Coverage for pygeodesy/karney.py: 92%

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

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.

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.

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>}.

17Karney-based functionality

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

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

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>}

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+}

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

33 classGeographicLib_1_1CassiniSoldner.html>}

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

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

38 classGeographicLib_1_1EllipticFunction.html>}

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

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

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

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

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>}

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

50 classGeographicLib_1_1PolygonAreaT.html>}

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>}

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

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

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

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

63 - L{Intersector} -- U{Intersect

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

66 - L{JacobiConformal} -- U{JacobiConformal

67 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1experimental_1_1JacobiConformal.html>}

69 - L{KTransverseMercator} - U{TransverseMercator

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

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

73 classGeographicLib_1_1LocalCartesian.html>}

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

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+}

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}

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

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

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

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>}

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

982. These C{pygeodesy} modules and classes

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 _ # noqa: E702 ;

145

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

147 _xgeographiclib, _zip

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

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

153 _version_info

154from 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!

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

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

160from pygeodesy.props import deprecated_method, property_RO, 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__ = '25.08.31'

169

170_2_4_ = '2.4'

171_K_2_0 = _getenv(_PYGEODESY_ENV(typename(_xgeographiclib)[2:]), _2_)

172_K_2_4 = _K_2_0 == _2_4_

173_K_2_0 = _K_2_4 or (_K_2_0 == _2_)

174_perimeter_ = 'perimeter'

175

176

177class _GTuple(_NamedTuple): # in .testNamedTuples

178 '''(INTERNAL) Helper.

179 '''

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

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

182

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

184 '''

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

186 if updates:

187 r.update(updates)

188 if self._iteration is not None:

189 r._iteration = self._iteration

190 return r

191

192

193class _Lat(Lat):

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

195 '''

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

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

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

199

200

201class _Lon(Lon):

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

203 '''

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

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

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

207

208

209class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea

210 '''3-Tuple C{(number, perimeter, area)} with the C{number}

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

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

213 '''

214 _Names_ = (_number_, _perimeter_, _area_)

215 _Units_ = ( Number_, _M, _M2)

216

217

218class Caps(object):

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

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

221

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

223

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

225

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

227

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

229

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

231

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

233

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

235

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

237

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

239

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

241

242 C{NONFINITONAN} - set all C{GDict} items to C{NAN} iff any argument is C{non-finite}.

243

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

245

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

247

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

249

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

251

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

253 '''

254 EMPTY = 0 # formerly aka NONE

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

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

257 _CAP_2 = 1 << 2

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

259 _CAP_4 = 1 << 4 # for goedesicw

260# = 1 << 5 # unused

261# = 1 << 6 # unused

262 _CAP_ALL = 0x1F

263# _CAP_MASK = _CAP_ALL

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

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

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

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

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

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

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

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

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

273

274 STANDARD = AZIMUTH | DISTANCE | LATITUDE | LONGITUDE

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

276

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

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

279 LINE_OFF = 1 << 16 # Line without updates from parent geodesic or rhumb

280 NONFINITONAN = 1 << 17 # see method GDict._toNAN

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

282

283 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE

284 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA

285

286 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE

287 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA

288

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

290

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

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

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

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

295 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \

296 _DEBUG_LINE | _SALP_CALPs_

297

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

299 _INVERSE3 = AZIMUTH | DISTANCE # for goedesicw only

300

301 _OUT_ALL = ALL # see geographiclib.geodesiccapabilities.py

302 _OUT_MASK = ALL | LONG_UNROLL | NONFINITONAN | REVERSE2 | _DEBUG_ALL

303

304 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE

305 _AZIMUTH_LATITUDE_LONG_UNROLL = AZIMUTH | LATITUDE | LONG_UNROLL

306 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE

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

308 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE

309# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE

310

311 def items(self):

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

313 '''

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

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

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

317 yield n, C

318

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

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

321 '''

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

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

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

325

326if _FOR_DOCS: # PYCHOK force ...

