Coverage for pygeodesy/datums.py: 94%
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« prev ^ index » next coverage.py v7.2.2, created at 2024-02-23 11:26 -0500
2# -*- coding: utf-8 -*-
4u'''Datums and transformations thereof.
6Classes L{Datum} and L{Transform} and registries L{Datums} and L{Transforms}, respectively.
8Pure Python implementation of geodesy tools for ellipsoidal earth models, including datums
9and ellipsoid parameters for different geographic coordinate systems and methods for
10converting between them and to cartesian coordinates. Transcoded from JavaScript originals by
11I{(C) Chris Veness 2005-2016} and published under the same MIT Licence**, see U{latlon-ellipsoidal.js
12<https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.
14Historical geodetic datums: a latitude/longitude point defines a geographic location on, above
15or below the earth’s surface. Latitude is measured in degrees from the equator, lomgitude from
16the International Reference Meridian and height in meters above an ellipsoid based on the given
17datum. The datum in turn is based on a reference ellipsoid and tied to geodetic survey
18reference points.
20Modern geodesy is generally based on the WGS84 datum (as used for instance by GPS systems), but
21previously various other reference ellipsoids and datum references were used.
23The UK Ordnance Survey National Grid References are still based on the otherwise historical OSGB36
24datum, q.v. U{"A Guide to Coordinate Systems in Great Britain", Section 6
25<https://www.OrdnanceSurvey.co.UK/docs/support/guide-coordinate-systems-great-britain.pdf>}.
27@var Datums.BD72: Datum(name='BD72', ellipsoid=Ellipsoids.Intl1924, transform=Transforms.BD72)
28@var Datums.DHDN: Datum(name='DHDN', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.DHDN)
29@var Datums.ED50: Datum(name='ED50', ellipsoid=Ellipsoids.Intl1924, transform=Transforms.ED50)
30@var Datums.GDA2020: Datum(name='GDA2020', ellipsoid=Ellipsoids.GRS80, transform=Transforms.WGS84)
31@var Datums.GRS80: Datum(name='GRS80', ellipsoid=Ellipsoids.GRS80, transform=Transforms.WGS84)
32@var Datums.Irl1975: Datum(name='Irl1975', ellipsoid=Ellipsoids.AiryModified, transform=Transforms.Irl1975)
33@var Datums.Krassovski1940: Datum(name='Krassovski1940', ellipsoid=Ellipsoids.Krassovski1940, transform=Transforms.Krassovski1940)
34@var Datums.Krassowsky1940: Datum(name='Krassowsky1940', ellipsoid=Ellipsoids.Krassowsky1940, transform=Transforms.Krassowsky1940)
35@var Datums.MGI: Datum(name='MGI', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.MGI)
36@var Datums.NAD27: Datum(name='NAD27', ellipsoid=Ellipsoids.Clarke1866, transform=Transforms.NAD27)
37@var Datums.NAD83: Datum(name='NAD83', ellipsoid=Ellipsoids.GRS80, transform=Transforms.NAD83)
38@var Datums.NTF: Datum(name='NTF', ellipsoid=Ellipsoids.Clarke1880IGN, transform=Transforms.NTF)
39@var Datums.OSGB36: Datum(name='OSGB36', ellipsoid=Ellipsoids.Airy1830, transform=Transforms.OSGB36)
40@var Datums.Potsdam: Datum(name='Potsdam', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.Bessel1841)
41@var Datums.Sphere: Datum(name='Sphere', ellipsoid=Ellipsoids.Sphere, transform=Transforms.WGS84)
42@var Datums.TokyoJapan: Datum(name='TokyoJapan', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.TokyoJapan)
43@var Datums.WGS72: Datum(name='WGS72', ellipsoid=Ellipsoids.WGS72, transform=Transforms.WGS72)
44@var Datums.WGS84: Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84)
46@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)
47@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)
48@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)
49@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)
50@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)
51@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)
52@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)
53@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)
