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_16th, \ 

138 _1_0, _2_0, _180_0, _N_180_0, _360_0 

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

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

141from pygeodesy.errors import GeodesicError, _ValueError, _xkwds, _xkwds_get 

142from pygeodesy.fmath import cbrt, fremainder, norm2, unstr, \ 

143 Fsum, hypot as _hypot # PYCHOK shared 

144from pygeodesy.interns import _2_, _a12_, _area_, _azi2_, _azi12_, _composite_, \ 

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

146 _number_, _s12_, _S12_ 

147from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv 

148from pygeodesy.named import _Dict, _NamedBase, _NamedTuple, notImplemented, _Pass 

149from pygeodesy.props import deprecated_method, Property_RO, property_RO 

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

151from pygeodesy.units import Bearing as _Azi, Degrees as _Deg, Lat, Lon, \ 

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

153 Precision_, _1mm as _TOL_M # PYCHOK shared 

154from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs 

155 

156# from math import fabs # from .utily 

157 

158__all__ = _ALL_LAZY.karney 

159__version__ = '23.08.20' 

160 

161_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_ 

162_perimeter_ = 'perimeter' 

163 

164 

165class _GTuple(_NamedTuple): # in .testNamedTuples 

166 '''(INTERNAL) Helper. 

167 ''' 

168 def toGDict(self, **updates): 

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

170 

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

172 ''' 

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

174 if updates: 

175 r.update(updates) 

176 if self._iteration is not None: 

177 r._iteration = self._iteration 

178 return r 

179 

180 

181class _Lat(Lat): 

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

183 ''' 

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

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

186 Lat.__new__(_Lat, *lat, **kwds) 

187 

188 

189class _Lon(Lon): 

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

191 ''' 

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

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

194 Lon.__new__(_Lon, *lon, **kwds) 

195 

196 

197class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea 

198 '''3-Tuple C{(number, perimeter, area)} with the C{number} 

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

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

201 ''' 

202 _Names_ = (_number_, _perimeter_, _area_) 

203 _Units_ = ( Number_, _M, _M2) 

204 

205 

206class Caps(object): # PYCHOK 

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

208 ''' 

209 EMPTY = 0 # formerly aka NONE 

210 _CAP_1 = 1 << 0 # for goedesicw only 

211 _CAP_1p = 1 << 1 # for goedesicw only 

212# _CAP_2 = 1 << 2 

213 _CAP_3 = 1 << 3 # for goedesicw only 

214# _CAP_4 = 1 << 4 

215# _CAP_ALL = 0x1F 

216# _CAP_MASK = _CAP_ALL 

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

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

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

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

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

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

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

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

225 

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

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

228 

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

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

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

232 _STD_LINE = _STD | _CAP_1p # for goedesicw only 

233 

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

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

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

237 

238 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE 

239 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA 

240 

241 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE 

242 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA 

243 

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

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

246 

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

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

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

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

251 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \ 

252 _DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs 

253 _OUT_ALL = ALL 

254 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL 

255 

256 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE 

257 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE 

258 _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK 

259 _LINE = AZIMUTH | LATITUDE | LONG_UNROLL 

260 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE 

261# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE 

262 

263Caps = Caps() # PYCHOK singleton 

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

265rhumb capabilities (C{caps}) and expected results (C{outmask}). 

266 

267C{AREA} - compute area C{S12}, 

268 

269C{AZIMUTH} - include azimuths C{azi1} and C{azi2}, 

270 

271C{DISTANCE} - compute distance C{s12}, 

272 

273C{DISTANCE_IN} - allow distance C{s12} in C{.Direct}, 

274 

275C{EMPTY} - nothing, formerly aka C{NONE}, 

276 

277C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21}, 

278 

279C{LATITUDE} - compute latitude C{lat2}, 

280 

281C{LINE_OFF} - Line without updates from parent geodesic or rhumb. 

282 

283C{LONGITUDE} - compute longitude C{lon2}, 

284 

285C{LONG_UNROLL} - unroll C{lon2} in C{.Direct}, 

286 

287C{REDUCEDLENGTH} - compute reduced length C{m12}, 

288 

289C{REVERSE2} - reverse C{azi2}, 

290 

291and C{ALL} - all of the above. 