327 pass # ... CAPS.__doc__ into epydoc

328else:

329 Caps = Caps() # PYCHOK singleton

330

331_key2Caps = dict(a12 =Caps.DISTANCE, # in GDict._toNAN, -._unCaps

332 azi1=Caps.AZIMUTH,

333 azi2=Caps.AZIMUTH,

334 lat1=Caps.LATITUDE,

335 lat2=Caps.LATITUDE,

336 lon1=Caps.LONGITUDE,

337 lon2=Caps.LONGITUDE,

338 m12 =Caps.REDUCEDLENGTH,

339 M12 =Caps.GEODESICSCALE,

340 M21 =Caps.GEODESICSCALE,

341 s12 =Caps.DISTANCE,

342 S12 =Caps.AREA)

343

344

345class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases

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

347 '''

348 ALL = Caps.ALL

349 AREA = Caps.AREA

350 AZIMUTH = Caps.AZIMUTH

351 DISTANCE = Caps.DISTANCE

352 DISTANCE_IN = Caps.DISTANCE_IN

353 EMPTY = Caps.EMPTY # aka NONE

354 GEODESICSCALE = Caps.GEODESICSCALE

355 LATITUDE = Caps.LATITUDE

356 LINE_CAPS = Caps.LINE_CAPS

357 LINE_OFF = Caps.LINE_OFF

358 LONGITUDE = Caps.LONGITUDE

359 LONG_UNROLL = Caps.LONG_UNROLL

360 NONFINITONAN = Caps.NONFINITONAN

361 REDUCEDLENGTH = Caps.REDUCEDLENGTH

362 STANDARD = Caps.STANDARD

363 STANDARD_LINE = Caps.STANDARD_LINE # for geodesici

364

365 _caps = 0 # None

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

367

368 @property_RO

369 def caps(self):

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

371 '''

372 return self._caps

373

374 def caps_(self, caps):

375 '''Check the available capabilities.

376

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

378 values for all capabilities to be checked.

379

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

381 otherwise (C{bool}).

382 '''

383 caps &= Caps._OUT_ALL

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

385

386 @property

387 def debug(self):

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

389 '''

390 return bool(self._debug)

391

392 @debug.setter # PYCHOK setter!

393 def debug(self, debug):

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

395 more details in L{GDict} results.

396 '''

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

398

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

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

401 '''

402 if iter is not None:

403 self._iteration = r._iteration = iter

404 return r

405

406

407class Direct9Tuple(_GTuple):

408 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc

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

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

411 C{meter} I{squared}.

412 '''

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

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

415

416

417class GDict(ADict): # XXX _NamedDict

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

419

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

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

422 '''

423 def toDirect9Tuple(self, dflt=NAN):

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

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

426

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

428

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

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

431 '''

432 return self._toTuple(Direct9Tuple, dflt)

433

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

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

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

437 result.

438

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

440

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

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

443 '''

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

445

446 def toInverse10Tuple(self, dflt=NAN):

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

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

449

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

451

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

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

454 '''

455 return self._toTuple(Inverse10Tuple, dflt)

456

457 def _toNAN(self, outmask, **specs): # .GeodesicExact._GDistInverse, .GeodesicLineExact._GenPosition

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

459 '''

460 if (outmask & Caps.NONFINITONAN):

461 def _t2(k):

462 return k, specs.get(k, NAN)

463

464 d = dict(_t2(k) for k, C in _key2Caps.items()

465 if (outmask & C) == C)

466 self.set_(**d) # self.update(d)

467 return self

468

469 @deprecated_method

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

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

472

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

474 '''

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

476

477 def toRhumb8Tuple(self, dflt=NAN):

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

479

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

481

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

483 azi12, s12, S12, a12)}.

