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# -*- coding: utf-8 -*-
Classes L{Datum} and L{Transform} and registries L{Datums} and L{Transforms}, respectively.
Pure Python implementation of geodesy tools for ellipsoidal earth models, including datums and ellipsoid parameters for different geographic coordinate systems and methods for converting between them and to cartesian coordinates. Transcoded from JavaScript originals by I{(C) Chris Veness 2005-2016} and published under the same MIT Licence**, see U{latlon-ellipsoidal.js <https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.
Historical geodetic datums: a latitude/longitude point defines a geographic location on or above/below the earth’s surface, measured in degrees from the equator and the International Reference Meridian and meters above the ellipsoid, and based on a given datum. The datum is based on a reference ellipsoid and tied to geodetic survey reference points.
Modern geodesy is generally based on the WGS84 datum (as used for instance by GPS systems), but previously various reference ellipsoids and datum references were used.
The UK Ordnance Survey National Grid References are still based on the otherwise historical OSGB36 datum, q.v. U{Ordnance Survey 'A guide to coordinate systems in Great Britain', Section 6<https://www.OrdnanceSurvey.co.UK/docs/support/ guide-coordinate-systems-great-britain.pdf>}.
@var Datums.BD72: Datum(name='BD72', ellipsoid=Ellipsoids.Intl1924, transform=Transforms.BD72) @var Datums.DHDN: Datum(name='DHDN', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.DHDN) @var Datums.ED50: Datum(name='ED50', ellipsoid=Ellipsoids.Intl1924, transform=Transforms.ED50) @var Datums.GDA2020: Datum(name='GDA2020', ellipsoid=Ellipsoids.GRS80, transform=Transforms.WGS84) @var Datums.GRS80: Datum(name='GRS80', ellipsoid=Ellipsoids.GRS80, transform=Transforms.WGS84) @var Datums.Irl1975: Datum(name='Irl1975', ellipsoid=Ellipsoids.AiryModified, transform=Transforms.Irl1975) @var Datums.Krassovski1940: Datum(name='Krassovski1940', ellipsoid=Ellipsoids.Krassovski1940, transform=Transforms.Krassovski1940) @var Datums.Krassowsky1940: Datum(name='Krassowsky1940', ellipsoid=Ellipsoids.Krassowsky1940, transform=Transforms.Krassowsky1940) @var Datums.MGI: Datum(name='MGI', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.MGI) @var Datums.NAD27: Datum(name='NAD27', ellipsoid=Ellipsoids.Clarke1866, transform=Transforms.NAD27) @var Datums.NAD83: Datum(name='NAD83', ellipsoid=Ellipsoids.GRS80, transform=Transforms.NAD83) @var Datums.NTF: Datum(name='NTF', ellipsoid=Ellipsoids.Clarke1880IGN, transform=Transforms.NTF) @var Datums.OSGB36: Datum(name='OSGB36', ellipsoid=Ellipsoids.Airy1830, transform=Transforms.OSGB36) @var Datums.Potsdam: Datum(name='Potsdam', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.Bessel1841) @var Datums.Sphere: Datum(name='Sphere', ellipsoid=Ellipsoids.Sphere, transform=Transforms.WGS84) @var Datums.TokyoJapan: Datum(name='TokyoJapan', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.TokyoJapan) @var Datums.WGS72: Datum(name='WGS72', ellipsoid=Ellipsoids.WGS72, transform=Transforms.WGS72) @var Datums.WGS84: Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84)
