1

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

3

4 u'''Datums and transformations thereof.

5

6 Classes L{Datum} and L{Transform} and registries L{Datums} and L{Transforms}, respectively.

7

8 Pure Python implementation of geodesy tools for ellipsoidal earth models, including datums

9 and ellipsoid parameters for different geographic coordinate systems and methods for

10 converting between them and to cartesian coordinates. Transcoded from JavaScript originals by

11 I{(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>}.

13

14 Historical geodetic datums: a latitude/longitude point defines a geographic location on, above

15 or below the earth’s surface. Latitude is measured in degrees from the equator, lomgitude from

16 the International Reference Meridian and height in meters above an ellipsoid based on the given

17 datum. The datum in turn is based on a reference ellipsoid and tied to geodetic survey

18 reference points.

19

20 Modern geodesy is generally based on the WGS84 datum (as used for instance by GPS systems), but

21 previously various other reference ellipsoids and datum references were used.

22

23 The UK Ordnance Survey National Grid References are still based on the otherwise historical OSGB36

24 datum, 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>}.

26

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)

45

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

68 from __future__ import division as _; del _ # PYCHOK semicolon

69

70 from pygeodesy.basics import islistuple, map2, neg, _passarg, _xinstanceof, _zip

71 from pygeodesy.constants import R_M, _float as _F, _0_0, _1_0, _2_0, _8_0, _3600_0

72# from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase as _CEB, \

73# LatLonEllipsoidalBase as _LLEB # MODS

74 from pygeodesy.ellipsoids import a_f2Tuple, Ellipsoid, Ellipsoid2, Ellipsoids, _EWGS84, \

75 Vector3Tuple

76 from pygeodesy.errors import _IsnotError, _TypeError, _xattr, _xellipsoidall, _xkwds, \

77 _xkwds_pop2

78 from pygeodesy.fmath import fdot, fmean, Fmt, _operator

79 from pygeodesy.interns import NN, _a_, _Airy1830_, _AiryModified_, _BAR_, _Bessel1841_, \

80 _Clarke1866_, _Clarke1880IGN_, _COMMASPACE_, _DOT_, \

81 _earth_, _ellipsoid_, _ellipsoidal_, _GRS80_, _Intl1924_, \

82 _MINUS_, _Krassovski1940_, _Krassowsky1940_, _NAD27_, \

83 _NAD83_, _PLUS_, _s_, _Sphere_, _spherical_, _transform_, \

84 _UNDER_, _WGS72_, _WGS84_, _under

85 from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS

86 from pygeodesy.named import _NamedEnum, _NamedEnumItem, _lazyNamedEnumItem as _lazy

87# from pygeodesy.namedTuples import Vector3Tuple # from .ellipsoids

88 from pygeodesy.props import Property_RO, property_RO

89# from pygeodesy.streprs import Fmt # from .fmath

90 from pygeodesy.units import _isRadius, Radius_, radians

91

92# from math import radians # from .units

93# import operator as _operator # from .fmath

94

95__all__ = _ALL_LAZY.datums

96__version__ = '24.03.07'

97

98_a_ellipsoid_ = _UNDER_(_a_, _ellipsoid_)

99_BD72_ = 'BD72'

100_DHDN_ = 'DHDN'

101_DHDNE_ = 'DHDNE'

102_DHDNW_ = 'DHDNW'

103_ED50_ = 'ED50'

104_GDA2020_ = 'GDA2020' # in .trf

105_Identity_ = 'Identity'

106_Irl1965_ = 'Irl1965'

107_Irl1975_ = 'Irl1975'

108_MGI_ = 'MGI'

109_Names7 = 'tx', 'ty', 'tz', _s_, 'sx', 'sy', 'sz' # in .trf

110_Names11 = _Names7[:3] + ('s1', 'rx', 'ry', 'rz') + _Names7[3:]

111_NTF_ = 'NTF'

112_OSGB36_ = 'OSGB36'

113_Potsdam_ = 'Potsdam'

114_RPS = radians(_1_0 / _3600_0) # radians per arc-second

115_S1_S = 1.e-6 # in .trf

116_TokyoJapan_ = 'TokyoJapan'

117

118

119 class Transform(_NamedEnumItem):

120 '''Helmert I{datum} transformation.

