def _board_to_cartesian(x, y, z):
    """Translate from logical board coordinates (x, y, z) into cartesian
    coordinates for printing hexagons.

    Example coordinates::

         ___     ___
        /-15\___/1 5\___
        \___/0 4\___/3 4\
        /-13\___/1 3\___/
        \___/0 2\___/2 2\___
            \___/1 1\___/3 1\
            /0 0\___/2 0\___/
            \___/   \___/

    Parameters
    ----------
    x, y, z : int
        The logical board coordinates.

    Returns
    -------
    x, y : int
        Equivalent Cartesian coordinates.
    """
    cx = (2*x) - y + (1 if z == 1 else 0)
    cy = (3*y) + z

    return (cx, cy)