@var Transforms.BD72: Transform(name='BD72', tx=106.86863, ty=-52.29778, tz=103.72389, rx=-0, ry=-0, rz=-0.00001, s=1.2727, s1=1, sx=-0.33657, sy=-0.45696, sz=-1.84218) @var Transforms.Bessel1841: Transform(name='Bessel1841', tx=-582, ty=-105, tz=-414, rx=-0.00001, ry=-0, rz=0.00001, s=-8.3, s1=0.99999, sx=-1.04, sy=-0.35, sz=3.08) @var Transforms.Clarke1866: Transform(name='Clarke1866', tx=8, ty=-160, tz=-176, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) @var Transforms.DHDN: Transform(name='DHDN', tx=-591.28, ty=-81.35, tz=-396.39, rx=0.00001, ry=-0, rz=-0.00001, s=-9.82, s1=0.99999, sx=1.477, sy=-0.0736, sz=-1.458) @var Transforms.ED50: Transform(name='ED50', tx=89.5, ty=93.8, tz=123.1, rx=0, ry=0, rz=0, s=-1.2, s1=1, sx=0, sy=0, sz=0.156) @var Transforms.Identity: Transform(name='Identity', tx=0, ty=0, tz=0, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) @var Transforms.Irl1965: Transform(name='Irl1965', tx=-482.53, ty=130.596, tz=-564.557, rx=0.00001, ry=0, rz=0, s=-8.15, s1=0.99999, sx=1.042, sy=0.214, sz=0.631) @var Transforms.Irl1975: Transform(name='Irl1975', tx=-482.53, ty=130.596, tz=-564.557, rx=-0.00001, ry=-0, rz=-0, s=-1.1, s1=1, sx=-1.042, sy=-0.214, sz=-0.631) @var Transforms.Krassovski1940: Transform(name='Krassovski1940', tx=-24, ty=123, tz=94, rx=-0, ry=0, rz=0, s=-2.423, s1=1, sx=-0.02, sy=0.26, sz=0.13) @var Transforms.Krassowsky1940: Transform(name='Krassowsky1940', tx=-24, ty=123, tz=94, rx=-0, ry=0, rz=0, s=-2.423, s1=1, sx=-0.02, sy=0.26, sz=0.13) @var Transforms.MGI: Transform(name='MGI', tx=-577.326, ty=-90.129, tz=-463.92, rx=0.00002, ry=0.00001, rz=0.00003, s=-2.423, s1=1, sx=5.137, sy=1.474, sz=5.297) @var Transforms.NAD27: Transform(name='NAD27', tx=8, ty=-160, tz=-176, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) @var Transforms.NAD83: Transform(name='NAD83', tx=1.004, ty=-1.91, tz=-0.515, rx=0, ry=0, rz=0, s=-0.0015, s1=1, sx=0.0267, sy=0.00034, sz=0.011) @var Transforms.NTF: Transform(name='NTF', tx=-168, ty=-60, tz=320, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) @var Transforms.OSGB36: Transform(name='OSGB36', tx=-446.448, ty=125.157, tz=-542.06, rx=-0, ry=-0, rz=-0, s=20.4894, s1=1.00002, sx=-0.1502, sy=-0.247, sz=-0.8421) @var Transforms.TokyoJapan: Transform(name='TokyoJapan', tx=148, ty=-507, tz=-685, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) @var Transforms.WGS72: Transform(name='WGS72', tx=0, ty=0, tz=-4.5, rx=0, ry=0, rz=0, s=-0.22, s1=1, sx=0, sy=0, sz=0.554) @var Transforms.WGS84: Transform(name='WGS84', tx=0, ty=0, tz=0, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) ''' # make sure int/int division yields float quotient, see .basics
Ellipsoid2, Ellipsoids _Clarke1866_, _Clarke1880IGN_, _COMMASPACE_, \ _DOT_, _ellipsoid_, _ellipsoidal_, _float as _F, \ _GRS80_, _Intl1924_, _Krassovski1940_, _NAD27_, \ _Krassowsky1940_, _NAD83_, _name_, _s_, _Sphere_, \ _spherical_, _sx_, _sy_, _sz_, _transform_, \ _tx_, _ty_, _tz_, _UNDER_, _WGS72_, _WGS84_, \ _0_0, _0_26, _1_0, _2_0, _8_0, _3600_0 _lazyNamedEnumItem as _lazy
'''(INTERNAL) rotation in C{radians} and C{degree seconds}. '''
'''Helmert transformation.
@see: L{Transform7Tuple}. '''
sx=0, sy=0, sz=0, s=0): '''New L{Transform}.
@kwarg name: Optional, unique name (C{str}). @kwarg tx: Optional X translation (C{meter}). @kwarg ty: Optional Y translation (C{meter}). @kwarg tz: Optional Z translation (C{meter}). @kwarg s: Optional scale (C{float}), ppm. @kwarg sx: Optional X rotation (C{degree seconds}). @kwarg sy: Optional Y rotation (C{degree seconds}). @kwarg sz: Optional Z rotation (C{degree seconds}).
@raise NameError: Transform with that B{C{name}} already exists. '''
'''Compare this and an other transform.
@arg other: The other transform (L{Transform}).
@return: C{True} if equal, C{False} otherwise. ''' self.tx == other.tx and self.ty == other.ty and self.tz == other.tz and self.rx == other.rx and self.ry == other.ry and self.rz == other.rz and self.s == other.s)
'''Return the inverse of this transform.
@kwarg name: Optional, unique name (C{str}).