54@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)
55@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)
56@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)
57@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)
58@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)
59@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)
60@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)
61@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)
62@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)
63@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)
64@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)
65@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)
66'''
67# make sure int/int division yields float quotient, see .basics
68from __future__ import division as _; del _ # PYCHOK semicolon
70from pygeodesy.basics import islistuple, map2, neg, _xinstanceof
71from pygeodesy.constants import R_M, _float as _F, _0_0, _0_26, _1_0, _2_0, _8_0, _3600_0
72# from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase as _CEB, \
73# LatLonEllipsoidalBase as _LLEB # MODS
74from pygeodesy.ellipsoids import a_f2Tuple, Ellipsoid, Ellipsoid2, Ellipsoids, _EWGS84, \
75 Vector3Tuple
76from pygeodesy.errors import _IsnotError, _TypeError, _xattr, _xellipsoidall, _xkwds, \
77 _xkwds_pop2
78from pygeodesy.fmath import fdot, fmean, Fmt
79from pygeodesy.interns import NN, _a_, _Airy1830_, _AiryModified_, _Bessel1841_, \
80 _Clarke1866_, _Clarke1880IGN_, _COMMASPACE_, _DOT_, \
81 _earth_, _ellipsoid_, _ellipsoidal_, _GRS80_, _Intl1924_, \
82 _MINUS_, _Krassovski1940_, _Krassowsky1940_, _NAD27_, \
83 _NAD83_, _s_, _Sphere_, _spherical_, _transform_, \
84 _UNDER_, _WGS72_, _WGS84_, _under
85from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS
86from pygeodesy.named import _NamedEnum, _NamedEnumItem, _lazyNamedEnumItem as _lazy
87# from pygeodesy.namedTuples import Vector3Tuple # from .ellipsoids
88from pygeodesy.props import Property_RO, property_RO
89# from pygeodesy.streprs import Fmt # from .fmath
90from pygeodesy.units import _isRadius, Radius_, radians
92# from math import radians # from .units
94__all__ = _ALL_LAZY.datums
95__version__ = '24.02.18'
97_a_ellipsoid_ = _UNDER_(_a_, _ellipsoid_)
98_BD72_ = 'BD72'
99_DHDN_ = 'DHDN'
100_DHDNE_ = 'DHDNE'
101_DHDNW_ = 'DHDNW'
102_ED50_ = 'ED50'
103_GDA2020_ = 'GDA2020' # in .trf
104_Identity_ = 'Identity'
105_Irl1965_ = 'Irl1965'
106_Irl1975_ = 'Irl1975'
107_MGI_ = 'MGI'
108_Names7 = 'tx', 'ty', 'tz', _s_, 'sx', 'sy', 'sz' # in .trf
109_Names11 = _Names7[:3] + ('s1', 'rx', 'ry', 'rz') + _Names7[3:]
110_NTF_ = 'NTF'
111_OSGB36_ = 'OSGB36'
112_Potsdam_ = 'Potsdam'
113_RPS = radians(_1_0 / _3600_0) # radians per degree-second
114_S1_S = 1.e-6 # in .trf
115_TokyoJapan_ = 'TokyoJapan'
118class Transform(_NamedEnumItem):
119 '''Helmert I{datum} transformation.
121 @see: L{TransformXform<trf.TransformXform>}.
122 '''
123 tx = _0_0 # x translation (C{meter})
124 ty = _0_0 # y translation (C{meter})
125 tz = _0_0 # z translation (C{meter})
127 rx = _0_0 # x rotation (C{radians})
128 ry = _0_0 # y rotation (C{radians})
129 rz = _0_0 # z rotation (C{radians})
131 s = _0_0 # scale ppm (C{float})
132 s1 = _1_0 # scale + 1 (C{float})
134 sx = _0_0 # x rotation (C{degree-seconds})
135 sy = _0_0 # y rotation (C{degree-seconds})
136 sz = _0_0 # z rotation (C{degree-seconds})
138 def __init__(self, name=NN, tx=0, ty=0, tz=0,
139 sx=0, sy=0, sz=0, s=0):
140 '''New L{Transform}.
142 @kwarg name: Optional, unique name (C{str}).
143 @kwarg tx: X translation (C{meter}).
144 @kwarg ty: Y translation (C{meter}).
145 @kwarg tz: Z translation (C{meter}).
146 @kwarg s: Scale (C{float}), ppm.
147 @kwarg sx: X rotation (C{degree-seconds}).
148 @kwarg sy: Y rotation (C{degree-seconds}).
149 @kwarg sz: Z rotation (C{degree-seconds}).
151 @raise NameError: Transform with that B{C{name}} already exists.
