How to use the geographiclib.geodesic.Geodesic function in geographiclib

if outmask & Geodesic.AZIMUTH:
      # minus signs give range [-180, 180). 0- converts -0 to +0.
      azi2 = 0 - math.atan2(-salp2, calp2) / Math.degree

    if outmask & (Geodesic.REDUCEDLENGTH | Geodesic.GEODESICSCALE):
      B22 = Geodesic.SinCosSeries(True, ssig2, csig2, self._C2a, Geodesic.nC2_)
      AB2 = (1 + self._A2m1) * (B22 - self._B21)
      J12 = (self._A1m1 - self._A2m1) * sig12 + (AB1 - AB2)
      if outmask & Geodesic.REDUCEDLENGTH:
        # Add parens around (_csig1 * ssig2) and (_ssig1 * csig2) to ensure
        # accurate cancellation in the case of coincident points.
        m12 = self._b * ((      dn2 * (self._csig1 * ssig2) -
                          self._dn1 * (self._ssig1 * csig2))
                         - self._csig1 * csig2 * J12)
      if outmask & Geodesic.GEODESICSCALE:
        t = (self._k2 * (ssig2 - self._ssig1) *
             (ssig2 + self._ssig1) / (self._dn1 + dn2))
        M12 = csig12 + (t * ssig2 - csig2 * J12) * self._ssig1 / self._dn1
        M21 = csig12 - (t * self._ssig1 - self._csig1 * J12) * ssig2 / dn2

    if outmask & Geodesic.AREA:
      B42 = Geodesic.SinCosSeries(False, ssig2, csig2, self._C4a, Geodesic.nC4_)
      # real salp12, calp12
      if self._calp0 == 0 or self._salp0 == 0:
        # alp12 = alp2 - alp1, used in atan2 so no need to normalized
        salp12 = salp2 * self._calp1 - calp2 * self._salp1
        calp12 = calp2 * self._calp1 + salp2 * self._salp1
        # The right thing appears to happen if alp1 = +/-180 and alp2 = 0, viz
        # salp12 = -0 and alp12 = -180.  However this depends on the sign being
        # attached to 0 correctly.  The following ensures the correct behavior.
        if salp12 == 0 and calp12 < 0:

def get_next_position(self, origin_lat, origin_lng, origin_alt, dest_lat, dest_lng, dest_alt, distance):
        polyline = PolylineObjectHandler.cached_polyline((self.bot.position[0], self.bot.position[1]), (dest_lat, dest_lng), google_map_api_key=self.bot.config.gmapkey)

        while True:
            _, (dest_lat, dest_lng) = polyline._step_dict[polyline._step_keys[polyline._last_step]]

            next_lat, next_lng, _ = super(PolylineWalker, self).get_next_position(origin_lat, origin_lng, origin_alt, dest_lat, dest_lng, dest_alt, distance)

            if polyline._last_step == len(polyline._step_keys) - 1:
                break
            else:
                travelled = Geodesic.WGS84.Inverse(origin_lat, origin_lng, next_lat, next_lng)["s12"]
                remaining = Geodesic.WGS84.Inverse(next_lat, next_lng, dest_lat, dest_lng)["s12"]
                step_distance = Geodesic.WGS84.Inverse(origin_lat, origin_lng, dest_lat, dest_lng)["s12"]

                if remaining < (self.precision + self.epsilon):
                    polyline._last_step += 1
                    distance = abs(distance - step_distance)
                else:
                    distance = abs(distance - travelled)

                if distance > (self.precision + self.epsilon):
                    origin_lat, origin_lng, origin_alt = dest_lat, dest_lng, dest_alt
                else:
                    break

        polyline._last_pos = (next_lat, next_lng)
        next_alt = polyline.get_alt() or origin_alt

        return next_lat, next_lng, next_alt + random_alt_delta()

salp2 = self._salp0; calp2 = self._calp0 * csig2 # No need to normalize

    if outmask & Geodesic.DISTANCE:
      s12 = self._b * ((1 + self._A1m1) * sig12 + AB1) if arcmode else s12_a12

    if outmask & Geodesic.LONGITUDE:
      # tan(omg2) = sin(alp0) * tan(sig2)
      somg2 = self._salp0 * ssig2; comg2 = csig2 # No need to normalize
      E = Math.copysign(1, self._salp0)          # East or west going?
      # omg12 = omg2 - omg1
      omg12 = (E * (sig12
                    - (math.atan2(          ssig2,       csig2) -
                       math.atan2(    self._ssig1, self._csig1))
                    + (math.atan2(E *       somg2,       comg2) -
                       math.atan2(E * self._somg1, self._comg1)))
               if outmask & Geodesic.LONG_UNROLL
               else math.atan2(somg2 * self._comg1 - comg2 * self._somg1,
                               comg2 * self._comg1 + somg2 * self._somg1))
      lam12 = omg12 + self._A3c * (
        sig12 + (Geodesic._SinCosSeries(True, ssig2, csig2, self._C3a)
                 - self._B31))
      lon12 = math.degrees(lam12)
      lon2 = (self.lon1 + lon12 if outmask & Geodesic.LONG_UNROLL else
              Math.AngNormalize(Math.AngNormalize(self.lon1) +
                                Math.AngNormalize(lon12)))

    if outmask & Geodesic.LATITUDE:
      lat2 = Math.atan2d(sbet2, self._f1 * cbet2)

    if outmask & Geodesic.AZIMUTH:
      azi2 = Math.atan2d(salp2, calp2)

(*lat1*, *lon1*), with azimuth *azi1* to be found.  The default
    value of *caps* is STANDARD | DISTANCE_IN.  The optional parameters
    *salp1* and *calp1* should not be supplied; they are part of the
    private interface.