@return: Inverse (Transform).
@raise NameError: Transform with that B{C{name}} already exists. ''' tx=-self.tx, ty=-self.ty, tz=-self.tz, sx=-self.sx, sy=-self.sy, sz=-self.sz, s=-self.s)
'''Return this transform as a string.
@kwarg prec: Optional number of decimals, unstripped (C{int}).
@return: Transform attributes (C{str}). ''' 'rx', 'ry', 'rz', _s_, 's1', _sx_, _sy_, _sz_)
'''Transform a (geocentric) Cartesian point, forward or inverse.
@arg x: X coordinate (C{meter}). @arg y: Y coordinate (C{meter}). @arg z: Z coordinate (C{meter}). @kwarg inverse: Optional direction, forward or inverse (C{bool}).
@return: A L{Vector3Tuple}C{(x, y, z)}, transformed. ''' else: # x', y', z' = (.tx + x * .s1 - y * .rz + z * .ry, # .ty + x * .rz + y * .s1 - z * .rx, # .tz - x * .ry + y * .rx + z * .s1) fdot(_xyz, self.ty, self.rz, _s1, -self.rx), fdot(_xyz, self.tz, -self.ry, self.rx, _s1), name=self.name)
'''(INTERNAL) L{Transform} registry, I{must} be a sub-class to accommodate the L{_LazyNamedEnumItem} properties. ''' '''(INTERNAL) Instantiate the C{Transform}. '''
'''Some pre-defined L{Transform}s, all I{lazily} instantiated.''' # <https://WikiPedia.org/wiki/Helmert_transformation> from WGS84 BD72 = _lazy(_BD72_, tx=_F(106.868628), ty=_F(-52.297783), tz=_F(103.723893), # <https://www.NGI.BE/FR/FR4-4.shtm> ETRS89 == WG84 # <https://GeoRepository.com/transformation_15929/BD72-to-WGS-84-3.html> sx=_F(-0.33657), sy=_F( -0.456955), sz=_F( -1.84218), s=_F( 1.2727)), Bessel1841 = _lazy(_Bessel1841_, tx=_F(-582.0), ty=_F(-105.0), tz=_F(-414.0), sx=_F( -1.04), sy=_F( -0.35), sz=_F( 3.08), s=_F( -8.3)), Clarke1866 = _lazy(_Clarke1866_, tx=_F(8), ty=_F(-160), tz=_F(-176)), DHDN = _lazy(_DHDN_, tx=_F(-591.28), ty=_F(-81.35), tz=_F(-396.39), sx=_F( 1.477), sy=_F( -0.0736), sz=_F( -1.458), s=_F( -9.82)), # Germany ED50 = _lazy(_ED50_, tx=_F(89.5), ty=_F(93.8), tz=_F(123.1), # <https://GeoNet.ESRI.com/thread/36583> sz=_F(-0.156) # <https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal.js> # <https://www.Gov.UK/guidance/oil-and-gas-petroleum-operations-notices#pon-4> sz=_F( 0.156), s=_F(-1.2)), Identity = _lazy(_Identity_), Irl1965 = _lazy(_Irl1965_, tx=_F(-482.530), ty=_F(130.596), tz=_F(-564.557), sx=_F( 1.042), sy=_F( 0.214), sz=_F( 0.631), s=_F( -8.15)), Irl1975 = _lazy(_Irl1975_, tx=_F(-482.530), ty=_F(130.596), tz=_F(-564.557), # XXX rotation signs may be opposite, to be checked sx=_F( -1.042), sy=_F( -0.214), sz=_F( -0.631), s=_F( -1.1)), Krassovski1940 = _lazy(_Krassovski1940_, tx=_F(-24.0), ty=_F(123.0), tz=_F(94.0), sx=_F( -0.02), sy= _0_26, sz=_F( 0.13), s=_F( -2.423)), # spelling Krassowsky1940 = _lazy(_Krassowsky1940_, tx=_F(-24.0), ty=_F(123.0), tz=_F(94.0), sx=_F( -0.02), sy= _0_26, sz=_F( 0.13), s=_F( -2.423)), # spelling MGI = _lazy(_MGI_, tx=_F(-577.326), ty=_F(-90.129), tz=_F(-463.920), sx=_F( 5.137), sy=_F( 1.474), sz=_F( 5.297), s=_F( -2.423)), # Austria NAD27 = _lazy(_NAD27_, tx=_8_0, ty=_F(-160), tz=_F(-176)), NAD83 = _lazy(_NAD83_, tx=_F( 1.004), ty=_F(-1.910), tz=_F(-0.515), sx=_F( 0.0267), sy=_F( 0.00034), sz=_F( 0.011), s=_F(-0.0015)), NTF = _lazy(_NTF_, tx=_F(-168), ty=_F(-60), tz=_F(320)), # XXX verify OSGB36 = _lazy(_OSGB36_, tx=_F(-446.448), ty=_F(125.157), tz=_F(-542.060), sx=_F( -0.1502), sy=_F( -0.2470), sz=_F( -0.8421), s=_F( 20.4894)), TokyoJapan = _lazy(_TokyoJapan_, tx=_F(148), ty=_F(-507), tz=_F(-685)), WGS72 = _lazy(_WGS72_, tz=_F(-4.5), sz=_F(0.554), s=_F(-0.22)), WGS84 = _lazy(_WGS84_), # unity )
'''Ellipsoid and transform parameters for an earth model. '''
'''New L{Datum}.