121

122 @see: L{TransformXform<trf.TransformXform>}.

123 '''

124 tx = _0_0 # x translation (C{meter})

125 ty = _0_0 # y translation (C{meter})

126 tz = _0_0 # z translation (C{meter})

127

128 rx = _0_0 # x rotation (C{radians})

129 ry = _0_0 # y rotation (C{radians})

130 rz = _0_0 # z rotation (C{radians})

131

132 s = _0_0 # scale ppm (C{float})

133 s1 = _1_0 # scale + 1 (C{float})

134

135 sx = _0_0 # x rotation (C{arc-seconds})

136 sy = _0_0 # y rotation (C{arc-seconds})

137 sz = _0_0 # z rotation (C{arc-seconds})

138

139 def __init__(self, name=NN, tx=0, ty=0, tz=0,

140 s=0, sx=0, sy=0, sz=0):

141 '''New L{Transform}.

142

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

144 @kwarg tx: X translation (C{meter}).

145 @kwarg ty: Y translation (C{meter}).

146 @kwarg tz: Z translation (C{meter}).

147 @kwarg s: Scale (C{float}), ppm.

148 @kwarg sx: X rotation (C{arc-seconds}).

149 @kwarg sy: Y rotation (C{arc-seconds}).

150 @kwarg sz: Z rotation (C{arc-seconds}).

151

152 @raise NameError: Transform with that B{C{name}} already exists.

153 '''

154 if tx:

155 self.tx = tx

156 if ty:

157 self.ty = ty

158 if tz:

159 self.tz = tz

160 if s:

161 self.s = s

162 self.s1 = _F(s * _S1_S + _1_0) # normalize ppM to (s + 1)

163 if sx: # secs to rads

164 self.rx, self.sx = self._rps2(sx)

165 if sy:

166 self.ry, self.sy = self._rps2(sy)

167 if sz:

168 self.rz, self.sz = self._rps2(sz)

169

170 self._register(Transforms, name)

171

172 def __eq__(self, other):

173 '''Compare this and an other transform.

174

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

176

177 @return: C{True} if equal, C{False} otherwise.

178 '''

179 return self is other or (isinstance(other, Transform)

180 and _equall(other, self))

181

182 def __hash__(self):

183 return hash(tuple(self))

184

185 def __iter__(self):

186 '''Yield the initial attribute values, I{in order}.

187 '''

188 for n in _Names7:

189 yield getattr(self, n)

190

191 def __matmul__(self, point): # PYCHOK Python 3.5+

192 '''Transform an I{ellipsoidal} B{C{point}} with this Helmert.

193

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

195

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

197

198 @see: Method C{B{point}.toTransform}.

199 '''

200 _ = _xellipsoidall(point)

201 return point.toTransform(self)

202

203 def __neg__(self):

204 return self.inverse()

205

206 def inverse(self, name=NN):

207 '''Return the inverse of this transform.

208

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

210

211 @return: Inverse (L{Transform}), unregistered.

212 '''

213 r = type(self)(**dict(self.items(inverse=True)))

214 n = name or _negastr(self.name)

215 if n:

216 r.name = n # unregistered

217 return r

218

219 @Property_RO

220 def isunity(self):

221 '''Is this a C{unity, identity} transform (C{bool}), like

222 WGS84 with translation, scale and rotation all zero?

223 '''

224 return not any(self)

225

226 def items(self, inverse=False):

227 '''Yield the initial attributes, each as 2-tuple C{(name, value)}.

228

229 @kwarg inverse: If C{True}, negate the values (C{bool}).

230 '''

231 _p = neg if inverse else _passarg

232 for n, x in _zip(_Names7, self):

233 yield n, _p(x)

234

235 def _rps2(self, s_):

236 '''(INTERNAL) Rotation in C{radians} and C{arc-seconds}.

237 '''

238 # _MR == _RPS * 1.e-3 # radians per milli-arc-second, equ (2)

239 # <https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>

240 return (_RPS * s_), s_

241

242 def _s_s1(self, s1): # in .trf

243 '''(INTERNAL) Set C{s1} and C{s}.

