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
