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=106.869, ty=-52.2978, tz=103.724, s1=1.0, rx=-1.63174e-06, ry=-2.21538e-06, rz=-8.93114e-06, s=1.2727, sx=-0.33657, sy=-0.456955, sz=-1.84218)

47@var Transforms.Bessel1841: Transform(name='Bessel1841', tx=-582, ty=-105, tz=-414, s1=0.999992, rx=-5.04206e-06, ry=-1.69685e-06, rz=1.49323e-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=-3.56823e-07, rz=-7.06858e-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=0.999997, rx=2.61799e-07, ry=-2.76344e-07, rz=1.35602e-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=0.999993, rx=-9.79324e-07, ry=-2.18166e-07, rz=1.19022e-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=0.999999, rx=0.0, ry=0.0, rz=7.56309e-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=130.596, tz=-564.557, s1=0.999992, rx=5.05176e-06, ry=1.0375e-06, rz=3.05917e-06, s=-8.15, sx=1.042, sy=0.214, sz=0.631)

55@var Transforms.Irl1975: Transform(name='Irl1975', tx=-482.53, ty=130.596, tz=-564.557, s1=0.999992, rx=5.05176e-06, ry=1.0375e-06, rz=3.05917e-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=0.999998, rx=-9.69627e-08, ry=1.26052e-06, rz=6.30258e-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=0.999998, rx=-9.69627e-08, ry=1.26052e-06, rz=6.30258e-07, s=-2.423, sx=-0.02, sy=0.26, sz=0.13)

58@var Transforms.MGI: Transform(name='MGI', tx=-577.326, ty=-90.129, tz=-463.92, s1=0.999998, rx=2.49049e-05, ry=7.14615e-06, rz=2.56806e-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=1.29445e-07, ry=1.64837e-09, rz=5.33295e-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=-446.448, ty=125.157, tz=-542.06, s1=1.00002, rx=-7.2819e-07, ry=-1.19749e-06, rz=-4.08262e-06, s=20.4894, 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=2.68587e-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, _xinstanceof

71 from 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

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

75 Vector3Tuple

76 from pygeodesy.errors import _IsnotError, _TypeError, _xattr

77 from pygeodesy.fmath import fdot, fmean, Fmt

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

79 _Clarke1866_, _Clarke1880IGN_, _COMMASPACE_, _DOT_, _earth_, \

80 _ellipsoid_, _ellipsoidal_, _GRS80_, _Intl1924_, _MINUS_, \

81 _Krassovski1940_, _Krassowsky1940_, _NAD27_, _NAD83_, _s_, \

82 _Sphere_, _spherical_, _sx_, _sy_, _sz_, _transform_, _tx_, \

83 _ty_, _tz_, _UNDER_, _WGS72_, _WGS84_, _under

84 from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS

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

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

87 from pygeodesy.props import Property_RO, property_RO

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

89 from pygeodesy.units import _isRadius, Radius_, radians

90

91# from math import radians # from .units

92

93__all__ = _ALL_LAZY.datums

94__version__ = '24.02.06'

95

96_a_ellipsoid_ = _UNDER_(_a_, _ellipsoid_)

97_BD72_ = 'BD72'

98_DHDN_ = 'DHDN'

99_DHDNE_ = 'DHDNE'

100_DHDNW_ = 'DHDNW'

101_ED50_ = 'ED50'

102_GDA2020_ = 'GDA2020'

103_Identity_ = 'Identity'

104_Irl1965_ = 'Irl1965'

105_Irl1975_ = 'Irl1975'

106_MGI_ = 'MGI'

107_NTF_ = 'NTF'

108_OSGB36_ = 'OSGB36'

109_Potsdam_ = 'Potsdam'

110_RPS = radians(_1_0 / _3600_0) # radians per degree-second

111_TokyoJapan_ = 'TokyoJapan'

112

113

114 class Transform(_NamedEnumItem):

115 '''Helmert I{datum} transformation.

116

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

118 '''

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

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

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

122

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

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

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

126

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

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

129

130 sx = _0_0 # x rotation (C{degree-seconds})

131 sy = _0_0 # y rotation (C{degree-seconds})

132 sz = _0_0 # z rotation (C{degree-seconds})

133

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

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

136 '''New L{Transform}.

137

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

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

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

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

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

143 @kwarg sx: X rotation (C{degree-seconds}).

