Coverage for pygeodesy/datums.py: 94%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''Datums and transformations thereof. 

5 

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

7 

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>}. 

13 

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. 

19 

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. 

22 

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>}. 

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 

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

69 

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 

91 

92# from math import radians # from .units 

93 

94__all__ = _ALL_LAZY.datums 

95__version__ = '24.02.18' 

96 

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' 

116 

117 

118class Transform(_NamedEnumItem): 

119 '''Helmert I{datum} transformation. 

120 

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}) 

126 

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

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

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

130 

131 s = _0_0 # scale ppm (C{float}) 

132 s1 = _1_0 # scale + 1 (C{float}) 

133 

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}) 

137 

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}. 

141 

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}). 

150 

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) 

168 

169 self._register(Transforms, name) 

170 

171 def __eq__(self, other): 

172 '''Compare this and an other transform. 

173 

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

175 

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))) 

180 

181 def __hash__(self): 

182 return self._hash # memoized 

183 

184 def __iter__(self): 

185 '''Yield the initial attribute values. 

186 ''' 

187 for _, x in self.items(): 

188 yield x 

189 

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

191 '''Convert an I{ellipsoidal} B{C{point}} with the Helmert transform. 

192 

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

194 ''' 

195 _ = _xellipsoidall(point) 

196 return point.toTransform(self) 

197 

198 def __neg__(self): 

199 return self.inverse() 

200 

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 

209 

210 @Property_RO 

211 def _hash(self): 

212 return hash(x for x in self) 

213 

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) 

219 

220 def inverse(self, name=NN): 

221 '''Return the inverse of this transform. 

222 

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

224 

225 @return: Inverse (L{Transform}). 

226 

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) 

232 

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) 

238 

239 def _rps2(self, s_): 

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

241 ''' 

242 return (_RPS * s_), s_ 

243 

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

245 '''Return this transform as a string. 

246 

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. 

251 

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

253 ''' 

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

255 

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

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

258 

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. 

267 

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 

291 

292 

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) 

301 

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) 

362 

363 

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}) 

369 

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

371 '''New L{Datum}. 

372 

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}). 

376 

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

378 

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) 

385 

386 self._transform = transform or Datum._transform 

387 _xinstanceof(Transform, transform=self.transform) 

388 

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

390 

391 def __eq__(self, other): 

392 '''Compare this and an other datum. 

393 

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

395 

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) 

401 

402 def __hash__(self): 

403 return self._hash # memoized 

404 

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

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

407 

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

409 ''' 

410 _ = _xellipsoidall(point) 

411 return point.toDatum(self) 

412 

413 def ecef(self, Ecef=None): 

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

415 

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

417 

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

419 

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

421 

422 @see: Module L{pygeodesy.ecef}. 

423 ''' 

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

425 

426 @Property_RO 

427 def ellipsoid(self): 

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

429 ''' 

430 return self._ellipsoid 

431 

432 @Property_RO 

433 def exactTM(self): 

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

435 ''' 

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

437 

438 @Property_RO 

439 def _hash(self): 

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

441 

442 @property_RO 

443 def isEllipsoidal(self): 

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

445 ''' 

446 return self.ellipsoid.isEllipsoidal 

447 

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 

453 

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 

459 

460 @property_RO 

461 def isSpherical(self): 

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

463 ''' 

464 return self.ellipsoid.isSpherical 

465 

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

467 '''Return this datum as a string. 

468 

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. 

472 

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) 

481 

482 @Property_RO 

483 def transform(self): 

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

485 ''' 

486 return self._transform 

487 

488 

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). 

492 

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 

510 

511 

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) 

518 

519 

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 

530 

531 

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. 

535 

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 

550 

551 

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 

581 

582 

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 

595 

596 

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) 

602 

603 

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. 

607 

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 

617 

618 

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) 

628 

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_), 

640 

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

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

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

644 

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

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

647 

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? 

653 

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

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

656 

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_), 

660 

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

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

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

664 

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

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

667 

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

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

670 

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_), 

674 

675 # Nouvelle Triangulation Francaise (Paris) XXX verify 

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

677 

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

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

680 

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

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

683 

684 # XXX psuedo-ellipsoids for spherical LatLon 

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

686 

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

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

689 

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

691 WGS72 = _lazy(_WGS72_, _WGS72_, _WGS72_), 

692 

693 WGS84 = _lazy(_WGS84_, _WGS84_, _WGS84_), 

694) 

695 

696_WGS84 = Datums.WGS84 

697assert _WGS84.ellipsoid is _EWGS84 

698# assert _WGS84.transform.isunity 

699 

700if __name__ == '__main__': 

701 

702 from pygeodesy.interns import _COMMA_, _NL_, _NLATvar_ 

703 from pygeodesy.lazily import printf 

704 

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)) 

709 

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.