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 U{geographiclib 

5<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. 

9All methods of the I{wrapped} L{Geodesic<geodesicw.Geodesic>} and L{GeodesicLine<geodesicw.GeodesicLine>} 

10classes return a L{GDict} instance offering access to the C{dict} items either by C{key} or by 

11C{attribute} name. 

12 

13With env variable C{PYGEODESY_GEOGRAPHICLIB} left undefined or set to C{"2"}, modules L{geodesicx}, 

14L{geodesicw} and this module will use U{GeographicLib 2.0<https://GeographicLib.SourceForge.io/C++/doc/>} 

15and newer transcoding, otherwise C{1.52} or older. 

16 

17Karney-based functionality 

18========================== 

19 

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

21 

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

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

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

25 

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

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

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

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

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

31 

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

33 classGeographicLib_1_1CassiniSoldner.html>} 

34 

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

36 

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

38 classGeographicLib_1_1EllipticFunction.html>} 

39 

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

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

42 

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

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

45 

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

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

48 

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

50 classGeographicLib_1_1PolygonAreaT.html>} 

51 

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

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

54 classGeographicLib_1_1GeodesicLineExact.html>} 

55 

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

57 

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

59 

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

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

62 

63 - L{JacobiConformal} -- U{JacobiConformal 

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

65 

66 - L{KTransverseMercator} - U{TransverseMercator 

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

68 

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

70 classGeographicLib_1_1LocalCartesian.html>} 

71 

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

73 

74 - L{rhumb.aux_}, L{RhumbAux}, L{RhumbLineAux} -- U{Rhumb 

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

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

77 

78 - L{rhumb.ekx}, L{Rhumb}, L{RhumbLine} -- U{Rhumb 

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

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

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

82 from I{GeographicLib 2.0} 

83 

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

85 

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

87 

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

89 

90 - L{atan1d}, L{atan2d}, L{sincos2}, L{sincos2d}, L{tand} -- U{geomath.Math 

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

92 

93are I{transcoded} from C++ classes in I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>}. 

94 

952. These C{pygeodesy} modules and classes 

96 

97 - L{ellipsoidalGeodSolve}, L{ellipsoidalKarney}, L{geodsolve}, L{karney}, L{rhumb.solve} 

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

99 L{GnomonicKarney}, L{HeightIDWkarney} 

100 

101are or use I{wrappers} around I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} 

102C{geodesic}, C++ utility U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} or 

103C++ utility U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}. 

104 

1053. All C{pygeodesy} functions and methods to compute I{ellipsoidal} intersections, nearest points and trilaterations 

106 

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

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

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

110 

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

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

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

114 

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

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

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

118 

119 - L{RhumbLineAux.Intersection} and L{RhumbLine.Intersection} 

120 

121are implementations of I{Karney}'s iterative solution posted under U{The B{ellipsoidal} case 

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

123on an ellipsoid of revolution<https://ArXiv.org/pdf/1102.1215.pdf>} (pp 20-21, section B{14. MARITIME BOUNDARIES}). 

124 

1254. The C{pygeodesy} methods to compute I{ellipsoidal} intersections and nearest points 

126 

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

128 

129are I{transcoded} of I{Karney}'s iterative C++ function U{rhumb-intercept 

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

131 

1325. Spherical functions 

133 

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

135 

136in C{pygeodesy} are based on I{Karney}'s post U{Area of a spherical polygon 

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

138''' 

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

140from __future__ import division as _; del _ # PYCHOK semicolon 

141 

142from pygeodesy.basics import _copysign, int1s, isint, itemsorted, neg, unsigned0, \ 

143 _xgeographiclib, _zip, _version_info 

144from pygeodesy.constants import NAN, _isfinite as _math_isfinite, _0_0, \ 

145 _1_16th, _1_0, _2_0, _180_0, _N_180_0, _360_0 

146from pygeodesy.errors import GeodesicError, _ValueError, _xkwds, _xkwds_get 

147from pygeodesy.fmath import cbrt, fremainder, norm2 

148# from pygeodesy.internals import _version_info # from .basics 

149from pygeodesy.interns import NN, _2_, _a12_, _area_, _azi2_, _azi12_, _composite_, \ 

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

151 _number_, _s12_, _S12_, _UNDER_, _BAR_ # PYCHOK used! 

