Coverage for pygeodesy/karney.py: 86%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''Wrapper around several C{geomath.Math} functions from I{Karney}'s Python package 

5U{geographiclib<https://PyPI.org/project/geographiclib>}, provided that package is installed. 

6 

7The I{wrapped} class methods return a L{GDict} instance offering access to the C{dict} items 

8either by C{key} or by C{attribute} name. 

9 

10With env variable C{PYGEODESY_GEOGRAPHICLIB} left undefined or set to C{"2"}, this module, 

11L{pygeodesy.geodesicw} and L{pygeodesy.geodesicx} will use U{GeographicLib 2.0 

12<https://GeographicLib.SourceForge.io/C++/doc/>} transcoding, otherwise C{1.52} or older. 

13 

14Karney-based functionality 

15========================== 

16 

171. The following classes and functions in C{pygeodesy} 

18 

19 - L{AlbersEqualArea}, L{AlbersEqualArea2}, L{AlbersEqualArea4}, 

20 L{AlbersEqualAreaCylindrical}, L{AlbersEqualAreaNorth}, L{AlbersEqualAreaSouth} -- 

21 U{AlbersEqualArea<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AlbersEqualArea.html>} 

22 

23 - L{CassiniSoldner} -- U{CassiniSoldner<https://GeographicLib.SourceForge.io/C++/doc/ 

24 classGeographicLib_1_1CassiniSoldner.html>} 

25 

26 - L{EcefKarney} -- U{Geocentric<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Geocentric.html>} 

27 

28 - L{Elliptic} -- U{EllipticFunction<https://GeographicLib.SourceForge.io/C++/doc/ 

29 classGeographicLib_1_1EllipticFunction.html>} 

30 

31 - L{EquidistantExact}, L{EquidistantGeodSolve}, L{EquidistantKarney} -- U{AzimuthalEquidistant 

32 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AzimuthalEquidistant.html>} 

33 

34 - L{Etm}, L{ExactTransverseMercator} -- U{TransverseMercatorExact 

35 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercatorExact.html>} 

36 

37 - L{Geodesic}, L{GeodesicLine} -- I{wrapped} U{geodesic.Geodesic<https://PyPI.org/project/geographiclib>}, 

38 I{wrapped} U{geodesicline.GeodesicLine<https://PyPI.org/project/geographiclib>} 

39 

40 - L{GeodesicAreaExact}, L{PolygonArea} -- U{PolygonArea<https://GeographicLib.SourceForge.io/html/ 

41 classGeographicLib_1_1PolygonAreaT.html>} 

42 

43 - L{GeodesicExact}, L{GeodesicLineExact} -- U{GeodesicExact<https://GeographicLib.SourceForge.io/C++/doc/ 

44 classGeographicLib_1_1GeodesicExact.html>}, U{GeodesicLineExact<https://GeographicLib.SourceForge.io/C++/doc/ 

45 classGeographicLib_1_1GeodesicLineExact.html>} 

46 

47 - L{GeoidKarney} -- U{Geoid<https://GeographicLib.SourceForge.io/C++/doc/geoid.html>} 

48 

49 - L{Georef} -- U{Georef<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Georef.html>} 

50 

51 - L{GnomonicExact}, L{GnomonicGeodSolve}, L{GnomonicKarney} -- U{Gnomonic 

52 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Gnomonic.html>} 

53 

54 - L{JacobiConformal} -- U{JacobiConformal 

55 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1JacobiConformal.html#details>} 

56 

57 - L{KTransverseMercator} - U{TransverseMercator 

58 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>} 

59 

60 - L{LocalCartesian}, L{Ltp} -- U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/ 

61 classGeographicLib_1_1LocalCartesian.html>} 

62 

63 - L{Osgr} -- U{OSGB<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1OSGB.html>}. 

64 

65 - L{Rhumb}, L{RhumbLine} -- U{Rhumb<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>}, 

66 U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>}, 

67 U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>} 

68 

69 - L{Ups} -- U{PolarStereographic<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1PolarStereographic.html>} 

70 

71 - L{Utm} -- U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>} 

72 

73 - L{UtmUps}, L{Epsg} -- U{UTMUPS<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1UTMUPS.html>} 

74 

75 - L{pygeodesy.atand}, L{pygeodesy.atan2d}, L{pygeodesy.sincos2}, L{pygeodesy.sincos2d}, L{pygeodesy.tand} -- U{geomath.Math 

76 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Math.html>} 

77 

78are I{transcoded} from C++ classes in I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>}. 

