def _direct(self, distance, bearing, llr, height=None):
'''(INTERNAL) Direct Vincenty method.
@raise TypeError: The B{C{other}} point is not L{LatLon}.
@raise ValueError: If this and the B{C{other}} point's L{Datum}
ellipsoids are not compatible.
@raise VincentyError: Vincenty fails to converge for the current
L{LatLon.epsilon} and L{LatLon.iterations}
limit.
'''
E = self.ellipsoid()
c1, s1, t1 = _r3(self.lat, E.f)
i = radians(bearing) # initial bearing (forward azimuth)
si, ci = sincos2(i)
s12 = atan2(t1, ci) * 2
sa = c1 * si
c2a = 1 - sa**2
if c2a < EPS:
c2a = 0
A, B = 1, 0
else: # e22 == (a / b)**2 - 1
A, B = _p2(c2a * E.e22)
s = d = distance / (E.b * A)
for self._iteration in range(self._iterations):
ss, cs = sincos2(s)
c2sm = cos(s12 + s)
s_, s = s, d + _ds(B, cs, ss, c2sm)
if abs(s - s_) < self._epsilon:
break
else:
raise VincentyError(_no_convergence_,
txt=repr(self)) # self.toRepr()
t = s1 * ss - c1 * cs * ci
# final bearing (reverse azimuth +/- 180)
r = degrees360(atan2(sa, -t))
if llr:
# destination latitude in [-90, 90)
a = degrees90(
atan2(s1 * cs + c1 * ss * ci, (1 - E.f) * hypot(sa, t)))
# destination longitude in [-180, 180)
b = degrees180(
atan2(ss * si, c1 * cs - s1 * ss * ci) -
_dl(E.f, c2a, sa, s, cs, ss, c2sm) + radians(self.lon))
h = self.height if height is None else height
d = self.classof(a, b, height=h, datum=self.datum)
else:
d = None
return Destination2Tuple(d, r)
def _direct(self, distance, bearing, LL, height):
'''(INTERNAL) Karney's C{Direct} method.
@return: A L{Destination2Tuple}C{(destination, final)} or
a L{Destination3Tuple}C{(lat, lon, final)} if
B{C{LL}} is C{None}.
'''
g = self.datum.ellipsoid.geodesic
r = g.Direct3(self.lat, self.lon, bearing, distance)
if LL:
h = self.height if height is None else height
d = LL(wrap90(r.lat), wrap180(r.lon), height=h, datum=self.datum)
r = Destination2Tuple(self._xnamed(d), wrap360(r.final))
return r
def destination2(self, distance, bearing, height=None):
'''Compute the destination point and the final bearing (reverse
azimuth) after having travelled for the given distance from
this point along a geodesic given by an initial bearing,
using Vincenty's direct method.
The distance must be in the same units as this point's datum
axes, conventionally meter. The distance is measured on the
surface of the ellipsoid, ignoring this point's height.
The initial and final bearing (forward and reverse azimuth)
are in compass degrees.
The destination point's height and datum are set to this
point's height and datum.
@param distance: Distance (C{meter}).
@param bearing: Initial bearing (compass C{degrees360}).
@keyword height: Optional height, overriding the default
height (C{meter}, same units as B{C{distance}}).
@return: A L{Destination2Tuple}C{(destination, final)}.
@raise TypeError: The B{C{other}} point is not L{LatLon}.
@raise ValueError: If this and the B{C{other}} point's L{Datum}
ellipsoids are not compatible.
@raise VincentyError: Vincenty fails to converge for the current
L{LatLon.epsilon} and L{LatLon.iterations}
limit.
@example:
>>> p = LatLon(-37.95103, 144.42487)
>>> b = 306.86816
>>> d, f = p.destination2(54972.271, b) # 37.652818°S, 143.926498°E, 307.1736
'''
r = Destination2Tuple(*self._direct(distance, bearing, True,
height=height))
return self._xnamed(r)
def destination2(self, distance, bearing, height=None):
'''Compute the destination point and the final bearing (reverse
azimuth) after having travelled for the given distance from
this point along a geodesic given by an initial bearing,
using Karney's Direct method.
The distance must be in the same units as this point's datum
axes, conventionally meter. The distance is measured on the
surface of the ellipsoid, ignoring this point's height.
The initial and final bearing (forward and reverse azimuth)
are in compass degrees.
The destination point's height and datum are set to this
point's height and datum.
@param distance: Distance (C{meter}).
@param bearing: Initial bearing (compass C{degrees360}).
@keyword height: Optional height, overriding the default
height (C{meter}, same units as C{distance}).
@return: A L{Destination2Tuple}C{(destination, final)}.
@raise ImportError: Package U{geographiclib
<https://PyPI.org/project/geographiclib>}
not installed or not found.
@example:
>>> p = LatLon(-37.95103, 144.42487)
>>> d, f = p.destination2(54972.271, 306.86816)
>>> d
LatLon(37°39′10.14″S, 143°55′35.39″E) # 37.652818°S, 143.926498°E
>>> f
307.1736313846665
'''
r = Destination2Tuple(*self._direct(distance, bearing, True,
height=height)[:2])
return self._xnamed(r)