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 

7Methods of the I{wrapped} L{Geodesic<geodesicw.Geodesic>} and L{GeodesicLine<geodesicw.GeodesicLine>} 

8classes return a L{GDict} instance offering access to the C{dict} items either by C{key} or by 

9C{attribute} name. 

10 

11With env variable C{PYGEODESY_GEOGRAPHICLIB} left undefined or set to C{"2"}, modules L{geodesicw}, 

12L{geodesicx} and this module will use U{GeographicLib 2.0+<https://GeographicLib.SourceForge.io/C++/doc/>} 

13and newer transcoding, otherwise C{1.52} or older. Set C{PYGEODESY_GEOGRAPHICLIB=2.4} to default to the 

14C{Jacobi amplitude} instead of C{Bulirsch}' function in methods L{ExactTransverseMercator.forward 

15<pygeodesy.ExactTransverseMercator.forward>} and L{reverse <pygeodesy.ExactTransverseMercator.reverse>}. 

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{Intersector} -- U{Intersect 

64 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Intersect.html>} from I{GeographicLib 2.3+} 

65 

66 - L{JacobiConformal} -- U{JacobiConformal 

67 <https://geographiclib.sourceforge.io/C++/doc/classGeographicLib_1_1experimental_1_1JacobiConformal.html>} 

68 

69 - L{KTransverseMercator} - U{TransverseMercator 

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

71 

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

73 classGeographicLib_1_1LocalCartesian.html>} 

74 

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

76 

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

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

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

80 

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

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

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

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

85 from I{GeographicLib 2.0} 

86 

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

88 

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

90 

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

92 

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

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

95 

96are I{transcoded} from C++ classes in I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>}. 

97 

982. These C{pygeodesy} modules and classes 

99 

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

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

102 L{GnomonicKarney}, L{HeightIDWkarney}, L{Intersectool} 

103 

104are or use I{wrappers} around I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} or 

105C++ utility U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}, 

106U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>} or 

107U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}. 

108 

1093. All C{pygeodesy} functions and methods to compute I{ellipsoidal} intersections, nearest points and trilaterations 

110 

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

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

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

114 

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

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

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

118 

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

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

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

122 

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

124 

125are implementations of I{Karney}'s iterative solution posted under U{The B{ellipsoidal} case 

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

127on an ellipsoid of revolution<https://ArXiv.org/pdf/1102.1215.pdf>} (pp 20-21, section B{14. MARITIME BOUNDARIES}). 

128 

1294. The C{pygeodesy} methods to compute I{ellipsoidal} intersections and nearest points 

130 

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

132 

133are I{transcoded} of I{Karney}'s iterative C++ function U{rhumb-intercept 

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

135 

1365. Spherical functions 

137 

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

139 

140in C{pygeodesy} are based on I{Karney}'s post U{Area of a spherical polygon 

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

142''' 

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

144from __future__ import division as _; del _ # PYCHOK semicolon 

145 

146from pygeodesy.basics import _copysign, isint, neg, unsigned0, _xgeographiclib, \ 

147 _zip, _version_info 

148from pygeodesy.constants import NAN, _isfinite as _math_isfinite, _0_0, \ 

149 _1_16th, _1_0, _2_0, _180_0, _N_180_0, _360_0 

150from pygeodesy.errors import GeodesicError, _ValueError, _xkwds 

151from pygeodesy.fmath import cbrt, fremainder, norm2 # Fhorner, Fsum 

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

153from pygeodesy.interns import NN, _2_, _a12_, _area_, _azi1_, _azi2_, _azi12_, \ 

154 _composite_, _lat1_, _lat2_, _lon1_, _lon2_, \ 

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

156 _UNDER_, _X_, _BAR_ # PYCHOK used! 

