Coverage for pygeodesy/karney.py: 94%

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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/>} and newer transcoding, otherwise C{1.52} 

13or older. 

14 

15Karney-based functionality 

16========================== 

17 

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

19 

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

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

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

23 

24 - L{AuxAngle}, L{AuxDST}, L{AuxDLat}, L{AuxLat} -- U{AuxAngle 

25 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxAngle.html>}, 

26 U{DST<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1DST.html>}, 

27 U{DAuxLatitude<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1DAuxLatitude.html>}, 

28 U{AuxLatitude<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxLatitude.html>} in I{GeographicLib 2.2+} 

29 

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

31 classGeographicLib_1_1CassiniSoldner.html>} 

32 

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

34 

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

36 classGeographicLib_1_1EllipticFunction.html>} 

37 

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

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

40 

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

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

43 

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

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

46 

47 - L{GeodesicAreaExact}, L{PolygonArea} -- U{PolygonArea<https://GeographicLib.SourceForge.io/C++/doc/ 

48 classGeographicLib_1_1PolygonAreaT.html>} 

49 

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

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

52 classGeographicLib_1_1GeodesicLineExact.html>} 

53 

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

55 

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

57 

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

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

60 

61 - L{JacobiConformal} -- U{JacobiConformal 

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

63 

64 - L{KTransverseMercator} - U{TransverseMercator 

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

66 

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

68 classGeographicLib_1_1LocalCartesian.html>} 

69 

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

71 

72 - L{rhumbaux} C{RhumbAux}, C{RhumbLineAux} -- U{Rhumb 

73 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>} and U{RhumbLine 

74 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>} in I{GeographicLib 2.2+} 

75 

76 - L{rhumbx} C{Rhumb}, C{RhumbLine} -- U{Rhumb 

77 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>}, 

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

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

80 in I{GeographicLib 2.0} 

81 

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

83 

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

85 

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

87 

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

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

90 

91are I{transcoded} from C++ classes in I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>}. 

92 

932. These C{pygeodesy} modules and classes 

94 

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

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

97 L{GnomonicKarney}, L{HeightIDWkarney} 

98 

99are or use I{wrappers} around I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} 

100C{geodesic}, C++ utility U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} or 

101C++ utility U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}. 

102 

1033. All C{pygeodesy} functions and methods to compute I{ellipsoidal} intersections, nearest points and trilaterations 

104 

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

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

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

108 

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

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

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

112 

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

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

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

116 

117 - L{RhumbLineAux.intersection2} and L{RhumbLineAux.nearestOn4} C{(exact=None)} in L{rhumbaux} and 

118 L{RhumbLine.intersection2} and L{RhumbLine.nearestOn4} C{(exact=None)} in L{rhumbx} 

119 

120are iterative implementations of I{Karney}'s solution posted here under U{The B{ellipsoidal} case 

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

122on an ellipsoid of revolution<https://ArXiv.org/pdf/1102.1215.pdf>} (pp 20-21, section B{14. MARITIME BOUNDARIES}). 

123 

1244. Spherical functions 

125 

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

127 

128in C{pygeodesy} are based on I{Karney}'s post U{Area of a spherical polygon 

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

130''' 

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

132from __future__ import division as _; del _ # PYCHOK semicolon 

133 

134from pygeodesy.basics import _copysign, neg, unsigned0, _xgeographiclib, \ 

135 _xImportError, _xversion_info, _xinstanceof, \ 

136 _zip, isodd # PYCHOK shared 

137from pygeodesy.constants import NAN, _isfinite as _math_isfinite, _0_0, _1_0, \ 

138 _1_16th, _180_0, _N_180_0, _360_0 

139from pygeodesy.datums import _WGS84, _a_ellipsoid # PYCHOK shared 

140from pygeodesy.errors import GeodesicError, _ValueError, _xkwds, _xkwds_get 

141from pygeodesy.fmath import cbrt, fremainder, norm2, hypot as _hypot, unstr # PYCHOK shared 