152from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv 

153from pygeodesy.named import ADict, _NamedBase, _NamedTuple, notImplemented, _Pass 

154from pygeodesy.props import deprecated_method, Property_RO 

155from pygeodesy.units import Bearing as _Azi, Degrees as _Deg, Lat, Lon, \ 

156 Meter as _M, Meter2 as _M2, Number_ 

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__ = '24.05.20' 

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): # NO name=NN 

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 of 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, iter=None, **unused): 

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

364 ''' 

365 if iter is not None: 

366 self._iteration = r._iteration = iter 

367 return r 

368 

369 

370class Direct9Tuple(_GTuple): 

371 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc 

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

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

374 C{meter} I{squared}. 

375 ''' 

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

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

378 

379 

380class GDict(ADict): # XXX _NamedDict 

381 '''A C{dict} with both C{key} I{and} C{attribute} access to the C{dict} items. 

382 

383 Results of all C{geodesic} and C{rhumb} methods (with capitalized named) are 

384 returned as L{GDict} instances, see for example L{GeodesicExact} and L{RhumbAux}. 

385 ''' 

386 def toDirect9Tuple(self, dflt=NAN): 

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

388 C{geographiclib.geodesic.Geodesic._GenDirect}. 

389 

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

391 

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

393 s12, m12, M12, M21, S12)} 

394 ''' 

395 return self._toTuple(Direct9Tuple, dflt) 

396 

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

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

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

400 result. 

401 

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

403 

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

405 s12, a12, m12, M12, M21, S12)}. 

406 ''' 

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

408 

409 def toInverse10Tuple(self, dflt=NAN): 

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

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

412 

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

414 

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

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

417 ''' 

418 return self._toTuple(Inverse10Tuple, dflt) 

419 

420 @deprecated_method 

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

422 '''DEPRECATED on 23.12.07, use method C{toRhumb8Tuple}. 

423 

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

425 ''' 

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

427 

428 def toRhumb8Tuple(self, dflt=NAN): 

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

430 

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

432 

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

434 azi12, s12, S12, a12)}. 

435 ''' 

436 return self._toTuple(Rhumb8Tuple, dflt) 

437 

438 def toRhumbSolve7Tuple(self, dflt=NAN): 

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

440 

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

442 

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

444 azi12, s12, S12)}. 

445 ''' 

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

447 

448 def _toTuple(self, nTuple, dflt): 

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

450 ''' 

451 _g = getattr 

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

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

454 

455 

456class Inverse10Tuple(_GTuple): 

457 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length 

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

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

460 C{calp2} of the initial C{1} and final C{2} (forward) azimuths. 

461 ''' 

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

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

464 

465 def toGDict(self, **updates): 

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

467 

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

469 ''' 

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

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

472 **updates) # PYCHOK indent 

473 

474 

475class _kWrapped(object): # in .geodesicw 

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

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

478 ''' 

479 

480 @Property_RO 

481 def geographiclib(self): 

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

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

484 otherwise raise a C{LazyImportError}. 

485 ''' 

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

487 from geographiclib.geodesic import Geodesic 

488 g.Geodesic = Geodesic 

489 from geographiclib.geodesicline import GeodesicLine 

490 g.GeodesicLine = GeodesicLine 

491 from geographiclib.geomath import Math 

492 g.Math = Math 

493 return g 

494 

495 @Property_RO 

496 def Math(self): 

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

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

499 otherwise C{None}. 

500 ''' 

501 try: 

502 g = self.geographiclib 

503 M = g.Math 

504 if _version_info(g) < (2,): 

505 if _K_2_0: 

506 M = None 

507# elif not _K_2_0: # XXX set 2.0? 

508# _K_2_0 = True 

509 except (AttributeError, ImportError): 

510 M = None 

511 return M 

512 

513_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py 

514 

515 

516class Rhumb8Tuple(_GTuple): 

517 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1}, 

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

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

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

521 ''' 

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

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

524 

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

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

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

528 

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

530 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments 

531 to specify or override L{Inverse10Tuple} items. 

