 0) return 1;
  if (ax - cx < 0 && bx - cx >= 0) return -1;
  if (ax - cx === 0 && bx - cx === 0) {
    return (ay - by >= 0 || by - cy >= 0) ? (ay - by) : (by - ay);
  }

  // compute the cross product of vectors (center -> a) x (center -> b)
  var det = (ax - cx) * (by - cy) - (bx - cx) * (ay - cy);
  if (det < 0) return  1;
  if (det > 0) return -1;

  // points a and b are on the same line from the center
  // check which point is closer to the center
  var d1 = (ax - cx) * (ax - cx) + (ay - cy) * (ay - cy);
  var d2 = (bx - cx) * (bx - cx) + (by - cy) * (by - cy);
  
  return d1 - d2;
}