142from pygeodesy.interns import _2_, _a12_, _area_, _azi2_, _azi12_, _composite_, \ 

143 _lat1_, _lat2_, _lon1_, _lon2_, _m12_, _M12_, _M21_, \ 

144 _number_, _s12_, _S12_ 

145from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv 

146from pygeodesy.named import _Dict, _NamedBase, _NamedTuple, notImplemented, _Pass 

147from pygeodesy.props import deprecated_method, Property_RO, property_RO 

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

149from pygeodesy.units import Bearing as _Azi, Degrees as _Deg, Lat, Lon, \ 

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

151 Precision_, _1mm as _TOL_M # PYCHOK shared 

152from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs 

153 

154# from math import fabs # from .utily 

155 

156__all__ = _ALL_LAZY.karney 

157__version__ = '23.08.09' 

158 

159_EWGS84 = _WGS84.ellipsoid # PYCHOK in .auxilats, .geodesicx.gx, .ktm, .solveBase 

160_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_ 

161_perimeter_ = 'perimeter' 

162 

163 

164class _GTuple(_NamedTuple): # in .testNamedTuples 

165 '''(INTERNAL) Helper. 

166 ''' 

167 def toGDict(self, **updates): 

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

169 

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

171 ''' 

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

173 if updates: 

174 r.update(updates) 

175 if self._iteration is not None: 

176 r._iteration = self._iteration 

177 return r 

178 

179 

180class _Lat(Lat): 

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

182 ''' 

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

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

185 Lat.__new__(_Lat, *lat, **kwds) 

186 

187 

188class _Lon(Lon): 

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

190 ''' 

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

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

193 Lon.__new__(_Lon, *lon, **kwds) 

194 

195 

196class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea 

197 '''3-Tuple C{(number, perimeter, area)} with the C{number} 

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

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

200 ''' 

201 _Names_ = (_number_, _perimeter_, _area_) 

202 _Units_ = ( Number_, _M, _M2) 

203 

204 

205class Caps(object): # PYCHOK 

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

207 ''' 

208 EMPTY = 0 # formerly aka NONE 

209 _CAP_1 = 1 << 0 # for goedesicw only 

210 _CAP_1p = 1 << 1 # for goedesicw only 

211# _CAP_2 = 1 << 2 

212 _CAP_3 = 1 << 3 # for goedesicw only 

213# _CAP_4 = 1 << 4 

214# _CAP_ALL = 0x1F 

215# _CAP_MASK = _CAP_ALL 

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

217 LONGITUDE = 1 << 8 # compute longitude C{lon2} _CAP_3 

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

219 DISTANCE = 1 << 10 # compute distance C{s12} _CAP_1 

220 DISTANCE_IN = 1 << 11 # allow distance C{s12} in Direct _CAP_1 | _CAP_1p 

221 REDUCEDLENGTH = 1 << 12 # compute reduced length C{m12} _CAP_1 | _CAP_2 

222 GEODESICSCALE = 1 << 13 # compute geodesic scales C{M12} and C{M21} _CAP_1 | _CAP_2 

223 AREA = 1 << 14 # compute area C{S12} _CAP_4 

224 

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

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

227 

228 _DIRECT3 = AZIMUTH | LATITUDE | LONGITUDE | _CAP_3 # for goedesicw only 

229 _INVERSE3 = AZIMUTH | DISTANCE | _CAP_1 # for goedesicw only 

230 _STD = STANDARD | _CAP_3 | _CAP_1 # for goedesicw only 

231 _STD_LINE = _STD | _CAP_1p # for goedesicw only 

232 

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

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

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

236 

237 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE 

238 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA 

239 

240 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE 

241 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA 

242 

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

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

245 

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

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

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

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

250 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \ 

251 _DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs 

252 _OUT_ALL = ALL 

253 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL 

254 

255 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE 

256 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE 

257 _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK 

258 _LINE = AZIMUTH | LATITUDE | LONG_UNROLL 

259 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE 

260# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE 

261 

262Caps = Caps() # PYCHOK singleton 

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

264rhumb capabilities (C{caps}) and expected results (C{outmask}). 

