
# -*- coding: utf-8 -*-

u'''Datums and transformations thereof.

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 2005-2024} 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, above
or below the earth’s surface.  Latitude is measured in degrees from the equator, lomgitude from
the International Reference Meridian and height in meters above an ellipsoid based on the given
datum.  The datum in turn 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 other 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{"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=106.87, ty=-52.298, tz=103.72, s1=1.0, rx=-1.6317e-06, ry=-2.2154e-06, rz=-8.9311e-06, s=1.2727, sx=-0.33657, sy=-0.45696, sz=-1.8422)
@var Transforms.Bessel1841: Transform(name='Bessel1841', tx=-582, ty=-105, tz=-414, s1=0.99999, rx=-5.0421e-06, ry=-1.6968e-06, rz=1.4932e-05, s=-8.3, sx=-1.04, sy=-0.35, sz=3.08)
@var Transforms.Clarke1866: Transform(name='Clarke1866', tx=8.0, ty=-160, tz=-176, s1=1.0, rx=0.0, ry=0.0, rz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
@var Transforms.DHDN: Transform(name='DHDN', tx=-591.28, ty=-81.35, tz=-396.39, s1=0.99999, rx=7.1607e-06, ry=-3.5682e-07, rz=-7.0686e-06, s=-9.82, sx=1.477, sy=-0.0736, sz=-1.458)
@var Transforms.DHDNE: Transform(name='DHDNE', tx=-612.4, ty=-77, tz=-440.2, s1=1.0, rx=2.618e-07, ry=-2.7634e-07, rz=1.356e-05, s=-2.55, sx=0.054, sy=-0.057, sz=2.797)
@var Transforms.DHDNW: Transform(name='DHDNW', tx=-598.1, ty=-73.7, tz=-418.2, s1=0.99999, rx=-9.7932e-07, ry=-2.1817e-07, rz=1.1902e-05, s=-6.7, sx=-0.202, sy=-0.045, sz=2.455)
@var Transforms.ED50: Transform(name='ED50', tx=89.5, ty=93.8, tz=123.1, s1=1.0, rx=0.0, ry=0.0, rz=7.5631e-07, s=-1.2, sx=0.0, sy=0.0, sz=0.156)
@var Transforms.Identity: Transform(name='Identity', tx=0.0, ty=0.0, tz=0.0, s1=1.0, rx=0.0, ry=0.0, rz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
@var Transforms.Irl1965: Transform(name='Irl1965', tx=-482.53, ty=130.6, tz=-564.56, s1=0.99999, rx=5.0518e-06, ry=1.0375e-06, rz=3.0592e-06, s=-8.15, sx=1.042, sy=0.214, sz=0.631)
@var Transforms.Irl1975: Transform(name='Irl1975', tx=-482.53, ty=130.6, tz=-564.56, s1=0.99999, rx=5.0518e-06, ry=1.0375e-06, rz=3.0592e-06, s=-8.15, sx=1.042, sy=0.214, sz=0.631)
@var Transforms.Krassovski1940: Transform(name='Krassovski1940', tx=-24, ty=123.0, tz=94.0, s1=1.0, rx=-9.6963e-08, ry=1.2605e-06, rz=6.3026e-07, s=-2.423, sx=-0.02, sy=0.26, sz=0.13)
@var Transforms.Krassowsky1940: Transform(name='Krassowsky1940', tx=-24, ty=123.0, tz=94.0, s1=1.0, rx=-9.6963e-08, ry=1.2605e-06, rz=6.3026e-07, s=-2.423, sx=-0.02, sy=0.26, sz=0.13)
@var Transforms.MGI: Transform(name='MGI', tx=-577.33, ty=-90.129, tz=-463.92, s1=1.0, rx=2.4905e-05, ry=7.1462e-06, rz=2.5681e-05, s=-2.423, sx=5.137, sy=1.474, sz=5.297)
@var Transforms.NAD27: Transform(name='NAD27', tx=8.0, ty=-160, tz=-176, s1=1.0, rx=0.0, ry=0.0, rz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
@var Transforms.NAD83: Transform(name='NAD83', tx=1.004, ty=-1.91, tz=-0.515, s1=1.0, rx=1.2945e-07, ry=1.6484e-09, rz=5.333e-08, s=-0.0015, sx=0.0267, sy=0.00034, sz=0.011)
@var Transforms.NTF: Transform(name='NTF', tx=-168, ty=-60, tz=320.0, s1=1.0, rx=0.0, ry=0.0, rz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
@var Transforms.OSGB36: Transform(name='OSGB36', tx=-446.45, ty=125.16, tz=-542.06, s1=1.0, rx=-7.2819e-07, ry=-1.1975e-06, rz=-4.0826e-06, s=20.489, sx=-0.1502, sy=-0.247, sz=-0.8421)
@var Transforms.TokyoJapan: Transform(name='TokyoJapan', tx=148.0, ty=-507, tz=-685, s1=1.0, rx=0.0, ry=0.0, rz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
@var Transforms.WGS72: Transform(name='WGS72', tx=0.0, ty=0.0, tz=-4.5, s1=1.0, rx=0.0, ry=0.0, rz=2.6859e-06, s=-0.22, sx=0.0, sy=0.0, sz=0.554)
@var Transforms.WGS84: Transform(name='WGS84', tx=0.0, ty=0.0, tz=0.0, s1=1.0, rx=0.0, ry=0.0, rz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
'''
# make sure int/int division yields float quotient, see .basics
from __future__ import division as _; del _  # noqa: E702 ;