152 '''
153 if tx:
154 self.tx = tx
155 if ty:
156 self.ty = ty
157 if tz:
158 self.tz = tz
159 if sx: # secs to rads
160 self.rx, self.sx = self._rps2(sx)
161 if sy:
162 self.ry, self.sy = self._rps2(sy)
163 if sz:
164 self.rz, self.sz = self._rps2(sz)
165 if s:
166 self.s = s
167 self.s1 = _F(s * _S1_S + _1_0) # normalize ppM to (s + 1)
169 self._register(Transforms, name)
171 def __eq__(self, other):
172 '''Compare this and an other transform.
174 @arg other: The other transform (L{Transform}).
176 @return: C{True} if equal, C{False} otherwise.
177 '''
178 return self is other or (isinstance(other, Transform) and all(
179 a == b for a, b in zip(self, other)))
181 def __hash__(self):
182 return self._hash # memoized
184 def __iter__(self):
185 '''Yield the initial attribute values.
186 '''
187 for _, x in self.items():
188 yield x
190 def __matmul__(self, point): # PYCHOK Python 3.5+
191 '''Convert an I{ellipsoidal} B{C{point}} with the Helmert transform.
193 @raise TypeError: Invalid B{C{point}}.
194 '''
195 _ = _xellipsoidall(point)
196 return point.toTransform(self)
198 def __neg__(self):
199 return self.inverse()
201# def __sub__(self, other):
202# _xinstanceof(Transform, other=other)
203#
204# def _sub(a, b):
205# for n in _Names11:
206# yield getattr(a, n) - getattr(b, n)
207#
208# return type(self)(_sub(self, other), name=_MINUS_) # .fsums._sub_op
210 @Property_RO
211 def _hash(self):
212 return hash(x for x in self)
214 def items(self):
215 '''Yield each attribute as 2-tuple C{(name, value)}.
216 '''
217 for n in _Names7:
218 yield n, getattr(self, n)
220 def inverse(self, name=NN):
221 '''Return the inverse of this transform.
223 @kwarg name: Optional, unique name (C{str}).
225 @return: Inverse (L{Transform}).
227 @raise NameError: Transform with that B{C{name}} already exists.
228 '''
229 d = dict((n, neg(v)) for n, v in self.items())
230 n = name or _minus(self.name)
231 return type(self)(name=n, **d)
233 @Property_RO
234 def isunity(self):
235 '''Is this a C{unity, identidy} transform (C{bool}), like WGS84?
236 '''
237 return not any(s for s in self)
239 def _rps2(self, s_):
240 '''(INTERNAL) Rotation in C{radians} and C{degree-seconds}.
241 '''
242 return (_RPS * s_), s_
244 def toStr(self, prec=5, fmt=Fmt.g, name=NN, **unused): # PYCHOK expected
245 '''Return this transform as a string.
247 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
248 @kwarg fmt: Optional C{float} format (C{letter}).
249 @kwarg name: Override name (C{str}) or C{None} to exclude
250 this transform's name.
252 @return: Transform attributes (C{str}).
253 '''
254 return self._instr(name, prec, *_Names11, fmt=fmt)
256 def transform(self, x, y, z, inverse=False, **Vector_and_kwds):
257 '''Transform a (geocentric) position, forward or inverse.
259 @arg x: X coordinate (C{meter}).
260 @arg y: Y coordinate (C{meter}).
261 @arg z: Z coordinate (C{meter}).
262 @kwarg inverse: If C{True}, apply the inverse transform (C{bool}).
263 @kwarg Vector_and_kwds: An optional, (3-D) C{B{Vector}=None} or
264 cartesian class and additional C{B{Vector}}
265 keyword arguments to return the transformed
266 point.
268 @return: The transformed position (L{Vector3Tuple}C{(x, y, z)})
269 unless some B{C{Vector_and_kwds}} is specified.
270 '''
271 if self.isunity:
272 r = Vector3Tuple(x, y, z, name=self.name)
273 else:
274 xyz1 = x, y, z, _1_0
275 s1 = self.s1
276 if inverse:
277 xyz1 = map2(neg, xyz1)
278 s1 -= _2_0 # = s * 1e-6 - 1 = (s1 - 1) - 1
279 # x', y', z' = (x * .s1 - y * .rz + z * .ry + .tx,
280 # x * .rz + y * .s1 - z * .rx + .ty,
281 # -x * .ry + y * .rx + z * .s1 + .tz)
282 r = Vector3Tuple(fdot(xyz1, s1, -self.rz, self.ry, self.tx),
283 fdot(xyz1, self.rz, s1, -self.rx, self.ty),
284 fdot(xyz1, -self.ry, self.rx, s1, self.tz),
285 name=self.name)
286 if Vector_and_kwds:
287 V, kwds = _xkwds_pop2(Vector_and_kwds, Vector=None)
288 if V:
289 r = V(r, **_xkwds(kwds, name=self.name))
290 return r
293class Transforms(_NamedEnum):
294 '''(INTERNAL) L{Transform} registry, I{must} be a sub-class
295 to accommodate the L{_LazyNamedEnumItem} properties.
