1

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

3

4 u'''Wrapper around several C{geomath.Math} functions from I{Karney}'s Python package

5 U{geographiclib<https://PyPI.org/project/geographiclib>}, provided that package is installed.

6

7 The I{wrapped} class methods return a L{GDict} instance offering access to the C{dict} items

8 either by C{key} or by C{attribute} name.

9

10 With env variable C{PYGEODESY_GEOGRAPHICLIB} left undefined or set to C{"2"}, this module,

11 L{pygeodesy.geodesicw} and L{pygeodesy.geodesicx} will use U{GeographicLib 2.0

12<https://GeographicLib.SourceForge.io/C++/doc/>} and newer transcoding, otherwise C{1.52}

13 or older.

14

15 Karney-based functionality

16==========================

17

18 1. The following classes and functions in C{pygeodesy}

19

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

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

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

23

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

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

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

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

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

29

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

31 classGeographicLib_1_1CassiniSoldner.html>}

32

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

34

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

36 classGeographicLib_1_1EllipticFunction.html>}

37

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

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

40

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

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

43

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

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

46

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

48 classGeographicLib_1_1PolygonAreaT.html>}

49

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

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

52 classGeographicLib_1_1GeodesicLineExact.html>}

53

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

55

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

57

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

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

60

61 - L{JacobiConformal} -- U{JacobiConformal

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

63

64 - L{KTransverseMercator} - U{TransverseMercator

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

66

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

68 classGeographicLib_1_1LocalCartesian.html>}

69

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

71

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

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

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

75

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

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

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

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

80 from I{GeographicLib 2.0}

81

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

83

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

85

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

87

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

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

90

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

92

93 2. These C{pygeodesy} modules and classes

94

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

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

97 L{GnomonicKarney}, L{HeightIDWkarney}

98

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

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

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

102

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

104

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

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

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

108

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

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

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

112

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

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

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

116

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

118

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

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

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

122

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

124

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

126

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

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

129

130 5. Spherical functions

131

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

133

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

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

136'''

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

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

139

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

141 _xgeographiclib, _xImportError, _xversion_info, \

142 _xinstanceof, _zip, isodd # PYCHOK shared

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

144 _1_16th, _1_0, _2_0, _180_0, _N_180_0, _360_0

145 from pygeodesy.errors import GeodesicError, itemsorted, _ValueError, _xkwds, \

146 _xkwds_get

147 from pygeodesy.fmath import cbrt, fremainder, hypot as _hypot, norm2, \

148 euclid, Fsum, unstr # PYCHOK shared

149# from pygeodesy.fsums import Fsum # from .fmath

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

151 _composite_, _lat1_, _lat2_, _lon1_, _lon2_, \

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

153 _UNDER_, _BAR_ # PYCHOK used!

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

155 from pygeodesy.named import _Dict, _NamedBase, _NamedTuple, notImplemented, _Pass

156 from pygeodesy.props import deprecated_method, Property_RO, property_RO # PYCHOK shared

157# from pygeodesy.streps import unstr # from .fmath

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

159 Meter as _M, Meter2 as _M2, Number_, \

160 Precision_, _1mm as _TOL_M # PYCHOK shared

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

162

163# from math import fabs # from .utily

164

165__all__ = _ALL_LAZY.karney

166__version__ = '23.12.10'

167

168_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_

169_perimeter_ = 'perimeter'

170

171

172 class _GTuple(_NamedTuple): # in .testNamedTuples

173 '''(INTERNAL) Helper.

174 '''

175 def toGDict(self, **updates):

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

177

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

179 '''

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

181 if updates:

182 r.update(updates)

183 if self._iteration is not None:

184 r._iteration = self._iteration

185 return r

186

187

188 class _Lat(Lat):

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

190 '''

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

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

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

194

195

196 class _Lon(Lon):

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

198 '''

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

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

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

202

203

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

205 '''3-Tuple C{(number, perimeter, area)} with the C{number}

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

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

208 '''

209 _Names_ = (_number_, _perimeter_, _area_)

210 _Units_ = ( Number_, _M, _M2)

211

212

213 class Caps(object): # PYCHOK

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

215 '''

