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_get1 

147from pygeodesy.fmath import cbrt, fremainder, norm2 

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

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

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

151 _M21_, _number_, _s12_, _S12_, _UNDER_, \ 

152 _BAR_, NN # PYCHOK used! 

153from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv 

154from pygeodesy.named import ADict, _NamedBase, _NamedTuple, notImplemented, _Pass 

155from pygeodesy.props import deprecated_method, Property_RO 

156from pygeodesy.units import Bearing as _Azi, Degrees as _Deg, Lat, Lon, \ 

157 Meter as _M, Meter2 as _M2, Number_ 

158from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs 

159 

160# from math import fabs # from .utily 

161 

162__all__ = _ALL_LAZY.karney 

163__version__ = '24.06.27' 

164 

165_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_ 

166_perimeter_ = 'perimeter' 

167 

168 

169class _GTuple(_NamedTuple): # in .testNamedTuples 

170 '''(INTERNAL) Helper. 

171 ''' 

172 def toGDict(self, **updates): # NO name=NN 

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

174 

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

176 ''' 

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

178 if updates: 

179 r.update(updates) 

180 if self._iteration is not None: 

181 r._iteration = self._iteration 

182 return r 

183 

184 

185class _Lat(Lat): 

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

187 ''' 

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

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

190 Lat.__new__(_Lat, *lat, **kwds) 

191 

192 

193class _Lon(Lon): 

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

195 ''' 

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

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

198 Lon.__new__(_Lon, *lon, **kwds) 

199 

200 

201class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea 

202 '''3-Tuple C{(number, perimeter, area)} with the C{number} 

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

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

205 ''' 

206 _Names_ = (_number_, _perimeter_, _area_) 

207 _Units_ = ( Number_, _M, _M2) 

208 

209 

210class Caps(object): # PYCHOK 

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

212 ''' 

213 EMPTY = 0 # formerly aka NONE 

214 _CAP_1 = 1 << 0 # for goedesicw only 

215 _CAP_1p = 1 << 1 # for goedesicw only 

216 _CAP_2 = 1 << 2 

217 _CAP_3 = 1 << 3 # for goedesicw only 

218# _CAP_4 = 1 << 4 

219# _CAP_ALL = 0x1F 

220# _CAP_MASK = _CAP_ALL 

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

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

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

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

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

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

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

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

229 

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

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

232 

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

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

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

236 _STD_LINE = _STD | _CAP_2 | _CAP_1p # for goedesici and -w 

237 

238 LINE_CAPS = _STD_LINE | REDUCEDLENGTH | GEODESICSCALE # .geodesici only 

239 

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

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

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

243 

244 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE 

245 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA 

246 

247 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE 

248 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA 

249 

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

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

252 

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

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

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

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

257 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \ 

258 _DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs 

259 

260 _OUT_ALL = ALL 

261 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL 

262 

263 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE 

264 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE 

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

266 _LINE = AZIMUTH | LATITUDE | LONG_UNROLL 

267 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE 

268# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE 

269 

270 def toStr(self, Csk, sep=_BAR_): 

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

272 ''' 

273 s = [] 

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

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

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

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

278 s.append(c) 

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

280 

281Caps = Caps() # PYCHOK singleton 

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

283rhumb capabilities (C{caps}) and expected results (C{outmask}). 

284 

285C{AREA} - compute area C{S12}, 

286 

287C{AZIMUTH} - include azimuths C{azi1} and C{azi2}, 

288 

289C{DISTANCE} - compute distance C{s12}, 

290 

291C{DISTANCE_IN} - allow distance C{s12} in C{.Direct}, 

292 

293C{EMPTY} - nothing, formerly aka C{NONE}, 

294 

295C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21}, 

296 

297C{LATITUDE} - compute latitude C{lat2}, 

298 

299C{LINE_OFF} - Line without updates from parent geodesic or rhumb. 

300 

301C{LONGITUDE} - compute longitude C{lon2}, 

302 

303C{LONG_UNROLL} - unroll C{lon2} in C{.Direct}, 

304 

305C{REDUCEDLENGTH} - compute reduced length C{m12}, 

306 

307C{REVERSE2} - reverse C{azi2}, 

308 

309and C{ALL} - all of the above. 