296 '''
297 def _Lazy(self, **name_tx_ty_tz_sx_sy_sz_s):
298 '''(INTERNAL) Instantiate the C{Transform}.
299 '''
300 return Transform(**name_tx_ty_tz_sx_sy_sz_s)
302Transforms = Transforms(Transform) # PYCHOK singleton
303'''Some pre-defined L{Transform}s, all I{lazily} instantiated.'''
304# <https://WikiPedia.org/wiki/Helmert_transformation> from WGS84 to ...
305Transforms._assert(
306 BD72 = _lazy(_BD72_, tx=_F(106.868628), ty=_F(-52.297783), tz=_F(103.723893),
307 # <https://www.NGI.Be/FR/FR4-4.shtm> ETRS89 == WG84
308 # <https://EPSG.org/transformation_15929/BD72-to-WGS-84-3.html>
309 sx=_F(-0.33657), sy=_F( -0.456955), sz=_F( -1.84218),
310 s=_F( 1.2727)),
311 Bessel1841 = _lazy(_Bessel1841_, tx=_F(-582.0), ty=_F(-105.0), tz=_F(-414.0),
312 sx=_F( -1.04), sy=_F( -0.35), sz=_F( 3.08),
313 s=_F( -8.3)),
314 Clarke1866 = _lazy(_Clarke1866_, tx=_F(8), ty=_F(-160), tz=_F(-176)),
315 DHDN = _lazy(_DHDN_, tx=_F(-591.28), ty=_F(-81.35), tz=_F(-396.39),
316 sx=_F( 1.477), sy=_F( -0.0736), sz=_F( -1.458),
317 s=_F( -9.82)), # Germany
318 DHDNE = _lazy(_DHDNE_, tx=_F(-612.4), ty=_F(-77.0), tz=_F(-440.2),
319 # <https://EPSG.org/transformation_15869/DHDN-to-WGS-84-3.html>
320 sx=_F( 0.054), sy=_F( -0.057), sz=_F( 2.797),
321 s=_F( -2.55)), # East Germany
322 DHDNW = _lazy(_DHDNW_, tx=_F(-598.1), ty=_F(-73.7), tz=_F(-418.2),
323 # <https://EPSG.org/transformation_1777/DHDN-to-WGS-84-2.html>
324 sx=_F( -0.202), sy=_F( -0.045), sz=_F( 2.455),
325 s=_F( -6.7)), # West Germany
326 ED50 = _lazy(_ED50_, tx=_F(89.5), ty=_F(93.8), tz=_F(123.1),
327 # <https://GeoNet.ESRI.com/thread/36583> sz=_F(-0.156)
328 # <https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal.js>
329 # <https://www.Gov.UK/guidance/oil-and-gas-petroleum-operations-notices#pon-4>
330 sz=_F( 0.156), s=_F(-1.2)),
331 Identity = _lazy(_Identity_),
332 Irl1965 = _lazy(_Irl1965_, tx=_F(-482.530), ty=_F(130.596), tz=_F(-564.557),
333 # <https://EPSG.org/transformation_1641/TM65-to-WGS-84-2.html>
334 sx=_F( 1.042), sy=_F( 0.214), sz=_F( 0.631),
335 s=_F( -8.15)),
336 Irl1975 = _lazy(_Irl1975_, tx=_F(-482.530), ty=_F(130.596), tz=_F(-564.557),
337 # <https://EPSG.org/transformation_1954/TM75-to-WGS-84-2.html>
338 sx=_F( 1.042), sy=_F( 0.214), sz=_F( 0.631),
339 s=_F( -8.15)),
340 Krassovski1940 = _lazy(_Krassovski1940_, tx=_F(-24.0), ty=_F(123.0), tz=_F(94.0),
341 sx=_F( -0.02), sy= _0_26, sz=_F( 0.13),
342 s=_F( -2.423)), # spelling
343 Krassowsky1940 = _lazy(_Krassowsky1940_, tx=_F(-24.0), ty=_F(123.0), tz=_F(94.0),
344 sx=_F( -0.02), sy= _0_26, sz=_F( 0.13),
345 s=_F( -2.423)), # spelling
346 MGI = _lazy(_MGI_, tx=_F(-577.326), ty=_F(-90.129), tz=_F(-463.920),
347 sx=_F( 5.137), sy=_F( 1.474), sz=_F( 5.297),
348 s=_F( -2.423)), # Austria
349 NAD27 = _lazy(_NAD27_, tx=_8_0, ty=_F(-160), tz=_F(-176)),
350 NAD83 = _lazy(_NAD83_, tx=_F( 1.004), ty=_F(-1.910), tz=_F(-0.515),
351 sx=_F( 0.0267), sy=_F( 0.00034), sz=_F( 0.011),
352 s=_F(-0.0015)),
