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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.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB 

from pygeodesy.datum import Datums 

from pygeodesy.fmath import EPS, fStr, hypot, _IsNotError 

from pygeodesy.lazily import _ALL_LAZY 

from pygeodesy.named import EasNor3Tuple, LatLon4Tuple, LatLonDatum3Tuple, \ 

_NamedBase, _NamedEnum, _NamedEnumItem, nameof, \ 

_xnamed 

from pygeodesy.utily import PI_2, degrees90, degrees180, false2f, \ 

issubclassof, property_RO, sincos2, tanPI_2_2, \ 

_TypeError 

 

from math import atan, copysign, log, radians, sin, sqrt 

 

# all public constants, classes and functions 

__all__ = _ALL_LAZY.lcc 

__version__ = '20.01.22' 

 

 

class Conic(_NamedEnumItem): 

'''Lambert conformal conic projection (1- or 2-SP). 

''' 

_auth = '' #: (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}) 

 

_lat0 = 0 #: (INTERNAL) Origin lat (C{radians}). 

_lon0 = 0 #: (INTERNAL) Origin lon (C{radians}). 

_par1 = 0 #: (INTERNAL) 1st std parallel (C{radians}). 

_par2 = 0 #: (INTERNAL) 2nd std parallel (C{radians}). 

_opt3 = 0 #: (INTERNAL) Optional, longitude (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='', auth=''): 

'''New Lambert conformal conic projection. 

 

@param latlon0: Origin with (ellipsoidal) datum (C{LatLon}). 

@param par1: First standard parallel (C{degrees90}). 

@keyword par2: Optional, second standard parallel (C{degrees90}). 

@keyword E0: Optional, false easting (C{meter}). 

@keyword N0: Optional, false northing (C{meter}). 

@keyword k0: Optional scale factor (C{scalar}). 

@keyword opt3: Optional meridian (C{degrees180}). 

@keyword name: Optional name of the conic (C{str}). 

@keyword auth: Optional authentication authority (C{str}). 

 

@return: A Lambert projection (L{Conic}). 

 

@raise TypeError: Non-ellipsoidal B{C{latlon0}}. 

 

@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: 

_TypeError(_LLEB, latlon0=latlon0) 

 

self._lat0, self._lon0 = latlon0.to2ab() 

self._par1 = radians(par1) 

if par2 is None: 

self._par2 = self._par1 

else: 

self._par2 = radians(par2) 

self._opt3 = radians(opt3) 

 

if k0 != 1: 

self._k0 = float(k0) 

if N0: 

self._N0 = float(N0) 

if E0: 

self._E0 = float(E0) 

 

self.toDatum(latlon0.datum)._dup2(self) 

self._register(Conics, name) 

elif name: 

self._name = name 

if auth: 

self._auth = 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._lat0) 

 

@property_RO 

def lon0(self): 

'''Get the central meridian (C{degrees180}). 

''' 

return degrees180(self._lon0) 

 

@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 self.name + '.' + self.datum.name 

 

@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 opt3(self): 

'''Get the optional meridian (C{degrees180}). 

''' 

return degrees180(self._opt3) 

 

@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. 

 

@param 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._lat0) 

t1 = c._tdef(c._lat0) 

t0 = t1 

k = 1 

n = sin(c._lat0) 

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._lat0) 

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. 

 

@keyword prec: Optional number of decimals, unstripped (C{int}). 

 

@return: Conic attributes (C{str}). 

''' 

if self._SP == 1: 

return self._fStr(prec, 'lat0', 'lon0', 'par1', 

'E0', 'N0', 'k0', 'SP', 

datum='(%s)' % (self.datum),) 

else: 

return self._fStr(prec, 'lat0', 'lon0', 'par1', 'par2', 

'E0', 'N0', 'k0', 'SP', 

datum='(%s)' % (self.datum),) 

 

def _dup2(self, c): 

'''(INTERNAL) Copy this conic to c. 

@param 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._lat0 = self._lat0 

c._lon0 = self._lon0 

c._par1 = self._par1 

c._par2 = self._par2 

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._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 

 

 

class Lcc(_NamedBase): 

'''Lambert conformal conic East-/Northing location. 

''' 

_easting = 0 #: (INTERNAL) Easting (C{float}). 

_height = 0 #: (INTERNAL) Height (C{meter}). 

_northing = 0 #: (INTERNAL) Northing (C{float}). 

_conic = None #: (INTERNAL) Lamber projection (L{Conic}). 

