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lcc.py
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lcc.py
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# -*- coding: utf-8 -*-
u'''Lambert conformal conic projection for 1- or 2-Standard Parallels
classes L{Conic}, L{Conics} registry, L{LCCError} and position class
L{Lcc}.
See U{LCC<https://WikiPedia.org/wiki/Lambert_conformal_conic_projection>},
U{Lambert Conformal Conic to Geographic Transformation Formulae
<https://www.Linz.govt.NZ/data/geodetic-system/coordinate-conversion/
projection-conversions/lambert-conformal-conic-geographic>},
U{Lambert Conformal Conic Projection
<https://MathWorld.Wolfram.com/LambertConformalConicProjection.html>}
and John P. Snyder U{'Map Projections - A Working Manual'
<https://pubs.er.USGS.gov/djvu/PP/PP_1395.pdf>}, 1987, pp 107-109.
@newfield example: Example, Examples
'''
from pygeodesy.basics import EPS, PI_2, property_RO, _xinstanceof, \
_xsubclassof, _xzipairs
from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB
from pygeodesy.datum import Datums, Lam_, Phi_
from pygeodesy.errors import _IsnotError, _ValueError
from pygeodesy.interns import _C_, _COMMA_SPACE_, _ellipsoidal_, \
_dot_, _h_, _k0_, _lat0_, _lon0_, \
_m_, NN, _SPACE_, _SQUARE_ # PYCHOK used!
from pygeodesy.lazily import _ALL_LAZY
from pygeodesy.named import EasNor3Tuple, LatLon2Tuple, \
LatLon4Tuple, LatLonDatum3Tuple, \
_NamedBase, _NamedEnum, _NamedEnumItem, nameof, \
PhiLam2Tuple, _xnamed # PYCHOK indent
from pygeodesy.streprs import fstr
from pygeodesy.units import Easting, Height, Northing, Scalar_
from pygeodesy.utily import degrees90, degrees180, sincos2, tanPI_2_2
from math import atan, copysign, hypot, log, radians, sin, sqrt
__all__ = _ALL_LAZY.lcc
__version__ = '20.07.08'
_E0_ = 'E0'
_N0_ = 'N0'
_par1_ = 'par1'
_par2_ = 'par2'
_SP_ = 'SP'
class Conic(_NamedEnumItem):
'''Lambert conformal conic projection (1- or 2-SP).
'''
_auth = NN #: (INTERNAL) authorization (C{str}).
_datum = None #: (INTERNAL) Datum (L{Datum}).
_name = 'Conic' #: (INTERNAL) Conic (L{Conic}).
_e = 0 #: (INTERNAL) Ellipsoid excentricity (C{float}).
_E0 = 0 #: (INTERNAL) False easting (C{float}).
_k0 = 1 #: (INTERNAL) Scale factor (C{float}).
_N0 = 0 #: (INTERNAL) false northing (C{float}).
_SP = 0 #: (INTERNAL) 1- or 2-SP (C{int})
_opt3 = 0 #: (INTERNAL) Optional, longitude (C{radians}).
_par1 = 0 #: (INTERNAL) 1st std parallel (C{radians}).
_par2 = 0 #: (INTERNAL) 2nd std parallel (C{radians}).
_phi0 = 0 #: (INTERNAL) Origin lat (C{radians}).
_lam0 = 0 #: (INTERNAL) Origin lon (C{radians}).
_aF = 0 #: (INTERNAL) Precomputed F.
_n = 0 #: (INTERNAL) Precomputed n.
_n_ = 0 #: (INTERNAL) Precomputed 1 / n.
_r0 = 0 #: (INTERNAL) Precomputed rho0.
def __init__(self, latlon0, par1, par2=None, E0=0, N0=0,
k0=1, opt3=0, name=NN, auth=NN):
'''New Lambert conformal conic projection.
@arg latlon0: Origin with (ellipsoidal) datum (C{LatLon}).
@arg par1: First standard parallel (C{degrees90}).
@kwarg par2: Optional, second standard parallel (C{degrees90}).
@kwarg E0: Optional, false easting (C{meter}).
@kwarg N0: Optional, false northing (C{meter}).
@kwarg k0: Optional scale factor (C{scalar}).
@kwarg opt3: Optional meridian (C{degrees180}).
@kwarg name: Optional name of the conic (C{str}).
