Coverage for pygeodesy/karney.py: 94%

282 statements  

« prev     ^ index     » next       coverage.py v7.2.2, created at 2023-09-15 09:43 -0400

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}, 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{rhumbx}, 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.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 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, 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, hypot as _hypot, norm2, \ 

143 Fsum, unstr # PYCHOK shared 

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

145from pygeodesy.interns import _2_, _a12_, _area_, _azi2_, _azi12_, _composite_, \ 

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

147 _number_, _s12_, _S12_ 

148from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv 

149from pygeodesy.named import _Dict, _NamedBase, _NamedTuple, notImplemented, _Pass 

150from pygeodesy.props import deprecated_method, Property_RO, property_RO 

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

152from pygeodesy.units import Bearing as _Azi, Degrees as _Deg, Lat, Lon, \ 

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

154 Precision_, _1mm as _TOL_M # PYCHOK shared 

155from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs 

156 

157# from math import fabs # from .utily 

158 

159__all__ = _ALL_LAZY.karney 

160__version__ = '23.09.15' 

161 

162_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_ 

163_perimeter_ = 'perimeter' 

164 

165 

166class _GTuple(_NamedTuple): # in .testNamedTuples 

167 '''(INTERNAL) Helper. 

168 ''' 

169 def toGDict(self, **updates): 

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

171 

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

173 ''' 

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

175 if updates: 

176 r.update(updates) 

177 if self._iteration is not None: 

178 r._iteration = self._iteration 

179 return r 

180 

181 

182class _Lat(Lat): 

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

184 ''' 

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

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

187 Lat.__new__(_Lat, *lat, **kwds) 

188 

189 

190class _Lon(Lon): 

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

192 ''' 

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

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

195 Lon.__new__(_Lon, *lon, **kwds) 

196 

197 

198class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea 

199 '''3-Tuple C{(number, perimeter, area)} with the C{number} 

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

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

202 ''' 

203 _Names_ = (_number_, _perimeter_, _area_) 

204 _Units_ = ( Number_, _M, _M2) 

205 

206 

207class Caps(object): # PYCHOK 

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

209 ''' 

210 EMPTY = 0 # formerly aka NONE 

211 _CAP_1 = 1 << 0 # for goedesicw only 

212 _CAP_1p = 1 << 1 # for goedesicw only 

213# _CAP_2 = 1 << 2 

214 _CAP_3 = 1 << 3 # for goedesicw only 

215# _CAP_4 = 1 << 4 

216# _CAP_ALL = 0x1F 

217# _CAP_MASK = _CAP_ALL 

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

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

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

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

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

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

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

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

226 

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

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

229 

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

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

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

233 _STD_LINE = _STD | _CAP_1p # for goedesicw only 

234 

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

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

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

238 

239 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE 

240 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA 

241 

242 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE 

243 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA 

244 

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

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

247 

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

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

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

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

252 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \ 

253 _DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs 

254 _OUT_ALL = ALL 

255 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL 

256 

257 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE 

258 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE 

259 _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK 

260 _LINE = AZIMUTH | LATITUDE | LONG_UNROLL 

261 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE 

262# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE 

263 

264Caps = Caps() # PYCHOK singleton 

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

266rhumb capabilities (C{caps}) and expected results (C{outmask}). 

267 

268C{AREA} - compute area C{S12}, 

269 

270C{AZIMUTH} - include azimuths C{azi1} and C{azi2}, 

271 

272C{DISTANCE} - compute distance C{s12}, 

273 

274C{DISTANCE_IN} - allow distance C{s12} in C{.Direct}, 

275 

276C{EMPTY} - nothing, formerly aka C{NONE}, 

277 

278C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21}, 

279 

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

281 

282C{LINE_OFF} - Line without updates from parent geodesic or rhumb. 

283 

284C{LONGITUDE} - compute longitude C{lon2}, 

285 

286C{LONG_UNROLL} - unroll C{lon2} in C{.Direct}, 

287 

288C{REDUCEDLENGTH} - compute reduced length C{m12}, 

289 

290C{REVERSE2} - reverse C{azi2}, 

291 

292and C{ALL} - all of the above. 

