# Coverage for pygeodesy/lcc.py : 91%

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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),