def translate_alpha_to_x(alpha, x_input, x_baseline):
  """Translates alpha to the point coordinates within straight-line interval.

   Args:
    alpha: the relative location of the point between x_baseline and x_input.
    x_input: the end point of the straight-line path.
    x_baseline: the start point of the straight-line path.

  Returns:
    The coordinates of the point within [x_baseline, x_input] interval
    that correspond to the given value of alpha.
  """
  assert 0 <= alpha <= 1.0
  return x_baseline + (x_input - x_baseline) * alpha