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{rhumb.aux_}, L{RhumbAux}, L{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>} from I{GeographicLib 2.2+} 

75 

76 - L{rhumb.ekx}, L{Rhumb}, L{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 from 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{atan1d}, L{atan2d}, L{sincos2}, L{sincos2d}, L{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{rhumb.solve} 

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.Intersection} and L{RhumbLine.Intersection} 

118 

119are implementations of I{Karney}'s iterative solution posted under U{The B{ellipsoidal} case 

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

121on an ellipsoid of revolution<https://ArXiv.org/pdf/1102.1215.pdf>} (pp 20-21, section B{14. MARITIME BOUNDARIES}). 

122 

1234. The C{pygeodesy} methods to compute I{ellipsoidal} intersections and nearest points 

124 

125 - L{RhumbLineAux.Intersecant2}, L{RhumbLineAux.PlumbTo}, L{RhumbLine.Intersecant2} and L{RhumbLine.PlumbTo} 

126 

127are I{transcoded} of I{Karney}'s iterative C++ U{rhumb-intercept 

128<https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/>} function. 

129 

1305. Spherical functions 

131 

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

133 

134in C{pygeodesy} are based on I{Karney}'s post U{Area of a spherical polygon 

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

136''' 

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

138from __future__ import division as _; del _ # PYCHOK semicolon 

139 

140from pygeodesy.basics import _copysign, int1s, isint, neg, unsigned0, \ 

141 _xgeographiclib, _xImportError, _xversion_info, \ 

142 _xinstanceof, _zip, isodd # PYCHOK shared 

143from pygeodesy.constants import NAN, _isfinite as _math_isfinite, _0_0, \ 

144 _1_16th, _1_0, _2_0, _180_0, _N_180_0, _360_0 

145from pygeodesy.errors import GeodesicError, itemsorted, _ValueError, _xkwds, \ 

146 _xkwds_get 

147from pygeodesy.fmath import cbrt, fremainder, hypot as _hypot, norm2, \ 

148 euclid, Fsum, unstr # PYCHOK shared 

149# from pygeodesy.fsums import Fsum # from .fmath 

150from pygeodesy.interns import NN, _2_, _a12_, _area_, _azi2_, _azi12_, \ 

151 _composite_, _lat1_, _lat2_, _lon1_, _lon2_, \ 

152 _m12_, _M12_, _M21_, _number_, _s12_, _S12_, \ 

153 _UNDER_, _BAR_ # PYCHOK used! 

154from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv 

155from pygeodesy.named import _Dict, _NamedBase, _NamedTuple, notImplemented, _Pass 

156from pygeodesy.props import deprecated_method, Property_RO, property_RO # PYCHOK shared 

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

158from pygeodesy.units import Bearing as _Azi, Degrees as _Deg, Lat, Lon, \ 

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

160 Precision_, _1mm as _TOL_M # PYCHOK shared 

161from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs 

162 

163# from math import fabs # from .utily 

164 

165__all__ = _ALL_LAZY.karney 

166__version__ = '23.12.10' 

167 

168_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_ 

169_perimeter_ = 'perimeter' 

170 

171 

172class _GTuple(_NamedTuple): # in .testNamedTuples 

173 '''(INTERNAL) Helper. 

174 ''' 

175 def toGDict(self, **updates): 

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

177 

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

179 ''' 

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

181 if updates: 

182 r.update(updates) 

183 if self._iteration is not None: 

184 r._iteration = self._iteration 

185 return r 

186 

187 

188class _Lat(Lat): 

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

190 ''' 

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

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

193 Lat.__new__(_Lat, *lat, **kwds) 

194 

195 

196class _Lon(Lon): 

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

198 ''' 

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

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

201 Lon.__new__(_Lon, *lon, **kwds) 

202 

203 

204class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea 

205 '''3-Tuple C{(number, perimeter, area)} with the C{number} 

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

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

208 ''' 

209 _Names_ = (_number_, _perimeter_, _area_) 

210 _Units_ = ( Number_, _M, _M2) 

211 

212 

213class Caps(object): # PYCHOK 

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

215 ''' 

