How to use the geographiclib.geodesic.Geodesic.SinCosSeries function in geographiclib
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borglab / gtsam / gtsam / 3rdparty / GeographicLib / python / geographiclib / geodesicline.py View on Github 
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:
salp12 = Geodesic.tiny_ * self._calp1
calp12 = -1
else:
# tan(alp) = tan(alp0) * sec(sig)
# tan(alp2-alp1) = (tan(alp2) -tan(alp1)) / (tan(alp2)*tan(alp1)+1)
# = calp0 * salp0 * (csig1-csig2) / (salp0^2 + calp0^2 * csig1*csig2)
# If csig12 > 0, writeserr = ((1 + self._A1m1) * (sig12 + (B12 - self._B11)) -
s12_a12 / self._b)
sig12 = sig12 - serr / math.sqrt(1 + self._k2 * Math.sq(ssig2))
ssig12 = math.sin(sig12); csig12 = math.cos(sig12)
# Update B12 below
# real omg12, lam12, lon12
# real ssig2, csig2, sbet2, cbet2, somg2, comg2, salp2, calp2
# sig2 = sig1 + sig12
ssig2 = self._ssig1 * csig12 + self._csig1 * ssig12
csig2 = self._csig1 * csig12 - self._ssig1 * ssig12
dn2 = math.sqrt(1 + self._k2 * Math.sq(ssig2))
if outmask & (
Geodesic.DISTANCE | Geodesic.REDUCEDLENGTH | Geodesic.GEODESICSCALE):
if arcmode or abs(self._f) > 0.01:
B12 = Geodesic.SinCosSeries(True, ssig2, csig2,
self._C1a, Geodesic.nC1_)
AB1 = (1 + self._A1m1) * (B12 - self._B11)
# sin(bet2) = cos(alp0) * sin(sig2)
sbet2 = self._calp0 * ssig2
# Alt: cbet2 = hypot(csig2, salp0 * ssig2)
cbet2 = math.hypot(self._salp0, self._calp0 * csig2)
if cbet2 == 0:
# I.e., salp0 = 0, csig2 = 0. Break the degeneracy in this case
cbet2 = csig2 = Geodesic.tiny_
# tan(omg2) = sin(alp0) * tan(sig2)
somg2 = self._salp0 * ssig2; comg2 = csig2 # No need to normalize
# tan(alp0) = cos(sig2)*tan(alp2)
salp2 = self._salp0; calp2 = self._calp0 * csig2 # No need to normalize
# omg12 = omg2 - omg1
omg12 = math.atan2(somg2 * self._comg1 - comg2 * self._somg1,
comg2 * self._comg1 + somg2 * self._somg1)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 = 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, Geodesic.nC2_)
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, Geodesic.nC3_-1)
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, Geodesic.nC4_)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 = list(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 = 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)# I.e., salp0 = 0, csig2 = 0. Break the degeneracy in this case
cbet2 = csig2 = Geodesic.tiny_
# tan(omg2) = sin(alp0) * tan(sig2)
somg2 = self._salp0 * ssig2; comg2 = csig2 # No need to normalize
# tan(alp0) = cos(sig2)*tan(alp2)
salp2 = self._salp0; calp2 = self._calp0 * csig2 # No need to normalize
# omg12 = omg2 - omg1
omg12 = math.atan2(somg2 * self._comg1 - comg2 * self._somg1,
comg2 * self._comg1 + somg2 * self._somg1)
if outmask & Geodesic.DISTANCE:
s12 = self._b * ((1 + self._A1m1) * sig12 + AB1) if arcmode else s12_a12
if outmask & Geodesic.LONGITUDE:
lam12 = omg12 + self._A3c * (
sig12 + (Geodesic.SinCosSeries(True, ssig2, csig2,
self._C3a, Geodesic.nC3_-1)
- self._B31))
lon12 = lam12 / Math.degree
# Use Math.AngNormalize2 because longitude might have wrapped
# multiple times.
lon12 = Math.AngNormalize2(lon12)
lon2 = Math.AngNormalize(self._lon1 + lon12)
if outmask & Geodesic.LATITUDE:
lat2 = math.atan2(sbet2, self._f1 * cbet2) / Math.degree
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):# f erri errd errda
# -1/5 12e6 1.2e9 69e6
# -1/10 123e3 12e6 765e3
# -1/20 1110 108e3 7155
# -1/50 18.63 200.9 27.12
# -1/100 18.63 23.78 23.37
# -1/150 18.63 21.05 20.26
# 1/150 22.35 24.73 25.83
# 1/100 22.35 25.03 25.31
# 1/50 29.80 231.9 30.44
# 1/20 5376 146e3 10e3
# 1/10 829e3 22e6 1.5e6
# 1/5 157e6 3.8e9 280e6
ssig2 = self._ssig1 * csig12 + self._csig1 * ssig12
csig2 = self._csig1 * csig12 - self._ssig1 * ssig12
B12 = Geodesic.SinCosSeries(True, ssig2, csig2,
self._C1a, Geodesic.nC1_)
serr = ((1 + self._A1m1) * (sig12 + (B12 - self._B11)) -
s12_a12 / self._b)
sig12 = sig12 - serr / math.sqrt(1 + self._k2 * Math.sq(ssig2))
ssig12 = math.sin(sig12); csig12 = math.cos(sig12)
# Update B12 below
# real omg12, lam12, lon12
# real ssig2, csig2, sbet2, cbet2, somg2, comg2, salp2, calp2
# sig2 = sig1 + sig12
ssig2 = self._ssig1 * csig12 + self._csig1 * ssig12
csig2 = self._csig1 * csig12 - self._ssig1 * ssig12
dn2 = math.sqrt(1 + self._k2 * Math.sq(ssig2))
if outmask & (
Geodesic.DISTANCE | Geodesic.REDUCEDLENGTH | Geodesic.GEODESICSCALE):
if arcmode or abs(self._f) > 0.01:- self._B31))
lon12 = lam12 / Math.degree
# Use Math.AngNormalize2 because longitude might have wrapped
# multiple times.
lon12 = Math.AngNormalize2(lon12)
lon2 = Math.AngNormalize(self._lon1 + lon12)
if outmask & Geodesic.LATITUDE:
lat2 = math.atan2(sbet2, self._f1 * cbet2) / Math.degree
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_)geographiclib
The geodesic routines from GeographicLib
MIT
Latest version published 2 years agoPackage Health Score
65 / 100Popular geographiclib functions
- geographiclib.geodesic.Geodesic
- geographiclib.geodesic.Geodesic._SinCosSeries
- geographiclib.geodesic.Geodesic.LATITUDE
- geographiclib.geodesic.Geodesic.LONGITUDE
- geographiclib.geodesic.Geodesic.SinCosSeries
- geographiclib.geodesic.Geodesic.WGS84
- geographiclib.geodesic.Geodesic.WGS84.Direct
- geographiclib.geodesic.Geodesic.WGS84.Inverse
- geographiclib.geodesicline.GeodesicLine
- geographiclib.geomath.Math
- geographiclib.geomath.Math.AngDiff
- geographiclib.geomath.Math.AngNormalize
- geographiclib.geomath.Math.AngRound
- geographiclib.geomath.Math.atan2d
- geographiclib.geomath.Math.LatFix
- geographiclib.geomath.Math.nan
- geographiclib.geomath.Math.norm
- geographiclib.geomath.Math.polyval
- geographiclib.geomath.Math.sincosd
- geographiclib.geomath.Math.sq