79 

802. These C{pygeodesy} modules and classes 

81 

82 - L{ellipsoidalGeodSolve}, L{ellipsoidalKarney}, L{geodsolve}, L{karney}, L{rhumbsolve} 

83 - L{EquidistantKarney}, L{FrechetKarney}, L{GeodesicSolve}, L{GeodesicLineSolve}, L{GnomonicGeodSolve}, 

84 L{GnomonicKarney}, L{HeightIDWkarney} 

85 

86are or use I{wrappers} around I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} 

87C{geodesic}, C++ utility U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} or 

88C++ utility U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}. 

89 

903. All C{pygeodesy} functions and methods to compute I{ellipsoidal} intersections, nearest points and trilaterations 

91 

92 - L{ellipsoidalExact.intersection3}, L{ellipsoidalExact.intersections2}, L{ellipsoidalExact.nearestOn}, 

93 L{ellipsoidalExact.LatLon.intersection3}, L{ellipsoidalExact.LatLon.intersections2}, 

94 L{ellipsoidalExact.LatLon.nearestOn}, L{ellipsoidalExact.LatLon.trilaterate5} 

95 

96 - L{ellipsoidalKarney.intersection3}, L{ellipsoidalKarney.intersections2}, L{ellipsoidalKarney.nearestOn}, 

97 L{ellipsoidalKarney.LatLon.intersection3}, L{ellipsoidalKarney.LatLon.intersections2}, 

98 L{ellipsoidalKarney.LatLon.nearestOn}, L{ellipsoidalKarney.LatLon.trilaterate5} 

99 

100 - L{ellipsoidalVincenty.intersection3}, L{ellipsoidalVincenty.intersections2}, L{ellipsoidalVincenty.nearestOn}, 

101 L{ellipsoidalVincenty.LatLon.intersection3}, L{ellipsoidalVincenty.LatLon.intersections2}, 

102 L{ellipsoidalVincenty.LatLon.nearestOn}, L{ellipsoidalVincenty.LatLon.trilaterate5} 

103 

104 - L{RhumbLine.intersection2}, L{RhumbLine.nearestOn4} 

105 

106are iterative implementations of I{Karney}'s solution posted here under U{The B{ellipsoidal} case 

107<https://GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>} and in paper U{Geodesics 

108on an ellipsoid of revolution<https://ArXiv.org/pdf/1102.1215.pdf>} (pp 20-21, section B{14. MARITIME BOUNDARIES}). 

109 

1104. Spherical functions 

111 

112 - L{pygeodesy.excessKarney_}, L{sphericalTrigonometry.areaOf} 

113 

114in C{pygeodesy} are based on I{Karney}'s post U{Area of a spherical polygon 

115<https://MathOverflow.net/questions/97711/the-area-of-spherical-polygons>}, 3rd Answer. 

116''' 

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

118from __future__ import division as _; del _ # PYCHOK semicolon 

119 

120from pygeodesy.basics import _copysign, neg, unsigned0, _xgeographiclib, \ 

121 _xImportError, _xversion_info, _xinstanceof, \ 

122 _zip, isodd # PYCHOK shared 

123from pygeodesy.constants import NAN, _isfinite as _math_isfinite, _0_0, _1_16th, \ 

124 _180_0, _N_180_0, _360_0 

125from pygeodesy.datums import _WGS84, _a_ellipsoid # PYCHOK shared 

126from pygeodesy.errors import _ValueError, _xkwds, _xkwds_get 

127from pygeodesy.fmath import cbrt, fremainder, norm2, hypot as _hypot, unstr # PYCHOK shared 

128from pygeodesy.interns import _2_, _a12_, _area_, _azi2_, _composite_, _lat2_, \ 

129 _lon2_, _m12_, _M12_, _M21_, _number_, _s12_, _S12_ 

130from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv 

131from pygeodesy.named import _Dict, _NamedBase, _NamedTuple, _Pass 

132from pygeodesy.props import deprecated_method, Property_RO, property_RO 

133# from pygeodesy.streps import unstr # from .fmath 

134from pygeodesy.units import Bearing as _Azi, Degrees as _Deg, Lat, Lon, \ 

135 Meter as _M, Meter2 as _M2, Number_, \ 

136 Precision_, _1mm as _TOL_M # PYCHOK shared 

137from pygeodesy.utily import atan2d, fabs, sincos2d, tand, unroll180, wrap360 # PYCHOK shared 

