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/>} transcoding, otherwise C{1.52} or older.

13

14 Karney-based functionality

15==========================

16

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

18

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

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

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

22

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

24 classGeographicLib_1_1CassiniSoldner.html>}

25

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

27

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

29 classGeographicLib_1_1EllipticFunction.html>}

30

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

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

33

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

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

36

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

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

39

40 - L{GeodesicAreaExact}, L{PolygonArea} -- U{PolygonArea<https://GeographicLib.SourceForge.io/html/

41 classGeographicLib_1_1PolygonAreaT.html>}

42

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

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

45 classGeographicLib_1_1GeodesicLineExact.html>}

46

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

48

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

50

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

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

53

54 - L{JacobiConformal} -- U{JacobiConformal

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

56

57 - L{KTransverseMercator} - U{TransverseMercator

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

59

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

61 classGeographicLib_1_1LocalCartesian.html>}

62

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

64

65 - L{Rhumb}, L{RhumbLine} -- U{Rhumb<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>},

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

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

68

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

70

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

72

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

74

75 - L{pygeodesy.atand}, L{pygeodesy.atan2d}, L{pygeodesy.sincos2}, L{pygeodesy.sincos2d}, L{pygeodesy.tand} -- U{geomath.Math

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

77

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

79

80 2. These C{pygeodesy} modules and classes

81

82 - L{ellipsoidalGeodSolve}, L{ellipsoidalKarney}, L{geodsolve}, L{karney}, L{rhumbsolve}

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

84 L{GnomonicKarney}, L{HeightIDWkarney}

85

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

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

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

89

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

91

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

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

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

95

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

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

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

99

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

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

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

103

104 - L{RhumbLine.intersection2}, L{RhumbLine.nearestOn4}

105

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

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

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

109

110 4. Spherical functions

111

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

113

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

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

116'''

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

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

119

120 from pygeodesy.basics import _copysign, neg, unsigned0, _xgeographiclib, \

121 _xImportError, _xversion_info, _xinstanceof, \

122 _zip, isodd # PYCHOK shared

123 from pygeodesy.constants import NAN, _isfinite as _math_isfinite, _0_0, _1_16th, \

124 _180_0, _N_180_0, _360_0

125 from pygeodesy.datums import _WGS84, _a_ellipsoid # PYCHOK shared

126 from pygeodesy.errors import _ValueError, _xkwds, _xkwds_get

127 from pygeodesy.fmath import cbrt, fremainder, norm2, hypot as _hypot, unstr # PYCHOK shared

128 from pygeodesy.interns import _2_, _a12_, _area_, _azi2_, _composite_, _lat2_, \

129 _lon2_, _m12_, _M12_, _M21_, _number_, _s12_, _S12_

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

131 from pygeodesy.named import _Dict, _NamedBase, _NamedTuple, _Pass

132 from pygeodesy.props import deprecated_method, Property_RO, property_RO

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

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

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

136 Precision_, _1mm as _TOL_M # PYCHOK shared

137 from pygeodesy.utily import atan2d, fabs, sincos2d, tand, unroll180, wrap360 # PYCHOK shared

138

139# from math import fabs # from .utily

140

141__all__ = _ALL_LAZY.karney

142__version__ = '23.04.07'

143

144_EWGS84 = _WGS84.ellipsoid # PYCHOK in .geodesicx.gx, .ktm, .rhumbx, .solveBase

145_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_

146_perimeter_ = 'perimeter'

147

148

149 class _GTuple(_NamedTuple): # in .testNamedTuples

150 '''(INTERNAL) Helper.

