Coverage for pygeodesy/datums.py: 95%

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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 or 

15above/below the earth’s surface, measured in degrees from the equator, from the International 

16Reference Meridian, in meters above the ellipsoid and based on a given datum. The datum in turn 

17is based on a reference ellipsoid and tied to geodetic survey reference points. 

18 

19Modern geodesy is generally based on the WGS84 datum (as used for instance by GPS systems), 

20but previously various reference ellipsoids and datum references were used. 

21 

22The UK Ordnance Survey National Grid References are still based on the otherwise historical 

23OSGB36 datum, q.v. U{"A Guide to Coordinate Systems in Great Britain", Section 6 

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

25 

26@var Datums.BD72: Datum(name='BD72', ellipsoid=Ellipsoids.Intl1924, transform=Transforms.BD72) 

27@var Datums.DHDN: Datum(name='DHDN', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.DHDN) 

28@var Datums.ED50: Datum(name='ED50', ellipsoid=Ellipsoids.Intl1924, transform=Transforms.ED50) 

29@var Datums.GDA2020: Datum(name='GDA2020', ellipsoid=Ellipsoids.GRS80, transform=Transforms.WGS84) 

30@var Datums.GRS80: Datum(name='GRS80', ellipsoid=Ellipsoids.GRS80, transform=Transforms.WGS84) 

31@var Datums.Irl1975: Datum(name='Irl1975', ellipsoid=Ellipsoids.AiryModified, transform=Transforms.Irl1975) 

32@var Datums.Krassovski1940: Datum(name='Krassovski1940', ellipsoid=Ellipsoids.Krassovski1940, transform=Transforms.Krassovski1940) 

33@var Datums.Krassowsky1940: Datum(name='Krassowsky1940', ellipsoid=Ellipsoids.Krassowsky1940, transform=Transforms.Krassowsky1940) 

34@var Datums.MGI: Datum(name='MGI', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.MGI) 

35@var Datums.NAD27: Datum(name='NAD27', ellipsoid=Ellipsoids.Clarke1866, transform=Transforms.NAD27) 

36@var Datums.NAD83: Datum(name='NAD83', ellipsoid=Ellipsoids.GRS80, transform=Transforms.NAD83) 

37@var Datums.NTF: Datum(name='NTF', ellipsoid=Ellipsoids.Clarke1880IGN, transform=Transforms.NTF) 

38@var Datums.OSGB36: Datum(name='OSGB36', ellipsoid=Ellipsoids.Airy1830, transform=Transforms.OSGB36) 

39@var Datums.Potsdam: Datum(name='Potsdam', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.Bessel1841) 

40@var Datums.Sphere: Datum(name='Sphere', ellipsoid=Ellipsoids.Sphere, transform=Transforms.WGS84) 

41@var Datums.TokyoJapan: Datum(name='TokyoJapan', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.TokyoJapan) 

42@var Datums.WGS72: Datum(name='WGS72', ellipsoid=Ellipsoids.WGS72, transform=Transforms.WGS72) 

43@var Datums.WGS84: Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84) 

44 

45@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) 

46@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) 

47@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) 

48@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) 

49@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) 

50@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) 

51@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) 

52@var Transforms.Irl1975: Transform(name='Irl1975', tx=-482.53, ty=130.596, tz=-564.557, rx=-0.00001, ry=-0, rz=-0, s=-1.1, s1=1, sx=-1.042, sy=-0.214, sz=-0.631) 

53@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) 

54@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) 

55@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) 

56@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) 

57@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) 

58@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) 

59@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) 

60@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) 

61@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) 

62@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) 

63''' 

64# make sure int/int division yields float quotient, see .basics 

65from __future__ import division as _; del _ # PYCHOK semicolon 

66 

67from pygeodesy.basics import islistuple, isscalar, map2, neg, _xinstanceof 

68from pygeodesy.constants import R_M, _float as _F, _0_0, _0_26, _1_0, _2_0, _8_0, _3600_0 

69from pygeodesy.ellipsoids import a_f2Tuple, Ellipsoid, Ellipsoid2, Ellipsoids, \ 

70 _EWGS84, Vector3Tuple 

71from pygeodesy.errors import _IsnotError, _xattr 

72from pygeodesy.fmath import fdot, fmean, Fmt 

73from pygeodesy.interns import NN, _a_, _Airy1830_, _AiryModified_, _Bessel1841_, _cartesian_, \ 

