Circle-circle intersection

circle_circle_intersection.js

/**
  * Intersection point of 2 circles
  *
  * http://paulbourke.net/geometry/circlesphere/
  * 
  * @param  {number} x0
  * @param  {number} y0
  * @param  {number} r0
  * @param  {number} x1
  * @param  {number} y1
  * @param  {number} r1
  * @return {null|Array.<Array.<number>>}
  */
function circleCircleIntersection (x0, y0, r0, x1, y1, r1) {
  let a, dx, dy, d, h, rx, ry;
  let x2, y2;

  // dx and dy are the vertical and horizontal distances between
  // the circle centers.
  dx = x1 - x0;
  dy = y1 - y0;

  // Determine the straight-line distance between the centers. */
  d = Math.sqrt(dx * dx + dy * dy);

  // no solution. circles do not intersect.
  if (d > (r0 + r1))         return null;
  // no solution. one circle is contained in the other
  if (d < Math.abs(r0 - r1)) return null;

  // 'point 2' is the point where the line through the circle
  // intersection points crosses the line between the circle
  // centers.

  // Determine the distance from point 0 to point 2.
  a = ((r0 * r0) - (r1 * r1) + (d * d)) / (2 * d);

  // Determine the coordinates of point 2.
  x2 = x0 + (dx * a / d);
  y2 = y0 + (dy * a / d);

  // Determine the distance from point 2 to either of the
  // intersection points.
  h = Math.sqrt((r0 * r0) - (a * a));

  // Now determine the offsets of the intersection points from point 2.
  rx = -dy * (h / d);
  ry =  dx * (h / d);

  // Determine the absolute intersection points
  return [
    [x2 + rx, y2 + ry],
    [x2 - rx, y2 - ry]
  ];
}