244 '''

245 Transform.isunity._update(self)

246 self.s1 = s1

247 self.s = s = (s1 - _1_0) / _S1_S

248 return s

249

250 def toStr(self, prec=5, fmt=Fmt.g, name=NN, **unused): # PYCHOK expected

251 '''Return this transform as a string.

252

253 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).

254 @kwarg fmt: Optional C{float} format (C{letter}).

255 @kwarg name: Override name (C{str}) or C{None} to exclude

256 this transform's name.

257

258 @return: Transform attributes (C{str}).

259 '''

260 return self._instr(name, prec, *_Names11, fmt=fmt)

261

262 def transform(self, x, y, z, inverse=False, **Vector_and_kwds):

263 '''Transform a (cartesian) position, forward or inverse.

264

265 @arg x: X coordinate (C{meter}).

266 @arg y: Y coordinate (C{meter}).

267 @arg z: Z coordinate (C{meter}).

268 @kwarg inverse: If C{True}, apply the inverse transform (C{bool}).

269 @kwarg Vector_and_kwds: An optional, (3-D) C{B{Vector}=None} or

270 cartesian class and additional C{B{Vector}} keyword

271 arguments to return the transformed position.

272

273 @return: The transformed position (L{Vector3Tuple}C{(x, y, z)})

274 unless some B{C{Vector_and_kwds}} are specified.

275 '''

276 if self.isunity:

277 r = Vector3Tuple(x, y, z, name=self.name) # == inverse

278 else:

279 xyz1 = x, y, z, _1_0

280 s1 = self.s1

281 if inverse:

282 xyz1 = map2(neg, xyz1)

283 s1 -= _2_0 # = s * 1e-6 - 1 = (s1 - 1) - 1

284 # x', y', z' = (x * .s1 - y * .rz + z * .ry + .tx,

285 # x * .rz + y * .s1 - z * .rx + .ty,

286 # -x * .ry + y * .rx + z * .s1 + .tz)

287 r = Vector3Tuple(fdot(xyz1, s1, -self.rz, self.ry, self.tx),

288 fdot(xyz1, self.rz, s1, -self.rx, self.ty),

289 fdot(xyz1, -self.ry, self.rx, s1, self.tz),

290 name=self.name)

291 if Vector_and_kwds:

292 V, kwds = _xkwds_pop2(Vector_and_kwds, Vector=None)

293 if V:

294 r = V(r, **_xkwds(kwds, name=self.name))

295 return r

296

297

298 class Transforms(_NamedEnum):

299 '''(INTERNAL) L{Transform} registry, I{must} be a sub-class

300 to accommodate the L{_LazyNamedEnumItem} properties.

301 '''

302 def _Lazy(self, **name_tx_ty_tz_s_sx_sy_sz):

303 '''(INTERNAL) Instantiate the C{Transform}.

304 '''

305 return Transform(**name_tx_ty_tz_s_sx_sy_sz)

306

307 Transforms = Transforms(Transform) # PYCHOK singleton

308'''Some pre-defined L{Transform}s, all I{lazily} instantiated.'''

309# <https://WikiPedia.org/wiki/Helmert_transformation> from WGS84 to ...