310 

311C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}''' 

312 

313_KEY2Caps = dict(m12=Caps.REDUCEDLENGTH, # see GDict._unCaps 

314 M12=Caps.GEODESICSCALE, 

315 M21=Caps.GEODESICSCALE, S12=Caps.AREA) 

316 

317 

318class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases 

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

320 ''' 

321 ALL = Caps.ALL 

322 AREA = Caps.AREA 

323 AZIMUTH = Caps.AZIMUTH 

324 DISTANCE = Caps.DISTANCE 

325 DISTANCE_IN = Caps.DISTANCE_IN 

326 EMPTY = Caps.EMPTY # aka NONE 

327 GEODESICSCALE = Caps.GEODESICSCALE 

328 LATITUDE = Caps.LATITUDE 

329 LINE_CAPS = Caps.LINE_CAPS 

330 LINE_OFF = Caps.LINE_OFF 

331 LONGITUDE = Caps.LONGITUDE 

332 LONG_UNROLL = Caps.LONG_UNROLL 

333 REDUCEDLENGTH = Caps.REDUCEDLENGTH 

334 STANDARD = Caps.STANDARD 

335 _STD_LINE = Caps._STD_LINE # for geodesici 

336 

337 _caps = 0 # None 

338 _debug = 0 # or Caps._DEBUG_... 

339 

340 @Property_RO 

341 def caps(self): 

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

343 ''' 

344 return self._caps 

345 

346 def caps_(self, caps): 

347 '''Check the available capabilities. 

348 

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

350 for all capabilities to be checked. 

351 

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

353 C{False} otherwise (C{bool}). 

354 ''' 

355 caps &= Caps._OUT_ALL 

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

357 

358 @property 

359 def debug(self): 

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

361 ''' 

362 return bool(self._debug) 

363 

364 @debug.setter # PYCHOK setter! 

365 def debug(self, debug): 

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

367 more details in L{GDict} results. 

368 ''' 

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

370 

371 def _iter2tion(self, r, iter=None, **unused): 

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

373 ''' 

374 if iter is not None: 

375 self._iteration = r._iteration = iter 

376 return r 

377 

378 

379class Direct9Tuple(_GTuple): 

380 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc 

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

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

383 C{meter} I{squared}. 

384 ''' 

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

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

387 

388 

389class GDict(ADict): # XXX _NamedDict 

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

391 

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

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

394 ''' 

395 def toDirect9Tuple(self, dflt=NAN): 

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

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

398 

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

400 

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

402 s12, m12, M12, M21, S12)} 

403 ''' 

404 return self._toTuple(Direct9Tuple, dflt) 

405 

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

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

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

409 result. 

410 

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

412 

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

414 s12, a12, m12, M12, M21, S12)}. 

415 ''' 

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

417 

418 def toInverse10Tuple(self, dflt=NAN): 

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

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

421 

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

423 

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

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

426 ''' 

427 return self._toTuple(Inverse10Tuple, dflt) 

428 

429 @deprecated_method 

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

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

432 

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

434 ''' 

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

436 

437 def toRhumb8Tuple(self, dflt=NAN): 

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

439 

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

441 

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

443 azi12, s12, S12, a12)}. 

444 ''' 

445 return self._toTuple(Rhumb8Tuple, dflt) 

446 

447 def toRhumbSolve7Tuple(self, dflt=NAN): 

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

449 

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

451 

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

453 azi12, s12, S12)}. 

454 ''' 

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

456 

457 def _toTuple(self, nTuple, dflt): 

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

459 ''' 

460 _g = getattr 

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

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

463 

464 def _unCaps(self, outmask): # in .geodsolve 

465 '''(INTERNAL) Remove superfluous items. 

466 ''' 

467 for k, m in _KEY2Caps.items(): 

468 if k in self and not (outmask & m): 

469 self.pop(k) # delattr(self, k) 

470 return self 

471 

472 

473class Inverse10Tuple(_GTuple): 

474 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length 

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

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

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

478 ''' 

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

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

481 

482 def toGDict(self, **updates): 

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

484 

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

486 ''' 

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

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

489 **updates) # PYCHOK indent 

490 

491 

492class _kWrapped(object): # in .geodesicw 

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

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

495 ''' 

496 

497 @Property_RO 

498 def geographiclib(self): 

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

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

501 otherwise raise a C{LazyImportError}. 

502 ''' 

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

504 from geographiclib.geodesic import Geodesic 

505 g.Geodesic = Geodesic 

506 from geographiclib.geodesicline import GeodesicLine 

507 g.GeodesicLine = GeodesicLine 

508 from geographiclib.geomath import Math 

509 g.Math = Math 

510 return g 

511 

512 @Property_RO 

513 def Math(self): 

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

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

516 otherwise C{None}. 

