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, _passarg, _xinstanceof, _zip 

71from pygeodesy.constants import R_M, _float as _F, _0_0, _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, _operator 

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_, _PLUS_, _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# import operator as _operator # from .fmath 

94 

95__all__ = _ALL_LAZY.datums 

96__version__ = '24.02.29' 

97 

98_a_ellipsoid_ = _UNDER_(_a_, _ellipsoid_) 

99_BD72_ = 'BD72' 

100_DHDN_ = 'DHDN' 

101_DHDNE_ = 'DHDNE' 

102_DHDNW_ = 'DHDNW' 

103_ED50_ = 'ED50' 

104_GDA2020_ = 'GDA2020' # in .trf 

105_Identity_ = 'Identity' 

106_Irl1965_ = 'Irl1965' 

107_Irl1975_ = 'Irl1975' 

108_MGI_ = 'MGI' 

109_Names7 = 'tx', 'ty', 'tz', _s_, 'sx', 'sy', 'sz' # in .trf 

110_Names11 = _Names7[:3] + ('s1', 'rx', 'ry', 'rz') + _Names7[3:] 

111_NTF_ = 'NTF' 

112_OSGB36_ = 'OSGB36' 

113_Potsdam_ = 'Potsdam' 

114_RPS = radians(_1_0 / _3600_0) # radians per degree-second 

115_S1_S = 1.e-6 # in .trf 

116_TokyoJapan_ = 'TokyoJapan' 

117 

118 

119class Transform(_NamedEnumItem): 

120 '''Helmert I{datum} transformation. 

121 

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

123 ''' 

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

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

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

127 

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

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

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

131 

132 s = _0_0 # scale ppm (C{float}) 

133 s1 = _1_0 # scale + 1 (C{float}) 

134 

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

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

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

138 

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

140 s=0, sx=0, sy=0, sz=0): 

141 '''New L{Transform}. 

142 

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

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

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

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

147 @kwarg s: Scale (C{float}), ppm. 

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

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

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

151 

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

153 ''' 

154 if tx: 

155 self.tx = tx 

156 if ty: 

157 self.ty = ty 

158 if tz: 

159 self.tz = tz 

160 if s: 

161 self.s = s 

162 self.s1 = _F(s * _S1_S + _1_0) # normalize ppM to (s + 1) 

163 if sx: # secs to rads 

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

165 if sy: 

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

167 if sz: 

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

169 

170 self._register(Transforms, name) 

171 

172 def __eq__(self, other): 

173 '''Compare this and an other transform. 

174 

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

176 

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

178 ''' 

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

180 and _equall(other, self)) 

181 

182 def __hash__(self): 

183 return hash(tuple(self)) 

184 

185 def __iter__(self): 

186 '''Yield the initial attribute values, I{in order}. 

187 ''' 

188 for n in _Names7: 

189 yield getattr(self, n) 

190 

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

192 '''Transform an I{ellipsoidal} B{C{point}} with this Helmert. 

193 

194 @return: A transformed copy of B{C{point}}. 

195 

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

197 

198 @see: Method C{B{point}.toTransform}. 

199 ''' 

200 _ = _xellipsoidall(point) 

201 return point.toTransform(self) 

202 

203 def __neg__(self): 

204 return self.inverse() 

205 

206 def inverse(self, name=NN): 

207 '''Return the inverse of this transform. 

208 

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

210 

211 @return: Inverse (L{Transform}), unregistered. 

212 ''' 

213 r = type(self)(**dict(self.items(inverse=True))) 

214 n = name or _negstr(self.name) 

215 if n: 

216 r.name = n # unregistered 

217 return r 

218 

219 @Property_RO 

220 def isunity(self): 

221 '''Is this a C{unity, identity} transform (C{bool}), like 

222 WGS84 with translation, scale and rotation all zero? 

223 ''' 

224 return not any(self) 

225 

226 def items(self, inverse=False): 

227 '''Yield the initial attributes, each as 2-tuple C{(name, value)}. 

228 

229 @kwarg inverse: If C{True}, negate the values (C{bool}). 

230 ''' 

231 _p = neg if inverse else _passarg 

232 for n, x in _zip(_Names7, self): 

233 yield n, _p(x) 

234 

235 def _rps2(self, s_): 

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

237 ''' 

238 return (_RPS * s_), s_ 

239 

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

241 '''Return this transform as a string. 