532 

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

534 m12, M12, M21, S12)} 

535 ''' 

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

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

538 if a12_azi1_azi2_m12_M12_M21: 

539 d.update(a12_azi1_azi2_m12_M12_M21) 

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

541 

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

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

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

545 

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

547 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword 

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

549 

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

551 m12, M12, M21, S12)}. 

552 ''' 

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

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

555 salp2=s, calp2=c, M21=_1_0) 

556 if a12_m12_M12_M21_salp1_calp1_salp2_calp2: 

557 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2) 

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

559 

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

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

562 ''' 

563 _g = self.toGDict(**updates).get 

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

565 return nTuple(t, name=self.name) 

566 

567 @deprecated_method 

568 def _to7Tuple(self): 

569 '''DEPRECATED, do not use!''' 

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

571 

572 

573def _around(x): # in .utily.sincos2d 

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

575 

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

577 

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

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

580 ''' 

581 try: 

582 return _wrapped.Math.AngRound(x) 

583 except AttributeError: 

584 if x: 

585 y = _1_16th - fabs(x) 

586 if y > 0: # fabs(x) < _1_16th 

587 x = _copysign(_1_16th - y, x) 

588 else: 

589 x = _0_0 # -0 to 0 

590 return x 

591 

592 

593def _atan2d(y, x): 

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

595 ''' 

596 try: 

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

598 except AttributeError: 

599 return atan2d(y, x) 

600 

601 

602def _cbrt(x): 

603 '''Return C{cubic root(B{x})}. 

604 ''' 

605 try: 

606 return _wrapped.Math.cbrt(x) 

607 except AttributeError: 

608 return cbrt(x) 

609 

610 

611def _copyBit(x, y): 

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

613 ''' 

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

615 

616 

617def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases 

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

619 ''' 

620 r = cx - sx 

621 if r: 

622 r *= (cx + sx) * _2_0 

623 return r 

624 

625 

626def _diff182(deg0, deg, K_2_0=False): 

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

628 

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

630 ''' 

631 try: 

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

633 except AttributeError: 

634 if K_2_0 or _K_2_0: # geographiclib 2.0 

635 _r, _360 = fremainder, _360_0 

636 d, t = _sum2(_r(-deg0, _360), 

637 _r( deg, _360)) 

638 d, t = _sum2(_r( d, _360), t) 

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

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

641 else: 

642 _n = _norm180 

643 d, t = _sum2(_n(-deg0), _n(deg)) 

644 d = _n(d) 

645 if t > 0 and d == _180_0: 

646 d = _N_180_0 

647 d, t = _sum2(d, t) 

648 return d, t 

649 

650 

651def _fix90(deg): # mimick Math.LatFix 

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

653 

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

655 ''' 

656 try: 

657 return _wrapped.Math.LatFix(deg) 

658 except AttributeError: 

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

660 

661 

662def _isfinite(x): # mimick geomath.Math.isfinite 

663 '''Check finiteness of C{x}. 

664 

665 @return: C{True} if finite. 

666 ''' 

667 try: 

668 return _wrapped.Math.isfinite(x) 

669 except AttributeError: 

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

671 

672 

673def _norm2(x, y): # mimick geomath.Math.norm 

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

675 

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

677 ''' 

678 try: 

679 return _wrapped.Math.norm(x, y) 

680 except AttributeError: 

681 return norm2(x, y) 

682 

683 

684def _norm180(deg): # mimick geomath.Math.AngNormalize 

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

686 

687 @return: Reduced angle C{degrees}. 

688 ''' 

689 try: 

690 return _wrapped.Math.AngNormalize(deg) 

691 except AttributeError: 

692 d = fremainder(deg, _360_0) 

693 if d in (_180_0, _N_180_0): 

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

695 return d 

696 

697 

698def _polygon(geodesic, points, closed, line, wrap): 

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

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

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

702 or C{geodesicw.Geodesic} instance. 