@kwarg auth: Optional authentication authority (C{str}).
@return: A Lambert projection (L{Conic}).
@raise TypeError: Non-ellipsoidal B{C{latlon0}}.
@raise ValueError: Invalid B{C{par1}}, B{C{par2}},
B{C{E0}}, B{C{N0}}, B{C{k0}}
or B{C{opt3}}.
@example:
>>> from pygeodesy import Conic, Datums, ellipsoidalNvector
>>> ll0 = ellipsoidalNvector.LatLon(23, -96, datum=Datums.NAD27)
>>> Snyder = Conic(ll0, 33, 45, E0=0, N0=0, name='Snyder')
'''
if latlon0 is not None:
_xinstanceof(_LLEB, latlon0=latlon0)
self._phi0, self._lam0 = latlon0.philam
self._par1 = Phi_(par1, name=_par1_)
self._par2 = self._par1 if par2 is None else Phi_(par2, name=_par2_)
if k0 != 1:
self._k0 = Scalar_(k0, name=_k0_)
if E0:
self._E0 = Northing(E0, name=_E0_, falsed=True)
if N0:
self._N0 = Easting(N0, name=_N0_, falsed=True)
if opt3:
self._opt3 = Lam_(opt3, name='opt3')
self.toDatum(latlon0.datum)._dup2(self)
self._register(Conics, name)
elif name:
self.name = name
if auth:
self._auth = str(auth)
@property_RO
def auth(self):
'''Get the authentication authority (C{str}).
'''
return self._auth
@property_RO
def datum(self):
'''Get the datum (L{Datum}).
'''
return self._datum
@property_RO
def E0(self):
'''Get the false easting (C{meter}).
'''
return self._E0
@property_RO
def k0(self):
'''Get scale factor (C{float}).
'''
return self._k0
@property_RO
def lat0(self):
'''Get the origin latitude (C{degrees90}).
'''
return degrees90(self._phi0)
@property_RO
def latlon0(self):
'''Get the central origin (L{LatLon2Tuple}C{(lat, lon)}).
'''
return self._xnamed(LatLon2Tuple(self.lat0, self.lon0))
@property_RO
def lam0(self):
'''Get the central meridian (C{radians}).
'''
return self._lam0
@property_RO
def lon0(self):
'''Get the central meridian (C{degrees180}).
'''
return degrees180(self._lam0)
@property_RO
def N0(self):
'''Get the false northing (C{meter}).
'''
return self._N0
@property_RO
def name2(self):
'''Get the conic and datum names as "conic.datum" (C{str}).
'''
return _dot_(self.name, self.datum.name)
@property_RO
def opt3(self):
'''Get the optional meridian (C{degrees180}).
'''
return degrees180(self._opt3)
@property_RO
def par1(self):
'''Get the 1st standard parallel (C{degrees90}).
'''
return degrees90(self._par1)
@property_RO
def par2(self):
'''Get the 2nd standard parallel (C{degrees90}).
'''
return degrees90(self._par2)
@property_RO
def phi0(self):
'''Get the origin latitude (C{radians}).
'''
return self._phi0
@property_RO
def philam0(self):
'''Get the central origin (L{PhiLam2Tuple}C{(phi, lam)}).
'''
return self._xnamed(PhiLam2Tuple(self.phi0, self.lam0))
@property_RO
def SP(self):
'''Get the number of standard parallels (C{int}).
'''
return self._SP
def toDatum(self, datum):
'''Convert this conic to the given datum.
@arg datum: Ellipsoidal datum to use (L{Datum}).
@return: Converted conic, unregistered (L{Conic}).
@raise TypeError: Non-ellipsoidal B{C{datum}}.
'''
E = datum.ellipsoid
if not E.isEllipsoidal:
raise _IsnotError(_ellipsoidal_, datum=datum)
c = self
if c._e != E.e or c._datum != datum:
c = Conic(None, 0, name=self._name)
self._dup2(c)
c._datum = datum
c._e = E.e
if abs(c._par1 - c._par2) < EPS:
m1 = c._mdef(c._phi0)
t1 = c._tdef(c._phi0)
t0 = t1
k = 1
n = sin(c._phi0)
sp = 1
else:
m1 = c._mdef(c._par1)
m2 = c._mdef(c._par2)
t1 = c._tdef(c._par1)
t2 = c._tdef(c._par2)
t0 = c._tdef(c._phi0)
k = c._k0
n = (log(m1) - log(m2)) \
/ (log(t1) - log(t2))
sp = 2
F = m1 / (n * pow(t1, n))
c._aF = k * E.a * F
c._n = n
c._n_ = 1 / n
c._r0 = c._rdef(t0)
c._SP = sp
return c
convertDatum = toDatum # alternate name
def toStr(self, prec=8): # PYCHOK expected
'''Return this conic as a string.