484 '''

485 return self._toTuple(Rhumb8Tuple, dflt)

486

487 def toRhumbSolve7Tuple(self, dflt=NAN):

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

489

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

491

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

493 azi12, s12, S12)}.

494 '''

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

496

497 def _toTuple(self, nTuple, dflt):

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

499 '''

500 _g = getattr

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

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

503

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

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

506 '''

507 X = GDict(self)

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

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

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

511 v = getattr(gl, n, X)

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

513 X[n] = v

514 return X

515

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

517 '''(INTERNAL) Remove superfluous items.

518 '''

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

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

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

522 return self

523

524

525class GeodSolve12Tuple(_GTuple):

526 '''12-Tuple C{(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)} with

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

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

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

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

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

532 '''

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

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

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

536

537

538class Inverse10Tuple(_GTuple):

539 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length

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

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

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

543 '''

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

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

546

547 def toGDict(self, **updates):

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

549

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

551 '''

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

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

554 **updates) # PYCHOK indent

555

556

557class _kWrapped(_CapsBase): # in .geodesicw

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

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

560 '''

561

562 @property_ROnce

563 def geographiclib(self):

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

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

566 otherwise raise a C{LazyImportError}.

567 '''

568 g = _xgeographiclib(type(self), 1, 49)

569 from geographiclib.geodesic import Geodesic

570 g.Geodesic = Geodesic

571 from geographiclib.geodesicline import GeodesicLine

572 g.GeodesicLine = GeodesicLine

573 from geographiclib.geomath import Math

574 g.Math = Math

575# from geographiclib.polygonarea import PolygonArea

576# g.PolygonArea = PolygonArea # see below

577 return g

578

579 @property_ROnce

580 def Math(self):

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

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

583 otherwise C{None}.

584 '''

585 try:

586 g = self.geographiclib

587 M = g.Math

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

589 if _K_2_0:

590 M = None

591# elif not _K_2_0: # XXX set 2.0?

592# _K_2_0 = True

593 except (AttributeError, ImportError):

594 M = None

595 return M

596

597 @property_RO

598 def Math_K_2(self):

599 return (_2_4_ if _K_2_4 else

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

601

602 @property_ROnce

603 def _PolygonArea(self): # lazy import

604 from geographiclib.polygonarea import PolygonArea

605 return PolygonArea

606

607_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py

608

609

610class Rhumb8Tuple(_GTuple):

611 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1},

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

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

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

615 '''

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

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

618

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

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

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

622

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

624 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments

625 to specify or override L{Inverse10Tuple} items.

626

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

628 m12, M12, M21, S12)}

629 '''

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

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

632 if a12_azi1_azi2_m12_M12_M21:

633 d.update(a12_azi1_azi2_m12_M12_M21)

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

635

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

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

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

639

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

641 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword

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

643

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

645 m12, M12, M21, S12)}.

646 '''

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

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

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

650 if a12_m12_M12_M21_salp1_calp1_salp2_calp2:

651 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2)

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

653

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

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

656 '''

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

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

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

660

661 @deprecated_method

662 def _to7Tuple(self):

663 '''DEPRECATED, do not use!'''

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

665

666

667class _Xables(object):

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

669 '''

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

671 ENV = NN

672

673 def GeoConvert(self, *dir_):

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

675

676 def GeodSolve(self, *dir_):

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

678

679 def IntersectTool(self, *dir_):

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

681

682 def RhumbSolve(self, *dir_):

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

684

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

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

687 if path:

688 try:

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

690 if base:

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

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

693 else:

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

695 return r

696 except (IndexError, IOError, OSError):

697 pass

698 return NN

699

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

701 n = typename(which, which)

702 self.ENV = E = _PYGEODESY_ENV(n)

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

704

705 def X_not(self, path):

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

707

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

709 os = _MODS.os # import os

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

711

712_Xables = _Xables() # PYCHOK singleton

713

714

715def _around(x): # in .utily.sincos2d

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

717

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

719

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

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

722 '''