144 @kwarg sy: Y rotation (C{degree-seconds}).

145 @kwarg sz: Z rotation (C{degree-seconds}).

146

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

148 '''

149 if tx:

150 self.tx = tx

151 if ty:

152 self.ty = ty

153 if tz:

154 self.tz = tz

155 if sx: # secs to rads

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

157 if sy:

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

159 if sz:

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

161 if s:

162 self.s = s

163 self.s1 = _F(s * 1e-6 + _1_0) # normalize ppm to (s + 1)

164

165 self._register(Transforms, name)

166

167 def __eq__(self, other):

168 '''Compare this and an other transform.

169

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

171

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

173 '''

174 return self is other or (isinstance(other, Transform) and all(

175 s == t for s, t in zip(self, other)))

176

177 def __hash__(self):

178 return self._hash # memoized

179

180 def __iter__(self):

181 '''Yield the attribute values.

182 '''

183 for _, x in self.items():

184 yield x

185

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

187 '''Helmert-transform an I{ellipsoidal} cartesian B{C{point}}.

188

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

190 '''

191 m = _MODS.ellipsoidalBase

192 _xinstanceof(m.CartesianEllipsoidalBase, point=point)

193 return point.toTransform(self)

194

195 def __neg__(self):

196 return self.inverse()

197

198 @Property_RO

199 def _hash(self):

200 return hash(x for x in self)

201

202 def items(self):

203 '''Yield each attribute as 2-tuple C{(name, value)}.

204 '''

205 for n in (_tx_, _ty_, _tz_, _s_, _sx_, _sy_, _sz_):

206 yield n, getattr(self, n)

207

208 def inverse(self, name=NN):

209 '''Return the inverse of this transform.

210

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

212

213 @return: Inverse (L{Transform}).

214

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

216 '''

217 d = dict((n, -v) for n, v in self.items())

218 n = name or _minus(self.name)

219 return type(self)(name=n, **d)

220

221 @Property_RO

222 def isunity(self):

223 '''Is this a C{unity, identidy} transform (C{bool}), like WGS84?

224 '''

225 return not any(s for s in self)

226

227 def _rps2(self, s_):

228 '''(INTERNAL) Rotation in C{radians} and C{degree-seconds}.

229 '''

230 return (_RPS * s_), s_

231

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

233 '''Return this transform as a string.

234

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

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

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

238 this transform's name.

239

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

241 '''

242 return self._instr(name, prec, _tx_, _ty_, _tz_,

243 's1', 'rx', 'ry', 'rz',

244 _s_, _sx_, _sy_, _sz_, fmt=fmt)

245

246 def transform(self, x, y, z, inverse=False):

247 '''Transform a (geocentric) position, forward or inverse.

248

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

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

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

252 @kwarg inverse: Optional direction, forward or inverse (C{bool}).

253

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

255 '''

256 if self.isunity:

257 return Vector3Tuple(x, y, z, name=self.name)

258

259 xyz1 = x, y, z, _1_0

260 s1 = self.s1

261 if inverse:

262 xyz1 = map2(neg, xyz1)

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

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

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

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

267 return Vector3Tuple(fdot(xyz1, s1, -self.rz, self.ry, self.tx),

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

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

270 name=self.name)

271

272

273 class Transforms(_NamedEnum):

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

275 to accommodate the L{_LazyNamedEnumItem} properties.

276 '''

277 def _Lazy(self, **name_tx_ty_tz_sx_sy_sz_s):

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

279 '''

280 return Transform(**name_tx_ty_tz_sx_sy_sz_s)