138 

139# from math import fabs # from .utily 

140 

141__all__ = _ALL_LAZY.karney 

142__version__ = '23.04.07' 

143 

144_EWGS84 = _WGS84.ellipsoid # PYCHOK in .geodesicx.gx, .ktm, .rhumbx, .solveBase 

145_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_ 

146_perimeter_ = 'perimeter' 

147 

148 

149class _GTuple(_NamedTuple): # in .testNamedTuples 

150 '''(INTERNAL) Helper. 

151 ''' 

152 def toGDict(self, **updates): 

153 '''Convert this C{*Tuple} to a L{GDict}. 

154 

155 @kwarg updates: Optional items to apply (C{nam=value} pairs) 

156 ''' 

157 r = GDict(_zip(self._Names_, self)) # strict=True 

158 if updates: 

159 r.update(updates) 

160 if self._iteration is not None: 

161 r._iteration = self._iteration 

162 return r 

163 

164 

165class _Lat(Lat): 

166 '''(INTERNAL) Latitude B{C{lat}}. 

167 ''' 

168 def __init__(self, *lat, **Error_name): 

169 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError) 

170 Lat.__new__(_Lat, *lat, **kwds) 

171 

172 

173class _Lon(Lon): 

174 '''(INTERNAL) Longitude B{C{lon}}. 

175 ''' 

176 def __init__(self, *lon, **Error_name): 

177 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError) 

178 Lon.__new__(_Lon, *lon, **kwds) 

179 

180 

181class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea 

182 '''3-Tuple C{(number, perimeter, area)} with the C{number} 

183 of points on the polygon or polyline, the C{perimeter} in 

184 C{meter} and the C{area} in C{meter} I{squared}. 

185 ''' 

186 _Names_ = (_number_, _perimeter_, _area_) 

187 _Units_ = ( Number_, _M, _M2) 

188 

189 

190class Caps(object): # PYCHOK 

191 '''(INTERNAL) Overriden by C{Caps} below. 

192 ''' 

193 EMPTY = 0 # formerly aka NONE 

194 LATITUDE = 1 << 7 # compute latitude C{lat2} 

195 LONGITUDE = 1 << 8 # compute longitude C{lon2} 

196 AZIMUTH = 1 << 9 # azimuths C{azi1} and C{azi2} 

197 DISTANCE = 1 << 10 # compute distance C{s12} 

198 DISTANCE_IN = 1 << 11 # allow distance C{s12} in Direct 

199 REDUCEDLENGTH = 1 << 12 # compute reduced length C{m12} 

200 GEODESICSCALE = 1 << 13 # compute geodesic scales C{M12} and C{M21} 

201 AREA = 1 << 14 # compute area C{S12} 

202 

203 STANDARD = AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE 

204 ALL = 0x7F80 # without LONG_UNROLL, LINE_OFF, REVERSE2 and _DEBUG_* 

205 

206 LINE_OFF = 1 << 15 # Line without updates from parent geodesic or rhumb 

207 LONG_UNROLL = 1 << 16 # unroll C{lon2} in .Direct and .Position 

208 REVERSE2 = 1 << 17 # reverse C{azi2} 

209 

210 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE 

211 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA 

212 

213 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE 

214 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA 

215 

216 _ANGLE_ONLY = 1 << 18 # angular distance C{a12} only 

217 _SALPs_CALPs = 1 << 19 # (INTERNAL) GeodesicExact._GenInverse 

218 

219 _DEBUG_AREA = 1 << 20 # (INTERNAL) include Line details 

220 _DEBUG_DIRECT = 1 << 21 # (INTERNAL) include Direct details 

221 _DEBUG_INVERSE = 1 << 22 # (INTERNAL) include Inverse details 

222 _DEBUG_LINE = 1 << 23 # (INTERNAL) include Line details 

223 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \ 

224 _DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs 

225 _OUT_ALL = ALL 

226 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL 

227 

228 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE 

229 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE 

230 _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK 

231 _LINE = AZIMUTH | LATITUDE | LONG_UNROLL 

232 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE 

233# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE 

234 

235Caps = Caps() # PYCHOK singleton 

236'''I{Enum}-style masks to be bit-C{or}'ed to specify geodesic or 

237rhumb capabilities (C{caps}) and expected results (C{outmask}). 