from pygeodesy.basics import _isin, islistuple, map2, neg, _xinstanceof, _zip
from pygeodesy.constants import R_M, _float as _F, _0_0, _1_0, _2_0, _8_0, _3600_0
# from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase as _CEB, \
#                                          LatLonEllipsoidalBase as _LLEB  # MODS
from pygeodesy.ellipsoids import a_f2Tuple, Ellipsoid, Ellipsoid2, Ellipsoids, _EWGS84, \
                                 Vector3Tuple
from pygeodesy.errors import _IsnotError, _TypeError, _xellipsoidall, _xkwds, _xkwds_pop2
from pygeodesy.fmath import fdot, fmean,  Fmt, _operator
from pygeodesy.internals import _passarg, _under
from pygeodesy.interns import NN, _a_, _Airy1830_, _AiryModified_, _BAR_, _Bessel1841_, \
                             _Clarke1866_, _Clarke1880IGN_, _COMMASPACE_, _DMAIN_,_DOT_, \
                             _earth_, _ellipsoid_, _ellipsoidal_, _GRS80_, _Intl1924_, \
                             _MINUS_, _Krassovski1940_, _Krassowsky1940_, _NAD27_, _NAD83_, \
                             _s_, _PLUS_, _Sphere_, _spherical_, _transform_, _UNDER_, \
                             _WGS72_, _WGS84_
from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS
from pygeodesy.named import _lazyNamedEnumItem as _lazy, _name__, _name2__, _NamedEnum, \
                                _NamedEnumItem
# from pygeodesy.namedTuples import Vector3Tuple  # from .ellipsoids
from pygeodesy.props import Property_RO, property_RO
# from pygeodesy.streprs import Fmt  # from .fmath
from pygeodesy.units import _isRadius, Radius_,  radians

# from math import radians  # from .units
# import operator as _operator  # from .fmath

__all__ = _ALL_LAZY.datums
__version__ = '26.01.13'

_a_ellipsoid_ = _UNDER_(_a_, _ellipsoid_)
_BD72_        = 'BD72'
_DHDN_        = 'DHDN'
_DHDNE_       = 'DHDNE'
_DHDNW_       = 'DHDNW'
_ED50_        = 'ED50'
_GDA2020_     = 'GDA2020'  # in .trf
_Identity_    = 'Identity'
_Irl1965_     = 'Irl1965'
_Irl1975_     = 'Irl1975'
_MGI_         = 'MGI'
_Names7       = 'tx', 'ty', 'tz', _s_, 'sx', 'sy', 'sz'  # in .trf
_Names11      = _Names7[:3]  +  ('s1', 'rx', 'ry', 'rz') + _Names7[3:]
_NTF_         = 'NTF'
_OSGB36_      = 'OSGB36'
_Potsdam_     = 'Potsdam'
_RPS          =  radians(_1_0 / _3600_0)  # radians per arc-second
_S1_S         =  1.e-6  # in .trf
_TokyoJapan_  = 'TokyoJapan'


class Transform(_NamedEnumItem):
    '''Helmert I{datum} transformation.