703 ''' 

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

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

706 

707 if _MODS.booleans.isBoolean(points): 

708 # recursive call for each boolean clip 

709 

710 def _a_p(clip, *args, **unused): 

711 return _polygon(geodesic, clip, *args) 

712 

713 if not closed: # closed only 

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

715 

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

717 

718 gP = geodesic.Polygon(line) 

719 _A = gP.AddPoint 

720 

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

722 p1 = p0 = Ps[0] 

723 

724 # note, lon deltas are unrolled, by default 

725 _A(p1.lat, p1.lon) 

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

727 if wrap and not Ps.looped: 

728 p2 = _unrollon(p1, p2) 

729 _A(p2.lat, p2.lon) 

730 p1 = p2 

731 if closed and line and p1 != p0: 

732 _A(p0.lat, p0.lon) 

733 

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

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

736 

737 

738def _polynomial(x, cs, i, j): # PYCHOK shared 

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

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

741 

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

743 ''' 

744 # assert 0 <= i <= j <= len(cs) 

745# try: 

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

747# except AttributeError: 

748# s, t = cs[i], _0_0 

749# for c in cs[i+1:j]: 

750# s, t = _sum2_(s * x, t * x, c) 

751# return s # + t 

752 s = cs[i] 

753 i += 1 

754 if x and i < j: 

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

756 return s # + t 

757 

758 

759def _remainder(x, y): 

760 '''Remainder of C{x / y}. 

761 

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

763 ''' 

764 try: 

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

766 except AttributeError: 

767 return fremainder(x, y) 

768 

769 

770if _K_2_0: 

771 from math import cos as _cos, sin as _sin 

772 

773 def _sincos2(rad): 

774 return _sin(rad), _cos(rad) 

775 

776 _signBit = _MODS.basics.signBit 

777else: 

778 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared 

779 

780 def _signBit(x): 

781 '''(INTERNAL) GeographicLib 1.52-. 

782 ''' 

783 return x < 0 

784 

785 

786def _sincos2d(deg): 

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

788 

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

790 ''' 

791 try: 

792 return _wrapped.Math.sincosd(deg) 

793 except AttributeError: 

794 return sincos2d(deg) 

795 

796 

797def _sincos2de(deg, t): 

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

799 

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

801 ''' 

802 try: 

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

804 except AttributeError: 

805 return sincos2d(deg, adeg=t) 

806 

807 

808def _sum2(u, v): # mimick geomath.Math.sum, actually sum2 

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

810 

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

812 

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

814 

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

816 ''' 

817 try: 

818 return _wrapped.Math.sum(u, v) 

819 except AttributeError: 

820 s = u + v 

821 r = s - v 

822 t = s - r 

823 # if Algorithm_3_1: 

824 # t = (u - t) + (v + r) 

825 # elif C_CPP: # Math::sum C/C++ 

826 # r -= u 

827 # t -= v 

828 # t += r 

829 # t = -t 

830 # else: 

831 t = (u - r) + (v - t) 

832 return s, t 

833 

834 

835def _sum2_(s, t, *vs, **x): 

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

837 

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

839 

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

841 

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

843 C++/doc/Accumulator_8hpp_source.html>} comments for more details and 

844 function C{_sum2} above. 

845 

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

847 ''' 

848 x = _xkwds_get(x, x=_1_0) 

849 p = x != _1_0 

850 

851 _s2, _u0 = _sum2, unsigned0 

852 for v in vs: 

853 if p: 

854 s *= x 

855 t *= x 

856 if v: 

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

858 if s: 

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

860 if s: 

861 t += u # accumulate u into t 

862# elif t: # s == 0 implies t == 0 

863# raise _AssertionError(t=t, txt_not_=_0_) 

864 else: 

865 s = _u0(u) # result is u, t = 0 

866 else: 

867 s, t = _u0(t), u 

868 return s, t 

869 

870 

871def _tand(x): 

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

873 ''' 

874 try: 

875 return _wrapped.Math.tand(x) 

876 except AttributeError: 

877 return tand(x) 

878 

879 

880def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2 

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

882 

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

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

885 ''' 

886 if wrap: 

887 d, t = _diff182(lon1, lon2) 

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

889 else: 

890 lon2 = _norm180(lon2) 

891 return (lon2 - lon1), lon2 

892 

893 

894def _unsigned2(x): 

895 '''(INTERNAL) Unsign B{C{x}}. 

896 ''' 

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

898 

899 

900__all__ += _ALL_DOCS(_CapsBase) 

901 

902# **) MIT License 

903# 

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

905# 

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

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

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

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

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

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

912# 

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

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

915# 

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

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

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

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

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

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

922# OTHER DEALINGS IN THE SOFTWARE.