242 

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

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

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

246 this transform's name. 

247 

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

249 ''' 

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

251 

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

253 '''Transform a (cartesian) position, forward or inverse. 

254 

255 @arg x: X coordinate (C{meter}). 

256 @arg y: Y coordinate (C{meter}). 

257 @arg z: Z coordinate (C{meter}). 

258 @kwarg inverse: If C{True}, apply the inverse transform (C{bool}). 

259 @kwarg Vector_and_kwds: An optional, (3-D) C{B{Vector}=None} or 

260 cartesian class and additional C{B{Vector}} keyword 

261 arguments to return the transformed position. 

262 

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

264 unless some B{C{Vector_and_kwds}} are specified. 

265 ''' 

266 if self.isunity: 

267 r = Vector3Tuple(x, y, z, name=self.name) # == inverse 

268 else: 

269 xyz1 = x, y, z, _1_0 

270 s1 = self.s1 

271 if inverse: 

272 xyz1 = map2(neg, xyz1) 

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

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

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

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

277 r = Vector3Tuple(fdot(xyz1, s1, -self.rz, self.ry, self.tx), 

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

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

280 name=self.name) 

281 if Vector_and_kwds: 

282 V, kwds = _xkwds_pop2(Vector_and_kwds, Vector=None) 

283 if V: 

284 r = V(r, **_xkwds(kwds, name=self.name)) 

285 return r 

286 

287 

288class Transforms(_NamedEnum): 

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

290 to accommodate the L{_LazyNamedEnumItem} properties. 

291 ''' 

292 def _Lazy(self, **name_tx_ty_tz_s_sx_sy_sz): 

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

294 ''' 

295 return Transform(**name_tx_ty_tz_s_sx_sy_sz) 