293 

294C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}''' 

295 

296 

297class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases 

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

299 ''' 

300 ALL = Caps.ALL 

301 AREA = Caps.AREA 

302 AZIMUTH = Caps.AZIMUTH 

303 DISTANCE = Caps.DISTANCE 

304 DISTANCE_IN = Caps.DISTANCE_IN 

305 EMPTY = Caps.EMPTY # aka NONE 

306 GEODESICSCALE = Caps.GEODESICSCALE 

307 LATITUDE = Caps.LATITUDE 

308 LINE_OFF = Caps.LINE_OFF 

309 LONGITUDE = Caps.LONGITUDE 

310 LONG_UNROLL = Caps.LONG_UNROLL 

311 REDUCEDLENGTH = Caps.REDUCEDLENGTH 

312 STANDARD = Caps.STANDARD 

313 

314 _caps = 0 # None 

315 _debug = 0 # or Caps._DEBUG_... 

316 

317 @Property_RO 

318 def caps(self): 

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

320 ''' 

321 return self._caps 

322 

323 def caps_(self, caps): 

324 '''Check the available capabilities. 

325 

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

327 for all capabilities to be checked. 

328 

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

330 C{False} otherwise (C{bool}). 

331 ''' 

332 caps &= Caps._OUT_ALL 

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

334 

335 @property 

336 def debug(self): 

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

338 ''' 

339 return bool(self._debug) 

340 

341 @debug.setter # PYCHOK setter! 

342 def debug(self, debug): 

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

344 more details in L{GDict} results. 

345 ''' 

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

347 

348 def _iter2tion(self, r, s): 

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

350 ''' 

351 i = _xkwds_get(s, iter=None) 

352 if i is not None: 

353 self._iteration = r._iteration = i 

354 return r 

355 

356 

357class Direct9Tuple(_GTuple): 

358 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc 

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

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

361 C{meter} I{squared}. 

362 ''' 

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

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

365 

366 

367class GDict(_Dict): # XXX _NamedDict 

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

369 to the C{dict} items. 

370 

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

372 L{GDict} instance. 

373 ''' 

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

375 

376 @property_RO 

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

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

379 C{None} if not available/applicable. 

380 ''' 

381 return self._iteration 

382 

383 def toDirect9Tuple(self, dflt=NAN): 

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

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

386 

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

388 

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

390 s12, m12, M12, M21, S12)} 

391 ''' 

392 return self._toTuple(Direct9Tuple, dflt) 

393 

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

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

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

397 result. 

398 

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

400 

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

402 s12, a12, m12, M12, M21, S12)}. 

403 ''' 

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

405 

406 def toInverse10Tuple(self, dflt=NAN): 

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

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

409 

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

411 

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

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

414 ''' 

415 return self._toTuple(Inverse10Tuple, dflt) 

416 

417 @deprecated_method 

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

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

420 

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

422 ''' 

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

424 

425 def toRhumb8Tuple(self, dflt=NAN): 

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

427 

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

429 

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

431 azi12, s12, S12, a12)}. 

432 ''' 

433 return self._toTuple(Rhumb8Tuple, dflt) 

434 

435 def toRhumbSolve7Tuple(self, dflt=NAN): 

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

437 

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

439 

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

441 azi12, s12, S12)}. 

442 ''' 

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

444 

445 def _toTuple(self, nTuple, dflt): 

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

447 ''' 

448 _g = getattr 

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

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

451 

452 

453class Inverse10Tuple(_GTuple): 

454 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length 

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

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

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

458 ''' 

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

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

461 

462 def toGDict(self, **updates): 

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

464 

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

466 ''' 

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

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

469 **updates) # PYCHOK indent 

470 

471 

472class _kWrapped(object): # in .geodesicw 

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

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

475 ''' 

476 

477 @Property_RO 

478 def geographiclib(self): 

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

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

481 otherwise an C{ImportError}. 

482 ''' 

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

484 from geographiclib.geodesic import Geodesic 

485 g.Geodesic = Geodesic 

486 from geographiclib.geodesicline import GeodesicLine 

487 g.GeodesicLine = GeodesicLine 

488 from geographiclib.geomath import Math 

489 g.Math = Math 

490 return g 

491 

492 @Property_RO # MCCABE 13 

493 def Math(self): 

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

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

496 otherwise C{None}. 

497 ''' 

498 try: 

499 g = self.geographiclib 

500 M = g.Math 

501 if _xversion_info(g) < (2,): 

502 if _K_2_0: 

503 M = None 

504# elif not _K_2_0: # XXX set 2.0? 