@kwarg prec: Optional number of decimals, unstripped (C{int}).
@return: Conic attributes (C{str}).
'''
if self._SP == 1:
return self._instr(prec, _lat0_, _lon0_, _par1_,
_E0_, _N0_, _k0_, _SP_,
datum=self.datum)
else:
return self._instr(prec, _lat0_, _lon0_, _par1_, _par2_,
_E0_, _N0_, _k0_, _SP_,
datum=self.datum)
def _dup2(self, c):
'''(INTERNAL) Copy this conic to c.
@arg c: Duplicate (L{Conic}).
'''
c._auth = self._auth
c._datum = self._datum
c._e = self._e
c._E0 = self._E0
c._k0 = self._k0
c._N0 = self._N0
c._SP = self._SP
c._par1 = self._par1
c._par2 = self._par2
c._phi0 = self._phi0
c._lam0 = self._lam0
c._opt3 = self._opt3
c._aF = self._aF
c._n = self._n
c._n_ = self._n_
c._r0 = self._r0
def _mdef(self, lat):
'''(INTERNAL) Compute m(lat).
'''
s, c = sincos2(lat)
s *= self._e
return c / sqrt(1 - s**2)
def _pdef(self, lat):
'''(INTERNAL) Compute p(lat).
'''
s = self._e * sin(lat)
return pow((1 - s) / (1 + s), self._e / 2)
def _rdef(self, t):
'''(INTERNAL) Compute r(t).
'''
return self._aF * pow(t, self._n)
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, 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
class Lcc(_NamedBase):
'''Lambert conformal conic East-/Northing location.
'''
_conic = None #: (INTERNAL) Lambert projection (L{Conic}).
_easting = 0 #: (INTERNAL) Easting (C{float}).
_height = 0 #: (INTERNAL) Height (C{meter}).
_latlon = None #: (INTERNAL) latlon cache (L{LatLon2Tuple}).
_northing = 0 #: (INTERNAL) Northing (C{float}).
_philam = None #: (INTERNAL) philam cache (L{PhiLam2Tuple}).
def __init__(self, e, n, h=0, conic=Conics.WRF_Lb, name=NN):
'''New L{Lcc} Lamber conformal conic position.
@arg e: Easting (C{meter}).
@arg n: Northing (C{meter}).
@kwarg h: Optional height (C{meter}).
@kwarg conic: Optional, the conic projection (L{Conic}).
@kwarg name: Optional name (C{str}).
@return: The Lambert location (L{Lcc}).
@raise LCCError: Invalid B{C{h}} or invalid or
negative B{C{e}} or B{C{n}}.
@raise TypeError: If B{C{conic}} is not L{Conic}.
@example:
>>> lb = Lcc(448251, 5411932.0001)
'''
_xinstanceof(Conic, conic=conic)
self._conic = conic
self._easting = Easting(e, falsed=conic.E0 > 0, Error=LCCError)
self._northing = Northing(n, falsed=conic.N0 > 0, Error=LCCError)
if h:
self._height = Height(h, name=_h_, Error=LCCError)
if name:
self.name = name
@property_RO
def conic(self):
'''Get the conic projection (L{Conic}).
'''
return self._conic
@property_RO
def easting(self):
'''Get the easting (C{meter}).
'''
return self._easting
@property_RO
def height(self):
'''Get the height (C{meter}).
'''
return self._height
@property_RO
def latlon(self):
'''Get the lat- and longitude in C{degrees} (L{LatLon2Tuple}).
'''
if self._latlon is None:
r = self.toLatLon(LatLon=None, datum=None)
self._latlon = LatLon2Tuple(r.lat, r.lon)
return self._xnamed(self._latlon)
@property_RO
def northing(self):
'''Get the northing (C{meter}).
'''
return self._northing
@property_RO
def philam(self):
'''Get the lat- and longitude in C{radians} (L{PhiLam2Tuple}).