723 try:

724 return _wrapped.Math.AngRound(x)

725 except AttributeError:

726 b, a = _1_16th, fabs(x)

727 if a < b:

728 a -= b

729 a += b

730 x = _copysign(a, x)

731 return x

732

733

734def _atan2d(y, x):

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

736 '''

737 try:

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

739 except AttributeError:

740 return atan2d(y, x)

741

742

743def _cbrt(x):

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

745 '''

746 try:

747 return _wrapped.Math.cbrt(x)

748 except AttributeError:

749 return cbrt(x)

750

751

752def _copyBit(x, y):

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

754 '''

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

756

757

758def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases

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

760 '''

761 r = cx - sx

762 if r:

763 r *= (cx + sx) * _2_0

764 return r

765

766

767def _diff182(deg0, deg, K_2_0=False):

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

769

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

771 '''

772 try:

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

774 except AttributeError:

775 if K_2_0 or _K_2_0: # geographiclib 2.0

776 _r, _360 = fremainder, _360_0

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

778 _r( deg, _360))

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

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

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

782 else:

783 _n = _norm180

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

785 d = _n(d)

786 if t > 0 and d == _180_0:

787 d = _N_180_0

788 d, t = _sum2(d, t)

789 return d, t

790

791

792def _fix90(deg): # mimick Math.LatFix

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

794

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

796 '''

797 try:

798 return _wrapped.Math.LatFix(deg)

799 except AttributeError:

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

801

802

803def _isfinite(x): # mimick geomath.Math.isfinite

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

805

806 @return: C{True} if finite.

807 '''

808 try:

809 return _wrapped.Math.isfinite(x)

810 except AttributeError:

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

812

813

814def _llz2gl(gl, **llz2): # see .geodesici._llz2G

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

816 '''

817 if llz2:

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

819 v = llz2.get(n, None)

820 if v is not None:

821 setattr(gl, n, v)

822 return gl

823

824

825def _norm2(x, y): # mimick geomath.Math.norm

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

827

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

829 '''

830 try:

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

832 except AttributeError:

833 return norm2(x, y)

834

835

836def _norm180(deg): # mimick geomath.Math.AngNormalize

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

838

839 @return: Reduced angle C{degrees}.

840 '''

841 try:

842 return _wrapped.Math.AngNormalize(deg)

843 except AttributeError:

844 d = fremainder(deg, _360_0)

845 if _isin(d, _180_0, _N_180_0):

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

847 return d

848

849

850def _polygon(geodesic, points, closed, line, wrap, polar):

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

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

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

854 or C{geodesicw.Geodesic} instance.

855 '''

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

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

858

859 if _MODS.booleans.isBoolean(points):

860 # recursive call for each boolean clip

861

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

863 return _polygon(geodesic, clip, *args)

864

865 if not closed: # closed only

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

867

868 return points._sum1(_a_p, closed, line, wrap, polar)

869

870 gP = geodesic.Polygon(line)

871 _A = gP.AddPoint

872

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

874 p1 = p0 = Ps[0]

875

876 # note, lon deltas are unrolled, by default

877 _A(p1.lat, p1.lon)

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

879 if wrap and not Ps.looped:

880 p2 = _unrollon(p1, p2)

881 _A(p2.lat, p2.lon)

882 p1 = p2

883 if closed and line and p1 != p0:

884 _A(p0.lat, p0.lon)

885

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

887 return gP.Compute(reverse=False, sign=True, polar=polar)[1 if line else 2]

888

889

890try:

891 from math import fma as _fma # since 3.13

892

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

894 for c in cs:

895 s = _fma(s, x, c)

896 return s

897

898except ImportError: # Python 3.12-

899

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

901 t = _0_0

902 for c in cs:

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

904 return s + t

905

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

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

908# S += s

909# return float(S)

910

911def _polynomial(x, cs, i, j): # PYCHOK shared

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

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

914

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

916 '''