310 Transforms._assert(

311 BD72 = _lazy(_BD72_, tx=_F(106.868628), ty=_F(-52.297783), tz=_F(103.723893), s=_F(1.2727),

312 # <https://www.NGI.Be/FR/FR4-4.shtm> ETRS89 == WG84

313 # <https://EPSG.org/transformation_15929/BD72-to-WGS-84-3.html>

314 sx=_F( -0.33657), sy=_F( -0.456955), sz=_F( -1.84218)),

315

316 Bessel1841 = _lazy(_Bessel1841_, tx=_F(-582.0), ty=_F(-105.0), tz=_F(-414.0), s=_F(-8.3),

317 sx=_F( -1.04), sy=_F( -0.35), sz=_F( 3.08)),

318

319 Clarke1866 = _lazy(_Clarke1866_, tx=_F(8), ty=_F(-160), tz=_F(-176)),

320

321 DHDN = _lazy(_DHDN_, tx=_F(-591.28), ty=_F(-81.35), tz=_F(-396.39), s=_F(-9.82),

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

323

324 DHDNE = _lazy(_DHDNE_, tx=_F(-612.4), ty=_F(-77.0), tz=_F(-440.2), s=_F(-2.55),

325 # <https://EPSG.org/transformation_15869/DHDN-to-WGS-84-3.html>

326 sx=_F( 0.054), sy=_F( -0.057), sz=_F( 2.797)), # East Germany

327

328 DHDNW = _lazy(_DHDNW_, tx=_F(-598.1), ty=_F(-73.7), tz=_F(-418.2), s=_F(-6.7),

329 # <https://EPSG.org/transformation_1777/DHDN-to-WGS-84-2.html>

330 sx=_F( -0.202), sy=_F( -0.045), sz=_F( 2.455)), # West Germany

331

332 ED50 = _lazy(_ED50_, tx=_F(89.5), ty=_F(93.8), tz=_F(123.1), s=_F(-1.2),

333 # <https://GeoNet.ESRI.com/thread/36583> sz=_F(-0.156)

334 # <https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal.js>

335 # <https://www.Gov.UK/guidance/oil-and-gas-petroleum-operations-notices#pon-4>

336 sz=_F( 0.156)),

337 Identity = _lazy(_Identity_),

338

339 Irl1965 = _lazy(_Irl1965_, tx=_F(-482.530), ty=_F(130.596), tz=_F(-564.557), s=_F(-8.15),

340 # <https://EPSG.org/transformation_1641/TM65-to-WGS-84-2.html>

341 sx=_F( 1.042), sy=_F( 0.214), sz=_F( 0.631)),

342 Irl1975 = _lazy(_Irl1975_, tx=_F(-482.530), ty=_F(130.596), tz=_F(-564.557), s=_F(-8.15),

343 # <https://EPSG.org/transformation_1954/TM75-to-WGS-84-2.html>

344 sx=_F( 1.042), sy=_F( 0.214), sz=_F( 0.631)),

345

346 Krassovski1940 = _lazy(_Krassovski1940_, tx=_F(-24.0), ty=_F(123.0), tz=_F(94.0), s=_F(-2.423),

347 sx=_F( -0.02), sy=_F( 0.26), sz=_F( 0.13)), # spelling

348

349 Krassowsky1940 = _lazy(_Krassowsky1940_, tx=_F(-24.0), ty=_F(123.0), tz=_F(94.0), s=_F(-2.423),

350 sx=_F( -0.02), sy=_F( 0.26), sz=_F( 0.13)), # spelling

351

352 MGI = _lazy(_MGI_, tx=_F(-577.326), ty=_F(-90.129), tz=_F(-463.920), s=_F(-2.423),

353 sx=_F( 5.137), sy=_F( 1.474), sz=_F( 5.297)), # Austria

354

355 NAD27 = _lazy(_NAD27_, tx=_8_0, ty=_F(-160), tz=_F(-176)),

356

357 NAD83 = _lazy(_NAD83_, tx=_F(1.004), ty=_F(-1.910), tz=_F(-0.515), s=_F(-0.0015),

358 sx=_F(0.0267), sy=_F( 0.00034), sz=_F( 0.011)),

359

360 NTF = _lazy(_NTF_, tx=_F(-168), ty=_F(-60), tz=_F(320)), # XXX verify

361

362 OSGB36 = _lazy(_OSGB36_, tx=_F(-446.448), ty=_F(125.157), tz=_F(-542.060), s=_F(20.4894),

363 # <https://EPSG.org/transformation_1314/OSGB36-to-WGS-84-6.html>

364 sx=_F( -0.1502), sy=_F( -0.2470), sz=_F( -0.8421)),

365

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

367

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

369

370 WGS84 = _lazy(_WGS84_), # unity

371)

372

373

374 class Datum(_NamedEnumItem):

375 '''Ellipsoid and transform parameters for an earth model.