353 NTF = _lazy(_NTF_, tx=_F(-168), ty=_F(-60), tz=_F(320)), # XXX verify
354 OSGB36 = _lazy(_OSGB36_, tx=_F(-446.448), ty=_F(125.157), tz=_F(-542.060),
355 # <https://EPSG.org/transformation_1314/OSGB36-to-WGS-84-6.html>
356 sx=_F( -0.1502), sy=_F( -0.2470), sz=_F( -0.8421),
357 s=_F( 20.4894)),
358 TokyoJapan = _lazy(_TokyoJapan_, tx=_F(148), ty=_F(-507), tz=_F(-685)),
359 WGS72 = _lazy(_WGS72_, tz=_F(-4.5), sz=_F(0.554), s=_F(-0.22)),
360 WGS84 = _lazy(_WGS84_), # unity
361)
364class Datum(_NamedEnumItem):
365 '''Ellipsoid and transform parameters for an earth model.
366 '''
367 _ellipsoid = Ellipsoids.WGS84 # default ellipsoid (L{Ellipsoid}, L{Ellipsoid2})
368 _transform = Transforms.WGS84 # default transform (L{Transform})
370 def __init__(self, ellipsoid, transform=None, name=NN):
371 '''New L{Datum}.
373 @arg ellipsoid: The ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
374 @kwarg transform: Optional transform (L{Transform}).
375 @kwarg name: Optional, unique name (C{str}).
377 @raise NameError: Datum with that B{C{name}} already exists.
379 @raise TypeError: If B{C{ellipsoid}} is not an L{Ellipsoid}
380 nor L{Ellipsoid2} or B{C{transform}} is
381 not a L{Transform}.
382 '''
383 self._ellipsoid = ellipsoid or Datum._ellipsoid
384 _xinstanceof(Ellipsoid, ellipsoid=self.ellipsoid)
386 self._transform = transform or Datum._transform
387 _xinstanceof(Transform, transform=self.transform)
389 self._register(Datums, name or self.transform.name or self.ellipsoid.name)
391 def __eq__(self, other):
392 '''Compare this and an other datum.
394 @arg other: The other datum (L{Datum}).
396 @return: C{True} if equal, C{False} otherwise.
397 '''
398 return self is other or (isinstance(other, Datum) and
399 self.ellipsoid == other.ellipsoid and
400 self.transform == other.transform)
402 def __hash__(self):
403 return self._hash # memoized
405 def __matmul__(self, point): # PYCHOK Python 3.5+
406 '''Convert an I{ellipsoidal} B{C{point}} to this datum.
408 @raise TypeError: Invalid B{C{point}}.
409 '''
410 _ = _xellipsoidall(point)
411 return point.toDatum(self)
413 def ecef(self, Ecef=None):
414 '''Return U{ECEF<https://WikiPedia.org/wiki/ECEF>} converter.
416 @kwarg Ecef: ECEF class to use, default L{EcefKarney}.
418 @return: An ECEF converter for this C{datum}.
420 @raise TypeError: Invalid B{C{Ecef}}.
422 @see: Module L{pygeodesy.ecef}.
423 '''
424 return _MODS.ecef._4Ecef(self, Ecef)
426 @Property_RO
427 def ellipsoid(self):
428 '''Get this datum's ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
429 '''
430 return self._ellipsoid
432 @Property_RO
433 def exactTM(self):
434 '''Get the C{ExactTM} projection (L{ExactTransverseMercator}).
435 '''
436 return _MODS.etm.ExactTransverseMercator(datum=self)
438 @Property_RO
439 def _hash(self):
440 return hash(self.ellipsoid) + hash(self.transform)
442 @property_RO
443 def isEllipsoidal(self):
444 '''Check whether this datum is ellipsoidal (C{bool}).