216 EMPTY = 0 # formerly aka NONE 

217 _CAP_1 = 1 << 0 # for goedesicw only 

218 _CAP_1p = 1 << 1 # for goedesicw only 

219# _CAP_2 = 1 << 2 

220 _CAP_3 = 1 << 3 # for goedesicw only 

221# _CAP_4 = 1 << 4 

222# _CAP_ALL = 0x1F 

223# _CAP_MASK = _CAP_ALL 

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

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

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

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

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

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

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

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

232 

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

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

235 

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

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

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

239 _STD_LINE = _STD | _CAP_1p # for goedesicw only 

240 

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

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

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

244 

245 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE 

246 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA 

247 

248 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE 

249 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA 

250 

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

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

253 

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

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

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

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

258 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \ 

259 _DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs 

260 

261 _OUT_ALL = ALL 

262 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL 

263 

264 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE 

265 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE 

266# _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK # == DISTANCE_IN in .gx, .gxline 

267 _LINE = AZIMUTH | LATITUDE | LONG_UNROLL 

268 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE 

269# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE 

270 

271 def toStr(self, Csk, sep=_BAR_): 

272 '''Return a C{Caps} or C{outmask} as C{str} or tuple of C{str}s. 

273 ''' 

274 s = [] 

275 for c, C in itemsorted(self.__class__.__dict__): 

276 if isint(C) and (Csk & C) and int1s(C) == 1 \ 

277 and (C in (Caps.REVERSE2, Caps._SALPs_CALPs) 

278 or c.replace(_UNDER_, NN).isupper()): 

279 s.append(c) 

280 return sep.join(s) if sep else tuple(s) 

281 

282Caps = Caps() # PYCHOK singleton 

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

284rhumb capabilities (C{caps}) and expected results (C{outmask}). 

285 

286C{AREA} - compute area C{S12}, 

287 

288C{AZIMUTH} - include azimuths C{azi1} and C{azi2}, 

289 

290C{DISTANCE} - compute distance C{s12}, 

291 

292C{DISTANCE_IN} - allow distance C{s12} in C{.Direct}, 

293 

294C{EMPTY} - nothing, formerly aka C{NONE}, 

295 

296C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21}, 

297 

298C{LATITUDE} - compute latitude C{lat2}, 

299 

300C{LINE_OFF} - Line without updates from parent geodesic or rhumb. 

301 

302C{LONGITUDE} - compute longitude C{lon2}, 

303 

304C{LONG_UNROLL} - unroll C{lon2} in C{.Direct}, 

305 

306C{REDUCEDLENGTH} - compute reduced length C{m12}, 

307 

308C{REVERSE2} - reverse C{azi2}, 

309 

310and C{ALL} - all of the above. 

311 

312C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}''' 

313 

314 

315class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases 

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

317 ''' 

318 ALL = Caps.ALL 

319 AREA = Caps.AREA 

320 AZIMUTH = Caps.AZIMUTH 

321 DISTANCE = Caps.DISTANCE 

322 DISTANCE_IN = Caps.DISTANCE_IN 

323 EMPTY = Caps.EMPTY # aka NONE 

324 GEODESICSCALE = Caps.GEODESICSCALE 

325 LATITUDE = Caps.LATITUDE 

326 LINE_OFF = Caps.LINE_OFF 

327 LONGITUDE = Caps.LONGITUDE 

328 LONG_UNROLL = Caps.LONG_UNROLL 

329 REDUCEDLENGTH = Caps.REDUCEDLENGTH 

330 STANDARD = Caps.STANDARD 

331 

332 _caps = 0 # None 

333 _debug = 0 # or Caps._DEBUG_... 

334 

335 @Property_RO 

336 def caps(self): 

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

338 ''' 

339 return self._caps 

340 

341 def caps_(self, caps): 

342 '''Check the available capabilities. 

343 

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

345 for all capabilities to be checked. 

346 

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

348 C{False} otherwise (C{bool}). 

349 ''' 

350 caps &= Caps._OUT_ALL 

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

352 

353 @property 

354 def debug(self): 

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

356 ''' 

357 return bool(self._debug) 

358 

359 @debug.setter # PYCHOK setter! 