292 

293C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}''' 

294 

295 

296class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases 

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

298 ''' 

299 ALL = Caps.ALL 

300 AREA = Caps.AREA 

301 AZIMUTH = Caps.AZIMUTH 

302 DISTANCE = Caps.DISTANCE 

303 DISTANCE_IN = Caps.DISTANCE_IN 

304 EMPTY = Caps.EMPTY # aka NONE 

305 GEODESICSCALE = Caps.GEODESICSCALE 

306 LATITUDE = Caps.LATITUDE 

307 LINE_OFF = Caps.LINE_OFF 

308 LONGITUDE = Caps.LONGITUDE 

309 LONG_UNROLL = Caps.LONG_UNROLL 

310 REDUCEDLENGTH = Caps.REDUCEDLENGTH 

311 STANDARD = Caps.STANDARD 

312 

313 _caps = 0 # None 

314 _debug = 0 # or Caps._DEBUG_... 

315 

316 @Property_RO 

317 def caps(self): 

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

319 ''' 

320 return self._caps 

321 

322 def caps_(self, caps): 

323 '''Check the available capabilities. 

324 

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

326 for all capabilities to be checked. 

327 

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

329 C{False} otherwise (C{bool}). 

330 ''' 

331 caps &= Caps._OUT_ALL 

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

333 

334 @property 

335 def debug(self): 

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

337 ''' 

338 return bool(self._debug) 

339 

340 @debug.setter # PYCHOK setter! 

341 def debug(self, debug): 

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

343 more details in L{GDict} results. 

344 ''' 

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

346 

347 def _iter2tion(self, r, s): 

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

349 ''' 

350 i = _xkwds_get(s, iter=None) 

351 if i is not None: 

352 self._iteration = r._iteration = i 

353 return r 

354 

355 

356class Direct9Tuple(_GTuple): 

357 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc 

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

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

360 C{meter} I{squared}. 

361 ''' 

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

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

364 

365 

366class GDict(_Dict): # XXX _NamedDict 

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

368 to the C{dict} items. 

369 

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

371 L{GDict} instance. 

372 ''' 

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

374 

375 @property_RO 

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

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

378 C{None} if not available/applicable. 

379 ''' 

380 return self._iteration 

381 

382 def toDirect9Tuple(self, dflt=NAN): 

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

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

385 

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

387 

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

389 s12, m12, M12, M21, S12)} 

390 ''' 

391 return self._toTuple(Direct9Tuple, dflt) 

392 

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

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

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

396 result. 

397 

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

399 

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

401 s12, a12, m12, M12, M21, S12)}. 

402 ''' 

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

404 

405 def toInverse10Tuple(self, dflt=NAN): 

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

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

408 

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

410 

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

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

413 ''' 

414 return self._toTuple(Inverse10Tuple, dflt) 

415 

416 @deprecated_method 

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

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

419 

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

421 ''' 

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

423 

424 def toRhumb8Tuple(self, dflt=NAN): 

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

426 

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

428 

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

430 azi12, s12, S12, a12)}. 

431 ''' 

432 return self._toTuple(Rhumb8Tuple, dflt) 

433 

434 def toRhumbSolve7Tuple(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{RhumbSolve7Tuple}C{(lat1, lon1, lat2, lon2, 

440 azi12, s12, S12)}. 

441 ''' 

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

443 

444 def _toTuple(self, nTuple, dflt): 

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

446 ''' 

447 _g = getattr 

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

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

450 

451 

452class Inverse10Tuple(_GTuple): 

453 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length 

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

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

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

457 ''' 

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

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

460 

461 def toGDict(self, **updates): 

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

463 

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

465 ''' 

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

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

468 **updates) # PYCHOK indent 

469 

470 

471class _kWrapped(object): # in .geodesicw 

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

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

474 ''' 

475 

476 @Property_RO 

477 def geographiclib(self): 

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

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

480 otherwise an C{ImportError}. 

481 ''' 

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

483 from geographiclib.geodesic import Geodesic 

484 g.Geodesic = Geodesic 

485 from geographiclib.geodesicline import GeodesicLine 

486 g.GeodesicLine = GeodesicLine 

487 from geographiclib.geomath import Math 

488 g.Math = Math 

489 return g 

490 

491 @Property_RO # MCCABE 13 

492 def Math(self): 

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

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

495 otherwise C{None}. 

496 ''' 

497 try: 

498 g = self.geographiclib 

499 M = g.Math 

500 if _xversion_info(g) < (2,): 

501 if _K_2_0: 

502 M = None 

503# elif not _K_2_0: # XXX set 2.0? 

