def toLatLon(self, LatLon=None, unfalse=True):
'''Convert this UPS coordinate to an (ellipsoidal) geodetic point.
@keyword LatLon: Optional, ellipsoidal (sub-)class to return
the point (C{LatLon}) or C{None}.
@keyword unfalse: Unfalse I{easting} and I{northing} if falsed
(C{bool}).
@return: This UPS coordinate as (I{LatLon}) or 5-tuple
(C{lat, lon, datum, convergence, scale}) if
I{LatLon} is C{None}.
@raise TypeError: If I{LatLon} is not ellipsoidal.
@raise UPSError: Invalid meridional radius or H-value.
'''
if self._latlon:
return self._latlon5(LatLon)
E = self.datum.ellipsoid # XXX vs LatLon.datum.ellipsoid
f = self.falsed if unfalse else 0
x = self.easting - f
y = self.northing - f
r = hypot(x, y)
t = (r / (2 * self.scale0 * E.a / E.es_c)) if r > 0 else EPS**2
t = E.es_tauf((1 / t - t) * 0.5)
if self.pole == 'N':
a, b, c = atan(t), atan2(x, -y), 1
else:
a, b, c = -atan(t), atan2(x, y), -1
a, b = degrees90(a), degrees180(b)
if not self._band:
self._band = _Band(a, b)
if not self._hemisphere:
self._hemisphere = _hemi(a)
ll = _LLEB(a, b, datum=self._datum, name=self.name)
ll._convergence = b * c # gamma
ll._scale = _scale(E, r, t) if r > 0 else self.scale0
self._latlon = ll
return self._latlon5(LatLon)
def toOsgr(latlon, lon=None, datum=Datums.WGS84, Osgr=Osgr, name=''):
'''Convert a lat-/longitude point to an OSGR coordinate.
@param latlon: Latitude (C{degrees}) or an (ellipsoidal)
geodetic C{LatLon} point.
@keyword lon: Optional longitude in degrees (scalar or C{None}).
@keyword datum: Optional datum to convert (C{Datum}).
@keyword Osgr: Optional (sub-)class to return the OSGR
coordinate (L{Osgr}) or C{None}.
@keyword name: Optional I{Osgr} name (C{str}).
@return: The OSGR coordinate (L{Osgr}) or 2-tuple (easting,
northing) if I{Osgr} is C{None}.
@raise TypeError: Non-ellipsoidal I{latlon} or I{datum}
conversion failed.
@raise ValueError: Invalid I{latlon} or I{lon}.
@example:
>>> p = LatLon(52.65798, 1.71605)
>>> r = toOsgr(p) # TG 51409 13177
>>> # for conversion of (historical) OSGB36 lat-/longitude:
>>> r = toOsgr(52.65757, 1.71791, datum=Datums.OSGB36)
'''
if not isinstance(latlon, _LLEB):
# XXX fix failing _LLEB.convertDatum()
latlon = _LLEB(*parseDMS2(latlon, lon), datum=datum)
elif lon is not None:
raise ValueError('%s not %s: %r' % ('lon', None, lon))
elif not name: # use latlon.name
name = _nameof(latlon) or name # PYCHOK no effect
E = _OSGB36.ellipsoid
ll = _ll2datum(latlon, _OSGB36, 'latlon')
a, b = map1(radians, ll.lat, ll.lon)
sa, ca = sincos2(a)
s = E.e2s2(sa)
v = E.a * _F0 / sqrt(s) # nu
r = s / E.e12 # nu / rho == v / (v * E.e12 / s)
x2 = r - 1 # η2
ta = tan(a)
ca3, ca5 = fpowers(ca, 5, 3) # PYCHOK false!
ta2, ta4 = fpowers(ta, 4, 2) # PYCHOK false!
vsa = v * sa
I4 = (E.b * _F0 * _M(E.Mabcd, a) + _N0, (vsa / 2) * ca,
(vsa / 24) * ca3 * fsum_(5, -ta2, 9 * x2),
(vsa / 720) * ca5 * fsum_(61, ta4, -58 * ta2))
V4 = (_E0, (v * ca), (v / 6) * ca3 * (r - ta2), (v / 120) * ca5 * fdot(
(-18, 1, 14, -58), ta2, 5 + ta4, x2, ta2 * x2))
d, d2, d3, d4, d5, d6 = fpowers(b - _B0, 6) # PYCHOK false!
n = fdot(I4, 1, d2, d4, d6)
e = fdot(V4, 1, d, d3, d5)
return (e, n) if Osgr is None else _xnamed(Osgr(e, n), name)
def toLatLon(self, LatLon=None, datum=Datums.WGS84):
'''Convert this OSGR coordinate to an (ellipsoidal) geodetic
point.
I{Note formulation implemented here due to Thomas, Redfearn,
etc. is as published by OS, but is inferior to Krüger as
used by e.g. Karney 2011.}
@keyword LatLon: Optional ellipsoidal (sub-)class to return
the point (C{LatLon}) or C{None}.