157from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv 

158from pygeodesy.named import ADict, _NamedBase, _NamedTuple, notImplemented, _Pass 

159from pygeodesy.props import deprecated_method, Property_RO, property_RO, \ 

160 property_ROnce 

161from pygeodesy.units import Azimuth as _Azi, Degrees as _Deg, Lat, Lon, \ 

162 Meter as _M, Meter2 as _M2, Number_ 

163from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs 

164 

165# from math import fabs # from .utily 

166 

167__all__ = _ALL_LAZY.karney 

168__version__ = '24.09.13' 

169 

170_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) 

171_K_2_4 = _K_2_0 == '2.4' 

172_K_2_0 = _K_2_0 == _2_ or _K_2_4 

173_perimeter_ = 'perimeter' 

174 

175 

176class _GTuple(_NamedTuple): # in .testNamedTuples 

177 '''(INTERNAL) Helper. 

178 ''' 

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

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

181 

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

183 ''' 

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

185 if updates: 

186 r.update(updates) 

187 if self._iteration is not None: 

188 r._iteration = self._iteration 

189 return r 

190 

191 

192class _Lat(Lat): 

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

194 ''' 

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

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

197 Lat.__new__(_Lat, *lat, **kwds) 

198 

199 

200class _Lon(Lon): 

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

202 ''' 

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

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

205 Lon.__new__(_Lon, *lon, **kwds) 

206 

207 

208class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea 

209 '''3-Tuple C{(number, perimeter, area)} with the C{number} 

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

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

212 ''' 

213 _Names_ = (_number_, _perimeter_, _area_) 

214 _Units_ = ( Number_, _M, _M2) 

215 

216 

217class Caps(object): 

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

219 ''' 

220 EMPTY = 0 # formerly aka NONE 

221 _CAP_1 = 1 << 0 # for goedesici/-w 

222 _CAP_1p = 1 << 1 # for goedesici/-w 

223 _CAP_2 = 1 << 2 

224 _CAP_3 = 1 << 3 # for goedesici/-w 

225 _CAP_4 = 1 << 4 # for goedesicw 

226 _CAP_ALL = 0x1F 

227# _CAP_MASK = _CAP_ALL 

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

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

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

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

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

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

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

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

236 

237 STANDARD = AZIMUTH | DISTANCE | LATITUDE | LONGITUDE 

238 

239 _DIRECT3 = AZIMUTH | LATITUDE | LONGITUDE # for goedesicw only 

240 _INVERSE3 = AZIMUTH | DISTANCE # for goedesicw only 

241 _STD = STANDARD # for goedesicw only 

242 _STD_LINE = _STD | DISTANCE_IN # for goedesici/-w 

243 

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

245 LONG_UNROLL = 1 << 15 # unroll C{lon2} in .Direct and .Position 

246# = 1 << 16 # unused 

247 LINE_OFF = 1 << 17 # Line without updates from parent geodesic or rhumb 

248 REVERSE2 = 1 << 18 # reverse C{azi2} 

249 ALL = 0x7F80 | _CAP_ALL # without LONG_UNROLL, LINE_OFF, REVERSE2 and _DEBUG_* 

250 

251 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE 

252 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA 

253 

254 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE 

255 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA 

256 

257 _SALP_CALPs_ = 1 << 19 # (INTERNAL) GeodesicExact._GenInverse 

258 

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

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

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

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

263 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \ 

264 _DEBUG_LINE | _SALP_CALPs_ 

265 

266 _OUT_ALL = ALL # see geographiclib.geodesiccapabilities.py 

267 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL 

268 

269 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE 

270 _AZIMUTH_LATITUDE_LONG_UNROLL = AZIMUTH | LATITUDE | LONG_UNROLL 

271 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE 

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

273 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE 

274# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE 

275 

276 def items(self): 

277 '''Yield all I{public} C{Caps} as 2-tuple C{(NAME, mask)}. 

278 ''' 

279 for n, C in Caps.__class__.__dict__.items(): 

280 if isint(C) and not n.startswith(_UNDER_) \ 

281 and n.replace(_UNDER_, NN).isupper(): 

282 yield n, C 

283 

284 def toStr(self, Cask, sep=_BAR_): 

285 '''Return C{Caps} or an C{outmask} as C{str} or tuple of C{str}s. 