151 '''

152 def toGDict(self, **updates):

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

154

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

156 '''

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

158 if updates:

159 r.update(updates)

160 if self._iteration is not None:

161 r._iteration = self._iteration

162 return r

163

164

165 class _Lat(Lat):

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

167 '''

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

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

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

171

172

173 class _Lon(Lon):

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

175 '''

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

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

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

179

180

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

182 '''3-Tuple C{(number, perimeter, area)} with the C{number}

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

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

185 '''

186 _Names_ = (_number_, _perimeter_, _area_)

187 _Units_ = ( Number_, _M, _M2)

188

189

190 class Caps(object): # PYCHOK

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

192 '''

193 EMPTY = 0 # formerly aka NONE

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

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

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

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

198 DISTANCE_IN = 1 << 11 # allow distance C{s12} in Direct

199 REDUCEDLENGTH = 1 << 12 # compute reduced length C{m12}

200 GEODESICSCALE = 1 << 13 # compute geodesic scales C{M12} and C{M21}

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

202

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

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

205

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

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

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

209

210 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE

211 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA

212

213 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE

214 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA

215

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

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

218

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

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

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

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

223 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \

224 _DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs

225 _OUT_ALL = ALL

226 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL

227

228 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE

229 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE

230 _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK

231 _LINE = AZIMUTH | LATITUDE | LONG_UNROLL

232 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE

233# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE

234

235 Caps = Caps() # PYCHOK singleton

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

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

238

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

240

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

242

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

244

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

246

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

248

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

250

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

252

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

254

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

256

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

258

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

260

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

262

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

264

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

266

267

268 class _CapsBase(_NamedBase): # in .geodesicx.gxbases, .rhumbx

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

270 '''

271 ALL = Caps.ALL

272 AREA = Caps.AREA

273 AZIMUTH = Caps.AZIMUTH

274 DISTANCE = Caps.DISTANCE

275 DISTANCE_IN = Caps.DISTANCE_IN

276 EMPTY = Caps.EMPTY # aka NONE

277 GEODESICSCALE = Caps.GEODESICSCALE

278 LATITUDE = Caps.LATITUDE

279 LINE_OFF = Caps.LINE_OFF

280 LONGITUDE = Caps.LONGITUDE

281 LONG_UNROLL = Caps.LONG_UNROLL

282 REDUCEDLENGTH = Caps.REDUCEDLENGTH

283 STANDARD = Caps.STANDARD

284

285 _caps = 0 # None

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

287

288 @Property_RO

289 def caps(self):

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

291 '''

292 return self._caps

293

294 def caps_(self, caps):

295 '''Check the available capabilities.

296

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

298 for all capabilities to be checked.

299

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

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

302 '''

303 caps &= Caps._OUT_ALL

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

305

306 @property

307 def debug(self):

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

309 '''

310 return bool(self._debug)

311

312 @debug.setter # PYCHOK setter!

313 def debug(self, debug):

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

315 more details in L{GDict} results.

316 '''

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

318

319 def _iter2tion(self, r, s):

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

321 '''

322 i = _xkwds_get(s, iter=None)

323 if i is not None:

324 self._iteration = r._iteration = i

325 return r

326

327

328 class Direct9Tuple(_GTuple):

329 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc

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

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

332 C{meter} I{squared}.

333 '''

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

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

336

337

338 class GDict(_Dict): # XXX _NamedDict

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

340 to the C{dict} items.

341

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

343 L{GDict} instance.

344 '''

345 _iteration = None # Iteration number (C{int}) or C{None}

346

347 @property_RO

348 def iteration(self): # see .named._NamedBase

349 '''Get the iteration number (C{int}) or

350 C{None} if not available/applicable.

351 '''

352 return self._iteration

353

354 def toDirect9Tuple(self, dflt=NAN):

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

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

357

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

359

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

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

362 '''

363 return self._toTuple(Direct9Tuple, dflt)

364

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

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

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

368 result.

369

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

371

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

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

374 '''

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

376

377 def toInverse10Tuple(self, dflt=NAN):

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

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

380

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

382

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

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

385 '''

386 return self._toTuple(Inverse10Tuple, dflt)

387

388 @deprecated_method

389 def toRhumb7Tuple(self, dflt=NAN):

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

391

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

393 '''

394 return self._toTuple(_MODS.deprecated.Rhumb7Tuple, dflt)

395

396 def toRhumb8Tuple(self, dflt=NAN):

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

398

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

400

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

402 azi12, s12, S12, a12)}.