@arg ellipsoid: The ellipsoid (L{Ellipsoid} or L{Ellipsoid2}). @kwarg transform: Optional transform (L{Transform}). @kwarg name: Optional, unique name (C{str}).
@raise NameError: Datum with that B{C{name}} already exists.
@raise TypeError: If B{C{ellipsoid}} is not an L{Ellipsoid} nor L{Ellipsoid2} or B{C{transform}} is not a L{Transform}. '''
'''Compare this and an other datum.
@arg other: The other datum (L{Datum}).
@return: C{True} if equal, C{False} otherwise. ''' self.ellipsoid == other.ellipsoid and self.transform == other.transform)
'''Return U{ECEF<https://WikiPedia.org/wiki/ECEF>} converter.
@kwarg Ecef: ECEF class to use (L{EcefKarney}, L{EcefVeness} or L{EcefYou}).
@return: An ECEF converter for this C{datum} (L{EcefKarney}, L{EcefVeness} or L{EcefYou}).
@raise TypeError: Invalid B{C{Ecef}}. '''
'''Get this datum's ellipsoid (L{Ellipsoid} or L{Ellipsoid2}). '''
'''Get the C{ExactTM} projection (L{ExactTransverseMercator}). '''
'''Check whether this datum is ellipsoidal (C{bool}). '''
'''Check whether this datum's ellipsoidal is I{oblate} (C{bool}). ''' return self._ellipsoid.isOblate
'''Check whether this datum's ellipsoidal is I{prolate} (C{bool}). ''' return self._ellipsoid.isProlate
'''Check whether this datum is (near-)spherical (C{bool}). '''
'''Return this datum as a string.
@return: Datum attributes (C{str}). '''
'''Get this datum's transform (L{Transform}). '''
'''(INTERNAL) Helper for C{_ellipsoid} and C{_ellipsoidal_datum}. ''' E = earth.ellipsoid n = NN(_UNDER_, name or earth.name) elif isinstance(earth, (tuple, list)) and len(earth) == 2: # no cover n = NN(_UNDER_, name or getattr(earth, _name_, NN)) a_f = a_f2Tuple(*earth) E = Ellipsoid(a_f.a, a_f.b, name=n) # PYCHOK .a else:
'''(INTERNAL) Create an L{Ellipsoid} or L{Ellipsoid2} from L{datum} or C{a_f2Tuple}. ''' _xinstanceof(Ellipsoid, Ellipsoid2, a_f2Tuple, Datum, earth=earth)
'''(INTERNAL) Create a L{Datum} from an L{Ellipsoid} or L{Ellipsoid2} or C{a_f2Tuple}. ''' else: raise _IsnotError(_ellipsoidal_, earth=earth)
'''(INTERNAL) Compute the mean radius of a L{Datum} from an L{Ellipsoid}, L{Ellipsoid2} or scalar earth C{radius} for several latitudes. ''' else: # no cover E = _ellipsoidal_datum(radius).ellipsoid r = fmean(map(E.Rgeocentric, lats)) if lats else E.Rmean
'''(INTERNAL) Create a L{Datum} from an L{Ellipsoid}, L{Ellipsoid2} or scalar earth C{radius}. ''' else: raise _IsnotError(_spherical_, earth=earth)
'''(INTERNAL) L{Datum} registry, I{must} be a sub-class to accommodate the L{_LazyNamedEnumItem} properties. ''' '''(INTERNAL) Instantiate the L{Datum}. ''' Transforms.get(transform_name), name=name)