@keyword datum: Optional datum to use (C{Datum}).
@return: The geodetic point (I{LatLon}) or 3-tuple (C{degrees90},
C{degrees180}, I{datum}) if I{LatLon} is C{None}.
@raise TypeError: If I{LatLon} is not ellipsoidal or if
I{datum} conversion failed.
@example:
>>> from pygeodesy import ellipsoidalVincenty as eV
>>> g = Osgr(651409.903, 313177.270)
>>> p = g.toLatLon(eV.LatLon) # 52°39′28.723″N, 001°42′57.787″E
>>> # to obtain (historical) OSGB36 lat-/longitude point
>>> p = g.toLatLon(eV.LatLon, datum=Datums.OSGB36) # 52°39′27.253″N, 001°43′04.518″E
'''
if self._latlon:
return self._latlon3(LatLon, datum)
E = _OSGB36.ellipsoid # Airy130
a_F0 = E.a * _F0
b_F0 = E.b * _F0
e, n = self._easting, self._northing
n_N0 = n - _N0
a, M = _A0, 0
sa = Fsum(a)
while True:
t = n_N0 - M
if t < _10um:
break
a = sa.fsum_(t / a_F0)
M = b_F0 * _M(E.Mabcd, a)
sa, ca = sincos2(a)
s = E.e2s2(sa)
v = a_F0 / sqrt(s) # nu
r = v * E.e12 / s # rho
vr = v / r # == s / E.e12
x2 = vr - 1 # η2
ta = tan(a)
v3, v5, v7 = fpowers(v, 7, 3) # PYCHOK false!
ta2, ta4, ta6 = fpowers(ta**2, 3) # PYCHOK false!
tar = ta / r
V4 = (a, tar / (2 * v), tar / (24 * v3) * fdot(
(1, 3, -9), 5 + x2, ta2, ta2 * x2), tar / (720 * v5) * fdot(
(61, 90, 45), 1, ta2, ta4))
csa = 1.0 / ca
X5 = (_B0, csa / v, csa / (6 * v3) * fsum_(vr, ta, ta),
csa / (120 * v5) * fdot(
(5, 28, 24), 1, ta2, ta4), csa / (5040 * v7) * fdot(
(61, 662, 1320, 720), ta, ta2, ta4, ta6))
d, d2, d3, d4, d5, d6, d7 = fpowers(e - _E0, 7) # PYCHOK false!
a = fdot(V4, 1, -d2, d4, -d6)
b = fdot(X5, 1, d, -d3, d5, -d7)
self._latlon = _LLEB(degrees90(a),
degrees180(b),
datum=_OSGB36,
name=self.name)
return self._latlon3(LatLon, datum)
def toLatLon(self, LatLon=None):
'''Convert this UTM coordinate to an (ellipsoidal) geodetic point.
@keyword LatLon: Optional, ellipsoidal (sub-)class to use
for the point (C{LatLon}) or C{None}.
@return: This UTM coordinate as (I{LatLon}) or 5-tuple
(lat, lon, datum, convergence, scale) if I{LatLon}
is C{None}.
@raise TypeError: If I{LatLon} is not ellipsoidal.
@raise UTMError: Invalid meridional radius or H-value.
@example:
>>> u = Utm(31, 'N', 448251.795, 5411932.678)
>>> from pygeodesy import ellipsoidalVincenty as eV
>>> ll = u.toLatLon(eV.LatLon) # 48°51′29.52″N, 002°17′40.20″E
'''
if self._latlon:
return self._latlon5(LatLon)
E = self._datum.ellipsoid # XXX vs LatLon.datum.ellipsoid
x = self._easting - _FalseEasting # relative to central meridian
y = self._northing
if self._hemi == 'S': # relative to equator
y -= _FalseNorthing
# from Karney 2011 Eq 15-22, 36
A0 = _K0 * E.A
if A0 < EPS:
raise UTMError('%s invalid: %r' % ('meridional', E.A))
x /= A0 # η eta
y /= A0 # ξ ksi
Ks = _Kseries(E.BetaKs, x, y) # Krüger series
y = -Ks.ys(-y) # ξ'
x = -Ks.xs(-x) # η'
shx = sinh(x)
cy, sy = cos(y), sin(y)
H = hypot(shx, cy)
if H < EPS:
raise UTMError('%s invalid: %r' % ('H', H))
T = t0 = sy / H # τʹ
q = 1.0 / E.e12
d = 1
sd = Fsum(T)
# toggles on +/-1.12e-16 eg. 31 N 400000 5000000
while abs(d) > EPS: # 1e-12
h = hypot1(T)
s = sinh(E.e * atanh(E.e * T / h))
t = T * hypot1(s) - s * h
d = (t0 - t) / hypot1(t) * (q + T**2) / h
T = sd.fsum_(d) # τi
a = atan(T) # lat
b = atan2(shx, cy) + radians(_cmlon(self._zone))
ll = _LLEB(degrees90(a),
degrees180(b),
datum=self._datum,
name=self.name)
# convergence: Karney 2011 Eq 26, 27
p = -Ks.ps(-1)
q = Ks.qs(0)
ll._convergence = degrees(atan(tan(y) * tanh(x)) + atan2(q, p))
# scale: Karney 2011 Eq 28
ll._scale = E.e2s(sin(a)) * hypot1(T) * H * (A0 / E.a / hypot(p, q))
self._latlon = ll
return self._latlon5(LatLon)
def _tdef(self, lat):
'''(INTERNAL) Compute t(lat).