281

282 Transforms = Transforms(Transform) # PYCHOK singleton

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

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

285 Transforms._assert(

286 BD72 = _lazy(_BD72_, tx=_F(106.868628), ty=_F(-52.297783), tz=_F(103.723893),

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

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

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

290 s=_F( 1.2727)),

291 Bessel1841 = _lazy(_Bessel1841_, tx=_F(-582.0), ty=_F(-105.0), tz=_F(-414.0),

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

293 s=_F( -8.3)),

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

295 DHDN = _lazy(_DHDN_, tx=_F(-591.28), ty=_F(-81.35), tz=_F(-396.39),

296 sx=_F( 1.477), sy=_F( -0.0736), sz=_F( -1.458),

297 s=_F( -9.82)), # Germany

298 DHDNE = _lazy(_DHDNE_, tx=_F(-612.4), ty=_F(-77.0), tz=_F(-440.2),

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

300 sx=_F( 0.054), sy=_F( -0.057), sz=_F( 2.797),

301 s=_F( -2.55)), # East Germany

302 DHDNW = _lazy(_DHDNW_, tx=_F(-598.1), ty=_F(-73.7), tz=_F(-418.2),

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

304 sx=_F( -0.202), sy=_F( -0.045), sz=_F( 2.455),

305 s=_F( -6.7)), # West Germany

306 ED50 = _lazy(_ED50_, tx=_F(89.5), ty=_F(93.8), tz=_F(123.1),

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

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

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

310 sz=_F( 0.156), s=_F(-1.2)),

311 Identity = _lazy(_Identity_),

312 Irl1965 = _lazy(_Irl1965_, tx=_F(-482.530), ty=_F(130.596), tz=_F(-564.557),

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

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

315 s=_F( -8.15)),

316 Irl1975 = _lazy(_Irl1975_, tx=_F(-482.530), ty=_F(130.596), tz=_F(-564.557),

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

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

319 s=_F( -8.15)),

320 Krassovski1940 = _lazy(_Krassovski1940_, tx=_F(-24.0), ty=_F(123.0), tz=_F(94.0),

321 sx=_F( -0.02), sy= _0_26, sz=_F( 0.13),

322 s=_F( -2.423)), # spelling

323 Krassowsky1940 = _lazy(_Krassowsky1940_, tx=_F(-24.0), ty=_F(123.0), tz=_F(94.0),

324 sx=_F( -0.02), sy= _0_26, sz=_F( 0.13),

325 s=_F( -2.423)), # spelling

326 MGI = _lazy(_MGI_, tx=_F(-577.326), ty=_F(-90.129), tz=_F(-463.920),

327 sx=_F( 5.137), sy=_F( 1.474), sz=_F( 5.297),

328 s=_F( -2.423)), # Austria

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

330 NAD83 = _lazy(_NAD83_, tx=_F( 1.004), ty=_F(-1.910), tz=_F(-0.515),

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

332 s=_F(-0.0015)),

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

334 OSGB36 = _lazy(_OSGB36_, tx=_F(-446.448), ty=_F(125.157), tz=_F(-542.060),

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

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

337 s=_F( 20.4894)),

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

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

340 WGS84 = _lazy(_WGS84_), # unity

341)

342

343

344 class Datum(_NamedEnumItem):

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

346 '''

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

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

349

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

351 '''New L{Datum}.

352

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

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

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

356

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

358

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

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

361 not a L{Transform}.

362 '''

363 self._ellipsoid = ellipsoid or Datum._ellipsoid

364 _xinstanceof(Ellipsoid, ellipsoid=self.ellipsoid)

365

366 self._transform = transform or Datum._transform

367 _xinstanceof(Transform, transform=self.transform)

368

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

370

371 def __eq__(self, other):

372 '''Compare this and an other datum.

373

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

375

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

377 '''

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

379 self.ellipsoid == other.ellipsoid and

380 self.transform == other.transform)

381

382 def __hash__(self):

383 return self._hash # memoized

384

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

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

387

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

389 '''

390 m = _MODS.ellipsoidalBase

391 _xinstanceof(m.CartesianEllipsoidalBase, m.LatLonEllipsoidalBase, point=point)

392 return point.toDatum(self)

393

394 def ecef(self, Ecef=None):

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

396

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

398

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

400

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

402

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

404 '''

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

406

407 @Property_RO

408 def ellipsoid(self):

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

410 '''

411 return self._ellipsoid

412

413 @Property_RO

414 def exactTM(self):

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

416 '''

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

418

419 @Property_RO

420 def _hash(self):

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

422

423 @property_RO

424 def isEllipsoidal(self):

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

426 '''

427 return self.ellipsoid.isEllipsoidal

428

429 @property_RO

430 def isOblate(self):

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

432 '''

433 return self.ellipsoid.isOblate

434

435 @property_RO

436 def isProlate(self):

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

438 '''

439 return self.ellipsoid.isProlate

440

441 @property_RO

442 def isSpherical(self):

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

444 '''

445 return self.ellipsoid.isSpherical

446

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

448 '''Return this datum as a string.

449

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

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

452 this datum's name.