517 ''' 

518 try: 

519 g = self.geographiclib 

520 M = g.Math 

521 if _version_info(g) < (2,): 

522 if _K_2_0: 

523 M = None 

524# elif not _K_2_0: # XXX set 2.0? 

525# _K_2_0 = True 

526 except (AttributeError, ImportError): 

527 M = None 

528 return M 

529 

530_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py 

531 

532 

533class Rhumb8Tuple(_GTuple): 

534 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1}, 

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

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

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

538 ''' 

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

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

541 

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

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

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

545 

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

547 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments 

548 to specify or override L{Inverse10Tuple} items. 

549 

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

551 m12, M12, M21, S12)} 

552 ''' 

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

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

555 if a12_azi1_azi2_m12_M12_M21: 

556 d.update(a12_azi1_azi2_m12_M12_M21) 

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

558 

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

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

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

562 

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

564 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword 

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

566 

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

568 m12, M12, M21, S12)}. 

569 ''' 

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

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

572 salp2=s, calp2=c, M21=_1_0) 

573 if a12_m12_M12_M21_salp1_calp1_salp2_calp2: 

574 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2) 

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

576 

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

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

579 ''' 

580 _g = self.toGDict(**updates).get 

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

582 return nTuple(t, name=self.name) 

583 

584 @deprecated_method 

585 def _to7Tuple(self): 

586 '''DEPRECATED, do not use!''' 

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

588 

589 

590def _around(x): # in .utily.sincos2d 

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

592 

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

594 

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

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

597 ''' 

598 try: 

599 return _wrapped.Math.AngRound(x) 

600 except AttributeError: 

601 if x: 

602 y = _1_16th - fabs(x) 

603 if y > 0: # fabs(x) < _1_16th 

604 x = _copysign(_1_16th - y, x) 

605 else: 

606 x = _0_0 # -0 to 0 

607 return x 

608 

609 

610def _atan2d(y, x): 

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

612 ''' 

613 try: 

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

615 except AttributeError: 

616 return atan2d(y, x) 

617 

618 

619def _cbrt(x): 

620 '''Return C{cubic root(B{x})}. 

621 ''' 

622 try: 

623 return _wrapped.Math.cbrt(x) 

624 except AttributeError: 

625 return cbrt(x) 

626 

627 

628def _copyBit(x, y): 

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

630 ''' 

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

632 

633 

634def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases 

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

636 ''' 

637 r = cx - sx 

638 if r: 

639 r *= (cx + sx) * _2_0 

640 return r 

641 

642 

643def _diff182(deg0, deg, K_2_0=False): 

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

645 

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

647 ''' 

648 try: 

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

650 except AttributeError: 

651 if K_2_0 or _K_2_0: # geographiclib 2.0 

652 _r, _360 = fremainder, _360_0 

653 d, t = _sum2(_r(-deg0, _360), 

654 _r( deg, _360)) 

655 d, t = _sum2(_r( d, _360), t) 

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

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

658 else: 

659 _n = _norm180 

660 d, t = _sum2(_n(-deg0), _n(deg)) 

661 d = _n(d) 

662 if t > 0 and d == _180_0: 

663 d = _N_180_0 

664 d, t = _sum2(d, t) 

665 return d, t 

666 

667 

668def _fix90(deg): # mimick Math.LatFix 

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

670 

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

672 ''' 

673 try: 

674 return _wrapped.Math.LatFix(deg) 

675 except AttributeError: 

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

677 

678 

679def _isfinite(x): # mimick geomath.Math.isfinite 

680 '''Check finiteness of C{x}. 

681 

682 @return: C{True} if finite. 

683 ''' 

684 try: 

685 return _wrapped.Math.isfinite(x) 

686 except AttributeError: 

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

688 

689 

690def _norm2(x, y): # mimick geomath.Math.norm 

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

692 

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

694 ''' 

695 try: 

696 return _wrapped.Math.norm(x, y) 

697 except AttributeError: 

698 return norm2(x, y) 

699 

700 

701def _norm180(deg): # mimick geomath.Math.AngNormalize 

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

703 

704 @return: Reduced angle C{degrees}. 

705 ''' 

706 try: 

707 return _wrapped.Math.AngNormalize(deg) 

708 except AttributeError: 

709 d = fremainder(deg, _360_0) 

710 if d in (_180_0, _N_180_0): 

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

712 return d 

713 

714 

715def _polygon(geodesic, points, closed, line, wrap): 

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

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

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

719 or C{geodesicw.Geodesic} instance. 