238 

239C{AREA} - compute area C{S12}, 

240 

241C{AZIMUTH} - include azimuths C{azi1} and C{azi2}, 

242 

243C{DISTANCE} - compute distance C{s12}, 

244 

245C{DISTANCE_IN} - allow distance C{s12} in C{.Direct}, 

246 

247C{EMPTY} - nothing, formerly aka C{NONE}, 

248 

249C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21}, 

250 

251C{LINE_OFF} - Line without updates from parent geodesic or rhumb. 

252 

253C{LATITUDE} - compute latitude C{lat2}, 

254 

255C{LONGITUDE} - compute longitude C{lon2}, 

256 

257C{LONG_UNROLL} - unroll C{lon2} in C{.Direct}, 

258 

259C{REDUCEDLENGTH} - compute reduced length C{m12}, 

260 

261C{REVERSE2} - reverse C{azi2}, 

262 

263and C{ALL} - all of the above. 

264 

265C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}''' 

266 

267 

268class _CapsBase(_NamedBase): # in .geodesicx.gxbases, .rhumbx 

269 '''(INTERNAL) Base class for C{[_]Geodesic*Exact}. 

270 ''' 

271 ALL = Caps.ALL 

272 AREA = Caps.AREA 

273 AZIMUTH = Caps.AZIMUTH 

274 DISTANCE = Caps.DISTANCE 

275 DISTANCE_IN = Caps.DISTANCE_IN 

276 EMPTY = Caps.EMPTY # aka NONE 

277 GEODESICSCALE = Caps.GEODESICSCALE 

278 LATITUDE = Caps.LATITUDE 

279 LINE_OFF = Caps.LINE_OFF 

280 LONGITUDE = Caps.LONGITUDE 

281 LONG_UNROLL = Caps.LONG_UNROLL 

282 REDUCEDLENGTH = Caps.REDUCEDLENGTH 

283 STANDARD = Caps.STANDARD 

284 

285 _caps = 0 # None 

286 _debug = 0 # or Caps._DEBUG_... 

287 

288 @Property_RO 

289 def caps(self): 

290 '''Get the capabilities (bit-or'ed C{Caps}). 

291 ''' 

292 return self._caps 

293 

294 def caps_(self, caps): 

295 '''Check the available capabilities. 

296 

297 @arg caps: Bit-or'ed combination of L{Caps} values 

298 for all capabilities to be checked. 

299 

300 @return: C{True} if I{all} B{C{caps}} are available, 

301 C{False} otherwise (C{bool}). 

302 ''' 

303 caps &= Caps._OUT_ALL 

304 return (self.caps & caps) == caps 

305 

306 @property 

307 def debug(self): 

308 '''Get the C{debug} option (C{bool}). 

309 ''' 

310 return bool(self._debug) 

311 

312 @debug.setter # PYCHOK setter! 

313 def debug(self, debug): 

314 '''Set the C{debug} option (C{bool}) to include 

315 more details in L{GDict} results. 

316 ''' 

317 self._debug = Caps._DEBUG_ALL if debug else 0 

318 

319 def _iter2tion(self, r, s): 

320 '''(INTERNAL) Copy C{C{s}.iter} into C{B{r}._iteration}. 

321 ''' 

322 i = _xkwds_get(s, iter=None) 

323 if i is not None: 

324 self._iteration = r._iteration = i 

325 return r 

326 

327 

328class Direct9Tuple(_GTuple): 

329 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc 

330 length C{a12}, angles C{lat2}, C{lon2} and azimuth C{azi2} in C{degrees}, 

331 distance C{s12} and reduced length C{m12} in C{meter} and area C{S12} in 

332 C{meter} I{squared}. 

333 ''' 

334 _Names_ = (_a12_, _lat2_, _lon2_, _azi2_, _s12_, _m12_, _M12_, _M21_, _S12_) 

335 _Units_ = (_Azi, _Lat, _Lon, _Azi, _M, _Pass, _Pass, _Pass, _M2) 

336 

337 

338class GDict(_Dict): # XXX _NamedDict 

339 '''Basic C{dict} with both key I{and} attribute access 

340 to the C{dict} items. 

