def _sine_net_to_path_points_test_function_to_approximate(t):
  """Function whose Fourier series over [-1, 1] converges reasonably quickly."""
  # The Fourier series converges reasonably quickly on the interval [-1, 1]
  # since
  #
  #        f(1) = f(-1)
  #       f'(1) = f'(-1)
  #      f''(1) = f''(-1)
  #     f'''(1) = f'''(-1).
  #
  # Multiplying by (2 - t) makes the function neither even nor odd, ensuring
  # that the Fourier series will contain both sine and cosine terms. Since we
  # use phases rather than separate sine and cosine terms, this ensures the
  # phases will be nontrivial.
  return (1 - t)**4 * (1 + t)**4 * (2 - t)