 

def __init__(self, e, n, h=0, conic=Conics.WRF_Lb, name=''): 

'''New L{Lcc} Lamber conformal conic position. 

 

@param e: Easting (C{meter}). 

@param n: Northing (C{meter}). 

@keyword h: Optional height (C{meter}). 

@keyword conic: Optional, the conic projection (L{Conic}). 

@keyword name: Optional name (C{str}). 

 

@return: The Lambert location (L{Lcc}). 

 

@raise TypeError: If B{C{conic}} is not L{Conic}. 

 

@raise LCCError: Invalid or negative B{C{e}} or B{C{n}}. 

 

@example: 

 

>>> lb = Lcc(448251, 5411932.0001) 

''' 

_TypeError(Conic, conic=conic) 

self._conic = conic 

self._easting = false2f(e, 'easting', false=conic.E0 > 0, Error=LCCError) 

self._northing = false2f(n, 'northing', false=conic.N0 > 0, Error=LCCError) 

if h: 

self._height = float(h) 

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 northing(self): 

'''Get the northing (C{meter}). 

''' 

return self._northing 

 

def to3lld(self, datum=None): 

'''Convert this L{Lcc} to a geodetic lat- and longitude. 

 

@keyword 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. 

''' 

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._lon0 

while True: 

p, x = x, c._xdef(t_ * c._pdef(x)) 

if abs(x - p) < 1e-9: # XXX EPS too small? 

break 

# x, y == lon, lat 

a = degrees90(x) 

b = degrees180((atan(e / n) + c._opt3) * c._n_ + c._lon0) 

 

return LatLonDatum3Tuple(a, b, c.datum) 

 

def toLatLon(self, LatLon=None, datum=None, height=None): 

'''Convert this L{Lcc} to an (ellipsoidal) geodetic point. 

 

@keyword LatLon: Optional, ellipsoidal (sub-)class to return 

the geodetic point (C{LatLon}) or C{None}. 

@keyword datum: Optional datum to use, otherwise use this 

B{C{Lcc}}'s conic.datum (C{Datum}). 

@keyword 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 and not issubclassof(LatLon, _LLEB): 

raise _IsNotError(_LLEB.__name__, LatLon=LatLon) 

 

a, b, d = self.to3lld(datum=datum) 

h = self.height if height is None else height 

 

r = LatLon4Tuple(a, b, h, d) if LatLon is None else \ 

LatLon(a, b, height=h, datum=d) 

return self._xnamed(r) 

 

def toStr(self, prec=0, sep=' ', m='m'): # PYCHOK expected 

'''Return a string representation of this L{Lcc} position. 

 

@keyword prec: Optional number of decimal, unstripped (C{int}). 

@keyword sep: Optional separator to join (C{str}). 

@keyword 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 sep.join(t) 

 

def toStr2(self, prec=0, fmt='[%s]', sep=', ', m='m', C=False): # PYCHOK expected 

'''Return a string representation of this L{Lcc} position. 

 

@keyword prec: Optional number of decimals, unstripped (C{int}). 

@keyword fmt: Optional, enclosing backets format (C{str}). 

@keyword sep: Optional separator between name:values (C{str}). 

@keyword m: Optional unit of the height, default meter (C{str}). 

@keyword 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=' ', m=m).split() 

k = 'ENH'[:len(t)] 

if C: 

k += 'C' 

t += [self.conic.name2] 

return fmt % (sep.join('%s:%s' % t for t in zip(k, t)),) 

 

 

def toLcc(latlon, conic=Conics.WRF_Lb, height=None, Lcc=Lcc, name=''): 

'''Convert an (ellipsoidal) geodetic point to a Lambert location. 

 

@param latlon: Ellipsoidal point (C{LatLon}). 

@keyword conic: Optional Lambert projection to use (L{Conic}). 

@keyword height: Optional height for the point, overriding 

the default height (C{meter}). 

@keyword Lcc: Optional (sub-)class to return the Lambert 

location (L{Lcc}). 

@keyword name: Optional B{C{Lcc}} name (C{str}). 

 

@return: The 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. 

''' 

if not isinstance(latlon, _LLEB): 

raise _IsNotError(_LLEB.__name__, latlon=latlon) 

 

a, b = latlon.to2ab() 

c = conic.toDatum(latlon.datum) 

 

t = c._n * (b - c._lon0) - 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) 

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=(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=(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=(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=(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=(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=(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=(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=(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84),