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=106.86863, ty=-52.29778, tz=103.72389, rx=-0, ry=-0, rz=-0.00001, s=1.2727, s1=1, sx=-0.33657, sy=-0.45696, sz=-1.84218) 

47@var Transforms.Bessel1841: Transform(name='Bessel1841', tx=-582, ty=-105, tz=-414, rx=-0.00001, ry=-0, rz=0.00001, s=-8.3, s1=0.99999, sx=-1.04, sy=-0.35, sz=3.08) 

48@var Transforms.Clarke1866: Transform(name='Clarke1866', tx=8, ty=-160, tz=-176, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) 

49@var Transforms.DHDN: Transform(name='DHDN', tx=-591.28, ty=-81.35, tz=-396.39, rx=0.00001, ry=-0, rz=-0.00001, s=-9.82, s1=0.99999, sx=1.477, sy=-0.0736, sz=-1.458) 

50@var Transforms.DHDNE: Transform(name='DHDNE', tx=-612.4, ty=-77, tz=-440.2, rx=0, ry=-0, rz=0.00001, s=-2.55, s1=1, 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, rx=-0, ry=-0, rz=0.00001, s=-6.7, s1=0.99999, 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, rx=0, ry=0, rz=0, s=-1.2, s1=1, sx=0, sy=0, sz=0.156) 

53@var Transforms.Identity: Transform(name='Identity', tx=0, ty=0, tz=0, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) 

54@var Transforms.Irl1965: Transform(name='Irl1965', tx=-482.53, ty=130.596, tz=-564.557, rx=0.00001, ry=0, rz=0, s=-8.15, s1=0.99999, 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, rx=0.00001, ry=0, rz=0, s=-8.15, s1=0.99999, sx=1.042, sy=0.214, sz=0.631) 

56@var Transforms.Krassovski1940: Transform(name='Krassovski1940', tx=-24, ty=123, tz=94, rx=-0, ry=0, rz=0, s=-2.423, s1=1, sx=-0.02, sy=0.26, sz=0.13) 

57@var Transforms.Krassowsky1940: Transform(name='Krassowsky1940', tx=-24, ty=123, tz=94, rx=-0, ry=0, rz=0, s=-2.423, s1=1, 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, rx=0.00002, ry=0.00001, rz=0.00003, s=-2.423, s1=1, sx=5.137, sy=1.474, sz=5.297) 

59@var Transforms.NAD27: Transform(name='NAD27', tx=8, ty=-160, tz=-176, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) 

60@var Transforms.NAD83: Transform(name='NAD83', tx=1.004, ty=-1.91, tz=-0.515, rx=0, ry=0, rz=0, s=-0.0015, s1=1, sx=0.0267, sy=0.00034, sz=0.011) 

61@var Transforms.NTF: Transform(name='NTF', tx=-168, ty=-60, tz=320, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) 

62@var Transforms.OSGB36: Transform(name='OSGB36', tx=-446.448, ty=125.157, tz=-542.06, rx=-0, ry=-0, rz=-0, s=20.4894, s1=1.00002, sx=-0.1502, sy=-0.247, sz=-0.8421) 

63@var Transforms.TokyoJapan: Transform(name='TokyoJapan', tx=148, ty=-507, tz=-685, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) 

64@var Transforms.WGS72: Transform(name='WGS72', tx=0, ty=0, tz=-4.5, rx=0, ry=0, rz=0, s=-0.22, s1=1, sx=0, sy=0, sz=0.554) 

65@var Transforms.WGS84: Transform(name='WGS84', tx=0, ty=0, tz=0, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) # .isunity 

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 

72from pygeodesy.ellipsoids import a_f2Tuple, Ellipsoid, Ellipsoid2, Ellipsoids, \ 

73 _EWGS84, Vector3Tuple 

74from pygeodesy.errors import _IsnotError, _TypeError, _xattr 

75from pygeodesy.fmath import fdot, fmean, Fmt 

76from pygeodesy.interns import NN, _a_, _Airy1830_, _AiryModified_, _Bessel1841_, _cartesian_, \ 

77 _Clarke1866_, _Clarke1880IGN_, _COMMASPACE_, _DOT_, _earth_, \ 

78 _ellipsoid_, _ellipsoidal_, _GRS80_, _Intl1924_, _Krassovski1940_, \ 

79 _Krassowsky1940_, _NAD27_, _NAD83_, _s_, _Sphere_, _spherical_, \ 

80 _sx_, _sy_, _sz_, _transform_, _tx_, _ty_, _tz_, _UNDER_, \ 

81 _WGS72_, _WGS84_, _under 

82from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS 

83from pygeodesy.named import _NamedEnum, _NamedEnumItem, Property_RO, property_RO, \ 