720 ''' 

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

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

723 

724 if _MODS.booleans.isBoolean(points): 

725 # recursive call for each boolean clip 

726 

727 def _a_p(clip, *args, **unused): 

728 return _polygon(geodesic, clip, *args) 

729 

730 if not closed: # closed only 

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

732 

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

734 

735 gP = geodesic.Polygon(line) 

736 _A = gP.AddPoint 

737 

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

739 p1 = p0 = Ps[0] 

740 

741 # note, lon deltas are unrolled, by default 

742 _A(p1.lat, p1.lon) 

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

744 if wrap and not Ps.looped: 

745 p2 = _unrollon(p1, p2) 

746 _A(p2.lat, p2.lon) 

747 p1 = p2 

748 if closed and line and p1 != p0: 

749 _A(p0.lat, p0.lon) 

750 

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

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

753 

754 

755def _polynomial(x, cs, i, j): # PYCHOK shared 

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

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

758 

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

760 ''' 

761 # assert 0 <= i <= j <= len(cs) 

762# try: 

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

764# except AttributeError: 

765# s, t = cs[i], _0_0 

766# for c in cs[i+1:j]: 

767# s, t = _sum2_(s * x, t * x, c) 

768# return s # + t 

769 s = cs[i] 

770 i += 1 

771 if x and i < j: 

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

773 return s # + t 

774 

775 

776def _remainder(x, y): 

777 '''Remainder of C{x / y}. 

778 

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

780 ''' 

781 try: 

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

783 except AttributeError: 

784 return fremainder(x, y) 

785 

786 

787if _K_2_0: 

788 from math import cos as _cos, sin as _sin 

789 

790 def _sincos2(rad): 

791 return _sin(rad), _cos(rad) 

792 

793 _signBit = _MODS.basics.signBit 

794else: 

795 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared 

796 

797 def _signBit(x): 

798 '''(INTERNAL) GeographicLib 1.52-. 

799 ''' 

800 return x < 0 

801 

802 

803def _sincos2d(deg): 

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

805 

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

807 ''' 

808 try: 

809 return _wrapped.Math.sincosd(deg) 

810 except AttributeError: 

811 return sincos2d(deg) 

812 

813 

814def _sincos2de(deg, t): 

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

816 

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

818 ''' 

819 try: 

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

821 except AttributeError: 

822 return sincos2d(deg, adeg=t) 

823 

824 

825def _sum2(u, v): # mimick geomath.Math.sum, actually sum2 

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

827 

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

829 

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

831 

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

833 ''' 

834 try: 

835 return _wrapped.Math.sum(u, v) 

836 except AttributeError: 

837 s = u + v 

838 r = s - v 

839 t = s - r 

840 # if Algorithm_3_1: 

841 # t = (u - t) + (v + r) 

842 # elif C_CPP: # Math::sum C/C++ 

843 # r -= u 

844 # t -= v 

845 # t += r 

846 # t = -t 

847 # else: 

848 t = (u - r) + (v - t) 

849 return s, t 

850 

851 

852def _sum2_(s, t, *vs, **x): 

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

854 

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

856 

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

858 

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

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

861 function C{_sum2} above. 

862 

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

864 ''' 

865 x = _xkwds_get1(x, x=_1_0) 

866 p = x != _1_0 

867 

868 _s2, _u0 = _sum2, unsigned0 

869 for v in vs: 

870 if p: 

871 s *= x 

872 t *= x 

873 if v: 

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

875 if s: 

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

877 if s: 

878 t += u # accumulate u into t 

879# elif t: # s == 0 implies t == 0 

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

881 else: 

882 s = _u0(u) # result is u, t = 0 

883 else: 

884 s, t = _u0(t), u 

885 return s, t 

886 

887 

888def _tand(x): 

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

890 ''' 

891 try: 

892 return _wrapped.Math.tand(x) 

893 except AttributeError: 

894 return tand(x) 

895 

896 

897def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2 

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

899 

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

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

902 ''' 

903 if wrap: 

904 d, t = _diff182(lon1, lon2) 

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

906 else: 

907 lon2 = _norm180(lon2) 

908 return (lon2 - lon1), lon2 

909 

910 

911def _unsigned2(x): 

912 '''(INTERNAL) Unsign B{C{x}}. 

913 ''' 

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

915 

916 

917__all__ += _ALL_DOCS(_CapsBase) 

918 

919# **) MIT License 

920# 

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

922# 

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

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

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

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

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

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

929# 

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

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

932# 

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

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

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

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

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

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

939# OTHER DEALINGS IN THE SOFTWARE.