360 def debug(self, debug): 

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

362 more details in L{GDict} results. 

363 ''' 

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

365 

366 def _iter2tion(self, r, s): 

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

368 ''' 

369 i = _xkwds_get(s, iter=None) 

370 if i is not None: 

371 self._iteration = r._iteration = i 

372 return r 

373 

374 

375class Direct9Tuple(_GTuple): 

376 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc 

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

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

379 C{meter} I{squared}. 

380 ''' 

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

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

383 

384 

385class GDict(_Dict): # XXX _NamedDict 

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

387 to the C{dict} items. 

388 

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

390 L{GDict} instance. 

391 ''' 

392 def toDirect9Tuple(self, dflt=NAN): 

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

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

395 

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

397 

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

399 s12, m12, M12, M21, S12)} 

400 ''' 

401 return self._toTuple(Direct9Tuple, dflt) 

402 

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

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

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

406 result. 

407 

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

409 

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

411 s12, a12, m12, M12, M21, S12)}. 

412 ''' 

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

414 

415 def toInverse10Tuple(self, dflt=NAN): 

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

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

418 

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

420 

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

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

423 ''' 

424 return self._toTuple(Inverse10Tuple, dflt) 

425 

426 @deprecated_method 

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

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

429 

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

431 ''' 

432 return self._toTuple(_MODS.deprecated.classes.Rhumb7Tuple, dflt) 

433 

434 def toRhumb8Tuple(self, dflt=NAN): 

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

436 

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

438 

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

440 azi12, s12, S12, a12)}. 

441 ''' 

442 return self._toTuple(Rhumb8Tuple, dflt) 

443 

444 def toRhumbSolve7Tuple(self, dflt=NAN): 

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

446 

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

448 

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

450 azi12, s12, S12)}. 

451 ''' 

452 return self._toTuple(_MODS.rhumb.solve.RhumbSolve7Tuple, dflt) 

453 

454 def _toTuple(self, nTuple, dflt): 

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

456 ''' 

457 _g = getattr 

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

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

460 

461 

462class Inverse10Tuple(_GTuple): 

463 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length 

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

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

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

467 ''' 

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

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

470 

471 def toGDict(self, **updates): 

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

473 

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

475 ''' 

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

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

478 **updates) # PYCHOK indent 

479 

480 

481class _kWrapped(object): # in .geodesicw 

482 ''''(INTERNAL) Wrapper around I{Karney}'s U{geographiclib 

483 <https://PyPI.org/project/geographiclib>}. 

484 ''' 

485 

486 @Property_RO 

487 def geographiclib(self): 

488 '''Lazily import C{geographiclib}, provided the U{geographiclib 

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

490 otherwise a C{LazyImportError}. 

491 ''' 

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

493 from geographiclib.geodesic import Geodesic 

494 g.Geodesic = Geodesic 

495 from geographiclib.geodesicline import GeodesicLine 

496 g.GeodesicLine = GeodesicLine 

497 from geographiclib.geomath import Math 

498 g.Math = Math 

499 return g 

500 

501 @Property_RO 

502 def Math(self): 

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

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

505 otherwise C{None}. 

506 ''' 

507 try: 

508 g = self.geographiclib 

509 M = g.Math 

510 if _xversion_info(g) < (2,): 

511 if _K_2_0: 

512 M = None 

513# elif not _K_2_0: # XXX set 2.0? 

514# _K_2_0 = True 

515 except (AttributeError, ImportError): 

516 M = None 

517 return M 

518 

519_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py 

520 

521 

522class Rhumb8Tuple(_GTuple): 

523 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1}, 

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

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

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

527 ''' 

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

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

530 

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

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

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

534 

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

536 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments 

537 to specify or override L{Inverse10Tuple} items. 

538 

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

540 m12, M12, M21, S12)} 

541 ''' 

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

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

544 if a12_azi1_azi2_m12_M12_M21: 

545 d.update(a12_azi1_azi2_m12_M12_M21) 

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

547 

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

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

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

551 

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

553 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword 

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

555 

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

557 m12, M12, M21, S12)}. 