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

918 try:

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

920 except AttributeError: # no .Math

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

922 else:

923 r = cs[i]

924 return float(r)

925

926

927def _remainder(x, y):

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

929

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

931 '''

932 try:

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

934 except AttributeError:

935 return fremainder(x, y)

936

937

938if _K_2_0:

939 from math import cos as _cos, sin as _sin

940

941 def _sincos2(rad):

942 return _sin(rad), _cos(rad)

943

944 _signBit = _MODS.basics.signBit

945else:

946 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared

947

948 def _signBit(x):

949 '''(INTERNAL) GeographicLib 1.52-.

950 '''

951 return x < 0

952

953

954def _sincos2d(deg):

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

956

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

958 '''

959 try:

960 return _wrapped.Math.sincosd(deg)

961 except AttributeError:

962 return sincos2d(deg)

963

964

965def _sincos2de(deg, t):

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

967

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

969 '''

970 try:

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

972 except AttributeError:

973 return sincos2d(deg, adeg=t)

974

975

976def _sum2(a, b): # mimick geomath.Math.sum, actually sum2

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

978

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

980

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

982

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

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

985 '''

986 try:

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

988 except AttributeError:

989 # if Algorithm_3_1:

990 s = a + b

991 r = s - b

992 t = s - r

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

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

995 # else:

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

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

998 return s, t

999

1000

1001def _sum3(s, t, *xs):

1002 '''Accumulate any B{C{xs}} into a previous C{_sum2(s, t)}.

1003

1004 @return: 3-Tuple C{(s, t, n)} where C{s} is the sum of B{s}, B{t} and all

1005 B{xs}, C{t} the residual and C{n} the number of zero C{xs}.

1006

1007 @see: I{Karney's} C++ U{Accumulator<https://GeographicLib.SourceForge.io/

1008 C++/doc/Accumulator_8hpp_source.html>} comments for more details and

1009 function C{_sum2} above.

1010

1011 @note: Not "error-free", see C{pygeodesy.test/testKarney.py}.

1012 '''

1013 z = 0

1014 for x in xs:

1015 if x:

1016 t, r = _sum2(t, x) # start at the least-

1017 if s:

1018 s, t = _sum2(s, t) # -significant end

1019 if s:

1020 t += r # accumulate r into t

1021 else:

1022 # assert t == 0 # s == 0 implies t == 0

1023 s = unsigned0(r) # result is r, t = 0

1024 else:

1025 s, t = unsigned0(t), r

1026 else:

1027 z += 1

1028 # assert fabs(s) >= fabs(t)

1029 return s, t, z

1030

1031

1032def _tand(x):

1033 '''Return C{tan(B{x})} in C{degrees}.

1034 '''

1035 try:

1036 return _wrapped.Math.tand(x)

1037 except AttributeError:

1038 return tand(x) # Error=None

1039

1040

1041def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2

1042 '''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}.

1043

1044 @return: 2-Tuple C{(B{lon2} - B{lon1}, B{lon2})} with B{C{lon2}}

1045 unrolled if C{B{wrap} is True}, normalized otherwise.

1046 '''

1047 if wrap:

1048 d, t = _diff182(lon1, lon2)

1049 lon2, t, _ = _sum3(d, t, lon1) # (lon1 + d) + t

1050 lon2 += t

1051 else:

1052 lon2 = _norm180(lon2)

1053 return (lon2 - lon1), lon2

1054

1055

1056def _unsigned2(x):

1057 '''(INTERNAL) Unsign B{C{x}}.

1058 '''

1059 return (neg(x), True) if _signBit(x) else (x, False)

1060

1061

1062__all__ += _ALL_DOCS(Caps, _CapsBase)

1063

1064# **) MIT License

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1073# Software is furnished to do so, subject to the following conditions:

1074#

1075# The above copyright notice and this permission notice shall be included

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