       @see: L{TransformXform<trf.TransformXform>}.
    '''
    tx = _0_0  # x translation (C{meter})
    ty = _0_0  # y translation (C{meter})
    tz = _0_0  # z translation (C{meter})

    rx = _0_0  # x rotation (C{radians})
    ry = _0_0  # y rotation (C{radians})
    rz = _0_0  # z rotation (C{radians})

    s  = _0_0  # scale ppm (C{float})
    s1 = _1_0  # scale + 1 (C{float})

    sx = _0_0  # x rotation (C{arc-seconds})
    sy = _0_0  # y rotation (C{arc-seconds})
    sz = _0_0  # z rotation (C{arc-seconds})

    def __init__(self, name=NN, tx=0, ty=0, tz=0,
                           s=0, sx=0, sy=0, sz=0):
        '''New L{Transform}.

           @kwarg name: Optional, unique name (C{str}).
           @kwarg tx: X translation (C{meter}).
           @kwarg ty: Y translation (C{meter}).
           @kwarg tz: Z translation (C{meter}).
           @kwarg s: Scale (C{float}), ppm.
           @kwarg sx: X rotation (C{arc-seconds}).
           @kwarg sy: Y rotation (C{arc-seconds}).
           @kwarg sz: Z rotation (C{arc-seconds}).

           @raise NameError: Transform with that B{C{name}} already exists.
        '''
        if tx:
            self.tx = tx
        if ty:
            self.ty = ty
        if tz:
            self.tz = tz
        if s:
            self.s  =    s
            self.s1 = _F(s * _S1_S + _1_0)  # normalize ppM to (s + 1)
        if sx:  # secs to rads
            self.rx, self.sx = self._rps2(sx)
        if sy:
            self.ry, self.sy = self._rps2(sy)
        if sz:
            self.rz, self.sz = self._rps2(sz)

        self._register(Transforms, name)

    def __eq__(self, other):
        '''Compare this and an other transform.

           @arg other: The other transform (L{Transform}).

           @return: C{True} if equal, C{False} otherwise.
        '''
        return self is other or (isinstance(other, Transform)
                                and _equall(other, self))

    def __hash__(self):
        return hash(tuple(self))

    def __iter__(self):
        '''Yield the initial attribute values, I{in order}.
        '''
        for n in _Names7:
            yield getattr(self, n)

    def __matmul__(self, point):  # PYCHOK Python 3.5+
        '''Transform an I{ellipsoidal} B{C{point}} with this Helmert.

           @return: A transformed copy of B{C{point}}.

           @raise TypeError: Invalid B{C{point}}.

           @see: Method C{B{point}.toTransform}.
        '''
        _ = _xellipsoidall(point)
        return point.toTransform(self)

    def __neg__(self):
        return self.inverse()

    def inverse(self, **name):
        '''Return the inverse of this transform.

           @kwarg name: Optional, unique name (C{str}).

           @return: Inverse (L{Transform}), unregistered.
        '''
        r =  type(self)(**dict(self.items(inverse=True)))
        n = _name__(**name) or _negastr(self.name)
        if n:
            r.name = n  # unregistered
        return r

    @Property_RO
    def isunity(self):
        '''Is this a C{unity, identity} transform (C{bool}), like
           WGS84 with translation, scale and rotation all zero?
        '''
        return not any(self)

    def items(self, inverse=False):
        '''Yield the initial attributes, each as 2-tuple C{(name, value)}.

           @kwarg inverse: If C{True}, negate the values (C{bool}).
        '''
        _p = neg if inverse else _passarg
        for n, x in _zip(_Names7, self):
            yield n, _p(x)

    def _rps2(self, s_):
        '''(INTERNAL) Rotation in C{radians} and C{arc-seconds}.
        '''
        # _MR == _RPS * 1.e-3  # radians per milli-arc-second, equ (2)
        # <https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>
        return (_RPS * s_), s_

    def _s_s1(self, s1):  # in .trf
        '''(INTERNAL) Set C{s1} and C{s}.
        '''
        Transform.isunity._update(self)
        self.s1 = s1
        self.s  = s = (s1 - _1_0) / _S1_S
        return s

    def toStr(self, prec=5, fmt=Fmt.g, **sep_name):  # PYCHOK expected
        '''Return this transform as a string.

           @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
           @kwarg fmt: Optional C{float} format (C{letter}).
           @kwarg sep_name: Optional C{B{name}=NN} (C{str}) or C{None}
                      to exclude this transform's name and separater
                      C{B{sep}=", "} to join the items (C{str}).

