1

2# -*- coding: utf-8 -*-

3

4 u'''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

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

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

9 C{attribute} name.

10

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

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

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

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

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

16

17 Karney-based functionality

18==========================

19

20 1. 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

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

97

98 2. 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

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

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

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

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

108

109 3. 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

125 are 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

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

128

129 4. 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

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

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

135

136 5. Spherical functions

137

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

139

140 in 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

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

145

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

147 _xgeographiclib, _zip

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

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

150 from pygeodesy.errors import GeodesicError, _ValueError, _xkwds

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

152 from pygeodesy.internals import _getenv, _popen2, _PYGEODESY_ENV, typename, \

153 _version_info

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

155 _composite_, _lat1_, _lat2_, _lon1_, _lon2_, \

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

157 _SPACE_, _UNDER_, _X_, _1_, _2_, _BAR_ # PYCHOK used!

158 from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _FOR_DOCS

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

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

161 property_ROnce

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

163 Meter as _M, Meter2 as _M2, Number_

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

165

166# from math import fabs # from .utily

167

168__all__ = _ALL_LAZY.karney

169__version__ = '25.04.14'

170

171_2_4_ = '2.4'

172_K_2_0 = _getenv(_PYGEODESY_ENV(typename(_xgeographiclib)[2:]), _2_)

173_K_2_4 = _K_2_0 == _2_4_

174_K_2_0 = _K_2_4 or (_K_2_0 == _2_)

175_perimeter_ = 'perimeter'

176

177

178 class _GTuple(_NamedTuple): # in .testNamedTuples

179 '''(INTERNAL) Helper.

180 '''

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

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

183

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

185 '''

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

187 if updates:

188 r.update(updates)

189 if self._iteration is not None:

190 r._iteration = self._iteration

191 return r

192

193

194 class _Lat(Lat):

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

196 '''

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

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

199 Lat.__new__(_Lat, *lat, **kwds)

200

201

202 class _Lon(Lon):

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

204 '''

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

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

207 Lon.__new__(_Lon, *lon, **kwds)

208

209

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

211 '''3-Tuple C{(number, perimeter, area)} with the C{number}

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

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

214 '''

215 _Names_ = (_number_, _perimeter_, _area_)

216 _Units_ = ( Number_, _M, _M2)

217

218

219 class Caps(object):

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

221 or C{-lines} capabilities (C{caps}) and method results (C{outmask}).

222

223 C{AREA} - compute the area C{S12},

224

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

226

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

228

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

230

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

232

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

234

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

236

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

238

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

240

241 C{LONG_UNROLL} - unroll C{lon2} in method C{.Direct},

242

243 C{REDUCEDLENGTH} - compute the reduced length C{m12},

244

245 C{REVERSE2} - reverse azimuth C{azi2} by 180 degrees,

246

247 and C{ALL} - all of the above.

248

249 C{STANDARD} = C{AZIMUTH | DISTANCE | LATITUDE | LONGITUDE}

250

251 C{LINE_CAPS} = C{STANDARD | DISTANCE_IN | REDUCEDLENGTH | GEODESICSCALE}

252 '''

253 EMPTY = 0 # formerly aka NONE

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

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

256 _CAP_2 = 1 << 2

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

258 _CAP_4 = 1 << 4 # for goedesicw

259# = 1 << 5 # unused

260# = 1 << 6 # unused

261 _CAP_ALL = 0x1F

262# _CAP_MASK = _CAP_ALL

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

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

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

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

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

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

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

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

271

272 STANDARD = AZIMUTH | DISTANCE | LATITUDE | LONGITUDE

273 STANDARD_LINE = STANDARD | DISTANCE_IN # for goedesici/-w

274

275 LINE_CAPS = STANDARD_LINE | REDUCEDLENGTH | GEODESICSCALE # .geodesici only

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

277# = 1 << 16 # unused

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

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

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

281

282 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE

283 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA

284

285 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE

286 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA

287

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

289

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

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

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

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

294 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \

295 _DEBUG_LINE | _SALP_CALPs_

296

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

298 _INVERSE3 = AZIMUTH | DISTANCE # for goedesicw only

299

300 _OUT_ALL = ALL # see geographiclib.geodesiccapabilities.py

301 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL

302

303 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE

304 _AZIMUTH_LATITUDE_LONG_UNROLL = AZIMUTH | LATITUDE | LONG_UNROLL

305 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE

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

307 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE

308# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE

309

310 def items(self):

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

312 '''

313 for n, C in type(self).__dict__.items():

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

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

316 yield n, C

317

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

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

320 '''

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

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

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

324

325 if _FOR_DOCS: # PYCHOK force ...