'''
if self._philam is None:
self._philam = PhiLam2Tuple(radians(self.latlon.lat),
radians(self.latlon.lon))
return self._xnamed(self._philam)
def to3lld(self, datum=None): # PYCHOK no cover
'''DEPRECATED, use method C{toLatLon}.
@kwarg datum: Optional datum to use, otherwise use this
B{C{Lcc}}'s conic.datum (C{Datum}).
@return: A L{LatLonDatum3Tuple}C{(lat, lon, datum)}.
@raise TypeError: If B{C{datum}} is not ellipsoidal.
'''
if datum in (None, self.conic.datum):
r = LatLonDatum3Tuple(self.latlon.lat,
self.latlon.lon,
self.conic.datum)
else:
r = self.toLatLon(LatLon=None, datum=datum)
r = LatLonDatum3Tuple(r.lat, r.lon, r.datum)
return self._xnamed(r)
def toLatLon(self, LatLon=None, datum=None, height=None):
'''Convert this L{Lcc} to an (ellipsoidal) geodetic point.
@kwarg LatLon: Optional, ellipsoidal class to return the
geodetic point (C{LatLon}) or C{None}.
@kwarg datum: Optional datum to use, otherwise use this
B{C{Lcc}}'s conic.datum (C{Datum}).
@kwarg height: Optional height for the point, overriding
the default height (C{meter}).
@return: The point (B{C{LatLon}}) or a
L{LatLon4Tuple}C{(lat, lon, height, datum)}
if B{C{LatLon}} is C{None}.
@raise TypeError: If B{C{LatLon}} or B{C{datum}} is
not ellipsoidal.
'''
if LatLon:
_xsubclassof(_LLEB, LatLon=LatLon)
c = self.conic
if datum:
c = c.toDatum(datum)
e = self.easting - c._E0
n = c._r0 - self.northing + c._N0
r_ = copysign(hypot(e, n), c._n)
t_ = pow(r_ / c._aF, c._n_)
x = c._xdef(t_) # XXX c._lam0
while True:
p, x = x, c._xdef(t_ * c._pdef(x))
if abs(x - p) < 1e-9: # XXX EPS too small?
break
lat = degrees90(x)
lon = degrees180((atan(e / n) + c._opt3) * c._n_ + c._lam0)
h = self.height if height is None else height
d = c.datum
r = LatLon4Tuple(lat, lon, h, d) if LatLon is None else \
LatLon(lat, lon, height=h, datum=d)
return self._xnamed(r)
def toRepr(self, prec=0, fmt=_SQUARE_, sep=_COMMA_SPACE_, m=_m_, C=False, **unused): # PYCHOK expected
'''Return a string representation of this L{Lcc} position.
@kwarg prec: Optional number of decimals, unstripped (C{int}).
@kwarg fmt: Optional, enclosing backets format (C{str}).
@kwarg sep: Optional separator between name:values (C{str}).
@kwarg m: Optional unit of the height, default meter (C{str}).
@kwarg C: Optionally, include name of conic and datum (C{bool}).
@return: This Lcc as "[E:meter, N:meter, H:m, C:Conic.Datum]"
(C{str}).
'''
t = self.toStr(prec=prec, sep=None, m=m)
k = 'ENH'[:len(t)]
if C:
k += _C_
t += [self.conic.name2]
return _xzipairs(k, t, sep=sep, fmt=fmt)
def toStr(self, prec=0, sep=_SPACE_, m=_m_): # PYCHOK expected
'''Return a string representation of this L{Lcc} position.
@kwarg prec: Optional number of decimal, unstripped (C{int}).
@kwarg sep: Optional separator to join (C{str}) or C{None}
to return an unjoined C{tuple} of C{str}s.
@kwarg m: Optional height units, default C{meter} (C{str}).
@return: This Lcc as "easting nothing" C{str} in C{meter} plus
" height" and 'm' if heigth is non-zero (C{str}).
@example:
>>> lb = Lcc(448251, 5411932.0001)
>>> lb.toStr(4) # 448251.0 5411932.0001
>>> lb.toStr(sep=', ') # 448251, 5411932
'''
t = [fstr(self._easting, prec=prec),
fstr(self._northing, prec=prec)]
if self._height:
t += ['%+.2f%s' % (self._height, m)]
return tuple(t) if sep is None else sep.join(t)
def toLcc(latlon, conic=Conics.WRF_Lb, height=None, Lcc=Lcc, name=NN,
**Lcc_kwds):
'''Convert an (ellipsoidal) geodetic point to a I{Lambert} location.