453

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

455 '''

456 t = [] if name is None else \

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

458 for a in (_ellipsoid_, _transform_):

459 v = getattr(self, a)

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

461 return sep.join(t)

462

463 @Property_RO

464 def transform(self):

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

466 '''

467 return self._transform

468

469

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

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

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

473

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

475 '''

476 if f is not None:

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

478 if raiser and not E:

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

480 elif a_earth is _EWGS84 or a_earth in (_EWGS84, _WGS84, None):

481 return

482 elif isinstance(a_earth, Datum):

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

484 else:

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

486 if raiser and not E:

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

488 if D is None:

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

490 inst._datum = D

491

492

493 def _earth_ellipsoid(earth, *name_raiser):

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

495 '''

496 return Ellipsoids.Sphere if earth is R_M else (

497 _EWGS84 if earth is _EWGS84 or earth is _WGS84 else

498 _spherical_datum(earth, *name_raiser).ellipsoid)

499

500

501 def _ED2(radius, name):

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

503 '''

504 D = Datums.Sphere

505 E = D.ellipsoid

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

507 n = _under(name)

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

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

510 return E, D

511

512

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

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

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

516

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

518 '''

519 if isinstance(earth, Datum):

520 D = earth

521 else:

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

523 if not E:

524 n = raiser or _earth_

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

526 if D is None:

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

528 if raiser and not D.isEllipsoidal:

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

530 return D

531

532

533 def _EnD3(earth, name):

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

535 '''

536 D = None

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

538 E = earth

539 n = _under(name or E.name)

540 elif isinstance(earth, Datum):

541 E = earth.ellipsoid

542 n = _under(name or earth.name)

543 D = earth

544 elif _isRadius(earth):

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

546 n = E.name

547 elif isinstance(earth, a_f2Tuple):

548 n = _under(name or earth.name)

549 E = earth.ellipsoid(name=n)

550 elif islistuple(earth, minum=2):

551 E = Ellipsoids.Sphere

552 a, f = earth[:2]

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

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

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

556 else:

557 n = E.name

558 D = Datums.Sphere

559 else:

560 E, n = None, NN

561 return E, n, D

562

563

564 def _mean_radius(radius, *lats):

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

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

567 '''

568 if radius is R_M:

569 r = radius

570 elif _isRadius(radius):

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

572 else:

573 E = _ellipsoidal_datum(radius).ellipsoid

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

575 return r

576

577

578 def _minus(name): # in .trf

579 '''(INTERNAL) Name of C{inverse} Xform.

580 '''

581 m = _MINUS_

582 return name[len(m):] if name.startswith(m) else NN(m, name)

583

584

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

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

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

588

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

590 '''

591 if _isRadius(earth):

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

593 else:

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

595 if raiser and not D.isSpherical:

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

597 return D

598

599

600 class Datums(_NamedEnum):

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

602 to accommodate the L{_LazyNamedEnumItem} properties.

603 '''

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

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

606 '''

607 return Datum(Ellipsoids.get(ellipsoid_name),

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

609

610 Datums = Datums(Datum) # PYCHOK singleton

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

612# Datums with associated ellipsoid and Helmert transform parameters

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

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

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

616 Datums._assert(

617 # Belgian Datum 1972, based on Hayford ellipsoid.

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

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

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

621

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

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

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

625

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

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

628

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

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

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

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

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

634

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

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

637

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

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

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

641

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

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

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

645

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

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

648

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

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

651

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

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

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

655

656 # Nouvelle Triangulation Francaise (Paris) XXX verify

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

658

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

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

661

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

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

664

665 # XXX psuedo-ellipsoids for spherical LatLon

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

667

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

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

670

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

672 WGS72 = _lazy(_WGS72_, _WGS72_, _WGS72_),

673

674 WGS84 = _lazy(_WGS84_, _WGS84_, _WGS84_),

675)

676

677_WGS84 = Datums.WGS84

678 assert _WGS84.ellipsoid is _EWGS84

679# assert _WGS84.transform.isunity

680

681 if __name__ == '__main__':

682

683 from pygeodesy.interns import _COMMA_, _NL_, _NLATvar_

684 from pygeodesy.lazily import printf

685

686 # __doc__ of this file, force all into registery

687 for r in (Datums, Transforms):

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

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

690

691# **) MIT License

692#

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

694#

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

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

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

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

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

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

701#

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

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

704#

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

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

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

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

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

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

711# OTHER DEALINGS IN THE SOFTWARE.