504# _K_2_0 = True 

505 except (AttributeError, ImportError): 

506 M = None 

507 return M 

508 

509_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py 

510 

511 

512class Rhumb8Tuple(_GTuple): 

513 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1}, 

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

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

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

517 ''' 

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

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

520 

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

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

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

524 

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

526 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments 

527 to specify or override L{Inverse10Tuple} items. 

528 

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

530 m12, M12, M21, S12)} 

531 ''' 

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

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

534 if a12_azi1_azi2_m12_M12_M21: 

535 d.update(a12_azi1_azi2_m12_M12_M21) 

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

537 

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

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

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

541 

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

543 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword 

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

545 

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

547 m12, M12, M21, S12)}. 

548 ''' 

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

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

551 salp2=s, calp2=c, M21=_1_0) 

552 if a12_m12_M12_M21_salp1_calp1_salp2_calp2: 

553 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2) 

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

555 

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

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

558 ''' 

559 _g = self.toGDict(**updates).get 

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

561 return nTuple(t, name=self.name) 

562 

563 @deprecated_method 

564 def _to7Tuple(self): 

565 '''DEPRECATED, do not use!''' 

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

567 

568 

569def _around(x): # in .utily.sincos2d 

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

571 

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

573 

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

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

576 ''' 

577 try: 

578 return _wrapped.Math.AngRound(x) 

579 except AttributeError: 

580 if x: 

581 y = _1_16th - fabs(x) 

582 if y > 0: # fabs(x) < _1_16th 

583 x = _copysign(_1_16th - y, x) 

584 else: 

585 x = _0_0 # -0 to 0 

586 return x 

587 

588 

589def _atan2d(y, x): 

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

591 ''' 

592 try: 

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

594 except AttributeError: 

595 return atan2d(y, x) 

596 

597 

598def _cbrt(x): 

599 '''Return C{cubic root(B{x})}. 

600 ''' 

601 try: 

602 return _wrapped.Math.cbrt(x) 

603 except AttributeError: 

604 return cbrt(x) 

605 

606 

607def _copyBit(x, y): 

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

609 ''' 

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

611 

612 

613def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases 

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

615 ''' 

616 r = cx - sx 

617 if r: 

618 r *= (cx + sx) * _2_0 

619 return r 

620 

621 

622def _diff182(deg0, deg, K_2_0=False): 

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

624 

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

626 ''' 

627 try: 

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

629 except AttributeError: 

630 if K_2_0 or _K_2_0: # geographiclib 2.0 

631 _r, _360 = fremainder, _360_0 

632 d, t = _sum2(_r(-deg0, _360), 

633 _r( deg, _360)) 

634 d, t = _sum2(_r( d, _360), t) 

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

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

637 else: 

638 _n = _norm180 

639 d, t = _sum2(_n(-deg0), _n(deg)) 

640 d = _n(d) 

641 if t > 0 and d == _180_0: 

642 d = _N_180_0 

643 d, t = _sum2(d, t) 

644 return d, t 

645 

646 

647def _fix90(deg): # mimick Math.LatFix 

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

649 

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

651 ''' 

652 try: 

653 return _wrapped.Math.LatFix(deg) 

654 except AttributeError: 

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

656 

657 

658def _isfinite(x): # mimick geomath.Math.isfinite 

659 '''Check finiteness of C{x}. 

660 

661 @return: C{True} if finite. 

662 ''' 

663 try: 

664 return _wrapped.Math.isfinite(x) 

665 except AttributeError: 

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

667 

668 

669def _norm2(x, y): # mimick geomath.Math.norm 

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

671 

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

673 ''' 

674 try: 

675 return _wrapped.Math.norm(x, y) 

676 except AttributeError: 

677 return norm2(x, y) 

678 

679 

680def _norm180(deg): # mimick geomath.Math.AngNormalize 

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

682 

683 @return: Reduced angle C{degrees}. 

684 ''' 

685 try: 

686 return _wrapped.Math.AngNormalize(deg) 

687 except AttributeError: 

688 d = fremainder(deg, _360_0) 

689 if d in (_180_0, _N_180_0): 

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

691 return d 

692 

693 

694def _polygon(geodesic, points, closed, line, wrap): 

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

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

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

698 or C{geodesicw.Geodesic} instance. 