445 '''
446 return self.ellipsoid.isEllipsoidal
448 @property_RO
449 def isOblate(self):
450 '''Check whether this datum's ellipsoidal is I{oblate} (C{bool}).
451 '''
452 return self.ellipsoid.isOblate
454 @property_RO
455 def isProlate(self):
456 '''Check whether this datum's ellipsoidal is I{prolate} (C{bool}).
457 '''
458 return self.ellipsoid.isProlate
460 @property_RO
461 def isSpherical(self):
462 '''Check whether this datum is (near-)spherical (C{bool}).
463 '''
464 return self.ellipsoid.isSpherical
466 def toStr(self, sep=_COMMASPACE_, name=NN, **unused): # PYCHOK expected
467 '''Return this datum as a string.
469 @kwarg sep: Separator to join (C{str}).
470 @kwarg name: Override name (C{str}) or C{None} to exclude
471 this datum's name.
473 @return: Datum attributes (C{str}).
474 '''
475 t = [] if name is None else \
476 [Fmt.EQUAL(name=repr(name or self.named))]
477 for a in (_ellipsoid_, _transform_):
478 v = getattr(self, a)
479 t.append(NN(Fmt.EQUAL(a, v.classname), _s_, _DOT_, v.name))
480 return sep.join(t)
482 @Property_RO
483 def transform(self):
484 '''Get this datum's transform (L{Transform}).
485 '''
486 return self._transform
489def _earth_datum(inst, a_earth, f=None, name=NN, raiser=_a_ellipsoid_): # in .karney, .trf, ...
490 '''(INTERNAL) Set C{inst._datum} from C{(B{a_..}, B{f})} or C{B{.._ellipsoid}}
491 (L{Ellipsoid}, L{Ellipsoid2}, L{Datum}, C{a_f2Tuple} or C{scalar} earth radius).
493 @note: C{B{raiser}='a_ellipsoid'} for backward naming compatibility.
494 '''
495 if f is not None:
496 E, n, D = _EnD3((a_earth, f), name)
497 if raiser and not E:
498 raise _TypeError(f=f, **{raiser: a_earth})
499 elif a_earth is _EWGS84 or a_earth in (_EWGS84, _WGS84, None):
500 return
501 elif isinstance(a_earth, Datum):
502 E, n, D = None, NN, a_earth
503 else:
504 E, n, D = _EnD3(a_earth, name)
505 if raiser and not E:
506 _xinstanceof(Ellipsoid, Ellipsoid2, a_f2Tuple, Datum, **{raiser: a_earth})
507 if D is None:
508 D = Datum(E, transform=Transforms.Identity, name=_under(n))
509 inst._datum = D
512def _earth_ellipsoid(earth, *name_raiser):
513 '''(INTERAL) Return the ellipsoid for the given C{earth} model.
514 '''
515 return Ellipsoids.Sphere if earth is R_M else (
516 _EWGS84 if earth is _EWGS84 or earth is _WGS84 else
517 _spherical_datum(earth, *name_raiser).ellipsoid)
520def _ED2(radius, name):
521 '''(INTERNAL) Helper for C{_EnD3} and C{_spherical_datum}.
522 '''
523 D = Datums.Sphere
524 E = D.ellipsoid
525 if name or radius != E.a: # != E.b
526 n = _under(name)
527 E = Ellipsoid(radius, radius, name=n)
528 D = Datum(E, transform=Transforms.Identity, name=n)
529 return E, D
532def _ellipsoidal_datum(earth, Error=TypeError, name=NN, raiser=NN):
533 '''(INTERNAL) Create a L{Datum} from an L{Ellipsoid} or L{Ellipsoid2},
534 C{a_f2Tuple}, 2-tuple or 2-list B{C{earth}} model.
536 @kwarg raiser: If not C{NN}, raise an B{C{Error}} if not ellipsoidal.
537 '''
538 if isinstance(earth, Datum):
539 D = earth
540 else:
541 E, n, D = _EnD3(earth, name)
542 if not E:
543 n = raiser or _earth_
544 _xinstanceof(Datum, Ellipsoid, Ellipsoid2, a_f2Tuple, **{n: earth})
545 if D is None:
546 D = Datum(E, transform=Transforms.Identity, name=_under(n))
547 if raiser and not D.isEllipsoidal:
548 raise _IsnotError(_ellipsoidal_, Error=Error, **{raiser: earth})
549 return D
552def _EnD3(earth, name):
553 '''(INTERNAL) Helper for C{_earth_datum} and C{_ellipsoidal_datum}.
