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, Vector3Tuple 

70from pygeodesy.errors import _IsnotError, _xattr 

71from pygeodesy.fmath import fdot, fmean, Fmt 

72from pygeodesy.interns import NN, _a_, _Airy1830_, _AiryModified_, _Bessel1841_, _cartesian_, \ 

73 _Clarke1866_, _Clarke1880IGN_, _COMMASPACE_, _DOT_, _earth_, \ 

74 _ellipsoid_, _ellipsoidal_, _GRS80_, _Intl1924_, _Krassovski1940_, \ 

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

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

77 _WGS72_, _WGS84_, _under 

78from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS 

79from pygeodesy.named import _NamedEnum, _NamedEnumItem, \ 

80 _lazyNamedEnumItem as _lazy, Property_RO 

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

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

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

84from pygeodesy.units import radians, Radius_ 

85 

86# from math import radians # from .units 

87 

88__all__ = _ALL_LAZY.datums 

89__version__ = '23.08.05' 

90 

91_a_ellipsoid_ = _UNDER_(_a_, _ellipsoid_) 

92_BD72_ = 'BD72' 

93_DHDN_ = 'DHDN' 

94_ED50_ = 'ED50' 

95_GDA2020_ = 'GDA2020' 

96_Identity_ = 'Identity' 

97_Inverse_ = 'Inverse' 

98_Irl1965_ = 'Irl1965' 

99_Irl1975_ = 'Irl1975' 

100_MGI_ = 'MGI' 

101_NTF_ = 'NTF' 

102_OSGB36_ = 'OSGB36' 

103_Potsdam_ = 'Potsdam' 

104_TokyoJapan_ = 'TokyoJapan' 

105 

106_r_s1 = radians(1 / _3600_0) # 1 degree second to radians 

107 

108 

109def _r_s2(s_): 

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

111 ''' 

112 return _F(_r_s1 * s_), s_ 

113 

114 

115class Transform(_NamedEnumItem): 

116 '''Helmert transformation. 

117 

118 @see: L{Helmert7Tuple}. 

119 ''' 

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

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

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

123 

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

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

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

127 

128 s = _0_0 # scale ppm (C{float}) 

129 s1 = _1_0 # scale + 1 (C{float}) 

130 

131 sx = _0_0 # x rotation (degree seconds) 

132 sy = _0_0 # y rotation (degree seconds) 

133 sz = _0_0 # z rotation (degree seconds) 

134 

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

136 sx=0, sy=0, sz=0, s=0): 

137 '''New L{Transform}. 

138 

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

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

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

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

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

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

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

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

147 

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

149 ''' 

150 if tx: 

151 self.tx = tx 

152 if ty: 

153 self.ty = ty 

154 if tz: 

155 self.tz = tz 

156 if sx: # secs to rads 

157 self.rx, self.sx = _r_s2(sx) 

158 if sy: 

159 self.ry, self.sy = _r_s2(sy) 

160 if sz: 

161 self.rz, self.sz = _r_s2(sz) 

162 if s: 

163 self.s = s 

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

165 

166 self._register(Transforms, name) 

167 

168 def __eq__(self, other): 

169 '''Compare this and an other transform. 

170 

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

172 

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

174 ''' 

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

176 and self.tx == other.tx 

177 and self.ty == other.ty 

178 and self.tz == other.tz 

179 and self.rx == other.rx 

180 and self.ry == other.ry 

181 and self.rz == other.rz 

182 and self.s == other.s) 

183 

184 def __hash__(self): 

185 return self._hash # memoized 

186 

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

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

189 

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

191 ''' 

192 try: # only CartesianBase 

193 return other.toTransform(self) 

194 except AttributeError: 

195 pass 

196 raise _IsnotError(_cartesian_, other=other) 

197 

198 @Property_RO 

199 def _hash(self): 

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

201 self.tx, self.ty, self.tz)) 

202 

203 def inverse(self, name=NN): 

204 '''Return the inverse of this transform. 

205 

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

207 

208 @return: Inverse (Transform). 

209 

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

211 ''' 

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

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

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

215 

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

217 '''Return this transform as a string. 