    """

    from geographiclib.geodesic import Geodesic
    self.a = geod.a
    """The equatorial radius in meters (readonly)"""
    self.f = geod.f
    """The flattening (readonly)"""
    self._b = geod._b
    self._c2 = geod._c2
    self._f1 = geod._f1
    self.caps = (caps | Geodesic.LATITUDE | Geodesic.AZIMUTH |
                  Geodesic.LONG_UNROLL)
    """the capabilities (readonly)"""

    # Guard against underflow in salp0
    self.lat1 = Math.LatFix(lat1)
    """the latitude of the first point in degrees (readonly)"""
    self.lon1 = lon1
    """the longitude of the first point in degrees (readonly)"""
    if Math.isnan(salp1) or Math.isnan(calp1):
      self.azi1 = Math.AngNormalize(azi1)
      self.salp1, self.calp1 = Math.sincosd(Math.AngRound(azi1))
    else:
      self.azi1 = azi1
      """the azimuth at the first point in degrees (readonly)"""
      self.salp1 = salp1
      """the sine of the azimuth at the first point (readonly)"""

for vcnt, vertex in enumerate(vertices):
            v = geom_to_4326.transform(vertex.x(), vertex.y())
            gline = geod.Inverse(cy, cx, v.y(), v.x())
            vdist = gline['s12']
            vazi = gline['azi1']
            if mode == 0:  # flip horizontally
                vazi = -1.0 * vazi
            elif mode == 1:  # Flip vertically
                vazi = -1.0 * (vazi + 180)
            elif mode == 2:  # Rotate 180
                vazi += 180
            elif mode == 3:  # Rotate 90
                vazi += 90
            else:
                vazi -= 90  # Rotate -90
            g = geod.Direct(cy, cx, vazi, vdist, Geodesic.LATITUDE | Geodesic.LONGITUDE)
            new_vertex = to_sink_crs.transform(g['lon2'], g['lat2'])
            geom.moveVertex(new_vertex.x(), new_vertex.y(), vcnt)
        layer.changeGeometry(feature.id(), geom)
    layer.updateExtents()
    iface.mapCanvas().refresh()

def Geodesic(self):
        '''(INTERNAL) Get the wrapped C{Geodesic} class, provided the
           U{GeographicLib}
           package is installed, otherwise throw an C{ImportError}.
        '''
        if _Wrapped._Geodesic is None:
            from geographiclib.geodesic import Geodesic as _Geodesic

            class Geodesic(_Geodesic):
                '''Karney U{Geodesic } wrapper.
                '''

                def Direct(self, lat1, lon1, azi1, s12, *outmask):
                    '''Return the C{Direct} result.
                    '''
                    d = _Geodesic.Direct(self, lat1, lon1, azi1, s12, *outmask)
                    return _Adict(d)

                def Direct3(self, lat1, lon1, azi1, s12):  # PYCHOK outmask
                    '''Return the destination lat, lon and reverse azimth
                       in C{degrees}.
                    '''
                    m = self.AZIMUTH | self.LATITUDE | self.LONGITUDE
                    d = self.Direct(lat1, lon1, azi1, s12, m)

"""Construct a PolygonArea object

    :param earth: a :class:`~geographiclib.geodesic.Geodesic` object
    :param polyline: if true, treat object as a polyline instead of a polygon

    Initially the polygon has no vertices.
    """

    from geographiclib.geodesic import Geodesic
    self.earth = earth
    """The geodesic object (readonly)"""
    self.polyline = polyline
    """Is this a polyline? (readonly)"""
    self.area0 = 4 * math.pi * earth._c2
    """The total area of the ellipsoid in meter^2 (readonly)"""
    self._mask = (Geodesic.LATITUDE | Geodesic.LONGITUDE |
                  Geodesic.DISTANCE |
                  (Geodesic.EMPTY if self.polyline else
                   Geodesic.AREA | Geodesic.LONG_UNROLL))
    if not self.polyline: self._areasum = Accumulator()
    self._perimetersum = Accumulator()
    self.num = 0
    """The current number of points in the polygon (readonly)"""
    self.lat1 = Math.nan
    """The current latitude in degrees (readonly)"""
    self.lon1 = Math.nan
    """The current longitude in degrees (readonly)"""
    self.Clear()