286 ''' 

287 s = (n for n, C in sorted(Caps.items()) 

288 if C and (Cask & C) == C) # and int1s(C) <= 3 

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

290 

291Caps = Caps() # PYCHOK singleton 

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

293rhumb capabilities (C{caps}) and results (C{outmask}). 

294 

295C{AREA} - compute area C{S12}, 

296 

297C{AZIMUTH} - include azimuths C{azi1} and C{azi2}, 

298 

299C{DISTANCE} - compute distance C{s12} and angular distance C{a12}, 

300 

301C{DISTANCE_IN} - allow distance C{s12} in C{.Direct}, 

302 

303C{EMPTY} - nothing, formerly aka C{NONE}, 

304 

305C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21}, 

306 

307C{LATITUDE} - compute latitude C{lat2}, 

308 

309C{LINE_OFF} - Line without updates from parent geodesic or rhumb. 

310 

311C{LONGITUDE} - compute longitude C{lon2}, 

312 

313C{LONG_UNROLL} - unroll C{lon2} in C{.Direct}, 

314 

315C{REDUCEDLENGTH} - compute reduced length C{m12}, 

316 

317C{REVERSE2} - reverse C{azi2}, 

318 

319and C{ALL} - all of the above. 

320 

321C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}''' 

322 

323_key2Caps = dict(a12 =Caps.DISTANCE, # in GDict._unCaps 

324 azi2=Caps.AZIMUTH, 

325 lat2=Caps.LATITUDE, 

326 lon2=Caps.LONGITUDE, 

327 m12 =Caps.REDUCEDLENGTH, 

328 M12 =Caps.GEODESICSCALE, 

329 M21 =Caps.GEODESICSCALE, 

330 s12 =Caps.DISTANCE, 

331 S12 =Caps.AREA) 

332 

333 

334class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases 

335 '''(INTERNAL) Base class for C{Geodesic*}, C{Geodesic*Exact}, C{Intersectool} and C{Rhumb*Base}. 

336 ''' 

337 ALL = Caps.ALL 

338 AREA = Caps.AREA 

339 AZIMUTH = Caps.AZIMUTH 

340 DISTANCE = Caps.DISTANCE 

341 DISTANCE_IN = Caps.DISTANCE_IN 

342 EMPTY = Caps.EMPTY # aka NONE 

343 GEODESICSCALE = Caps.GEODESICSCALE 

344 LATITUDE = Caps.LATITUDE 

345 LINE_CAPS = Caps.LINE_CAPS 

346 LINE_OFF = Caps.LINE_OFF 

347 LONGITUDE = Caps.LONGITUDE 

348 LONG_UNROLL = Caps.LONG_UNROLL 

349 REDUCEDLENGTH = Caps.REDUCEDLENGTH 

350 STANDARD = Caps.STANDARD 

351 _STD_LINE = Caps._STD_LINE # for geodesici 

352 

353 _caps = 0 # None 

354 _debug = 0 # or Caps._DEBUG_... 

355 

356 @Property_RO 

357 def caps(self): 

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

359 ''' 

360 return self._caps 

361 

362 def caps_(self, caps): 

363 '''Check the available capabilities. 

364 

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

366 for all capabilities to be checked. 

367 

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

369 C{False} otherwise (C{bool}). 

370 ''' 

371 caps &= Caps._OUT_ALL 

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

373 

374 @property 

375 def debug(self): 

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

377 ''' 

378 return bool(self._debug) 

379 

380 @debug.setter # PYCHOK setter! 

381 def debug(self, debug): 

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

383 more details in L{GDict} results. 