376 '''

377 _ellipsoid = Ellipsoids.WGS84 # default ellipsoid (L{Ellipsoid}, L{Ellipsoid2})

378 _transform = Transforms.WGS84 # default transform (L{Transform})

379

380 def __init__(self, ellipsoid, transform=None, name=NN):

381 '''New L{Datum}.

382

383 @arg ellipsoid: The ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).

384 @kwarg transform: Optional transform (L{Transform}).

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

386

387 @raise NameError: Datum with that B{C{name}} already exists.

388

389 @raise TypeError: If B{C{ellipsoid}} is not an L{Ellipsoid}

390 nor L{Ellipsoid2} or B{C{transform}} is

391 not a L{Transform}.

392 '''

393 self._ellipsoid = ellipsoid or Datum._ellipsoid

394 _xinstanceof(Ellipsoid, ellipsoid=self.ellipsoid)

395

396 self._transform = transform or Datum._transform

397 _xinstanceof(Transform, transform=self.transform)

398

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

400

401 def __eq__(self, other):

402 '''Compare this and an other datum.

403

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

405

406 @return: C{True} if equal, C{False} otherwise.

407 '''

408 return self is other or (isinstance(other, Datum) and

409 self.ellipsoid == other.ellipsoid and

410 self.transform == other.transform)

411

412 def __hash__(self):

413 return self._hash # memoized

414

415 def __matmul__(self, point): # PYCHOK Python 3.5+

416 '''Convert an I{ellipsoidal} B{C{point}} to this datum.

417

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

419 '''

420 _ = _xellipsoidall(point)

421 return point.toDatum(self)

422

423 def ecef(self, Ecef=None):

424 '''Return U{ECEF<https://WikiPedia.org/wiki/ECEF>} converter.

425

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

427

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

429

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

431

432 @see: Module L{pygeodesy.ecef}.

433 '''

434 return _MODS.ecef._4Ecef(self, Ecef)

435

436 @Property_RO

437 def ellipsoid(self):

438 '''Get this datum's ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).

439 '''

440 return self._ellipsoid

441

442 @Property_RO

443 def exactTM(self):

444 '''Get the C{ExactTM} projection (L{ExactTransverseMercator}).

445 '''

446 return _MODS.etm.ExactTransverseMercator(datum=self)

447

448 @Property_RO

449 def _hash(self):

450 return hash(self.ellipsoid) + hash(self.transform)

451

452 @property_RO

453 def isEllipsoidal(self):

454 '''Check whether this datum is ellipsoidal (C{bool}).

455 '''

456 return self.ellipsoid.isEllipsoidal

457

458 @property_RO

459 def isOblate(self):

460 '''Check whether this datum's ellipsoidal is I{oblate} (C{bool}).

461 '''

462 return self.ellipsoid.isOblate

463

464 @property_RO

465 def isProlate(self):

466 '''Check whether this datum's ellipsoidal is I{prolate} (C{bool}).

467 '''

468 return self.ellipsoid.isProlate

469

470 @property_RO

471 def isSpherical(self):

472 '''Check whether this datum is (near-)spherical (C{bool}).

473 '''

474 return self.ellipsoid.isSpherical

475

476 def toStr(self, sep=_COMMASPACE_, name=NN, **unused): # PYCHOK expected

477 '''Return this datum as a string.

478

479 @kwarg sep: Separator to join (C{str}).

480 @kwarg name: Override name (C{str}) or C{None} to exclude

481 this datum's name.

482

483 @return: Datum attributes (C{str}).

484 '''

485 t = [] if name is None else \

486 [Fmt.EQUAL(name=repr(name or self.named))]

487 for a in (_ellipsoid_, _transform_):

488 v = getattr(self, a)

489 t.append(NN(Fmt.EQUAL(a, v.classname), _s_, _DOT_, v.name))

490 return sep.join(t)

491

492 @Property_RO

493 def transform(self):

494 '''Get this datum's transform (L{Transform}).

495 '''

496 return self._transform

497

498

499 def _earth_datum(inst, a_earth, f=None, name=NN, raiser=_a_ellipsoid_): # in .karney, .trf, ...

