def toOsgr(latlon,
lon=None,
datum=Datums.WGS84,
Osgr=Osgr,
name=NN,
**Osgr_kwds):
'''Convert a lat-/longitude point to an OSGR coordinate.
@arg latlon: Latitude (C{degrees}) or an (ellipsoidal) geodetic
C{LatLon} point.
@kwarg lon: Optional longitude in degrees (scalar or C{None}).
@kwarg datum: Optional datum to convert B{C{lat, lon}} from
(L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
L{a_f2Tuple}).
@kwarg Osgr: Optional class to return the OSGR coordinate
(L{Osgr}) or C{None}.
@kwarg name: Optional B{C{Osgr}} name (C{str}).
@kwarg Osgr_kwds: Optional, additional B{C{Osgr}} keyword
arguments, ignored if B{C{Osgr=None}}.
@return: The OSGR coordinate (B{C{Osgr}}) or an
L{EasNor2Tuple}C{(easting, northing)} if B{C{Osgr}}
is C{None}.
@raise OSGRError: Invalid B{C{latlon}} or B{C{lon}}.
@raise TypeError: Non-ellipsoidal B{C{latlon}} or invalid
B{C{datum}} or conversion failed.
@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 OSGRError(lon=lon, txt='not %s' % (None, ))
elif not name: # use latlon.name
name = nameof(latlon)
# if necessary, convert to OSGB36 first
ll = _ll2datum(latlon, _Datums_OSGB36, _latlon_)
try:
a, b = ll.philam
except AttributeError:
a, b = map1(radians, ll.lat, ll.lon)
sa, ca = sincos2(a)
E = _Datums_OSGB36.ellipsoid
s = E.e2s2(sa) # r, v = E.roc2_(sa, _F0); r = v / r
v = E.a * _F0 / sqrt(s) # nu
r = s / E.e12 # nu / rho == v / (v * E.e12 / s) == s / E.e12
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)
if Osgr is None:
r = _EasNor2Tuple(e, n)
else:
r = Osgr(e, n, datum=_Datums_OSGB36, **Osgr_kwds)
if lon is None and isinstance(latlon, _LLEB):
r._latlon = latlon # XXX weakref(latlon)?
return _xnamed(r, name)
def toLatLon(self, LatLon=None, datum=Datums.WGS84):
'''Convert this OSGR coordinate to an (ellipsoidal) geodetic
point.
While OS grid references are based on the OSGB36 datum, the
I{Ordnance Survey} have deprecated the use of OSGB36 for
lat-/longitude coordinates (in favour of WGS84). Hence, this
method returns WGS84 by default with OSGB36 as an option,
U{see<https://www.OrdnanceSurvey.co.UK/blog/2014/12/2>}.
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.}
@kwarg LatLon: Optional ellipsoidal class to return the
geodetic point (C{LatLon}) or C{None}.
@kwarg datum: Optional datum to convert to (L{Datum},
L{Ellipsoid}, L{Ellipsoid2}, L{Ellipsoid2}
or L{a_f2Tuple}).
@return: The geodetic point (B{C{LatLon}}) or a
L{LatLonDatum3Tuple}C{(lat, lon, datum)}
if B{C{LatLon}} is C{None}.
@raise OSGRError: No convergence.
@raise TypeError: If B{C{LatLon}} is not ellipsoidal or
B{C{datum}} is invalid or 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 = self.datum.ellipsoid # _Datums_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, n_N0
sa = Fsum(a)
for self._iteration in range(1, _TRIPS):
a = sa.fsum_(m / a_F0)
m = n_N0 - b_F0 * _M(E.Mabcd, a) # meridional arc
if abs(m) < _10um:
break
else:
t = _dot_(_item_ps(self.classname, self.toStr(prec=-3)),
self.toLatLon.__name__)
raise OSGRError(_no_convergence_, txt=t)
sa, ca = sincos2(a)
s = E.e2s2(sa) # r, v = E.roc2_(sa, _F0)
v = a_F0 / sqrt(s) # nu
r = v * E.e12 / s # rho = a_F0 * E.e12 / pow(s, 1.5) == a_F0 * E.e12 / (s * sqrt(s))
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, ta2, ta2),
csa / (120 * v5) * fdot(
(5, 28, 24), 1, ta2, ta4), csa / (5040 * v7) * fdot(
(61, 662, 1320, 720), 1, 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)
r = _LLEB(degrees90(a),
degrees180(b),
datum=self.datum,
name=self.name)
r._iteration = self._iteration # only ellipsoidal LatLon
self._latlon = r
return self._latlon3(LatLon, datum)
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._phi0
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 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 B{C{Osgr}} name (C{str}).
@return: The OSGR coordinate (B{C{Osgr}}) or an
L{EasNor2Tuple}C{(easting, northing)} if B{C{Osgr}}
is C{None}.
@raise TypeError: Non-ellipsoidal B{C{latlon}} or B{C{datum}}
conversion failed.
@raise OSGRError: Invalid B{C{latlon}} or B{C{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 OSGRError('%s not %s: %r' % ('lon', None, lon))
elif not name: # use latlon.name
name = nameof(latlon)
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, r = E.roc2_(sa, _F0); r = v / r
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)
if Osgr is None:
r = EasNor2Tuple(e, n)
else:
r = Osgr(e, n)
if lon is None and isinstance(latlon, _LLEB):
r._latlon = latlon # XXX weakref(latlon)?
return _xnamed(r, 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 (B{C{LatLon}}) or a
L{LatLonDatum3Tuple}C{(lat, lon, datum)}
if B{C{LatLon}} is C{None}.
@raise TypeError: If B{C{LatLon}} is not ellipsoidal or if
B{C{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, r = E.roc2_(sa, _F0)
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 _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, 44, E0=700000, N0=6600000, name='Fr93Lb', auth='EPSG:2154'), # RFG93, France
MaNLb = Conic(_LLEB(33.3, -5.4, datum=Datums.NTF), 31.73, 34.87, E0=500000, N0=300000, name='MaNLb'), # Marocco
MxLb = Conic(_LLEB(12, -102, datum=Datums.WGS84), 17.5, 29.5, E0=2500000, N0=0, name='MxLb', auth='EPSG:2155'), # Mexico
PyT_Lb = Conic(_LLEB(46.8, 2.33722917, datum=Datums.NTF), 45.89893890000052, 47.69601440000037, E0=600000, N0=200000, name='PyT_Lb', auth='Test'), # France?
USA_Lb = Conic(_LLEB(23, -96, datum=Datums.WGS84), 33, 45, E0=0, N0=0, name='USA_Lb'), # Conterminous, contiguous USA?
WRF_Lb = Conic(_LLEB(40, -97, datum=Datums.WGS84), 33, 45, E0=0, N0=0, name='WRF_Lb', auth='EPSG:4326') # World
)
class LCCError(ValueError):
'''Lambert Conformal Conic C{LCC} or other L{Lcc} issue.
'''
pass