           @return: Transform attributes (C{str}).
        '''
        return self._instr(*_Names11, fmt=fmt, prec=prec, **sep_name)

    def transform(self, x, y, z, inverse=False, **Vector_and_kwds):
        '''Transform a (cartesian) position, forward or inverse.

           @arg x: X coordinate (C{meter}).
           @arg y: Y coordinate (C{meter}).
           @arg z: Z coordinate (C{meter}).
           @kwarg inverse: If C{True}, apply the inverse transform (C{bool}).
           @kwarg Vector_and_kwds: An optional, (3-D) C{B{Vector}=None} or
                         cartesian class and additional C{B{Vector}} keyword
                         arguments to return the transformed position.

           @return: The transformed position (L{Vector3Tuple}C{(x, y, z)})
                    unless some B{C{Vector_and_kwds}} are specified.
        '''
        if self.isunity:
            r = Vector3Tuple(x, y, z, name=self.name)  # == inverse
        else:
            xyz1 = x, y, z, _1_0
            s1   = self.s1
            if inverse:
                xyz1 =  map2(neg, xyz1)
                s1  -= _2_0  # = s * 1e-6 - 1 = (s1 - 1) - 1
            # x', y', z' = (x * .s1 - y * .rz + z * .ry + .tx,
            #               x * .rz + y * .s1 - z * .rx + .ty,
            #              -x * .ry + y * .rx + z * .s1 + .tz)
            r = Vector3Tuple(fdot(xyz1,       s1, -self.rz,  self.ry, self.tx),
                             fdot(xyz1,  self.rz,       s1, -self.rx, self.ty),
                             fdot(xyz1, -self.ry,  self.rx,       s1, self.tz),
                             name=self.name)
        if Vector_and_kwds:
            V, kwds = _xkwds_pop2(Vector_and_kwds, Vector=None)
            if V:
                r = V(r, **_xkwds(kwds, name=self.name))
        return r


class Transforms(_NamedEnum):
    '''(INTERNAL) L{Transform} registry, I{must} be a sub-class
       to accommodate the L{_LazyNamedEnumItem} properties.
    '''
    def _Lazy(self, **name_tx_ty_tz_s_sx_sy_sz):
        '''(INTERNAL) Instantiate the C{Transform}.
        '''
        return Transform(**name_tx_ty_tz_s_sx_sy_sz)

Transforms = Transforms(Transform)  # PYCHOK singleton
'''Some pre-defined L{Transform}s, all I{lazily} instantiated.'''
# <https://WikiPedia.org/wiki/Helmert_transformation> from WGS84 to ...
Transforms._assert(
    BD72           = _lazy(_BD72_, tx=_F(106.868628), ty=_F(-52.297783), tz=_F(103.723893), s=_F(1.2727),
                                   # <https://www.NGI.Be/FR/FR4-4.shtm> ETRS89 == WG84
                                   # <https://EPSG.org/transformation_15929/BD72-to-WGS-84-3.html>
                                   sx=_F( -0.33657),  sy=_F( -0.456955), sz=_F( -1.84218)),

    Bessel1841     = _lazy(_Bessel1841_, tx=_F(-582.0),  ty=_F(-105.0),  tz=_F(-414.0), s=_F(-8.3),
                                         sx=_F(  -1.04), sy=_F(  -0.35), sz=_F(   3.08)),

    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), s=_F(-9.82),
                                   sx=_F(   1.477), sy=_F( -0.0736), sz=_F(  -1.458)),  # Germany

    DHDNE          = _lazy(_DHDNE_, tx=_F(-612.4),   ty=_F(-77.0),   tz=_F(-440.2), s=_F(-2.55),
                                    # <https://EPSG.org/transformation_15869/DHDN-to-WGS-84-3.html>
                                    sx=_F(   0.054), sy=_F( -0.057), sz=_F(   2.797)),  # East Germany

    DHDNW          = _lazy(_DHDNW_, tx=_F(-598.1),   ty=_F(-73.7),   tz=_F(-418.2), s=_F(-6.7),
                                    # <https://EPSG.org/transformation_1777/DHDN-to-WGS-84-2.html>
                                    sx=_F(  -0.202), sy=_F( -0.045), sz=_F(   2.455)),  # West Germany

    ED50           = _lazy(_ED50_, tx=_F(89.5), ty=_F(93.8), tz=_F(123.1), s=_F(-1.2),
                                   # <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)),
    Identity       = _lazy(_Identity_),