84 _lazyNamedEnumItem as _lazy 

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

86# from pygeodesy.props import Property_RO, property_RO # from .named 

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

88from pygeodesy.units import _isRadius, radians, Radius_ 

89 

90# from math import radians # from .units 

91 

92__all__ = _ALL_LAZY.datums 

93__version__ = '24.01.25' 

94 

95_a_ellipsoid_ = _UNDER_(_a_, _ellipsoid_) 

96_BD72_ = 'BD72' 

97_DHDN_ = 'DHDN' 

98_DHDNE_ = 'DHDNE' 

99_DHDNW_ = 'DHDNW' 

100_ED50_ = 'ED50' 

101_GDA2020_ = 'GDA2020' 

102_Identity_ = 'Identity' 

103_Inverse_ = 'Inverse' 

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 

114def _rps2(s_): 

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

116 ''' 

117 return (_RPS * s_), s_ 

118 

119 

120class Transform(_NamedEnumItem): 

121 '''Helmert transformation. 

122 

123 @see: L{Helmert7Tuple}. 

124 ''' 

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

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

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

128 

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

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

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

132 

133 s = _0_0 # scale ppm (C{float}) 

134 s1 = _1_0 # scale + 1 (C{float}) 

135 

136 sx = _0_0 # x rotation (degree seconds) 

137 sy = _0_0 # y rotation (degree seconds) 

138 sz = _0_0 # z rotation (degree seconds) 

139 

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

141 sx=0, sy=0, sz=0, s=0): 

142 '''New L{Transform}. 

143 

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

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

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

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

148 @kwarg s: Optional scale (C{float}), ppm. 

149 @kwarg sx: Optional X rotation (C{degree seconds}). 

150 @kwarg sy: Optional Y rotation (C{degree seconds}). 

151 @kwarg sz: Optional Z rotation (C{degree seconds}). 

152 

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

154 ''' 

155 if tx: 

156 self.tx = tx 

157 if ty: 

158 self.ty = ty 

159 if tz: 

160 self.tz = tz 

161 if sx: # secs to rads 

162 self.rx, self.sx = _rps2(sx) 

163 if sy: 

164 self.ry, self.sy = _rps2(sy) 

165 if sz: 

166 self.rz, self.sz = _rps2(sz) 

167 if s: 

168 self.s = s 

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

170 

171 self._register(Transforms, name) 

172 

173 def __eq__(self, other): 

174 '''Compare this and an other transform. 

175 

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

177 

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

179 ''' 

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

181 and self.tx == other.tx 

182 and self.ty == other.ty 

183 and self.tz == other.tz 

184 and self.rx == other.rx 

185 and self.ry == other.ry 

186 and self.rz == other.rz 

187 and self.s == other.s) 

188 

189 def __hash__(self): 

190 return self._hash # memoized 

191 

192 def __matmul__(self, other): # PYCHOK Python 3.5+ 

193 '''Helmert-transform a cartesian B{C{other}}. 

194 

195 @raise TypeError: Invalid B{C{other}}. 

196 ''' 

197 try: # only CartesianBase 

198 return other.toTransform(self) 

199 except AttributeError: 

200 pass 

201 raise _IsnotError(_cartesian_, other=other) 

202 

203 @Property_RO 

204 def _hash(self): 

205 return hash((self.tx, self.ty, self.tz, 

206 self.rx, self.ry, self.rz, self.s)) 

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 (Transform). 

214 

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

216 ''' 

217 return Transform(name=name or (self.name + _Inverse_), 

218 tx=-self.tx, ty=-self.ty, tz=-self.tz, 

219 sx=-self.sx, sy=-self.sy, sz=-self.sz, s=-self.s) 

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((self.tx, self.ty, self.tz, 

226 self.rx, self.ry, self.rz, self.s)) 

227 

228 def toStr(self, prec=5, name=NN, **unused): # PYCHOK expected 

229 '''Return this transform as a string. 

230 

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

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

233 this transform's name. 

234 

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

236 ''' 

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

238 'rx', 'ry', 'rz', _s_, 's1', 

239 _sx_, _sy_, _sz_) 

240 

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

242 '''Transform a (geocentric) Cartesian point, forward or inverse. 

243 

244 @arg x: X coordinate (C{meter}). 

245 @arg y: Y coordinate (C{meter}). 

246 @arg z: Z coordinate (C{meter}). 

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

248 

249 @return: A L{Vector3Tuple}C{(x, y, z)}, transformed. 