74 _Clarke1866_, _Clarke1880IGN_, _COMMASPACE_, _DOT_, _earth_, \ 

75 _ellipsoid_, _ellipsoidal_, _GRS80_, _Intl1924_, _Krassovski1940_, \ 

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

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

78 _WGS72_, _WGS84_, _under 

79from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS 

80from pygeodesy.named import _NamedEnum, _NamedEnumItem, \ 

81 _lazyNamedEnumItem as _lazy, Property_RO 

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

83# from pygeodesy.props import Property_RO # from .named 

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

85from pygeodesy.units import radians, Radius_ 

86 

87# from math import radians # from .units 

88 

89__all__ = _ALL_LAZY.datums 

90__version__ = '23.08.20' 

91 

92_a_ellipsoid_ = _UNDER_(_a_, _ellipsoid_) 

93_BD72_ = 'BD72' 

94_DHDN_ = 'DHDN' 

95_ED50_ = 'ED50' 

96_GDA2020_ = 'GDA2020' 

97_Identity_ = 'Identity' 

98_Inverse_ = 'Inverse' 

99_Irl1965_ = 'Irl1965' 

100_Irl1975_ = 'Irl1975' 

101_MGI_ = 'MGI' 

102_NTF_ = 'NTF' 

103_OSGB36_ = 'OSGB36' 

104_Potsdam_ = 'Potsdam' 

105_TokyoJapan_ = 'TokyoJapan' 

106 

107_r_s1 = radians(1 / _3600_0) # 1 degree second to radians 

108 

109 

110def _r_s2(s_): 

111 '''(INTERNAL) rotation in C{radians} and C{degree seconds}. 

112 ''' 

113 return _F(_r_s1 * s_), s_ 

114 

115 

116class Transform(_NamedEnumItem): 

117 '''Helmert transformation. 

118 

119 @see: L{Helmert7Tuple}. 

120 ''' 

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

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

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

124 

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

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

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

128 

129 s = _0_0 # scale ppm (C{float}) 

130 s1 = _1_0 # scale + 1 (C{float}) 

131 

132 sx = _0_0 # x rotation (degree seconds) 

133 sy = _0_0 # y rotation (degree seconds) 

134 sz = _0_0 # z rotation (degree seconds) 

135 

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

137 sx=0, sy=0, sz=0, s=0): 

138 '''New L{Transform}. 

139 

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

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

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

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

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

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

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

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

148 

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

150 ''' 

151 if tx: 

152 self.tx = tx 

153 if ty: 

154 self.ty = ty 

155 if tz: 

156 self.tz = tz 

157 if sx: # secs to rads 

158 self.rx, self.sx = _r_s2(sx) 

159 if sy: 

160 self.ry, self.sy = _r_s2(sy) 

161 if sz: 

162 self.rz, self.sz = _r_s2(sz) 

163 if s: 

164 self.s = s 

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

166 

167 self._register(Transforms, name) 

168 

169 def __eq__(self, other): 

170 '''Compare this and an other transform. 

171 

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

173 

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

175 ''' 

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

177 and self.tx == other.tx 

178 and self.ty == other.ty 

179 and self.tz == other.tz 

180 and self.rx == other.rx 

181 and self.ry == other.ry 

182 and self.rz == other.rz 

183 and self.s == other.s) 

184 

185 def __hash__(self): 

186 return self._hash # memoized 

187 

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

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

190 

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

192 ''' 

193 try: # only CartesianBase 

194 return other.toTransform(self) 

195 except AttributeError: 

196 pass 

197 raise _IsnotError(_cartesian_, other=other) 

198 

199 @Property_RO 

200 def _hash(self): 

201 return hash((self.rx, self.ry, self.rz, self.s, 

202 self.tx, self.ty, self.tz)) 

203 

204 def inverse(self, name=NN): 

205 '''Return the inverse of this transform. 

206 

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

208 

209 @return: Inverse (Transform). 

210 

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

212 ''' 

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

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

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

216 

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

218 '''Return this transform as a string. 

219 

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

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

222 this transform's name. 

223 

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

225 ''' 

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

227 'rx', 'ry', 'rz', _s_, 's1', 

228 _sx_, _sy_, _sz_) 

229 

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

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

232 

233 @arg x: X coordinate (C{meter}). 

234 @arg y: Y coordinate (C{meter}). 

235 @arg z: Z coordinate (C{meter}). 

