def _overlap(x1,w1, x2, w2):
  """
  A utility function for testing for overlap on a single axis. Returns true
  if a line w1 above and below point x1 overlaps a line w2 above and below point x2.
  """
  if x1+w1 < x2-w2: return False
  if x1-w1 > x2+w2: return False

  return True