326 pass # ... CAPS.__doc__ into epydoc

327 else:

328 Caps = Caps() # PYCHOK singleton

329

330_key2Caps = dict(a12 =Caps.DISTANCE, # in GDict._unCaps

331 azi2=Caps.AZIMUTH,

332 lat2=Caps.LATITUDE,

333 lon2=Caps.LONGITUDE,

334 m12 =Caps.REDUCEDLENGTH,

335 M12 =Caps.GEODESICSCALE,

336 M21 =Caps.GEODESICSCALE,

337 s12 =Caps.DISTANCE,

338 S12 =Caps.AREA)

339

340

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

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

343 '''

344 ALL = Caps.ALL

345 AREA = Caps.AREA

346 AZIMUTH = Caps.AZIMUTH

347 DISTANCE = Caps.DISTANCE

348 DISTANCE_IN = Caps.DISTANCE_IN

349 EMPTY = Caps.EMPTY # aka NONE

350 GEODESICSCALE = Caps.GEODESICSCALE

351 LATITUDE = Caps.LATITUDE

352 LINE_CAPS = Caps.LINE_CAPS

353 LINE_OFF = Caps.LINE_OFF

354 LONGITUDE = Caps.LONGITUDE

355 LONG_UNROLL = Caps.LONG_UNROLL

356 REDUCEDLENGTH = Caps.REDUCEDLENGTH

357 STANDARD = Caps.STANDARD

358 STANDARD_LINE = Caps.STANDARD_LINE # for geodesici

359

360 _caps = 0 # None

361 _debug = 0 # or Caps._DEBUG_...

362

363 @Property_RO

364 def caps(self):

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

366 '''

367 return self._caps

368

369 def caps_(self, caps):

370 '''Check the available capabilities.

371

372 @arg caps: Bit-or'ed combination of L{Caps<pygeodesy.karney.Caps>}

373 values for all capabilities to be checked.

374

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

376 otherwise (C{bool}).

377 '''

378 caps &= Caps._OUT_ALL

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

380

381 @property

382 def debug(self):

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

384 '''

385 return bool(self._debug)

386

387 @debug.setter # PYCHOK setter!

388 def debug(self, debug):

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

390 more details in L{GDict} results.

391 '''

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

393

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

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

396 '''

397 if iter is not None:

398 self._iteration = r._iteration = iter

399 return r

400

401

402 class Direct9Tuple(_GTuple):

403 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc

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

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

406 C{meter} I{squared}.

407 '''

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

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

410

411

412 class GDict(ADict): # XXX _NamedDict

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

414

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

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

417 '''

418 def toDirect9Tuple(self, dflt=NAN):

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

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

421

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

423

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

425 s12, m12, M12, M21, S12)}

426 '''

427 return self._toTuple(Direct9Tuple, dflt)

428

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

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

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

432 result.

433

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

435

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

437 s12, a12, m12, M12, M21, S12)}.

438 '''

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

440

441 def toInverse10Tuple(self, dflt=NAN):

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

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

444

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

446

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

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

449 '''

450 return self._toTuple(Inverse10Tuple, dflt)

451

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

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

454 '''

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

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

457

458 @deprecated_method

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

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

461

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

463 '''

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

465

466 def toRhumb8Tuple(self, dflt=NAN):

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

468

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

470

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

472 azi12, s12, S12, a12)}.

473 '''

474 return self._toTuple(Rhumb8Tuple, dflt)

475

476 def toRhumbSolve7Tuple(self, dflt=NAN):

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

478

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

480

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

482 azi12, s12, S12)}.