265 

266C{AREA} - compute area C{S12}, 

267 

268C{AZIMUTH} - include azimuths C{azi1} and C{azi2}, 

269 

270C{DISTANCE} - compute distance C{s12}, 

271 

272C{DISTANCE_IN} - allow distance C{s12} in C{.Direct}, 

273 

274C{EMPTY} - nothing, formerly aka C{NONE}, 

275 

276C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21}, 

277 

278C{LINE_OFF} - Line without updates from parent geodesic or rhumb. 

279 

280C{LATITUDE} - compute latitude C{lat2}, 

281 

282C{LONGITUDE} - compute longitude C{lon2}, 

283 

284C{LONG_UNROLL} - unroll C{lon2} in C{.Direct}, 

285 

286C{REDUCEDLENGTH} - compute reduced length C{m12}, 

287 

288C{REVERSE2} - reverse C{azi2}, 

289 

290and C{ALL} - all of the above. 

291 

292C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}''' 

293 

294 

295class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases 

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

297 ''' 

298 ALL = Caps.ALL 

299 AREA = Caps.AREA 

300 AZIMUTH = Caps.AZIMUTH 

301 DISTANCE = Caps.DISTANCE 

302 DISTANCE_IN = Caps.DISTANCE_IN 

303 EMPTY = Caps.EMPTY # aka NONE 

304 GEODESICSCALE = Caps.GEODESICSCALE 

305 LATITUDE = Caps.LATITUDE 

306 LINE_OFF = Caps.LINE_OFF 

307 LONGITUDE = Caps.LONGITUDE 

308 LONG_UNROLL = Caps.LONG_UNROLL 

309 REDUCEDLENGTH = Caps.REDUCEDLENGTH 

310 STANDARD = Caps.STANDARD 

311 

312 _caps = 0 # None 

313 _debug = 0 # or Caps._DEBUG_... 

314 

315 @Property_RO 

316 def caps(self): 

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

318 ''' 

319 return self._caps 

320 

321 def caps_(self, caps): 

322 '''Check the available capabilities. 

323 

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

325 for all capabilities to be checked. 

326 

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

328 C{False} otherwise (C{bool}). 

329 ''' 

330 caps &= Caps._OUT_ALL 

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

332 

333 @property 

334 def debug(self): 

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

336 ''' 

337 return bool(self._debug) 

338 

339 @debug.setter # PYCHOK setter! 

340 def debug(self, debug): 

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

342 more details in L{GDict} results. 

343 ''' 

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

345 

346 def _iter2tion(self, r, s): 

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

348 ''' 

349 i = _xkwds_get(s, iter=None) 

350 if i is not None: 

351 self._iteration = r._iteration = i 

352 return r 

353 

354 

355class Direct9Tuple(_GTuple): 

356 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc 

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

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

359 C{meter} I{squared}. 

360 ''' 

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

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

363 

364 

365class GDict(_Dict): # XXX _NamedDict 

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

367 to the C{dict} items. 

368 

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

370 L{GDict} instance. 

371 ''' 

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

373 

374 @property_RO 

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

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

377 C{None} if not available/applicable. 

378 ''' 

379 return self._iteration 

380 

381 def toDirect9Tuple(self, dflt=NAN): 

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

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

384 

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

386 

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

388 s12, m12, M12, M21, S12)} 

389 ''' 

390 return self._toTuple(Direct9Tuple, dflt) 

391 

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

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

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

395 result. 

396 

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

398 

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

400 s12, a12, m12, M12, M21, S12)}. 

401 ''' 

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

403 

404 def toInverse10Tuple(self, dflt=NAN): 

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

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

407 

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

409 

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

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

412 ''' 

413 return self._toTuple(Inverse10Tuple, dflt) 

414 

415 @deprecated_method 

416 def toRhumb7Tuple(self, dflt=NAN): # PYCHOK no cover 

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

418 

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

420 ''' 

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

422 

423 def toRhumb8Tuple(self, dflt=NAN): 

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

425 

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

427 

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

429 azi12, s12, S12, a12)}. 