250 ''' 

251 if self.isunity: 

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

253 

254 xyz1 = x, y, z, _1_0 

255 s1 = self.s1 

256 if inverse: 

257 xyz1 = map2(neg, xyz1) 

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

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

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

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

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

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

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

265 name=self.name) 

266 

267 

268class Transforms(_NamedEnum): 

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

270 to accommodate the L{_LazyNamedEnumItem} properties. 

271 ''' 

272 def _Lazy(self, **name_tx_ty_tz_sx_sy_sz_s): 

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

274 ''' 

275 return Transform(**name_tx_ty_tz_sx_sy_sz_s) 

276 

277Transforms = Transforms(Transform) # PYCHOK singleton 

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

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

280Transforms._assert( 

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

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

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

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

285 s=_F( 1.2727)), 

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

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

288 s=_F( -8.3)), 

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

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

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

292 s=_F( -9.82)), # Germany 

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

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

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

296 s=_F( -2.55)), # East Germany 

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

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

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

300 s=_F( -6.7)), # West Germany 

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

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

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

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

305 sz=_F( 0.156), s=_F(-1.2)), 

306 Identity = _lazy(_Identity_), 

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

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

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

310 s=_F( -8.15)), 

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

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

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

314 s=_F( -8.15)), 

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

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

317 s=_F( -2.423)), # spelling 

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

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

320 s=_F( -2.423)), # spelling 

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

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

323 s=_F( -2.423)), # Austria 

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

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

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

327 s=_F(-0.0015)), 

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

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

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

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

332 s=_F( 20.4894)), 

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

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

335 WGS84 = _lazy(_WGS84_), # unity 

336) 

337 

338 

339class Datum(_NamedEnumItem): 

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

341 ''' 

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

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

344 

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

346 '''New L{Datum}. 

347 

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

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

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

351 

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

353 

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

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

356 not a L{Transform}. 

357 ''' 

358 self._ellipsoid = ellipsoid or Datum._ellipsoid 

359 _xinstanceof(Ellipsoid, ellipsoid=self.ellipsoid) 

360 

361 self._transform = transform or Datum._transform 

362 _xinstanceof(Transform, transform=self.transform) 

363 

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

365 

366 def __eq__(self, other): 

367 '''Compare this and an other datum. 

368 

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

370 

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

372 ''' 

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

374 self.ellipsoid == other.ellipsoid and 

375 self.transform == other.transform) 

376 

377 def __hash__(self): 

378 return self._hash # memoized 

379 

380 def __matmul__(self, other): # PYCHOK Python 3.5+ 

381 '''Convert cartesian or ellipsoidal B{C{other}} to this datum. 

382 

383 @raise TypeError: Invalid B{C{other}}. 

384 ''' 

385 try: # only CartesianBase and LatLonEllipsoidalBase 

386 return other.toDatum(self) 

387 except AttributeError: 

388 pass 

389 raise _IsnotError(_cartesian_, _ellipsoidal_, other=other) 

390 

391 def ecef(self, Ecef=None): 

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

393 

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

395 

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

397 

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

399 

400 @see: Module L{pygeodesy.ecef}. 

401 ''' 

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

403 

404 @Property_RO 

405 def ellipsoid(self): 

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

407 ''' 

408 return self._ellipsoid 

409 

410 @Property_RO 

411 def exactTM(self): 

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

413 ''' 

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

415 

416 @Property_RO 

417 def _hash(self): 

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

419 

420 @property_RO 

421 def isEllipsoidal(self): 

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

423 ''' 

424 return self.ellipsoid.isEllipsoidal 

425 

426 @property_RO 

427 def isOblate(self): 

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

429 ''' 

430 return self.ellipsoid.isOblate 

431 

432 @property_RO 

433 def isProlate(self): 

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

435 ''' 

436 return self.ellipsoid.isProlate 

437 

438 @property_RO 

439 def isSpherical(self): 

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

441 ''' 

442 return self.ellipsoid.isSpherical 

443 

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

445 '''Return this datum as a string. 

446 

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

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

449 this datum's name. 

450 

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

452 ''' 

453 t = [] if name is None else \ 

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

455 for a in (_ellipsoid_, _transform_): 

456 v = getattr(self, a) 

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

458 return sep.join(t) 

459 

460 @Property_RO 

461 def transform(self): 

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

463 ''' 

464 return self._transform 

465 

466 

467def _earth_datum(inst, a_earth, f=None, name=NN, raiser=_a_ellipsoid_): # in .karney, .trf, ... 