384 ''' 

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

386 

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

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

389 ''' 

390 if iter is not None: 

391 self._iteration = r._iteration = iter 

392 return r 

393 

394 

395class Direct9Tuple(_GTuple): 

396 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc 

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

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

399 C{meter} I{squared}. 

400 ''' 

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

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

403 

404 

405class GDict(ADict): # XXX _NamedDict 

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

407 

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

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

410 ''' 

411 def toDirect9Tuple(self, dflt=NAN): 

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

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

414 

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

416 

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

418 s12, m12, M12, M21, S12)} 

419 ''' 

420 return self._toTuple(Direct9Tuple, dflt) 

421 

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

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

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

425 result. 

426 

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

428 

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

430 s12, a12, m12, M12, M21, S12)}. 

431 ''' 

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

433 

434 def toInverse10Tuple(self, dflt=NAN): 

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

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

437 

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

439 

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

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

442 ''' 

443 return self._toTuple(Inverse10Tuple, dflt) 

444 

445 def _toNAN(self, outmask): # .GeodesicLineExact._GenPosition 

446 '''(INTERNAL) Convert this C{GDict} to all C{NAN}s. 

447 ''' 

448 d = dict((n, NAN) for n in GeodSolve12Tuple._Names_) 

449 return self.set_(**d)._unCaps(outmask) 

450 

451 @deprecated_method 

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

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

454 

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

456 ''' 

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

458 

459 def toRhumb8Tuple(self, dflt=NAN): 

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

461 

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

463 

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

465 azi12, s12, S12, a12)}. 

466 ''' 

467 return self._toTuple(Rhumb8Tuple, dflt) 

468 

469 def toRhumbSolve7Tuple(self, dflt=NAN): 

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

471 

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

473 

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

475 azi12, s12, S12)}. 

476 ''' 

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

478 

479 def _toTuple(self, nTuple, dflt): 

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

481 ''' 

482 _g = getattr 

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

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

485 

486 def _2X(self, gl, _2X=_X_): # .Intersectool, .Intersector 

487 '''(INTERNAL) Rename C{-2} attr to C{-X} or C{-M}. 

488 ''' 

489 X = GDict(self) 

490 for n in (_lat2_, _lon2_, _azi2_, _s12_, _a12_): 

491 if n in X: # X._X = X._2 

492 X[n[:-1] + _2X] = X.pop(n) 

493 v = getattr(gl, n, X) 

494 if v is not X: # X._2 = gl._2 

495 X[n] = v 

496 return X 

497 

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

499 '''(INTERNAL) Remove superfluous items. 

500 ''' 

501 for k, C in _key2Caps.items(): 

502 if k in self and (outmask & C) != C: 

503 self.pop(k) # delattr(self, k) 

504 return self 

505 

506 

507class GeodSolve12Tuple(_GTuple): 

508 '''12-Tuple C{(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)} with 

509 angles C{lat1}, C{lon1}, C{azi1}, C{lat2}, C{lon2} and C{azi2} and arc C{a12} all in 

510 C{degrees}, initial C{azi1} and final C{azi2} forward azimuths, distance C{s12} and 

511 reduced length C{m12} in C{meter}, area C{S12} in C{meter} I{squared} and geodesic 

512 scale factors C{M12} and C{M21}, both C{scalar}, see U{GeodSolve 

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

514 ''' 

515 # from GeodSolve --help option -f ... lat1 lon1 azi1 lat2 lon2 azi2 s12 a12 m12 M12 M21 S12 

516 _Names_ = (_lat1_, _lon1_, _azi1_, _lat2_, _lon2_, _azi2_, _s12_, _a12_, _m12_, _M12_, _M21_, _S12_) 

517 _Units_ = (_Lat, _Lon, _Azi, _Lat, _Lon, _Azi, _M, _Deg, _Pass, _Pass, _Pass, _M2) 

518 

519 

520class Inverse10Tuple(_GTuple): 

521 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length 

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

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

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

525 ''' 

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

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

528 

529 def toGDict(self, **updates): 

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

531 

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

533 ''' 

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

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

536 **updates) # PYCHOK indent 

537 

538 

539class _kWrapped(object): # in .geodesicw 

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

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

542 ''' 

543 

544 @property_ROnce 

545 def geographiclib(self): 

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

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

548 otherwise raise a C{LazyImportError}. 