430 ''' 

431 return self._toTuple(Rhumb8Tuple, dflt) 

432 

433 def toRhumbSolve7Tuple(self, dflt=NAN): 

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

435 

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

437 

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

439 azi12, s12, S12)}. 

440 ''' 

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

442 

443 def _toTuple(self, nTuple, dflt): 

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

445 ''' 

446 _g = getattr 

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

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

449 

450 

451class Inverse10Tuple(_GTuple): 

452 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length 

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

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

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

456 ''' 

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

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

459 

460 def toGDict(self, **updates): 

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

462 

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

464 ''' 

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

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

467 **updates) # PYCHOK indent 

468 

469 

470class _kWrapped(object): 

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

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

473 ''' 

474 

475 @Property_RO 

476 def geographiclib(self): 

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

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

479 otherwise an C{ImportError}. 

480 ''' 

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

482 from geographiclib.geodesic import Geodesic 

483 g.Geodesic = Geodesic 

484 from geographiclib.geodesicline import GeodesicLine 

485 g.GeodesicLine = GeodesicLine 

486 from geographiclib.geomath import Math 

487 g.Math = Math 

488 return g 

489 

490 @Property_RO # MCCABE 13 

491 def Math(self): 

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

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

494 otherwise C{None}. 

495 ''' 

496 try: 

497 g = self.geographiclib 

498 M = g.Math 

499 if _xversion_info(g) < (2,): 

500 if _K_2_0: 

501 M = None 

502# elif not _K_2_0: # XXX set 2.0? 

503# _K_2_0 = True 

504 except (AttributeError, ImportError): 

505 M = None 

506 return M 

507 

508_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py 

509 

510 

511class Rhumb8Tuple(_GTuple): 

512 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1}, 

513 C{lat2} and longitudes C{lon1}, C{lon2} of both points, the azimuth of the 

514 rhumb line C{azi12}, the distance C{s12}, the area C{S12} under the rhumb 

515 line and the angular distance C{a12} between both points. 

516 ''' 

517 _Names_ = (_lat1_, _lon1_, _lat2_, _lon2_, _azi12_, _s12_, _S12_, _a12_) 

518 _Units_ = ( Lat, Lon, Lat, Lon, _Azi, _M, _M2, _Deg) 

519 

520 def toDirect9Tuple(self, dflt=NAN, **a12_azi1_azi2_m12_M12_M21): 

521 '''Convert this L{Rhumb8Tuple} result to a 9-tuple, like I{Karney}'s 

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

523 

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

525 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments 

526 to specify or override L{Inverse10Tuple} items. 

527 

528 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, s12, 

529 m12, M12, M21, S12)} 

530 ''' 

531 d = dict(azi1=self.azi12, M12=_1_0, m12=self.s12, # PYCHOK attr 

532 azi2=self.azi12, M21=_1_0) # PYCHOK attr 

533 if a12_azi1_azi2_m12_M12_M21: 

534 d.update(a12_azi1_azi2_m12_M12_M21) 

535 return self._toTuple(Direct9Tuple, dflt, d) 

536 

537 def toInverse10Tuple(self, dflt=NAN, **a12_m12_M12_M21_salp1_calp1_salp2_calp2): 

538 '''Convert this L{Rhumb8Tuple} to a 10-tuple, like I{Karney}'s 

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

540 

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

542 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword 

543 arguments to specify or override L{Inverse10Tuple} items. 

544 

545 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1, salp2, calp2, 

546 m12, M12, M21, S12)}. 

547 ''' 

548 s, c = sincos2d(self.azi12) # PYCHOK attr 

549 d = dict(salp1=s, calp1=c, M12=_1_0, m12=self.s12, # PYCHOK attr 

550 salp2=s, calp2=c, M21=_1_0) 

551 if a12_m12_M12_M21_salp1_calp1_salp2_calp2: 

552 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2) 

553 return self._toTuple(Inverse10Tuple, dflt, d) 

554 

555 def _toTuple(self, nTuple, dflt, updates={}): 

556 '''(INTERNAL) Convert this C{Rhumb8Tuple} to an B{C{nTuple}}. 