505# _K_2_0 = True 

506 except (AttributeError, ImportError): 

507 M = None 

508 return M 

509 

510_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py 

511 

512 

513class Rhumb8Tuple(_GTuple): 

514 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1}, 

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

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

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

518 ''' 

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

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

521 

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

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

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

525 

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

527 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments 

528 to specify or override L{Inverse10Tuple} items. 

529 

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

531 m12, M12, M21, S12)} 

532 ''' 

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

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

535 if a12_azi1_azi2_m12_M12_M21: 

536 d.update(a12_azi1_azi2_m12_M12_M21) 

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

538 

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

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

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

542 

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

544 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword 

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

546 

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

548 m12, M12, M21, S12)}. 

549 ''' 

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

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

552 salp2=s, calp2=c, M21=_1_0) 

553 if a12_m12_M12_M21_salp1_calp1_salp2_calp2: 

554 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2) 

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

556 

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

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

559 ''' 

560 _g = self.toGDict(**updates).get 

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

562 return nTuple(t, name=self.name) 

563 

564 @deprecated_method 

565 def _to7Tuple(self): 

566 '''DEPRECATED, do not use!''' 

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

568 

569 

570def _around(x): # in .utily.sincos2d 

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

572 

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

574 

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

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

577 ''' 

578 try: 

579 return _wrapped.Math.AngRound(x) 

580 except AttributeError: 

581 if x: 

582 y = _1_16th - fabs(x) 

583 if y > 0: # fabs(x) < _1_16th 

584 x = _copysign(_1_16th - y, x) 

585 else: 

586 x = _0_0 # -0 to 0 

587 return x 

588 

589 

590def _atan2d(y, x): 

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

592 ''' 

593 try: 

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

595 except AttributeError: 

596 return atan2d(y, x) 

597 

598 

599def _cbrt(x): 

600 '''Return C{cubic root(B{x})}. 

601 ''' 

602 try: 

603 return _wrapped.Math.cbrt(x) 

604 except AttributeError: 

605 return cbrt(x) 

606 

607 

608def _copyBit(x, y): 

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

610 ''' 

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

612 

613 

614def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases 

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

616 ''' 

617 r = cx - sx 

618 if r: 

619 r *= (cx + sx) * _2_0 

620 return r 

621 

622 

623def _diff182(deg0, deg, K_2_0=False): 

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

625 

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

627 ''' 

628 try: 

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

630 except AttributeError: 

631 if K_2_0 or _K_2_0: # geographiclib 2.0 

632 _r, _360 = fremainder, _360_0 

633 d, t = _sum2(_r(-deg0, _360), 

634 _r( deg, _360)) 

635 d, t = _sum2(_r( d, _360), t) 

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

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

638 else: 

639 _n = _norm180 

640 d, t = _sum2(_n(-deg0), _n(deg)) 

641 d = _n(d) 

642 if t > 0 and d == _180_0: 

643 d = _N_180_0 

644 d, t = _sum2(d, t) 

645 return d, t 

646 

647 

648def _fix90(deg): # mimick Math.LatFix 

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

650 

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

652 ''' 

653 try: 

654 return _wrapped.Math.LatFix(deg) 

655 except AttributeError: 

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

657 

658 

659def _isfinite(x): # mimick geomath.Math.isfinite 

660 '''Check finiteness of C{x}. 

661 

662 @return: C{True} if finite. 

663 ''' 

664 try: 

665 return _wrapped.Math.isfinite(x) 

666 except AttributeError: 

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

668 

669 

670def _norm2(x, y): # mimick geomath.Math.norm 

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

672 

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

674 ''' 

675 try: 

676 return _wrapped.Math.norm(x, y) 

677 except AttributeError: 

678 return norm2(x, y) 

679 

680 

681def _norm180(deg): # mimick geomath.Math.AngNormalize 

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

683 

684 @return: Reduced angle C{degrees}. 

685 ''' 

686 try: 

687 return _wrapped.Math.AngNormalize(deg) 

688 except AttributeError: 

689 d = fremainder(deg, _360_0) 

690 if d in (_180_0, _N_180_0): 

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

692 return d 

693 

694 

695def _polygon(geodesic, points, closed, line, wrap): 

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

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

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

699 or C{geodesicw.Geodesic} instance. 