218 

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

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

221 this transform's name. 

222 

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

224 ''' 

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

226 'rx', 'ry', 'rz', _s_, 's1', 

227 _sx_, _sy_, _sz_) 

228 

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

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

231 

232 @arg x: X coordinate (C{meter}). 

233 @arg y: Y coordinate (C{meter}). 

234 @arg z: Z coordinate (C{meter}). 

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

236 

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

238 ''' 

239 xyz1 = x, y, z, _1_0 

240 s1 = self.s1 

241 if inverse: 

242 xyz1 = map2(neg, xyz1) 

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

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

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

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

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

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

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

250 name=self.name) 

251 

252 

253class Transforms(_NamedEnum): 

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

255 to accommodate the L{_LazyNamedEnumItem} properties. 

256 ''' 

257 def _Lazy(self, **name_tx_ty_tz_sx_sy_sz_s): 

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

259 ''' 

260 return Transform(**name_tx_ty_tz_sx_sy_sz_s) 

261 

262Transforms = Transforms(Transform) # PYCHOK singleton 

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

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

265Transforms._assert( 

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

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

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

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

270 s=_F( 1.2727)), 

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

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

273 s=_F( -8.3)), 

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

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

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

277 s=_F( -9.82)), # Germany 

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

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

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

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

282 sz=_F( 0.156), s=_F(-1.2)), 

283 Identity = _lazy(_Identity_), 

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

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

286 s=_F( -8.15)), 

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

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

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

290 s=_F( -1.1)), 

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

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

293 s=_F( -2.423)), # spelling 

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

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

296 s=_F( -2.423)), # spelling 

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

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

299 s=_F( -2.423)), # Austria 

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

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

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

303 s=_F(-0.0015)), 

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

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

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

307 s=_F( 20.4894)), 

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

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

310 WGS84 = _lazy(_WGS84_), # unity 

311) 

312 

313 

314class Datum(_NamedEnumItem): 

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

316 ''' 

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

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

319 

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

321 '''New L{Datum}. 

322 

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

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

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

326 

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

328 

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

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

331 not a L{Transform}. 

332 ''' 

333 self._ellipsoid = ellipsoid or Datum._ellipsoid 

334 _xinstanceof(Ellipsoid, ellipsoid=self.ellipsoid) 

335 

336 self._transform = transform or Datum._transform 

337 _xinstanceof(Transform, transform=self.transform) 

338 

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

340 

341 def __eq__(self, other): 

342 '''Compare this and an other datum. 

343 

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

345 

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

347 ''' 

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

349 self.ellipsoid == other.ellipsoid and 

350 self.transform == other.transform) 

351 

352 def __hash__(self): 

353 return self._hash # memoized 

354 

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

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

357 

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

359 ''' 

360 try: # only CartesianBase and EllipsoidalLatLonBase 

361 return other.toDatum(self) 

362 except AttributeError: 

363 pass 

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

365 

366 def ecef(self, Ecef=None): 

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

368 

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

370 

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

372 

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

374 

375 @see: Module L{pygeodesy.ecef}. 

376 ''' 

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

378 

379 @Property_RO 

380 def ellipsoid(self): 

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

382 ''' 

383 return self._ellipsoid 

384 

385 @Property_RO 

386 def exactTM(self): 

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

388 ''' 

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

390 

391 @Property_RO 

392 def _hash(self): 

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

394 

395 @Property_RO 

396 def isEllipsoidal(self): 

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

398 ''' 

399 return self.ellipsoid.isEllipsoidal 

400 

401 @Property_RO 

402 def isOblate(self): 

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

404 ''' 

405 return self.ellipsoid.isOblate 

406 

407 @Property_RO 

408 def isProlate(self): 

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

410 ''' 

411 return self.ellipsoid.isProlate 

412 

413 @Property_RO 

414 def isSpherical(self): 

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

416 ''' 

417 return self.ellipsoid.isSpherical 

418 

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

420 '''Return this datum as a string. 

421 

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

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

424 this datum's name. 