    Irl1965        = _lazy(_Irl1965_, tx=_F(-482.530), ty=_F(130.596), tz=_F(-564.557), s=_F(-8.15),
                                       # <https://EPSG.org/transformation_1641/TM65-to-WGS-84-2.html>
                                      sx=_F(   1.042), sy=_F(  0.214), sz=_F(   0.631)),
    Irl1975        = _lazy(_Irl1975_, tx=_F(-482.530), ty=_F(130.596), tz=_F(-564.557), s=_F(-8.15),
                                      # <https://EPSG.org/transformation_1954/TM75-to-WGS-84-2.html>
                                      sx=_F(   1.042), sy=_F(  0.214), sz=_F(   0.631)),

    Krassovski1940 = _lazy(_Krassovski1940_, tx=_F(-24.0),  ty=_F(123.0),  tz=_F(94.0), s=_F(-2.423),
                                             sx=_F( -0.02), sy=_F(  0.26), sz=_F( 0.13)),  # spelling

    Krassowsky1940 = _lazy(_Krassowsky1940_, tx=_F(-24.0),  ty=_F(123.0),  tz=_F(94.0), s=_F(-2.423),
                                             sx=_F( -0.02), sy=_F(  0.26), sz=_F( 0.13)),  # spelling

    MGI            = _lazy(_MGI_, tx=_F(-577.326), ty=_F(-90.129), tz=_F(-463.920), s=_F(-2.423),
                                  sx=_F(   5.137), sy=_F(  1.474), sz=_F(   5.297)),  # 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), s=_F(-0.0015),
                                    sx=_F(0.0267), sy=_F( 0.00034), sz=_F( 0.011)),

    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), s=_F(20.4894),
                                     # <https://EPSG.org/transformation_1314/OSGB36-to-WGS-84-6.html>
                                     sx=_F(  -0.1502), sy=_F( -0.2470), sz=_F(  -0.8421)),

    TokyoJapan     = _lazy(_TokyoJapan_, tx=_F(148), ty=_F(-507), tz=_F(-685)),

    WGS72          = _lazy(_WGS72_, tz=_F(-4.5), s=_F(-0.22), sz=_F(0.554)),

    WGS84          = _lazy(_WGS84_),  # unity
)


class Datum(_NamedEnumItem):
    '''Ellipsoid and transform parameters for an earth model.
    '''
    _ellipsoid = Ellipsoids.WGS84  # default ellipsoid (L{Ellipsoid}, L{Ellipsoid2})
    _transform = Transforms.WGS84  # default transform (L{Transform})

    def __init__(self, ellipsoid, transform=None, **name):
        '''New L{Datum}.

           @arg ellipsoid: The ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
           @kwarg transform: Optional transform (L{Transform}).
           @kwarg name: Optional, unique C{B{name}=NN} (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}.
        '''
        self._ellipsoid = ellipsoid or Datum._ellipsoid
        _xinstanceof(Ellipsoid, ellipsoid=self.ellipsoid)

        self._transform = transform or Datum._transform
        _xinstanceof(Transform, transform=self.transform)

        self._register(Datums, _name__(name) or self.transform.name
                                             or self.ellipsoid.name)

    def __eq__(self, other):
        '''Compare this and an other datum.

           @arg other: The other datum (L{Datum}).

           @return: C{True} if equal, C{False} otherwise.
        '''
        return self is other or (isinstance(other, Datum)   and
                          self.ellipsoid == other.ellipsoid and
                          self.transform == other.transform)

    def __hash__(self):
        return self._hash  # memoized

    def __matmul__(self, point):  # PYCHOK Python 3.5+
        '''Convert an I{ellipsoidal} B{C{point}} to this datum.

           @raise TypeError: Invalid B{C{point}}.
        '''
        _ = _xellipsoidall(point)
        return point.toDatum(self)

    def ecef(self, Ecef=None):
        '''Return U{ECEF<https://WikiPedia.org/wiki/ECEF>} converter.

           @kwarg Ecef: ECEF class to use, default L{EcefKarney}.

           @return: An ECEF converter for this C{datum}.

           @raise TypeError: Invalid B{C{Ecef}}.