483 '''

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

485

486 def _toTuple(self, nTuple, dflt):

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

488 '''

489 _g = getattr

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

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

492

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

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

495 '''

496 X = GDict(self)

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

498 if n in X: # X._X = X._2

499 X[n[:-1] + _2X] = X.pop(n)

500 v = getattr(gl, n, X)

501 if v is not X: # X._2 = gl._2

502 X[n] = v

503 return X

504

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

506 '''(INTERNAL) Remove superfluous items.

507 '''

508 for k, C in _key2Caps.items():

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

510 self.pop(k) # delattr(self, k)

511 return self

512

513

514 class GeodSolve12Tuple(_GTuple):

515 '''12-Tuple C{(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)} with

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

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

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

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

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

521 '''

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

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

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

525

526

527 class Inverse10Tuple(_GTuple):

528 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length

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

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

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

532 '''

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

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

535

536 def toGDict(self, **updates):

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

538

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

540 '''

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

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

543 **updates) # PYCHOK indent

544

545

546 class _kWrapped(object): # in .geodesicw

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

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

549 '''

550

551 @property_ROnce

552 def geographiclib(self):

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

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

555 otherwise raise a C{LazyImportError}.

556 '''

557 g = _xgeographiclib(type(self).__module__, 1, 49)

558 from geographiclib.geodesic import Geodesic

559 g.Geodesic = Geodesic

560 from geographiclib.geodesicline import GeodesicLine

561 g.GeodesicLine = GeodesicLine

562 from geographiclib.geomath import Math

563 g.Math = Math

564 return g

565

566 @property_ROnce

567 def Math(self):

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

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

570 otherwise C{None}.

571 '''

572 try:

573 g = self.geographiclib

574 M = g.Math

575 if _version_info(g) < (2,):

576 if _K_2_0:

577 M = None

578# elif not _K_2_0: # XXX set 2.0?

579# _K_2_0 = True

580 except (AttributeError, ImportError):

581 M = None

582 return M

583

584 @property_RO

585 def Math_K_2(self):

586 return (_2_4_ if _K_2_4 else

587 (_2_ if _K_2_0 else _1_)) if self.Math else NN

588

589_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py

590

591

592 class Rhumb8Tuple(_GTuple):

593 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1},

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

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

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

597 '''

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

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

600

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

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

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

604

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

606 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments

607 to specify or override L{Inverse10Tuple} items.

608

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

610 m12, M12, M21, S12)}

611 '''

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

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

614 if a12_azi1_azi2_m12_M12_M21:

615 d.update(a12_azi1_azi2_m12_M12_M21)

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

617

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

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

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

621

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

623 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword

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

625

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

627 m12, M12, M21, S12)}.

628 '''

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

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

631 salp2=s, calp2=c, M21=_1_0)

632 if a12_m12_M12_M21_salp1_calp1_salp2_calp2:

633 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2)

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

635

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

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

638 '''

639 _g = self.toGDict(**updates).get

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

641 return nTuple(t, name=self.name)

642

643 @deprecated_method

644 def _to7Tuple(self):

645 '''DEPRECATED, do not use!'''

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

647

648

649 class _Xables(object):

650 '''(INTERNAL) Get I{Karney}'s executable paths from/and env vars.

651 '''

652 bin_ = '/opt/local/bin/' # '/opt/local/Cellar/geographiclib/2.3/bin/' # HomeBrew on macOS

653 ENV = NN

654

655 def GeoConvert(self, *dir_):

656 return self._path(self.GeoConvert, *dir_)

657

658 def GeodSolve(self, *dir_):

659 return self._path(self.GeodSolve, *dir_)

660

661 def IntersectTool(self, *dir_):

662 return self._path(self.IntersectTool, *dir_)

663

664 def RhumbSolve(self, *dir_):

665 return self._path(self.RhumbSolve, *dir_)

666

667 def name_version(self, path, base=True):

668 # return C{(path + ' ' + version)} of an executable

669 if path:

670 try:

671 r, s = _popen2((path, '--version'))

672 if base:

673 path = _MODS.os.path.basename(path)

674 r = _SPACE_(path, r.split()[-1])

675 else:

676 r = _MODS.streprs.Fmt.PARENSPACED(r, s)

677 return r

678 except (IndexError, IOError, OSError):

679 pass

680 return NN

681

682 def _path(self, which, *dir_):

683 n = typename(which, which)

684 self.ENV = E = _PYGEODESY_ENV(n)

685 return _getenv(E, NN) or (NN(dir_[0], n) if dir_ else E)

686

687 def X_not(self, path):

688 return 'env %s=%r not executable' % (self.ENV, path)

689

690 def X_OK(self, path): # is C{path} an executable?