'''Some pre-defined L{Datum}s, all I{lazily} instantiated.''' # Datums with associated ellipsoid and Helmert transform parameters # to convert from WGS84 into the given datum. More are available at # <https://Earth-Info.NGA.mil/GandG/coordsys/datums/NATO_DT.pdf> and # <XXX://www.FieldenMaps.info/cconv/web/cconv_params.js>. # Belgian Datum 1972, based on Hayford ellipsoid. # <https://NL.WikiPedia.org/wiki/Belgian_Datum_1972> # <https://SpatialReference.org/ref/sr-org/7718/html/> BD72 = _lazy(_BD72_, _Intl1924_, _BD72_),
# Germany <https://WikiPedia.org/wiki/Bessel-Ellipsoid> # <https://WikiPedia.org/wiki/Helmert_transformation> DHDN = _lazy(_DHDN_, _Bessel1841_, _DHDN_),
# <https://www.Gov.UK/guidance/oil-and-gas-petroleum-operations-notices#pon-4> ED50 = _lazy(_ED50_, _Intl1924_, _ED50_),
# Australia <https://ICSM.Gov.AU/datum/gda2020-and-gda94-technical-manuals> # ADG66 = _lazy(_ADG66_, _ANS_, _WGS84_), # XXX Transform? # ADG84 = _lazy(_ADG84_, _ANS_, _WGS84_), # XXX Transform? # GDA94 = _lazy(_GDA94_, _GRS80_, _WGS84_), GDA2020 = _lazy(_GDA2020_, _GRS80_, _WGS84_), # XXX Transform?
# <https://WikiPedia.org/wiki/GRS_80> GRS80 = _lazy(_GRS80_, _GRS80_, _WGS84_),
# <https://OSI.IE/OSI/media/OSI/Content/Publications/transformations_booklet.pdf> # Irl1975 = _lazy(_Irl1965_, _AiryModified_, _Irl1965_), Irl1975 = _lazy(_Irl1975_, _AiryModified_, _Irl1975_),
# Germany <https://WikiPedia.org/wiki/Helmert_transformation> Krassovski1940 = _lazy(_Krassovski1940_, _Krassovski1940_, _Krassovski1940_), # XXX spelling? Krassowsky1940 = _lazy(_Krassowsky1940_, _Krassowsky1940_, _Krassowsky1940_), # XXX spelling?
# Austria <https://DE.WikiPedia.org/wiki/Datum_Austria> MGI = _lazy(_MGI_, _Bessel1841_, _MGI_),
# <https://WikiPedia.org/wiki/Helmert_transformation> NAD27 = _lazy(_NAD27_, _Clarke1866_, _NAD27_),
# NAD83 (2009) == WGS84 - <https://www.UVM.edu/giv/resources/WGS84_NAD83.pdf> # (If you *really* must convert WGS84<->NAD83, you need more than this!) NAD83 = _lazy(_NAD83_, _GRS80_, _NAD83_),
# Nouvelle Triangulation Francaise (Paris) XXX verify NTF = _lazy(_NTF_, _Clarke1880IGN_, _NTF_),
# <https://www.OrdnanceSurvey.co.UK/docs/support/guide-coordinate-systems-great-britain.pdf> OSGB36 = _lazy(_OSGB36_, _Airy1830_, _OSGB36_),
# Germany <https://WikiPedia.org/wiki/Helmert_transformation> Potsdam = _lazy(_Potsdam_, _Bessel1841_, _Bessel1841_),
# XXX psuedo-ellipsoids for spherical LatLon Sphere = _lazy(_Sphere_, _Sphere_, _WGS84_),
# <https://www.GeoCachingToolbox.com?page=datumEllipsoidDetails> TokyoJapan = _lazy(_TokyoJapan_, _Bessel1841_, _TokyoJapan_),
# <https://www.ICAO.int/safety/pbn/documentation/eurocontrol/eurocontrol%20wgs%2084%20implementation%20manual.pdf> WGS72 = _lazy(_WGS72_, _WGS72_, _WGS72_),
WGS84 = _lazy(_WGS84_, _WGS84_, _WGS84_), )
if __name__ == '__main__':
from pygeodesy.interns import _COMMA_, _NL_, _NL_var_
# __doc__ of this file, force all into registery for r in (Datums, Transforms): t = [NN] + r.toRepr(all=True).split(_NL_) print(_NL_var_.join(i.strip(_COMMA_) for i in t))
# **) MIT License # # Copyright (C) 2016-2021 -- 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. |