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

237 

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

239 ''' 

240 xyz1 = x, y, z, _1_0 

241 s1 = self.s1 

242 if inverse: 

243 xyz1 = map2(neg, xyz1) 

244 s1 -= _2_0 # = -(1 - s * 1e-6)) = -(1 - (s1 - 1)) = -(2 - s1) 

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

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

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

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

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

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

251 name=self.name) 

252 

253 

254class Transforms(_NamedEnum): 

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

256 to accommodate the L{_LazyNamedEnumItem} properties. 

257 ''' 

258 def _Lazy(self, **name_tx_ty_tz_sx_sy_sz_s): 

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

260 ''' 

261 return Transform(**name_tx_ty_tz_sx_sy_sz_s) 

262 

263Transforms = Transforms(Transform) # PYCHOK singleton 

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

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

266Transforms._assert( 

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

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

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

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

271 s=_F( 1.2727)), 

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

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

274 s=_F( -8.3)), 

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

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

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

278 s=_F( -9.82)), # Germany 

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

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

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

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

283 sz=_F( 0.156), s=_F(-1.2)), 

284 Identity = _lazy(_Identity_), 

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

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

287 s=_F( -8.15)), 

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

289 # XXX rotation signs may be opposite, to be checked 

290 sx=_F( -1.042), sy=_F( -0.214), sz=_F( -0.631), 

291 s=_F( -1.1)), 

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

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

294 s=_F( -2.423)), # spelling 

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

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

297 s=_F( -2.423)), # spelling 

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

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

300 s=_F( -2.423)), # Austria 

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

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

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

304 s=_F(-0.0015)), 

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

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

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

308 s=_F( 20.4894)), 

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

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

311 WGS84 = _lazy(_WGS84_), # unity 

312) 

313 

314 

315class Datum(_NamedEnumItem): 

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

317 ''' 

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

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

320 

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

322 '''New L{Datum}. 

323 

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

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

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

327 

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

329 

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

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

332 not a L{Transform}. 

333 ''' 

334 self._ellipsoid = ellipsoid or Datum._ellipsoid 

335 _xinstanceof(Ellipsoid, ellipsoid=self.ellipsoid) 

336 

337 self._transform = transform or Datum._transform 

338 _xinstanceof(Transform, transform=self.transform) 

339 

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

341 

342 def __eq__(self, other): 

343 '''Compare this and an other datum. 

344 

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

346 

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

348 ''' 

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

350 self.ellipsoid == other.ellipsoid and 

351 self.transform == other.transform) 

352 

353 def __hash__(self): 

354 return self._hash # memoized 

355 

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

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

358 

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

360 ''' 

361 try: # only CartesianBase and EllipsoidalLatLonBase 

362 return other.toDatum(self) 

363 except AttributeError: 

364 pass 

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

366 

367 def ecef(self, Ecef=None): 

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

369 

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

371 

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

373 

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

375 

376 @see: Module L{pygeodesy.ecef}. 

377 ''' 

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

379 

380 @Property_RO 

381 def ellipsoid(self): 

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

383 ''' 

384 return self._ellipsoid 

385 

386 @Property_RO 

387 def exactTM(self): 

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

389 ''' 

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

391 

392 @Property_RO 

393 def _hash(self): 

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

395 

396 @Property_RO 

397 def isEllipsoidal(self): 

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

399 ''' 

400 return self.ellipsoid.isEllipsoidal 

401 

402 @Property_RO 

403 def isOblate(self): 

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

405 ''' 

406 return self.ellipsoid.isOblate 

407 

408 @Property_RO 

409 def isProlate(self): 

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

411 ''' 

412 return self.ellipsoid.isProlate 

413 

414 @Property_RO 

415 def isSpherical(self): 

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

417 ''' 

418 return self.ellipsoid.isSpherical 

419 

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

421 '''Return this datum as a string. 

422 

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

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

425 this datum's name. 

426 

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

428 ''' 

429 t = [] if name is None else \ 

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

431 for a in (_ellipsoid_, _transform_): 

432 v = getattr(self, a) 

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

434 return sep.join(t) 

435 

436 @Property_RO 

437 def transform(self): 

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

439 ''' 

440 return self._transform 

441 

442 

443def _En2(earth, name): 

444 '''(INTERNAL) Helper for C{_ellipsoid} and C{_ellipsoidal_datum}. 