691 os = _MODS.os # import os

692 return os.access(path, os.X_OK) if path else False

693

694_Xables = _Xables() # PYCHOK singleton

695

696

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

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

699

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

701

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

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

704 '''

705 try:

706 return _wrapped.Math.AngRound(x)

707 except AttributeError:

708 if x:

709 y = _1_16th - fabs(x)

710 if y > 0: # fabs(x) < _1_16th

711 x = _copysign(_1_16th - y, x)

712 else:

713 x = _0_0 # -0 to 0

714 return x

715

716

717 def _atan2d(y, x):

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

719 '''

720 try:

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

722 except AttributeError:

723 return atan2d(y, x)

724

725

726 def _cbrt(x):

727 '''Return C{cubic root(B{x})}.

728 '''

729 try:

730 return _wrapped.Math.cbrt(x)

731 except AttributeError:

732 return cbrt(x)

733

734

735 def _copyBit(x, y):

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

737 '''

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

739

740

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

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

743 '''

744 r = cx - sx

745 if r:

746 r *= (cx + sx) * _2_0

747 return r

748

749

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

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

752

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

754 '''

755 try:

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

757 except AttributeError:

758 if K_2_0 or _K_2_0: # geographiclib 2.0

759 _r, _360 = fremainder, _360_0

760 d, t = _sum2(_r(-deg0, _360),

761 _r( deg, _360))

762 d, t = _sum2(_r( d, _360), t)

763 if _isin(d, _0_0, _180_0, _N_180_0):

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

765 else:

766 _n = _norm180

767 d, t = _sum2(_n(-deg0), _n(deg))

768 d = _n(d)

769 if t > 0 and d == _180_0:

770 d = _N_180_0

771 d, t = _sum2(d, t)

772 return d, t

773

774

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

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

777

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

779 '''

780 try:

781 return _wrapped.Math.LatFix(deg)

782 except AttributeError:

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

784

785

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

787 '''Check finiteness of C{x}.

788

789 @return: C{True} if finite.

790 '''

791 try:

792 return _wrapped.Math.isfinite(x)

793 except AttributeError:

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

795

796

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

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

799 '''

800 if llz2:

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

802 v = llz2.get(n, None)

803 if v is not None:

804 setattr(gl, n, v)

805 return gl

806

807

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

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

810

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

812 '''

813 try:

814 return _wrapped.Math.norm(x, y)

815 except AttributeError:

816 return norm2(x, y)

817

818

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

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

821

822 @return: Reduced angle C{degrees}.

823 '''

824 try:

825 return _wrapped.Math.AngNormalize(deg)

826 except AttributeError:

827 d = fremainder(deg, _360_0)

828 if _isin(d, _180_0, _N_180_0):

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

830 return d

831

832

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

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

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

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

837 or C{geodesicw.Geodesic} instance.

838 '''

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

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

841

842 if _MODS.booleans.isBoolean(points):

843 # recursive call for each boolean clip

844

845 def _a_p(clip, *args, **unused):

846 return _polygon(geodesic, clip, *args)

847

848 if not closed: # closed only

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

850

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

852

853 gP = geodesic.Polygon(line)

854 _A = gP.AddPoint

855

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

857 p1 = p0 = Ps[0]

858

859 # note, lon deltas are unrolled, by default

860 _A(p1.lat, p1.lon)

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

862 if wrap and not Ps.looped:

863 p2 = _unrollon(p1, p2)

864 _A(p2.lat, p2.lon)

865 p1 = p2

866 if closed and line and p1 != p0:

867 _A(p0.lat, p0.lon)

868

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

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

871

872

873 try:

874 from math import fma as _fma # since 3.13

875

876 def _poly_fma(x, s, *cs):

877 for c in cs:

878 s = _fma(s, x, c)

879 return s

880

881 except ImportError: # Python 3.12-

882

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

884 t = _0_0

885 for c in cs:

886 s, t, _ = _sum3(s * x, t * x, c)

887 return s + t

888

889# def _poly_fma(x, s, *cs):

890# S = Fhorner(x, *cs, incx=False)

891# S += s

892# return float(S)

893

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

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

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

897

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

899 '''

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

901 try:

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

903 except AttributeError: # no .Math

904 r = _poly_fma(x, _0_0, *cs[i:j])

905 else:

906 r = cs[i]

907 return float(r)

908

909

910 def _remainder(x, y):

911 '''Remainder of C{x / y}.