           @see: Module L{pygeodesy.ecef}.
        '''
        return _MODS.ecef._4Ecef(self, Ecef)

    @Property_RO
    def ellipsoid(self):
        '''Get this datum's ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
        '''
        return self._ellipsoid

    @Property_RO
    def exactTM(self):
        '''Get the C{ExactTM} projection (L{ExactTransverseMercator}).
        '''
        return _MODS.etm.ExactTransverseMercator(datum=self)

    @Property_RO
    def _hash(self):
        return hash(self.ellipsoid) + hash(self.transform)

    @property_RO
    def isEllipsoidal(self):
        '''Check whether this datum is ellipsoidal (C{bool}).
        '''
        return self.ellipsoid.isEllipsoidal

    @property_RO
    def isOblate(self):
        '''Check whether this datum's ellipsoidal is I{oblate} (C{bool}).
        '''
        return self.ellipsoid.isOblate

    @property_RO
    def isProlate(self):
        '''Check whether this datum's ellipsoidal is I{prolate} (C{bool}).
        '''
        return self.ellipsoid.isProlate

    @property_RO
    def isSpherical(self):
        '''Check whether this datum is (near-)spherical (C{bool}).
        '''
        return self.ellipsoid.isSpherical

    def toStr(self, sep=_COMMASPACE_, **name):  # PYCHOK expected
        '''Return this datum as a string.

           @kwarg sep: Separator to join (C{str}).
           @kwarg name: Optional, override C{B{name}=NN} (C{str}) or
                        C{None} to exclude this datum's name.

           @return: Datum attributes (C{str}).
        '''
        name, _ = _name2__(**name)  # name=None
        t = [] if name is None else \
            [Fmt.EQUAL(name=repr(name or self.named))]
        for a in (_ellipsoid_, _transform_):
            v = getattr(self, a)
            t.append(NN(Fmt.EQUAL(a, v.classname), _s_, _DOT_, v.name))
        return sep.join(t)

    @Property_RO
    def transform(self):
        '''Get this datum's transform (L{Transform}).
        '''
        return self._transform


def _earth_datum(inst, a_earth, f=None, raiser=_a_ellipsoid_, **name):  # in .karney, .trf, ...
    '''(INTERNAL) Set C{inst._datum} from C{(B{a_..}, B{f})} or C{B{.._ellipsoid}}
       (L{Ellipsoid}, L{Ellipsoid2}, L{Datum}, C{a_f2Tuple} or C{scalar} earth radius).

       @note: C{B{raiser}='a_ellipsoid'} for backward naming compatibility.
    '''
    if f is not None:
        E, n, D = _EnD3((a_earth, f), name)
        if raiser and not E:
            raise _TypeError(f=f, **{raiser: a_earth})
    elif _isin(a_earth, None, _EWGS84, _WGS84) and inst._datum is _WGS84:
        return
    elif isinstance(a_earth, Datum):
        E, n, D =  None, NN, a_earth
    else:
        E, n, D = _EnD3(a_earth, name)
        if raiser and not E:
            _xinstanceof(Ellipsoid, Ellipsoid2, a_f2Tuple, Datum, **{raiser: a_earth})
    if D is None:
        D = Datum(E, transform=Transforms.Identity, name=_under(n))
    inst._datum = D


def _earth_ellipsoid(earth, **name_raiser):
    '''(INTERAL) Return the ellipsoid for the given C{earth} model.
    '''
    return Ellipsoids.Sphere if earth is  R_M else (
          _EWGS84            if earth is _EWGS84 or earth is _WGS84 else
          _spherical_datum(earth, **name_raiser).ellipsoid)


def _ED2(radius, name):
    '''(INTERNAL) Helper for C{_EnD3} and C{_spherical_datum}.
    '''
    D = Datums.Sphere
    E = D.ellipsoid
    if name or radius != E.a:  # != E.b
        n = _under(_name__(name, _or_nameof=D))
        E =  Ellipsoid(radius, radius, name=n)
        D =  Datum(E, transform=Transforms.Identity, name=n)
    return E, D


def _ellipsoidal_datum(earth, Error=TypeError, raiser=NN, **name):
    '''(INTERNAL) Create a L{Datum} from an L{Ellipsoid} or L{Ellipsoid2},
       C{a_f2Tuple}, 2-tuple or 2-list B{C{earth}} model.