216 EMPTY = 0 # formerly aka NONE

217 _CAP_1 = 1 << 0 # for goedesicw only

218 _CAP_1p = 1 << 1 # for goedesicw only

219# _CAP_2 = 1 << 2

220 _CAP_3 = 1 << 3 # for goedesicw only

221# _CAP_4 = 1 << 4

222# _CAP_ALL = 0x1F

223# _CAP_MASK = _CAP_ALL

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

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

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

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

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

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

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

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

232

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

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

235

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

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

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

239 _STD_LINE = _STD | _CAP_1p # for goedesicw only

240

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

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

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

244

245 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE

246 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA

247

248 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE

249 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA

250

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

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

253

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

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

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

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

258 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \

259 _DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs

260

261 _OUT_ALL = ALL

262 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL

263

264 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE

265 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE

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

267 _LINE = AZIMUTH | LATITUDE | LONG_UNROLL

268 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE

269# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE

270

271 def toStr(self, Csk, sep=_BAR_):

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

273 '''

274 s = []

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

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

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

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

279 s.append(c)

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

281

282 Caps = Caps() # PYCHOK singleton

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

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

285

286 C{AREA} - compute area C{S12},

287

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

289

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

291

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

293

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

295

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

297

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

299

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

301

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

303

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

305

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

307

308 C{REVERSE2} - reverse C{azi2},

309

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

311

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

313

314

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

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

317 '''

318 ALL = Caps.ALL

319 AREA = Caps.AREA

320 AZIMUTH = Caps.AZIMUTH

321 DISTANCE = Caps.DISTANCE

322 DISTANCE_IN = Caps.DISTANCE_IN

323 EMPTY = Caps.EMPTY # aka NONE

324 GEODESICSCALE = Caps.GEODESICSCALE

325 LATITUDE = Caps.LATITUDE

326 LINE_OFF = Caps.LINE_OFF

327 LONGITUDE = Caps.LONGITUDE

328 LONG_UNROLL = Caps.LONG_UNROLL

329 REDUCEDLENGTH = Caps.REDUCEDLENGTH

330 STANDARD = Caps.STANDARD

331

332 _caps = 0 # None

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

334

335 @Property_RO

336 def caps(self):

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

338 '''

339 return self._caps

340

341 def caps_(self, caps):

342 '''Check the available capabilities.

343

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

345 for all capabilities to be checked.

346

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

348 C{False} otherwise (C{bool}).

349 '''

350 caps &= Caps._OUT_ALL

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

352

353 @property

354 def debug(self):

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

356 '''

357 return bool(self._debug)

358

359 @debug.setter # PYCHOK setter!

360 def debug(self, debug):

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

362 more details in L{GDict} results.

363 '''

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

365

366 def _iter2tion(self, r, s):

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

368 '''

369 i = _xkwds_get(s, iter=None)

370 if i is not None:

371 self._iteration = r._iteration = i

372 return r

373

374

375 class Direct9Tuple(_GTuple):

376 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc

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

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

379 C{meter} I{squared}.

380 '''

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

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

383

384

385 class GDict(_Dict): # XXX _NamedDict

386 '''Basic C{dict} with both key I{and} attribute access

387 to the C{dict} items.

388

389 Results of all C{geodesic} methods are returned as a

390 L{GDict} instance.

391 '''

392 def toDirect9Tuple(self, dflt=NAN):

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

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

395

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

397

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

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

400 '''

401 return self._toTuple(Direct9Tuple, dflt)

402

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

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

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

406 result.

407

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

409

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

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

412 '''

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

414

415 def toInverse10Tuple(self, dflt=NAN):

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

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

418

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

420

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

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

423 '''

424 return self._toTuple(Inverse10Tuple, dflt)

425

426 @deprecated_method

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

428 '''DEPRECATED, used method C{toRhumb8Tuple}.

429

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

431 '''

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

433

434 def toRhumb8Tuple(self, dflt=NAN):

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

436

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

438

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

440 azi12, s12, S12, a12)}.

441 '''

442 return self._toTuple(Rhumb8Tuple, dflt)

443

444 def toRhumbSolve7Tuple(self, dflt=NAN):

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

446

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

448

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

450 azi12, s12, S12)}.