700 ''' 

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

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

703 

704 if _MODS.booleans.isBoolean(points): 

705 # recursive call for each boolean clip 

706 

707 def _a_p(clip, *args, **unused): 

708 return _polygon(geodesic, clip, *args) 

709 

710 if not closed: # closed only 

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

712 

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

714 

715 gP = geodesic.Polygon(line) 

716 _A = gP.AddPoint 

717 

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

719 p1 = p0 = Ps[0] 

720 

721 # note, lon deltas are unrolled, by default 

722 _A(p1.lat, p1.lon) 

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

724 if wrap and not Ps.looped: 

725 p2 = _unrollon(p1, p2) 

726 _A(p2.lat, p2.lon) 

727 p1 = p2 

728 if closed and line and p1 != p0: 

729 _A(p0.lat, p0.lon) 

730 

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

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

733 

734 

735def _polynomial(x, cs, i, j): # PYCHOK shared 

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

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

738 

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

740 ''' 

741 # assert 0 <= i <= j <= len(cs) 

742# try: 

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

744# except AttributeError: 

745# pass 

746 s, t = cs[i], _0_0 

747 for c in cs[i+1:j]: 

748 s, t = _sum2_(s * x, t * x, c) 

749 return s # + t 

750 

751 

752def _remainder(x, y): 

753 '''Remainder of C{x / y}. 

754 

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

756 ''' 

757 try: 

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

759 except AttributeError: 

760 return fremainder(x, y) 

761 

762 

763if _K_2_0: 

764 from math import cos as _cos, sin as _sin 

765 

766 def _sincos2(rad): 

767 return _sin(rad), _cos(rad) 

768 

769 _signBit = _MODS.basics.signBit 

770else: 

771 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared 

772 

773 def _signBit(x): 

774 '''(INTERNAL) GeographicLib 1.52-. 

775 ''' 

776 return x < 0 

777 

778 

779def _sincos2d(deg): 

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

781 

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

783 ''' 

784 try: 

785 return _wrapped.Math.sincosd(deg) 

786 except AttributeError: 

787 return sincos2d(deg) 

788 

789 

790def _sincos2de(deg, t): 

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

792 

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

794 ''' 

795 try: 

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

797 except AttributeError: 

798 return sincos2d(deg, adeg=t) 

799 

800 

801def _sum2(u, v): # mimick geomath.Math.sum, actually sum2 

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

803 

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

805 

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

807 

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

809 ''' 

810 try: 

811 return _wrapped.Math.sum(u, v) 

812 except AttributeError: 

813 s = u + v 

814 r = s - v 

815 t = s - r 

816 # if Algorithm_3_1: 

817 # t = (u - t) + (v + r) 

818 # elif C_CPP: # Math::sum C/C++ 

819 # r -= u 

820 # t -= v 

821 # t += r 

822 # t = -t 

823 # else: 

824 t = (u - r) + (v - t) 

825 return s, t 

826 

827 

828def _sum2_(s, t, *vs): 

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

830 

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

832 

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

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

835 function C{_sum2} above. 

836 

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

838 ''' 

839 _s2, _u0 = _sum2, unsigned0 

840 for v in vs: 

841 if v: 

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

843 if s: 

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

845 if s: 

846 t += u # accumulate u into t 

847# elif t: # s == 0 implies t == 0 

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

849 else: 

850 s = _u0(u) # result is u, t = 0 

851 else: 

852 s, t = _u0(t), u 

853 return s, t 

854 

855 

856def _tand(x): 

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

858 ''' 

859 try: 

860 return _wrapped.Math.tand(x) 

861 except AttributeError: 

862 return tand(x) 

863 

864 

865def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2 

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

867 

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

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

870 ''' 

871 if wrap: 

872 d, t = _diff182(lon1, lon2) 

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

874 else: 

875 lon2 = _norm180(lon2) 

876 return (lon2 - lon1), lon2 

877 

878 

879def _unsigned2(x): 

880 '''(INTERNAL) Unsign B{C{x}}. 

881 ''' 

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

883 

884 

885__all__ += _ALL_DOCS(_CapsBase) 

886 

887# **) MIT License 

888# 

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

890# 

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

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

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

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

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

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

897# 

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

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

900# 

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

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

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

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

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

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

907# OTHER DEALINGS IN THE SOFTWARE.