341 

342 Results of all C{geodesic} methods are returned as a 

343 L{GDict} instance. 

344 ''' 

345 _iteration = None # Iteration number (C{int}) or C{None} 

346 

347 @property_RO 

348 def iteration(self): # see .named._NamedBase 

349 '''Get the iteration number (C{int}) or 

350 C{None} if not available/applicable. 

351 ''' 

352 return self._iteration 

353 

354 def toDirect9Tuple(self, dflt=NAN): 

355 '''Convert this L{GDict} result to a 9-tuple, like I{Karney}'s 

356 method C{geographiclib.geodesic.Geodesic._GenDirect}. 

357 

358 @kwarg dflt: Default value for missing items (C{any}). 

359 

360 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, 

361 s12, m12, M12, M21, S12)} 

362 ''' 

363 return self._toTuple(Direct9Tuple, dflt) 

364 

365 def toGeodSolve12Tuple(self, dflt=NAN): # PYCHOK 12 args 

366 '''Convert this L{GDict} result to a 12-Tuple, compatible with I{Karney}'s 

367 U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} 

368 result. 

369 

370 @kwarg dflt: Default value for missing items (C{any}). 

371 

372 @return: L{GeodSolve12Tuple}C{(lat1, lon1, azi1, lat2, lon2, azi2, 

373 s12, a12, m12, M12, M21, S12)}. 

374 ''' 

375 return self._toTuple(_MODS.geodsolve.GeodSolve12Tuple, dflt) 

376 

377 def toInverse10Tuple(self, dflt=NAN): 

378 '''Convert this L{GDict} result to a 10-tuple, like I{Karney}'s 

379 method C{geographiclib.geodesic.Geodesic._GenInverse}. 

380 

381 @kwarg dflt: Default value for missing items (C{any}). 

382 

383 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1, 

384 salp2, calp2, m12, M12, M21, S12)}. 

385 ''' 

386 return self._toTuple(Inverse10Tuple, dflt) 

387 

388 @deprecated_method 

389 def toRhumb7Tuple(self, dflt=NAN): 

390 '''DEPRECATED, used method C{toRhumb8Tuple}. 

391 

392 @return: A I{DEPRECATED} L{Rhumb7Tuple}. 

393 ''' 

394 return self._toTuple(_MODS.deprecated.Rhumb7Tuple, dflt) 

395 

396 def toRhumb8Tuple(self, dflt=NAN): 

397 '''Convert this L{GDict} result to a 8-tuple. 

398 

399 @kwarg dflt: Default value for missing items (C{any}). 

400 

401 @return: L{Rhumb8Tuple}C{(lat1, lon1, lat2, lon2, 

402 azi12, s12, S12, a12)}. 

403 ''' 

404 return self._toTuple(_MODS.rhumbx.Rhumb8Tuple, dflt) 

405 

406 def toRhumbSolve7Tuple(self, dflt=NAN): 

407 '''Convert this L{GDict} result to a 8-tuple. 

408 

409 @kwarg dflt: Default value for missing items (C{any}). 

410 

411 @return: L{RhumbSolve7Tuple}C{(lat1, lon1, lat2, lon2, 

412 azi12, s12, S12)}. 

413 ''' 

414 return self._toTuple(_MODS.rhumbsolve.RhumbSolve7Tuple, dflt) 

415 

416 def _toTuple(self, nTuple, dflt): 

417 '''(INTERNAL) Convert this C{GDict} to an B{C{nTuple}}. 

418 ''' 

419 _g = getattr 

420 t = tuple(_g(self, n, dflt) for n in nTuple._Names_) 

421 return nTuple(t, iteration=self._iteration) 

422 

423 

424class GeodesicError(_ValueError): 

425 '''Error raised for L{pygeodesy.geodesicx} lack of convergence 

426 or other L{pygeodesy.geodesicx} or L{pygeodesy.karney} issues. 

427 ''' 

428 pass 

429 

430 

431class Inverse10Tuple(_GTuple): 

432 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length 

433 C{a12} in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter}, area 

434 C{S12} in C{meter} I{squared} and the sines C{salp1}, C{salp2} and cosines C{calp1}, 

435 C{calp2} of the initial C{1} and final C{2} foward azimuths. 

436 ''' 

437 _Names_ = (_a12_, _s12_, 'salp1', 'calp1', 'salp2', 'calp2', _m12_, _M12_, _M21_, _S12_) 

438 _Units_ = (_Azi, _M, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _M2) 

439 

440 def toGDict(self, **updates): 

441 '''Convert this C{Inverse10Tuple} to a L{GDict}. 