@arg latlon: Ellipsoidal point (C{LatLon}).
@kwarg conic: Optional Lambert projection to use (L{Conic}).
@kwarg height: Optional height for the point, overriding the
default height (C{meter}).
@kwarg Lcc: Optional class to return the I{Lambert} location
(L{Lcc}).
@kwarg name: Optional B{C{Lcc}} name (C{str}).
@kwarg Lcc_kwds: Optional, additional B{C{Lcc}} keyword
arguments, ignored if B{C{Lcc=None}}.
@return: The I{Lambert} location (L{Lcc}) or an
L{EasNor3Tuple}C{(easting, northing, height)}
if B{C{Lcc}} is C{None}.
@raise TypeError: If B{C{latlon}} is not ellipsoidal.
'''
_xinstanceof(_LLEB, latlon=latlon)
a, b = latlon.philam
c = conic.toDatum(latlon.datum)
t = c._n * (b - c._lam0) - c._opt3
st, ct = sincos2(t)
r = c._rdef(c._tdef(a))
e = c._E0 + r * st
n = c._N0 + c._r0 - r * ct
h = latlon.height if height is None else height
r = EasNor3Tuple(e, n, h) if Lcc is None else \
Lcc(e, n, h=h, conic=c, **Lcc_kwds)
return _xnamed(r, name or nameof(latlon))
if __name__ == '__main__':
# print all
for c in (Conics,):
c = '\n' + repr(c)
print('\n# '.join(c.split('\n')))
# **) MIT License
#
# Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved.
#
# Permission is hereby granted, free of charge, to any person obtaining a
# copy of this software and associated documentation files (the "Software"),
# to deal in the Software without restriction, including without limitation
# the rights to use, copy, modify, merge, publish, distribute, sublicense,
# and/or sell copies of the Software, and to permit persons to whom the
# Software is furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included
# in all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
# OTHER DEALINGS IN THE SOFTWARE.
# % python -m pygeodesy.lcc
# Conics.Be08Lb: Conic(name='Be08Lb', lat0=50.797815, lon0=4.35921583, par1=49.833333, par2=51.166667, E0=649328, N0=665262, k0=1, SP=2, datum=Datum(name='GRS80', ellipsoid=Ellipsoids.GRS80, transform=Transforms.WGS84),
# Conics.Be72Lb: Conic(name='Be72Lb', lat0=90, lon0=4.3674867, par1=49.8333339, par2=51.1666672, E0=150000.013, N0=5400088.438, k0=1, SP=2, datum=Datum(name='NAD83', ellipsoid=Ellipsoids.GRS80, transform=Transforms.NAD83),
# Conics.Fr93Lb: Conic(name='Fr93Lb', lat0=46.5, lon0=3, par1=49, par2=44, E0=700000, N0=6600000, k0=1, SP=2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84),
# Conics.MaNLb: Conic(name='MaNLb', lat0=33.3, lon0=-5.4, par1=31.73, par2=34.87, E0=500000, N0=300000, k0=1, SP=2, datum=Datum(name='NTF', ellipsoid=Ellipsoids.Clarke1880IGN, transform=Transforms.NTF),
# Conics.MxLb: Conic(name='MxLb', lat0=12, lon0=-102, par1=17.5, par2=29.5, E0=2500000, N0=0, k0=1, SP=2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84),
# Conics.PyT_Lb: Conic(name='PyT_Lb', lat0=46.8, lon0=2.33722917, par1=45.8989389, par2=47.6960144, E0=600000, N0=200000, k0=1, SP=2, datum=Datum(name='NTF', ellipsoid=Ellipsoids.Clarke1880IGN, transform=Transforms.NTF),
# Conics.USA_Lb: Conic(name='USA_Lb', lat0=23, lon0=-96, par1=33, par2=45, E0=0, N0=0, k0=1, SP=2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84),
# Conics.WRF_Lb: Conic(name='WRF_Lb', lat0=40, lon0=-97, par1=33, par2=45, E0=0, N0=0, k0=1, SP=2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84)