557 ''' 

558 _g = self.toGDict(**updates).get 

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

560 return nTuple(t, name=self.name) 

561 

562 @deprecated_method 

563 def _to7Tuple(self): 

564 '''DEPRECATED, do not use!''' 

565 return _MODS.deprecated.Rhumb7Tuple(self[:-1]) 

566 

567 

568def _around(x): # in .utily.sincos2d 

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

570 

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

572 

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

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

575 ''' 

576 try: 

577 return _wrapped.Math.AngRound(x) 

578 except AttributeError: 

579 if x: 

580 y = _1_16th - fabs(x) 

581 if y > 0: # fabs(x) < _1_16th 

582 x = _copysign(_1_16th - y, x) 

583 else: 

584 x = _0_0 # -0 to 0 

585 return x 

586 

587 

588def _atan2d(y, x): 

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

590 ''' 

591 try: 

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

593 except AttributeError: 

594 return atan2d(y, x) 

595 

596 

597def _cbrt(x): 

598 '''Return C{cubic root(B{x})}. 

599 ''' 

600 try: 

601 return _wrapped.Math.cbrt(x) 

602 except AttributeError: 

603 return cbrt(x) 

604 

605 

606def _copyBit(x, y): 

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

608 ''' 

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

610 

611 

612def _diff182(deg0, deg, K_2_0=False): 

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

614 

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

616 ''' 

617 try: 

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

619 except AttributeError: 

620 if K_2_0 or _K_2_0: # geographiclib 2.0 

621 _r, _360 = fremainder, _360_0 

622 d, t = _sum2(_r(-deg0, _360), 

623 _r( deg, _360)) 

624 d, t = _sum2(_r( d, _360), t) 

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

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

627 else: 

628 _n = _norm180 

629 d, t = _sum2(_n(-deg0), _n(deg)) 

630 d = _n(d) 

631 if t > 0 and d == _180_0: 

632 d = _N_180_0 

633 d, t = _sum2(d, t) 

634 return d, t 

635 

636 

637def _fix90(deg): # mimick Math.LatFix 

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

639 

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

641 ''' 

642 try: 

643 return _wrapped.Math.LatFix(deg) 

644 except AttributeError: 

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

646 

647 

648def _isfinite(x): # mimick geomath.Math.AngNormalize 

649 '''Check finiteness of C{x}. 

650 

651 @return: C{True} if finite. 

652 ''' 

653 try: 

654 return _wrapped.Math.isfinite(x) 

655 except AttributeError: 

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

657 

658 

659def _norm2(x, y): # mimick geomath.Math.norm 

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

661 

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

663 ''' 

664 try: 

665 return _wrapped.Math.norm(x, y) 

666 except AttributeError: 

667 return norm2(x, y) 

668 

669 

670def _norm180(deg): # mimick geomath.Math.AngNormalize 

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

672 

673 @return: Reduced angle C{degrees}. 

674 ''' 

675 try: 

676 return _wrapped.Math.AngNormalize(deg) 

677 except AttributeError: 

678 d = fremainder(deg, _360_0) 

679 if d in (_180_0, _N_180_0): 

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

681 return d 

682 

683 

684def _polygon(geodesic, points, closed, line, wrap): 

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

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

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

688 or C{geodesicw.Geodesic} instance. 