442 

443 @kwarg updates: Optional items to apply (C{nam=value} pairs) 

444 ''' 

445 return _GTuple.toGDict(self, azi1=atan2d(self.salp1, self.calp1), # PYCHOK indent, namedTuple 

446 azi2=atan2d(self.salp2, self.calp2), # PYCHOK namedTuple 

447 **updates) # PYCHOK indent 

448 

449 

450class _kWrapped(object): 

451 ''''(INTERNAL) Wrapper for some of I{Karney}'s U{geographiclib 

452 <https://PyPI.org/project/geographiclib>} classes. 

453 ''' 

454 

455 @Property_RO 

456 def geographiclib(self): 

457 '''Get the imported C{geographiclib}, provided the U{geographiclib 

458 <https://PyPI.org/project/geographiclib>} package is installed, 

459 otherwise an C{ImportError}. 

460 ''' 

461 g = _xgeographiclib(self.__class__, 1, 49) 

462 from geographiclib.geodesic import Geodesic 

463 g.Geodesic = Geodesic 

464 from geographiclib.geodesicline import GeodesicLine 

465 g.GeodesicLine = GeodesicLine 

466 from geographiclib.geomath import Math 

467 g.Math = Math 

468 return g 

469 

470 @Property_RO # MCCABE 13 

471 def Math(self): 

472 '''Wrap the C{geomath.Math} class, provided the U{geographiclib 

473 <https://PyPI.org/project/geographiclib>} package is installed, 

474 otherwise C{None}. 

475 ''' 

476 try: 

477 g = self.geographiclib 

478 M = g.Math 

479 if _xversion_info(g) < (2,): 

480 if _K_2_0: 

481 M = None 

482# elif not _K_2_0: # XXX set 2.0? 

483# _K_2_0 = True 

484 except (AttributeError, ImportError): 

485 M = None 

486 return M 

487 

488_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py 

489 

490 

491def _around(x): # in .utily.sincos2d 

492 '''I{Coarsen} a scalar by rounding small values to underflow to C{0.0}. 

493 

494 @return: Coarsened value (C{float}). 

495 

496 @see: I{Karney}'s U{geomath.Math.AngRound<https://SourceForge.net/p/ 

497 geographiclib/code/ci/release/tree/python/geographiclib/geomath.py>} 

498 ''' 

499 try: 

500 return _wrapped.Math.AngRound(x) 

501 except AttributeError: 

502 pass 

503 if x: 

504 y = _1_16th - fabs(x) 

505 if y > 0: # fabs(x) < _1_16th 

506 x = _copysign(_1_16th - y, x) 

507 else: 

508 x = _0_0 # -0 to 0 

509 return x 

510 

511 

512def _atan2d(y, x): 

513 '''Return C{atan2(B{y}, B{x})} in C{degrees}. 

514 ''' 

515 try: 

516 return _wrapped.Math.atan2d(y, x) 

517 except AttributeError: 

518 return atan2d(y, x) 

519 

520 

521def _cbrt(x): 

522 '''Return C{cubic root(B{x})}. 

523 ''' 

524 try: 

525 return _wrapped.Math.cbrt(x) 

526 except AttributeError: 

527 return cbrt(x) 

528 

529 

530def _copyBit(x, y): 

531 '''Like C{copysign0(B{x}, B{y})}, with C{B{x} > 0}. 

532 ''' 

533 return (-x) if _signBit(y) else x 

534 

535 

536def _diff182(deg0, deg): 

537 '''Compute C{deg - deg0}, reduced to C{[-180,180]} accurately. 

538 

539 @return: 2-Tuple C{(delta_angle, residual)} in C{degrees}. 

540 ''' 

541 try: 

542 return _wrapped.Math.AngDiff(deg0, deg) 

543 except AttributeError: 

544 pass 

545 if _K_2_0: # geographiclib 2.0 

546 d, t = _sum2(fremainder(-deg0, _360_0), 

547 fremainder( deg, _360_0)) 

548 d, t = _sum2(fremainder( d, _360_0), t) 

549 if d in (_0_0, _180_0, _N_180_0): 

550 d = _copysign(d, -t if t else (deg - deg0)) 

551 else: 

552 d, t = _sum2(_norm180(-deg0), _norm180(deg)) 

553 d = _norm180(d) 

554 if t > 0 and d == _180_0: 

555 d = _N_180_0 

556 d, t = _sum2(d, t) 

557 return d, t 

558 

559 

560def _fix90(deg): # mimick Math.LatFix 

561 '''Replace angle in C{degrees} outside [-90,90] by NAN. 