'''
return max(0, tanPI_2_2(-lat) / self._pdef(lat))
def _xdef(self, t_x):
'''(INTERNAL) Compute x(t_x).
'''
return PI_2 - 2 * atan(t_x) # XXX + self._lat0
Conics = _NamedEnum('Conics', Conic) #: Registered conics.
Conics._assert( # <https://SpatialReference.org/ref/sr-org/...>
# AsLb = Conic(_LLEB(-14.2666667, 170, datum=Datums.NAD27), 0, 0, E0=500000, N0=0, name='AsLb', auth='EPSG:2155'), # American Samoa ... SP=1 !
Be08Lb=Conic(_LLEB(50.7978150, 4.359215833, datum=Datums.GRS80),
49.833333,
51.166667,
E0=649328.0,
N0=665262.0,
name='Be08Lb',
auth='EPSG:9802'), # Belgium
Be72Lb=Conic(_LLEB(90, 4.3674867, datum=Datums.NAD83),
49.8333339,
51.1666672,
E0=150000.013,
N0=5400088.438,
name='Be72Lb',
auth='EPSG:31370'), # Belgium
Fr93Lb=Conic(_LLEB(46.5, 3, datum=Datums.WGS84),
49,
def toLatLon(self, LatLon=None, eps=EPS, unfalse=True):
'''Convert this UTM coordinate to an (ellipsoidal) geodetic point.
@keyword LatLon: Optional, ellipsoidal (sub-)class to return
the point (C{LatLon}) or C{None}.
@keyword eps: Optional convergence limit, L{EPS} or above
(C{float}).
@keyword unfalse: Unfalse I{easting} and I{northing} if falsed
(C{bool}).
@return: This UTM coordinate as (I{LatLon}) or 5-tuple
(lat, lon, datum, convergence, scale) if I{LatLon}
is C{None}.
@raise TypeError: If I{LatLon} is not ellipsoidal.
@raise UTMError: Invalid meridional radius or H-value.
@example:
>>> u = Utm(31, 'N', 448251.795, 5411932.678)
>>> from pygeodesy import ellipsoidalVincenty as eV
>>> ll = u.toLatLon(eV.LatLon) # 48°51′29.52″N, 002°17′40.20″E
'''
if eps < EPS:
eps = EPS # less doesn't converge
if self._latlon and self._latlon_eps == eps:
return self._latlon5(LatLon)
E = self._datum.ellipsoid # XXX vs LatLon.datum.ellipsoid
x = self._easting
y = self._northing
if unfalse and self._falsed:
x -= _FalseEasting # relative to central meridian
if self._hemisphere == 'S': # relative to equator
y -= _FalseNorthing
# from Karney 2011 Eq 15-22, 36
A0 = _K0 * E.A
if A0 < EPS:
raise UTMError('%s invalid: %r' % ('meridional', E.A))
x /= A0 # η eta
y /= A0 # ξ ksi
Ks = _Kseries(E.BetaKs, x, y) # Krüger series
y = -Ks.ys(-y) # ξ'
x = -Ks.xs(-x) # η'
shx = sinh(x)
sy, cy = sincos2(y)
H = hypot(shx, cy)
if H < EPS:
raise UTMError('%s invalid: %r' % ('H', H))
d = 1.0 + eps
q = 1.0 / E.e12
T = t0 = sy / H # τʹ
sd = Fsum(T)
while abs(d) > eps:
h = hypot1(T)
s = sinh(E.e * atanh(E.e * T / h))
t = T * hypot1(s) - s * h
d = (t0 - t) / hypot1(t) * ((q + T**2) / h)
T, d = sd.fsum2_(d) # τi, (τi - τi-1)
a = atan(T) # lat
b = atan2(shx, cy) + radians(_cmlon(self._zone))
ll = _LLEB(degrees90(a),
degrees180(b),
datum=self._datum,
name=self.name)
# convergence: Karney 2011 Eq 26, 27
p = -Ks.ps(-1)
q = Ks.qs(0)
ll._convergence = degrees(atan(tan(y) * tanh(x)) + atan2(q, p))
# scale: Karney 2011 Eq 28
ll._scale = E.e2s(sin(a)) * hypot1(T) * H * (A0 / E.a / hypot(p, q))
self._latlon, self._latlon_eps = ll, eps
return self._latlon5(LatLon)