445 ''' 

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

447 E = earth 

448 n = _under(name or E.name) 

449 elif isinstance(earth, Datum): 

450 E = earth.ellipsoid 

451 n = _under(name or earth.name) 

452 elif isinstance(earth, a_f2Tuple): 

453 n = _under(name or earth.name) 

454 E = Ellipsoid(earth.a, earth.b, name=n) 

455 elif islistuple(earth, minum=2): 

456 a, f = earth[:2] 

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

458 E = Ellipsoid(a, f=f, name=n) 

459 else: 

460 E, n = None, NN 

461 return E, n 

462 

463 

464def _a_ellipsoid(a_ellipsoid, f=None, name=NN, raiser=_a_ellipsoid_): # in .karney, .trf, ... 

465 '''(INTERNAL) Get an ellipsoid from C{(B{a_..}, B{f})} or C{B{.._ellipsoid}}, 

466 an L{Ellipsoid} or L{Ellipsoid2} from L{Datum} or C{a_f2Tuple}. 

467 ''' 

468 if f is None: 

469 E, _ = _En2(a_ellipsoid, name) 

470 if raiser and not E: 

471 _xinstanceof(Ellipsoid, Ellipsoid2, a_f2Tuple, Datum, **{raiser: a_ellipsoid}) 

472 else: 

473 E = Ellipsoid2(a_ellipsoid, f, name=name) 

474 return E 

475 

476 

477def _ellipsoidal_datum(earth, Error=TypeError, name=NN, raiser=NN): 

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

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

480 

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

482 ''' 

483 if isinstance(earth, Datum): 

484 d = earth 

485 else: 

486 E, n = _En2(earth, name) 

487 if not E: 

488 n = raiser or _earth_ 

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

490 d = Datum(E, transform=Transforms.Identity, name=n) 

491 if raiser and not d.isEllipsoidal: 

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

493 return d 

494 

495 

496def _mean_radius(radius, *lats): 

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

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

499 ''' 

500 if radius is R_M: 

501 r = radius 

502 elif isscalar(radius): 

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

504 else: 

505 E = _ellipsoidal_datum(radius).ellipsoid 

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

507 return r 

508 

509 

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

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

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

513 

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

515 ''' 

516 if isscalar(earth): 

517 E = Datums.Sphere.ellipsoid 

518 if earth == E.a == E.b and not name: 

519 d = Datums.Sphere 

520 else: 

521 r = Radius_(earth, Error=Error) # invalid datum 

522 n = _under(name) 

523 E = Ellipsoid(r, r, name=n) 

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

525 else: 

526 d = _ellipsoidal_datum(earth, Error=Error, name=name) 

527 if raiser and not d.isSpherical: 

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

529 return d 

530 

531 

532class Datums(_NamedEnum): 

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

534 to accommodate the L{_LazyNamedEnumItem} properties. 

535 ''' 

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

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

538 ''' 

539 return Datum(Ellipsoids.get(ellipsoid_name), 

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

541 

542Datums = Datums(Datum) # PYCHOK singleton 

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

544# Datums with associated ellipsoid and Helmert transform parameters 

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

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

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

548Datums._assert( 

549 # Belgian Datum 1972, based on Hayford ellipsoid. 

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

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

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

553 

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

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

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

557 

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

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

560 

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

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

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

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

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

566 

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

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

569 

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

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

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

573 

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

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

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

577 

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

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

580 

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

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

583 

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

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

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

587 

588 # Nouvelle Triangulation Francaise (Paris) XXX verify 

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

590 

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

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

593 

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

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

596 

597 # XXX psuedo-ellipsoids for spherical LatLon 

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

599 

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

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

602 

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

604 WGS72 = _lazy(_WGS72_, _WGS72_, _WGS72_), 

605 

606 WGS84 = _lazy(_WGS84_, _WGS84_, _WGS84_), 

607) 

608 

609_WGS84 = Datums.WGS84 

610assert _WGS84.ellipsoid is _EWGS84 

611 

612if __name__ == '__main__': 

613 

614 from pygeodesy.interns import _COMMA_, _NL_, _NLATvar_ 

615 from pygeodesy.lazily import printf 

616 

617 # __doc__ of this file, force all into registery 

618 for r in (Datums, Transforms): 

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

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

621 

622# **) MIT License 

623# 

624# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved. 

625# 

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

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

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

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

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

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

632# 

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

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

635# 

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

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

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

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

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

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

642# OTHER DEALINGS IN THE SOFTWARE.