554 '''
555 D = None
556 if isinstance(earth, (Ellipsoid, Ellipsoid2)):
557 E = earth
558 n = _under(name or E.name)
559 elif isinstance(earth, Datum):
560 E = earth.ellipsoid
561 n = _under(name or earth.name)
562 D = earth
563 elif _isRadius(earth):
564 E, D = _ED2(Radius_(earth), name)
565 n = E.name
566 elif isinstance(earth, a_f2Tuple):
567 n = _under(name or earth.name)
568 E = earth.ellipsoid(name=n)
569 elif islistuple(earth, minum=2):
570 E = Ellipsoids.Sphere
571 a, f = earth[:2]
572 if f or a != E.a: # != E.b
573 n = _under(name or _xattr(earth, name=NN))
574 E = Ellipsoid(a, f=f, name=n)
575 else:
576 n = E.name
577 D = Datums.Sphere
578 else:
579 E, n = None, NN
580 return E, n, D
583def _mean_radius(radius, *lats):
584 '''(INTERNAL) Compute the mean radius of a L{Datum} from an L{Ellipsoid},
585 L{Ellipsoid2} or scalar earth C{radius} over several latitudes.
586 '''
587 if radius is R_M:
588 r = radius
589 elif _isRadius(radius):
590 r = Radius_(radius, low=0, Error=TypeError)
591 else:
592 E = _ellipsoidal_datum(radius).ellipsoid
593 r = fmean(map(E.Rgeocentric, lats)) if lats else E.Rmean
594 return r
597def _minus(name): # in .trf
598 '''(INTERNAL) Name of C{inverse} Xform.
599 '''
600 m = _MINUS_
601 return name[len(m):] if name.startswith(m) else NN(m, name)
604def _spherical_datum(earth, Error=TypeError, name=NN, raiser=NN):
605 '''(INTERNAL) Create a L{Datum} from an L{Ellipsoid}, L{Ellipsoid2},
606 C{a_f2Tuple}, 2-tuple, 2-list B{C{earth}} model or C{scalar} radius.
608 @kwarg raiser: If not C{NN}, raise an B{C{Error}} if not spherical.
609 '''
610 if _isRadius(earth):
611 _, D = _ED2(Radius_(earth, Error=Error), name)
612 else:
613 D = _ellipsoidal_datum(earth, Error=Error, name=name)
614 if raiser and not D.isSpherical:
615 raise _IsnotError(_spherical_, Error=Error, **{raiser: earth})
616 return D
619class Datums(_NamedEnum):
620 '''(INTERNAL) L{Datum} registry, I{must} be a sub-class
621 to accommodate the L{_LazyNamedEnumItem} properties.
622 '''
623 def _Lazy(self, ellipsoid_name, transform_name, name=NN):
624 '''(INTERNAL) Instantiate the L{Datum}.
625 '''
626 return Datum(Ellipsoids.get(ellipsoid_name),
627 Transforms.get(transform_name), name=name)
629Datums = Datums(Datum) # PYCHOK singleton
630'''Some pre-defined L{Datum}s, all I{lazily} instantiated.'''
631# Datums with associated ellipsoid and Helmert transform parameters
632# to convert from WGS84 into the given datum. More are available at
633# <https://Earth-Info.NGA.mil/GandG/coordsys/datums/NATO_DT.pdf> and
634# <XXX://www.FieldenMaps.info/cconv/web/cconv_params.js>.
635Datums._assert(
636 # Belgian Datum 1972, based on Hayford ellipsoid.
637 # <https://NL.WikiPedia.org/wiki/Belgian_Datum_1972>
638 # <https://SpatialReference.org/ref/sr-org/7718/html/>
639 BD72 = _lazy(_BD72_, _Intl1924_, _BD72_),
641 # Germany <https://WikiPedia.org/wiki/Bessel-Ellipsoid>
642 # <https://WikiPedia.org/wiki/Helmert_transformation>
643 DHDN = _lazy(_DHDN_, _Bessel1841_, _DHDN_),
645 # <https://www.Gov.UK/guidance/oil-and-gas-petroleum-operations-notices#pon-4>
646 ED50 = _lazy(_ED50_, _Intl1924_, _ED50_),
648 # Australia <https://ICSM.Gov.AU/datum/gda2020-and-gda94-technical-manuals>
649# ADG66 = _lazy(_ADG66_, _ANS_, _WGS84_), # XXX Transform?
