def __init__(self, geod, lat1, lon1, azi1, caps=GeodesicCapability.ALL):
from geographiclib.geodesic import Geodesic
self._a = geod._a
self._f = geod._f
self._b = geod._b
self._c2 = geod._c2
self._f1 = geod._f1
self._caps = caps | Geodesic.LATITUDE | Geodesic.AZIMUTH
# Guard against underflow in salp0
azi1 = Geodesic.AngRound(Math.AngNormalize(azi1))
lon1 = Math.AngNormalize(lon1)
self._lat1 = lat1
self._lon1 = lon1
self._azi1 = azi1
# alp1 is in [0, pi]
alp1 = azi1 * Math.degree
# Enforce sin(pi) == 0 and cos(pi/2) == 0. Better to face the ensuing
# problems directly than to skirt them.
self._salp1 = 0 if azi1 == -180 else math.sin(alp1)
self._calp1 = 0 if abs(azi1) == 90 else math.cos(alp1)
# real cbet1, sbet1, phi
phi = lat1 * Math.degree
# Ensure cbet1 = +epsilon at poles
sbet1 = self._f1 * math.sin(phi)
cbet1 = Geodesic.tiny_ if abs(lat1) == 90 else math.cos(phi)
sbet1, cbet1 = Geodesic.SinCosNorm(sbet1, cbet1)
self._dn1 = math.sqrt(1 + geod._ep2 * Math.sq(sbet1))
# Evaluate alp0 from sin(alp1) * cos(bet1) = sin(alp0),
self._salp0 = self._salp1 * cbet1 # alp0 in [0, pi/2 - |bet1|]
# Alt: calp0 = hypot(sbet1, calp1 * cbet1). The following
# is slightly better (consider the case salp1 = 0).
self._calp0 = math.hypot(self._calp1, self._salp1 * sbet1)
# Evaluate sig with tan(bet1) = tan(sig1) * cos(alp1).
# sig = 0 is nearest northward crossing of equator.
# With bet1 = 0, alp1 = pi/2, we have sig1 = 0 (equatorial line).
# With bet1 = pi/2, alp1 = -pi, sig1 = pi/2
# With bet1 = -pi/2, alp1 = 0 , sig1 = -pi/2
# Evaluate omg1 with tan(omg1) = sin(alp0) * tan(sig1).
# With alp0 in (0, pi/2], quadrants for sig and omg coincide.
# No atan2(0,0) ambiguity at poles since cbet1 = +epsilon.
# With alp0 = 0, omg1 = 0 for alp1 = 0, omg1 = pi for alp1 = pi.
self._ssig1 = sbet1
self._somg1 = self._salp0 * sbet1
self._csig1 = self._comg1 = (cbet1 * self._calp1
if sbet1 != 0 or self._calp1 != 0 else 1)
# sig1 in (-pi, pi]
self._ssig1, self._csig1 = Geodesic.SinCosNorm(self._ssig1,
self._csig1)
# No need to normalize
# self._somg1, self._comg1 = Geodesic.SinCosNorm(self._somg1, self._comg1)
self._k2 = Math.sq(self._calp0) * geod._ep2
eps = self._k2 / (2 * (1 + math.sqrt(1 + self._k2)) + self._k2)
if self._caps & Geodesic.CAP_C1:
self._A1m1 = Geodesic.A1m1f(eps)
self._C1a = range(Geodesic.nC1_ + 1)
Geodesic.C1f(eps, self._C1a)
self._B11 = Geodesic.SinCosSeries(True, self._ssig1, self._csig1,
self._C1a, Geodesic.nC1_)
s = math.sin(self._B11)
c = math.cos(self._B11)
# tau1 = sig1 + B11
self._stau1 = self._ssig1 * c + self._csig1 * s
self._ctau1 = self._csig1 * c - self._ssig1 * s
# Not necessary because C1pa reverts C1a
# _B11 = -SinCosSeries(true, _stau1, _ctau1, _C1pa, nC1p_)
if self._caps & Geodesic.CAP_C1p:
self._C1pa = range(Geodesic.nC1p_ + 1)
Geodesic.C1pf(eps, self._C1pa)
if self._caps & Geodesic.CAP_C2:
self._A2m1 = Geodesic.A2m1f(eps)
self._C2a = range(Geodesic.nC2_ + 1)
Geodesic.C2f(eps, self._C2a)
self._B21 = Geodesic.SinCosSeries(True, self._ssig1, self._csig1,
self._C2a, Geodesic.nC2_)
if self._caps & Geodesic.CAP_C3:
self._C3a = range(Geodesic.nC3_)
geod.C3f(eps, self._C3a)
self._A3c = -self._f * self._salp0 * geod.A3f(eps)
self._B31 = Geodesic.SinCosSeries(True, self._ssig1, self._csig1,
self._C3a, Geodesic.nC3_ - 1)
if self._caps & Geodesic.CAP_C4:
self._C4a = range(Geodesic.nC4_)
geod.C4f(eps, self._C4a)
# Multiplier = a^2 * e^2 * cos(alpha0) * sin(alpha0)
self._A4 = Math.sq(self._a) * self._calp0 * self._salp0 * geod._e2
self._B41 = Geodesic.SinCosSeries(False, self._ssig1, self._csig1,
self._C4a, Geodesic.nC4_)
def __init__(self, geod, lat1, lon1, azi1, caps = GeodesicCapability.ALL):
"""Construct a GeodesicLine object describing a geodesic line
starting at (lat1, lon1) with azimuth azi1. geod is a Geodesic
object (which embodies the ellipsoid parameters). caps is caps is
an or'ed combination of bit the following values indicating the
capabilities of the returned object
Geodesic.LATITUDE
Geodesic.LONGITUDE
Geodesic.AZIMUTH
Geodesic.DISTANCE
Geodesic.REDUCEDLENGTH
Geodesic.GEODESICSCALE
Geodesic.AREA
Geodesic.DISTANCE_IN
Geodesic.ALL (all of the above)
The default value of caps is ALL.
