def vreckon(Lat1: float, Lon1: float, Rng: float, Azim: float,
            ell: Ellipsoid = None) -> Tuple[float, float, float]:
    """
    This is the Vincenty "forward" solution.

    Computes points at a specified azimuth and range in an ellipsoidal earth.
    Using the reference ellipsoid, travel a given distance along a given azimuth starting at a given initial point,
    and return the endpoint within a few millimeters of accuracy, using Vincenty's algorithm.

    ```python
    lat2, lon2 = vreckon(lat1, lon1, rng, azim)
    ```

    Parameters
    ----------

    Lat1 : float
        inital geodetic latitude (degrees)
    Lon1 : float
        initial geodetic longitude (degrees)
    Rng : float
        ground distance (meters)
    Azim : float
        intial azimuth (degrees) clockwide from north.
    ell : Ellipsoid, optional
          reference ellipsoid

    Results
    -------

    Lat2 : float
        final geodetic latitude (degrees)
    Lon2 : float
        final geodetic longitude (degrees)
    a21 : float
        reverse azimuth (degrees), at final point facing back toward the intial point


    Original algorithm: T. Vincenty, "Direct and Inverse Solutions of Geodesics on the Ellipsoid with Application of Nested Equations", Survey Review, vol. 23, no. 176, April 1975, pp 88-93. http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf

    Notes:

      1. The Vincenty reckoning algorithm was transcribed verbatim into JavaScript by Chris Veness.
         It was modified and translated to Matlab by Michael Kleder.
         Mr. Veness's website is: http://www.movable-type.co.uk/scripts/latlong-vincenty-direct.html
      2. Error correcting code, polar error corrections, WGS84 ellipsoid parameters, testing, and comments by Michael Kleder.
      3. By convention, when starting at a pole, the longitude of the initial point (otherwise meaningless) determines the longitude line along which to traverse, and hence the longitude of the final point.
      4. The convention noted in (3) above creates a discrepancy with VDIST when the the intial or final point is at a pole. In the VDIST
         function, when traversing from a pole, the azimuth is  0 when
         heading away from the south pole and 180 when heading away from the north pole. In contrast, this VRECKON function uses the azimuth as noted in (3) above when traversing away form a pole.
      5. In testing, where the traversal subtends no more than 178 degrees, this function correctly inverts the VDIST function to within 0.2 millimeters of distance, 5e-10 degrees of forward azimuth,
         and 5e-10 degrees of reverse azimuth. Precision reduces as test
         points approach antipodal because the precision of VDIST is reduced
         for nearly antipodal points. (A warning is given by VDIST.)
      6. Tested but no warranty. Use at your own risk.
      7. Ver 1.0, Michael Kleder, November 2007. Ver 2.0, Joaquim Luis, September 2008

    Added ellipsoid and vectorized whenever possible. Also, lon2 is always converted to the [-180 180] interval.
    Joaquim Luis
    """

    lat1 = np.atleast_1d(Lat1)
    lon1 = np.atleast_1d(Lon1)
    rng = np.atleast_1d(Rng)
    azim = np.atleast_1d(Azim)

    if rng.ndim != 1 or azim.ndim != 1:
        raise ValueError('Range and azimuth must be scalar or vector')

    if abs(lat1) > 90:
        raise ValueError('VRECKON: Input lat. must be between -90 and 90 deg., inclusive.')

    if lat1.size > 1 and rng.size > 1:
        raise ValueError('VRECKON: Variable ranges are only allowed for a single point.')

    if ell is not None:
        a = ell.a
        b = ell.b
        f = ell.f
    else:   # Supply WGS84 earth ellipsoid axis lengths in meters:
        a = 6378137                 # semimajor axis
        b = 6356752.31424518   # WGS84 earth flattening coefficient definition
        f = (a - b) / a

    lat1 = np.radians(lat1)            # intial latitude in radians
    lon1 = np.radians(lon1)            # intial longitude in radians

