code: def transform_e1e2(x, y, e1, e2, center_x=0, center_y=0):
      
      x_shift = x - center_x
      y_shift = y - center_y
      x_ = (1-e1) * x_shift - e2 * y_shift
      y_ = -e2 * x_shift + (1 + e1) * y_shift
      det = np.sqrt((1-e1)*(1+e1) + e2**2)
      return x_ / det, y_ / det
docs: maps the coordinates x, y with eccentricities e1 e2 into a new elliptical coordiante system
  
      :param x:
      :param y:
      :param e1:
      :param e2:
      :param center_x:
      :param center_y:
      :return: