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{pygeodesy.atan1d}, 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{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.Intersecant2}, L{RhumbLineAux.Intersection} and L{RhumbLineAux.PlumbTo} C{(exact=None)} in L{rhumb.aux_} 

118 and L{RhumbLine.Intersecant2}, L{RhumbLine.Intersection} and L{RhumbLine.PlumbTo} C{(exact=None)} in L{rhumb.ekx} 

119 

120are implementations of I{Karney}'s iterative solution posted 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, int1s, isint, neg, unsigned0, \ 

135 _xgeographiclib, _xImportError, _xversion_info, \ 

136 _xinstanceof, _zip, isodd # PYCHOK shared 

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

138 _1_16th, _1_0, _2_0, _180_0, _N_180_0, _360_0 

139from pygeodesy.datums import _earth_datum, _EWGS84, _WGS84 # PYCHOK shared 

140# from pygeodesy.ellipsoids import _EWGS84 # from .datums 

141from pygeodesy.errors import GeodesicError, itemsorted, _ValueError, _xkwds, \ 

142 _xkwds_get 

143from pygeodesy.fmath import cbrt, fremainder, hypot as _hypot, norm2, \ 

144 euclid, Fsum, unstr # PYCHOK shared 

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

146from pygeodesy.interns import NN, _2_, _a12_, _area_, _azi2_, _azi12_, \ 

147 _composite_, _lat1_, _lat2_, _lon1_, _lon2_, \ 

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

149 _UNDER_, _BAR_ # PYCHOK used! 

150from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv 

151from pygeodesy.named import _Dict, _NamedBase, _NamedTuple, notImplemented, _Pass 

152from pygeodesy.props import deprecated_method, Property_RO, property_RO # PYCHOK shared 

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

154from pygeodesy.units import Bearing as _Azi, Degrees as _Deg, Lat, Lon, \ 

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

156 Precision_, _1mm as _TOL_M # PYCHOK shared 

157from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs 

158 

159# from math import fabs # from .utily 

160 

161__all__ = _ALL_LAZY.karney 

162__version__ = '23.12.02' 

163 

164_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_ 

165_perimeter_ = 'perimeter' 

166 

167 

168class _GTuple(_NamedTuple): # in .testNamedTuples 

169 '''(INTERNAL) Helper. 

170 ''' 

171 def toGDict(self, **updates): 

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

173 

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

175 ''' 

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

177 if updates: 

178 r.update(updates) 

179 if self._iteration is not None: 

180 r._iteration = self._iteration 

181 return r 

182 

183 

184class _Lat(Lat): 

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

186 ''' 

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

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

189 Lat.__new__(_Lat, *lat, **kwds) 

190 

191 

192class _Lon(Lon): 

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

194 ''' 

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

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

197 Lon.__new__(_Lon, *lon, **kwds) 

198 

199 

200class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea 

201 '''3-Tuple C{(number, perimeter, area)} with the C{number} 

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

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

204 ''' 

205 _Names_ = (_number_, _perimeter_, _area_) 

206 _Units_ = ( Number_, _M, _M2) 

207 

208 

209class Caps(object): # PYCHOK 

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

211 ''' 

212 EMPTY = 0 # formerly aka NONE 

213 _CAP_1 = 1 << 0 # for goedesicw only 

214 _CAP_1p = 1 << 1 # for goedesicw only 

215# _CAP_2 = 1 << 2 

216 _CAP_3 = 1 << 3 # for goedesicw only 

217# _CAP_4 = 1 << 4 

218# _CAP_ALL = 0x1F 

219# _CAP_MASK = _CAP_ALL 

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

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

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

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

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

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

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

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

228 

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

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

231 

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

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

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

235 _STD_LINE = _STD | _CAP_1p # for goedesicw only 

236 

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

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

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

240 

241 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE 

242 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA 

243 

244 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE 

245 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA 

246 

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

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

249 

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

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

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

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

254 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \ 

255 _DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs 

256 

257 _OUT_ALL = ALL 

258 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL 

259 

260 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE 

261 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE 

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

263 _LINE = AZIMUTH | LATITUDE | LONG_UNROLL 

264 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE 

265# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE 

266 

267 def toStr(self, Csk, sep=_BAR_): 

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

269 ''' 

270 s = [] 

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

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

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

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

275 s.append(c) 

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

277 

278Caps = Caps() # PYCHOK singleton 

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

280rhumb capabilities (C{caps}) and expected results (C{outmask}). 

281 

282C{AREA} - compute area C{S12}, 

283 

284C{AZIMUTH} - include azimuths C{azi1} and C{azi2}, 

285 

286C{DISTANCE} - compute distance C{s12}, 

287 

288C{DISTANCE_IN} - allow distance C{s12} in C{.Direct}, 

289 

290C{EMPTY} - nothing, formerly aka C{NONE}, 

291 

292C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21}, 

293 

294C{LATITUDE} - compute latitude C{lat2}, 

295 

296C{LINE_OFF} - Line without updates from parent geodesic or rhumb. 

297 

298C{LONGITUDE} - compute longitude C{lon2}, 

299 

300C{LONG_UNROLL} - unroll C{lon2} in C{.Direct}, 

301 

302C{REDUCEDLENGTH} - compute reduced length C{m12}, 

303 

304C{REVERSE2} - reverse C{azi2}, 

305 

306and C{ALL} - all of the above. 

307 

308C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}''' 

309 

310 

311class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases 

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

313 ''' 

314 ALL = Caps.ALL 

315 AREA = Caps.AREA 

316 AZIMUTH = Caps.AZIMUTH 

317 DISTANCE = Caps.DISTANCE 

318 DISTANCE_IN = Caps.DISTANCE_IN 

319 EMPTY = Caps.EMPTY # aka NONE 

320 GEODESICSCALE = Caps.GEODESICSCALE 

321 LATITUDE = Caps.LATITUDE 

322 LINE_OFF = Caps.LINE_OFF 

323 LONGITUDE = Caps.LONGITUDE 

324 LONG_UNROLL = Caps.LONG_UNROLL 

325 REDUCEDLENGTH = Caps.REDUCEDLENGTH 

326 STANDARD = Caps.STANDARD 

327 

328 _caps = 0 # None 

329 _debug = 0 # or Caps._DEBUG_... 

330 

331 @Property_RO 

332 def caps(self): 

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

334 ''' 

335 return self._caps 

336 

337 def caps_(self, caps): 

338 '''Check the available capabilities. 

339 

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

341 for all capabilities to be checked. 

342 

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

344 C{False} otherwise (C{bool}). 

345 ''' 

346 caps &= Caps._OUT_ALL 

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

348 

349 @property 

350 def debug(self): 

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

352 ''' 

353 return bool(self._debug) 

354 

355 @debug.setter # PYCHOK setter! 

356 def debug(self, debug): 

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

358 more details in L{GDict} results. 

359 ''' 

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

361 

362 def _iter2tion(self, r, s): 

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

364 ''' 

365 i = _xkwds_get(s, iter=None) 

366 if i is not None: 

367 self._iteration = r._iteration = i 

368 return r 

369 

370 

371class Direct9Tuple(_GTuple): 

372 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc 

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

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

375 C{meter} I{squared}. 

376 ''' 

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

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

379 

380 

381class GDict(_Dict): # XXX _NamedDict 

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

383 to the C{dict} items. 

384 

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

386 L{GDict} instance. 

387 ''' 

388 def toDirect9Tuple(self, dflt=NAN): 

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

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

391 

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

393 

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

395 s12, m12, M12, M21, S12)} 

396 ''' 

397 return self._toTuple(Direct9Tuple, dflt) 

398 

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

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

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

402 result. 

403 

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

405 

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

407 s12, a12, m12, M12, M21, S12)}. 

408 ''' 

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

410 

411 def toInverse10Tuple(self, dflt=NAN): 

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

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

414 

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

416 

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

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

419 ''' 

420 return self._toTuple(Inverse10Tuple, dflt) 

421 

422 @deprecated_method 

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

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

425 

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

427 ''' 

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

429 

430 def toRhumb8Tuple(self, dflt=NAN): 

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

432 

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

434 

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

436 azi12, s12, S12, a12)}. 

437 ''' 

438 return self._toTuple(Rhumb8Tuple, dflt) 

439 

440 def toRhumbSolve7Tuple(self, dflt=NAN): 

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

442 

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

444 

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

446 azi12, s12, S12)}. 

447 ''' 

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

449 

450 def _toTuple(self, nTuple, dflt): 

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

452 ''' 

453 _g = getattr 

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

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

456 

457 

458class Inverse10Tuple(_GTuple): 

459 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length 

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

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

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

463 ''' 

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

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

466 

467 def toGDict(self, **updates): 

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

469 

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

471 ''' 

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

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

474 **updates) # PYCHOK indent 

475 

476 

477class _kWrapped(object): # in .geodesicw 

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

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

480 ''' 

481 

482 @Property_RO 

483 def geographiclib(self): 

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

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

486 otherwise an C{ImportError}. 

487 ''' 

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

489 from geographiclib.geodesic import Geodesic 

490 g.Geodesic = Geodesic 

491 from geographiclib.geodesicline import GeodesicLine 

492 g.GeodesicLine = GeodesicLine 

493 from geographiclib.geomath import Math 

494 g.Math = Math 

495 return g 

496 

497 @Property_RO # MCCABE 13 

498 def Math(self): 

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

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

501 otherwise C{None}. 

502 ''' 

503 try: 

504 g = self.geographiclib 

505 M = g.Math 

506 if _xversion_info(g) < (2,): 

507 if _K_2_0: 

508 M = None 

509# elif not _K_2_0: # XXX set 2.0? 

510# _K_2_0 = True 

511 except (AttributeError, ImportError): 

512 M = None 

513 return M 

514 

515_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py 

516 

517 

518class Rhumb8Tuple(_GTuple): 

519 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1}, 

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

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

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

523 ''' 

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

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

526 

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

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

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

530 

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

532 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments 

533 to specify or override L{Inverse10Tuple} items. 

534 

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

536 m12, M12, M21, S12)} 

537 ''' 

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

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

540 if a12_azi1_azi2_m12_M12_M21: 

541 d.update(a12_azi1_azi2_m12_M12_M21) 

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

543 

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

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

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

547 

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

549 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword 

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

551 

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

553 m12, M12, M21, S12)}. 

554 ''' 

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

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

557 salp2=s, calp2=c, M21=_1_0) 

558 if a12_m12_M12_M21_salp1_calp1_salp2_calp2: 

559 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2) 

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

561 

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

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

564 ''' 

565 _g = self.toGDict(**updates).get 

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

567 return nTuple(t, name=self.name) 

568 

569 @deprecated_method 

570 def _to7Tuple(self): 

571 '''DEPRECATED, do not use!''' 

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

573 

574 

575def _around(x): # in .utily.sincos2d 

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

577 

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

579 

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

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

582 ''' 

583 try: 

584 return _wrapped.Math.AngRound(x) 

585 except AttributeError: 

586 if x: 

587 y = _1_16th - fabs(x) 

588 if y > 0: # fabs(x) < _1_16th 

589 x = _copysign(_1_16th - y, x) 

590 else: 

591 x = _0_0 # -0 to 0 

592 return x 

593 

594 

595def _atan2d(y, x): 

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

597 ''' 

598 try: 

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

600 except AttributeError: 

601 return atan2d(y, x) 

602 

603 

604def _cbrt(x): 

605 '''Return C{cubic root(B{x})}. 

606 ''' 

607 try: 

608 return _wrapped.Math.cbrt(x) 

609 except AttributeError: 

610 return cbrt(x) 

611 

612 

613def _copyBit(x, y): 

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

615 ''' 

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

617 

618 

619def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases 

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

621 ''' 

622 r = cx - sx 

623 if r: 

624 r *= (cx + sx) * _2_0 

625 return r 

626 

627 

628def _diff182(deg0, deg, K_2_0=False): 

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

630 

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

632 ''' 

633 try: 

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

635 except AttributeError: 

636 if K_2_0 or _K_2_0: # geographiclib 2.0 

637 _r, _360 = fremainder, _360_0 

638 d, t = _sum2(_r(-deg0, _360), 

639 _r( deg, _360)) 

640 d, t = _sum2(_r( d, _360), t) 

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

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

643 else: 

644 _n = _norm180 

645 d, t = _sum2(_n(-deg0), _n(deg)) 

646 d = _n(d) 

647 if t > 0 and d == _180_0: 

648 d = _N_180_0 

649 d, t = _sum2(d, t) 

650 return d, t 

651 

652 

653def _fix90(deg): # mimick Math.LatFix 

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

655 

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

657 ''' 

658 try: 

659 return _wrapped.Math.LatFix(deg) 

660 except AttributeError: 

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

662 

663 

664def _isfinite(x): # mimick geomath.Math.isfinite 

665 '''Check finiteness of C{x}. 

666 

667 @return: C{True} if finite. 

668 ''' 

669 try: 

670 return _wrapped.Math.isfinite(x) 

671 except AttributeError: 

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

673 

674 

675def _norm2(x, y): # mimick geomath.Math.norm 

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

677 

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

679 ''' 

680 try: 

681 return _wrapped.Math.norm(x, y) 

682 except AttributeError: 

683 return norm2(x, y) 

684 

685 

686def _norm180(deg): # mimick geomath.Math.AngNormalize 

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

688 

689 @return: Reduced angle C{degrees}. 

690 ''' 

691 try: 

692 return _wrapped.Math.AngNormalize(deg) 

693 except AttributeError: 

694 d = fremainder(deg, _360_0) 

695 if d in (_180_0, _N_180_0): 

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

697 return d 

698 

699 

700def _polygon(geodesic, points, closed, line, wrap): 

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

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

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

704 or C{geodesicw.Geodesic} instance. 

705 ''' 

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

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

708 

709 if _MODS.booleans.isBoolean(points): 

710 # recursive call for each boolean clip 

711 

712 def _a_p(clip, *args, **unused): 

713 return _polygon(geodesic, clip, *args) 

714 

715 if not closed: # closed only 

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

717 

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

719 

720 gP = geodesic.Polygon(line) 

721 _A = gP.AddPoint 

722 

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

724 p1 = p0 = Ps[0] 

725 

726 # note, lon deltas are unrolled, by default 

727 _A(p1.lat, p1.lon) 

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

729 if wrap and not Ps.looped: 

730 p2 = _unrollon(p1, p2) 

731 _A(p2.lat, p2.lon) 

732 p1 = p2 

733 if closed and line and p1 != p0: 

734 _A(p0.lat, p0.lon) 

735 

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

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

738 

739 

740def _polynomial(x, cs, i, j): # PYCHOK shared 

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

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

743 

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

745 ''' 

746 # assert 0 <= i <= j <= len(cs) 

747# try: 

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

749# except AttributeError: 

750# pass 

751 s, t = cs[i], _0_0 

752 for c in cs[i+1:j]: 

753 s, t = _sum2_(s * x, t * x, c) 

754 return s # + t 

755 

756 

757def _remainder(x, y): 

758 '''Remainder of C{x / y}. 

759 

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

761 ''' 

762 try: 

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

764 except AttributeError: 

765 return fremainder(x, y) 

766 

767 

768if _K_2_0: 

769 from math import cos as _cos, sin as _sin 

770 

771 def _sincos2(rad): 

772 return _sin(rad), _cos(rad) 

773 

774 _signBit = _MODS.basics.signBit 

775else: 

776 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared 

777 

778 def _signBit(x): 

779 '''(INTERNAL) GeographicLib 1.52-. 

780 ''' 

781 return x < 0 

782 

783 

784def _sincos2d(deg): 

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

786 

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

788 ''' 

789 try: 

790 return _wrapped.Math.sincosd(deg) 

791 except AttributeError: 

792 return sincos2d(deg) 

793 

794 

795def _sincos2de(deg, t): 

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

797 

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

799 ''' 

800 try: 

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

802 except AttributeError: 

803 return sincos2d(deg, adeg=t) 

804 

805 

806def _sum2(u, v): # mimick geomath.Math.sum, actually sum2 

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

808 

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

810 

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

812 

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

814 ''' 

815 try: 

816 return _wrapped.Math.sum(u, v) 

817 except AttributeError: 

818 s = u + v 

819 r = s - v 

820 t = s - r 

821 # if Algorithm_3_1: 

822 # t = (u - t) + (v + r) 

823 # elif C_CPP: # Math::sum C/C++ 

824 # r -= u 

825 # t -= v 

826 # t += r 

827 # t = -t 

828 # else: 

829 t = (u - r) + (v - t) 

830 return s, t 

831 

832 

833def _sum2_(s, t, *vs): 

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

835 

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

837 

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

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

840 function C{_sum2} above. 

841 

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

843 ''' 

844 _s2, _u0 = _sum2, unsigned0 

845 for v in vs: 

846 if v: 

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

848 if s: 

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

850 if s: 

851 t += u # accumulate u into t 

852# elif t: # s == 0 implies t == 0 

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

854 else: 

855 s = _u0(u) # result is u, t = 0 

856 else: 

857 s, t = _u0(t), u 

858 return s, t 

859 

860 

861def _tand(x): 

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

863 ''' 

864 try: 

865 return _wrapped.Math.tand(x) 

866 except AttributeError: 

867 return tand(x) 

868 

869 

870def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2 

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

872 

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

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

875 ''' 

876 if wrap: 

877 d, t = _diff182(lon1, lon2) 

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

879 else: 

880 lon2 = _norm180(lon2) 

881 return (lon2 - lon1), lon2 

882 

883 

884def _unsigned2(x): 

885 '''(INTERNAL) Unsign B{C{x}}. 

886 ''' 

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

888 

889 

890__all__ += _ALL_DOCS(_CapsBase) 

891 

892# **) MIT License 

893# 

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

895# 

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

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

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

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

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

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

902# 

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

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

905# 

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

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

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

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

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

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

912# OTHER DEALINGS IN THE SOFTWARE.