689 ''' 

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

691 notImplemented(None, wrap=wrap, up=3) 

692 

693 if _MODS.booleans.isBoolean(points): 

694 # recursive call for each boolean clip 

695 

696 def _a_p(clip, *args, **unused): 

697 return _polygon(geodesic, clip, *args) 

698 

699 if not closed: # closed only 

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

701 

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

703 

704 gP = geodesic.Polygon(line) 

705 _A = gP.AddPoint 

706 

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

708 p1 = p0 = Ps[0] 

709 

710 # note, lon deltas are unrolled, by default 

711 _A(p1.lat, p1.lon) 

712 for p2 in Ps.iterate(closed=closed): 

713 if wrap and not Ps.looped: 

714 p2 = _unrollon(p1, p2) 

715 _A(p2.lat, p2.lon) 

716 p1 = p2 

717 if closed and line and p1 != p0: 

718 _A(p0.lat, p0.lon) 

719 

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

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

722 

723 

724def _polynomial(x, cs, i, j): # PYCHOK shared 

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

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

727 

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

729 ''' 

730 # assert 0 <= i <= j <= len(cs) 

731# try: 

732# return _wrapped.Math.polyval(j - i - 1, cs, i, x) 

733# except AttributeError: 

734# pass 

735 s, t = cs[i], _0_0 

736 for c in cs[i+1:j]: 

737 s, t = _sum2_(s * x, t * x, c) 

738 return s # + t 

739 

740 

741def _remainder(x, y): 

742 '''Remainder of C{x / y}. 

743 

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

745 ''' 

746 try: 

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

748 except AttributeError: 

749 return fremainder(x, y) 

750 

751 

752if _K_2_0: 

753 from pygeodesy.basics import signBit as _signBit 

754 from math import cos as _cos, sin as _sin 

755 

756 def _sincos2(rad): 

757 return _sin(rad), _cos(rad) 

758 

759else: 

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

761 

762 def _signBit(x): 

763 '''(INTERNAL) GeographicLin 1.52-. 

764 ''' 

765 return x < 0 

766 

767 

768def _sincos2d(deg): 

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

770 

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

772 ''' 

773 try: 

774 return _wrapped.Math.sincosd(deg) 

775 except AttributeError: 

776 return sincos2d(deg) 

777 

778 

779def _sincos2de(deg, t): 

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

781 

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

783 ''' 

784 try: 

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

786 except AttributeError: 

787 return sincos2d(deg, adeg=t) 

788 

789 

790def _sum2(u, v): # mimick geomath.Math.sum, actually sum2 

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

792 

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

794 

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

796 

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

798 ''' 

799 try: 

800 return _wrapped.Math.sum(u, v) 

801 except AttributeError: 

802 s = u + v 

803 r = s - v 

804 t = s - r 

805 # if Algorithm_3_1: 

806 # t = (u - t) + (v + r) 

807 # elif C_CPP: # Math::sum C/C++ 

808 # r -= u 

809 # t -= v 

810 # t += r 

811 # t = -t 

812 # else: 

813 t = (u - r) + (v - t) 

814 return s, t 

815 

816 

817def _sum2_(s, t, *vs): 

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

819 

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

821 

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

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

824 function C{_sum2} above. 

825 

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

827 ''' 

828 _s2, _u0 = _sum2, unsigned0 

829 for v in vs: 

830 if v: 

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

832 if s: 

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

834 if s: 

835 t += u # accumulate u into t 

836# elif t: # s == 0 implies t == 0 

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

838 else: 

839 s = _u0(u) # result is u, t = 0 

840 else: 

841 s, t = _u0(t), u 

842 return s, t 

843 

844 

845def _tand(x): 

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

847 ''' 

848 try: 

849 return _wrapped.Math.tand(x) 

850 except AttributeError: 

851 return tand(x) 

852 

853 

854def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2 

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

856 

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

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

859 ''' 

860 if wrap: 

861 d, t = _diff182(lon1, lon2) 

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

863 else: 

864 lon2 = _norm180(lon2) 

865 return (lon2 - lon1), lon2 

866 

867 

868def _unsigned2(x): 

869 '''(INTERNAL) Unsign B{C{x}}. 

870 ''' 

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

872 

873 

874__all__ += _ALL_DOCS(_CapsBase) 

875 

876# **) MIT License 

877# 

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

879# 

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

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

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

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

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

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

886# 

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

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

889# 

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

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

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

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

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

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

896# OTHER DEALINGS IN THE SOFTWARE.