549 ''' 

550 g = _xgeographiclib(self.__class__.__module__, 1, 49) 

551 from geographiclib.geodesic import Geodesic 

552 g.Geodesic = Geodesic 

553 from geographiclib.geodesicline import GeodesicLine 

554 g.GeodesicLine = GeodesicLine 

555 from geographiclib.geomath import Math 

556 g.Math = Math 

557 return g 

558 

559 @property_ROnce 

560 def Math(self): 

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

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

563 otherwise C{None}. 

564 ''' 

565 try: 

566 g = self.geographiclib 

567 M = g.Math 

568 if _version_info(g) < (2,): 

569 if _K_2_0: 

570 M = None 

571# elif not _K_2_0: # XXX set 2.0? 

572# _K_2_0 = True 

573 except (AttributeError, ImportError): 

574 M = None 

575 return M 

576 

577 @property_RO 

578 def Math_K_2(self): 

579 return ('_K_2_4' if _K_2_4 else 

580 ('_K_2_0' if _K_2_0 else '_K_1_0')) if self.Math else NN 

581 

582_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py 

583 

584 

585class Rhumb8Tuple(_GTuple): 

586 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1}, 

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

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

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

590 ''' 

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

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

593 

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

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

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

597 

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

599 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments 

600 to specify or override L{Inverse10Tuple} items. 

601 

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

603 m12, M12, M21, S12)} 

604 ''' 

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

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

607 if a12_azi1_azi2_m12_M12_M21: 

608 d.update(a12_azi1_azi2_m12_M12_M21) 

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

610 

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

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

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

614 

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

616 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword 

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

618 

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

620 m12, M12, M21, S12)}. 

621 ''' 

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

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

624 salp2=s, calp2=c, M21=_1_0) 

625 if a12_m12_M12_M21_salp1_calp1_salp2_calp2: 

626 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2) 

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

628 

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

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

631 ''' 

632 _g = self.toGDict(**updates).get 

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

634 return nTuple(t, name=self.name) 

635 

636 @deprecated_method 

637 def _to7Tuple(self): 

638 '''DEPRECATED, do not use!''' 

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

640 

641 

642def _around(x): # in .utily.sincos2d 

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

644 

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

646 

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

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

649 ''' 

650 try: 

651 return _wrapped.Math.AngRound(x) 

652 except AttributeError: 

653 if x: 

654 y = _1_16th - fabs(x) 

655 if y > 0: # fabs(x) < _1_16th 

656 x = _copysign(_1_16th - y, x) 

657 else: 

658 x = _0_0 # -0 to 0 

659 return x 

660 

661 

662def _atan2d(y, x): 

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

664 ''' 

665 try: 

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

667 except AttributeError: 

668 return atan2d(y, x) 

669 

670 

671def _cbrt(x): 

672 '''Return C{cubic root(B{x})}. 

673 ''' 

674 try: 

675 return _wrapped.Math.cbrt(x) 

676 except AttributeError: 

677 return cbrt(x) 

678 

679 

680def _copyBit(x, y): 

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

682 ''' 

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

684 

685 

686def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases 

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

688 ''' 

689 r = cx - sx 

690 if r: 

691 r *= (cx + sx) * _2_0 

692 return r 

693 

694 

695def _diff182(deg0, deg, K_2_0=False): 

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

697 

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

699 ''' 

700 try: 

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

702 except AttributeError: 

703 if K_2_0 or _K_2_0: # geographiclib 2.0 

704 _r, _360 = fremainder, _360_0 

705 d, t = _sum2(_r(-deg0, _360), 

706 _r( deg, _360)) 

707 d, t = _sum2(_r( d, _360), t) 

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

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

710 else: 

711 _n = _norm180 

712 d, t = _sum2(_n(-deg0), _n(deg)) 

713 d = _n(d) 

714 if t > 0 and d == _180_0: 

715 d = _N_180_0 

716 d, t = _sum2(d, t) 

717 return d, t 

718 

719 

720def _fix90(deg): # mimick Math.LatFix 

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

722 

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

724 ''' 

725 try: 

726 return _wrapped.Math.LatFix(deg) 

727 except AttributeError: 

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

729 

730 

731def _isfinite(x): # mimick geomath.Math.isfinite 

732 '''Check finiteness of C{x}. 