500 '''(INTERNAL) Set C{inst._datum} from C{(B{a_..}, B{f})} or C{B{.._ellipsoid}}

501 (L{Ellipsoid}, L{Ellipsoid2}, L{Datum}, C{a_f2Tuple} or C{scalar} earth radius).

502

503 @note: C{B{raiser}='a_ellipsoid'} for backward naming compatibility.

504 '''

505 if f is not None:

506 E, n, D = _EnD3((a_earth, f), name)

507 if raiser and not E:

508 raise _TypeError(f=f, **{raiser: a_earth})

509 elif a_earth in (_EWGS84, _WGS84, None) and inst._datum is _WGS84:

510 return

511 elif isinstance(a_earth, Datum):

512 E, n, D = None, NN, a_earth

513 else:

514 E, n, D = _EnD3(a_earth, name)

515 if raiser and not E:

516 _xinstanceof(Ellipsoid, Ellipsoid2, a_f2Tuple, Datum, **{raiser: a_earth})

517 if D is None:

518 D = Datum(E, transform=Transforms.Identity, name=_under(n))

519 inst._datum = D

520

521

522 def _earth_ellipsoid(earth, *name_raiser):

523 '''(INTERAL) Return the ellipsoid for the given C{earth} model.

524 '''

525 return Ellipsoids.Sphere if earth is R_M else (

526 _EWGS84 if earth is _EWGS84 or earth is _WGS84 else

527 _spherical_datum(earth, *name_raiser).ellipsoid)

528

529

530 def _ED2(radius, name):

531 '''(INTERNAL) Helper for C{_EnD3} and C{_spherical_datum}.

532 '''

533 D = Datums.Sphere

534 E = D.ellipsoid

535 if name or radius != E.a: # != E.b

536 n = _under(name)

537 E = Ellipsoid(radius, radius, name=n)

538 D = Datum(E, transform=Transforms.Identity, name=n)

539 return E, D

540

541

542 def _ellipsoidal_datum(earth, Error=TypeError, name=NN, raiser=NN):

543 '''(INTERNAL) Create a L{Datum} from an L{Ellipsoid} or L{Ellipsoid2},

544 C{a_f2Tuple}, 2-tuple or 2-list B{C{earth}} model.

545

546 @kwarg raiser: If not C{NN}, raise an B{C{Error}} if not ellipsoidal.

547 '''

548 if isinstance(earth, Datum):

549 D = earth

550 else:

551 E, n, D = _EnD3(earth, name)

552 if not E:

553 n = raiser or _earth_

554 _xinstanceof(Datum, Ellipsoid, Ellipsoid2, a_f2Tuple, **{n: earth})

555 if D is None:

556 D = Datum(E, transform=Transforms.Identity, name=_under(n))

557 if raiser and not D.isEllipsoidal:

558 raise _IsnotError(_ellipsoidal_, Error=Error, **{raiser: earth})

559 return D

560

561

562 def _EnD3(earth, name):

563 '''(INTERNAL) Helper for C{_earth_datum} and C{_ellipsoidal_datum}.

564 '''

565 D = None

566 if isinstance(earth, (Ellipsoid, Ellipsoid2)):

567 E = earth

568 n = _under(name or E.name)

569 elif isinstance(earth, Datum):

570 E = earth.ellipsoid

571 n = _under(name or earth.name)

572 D = earth

573 elif _isRadius(earth):

574 E, D = _ED2(Radius_(earth), name)

575 n = E.name

576 elif isinstance(earth, a_f2Tuple):

577 n = _under(name or earth.name)

578 E = earth.ellipsoid(name=n)

579 elif islistuple(earth, minum=2):

580 E = Ellipsoids.Sphere

581 a, f = earth[:2]

582 if f or a != E.a: # != E.b

583 n = _under(name or _xattr(earth, name=NN))

584 E = Ellipsoid(a, f=f, name=n)

585 else:

586 n = E.name

587 D = Datums.Sphere

588 else:

589 E, n = None, NN

590 return E, n, D

591

592

593 def _equall(t1, t2): # in .trf

594 '''(INTERNAL) Return L{Transform} C{t1 == t2}.