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

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

470 

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

472 ''' 

473 if f is not None: 

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

475 if raiser and not E: 

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

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

478 return 

479 elif isinstance(a_earth, Datum): 

480 E, n, D = None, NN, a_earth 

481 else: 

482 E, n, D = _EnD3(a_earth, name) 

483 if raiser and not E: 

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

485 if D is None: 

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

487 inst._datum = D 

488 

489 

490def _earth_ellipsoid(earth, *name_raiser): 

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

492 ''' 

493 return Ellipsoids.Sphere if earth is R_M else ( 

494 _EWGS84 if earth is _EWGS84 or earth is _WGS84 else 

495 _spherical_datum(earth, *name_raiser).ellipsoid) 

496 

497 

498def _ED2(radius, name): 

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

500 ''' 

501 D = Datums.Sphere 

502 E = D.ellipsoid 

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

504 n = _under(name) 

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

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

507 return E, D 

508 

509 

510def _ellipsoidal_datum(earth, Error=TypeError, name=NN, raiser=NN): 

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

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

513 

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

515 ''' 

516 if isinstance(earth, Datum): 

517 D = earth 

518 else: 

519 E, n, D = _EnD3(earth, name) 

520 if not E: 

521 n = raiser or _earth_ 

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

523 if D is None: 

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

525 if raiser and not D.isEllipsoidal: 

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

527 return D 

528 

529 

530def _EnD3(earth, name): 

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

532 ''' 

533 D = None 

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

535 E = earth 

536 n = _under(name or E.name) 

537 elif isinstance(earth, Datum): 

538 E = earth.ellipsoid 

539 n = _under(name or earth.name) 

540 D = earth 

541 elif _isRadius(earth): 

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

543 n = E.name 

544 elif isinstance(earth, a_f2Tuple): 

545 n = _under(name or earth.name) 

546 E = earth.ellipsoid(name=n) 

547 elif islistuple(earth, minum=2): 

548 E = Ellipsoids.Sphere 

549 a, f = earth[:2] 

550 if f or a != E.a: # != E.b 

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

552 E = Ellipsoid(a, f=f, name=n) 

553 else: 

554 n = E.name 

555 D = Datums.Sphere 

556 else: 

557 E, n = None, NN 

558 return E, n, D 

559 

560 

561def _mean_radius(radius, *lats): 

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

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

564 ''' 

565 if radius is R_M: 

566 r = radius 

567 elif _isRadius(radius): 

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

569 else: 

570 E = _ellipsoidal_datum(radius).ellipsoid 

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

572 return r 

573 

574 

575def _spherical_datum(earth, Error=TypeError, name=NN, raiser=NN): 

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

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

578 

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

580 ''' 

581 if _isRadius(earth): 

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

583 else: 

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

585 if raiser and not D.isSpherical: 

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

587 return D 

588 

589 

590class Datums(_NamedEnum): 

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

592 to accommodate the L{_LazyNamedEnumItem} properties. 

593 ''' 

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

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

596 ''' 

597 return Datum(Ellipsoids.get(ellipsoid_name), 

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

599 

600Datums = Datums(Datum) # PYCHOK singleton 

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

602# Datums with associated ellipsoid and Helmert transform parameters 

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

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

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

606Datums._assert( 

607 # Belgian Datum 1972, based on Hayford ellipsoid. 

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

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

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

611 

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

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

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

615 

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

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

618 

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

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

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

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

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

624 

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

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

627 

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

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

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

631 

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

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

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

635 

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

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

638 

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

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

641 

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

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

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

645 

646 # Nouvelle Triangulation Francaise (Paris) XXX verify 

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

648 

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

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

651 

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

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

654 

655 # XXX psuedo-ellipsoids for spherical LatLon 

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

657 

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

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

660 

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

662 WGS72 = _lazy(_WGS72_, _WGS72_, _WGS72_), 

663 

664 WGS84 = _lazy(_WGS84_, _WGS84_, _WGS84_), 

665) 

666 

667_WGS84 = Datums.WGS84 

668assert _WGS84.ellipsoid is _EWGS84 

669# assert _WGS84.transform.isunity 

670 

671if __name__ == '__main__': 

672 

673 from pygeodesy.interns import _COMMA_, _NL_, _NLATvar_ 

674 from pygeodesy.lazily import printf 

675 

676 # __doc__ of this file, force all into registery 

677 for r in (Datums, Transforms): 

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

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

680 

681# **) MIT License 

682# 

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

684# 

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

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

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

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

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

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

691# 

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

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

694# 

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

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

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

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

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

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

701# OTHER DEALINGS IN THE SOFTWARE.