699 ''' 

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

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

702 

703 if _MODS.booleans.isBoolean(points): 

704 # recursive call for each boolean clip 

705 

706 def _a_p(clip, *args, **unused): 

707 return _polygon(geodesic, clip, *args) 

708 

709 if not closed: # closed only 

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

711 

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

713 

714 gP = geodesic.Polygon(line) 

715 _A = gP.AddPoint 

716 

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

718 p1 = p0 = Ps[0] 

719 

720 # note, lon deltas are unrolled, by default 

721 _A(p1.lat, p1.lon) 

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

723 if wrap and not Ps.looped: 

724 p2 = _unrollon(p1, p2) 

725 _A(p2.lat, p2.lon) 

726 p1 = p2 

727 if closed and line and p1 != p0: 

728 _A(p0.lat, p0.lon) 

729 

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

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

732 

733 

734def _polynomial(x, cs, i, j): # PYCHOK shared 

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

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

737 

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

739 ''' 

740 # assert 0 <= i <= j <= len(cs) 

741# try: 

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

743# except AttributeError: 

744# pass 

745 s, t = cs[i], _0_0 

746 for c in cs[i+1:j]: 

747 s, t = _sum2_(s * x, t * x, c) 

748 return s # + t 

749 

750 

751def _remainder(x, y): 

752 '''Remainder of C{x / y}. 

753 

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

755 ''' 

756 try: 

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

758 except AttributeError: 

759 return fremainder(x, y) 

760 

761 

762if _K_2_0: 

763 from math import cos as _cos, sin as _sin 

764 

765 def _sincos2(rad): 

766 return _sin(rad), _cos(rad) 

767 

768 _signBit = _MODS.basics.signBit 

769else: 

770 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared 

771 

772 def _signBit(x): 

773 '''(INTERNAL) GeographicLib 1.52-. 

774 ''' 

775 return x < 0 

776 

777 

778def _sincos2d(deg): 

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

780 

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

782 ''' 

783 try: 

784 return _wrapped.Math.sincosd(deg) 

785 except AttributeError: 

786 return sincos2d(deg) 

787 

788 

789def _sincos2de(deg, t): 

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

791 

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

793 ''' 

794 try: 

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

796 except AttributeError: 

797 return sincos2d(deg, adeg=t) 

798 

799 

800def _sum2(u, v): # mimick geomath.Math.sum, actually sum2 

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

802 

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

804 

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

806 

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

808 ''' 

809 try: 

810 return _wrapped.Math.sum(u, v) 

811 except AttributeError: 

812 s = u + v 

813 r = s - v 

814 t = s - r 

815 # if Algorithm_3_1: 

816 # t = (u - t) + (v + r) 

817 # elif C_CPP: # Math::sum C/C++ 

818 # r -= u 

819 # t -= v 

820 # t += r 

821 # t = -t 

822 # else: 

823 t = (u - r) + (v - t) 

824 return s, t 

825 

826 

827def _sum2_(s, t, *vs): 

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

829 

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

831 

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

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

834 function C{_sum2} above. 

835 

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

837 ''' 

838 _s2, _u0 = _sum2, unsigned0 

839 for v in vs: 

840 if v: 

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

842 if s: 

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

844 if s: 

845 t += u # accumulate u into t 

846# elif t: # s == 0 implies t == 0 

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

848 else: 

849 s = _u0(u) # result is u, t = 0 

850 else: 

851 s, t = _u0(t), u 

852 return s, t 

853 

854 

855def _tand(x): 

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

857 ''' 

858 try: 

859 return _wrapped.Math.tand(x) 

860 except AttributeError: 

861 return tand(x) 

862 

863 

864def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2 

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

866 

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

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

869 ''' 

870 if wrap: 

871 d, t = _diff182(lon1, lon2) 

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

873 else: 

874 lon2 = _norm180(lon2) 

875 return (lon2 - lon1), lon2 

876 

877 

878def _unsigned2(x): 

879 '''(INTERNAL) Unsign B{C{x}}. 

880 ''' 

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

882 

883 

884__all__ += _ALL_DOCS(_CapsBase) 

885 

886# **) MIT License 

887# 

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

889# 

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

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

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

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

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

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

896# 

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

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

899# 

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

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

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

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

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

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

906# OTHER DEALINGS IN THE SOFTWARE.