595 '''

596 return all(map(_operator.eq, t1, t2))

597

598

599 def _mean_radius(radius, *lats):

600 '''(INTERNAL) Compute the mean radius of a L{Datum} from an L{Ellipsoid},

601 L{Ellipsoid2} or scalar earth C{radius} over several latitudes.

602 '''

603 if radius is R_M:

604 r = radius

605 elif _isRadius(radius):

606 r = Radius_(radius, low=0, Error=TypeError)

607 else:

608 E = _ellipsoidal_datum(radius).ellipsoid

609 r = fmean(map(E.Rgeocentric, lats)) if lats else E.Rmean

610 return r

611

612

613 def _negastr(name): # in .trf

614 '''(INTERNAL) Negate a C{Transform/-Xform} name.

615 '''

616 b, m, p = _BAR_, _MINUS_, _PLUS_

617 n = name.replace(m, b).replace(p, m).replace(b, p)

618 # as good and fast as (in Python 3+ only) ...

619 # _MINUSxPLUS = str.maketrans({_MINUS_: _PLUS_, _PLUS_: _MINUS_})

620 # def _negastr(name):

621 # n = name.translate(_MINUSxPLUS)

622 # ...

623 return n.lstrip(p) if n.startswith(p) else NN(m, n)

624

625

626 def _spherical_datum(earth, Error=TypeError, name=NN, raiser=NN):

627 '''(INTERNAL) Create a L{Datum} from an L{Ellipsoid}, L{Ellipsoid2},

628 C{a_f2Tuple}, 2-tuple, 2-list B{C{earth}} model or C{scalar} radius.

629

630 @kwarg raiser: If not C{NN}, raise an B{C{Error}} if not spherical.

631 '''

632 if _isRadius(earth):

633 _, D = _ED2(Radius_(earth, Error=Error), name)

634 else:

635 D = _ellipsoidal_datum(earth, Error=Error, name=name)

636 if raiser and not D.isSpherical:

637 raise _IsnotError(_spherical_, Error=Error, **{raiser: earth})

638 return D

639

640

641 class Datums(_NamedEnum):

642 '''(INTERNAL) L{Datum} registry, I{must} be a sub-class

643 to accommodate the L{_LazyNamedEnumItem} properties.

644 '''

645 def _Lazy(self, ellipsoid_name, transform_name, name=NN):

646 '''(INTERNAL) Instantiate the L{Datum}.

647 '''

648 return Datum(Ellipsoids.get(ellipsoid_name),

649 Transforms.get(transform_name), name=name)

650

651 Datums = Datums(Datum) # PYCHOK singleton

652'''Some pre-defined L{Datum}s, all I{lazily} instantiated.'''

653# Datums with associated ellipsoid and Helmert transform parameters

654# to convert from WGS84 into the given datum. More are available at

655# <https://Earth-Info.NGA.mil/GandG/coordsys/datums/NATO_DT.pdf> and

656# <XXX://www.FieldenMaps.info/cconv/web/cconv_params.js>.

657 Datums._assert(

658 # Belgian Datum 1972, based on Hayford ellipsoid.

659 # <https://NL.WikiPedia.org/wiki/Belgian_Datum_1972>

660 # <https://SpatialReference.org/ref/sr-org/7718/html/>

661 BD72 = _lazy(_BD72_, _Intl1924_, _BD72_),

662

663 # Germany <https://WikiPedia.org/wiki/Bessel-Ellipsoid>

664 # <https://WikiPedia.org/wiki/Helmert_transformation>

665 DHDN = _lazy(_DHDN_, _Bessel1841_, _DHDN_),

666

667 # <https://www.Gov.UK/guidance/oil-and-gas-petroleum-operations-notices#pon-4>

668 ED50 = _lazy(_ED50_, _Intl1924_, _ED50_),

669

670 # Australia <https://ICSM.Gov.AU/datum/gda2020-and-gda94-technical-manuals>

671# ADG66 = _lazy(_ADG66_, _ANS_, _WGS84_), # XXX Transform?

672# ADG84 = _lazy(_ADG84_, _ANS_, _WGS84_), # XXX Transform?