"""
from geographiclib.geodesic import Geodesic
self._a = geod._a
self._f = geod._f
self._b = geod._b
self._c2 = geod._c2
self._f1 = geod._f1
self._caps = (caps | Geodesic.LATITUDE | Geodesic.AZIMUTH |
Geodesic.LONG_UNROLL)
# Guard against underflow in salp0
self._lat1 = Math.LatFix(lat1)
self._lon1 = lon1
self._azi1 = Math.AngNormalize(azi1)
self._salp1, self._calp1 = Math.sincosd(Math.AngRound(azi1))
# real cbet1, sbet1
sbet1, cbet1 = Math.sincosd(Math.AngRound(lat1)); sbet1 *= self._f1
# Ensure cbet1 = +epsilon at poles
sbet1, cbet1 = Math.norm(sbet1, cbet1); cbet1 = max(Geodesic.tiny_, cbet1)
self._dn1 = math.sqrt(1 + geod._ep2 * Math.sq(sbet1))
# Evaluate alp0 from sin(alp1) * cos(bet1) = sin(alp0),
self._salp0 = self._salp1 * cbet1 # alp0 in [0, pi/2 - |bet1|]
# Alt: calp0 = hypot(sbet1, calp1 * cbet1). The following
# is slightly better (consider the case salp1 = 0).
self._calp0 = math.hypot(self._calp1, self._salp1 * sbet1)
# Evaluate sig with tan(bet1) = tan(sig1) * cos(alp1).
# sig = 0 is nearest northward crossing of equator.
# With bet1 = 0, alp1 = pi/2, we have sig1 = 0 (equatorial line).
# With bet1 = pi/2, alp1 = -pi, sig1 = pi/2
# With bet1 = -pi/2, alp1 = 0 , sig1 = -pi/2
# Evaluate omg1 with tan(omg1) = sin(alp0) * tan(sig1).
# With alp0 in (0, pi/2], quadrants for sig and omg coincide.
# No atan2(0,0) ambiguity at poles since cbet1 = +epsilon.
# With alp0 = 0, omg1 = 0 for alp1 = 0, omg1 = pi for alp1 = pi.
self._ssig1 = sbet1; self._somg1 = self._salp0 * sbet1
self._csig1 = self._comg1 = (cbet1 * self._calp1
if sbet1 != 0 or self._calp1 != 0 else 1)
# sig1 in (-pi, pi]
self._ssig1, self._csig1 = Math.norm(self._ssig1, self._csig1)
# No need to normalize
# self._somg1, self._comg1 = Math.norm(self._somg1, self._comg1)
self._k2 = Math.sq(self._calp0) * geod._ep2
eps = self._k2 / (2 * (1 + math.sqrt(1 + self._k2)) + self._k2)
if self._caps & Geodesic.CAP_C1:
self._A1m1 = Geodesic.A1m1f(eps)
self._C1a = list(range(Geodesic.nC1_ + 1))
Geodesic.C1f(eps, self._C1a)
self._B11 = Geodesic.SinCosSeries(
True, self._ssig1, self._csig1, self._C1a)
s = math.sin(self._B11); c = math.cos(self._B11)
# tau1 = sig1 + B11
self._stau1 = self._ssig1 * c + self._csig1 * s
self._ctau1 = self._csig1 * c - self._ssig1 * s
# Not necessary because C1pa reverts C1a
# _B11 = -SinCosSeries(true, _stau1, _ctau1, _C1pa)
if self._caps & Geodesic.CAP_C1p:
self._C1pa = list(range(Geodesic.nC1p_ + 1))
Geodesic.C1pf(eps, self._C1pa)
if self._caps & Geodesic.CAP_C2:
self._A2m1 = Geodesic.A2m1f(eps)
self._C2a = list(range(Geodesic.nC2_ + 1))
Geodesic.C2f(eps, self._C2a)
self._B21 = Geodesic.SinCosSeries(
True, self._ssig1, self._csig1, self._C2a)
if self._caps & Geodesic.CAP_C3:
self._C3a = list(range(Geodesic.nC3_))
geod.C3f(eps, self._C3a)
self._A3c = -self._f * self._salp0 * geod.A3f(eps)
self._B31 = Geodesic.SinCosSeries(
True, self._ssig1, self._csig1, self._C3a)
if self._caps & Geodesic.CAP_C4:
self._C4a = list(range(Geodesic.nC4_))
geod.C4f(eps, self._C4a)
# Multiplier = a^2 * e^2 * cos(alpha0) * sin(alpha0)
self._A4 = Math.sq(self._a) * self._calp0 * self._salp0 * geod._e2
self._B41 = Geodesic.SinCosSeries(
False, self._ssig1, self._csig1, self._C4a)