451 '''

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

453

454 def _toTuple(self, nTuple, dflt):

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

456 '''

457 _g = getattr

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

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

460

461

462 class Inverse10Tuple(_GTuple):

463 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length

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

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

466 C{calp2} of the initial C{1} and final C{2} foward azimuths.

467 '''

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

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

470

471 def toGDict(self, **updates):

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

473

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

475 '''

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

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

478 **updates) # PYCHOK indent

479

480

481 class _kWrapped(object): # in .geodesicw

482 ''''(INTERNAL) Wrapper around I{Karney}'s U{geographiclib

483 <https://PyPI.org/project/geographiclib>}.

484 '''

485

486 @Property_RO

487 def geographiclib(self):

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

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

490 otherwise a C{LazyImportError}.

491 '''

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

493 from geographiclib.geodesic import Geodesic

494 g.Geodesic = Geodesic

495 from geographiclib.geodesicline import GeodesicLine

496 g.GeodesicLine = GeodesicLine

497 from geographiclib.geomath import Math

498 g.Math = Math

499 return g

500

501 @Property_RO

502 def Math(self):

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

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

505 otherwise C{None}.

506 '''

507 try:

508 g = self.geographiclib

509 M = g.Math

510 if _xversion_info(g) < (2,):

511 if _K_2_0:

512 M = None

513# elif not _K_2_0: # XXX set 2.0?

514# _K_2_0 = True

515 except (AttributeError, ImportError):

516 M = None

517 return M

518

519_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py

520

521

522 class Rhumb8Tuple(_GTuple):

523 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1},

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

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

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

527 '''

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

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

530

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

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

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

534

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

536 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments

537 to specify or override L{Inverse10Tuple} items.

538

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

540 m12, M12, M21, S12)}

541 '''

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

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

544 if a12_azi1_azi2_m12_M12_M21:

545 d.update(a12_azi1_azi2_m12_M12_M21)

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

547

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

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

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

551

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

553 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword

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

555

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

557 m12, M12, M21, S12)}.

558 '''

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

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

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

562 if a12_m12_M12_M21_salp1_calp1_salp2_calp2:

563 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2)

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

565

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

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

568 '''

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

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

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

572

573 @deprecated_method

574 def _to7Tuple(self):

575 '''DEPRECATED, do not use!'''

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

577

578

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

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

581

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

583

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

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

586 '''

587 try:

588 return _wrapped.Math.AngRound(x)

589 except AttributeError:

590 if x:

591 y = _1_16th - fabs(x)

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

593 x = _copysign(_1_16th - y, x)

594 else:

595 x = _0_0 # -0 to 0

596 return x

597

598

599 def _atan2d(y, x):

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

601 '''

602 try:

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

604 except AttributeError:

605 return atan2d(y, x)

606

607

608 def _cbrt(x):

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

610 '''

611 try:

612 return _wrapped.Math.cbrt(x)

613 except AttributeError:

614 return cbrt(x)

615

616

617 def _copyBit(x, y):

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

619 '''

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

621

622

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

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

625 '''

626 r = cx - sx

627 if r:

628 r *= (cx + sx) * _2_0

629 return r

630

631

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

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

634

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

636 '''

637 try:

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

639 except AttributeError:

640 if K_2_0 or _K_2_0: # geographiclib 2.0

641 _r, _360 = fremainder, _360_0

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

643 _r( deg, _360))

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

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

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

647 else:

648 _n = _norm180

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

650 d = _n(d)

651 if t > 0 and d == _180_0:

652 d = _N_180_0

653 d, t = _sum2(d, t)

654 return d, t

655

656

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

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

659

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

661 '''

662 try:

663 return _wrapped.Math.LatFix(deg)

664 except AttributeError:

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

666

667

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

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

670

671 @return: C{True} if finite.

672 '''

673 try:

674 return _wrapped.Math.isfinite(x)

675 except AttributeError:

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

677

678

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

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

681

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

683 '''

684 try:

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

686 except AttributeError:

687 return norm2(x, y)

688

689

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

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

692

693 @return: Reduced angle C{degrees}.