673# GDA94 = _lazy(_GDA94_, _GRS80_, _WGS84_),

674 GDA2020 = _lazy(_GDA2020_, _GRS80_, _WGS84_), # XXX Transform?

675

676 # <https://WikiPedia.org/wiki/GRS_80>

677 GRS80 = _lazy(_GRS80_, _GRS80_, _WGS84_),

678

679 # <https://OSI.IE/wp-content/uploads/2015/05/transformations_booklet.pdf> Table 2

680# Irl1975 = _lazy(_Irl1965_, _AiryModified_, _Irl1965_),

681 Irl1975 = _lazy(_Irl1975_, _AiryModified_, _Irl1975_),

682

683 # Germany <https://WikiPedia.org/wiki/Helmert_transformation>

684 Krassovski1940 = _lazy(_Krassovski1940_, _Krassovski1940_, _Krassovski1940_), # XXX spelling?

685 Krassowsky1940 = _lazy(_Krassowsky1940_, _Krassowsky1940_, _Krassowsky1940_), # XXX spelling?

686

687 # Austria <https://DE.WikiPedia.org/wiki/Datum_Austria>

688 MGI = _lazy(_MGI_, _Bessel1841_, _MGI_),

689

690 # <https://WikiPedia.org/wiki/Helmert_transformation>

691 NAD27 = _lazy(_NAD27_, _Clarke1866_, _NAD27_),

692

693 # NAD83 (2009) == WGS84 - <https://www.UVM.edu/giv/resources/WGS84_NAD83.pdf>

694 # (If you *really* must convert WGS84<->NAD83, you need more than this!)

695 NAD83 = _lazy(_NAD83_, _GRS80_, _NAD83_),

696

697 # Nouvelle Triangulation Francaise (Paris) XXX verify

698 NTF = _lazy(_NTF_, _Clarke1880IGN_, _NTF_),

699

700 # <https://www.OrdnanceSurvey.co.UK/docs/support/guide-coordinate-systems-great-britain.pdf>

701 OSGB36 = _lazy(_OSGB36_, _Airy1830_, _OSGB36_),

702

703 # Germany <https://WikiPedia.org/wiki/Helmert_transformation>

704 Potsdam = _lazy(_Potsdam_, _Bessel1841_, _Bessel1841_),

705

706 # XXX psuedo-ellipsoids for spherical LatLon

707 Sphere = _lazy(_Sphere_, _Sphere_, _WGS84_),

708

709 # <https://www.GeoCachingToolbox.com?page=datumEllipsoidDetails>

710 TokyoJapan = _lazy(_TokyoJapan_, _Bessel1841_, _TokyoJapan_),

711

712 # <https://www.ICAO.int/safety/pbn/documentation/eurocontrol/eurocontrol%20wgs%2084%20implementation%20manual.pdf>

713 WGS72 = _lazy(_WGS72_, _WGS72_, _WGS72_),

714

715 WGS84 = _lazy(_WGS84_, _WGS84_, _WGS84_),

716)

717

718_WGS84 = Datums.WGS84

719 assert _WGS84.ellipsoid is _EWGS84

720# assert _WGS84.transform.isunity

721

722 if __name__ == '__main__':

723

724 from pygeodesy.interns import _COMMA_, _NL_, _NLATvar_

725 from pygeodesy.lazily import printf

726

727 # __doc__ of this file, force all into registery

728 for r in (Datums, Transforms):

729 t = [NN] + r.toRepr(all=True, asorted=True).split(_NL_)

730 printf(_NLATvar_.join(i.strip(_COMMA_) for i in t))

731

732# **) MIT License

733#

734# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

735#

736# Permission is hereby granted, free of charge, to any person obtaining a

737# copy of this software and associated documentation files (the "Software"),

738# to deal in the Software without restriction, including without limitation

739# the rights to use, copy, modify, merge, publish, distribute, sublicense,

740# and/or sell copies of the Software, and to permit persons to whom the

741# Software is furnished to do so, subject to the following conditions:

742#

743# The above copyright notice and this permission notice shall be included

744# in all copies or substantial portions of the Software.

745#

746# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

747# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

748# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

749# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

750# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

751# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

752# OTHER DEALINGS IN THE SOFTWARE.