562 

563 @return: Angle C{degrees} or NAN. 

564 ''' 

565 try: 

566 return _wrapped.Math.LatFix(deg) 

567 except AttributeError: 

568 return NAN if fabs(deg) > 90 else deg 

569 

570 

571def _isfinite(x): # mimick geomath.Math.AngNormalize 

572 '''Check finiteness of C{x}. 

573 

574 @return: C{True} if finite. 

575 ''' 

576 try: 

577 return _wrapped.Math.isfinite(x) 

578 except AttributeError: 

579 return _math_isfinite(x) # and fabs(x) <= _MAX 

580 

581 

582def _norm2(x, y): # mimick geomath.Math.norm 

583 '''Normalize C{B{x}} and C{B{y}}. 

584 

585 @return: 2-Tuple of C{(B{x}, B{y})}, normalized. 

586 ''' 

587 try: 

588 return _wrapped.Math.norm(x, y) 

589 except AttributeError: 

590 return norm2(x, y) 

591 

592 

593def _norm180(deg): # mimick geomath.Math.AngNormalize 

594 '''Reduce angle in C{degrees} to (-180,180]. 

595 

596 @return: Reduced angle C{degrees}. 

597 ''' 

598 try: 

599 return _wrapped.Math.AngNormalize(deg) 

600 except AttributeError: 

601 pass 

602 d = fremainder(deg, _360_0) 

603 if d in (_180_0, -_180_0): 

604 d = _copysign(_180_0, deg) if _K_2_0 else _180_0 

605 return d 

606 

607 

608def _polygon(geodesic, points, closed, line, wrap): 

609 '''(INTERNAL) Compute the area or perimeter of a polygon, 

610 using a L{GeodesicExact}, L{GeodesicSolve} or (if the 

611 C{geographiclib} package is installed) a C{Geodesic} 

612 or C{geodesicw.Geodesic} instance. 

613 ''' 

614 if not wrap: # capability LONG_UNROLL can't be off 

615 raise _ValueError(wrap=wrap) 

616 

617 if _MODS.booleans.isBoolean(points): 

618 # recursive call for each boolean clip 

619 

620 def _a_p(clip, *args, **unused): 

621 return _polygon(geodesic, clip, *args) 

622 

623 if not closed: # closed only 

624 raise _ValueError(closed=closed, points=_composite_) 

625 

626 return points._sum1(_a_p, closed, line, wrap) 

627 

628 gP = geodesic.Polygon(line) 

629 _A = gP.AddPoint 

630 

631 Ps = _MODS.iters.PointsIter(points, loop=1) # base=LatLonEllipsoidalBase(0, 0) 

632 p0 = Ps[0] 

633 

634 # note, lon deltas are unrolled, by default 

635 _A(p0.lat, p0.lon) 

636 for p in Ps.iterate(closed=closed): 

637 _A(p.lat, p.lon) 

638 if closed and line and p != p0: 

639 _A(p0.lat, p0.lon) 

640 

641 # gP.Compute returns (number_of_points, perimeter, signed area) 

642 return gP.Compute(False, True)[1 if line else 2] 

643 

644 

645def _polynomial(x, cs, i, j): # PYCHOK shared 

646 '''(INTERNAL) Like C++ C{GeographicLib.Math.hpp.polyval} but with a 

647 different signature and cascaded summation as C{karney._sum2_}. 

648 

649 @return: M{sum(cs[k] * x**(j - k - 1) for k in range(i, j)} 

650 ''' 

651 s, t = cs[i], _0_0 

652 _s2_ = _sum2_ 

653 for c in cs[i+1:j]: 

654 s, t = _s2_(s * x, t * x, c) 

655 return s # + t 

656 

657 

658def _remainder(x, y): 

659 '''Remainder of C{x / y}. 

660 

661 @return: Remainder in the range M{[-y / 2, y / 2]}, preserving signed 0.0. 