    # correct for errors at exact poles by adjusting 0.6 millimeters:
    kidx = abs(pi / 2 - abs(lat1)) < 1e-10
    lat1[kidx] = sign(lat1[kidx]) * (pi / 2 - (1e-10))

    if rng.size != azim.size and rng.size == 1:
        rng = np.broadcast_to(rng, azim.size)

    alpha1 = np.radians(azim)  # inital azimuth in radians
    sinAlpha1 = sin(alpha1)
    cosAlpha1 = cos(alpha1)

    tanU1 = (1 - f) * tan(lat1)
    cosU1 = 1 / sqrt(1 + tanU1 ** 2)
    sinU1 = tanU1 * cosU1
    sigma1 = arctan2(tanU1, cosAlpha1)
    sinAlpha = cosU1 * sinAlpha1
    cosSqAlpha = 1 - sinAlpha * sinAlpha
    uSq = cosSqAlpha * (a**2 - b**2) / b**2
    A = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 * uSq)))
    B = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq)))

    sigma = rng / (b * A)
    sigmaP = 2 * pi

    if sigma.size == 1:
        sinSigma = nan
        cosSigma = nan
        cos2SigmaM = nan
        while abs(sigma - sigmaP) > 1e-12:
            cos2SigmaM = cos(2 * sigma1 + sigma)
            sinSigma = sin(sigma)
            cosSigma = cos(sigma)
            deltaSigma = (B * sinSigma *
                          (cos2SigmaM + B / 4 *
                           (cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM) -
                            B / 6 * cos2SigmaM *
                            (-3 + 4 * sinSigma * sinSigma) *
                            (-3 + 4 * cos2SigmaM * cos2SigmaM))))
            sigmaP = sigma
            sigma = rng / (b * A) + deltaSigma
    else:
        # This part is not vectorized
        cos2SigmaM = np.empty(sigma.size)
        sinSigma = np.empty(sigma.size)
        cosSigma = np.empty(sigma.size)

        for k in range(sigma.size):
            while (abs(sigma[k] - sigmaP) > 1e-12).any():
                cos2SigmaM[k] = cos(2 * sigma1[k] + sigma[k])
                sinSigma[k] = sin(sigma[k])
                cosSigma[k] = cos(sigma[k])
                tmp = 2 * cos2SigmaM[k] * cos2SigmaM[k]
                deltaSigma = (B[k] * sinSigma[k] *
                              (cos2SigmaM[k] + B[k] / 4 *
                               (cosSigma[k] * (-1 + tmp) -
                                B[k] / 6 * cos2SigmaM[k] *
                                (-3 + 4 * sinSigma[k] * sinSigma[k]) *
                                  (-3 + 2 * tmp))))
                sigmaP = sigma[k]
                sigma[k] = rng[k] / (b * A[k]) + deltaSigma

    tmp = sinU1 * sinSigma - cosU1 * cosSigma * cosAlpha1
    lat2 = arctan2(sinU1 * cosSigma + cosU1 * sinSigma * cosAlpha1,
                   (1 - f) * sqrt(sinAlpha * sinAlpha + tmp**2))

    lamb = arctan2(sinSigma * sinAlpha1,
                   cosU1 * cosSigma - sinU1 * sinSigma * cosAlpha1)

    C = f / 16 * cosSqAlpha * (4 + f * (4 - 3 * cosSqAlpha))
    L = lamb - (f * (1 - C) *
                sinAlpha * (sigma + C * sinSigma *
                            (cos2SigmaM + C * cosSigma *
                             (-1 + 2 * cos2SigmaM * cos2SigmaM))))

    lon2 = np.degrees(lon1 + L)

    # Truncates angles into the [-pi pi] range
    # if (lon2 > pi).any():
    #    lon2 = pi*((absolute(lon2)/pi) -
    #       2*ceil(((absolute(lon2)/pi)-1)/2)) * sign(lon2)

    # lon2 = mod(lon2,360); % follow [0,360] convention
    lon2 = (lon2 + 180) % 360 - 180  # no parenthesis on RHS

    a21 = arctan2(sinAlpha, -tmp)
    a21 = 180. + np.degrees(a21)  # note direction reversal

    return np.degrees(lat2).squeeze()[()], lon2.squeeze()[()], a21.squeeze()[()] % 360.