558 ''' 

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

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

561 salp2=s, calp2=c, M21=_1_0) 

562 if a12_m12_M12_M21_salp1_calp1_salp2_calp2: 

563 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2) 

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

565 

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

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

568 ''' 

569 _g = self.toGDict(**updates).get 

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

571 return nTuple(t, name=self.name) 

572 

573 @deprecated_method 

574 def _to7Tuple(self): 

575 '''DEPRECATED, do not use!''' 

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

577 

578 

579def _around(x): # in .utily.sincos2d 

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

581 

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

583 

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

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

586 ''' 

587 try: 

588 return _wrapped.Math.AngRound(x) 

589 except AttributeError: 

590 if x: 

591 y = _1_16th - fabs(x) 

592 if y > 0: # fabs(x) < _1_16th 

593 x = _copysign(_1_16th - y, x) 

594 else: 

595 x = _0_0 # -0 to 0 

596 return x 

597 

598 

599def _atan2d(y, x): 

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

601 ''' 

602 try: 

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

604 except AttributeError: 

605 return atan2d(y, x) 

606 

607 

608def _cbrt(x): 

609 '''Return C{cubic root(B{x})}. 

610 ''' 

611 try: 

612 return _wrapped.Math.cbrt(x) 

613 except AttributeError: 

614 return cbrt(x) 

615 

616 

617def _copyBit(x, y): 

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

619 ''' 

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

621 

622 

623def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases 

624 '''Return M{2 * cos(2 * x)} from cos(x) and sin(x). 

625 ''' 

626 r = cx - sx 

627 if r: 

628 r *= (cx + sx) * _2_0 

629 return r 

630 

631 

632def _diff182(deg0, deg, K_2_0=False): 

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

634 

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

636 ''' 

637 try: 

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

639 except AttributeError: 

640 if K_2_0 or _K_2_0: # geographiclib 2.0 

641 _r, _360 = fremainder, _360_0 

642 d, t = _sum2(_r(-deg0, _360), 

643 _r( deg, _360)) 

644 d, t = _sum2(_r( d, _360), t) 

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

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

647 else: 

648 _n = _norm180 

649 d, t = _sum2(_n(-deg0), _n(deg)) 

650 d = _n(d) 

651 if t > 0 and d == _180_0: 

652 d = _N_180_0 

653 d, t = _sum2(d, t) 

654 return d, t 

655 

656 

657def _fix90(deg): # mimick Math.LatFix 

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

659 

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

661 ''' 

662 try: 

663 return _wrapped.Math.LatFix(deg) 

664 except AttributeError: 

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

666 

667 

668def _isfinite(x): # mimick geomath.Math.isfinite 

669 '''Check finiteness of C{x}. 

670 

671 @return: C{True} if finite. 

672 ''' 

673 try: 

674 return _wrapped.Math.isfinite(x) 

675 except AttributeError: 

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

677 

678 

679def _norm2(x, y): # mimick geomath.Math.norm 

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

681 

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

683 ''' 

684 try: 

685 return _wrapped.Math.norm(x, y) 

686 except AttributeError: 

687 return norm2(x, y) 

688 

689 

690def _norm180(deg): # mimick geomath.Math.AngNormalize 

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

692 

693 @return: Reduced angle C{degrees}. 

694 ''' 

695 try: 

696 return _wrapped.Math.AngNormalize(deg) 

697 except AttributeError: 

698 d = fremainder(deg, _360_0) 

699 if d in (_180_0, _N_180_0): 

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

701 return d 

702 

703 

704def _polygon(geodesic, points, closed, line, wrap): 

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

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

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

708 or C{geodesicw.Geodesic} instance. 

709 ''' 

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

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

712 

713 if _MODS.booleans.isBoolean(points): 

714 # recursive call for each boolean clip 

715 

716 def _a_p(clip, *args, **unused): 

717 return _polygon(geodesic, clip, *args) 

718 

719 if not closed: # closed only 

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

721 

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

723 

724 gP = geodesic.Polygon(line) 

725 _A = gP.AddPoint 

726 

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

728 p1 = p0 = Ps[0] 

729 

730 # note, lon deltas are unrolled, by default 

731 _A(p1.lat, p1.lon) 

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

733 if wrap and not Ps.looped: 

734 p2 = _unrollon(p1, p2) 

735 _A(p2.lat, p2.lon) 

736 p1 = p2 

737 if closed and line and p1 != p0: 

738 _A(p0.lat, p0.lon) 

739 

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

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

742 

743 

744def _polynomial(x, cs, i, j): # PYCHOK shared 

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

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

747 

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

749 ''' 

750 # assert 0 <= i <= j <= len(cs) 

751# try: 

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

753# except AttributeError: 

754# s, t = cs[i], _0_0 

755# for c in cs[i+1:j]: 

756# s, t = _sum2_(s * x, t * x, c) 

757# return s # + t 

758 s, _ = _sum2_(cs[i], _0_0, x=x, *cs[i+1:j]) 

759 return s # + t 

760 

761 

762def _remainder(x, y): 

763 '''Remainder of C{x / y}. 

764 

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

766 ''' 

767 try: 

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

769 except AttributeError: 

770 return fremainder(x, y) 

771 

772 

773if _K_2_0: 

774 from math import cos as _cos, sin as _sin 

775 

776 def _sincos2(rad): 

777 return _sin(rad), _cos(rad) 

778 

779 _signBit = _MODS.basics.signBit 

780else: 

781 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared 

782 

783 def _signBit(x): 

784 '''(INTERNAL) GeographicLib 1.52-. 

785 ''' 

786 return x < 0 

787 

788 

789def _sincos2d(deg): 

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

791 

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

793 ''' 

794 try: 

795 return _wrapped.Math.sincosd(deg) 

796 except AttributeError: 

797 return sincos2d(deg) 

798 

799 

800def _sincos2de(deg, t): 

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

802 

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

804 ''' 

805 try: 

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

807 except AttributeError: 

808 return sincos2d(deg, adeg=t) 

809 

810 

811def _sum2(u, v): # mimick geomath.Math.sum, actually sum2 

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

813 

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

815 

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

817 

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

819 ''' 

820 try: 

821 return _wrapped.Math.sum(u, v) 

822 except AttributeError: 

823 s = u + v 

824 r = s - v 

825 t = s - r 

826 # if Algorithm_3_1: 

827 # t = (u - t) + (v + r) 

828 # elif C_CPP: # Math::sum C/C++ 

829 # r -= u 

830 # t -= v 

831 # t += r 

832 # t = -t 

833 # else: 

834 t = (u - r) + (v - t) 

835 return s, t 

836 

837 

838def _sum2_(s, t, *vs, **x): 

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

840 

841 @kwarg x: Optional polynomial C{B{x}=1} (C{scalar}). 

842 

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

844 

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

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

847 function C{_sum2} above. 

848 

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

850 ''' 

851 x = _xkwds_get(x, x=0) 

852 

853 _s2, _u0 = _sum2, unsigned0 

854 for v in vs: 

855 if x: 

856 s *= x 

857 t *= x 

858 if v: 

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

860 if s: 

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

862 if s: 

863 t += u # accumulate u into t 

864# elif t: # s == 0 implies t == 0 

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

866 else: 

867 s = _u0(u) # result is u, t = 0 

868 else: 

869 s, t = _u0(t), u 

870 return s, t 

871 

872 

873def _tand(x): 

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

875 ''' 

876 try: 

877 return _wrapped.Math.tand(x) 

878 except AttributeError: 

879 return tand(x) 

880 

881 

882def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2 

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

884 

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

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

887 ''' 

888 if wrap: 

889 d, t = _diff182(lon1, lon2) 

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

891 else: 

892 lon2 = _norm180(lon2) 

893 return (lon2 - lon1), lon2 

894 

895 

896def _unsigned2(x): 

897 '''(INTERNAL) Unsign B{C{x}}. 

898 ''' 

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

900 

901 

902__all__ += _ALL_DOCS(_CapsBase) 

903 

904# **) MIT License 

905# 

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

907# 

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

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

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

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

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

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

914# 

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

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

917# 

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

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

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

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

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

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

924# OTHER DEALINGS IN THE SOFTWARE.