733 

734 @return: C{True} if finite. 

735 ''' 

736 try: 

737 return _wrapped.Math.isfinite(x) 

738 except AttributeError: 

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

740 

741 

742def _llz2gl(gl, **llz2): # see .geodesici._llz2G 

743 '''(INTERNAL) Set C{gl.lat2, .lon2, .azi2} from C{llz2}. 

744 ''' 

745 if llz2: 

746 for n in (_lat2_, _lon2_, _azi2_): # _lat1_, _lon1_, _azi1_ 

747 v = llz2.get(n, None) 

748 if v is not None: 

749 setattr(gl, n, v) 

750 return gl 

751 

752 

753def _norm2(x, y): # mimick geomath.Math.norm 

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

755 

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

757 ''' 

758 try: 

759 return _wrapped.Math.norm(x, y) 

760 except AttributeError: 

761 return norm2(x, y) 

762 

763 

764def _norm180(deg): # mimick geomath.Math.AngNormalize 

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

766 

767 @return: Reduced angle C{degrees}. 

768 ''' 

769 try: 

770 return _wrapped.Math.AngNormalize(deg) 

771 except AttributeError: 

772 d = fremainder(deg, _360_0) 

773 if d in (_180_0, _N_180_0): 

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

775 return d 

776 

777 

778def _polygon(geodesic, points, closed, line, wrap): 

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

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

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

782 or C{geodesicw.Geodesic} instance. 

783 ''' 

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

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

786 

787 if _MODS.booleans.isBoolean(points): 

788 # recursive call for each boolean clip 

789 

790 def _a_p(clip, *args, **unused): 

791 return _polygon(geodesic, clip, *args) 

792 

793 if not closed: # closed only 

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

795 

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

797 

798 gP = geodesic.Polygon(line) 

799 _A = gP.AddPoint 

800 

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

802 p1 = p0 = Ps[0] 

803 

804 # note, lon deltas are unrolled, by default 

805 _A(p1.lat, p1.lon) 

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

807 if wrap and not Ps.looped: 

808 p2 = _unrollon(p1, p2) 

809 _A(p2.lat, p2.lon) 

810 p1 = p2 

811 if closed and line and p1 != p0: 

812 _A(p0.lat, p0.lon) 

813 

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

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

816 

817 

818try: 

819 from math import fma as _fma # since 3.13 

820 

821 def _poly_fma(x, s, *cs): 

822 for c in cs: 

823 s = _fma(s, x, c) 

824 return s 

825 

826except ImportError: # Python 3.12- 

827 

828 def _poly_fma(x, s, *cs): # PYCHOK redef 

829 t = _0_0 

830 for c in cs: 

831 s, t, _ = _sum3(s * x, t * x, c) 

832 return s + t 

833 

834# def _poly_fma(x, *cs): 

835# S = Fhorner(x, *cs, incx=False) 

836# return float(S) 

837 

838def _polynomial(x, cs, i, j): # PYCHOK shared 

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

840 signature and cascaded summation different from C{karney._sum3}. 

841 

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

843 ''' 

844 if (i + 1) < j <= len(cs): # load _Rtuple._tuple 

845 try: 

846 r = _wrapped.Math.polyval(j - i - 1, cs, i, x) 

847 except AttributeError: 

848 r = _poly_fma(x, *cs[i:j]) 

849 else: 

850 r = cs[i] 

851 return float(r) 

852 

853 

854def _remainder(x, y): 

855 '''Remainder of C{x / y}. 