912

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

914 '''

915 try:

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

917 except AttributeError:

918 return fremainder(x, y)

919

920

921 if _K_2_0:

922 from math import cos as _cos, sin as _sin

923

924 def _sincos2(rad):

925 return _sin(rad), _cos(rad)

926

927 _signBit = _MODS.basics.signBit

928 else:

929 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared

930

931 def _signBit(x):

932 '''(INTERNAL) GeographicLib 1.52-.

933 '''

934 return x < 0

935

936

937 def _sincos2d(deg):

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

939

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

941 '''

942 try:

943 return _wrapped.Math.sincosd(deg)

944 except AttributeError:

945 return sincos2d(deg)

946

947

948 def _sincos2de(deg, t):

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

950

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

952 '''

953 try:

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

955 except AttributeError:

956 return sincos2d(deg, adeg=t)

957

958

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

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

961

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

963

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

965

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

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

968 '''

969 try:

970 return _wrapped.Math.sum(a, b)

971 except AttributeError:

972 # if Algorithm_3_1:

973 s = a + b

974 r = s - b

975 t = s - r

976 # elif C_CPP: # Math::sum C/C++

977 # r -= a; t -= b; t += r; t = -t

978 # else:

979 t = (a - r) + (b - t)

980 # assert fabs(s) >= fabs(t)

981 return s, t

982

983

984 def _sum3(s, t, *xs):

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

986

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

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

989

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

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

992 function C{_sum2} above.

993

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

995 '''

996 z = 0

997 for x in xs:

998 if x:

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

1000 if s:

1001 s, t = _sum2(s, t) # -significant end

1002 if s:

1003 t += r # accumulate r into t

1004 else:

1005 # assert t == 0 # s == 0 implies t == 0

1006 s = unsigned0(r) # result is r, t = 0

1007 else:

1008 s, t = unsigned0(t), r

1009 else:

1010 z += 1

1011 # assert fabs(s) >= fabs(t)

1012 return s, t, z

1013

1014

1015 def _tand(x):

1016 '''Return C{tan(B{x})} in C{degrees}.

1017 '''

1018 try:

1019 return _wrapped.Math.tand(x)

1020 except AttributeError:

1021 return tand(x) # Error=None

1022

1023

1024 def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2

1025 '''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}.

1026

1027 @return: 2-Tuple C{(B{lon2} - B{lon1}, B{lon2})} with B{C{lon2}}

1028 unrolled if C{B{wrap} is True}, normalized otherwise.

1029 '''

1030 if wrap:

1031 d, t = _diff182(lon1, lon2)

1032 lon2, t, _ = _sum3(d, t, lon1) # (lon1 + d) + t

1033 lon2 += t

1034 else:

1035 lon2 = _norm180(lon2)

1036 return (lon2 - lon1), lon2

1037

1038

1039 def _unsigned2(x):

1040 '''(INTERNAL) Unsign B{C{x}}.

1041 '''

1042 return (neg(x), True) if _signBit(x) else (x, False)

1043

1044

1045__all__ += _ALL_DOCS(Caps, _CapsBase)

1046

1047# **) MIT License

1048#

1049# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.

1050#

1051# Permission is hereby granted, free of charge, to any person obtaining a

1052# copy of this software and associated documentation files (the "Software"),

1053# to deal in the Software without restriction, including without limitation

1054# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1055# and/or sell copies of the Software, and to permit persons to whom the

1056# Software is furnished to do so, subject to the following conditions:

1057#

1058# The above copyright notice and this permission notice shall be included

1059# in all copies or substantial portions of the Software.

1060#

1061# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1062# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1063# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1064# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1065# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1066# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1067# OTHER DEALINGS IN THE SOFTWARE.