662 ''' 

663 try: 

664 return _wrapped.Math.remainder(x, y) 

665 except AttributeError: 

666 return fremainder(x, y) 

667 

668 

669if _K_2_0: 

670 from pygeodesy.basics import signBit as _signBit 

671 from math import cos as _cos, sin as _sin 

672 

673 def _sincos2(rad): 

674 return _sin(rad), _cos(rad) 

675 

676else: 

677 from pygeodesy.utily import sincos2 as _sincos2 # PYCHOK shared 

678 

679 def _signBit(x): 

680 '''(INTERNAL) GeographicLin 1.52-. 

681 ''' 

682 return x < 0 

683 

684 

685def _sincos2d(deg): 

686 '''Return sine and cosine of an angle in C{degrees}. 

687 

688 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}. 

689 ''' 

690 try: 

691 return _wrapped.Math.sincosd(deg) 

692 except AttributeError: 

693 return sincos2d(deg) 

694 

695 

696def _sincos2de(deg, t): 

697 '''Return sine and cosine of a corrected angle in C{degrees}. 

698 

699 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}. 

700 ''' 

701 try: 

702 return _wrapped.Math.sincosde(deg, t) 

703 except AttributeError: 

704 return sincos2d(deg, adeg=t) 

705 

706 

707def _sum2(u, v): # mimick geomath.Math.sum, actually sum2 

708 '''Error-free summation like C{geomath.Math.sum}. 

709 

710 @return: 2-Tuple C{(B{u} + B{v}, residual)}. 

711 

712 @note: The C{residual} can be the same as B{C{u}} or B{C{v}}. 

713 

714 @see: U{Algorithm 3.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}. 

715 ''' 

716 try: 

717 return _wrapped.Math.sum(u, v) 

718 except AttributeError: 

719 pass 

720 s = u + v 

721 r = s - v 

722 t = s - r 

723 # if Algorithm_3_1: 

724 # t = (u - t) + (v + r) 

725 # elif C_CPP: # Math::sum C/C++ 

726 # r -= u 

727 # t -= v 

728 # t += r 

729 # t = -t 

730 # else: 

731 t = (u - r) + (v - t) 

732 return s, t 

733 

734 

735def _sum2_(s, t, *vs): 

736 '''Accumulate any B{C{vs}} into a previous C{_sum2(s, t)}. 

737 

738 @return: 2-Tuple C{(B{s} + B{t} + sum(B{vs}), residual)}. 

739 

740 @see: I{Karney's} C++ U{Accumulator<https://GeographicLib.SourceForge.io/ 

741 html/Accumulator_8hpp_source.html>} comments for more details and 

742 function C{_sum2} above. 

743 

744 @note: NOT "error-free", see C{pygeodesy.test/testKarney.py}. 

745 ''' 

746 _s2, _u0 = _sum2, unsigned0 

747 for v in vs: 

748 if v: 

749 t, u = _s2(t, v) # start at the least- 

750 if s: 

751 s, t = _s2(s, t) # significant end 

752 if s: 

753 t += u # accumulate u into t 

754# elif t: # s == 0 implies t == 0 

755# raise _AssertionError(t=t, txt=_not_(_0_)) 

756 else: 

757 s = _u0(u) # result is u, t = 0 

758 else: 

759 s, t = _u0(t), u 

760 return s, t 

761 

762 

763def _tand(x): 

764 '''Return C{tan(B{x})} in C{degrees}. 

765 ''' 

766 try: 

767 return _wrapped.Math.tand(x) 

768 except AttributeError: 

769 return tand(x) 

770 

771 

772def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2 

773 '''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}. 

774 

775 @return: 2-Tuple C{(B{lon2} - B{lon1}, B{lon2})} with B{C{lon2}} 

776 unrolled if B{C{wrap}} is C{True}, normalized otherwise. 

777 ''' 

778 if wrap: 

779 d, t = _diff182(lon1, lon2) 

780 lon2, _ = _sum2_(d, t, lon1) # (lon1 + d) + t 

781 else: 

782 lon2 = _norm180(lon2) 

783 return (lon2 - lon1), lon2 

784 

785 

786def _unsigned2(x): 

787 '''(INTERNAL) Unsign B{C{x}}. 

788 ''' 

789 return (neg(x), True) if _signBit(x) else (x, False) 

790 

791 

792__all__ += _ALL_DOCS(_CapsBase) 

793 

794# **) MIT License 

795# 

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

797# 

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

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

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

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

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

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

804# 

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

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

807# 

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

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

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

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

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

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

814# OTHER DEALINGS IN THE SOFTWARE.