       @kwarg raiser: If not C{NN}, raise an B{C{Error}} if not ellipsoidal.
    '''
    if isinstance(earth, Datum):
        D = earth
    else:
        E, n, D = _EnD3(earth, name)
        if not E:
            n = raiser or _earth_
            _xinstanceof(Datum, Ellipsoid, Ellipsoid2, a_f2Tuple, **{n: earth})
        if D is None:
            D = Datum(E, transform=Transforms.Identity, name=_under(n))
    if raiser and not D.isEllipsoidal:
        raise _IsnotError(_ellipsoidal_, Error=Error, **{raiser: earth})
    return D


def _EnD3(earth, name):
    '''(INTERNAL) Helper for C{_earth_datum} and C{_ellipsoidal_datum}.
    '''
    D, n = None, _under(_name__(name, _or_nameof=earth))
    if isinstance(earth, (Ellipsoid, Ellipsoid2)):
        E = earth
    elif isinstance(earth, Datum):
        E = earth.ellipsoid
        D = earth
    elif _isRadius(earth):
        E, D = _ED2(Radius_(earth), n)
        n = E.name
    elif isinstance(earth, a_f2Tuple):
        E = earth.ellipsoid(name=n)
    elif islistuple(earth, minum=2):
        E = Ellipsoids.Sphere
        a, f = earth[:2]
        if f or a != E.a:  # != E.b
            E = Ellipsoid(a, f=f, name=n)
        else:
            n = E.name
            D = Datums.Sphere
    else:
        E, n = None, NN
    return E, n, D


def _equall(t1, t2):  # in .trf
    '''(INTERNAL) Return L{Transform} C{t1 == t2}.
    '''
    return all(map(_operator.eq, t1, t2))


def _mean_radius(radius, *lats):
    '''(INTERNAL) Compute the mean radius of a L{Datum} from an L{Ellipsoid},
       L{Ellipsoid2} or scalar earth C{radius} over several latitudes.
    '''
    if radius is R_M:
        r =  radius
    elif _isRadius(radius):
        r =  Radius_(radius, low=0, Error=TypeError)
    else:
        E = _ellipsoidal_datum(radius).ellipsoid
        r =  fmean(map(E.Rgeocentric, lats)) if lats else E.Rmean
    return r


def _negastr(name):  # in .trf, test/testTrf
    '''(INTERNAL) Negate a C{Transform/-Xform} name.
    '''
    b, m, p = _BAR_, _MINUS_, _PLUS_
    n = name.replace(m, b).replace(p, m).replace(b, p)
    # as good and fast as (in Python 3+ only) ...
    # _MINUSxPLUS = str.maketrans({_MINUS_: _PLUS_, _PLUS_: _MINUS_})
    # def _negastr(name):
    #     n = name.translate(_MINUSxPLUS)
    #     ...
    return n.lstrip(p) if n.startswith(p) else NN(m, n)


def _spherical_datum(earth, Error=TypeError, raiser=NN, **name):
    '''(INTERNAL) Create a L{Datum} from an L{Ellipsoid}, L{Ellipsoid2},
       C{a_f2Tuple}, 2-tuple, 2-list B{C{earth}} model or C{scalar} radius.

       @kwarg raiser: If not C{NN}, raise an B{C{Error}} if not spherical.
    '''
    if isinstance(earth, Datum):
        D = earth
    elif _isRadius(earth):
        _, D = _ED2(Radius_(earth, Error=Error), name)
    else:
        D = _ellipsoidal_datum(earth, Error=Error, **name)
    if raiser and not D.isSpherical:
        raise _IsnotError(_spherical_, Error=Error, **{raiser: earth})
    return D


class Datums(_NamedEnum):
    '''(INTERNAL) L{Datum} registry, I{must} be a sub-class
       to accommodate the L{_LazyNamedEnumItem} properties.
    '''
    def _Lazy(self, ellipsoid_name, transform_name, **name):
        '''(INTERNAL) Instantiate the L{Datum}.
        '''
        return Datum(Ellipsoids.get(ellipsoid_name),
                     Transforms.get(transform_name), **name)

Datums = Datums(Datum)  # PYCHOK singleton
'''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>.
Datums._assert(
    # 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/wp-content/uploads/2015/05/transformations_booklet.pdf> Table 2
#   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_),
)

_WGS84 = Datums.WGS84
assert _WGS84.ellipsoid is _EWGS84
# assert _WGS84.transform.isunity

if __name__ == _DMAIN_:

    from pygeodesy.internals import _pregistry
    # __doc__ of this file, force all into registry
    _pregistry(Datums)
    _pregistry(Transforms)

# **) MIT License
#
# Copyright (C) 2016-2026 -- 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.