296 

297Transforms = Transforms(Transform) # PYCHOK singleton 

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

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

300Transforms._assert( 

301 BD72 = _lazy(_BD72_, tx=_F(106.868628), ty=_F(-52.297783), tz=_F(103.723893), s=_F(1.2727), 

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

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

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

305 

306 Bessel1841 = _lazy(_Bessel1841_, tx=_F(-582.0), ty=_F(-105.0), tz=_F(-414.0), s=_F(-8.3), 

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

308 

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

310 

311 DHDN = _lazy(_DHDN_, tx=_F(-591.28), ty=_F(-81.35), tz=_F(-396.39), s=_F(-9.82), 

312 sx=_F( 1.477), sy=_F( -0.0736), sz=_F( -1.458)), # Germany 

313 

314 DHDNE = _lazy(_DHDNE_, tx=_F(-612.4), ty=_F(-77.0), tz=_F(-440.2), s=_F(-2.55), 

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

316 sx=_F( 0.054), sy=_F( -0.057), sz=_F( 2.797)), # East Germany 

317 

318 DHDNW = _lazy(_DHDNW_, tx=_F(-598.1), ty=_F(-73.7), tz=_F(-418.2), s=_F(-6.7), 

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

320 sx=_F( -0.202), sy=_F( -0.045), sz=_F( 2.455)), # West Germany 

321 

322 ED50 = _lazy(_ED50_, tx=_F(89.5), ty=_F(93.8), tz=_F(123.1), s=_F(-1.2), 

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

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

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

326 sz=_F( 0.156)), 

327 Identity = _lazy(_Identity_), 

328 

329 Irl1965 = _lazy(_Irl1965_, tx=_F(-482.530), ty=_F(130.596), tz=_F(-564.557), s=_F(-8.15), 

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

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

332 Irl1975 = _lazy(_Irl1975_, tx=_F(-482.530), ty=_F(130.596), tz=_F(-564.557), s=_F(-8.15), 

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

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

335 

336 Krassovski1940 = _lazy(_Krassovski1940_, tx=_F(-24.0), ty=_F(123.0), tz=_F(94.0), s=_F(-2.423), 

337 sx=_F( -0.02), sy=_F( 0.26), sz=_F( 0.13)), # spelling 

338 

339 Krassowsky1940 = _lazy(_Krassowsky1940_, tx=_F(-24.0), ty=_F(123.0), tz=_F(94.0), s=_F(-2.423), 

340 sx=_F( -0.02), sy=_F( 0.26), sz=_F( 0.13)), # spelling 

341 

342 MGI = _lazy(_MGI_, tx=_F(-577.326), ty=_F(-90.129), tz=_F(-463.920), s=_F(-2.423), 

343 sx=_F( 5.137), sy=_F( 1.474), sz=_F( 5.297)), # Austria 

344 

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

346 

347 NAD83 = _lazy(_NAD83_, tx=_F(1.004), ty=_F(-1.910), tz=_F(-0.515), s=_F(-0.0015), 

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

349 

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

351 

352 OSGB36 = _lazy(_OSGB36_, tx=_F(-446.448), ty=_F(125.157), tz=_F(-542.060), s=_F(20.4894), 

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

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

355 

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

357 

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

359 

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 in (_EWGS84, _WGS84, None) and inst._datum is _WGS84: 

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 _equall(t1, t2): # in .trf 

584 '''(INTERNAL) Return L{Transform} C{t1 == t2}. 

585 ''' 

586 return all(map(_operator.eq, t1, t2)) 

587 

588 

589def _mean_radius(radius, *lats): 

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

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

592 ''' 

593 if radius is R_M: 

594 r = radius 

595 elif _isRadius(radius): 

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

597 else: 

598 E = _ellipsoidal_datum(radius).ellipsoid 

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

600 return r 

601 

602 

603try: 

604 _MINUSxPLUS = str.maketrans({_MINUS_: _PLUS_, _PLUS_: _MINUS_}) 

605 

606 def _negstr(name): # in .trf 

607 '''(INTERNAL) Negate a C{Transform/-Xform} name. 

608 ''' 

609 n = name.translate(_MINUSxPLUS) 

610 return n.lstrip(_PLUS_) if n.startswith(_PLUS_) else NN(_MINUS_, n) 

611 

612except AttributeError: # no str.maketran in Python 2- 

613 from pygeodesy.interns import _BAR_ 

614 

615 def _negstr(name): # PYCHOK in .trf 

616 '''(INTERNAL) Negate a C{Transform/-Xform} name. 

617 ''' 

618 b, m, p = _BAR_, _MINUS_, _PLUS_ 

619 n = name.replace(m, b).replace(p, m).replace(b, p) 

620 return n.lstrip(p) if n.startswith(p) else NN(m, n) 

621 

622 

623def _spherical_datum(earth, Error=TypeError, name=NN, raiser=NN): 

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

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

626 

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

628 ''' 

629 if _isRadius(earth): 

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

631 else: 

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

633 if raiser and not D.isSpherical: 

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

635 return D 

636 

637 

638class Datums(_NamedEnum): 

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

640 to accommodate the L{_LazyNamedEnumItem} properties. 

641 ''' 

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

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

644 ''' 

645 return Datum(Ellipsoids.get(ellipsoid_name), 

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

647 

648Datums = Datums(Datum) # PYCHOK singleton 

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

650# Datums with associated ellipsoid and Helmert transform parameters 

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

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

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

654Datums._assert( 

655 # Belgian Datum 1972, based on Hayford ellipsoid. 

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

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

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

659 

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

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

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

663 

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

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

666 

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

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

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

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

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

672 

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

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

675 

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

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

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

679 

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

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

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

683 

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

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

686 

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

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

689 

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

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

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

693 

694 # Nouvelle Triangulation Francaise (Paris) XXX verify 

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

696 

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

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

699 

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

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

702 

703 # XXX psuedo-ellipsoids for spherical LatLon 

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

705 

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

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

708 

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

710 WGS72 = _lazy(_WGS72_, _WGS72_, _WGS72_), 

711 

712 WGS84 = _lazy(_WGS84_, _WGS84_, _WGS84_), 

713) 

714 

715_WGS84 = Datums.WGS84 

716assert _WGS84.ellipsoid is _EWGS84 

717# assert _WGS84.transform.isunity 

718 

719if __name__ == '__main__': 

720 

721 from pygeodesy.interns import _COMMA_, _NL_, _NLATvar_ 

722 from pygeodesy.lazily import printf 

723 

724 # __doc__ of this file, force all into registery 

725 for r in (Datums, Transforms): 

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

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

728 

729# **) MIT License 

730# 

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

732# 

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

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

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

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

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

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

739# 

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

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

742# 

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

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

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

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

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

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

749# OTHER DEALINGS IN THE SOFTWARE.