from typing import Tuple
from typing import List


def _get_lie_algebra(segment_sign: Tuple[int, int, int],
                     radius: float) -> List[Tuple[float, float, float]]:
    """
    Gets the Lie algebra for an arcline path.
    :param segment_sign: Tuple of signs for each segment in the arcline path.
    :param radius: Radius of curvature of the arcline path.
    :return: List of lie algebra poses.
    """

    return [(1.0, 0.0, segment_sign[0] / radius),
            (1.0, 0.0, segment_sign[1] / radius),
            (1.0, 0.0, segment_sign[2] / radius)]