694 '''

695 try:

696 return _wrapped.Math.AngNormalize(deg)

697 except AttributeError:

698 d = fremainder(deg, _360_0)

699 if d in (_180_0, _N_180_0):

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

701 return d

702

703

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

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

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

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

708 or C{geodesicw.Geodesic} instance.

709 '''

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

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

712

713 if _MODS.booleans.isBoolean(points):

714 # recursive call for each boolean clip

715

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

717 return _polygon(geodesic, clip, *args)

718

719 if not closed: # closed only

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

721

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

723

724 gP = geodesic.Polygon(line)

725 _A = gP.AddPoint

726

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

728 p1 = p0 = Ps[0]

729

730 # note, lon deltas are unrolled, by default

731 _A(p1.lat, p1.lon)

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

733 if wrap and not Ps.looped:

734 p2 = _unrollon(p1, p2)

735 _A(p2.lat, p2.lon)

736 p1 = p2

737 if closed and line and p1 != p0:

738 _A(p0.lat, p0.lon)

739

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

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

742

743

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

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

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

747

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

749 '''

750 # assert 0 <= i <= j <= len(cs)

751# try:

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

753# except AttributeError:

754# s, t = cs[i], _0_0

755# for c in cs[i+1:j]:

756# s, t = _sum2_(s * x, t * x, c)

757# return s # + t

758 s, _ = _sum2_(cs[i], _0_0, x=x, *cs[i+1:j])

759 return s # + t

760

761

762 def _remainder(x, y):

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

764

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

766 '''

767 try:

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

769 except AttributeError:

770 return fremainder(x, y)

771

772

773 if _K_2_0:

774 from math import cos as _cos, sin as _sin

775

776 def _sincos2(rad):

777 return _sin(rad), _cos(rad)

778

779 _signBit = _MODS.basics.signBit

780 else:

781 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared

782

783 def _signBit(x):

784 '''(INTERNAL) GeographicLib 1.52-.

785 '''

786 return x < 0

787

788

789 def _sincos2d(deg):

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

791

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

793 '''

794 try:

795 return _wrapped.Math.sincosd(deg)

796 except AttributeError:

797 return sincos2d(deg)

798

799

800 def _sincos2de(deg, t):

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

802

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

804 '''

805 try:

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

807 except AttributeError:

808 return sincos2d(deg, adeg=t)

809

810

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

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

813

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

815

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

817

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

819 '''

820 try:

821 return _wrapped.Math.sum(u, v)

822 except AttributeError:

823 s = u + v

824 r = s - v

825 t = s - r

826 # if Algorithm_3_1:

827 # t = (u - t) + (v + r)

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

829 # r -= u

830 # t -= v

831 # t += r

832 # t = -t

833 # else:

834 t = (u - r) + (v - t)

835 return s, t

836

837

838 def _sum2_(s, t, *vs, **x):

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

840

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

842

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

844

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

846 html/Accumulator_8hpp_source.html>} comments for more details and

847 function C{_sum2} above.

848

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

850 '''

851 x = _xkwds_get(x, x=0)

852

853 _s2, _u0 = _sum2, unsigned0

854 for v in vs:

855 if x:

856 s *= x

857 t *= x

858 if v:

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

860 if s:

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

862 if s:

863 t += u # accumulate u into t

864# elif t: # s == 0 implies t == 0

865# raise _AssertionError(t=t, txt=_not_(_0_))

866 else:

867 s = _u0(u) # result is u, t = 0

868 else:

869 s, t = _u0(t), u

870 return s, t

871

872

873 def _tand(x):

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

875 '''

876 try:

877 return _wrapped.Math.tand(x)

878 except AttributeError:

879 return tand(x)

880

881

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

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

884

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

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

887 '''

888 if wrap:

889 d, t = _diff182(lon1, lon2)

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

891 else:

892 lon2 = _norm180(lon2)

893 return (lon2 - lon1), lon2

894

895

896 def _unsigned2(x):

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

898 '''

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

900

901

902__all__ += _ALL_DOCS(_CapsBase)

903

904# **) MIT License

905#

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

907#

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

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

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

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

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

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

914#

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

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

917#

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

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

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

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

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

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

924# OTHER DEALINGS IN THE SOFTWARE.