circle_circle_intersection.coffee

tributary.circle_circle_intersection = (p0, r0, p1, r1) ->
  # literal translation of
  # http://paulbourke.net/geometry/circlesphere/tvoght.c

  # dx and dy are the x, y distances between the circle centers.
  [x0, y0] = [p0.x, p0.y]
  [x1, y1] = [p1.x, p1.y]
  [dx, dy] = [x1 - x0, y1 - y0]

  # Determine the straight-line distance between the centers.
  # d = hypot(dx,dy); // Suggested by Keith Briggs
  d = Math.sqrt((dy*dy) + (dx*dx));

  # Check for solvability. quit early
  return None if (d > (r0 + r1)) or (d < Math.abs(r0 - r1))

  # the distance from point 0 to point 2.
  a = ((r0*r0) - (r1*r1) + (d*d)) / (2.0 * d) ;

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

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

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

  # absolute intersection points.
  [{x: x2 + rx, y: y2 + ry}, {x: x2 - rx, y: y2 - ry}]