650# ADG84 = _lazy(_ADG84_, _ANS_, _WGS84_), # XXX Transform?
651# GDA94 = _lazy(_GDA94_, _GRS80_, _WGS84_),
652 GDA2020 = _lazy(_GDA2020_, _GRS80_, _WGS84_), # XXX Transform?
654 # <https://WikiPedia.org/wiki/GRS_80>
655 GRS80 = _lazy(_GRS80_, _GRS80_, _WGS84_),
657 # <https://OSI.IE/wp-content/uploads/2015/05/transformations_booklet.pdf> Table 2
658# Irl1975 = _lazy(_Irl1965_, _AiryModified_, _Irl1965_),
659 Irl1975 = _lazy(_Irl1975_, _AiryModified_, _Irl1975_),
661 # Germany <https://WikiPedia.org/wiki/Helmert_transformation>
662 Krassovski1940 = _lazy(_Krassovski1940_, _Krassovski1940_, _Krassovski1940_), # XXX spelling?
663 Krassowsky1940 = _lazy(_Krassowsky1940_, _Krassowsky1940_, _Krassowsky1940_), # XXX spelling?
665 # Austria <https://DE.WikiPedia.org/wiki/Datum_Austria>
666 MGI = _lazy(_MGI_, _Bessel1841_, _MGI_),
668 # <https://WikiPedia.org/wiki/Helmert_transformation>
669 NAD27 = _lazy(_NAD27_, _Clarke1866_, _NAD27_),
671 # NAD83 (2009) == WGS84 - <https://www.UVM.edu/giv/resources/WGS84_NAD83.pdf>
672 # (If you *really* must convert WGS84<->NAD83, you need more than this!)
673 NAD83 = _lazy(_NAD83_, _GRS80_, _NAD83_),
675 # Nouvelle Triangulation Francaise (Paris) XXX verify
676 NTF = _lazy(_NTF_, _Clarke1880IGN_, _NTF_),
678 # <https://www.OrdnanceSurvey.co.UK/docs/support/guide-coordinate-systems-great-britain.pdf>
679 OSGB36 = _lazy(_OSGB36_, _Airy1830_, _OSGB36_),
681 # Germany <https://WikiPedia.org/wiki/Helmert_transformation>
682 Potsdam = _lazy(_Potsdam_, _Bessel1841_, _Bessel1841_),
684 # XXX psuedo-ellipsoids for spherical LatLon
685 Sphere = _lazy(_Sphere_, _Sphere_, _WGS84_),
687 # <https://www.GeoCachingToolbox.com?page=datumEllipsoidDetails>
688 TokyoJapan = _lazy(_TokyoJapan_, _Bessel1841_, _TokyoJapan_),
690 # <https://www.ICAO.int/safety/pbn/documentation/eurocontrol/eurocontrol%20wgs%2084%20implementation%20manual.pdf>
691 WGS72 = _lazy(_WGS72_, _WGS72_, _WGS72_),
693 WGS84 = _lazy(_WGS84_, _WGS84_, _WGS84_),
694)
696_WGS84 = Datums.WGS84
697assert _WGS84.ellipsoid is _EWGS84
698# assert _WGS84.transform.isunity
700if __name__ == '__main__':
702 from pygeodesy.interns import _COMMA_, _NL_, _NLATvar_
703 from pygeodesy.lazily import printf
705 # __doc__ of this file, force all into registery
706 for r in (Datums, Transforms):
707 t = [NN] + r.toRepr(all=True, asorted=True).split(_NL_)
708 printf(_NLATvar_.join(i.strip(_COMMA_) for i in t))
710# **) MIT License
711#
712# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
713#
714# Permission is hereby granted, free of charge, to any person obtaining a
715# copy of this software and associated documentation files (the "Software"),
716# to deal in the Software without restriction, including without limitation
717# the rights to use, copy, modify, merge, publish, distribute, sublicense,
718# and/or sell copies of the Software, and to permit persons to whom the
719# Software is furnished to do so, subject to the following conditions:
720#
721# The above copyright notice and this permission notice shall be included
722# in all copies or substantial portions of the Software.
723#
724# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
725# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
726# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
727# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
728# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
729# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
730# OTHER DEALINGS IN THE SOFTWARE.