425 

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

427 ''' 

428 t = [] if name is None else \ 

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

430 for a in (_ellipsoid_, _transform_): 

431 v = getattr(self, a) 

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

433 return sep.join(t) 

434 

435 @Property_RO 

436 def transform(self): 

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

438 ''' 

439 return self._transform 

440 

441 

442def _En2(earth, name): 

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

444 ''' 

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

446 E = earth 

447 n = _under(name or E.name) 

448 elif isinstance(earth, Datum): 

449 E = earth.ellipsoid 

450 n = _under(name or earth.name) 

451 elif isinstance(earth, a_f2Tuple): 

452 n = _under(name or earth.name) 

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

454 elif islistuple(earth, minum=2): 

455 a, f = earth[:2] 

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

457 E = Ellipsoid(a, f=f, name=n) 

458 else: 

459 E, n = None, NN 

460 return E, n 

461 

462 

463def _a_ellipsoid(a_ellipsoid, f=None, name=NN, raiser=_a_ellipsoid_): # in .karney, .trf, ... 

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

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

466 ''' 

467 if f is None: 

468 E, _ = _En2(a_ellipsoid, name) 

469 if raiser and not E: 

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

471 else: 

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

473 return E 

474 

475 

476def _ellipsoidal_datum(earth, Error=TypeError, name=NN, raiser=NN): 

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

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

479 

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

481 ''' 

482 if isinstance(earth, Datum): 

483 d = earth 

484 else: 

485 E, n = _En2(earth, name) 

486 if not E: 

487 n = raiser or _earth_ 

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

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

490 if raiser and not d.isEllipsoidal: 

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

492 return d 

493 

494 

495def _mean_radius(radius, *lats): 

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

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

498 ''' 

499 if radius is R_M: 

500 r = radius 

501 elif isscalar(radius): 

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

503 else: 

504 E = _ellipsoidal_datum(radius).ellipsoid 

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

506 return r 

507 

508 

509def _spherical_datum(earth, Error=TypeError, name=NN, raiser=NN): 

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

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

512 

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

514 ''' 

515 if isscalar(earth): 

516 E = Datums.Sphere.ellipsoid 

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

518 d = Datums.Sphere 

519 else: 

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

521 n = _under(name) 

522 E = Ellipsoid(r, r, name=n) 

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

524 else: 

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

526 if raiser and not d.isSpherical: 

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

528 return d 

529 

530 

531class Datums(_NamedEnum): 

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

533 to accommodate the L{_LazyNamedEnumItem} properties. 

534 ''' 

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

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

537 ''' 

538 return Datum(Ellipsoids.get(ellipsoid_name), 

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

540 

541Datums = Datums(Datum) # PYCHOK singleton 

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

543# Datums with associated ellipsoid and Helmert transform parameters 

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

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

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

547Datums._assert( 

548 # Belgian Datum 1972, based on Hayford ellipsoid. 

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

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

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

552 

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

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

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

556 

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

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

559 

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

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

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

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

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

565 

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

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

568 

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

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

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

572 

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

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

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

576 

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

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

579 

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

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

582 

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

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

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

586 

587 # Nouvelle Triangulation Francaise (Paris) XXX verify 

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

589 

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

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

592 

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

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

595 

596 # XXX psuedo-ellipsoids for spherical LatLon 

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

598 

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

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

601 

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

603 WGS72 = _lazy(_WGS72_, _WGS72_, _WGS72_), 

604 

605 WGS84 = _lazy(_WGS84_, _WGS84_, _WGS84_), 

606) 

607 

608_WGS84 = Datums.WGS84 # PYCHOK exported internally 

609 

610if __name__ == '__main__': 

611 

612 from pygeodesy.interns import _COMMA_, _NL_, _NLATvar_ 

613 from pygeodesy.lazily import printf 

614 

615 # __doc__ of this file, force all into registery 

616 for r in (Datums, Transforms): 

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

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

619 

620# **) MIT License 

621# 

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

623# 

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

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

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

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

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

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

630# 

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

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

633# 

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

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

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

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

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

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

640# OTHER DEALINGS IN THE SOFTWARE.