856 

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

858 ''' 

859 try: 

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

861 except AttributeError: 

862 return fremainder(x, y) 

863 

864 

865if _K_2_0: 

866 from math import cos as _cos, sin as _sin 

867 

868 def _sincos2(rad): 

869 return _sin(rad), _cos(rad) 

870 

871 _signBit = _MODS.basics.signBit 

872else: 

873 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared 

874 

875 def _signBit(x): 

876 '''(INTERNAL) GeographicLib 1.52-. 

877 ''' 

878 return x < 0 

879 

880 

881def _sincos2d(deg): 

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

883 

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

885 ''' 

886 try: 

887 return _wrapped.Math.sincosd(deg) 

888 except AttributeError: 

889 return sincos2d(deg) 

890 

891 

892def _sincos2de(deg, t): 

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

894 

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

896 ''' 

897 try: 

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

899 except AttributeError: 

900 return sincos2d(deg, adeg=t) 

901 

902 

903def _sum2(a, b): # mimick geomath.Math.sum, actually sum2 

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

905 

906 @return: 2-Tuple C{(B{a} + B{b}, residual)}. 

907 

908 @note: The C{residual} can be the same as B{C{a}} or B{C{b}}. 

909 

910 @see: U{TwoSum<https://accurate-algorithms.readthedocs.io/en/latest/ch04summation.html>} 

911 and I{Knuth}'s U{Algorithm 3.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}. 

912 ''' 

913 try: 

914 return _wrapped.Math.sum(a, b) 

915 except AttributeError: 

916 # if Algorithm_3_1: 

917 s = a + b 

918 r = s - b 

919 t = s - r 

920 # elif C_CPP: # Math::sum C/C++ 

921 # r -= a; t -= b; t += r; t = -t 

922 # else: 

923 t = (a - r) + (b - t) 

924 # assert fabs(s) >= fabs(t) 

925 return s, t 

926 

927 

928def _sum3(s, t, *xs): 

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

930 

931 @return: 3-Tuple C{(s, t, n)} where C{s} is the sum of B{s}, B{t} and all 

932 B{xs}, C{t} the residual and C{n} the number of zero C{xs}. 

933 

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

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

936 function C{_sum2} above. 

937 

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

939 ''' 

940 z = 0 

941 for x in xs: 

942 if x: 

943 t, r = _sum2(t, x) # start at the least- 

944 if s: 

945 s, t = _sum2(s, t) # -significant end 

946 if s: 

947 t += r # accumulate r into t 

948 else: 

949 # assert t == 0 # s == 0 implies t == 0 

950 s = unsigned0(r) # result is r, t = 0 

951 else: 

952 s, t = unsigned0(t), r 

953 else: 

954 z += 1 

955 # assert fabs(s) >= fabs(t) 

956 return s, t, z 

957 

958 

959def _tand(x): 

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

961 ''' 

962 try: 

963 return _wrapped.Math.tand(x) 

964 except AttributeError: 

965 return tand(x) 

966 

967 

968def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2 

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

970 

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

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

973 ''' 

974 if wrap: 

975 d, t = _diff182(lon1, lon2) 

976 lon2, t, _ = _sum3(d, t, lon1) # (lon1 + d) + t 

977 lon2 += t 

978 else: 

979 lon2 = _norm180(lon2) 

980 return (lon2 - lon1), lon2 

981 

982 

983def _unsigned2(x): 

984 '''(INTERNAL) Unsign B{C{x}}. 

985 ''' 

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

987 

988 

989__all__ += _ALL_DOCS(_CapsBase) 

990 

991# **) MIT License 

992# 

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

994# 

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

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

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

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

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

1000# Software is furnished to do so, subject to the following conditions: 

1001# 

1002# The above copyright notice and this permission notice shall be included 

1003# in all copies or substantial portions of the Software. 

1004# 

1005# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1006# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1007# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1008# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1009# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1010# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1011# OTHER DEALINGS IN THE SOFTWARE.