403 '''

404 return self._toTuple(_MODS.rhumbx.Rhumb8Tuple, dflt)

405

406 def toRhumbSolve7Tuple(self, dflt=NAN):

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

408

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

410

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

412 azi12, s12, S12)}.

413 '''

414 return self._toTuple(_MODS.rhumbsolve.RhumbSolve7Tuple, dflt)

415

416 def _toTuple(self, nTuple, dflt):

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

418 '''

419 _g = getattr

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

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

422

423

424 class GeodesicError(_ValueError):

425 '''Error raised for L{pygeodesy.geodesicx} lack of convergence

426 or other L{pygeodesy.geodesicx} or L{pygeodesy.karney} issues.

427 '''

428 pass

429

430

431 class Inverse10Tuple(_GTuple):

432 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length

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

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

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

436 '''

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

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

439

440 def toGDict(self, **updates):

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

442

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

444 '''

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

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

447 **updates) # PYCHOK indent

448

449

450 class _kWrapped(object):

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

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

453 '''

454

455 @Property_RO

456 def geographiclib(self):

457 '''Get the imported C{geographiclib}, provided the U{geographiclib

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

459 otherwise an C{ImportError}.

460 '''

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

462 from geographiclib.geodesic import Geodesic

463 g.Geodesic = Geodesic

464 from geographiclib.geodesicline import GeodesicLine

465 g.GeodesicLine = GeodesicLine

466 from geographiclib.geomath import Math

467 g.Math = Math

468 return g

469

470 @Property_RO # MCCABE 13

471 def Math(self):

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

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

474 otherwise C{None}.

475 '''

476 try:

477 g = self.geographiclib

478 M = g.Math

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

480 if _K_2_0:

481 M = None

482# elif not _K_2_0: # XXX set 2.0?

483# _K_2_0 = True

484 except (AttributeError, ImportError):

485 M = None

486 return M

487

488_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py

489

490

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

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

493

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

495

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

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

498 '''

499 try:

500 return _wrapped.Math.AngRound(x)

501 except AttributeError:

502 pass

503 if x:

504 y = _1_16th - fabs(x)

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

506 x = _copysign(_1_16th - y, x)

507 else:

508 x = _0_0 # -0 to 0

509 return x

510

511

512 def _atan2d(y, x):

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

514 '''

515 try:

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

517 except AttributeError:

518 return atan2d(y, x)

519

520

521 def _cbrt(x):

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

523 '''

524 try:

525 return _wrapped.Math.cbrt(x)

526 except AttributeError:

527 return cbrt(x)

528

529

530 def _copyBit(x, y):

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

532 '''

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

534

535

536 def _diff182(deg0, deg):

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

538

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

540 '''

541 try:

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

543 except AttributeError:

544 pass

545 if _K_2_0: # geographiclib 2.0

546 d, t = _sum2(fremainder(-deg0, _360_0),

547 fremainder( deg, _360_0))

548 d, t = _sum2(fremainder( d, _360_0), t)

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

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

551 else:

552 d, t = _sum2(_norm180(-deg0), _norm180(deg))

553 d = _norm180(d)

554 if t > 0 and d == _180_0:

555 d = _N_180_0

556 d, t = _sum2(d, t)

557 return d, t

558

559

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

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

562

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

564 '''

565 try:

566 return _wrapped.Math.LatFix(deg)

567 except AttributeError:

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

569

570

571 def _isfinite(x): # mimick geomath.Math.AngNormalize

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

573

574 @return: C{True} if finite.

575 '''

576 try:

577 return _wrapped.Math.isfinite(x)

578 except AttributeError:

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

580

581

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

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

584

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

586 '''

587 try:

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

589 except AttributeError:

590 return norm2(x, y)

591

592

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

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

595

596 @return: Reduced angle C{degrees}.

597 '''

598 try:

599 return _wrapped.Math.AngNormalize(deg)

600 except AttributeError:

601 pass

602 d = fremainder(deg, _360_0)

603 if d in (_180_0, -_180_0):

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

605 return d

606

607

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

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

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

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

612 or C{geodesicw.Geodesic} instance.

613 '''

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

615 raise _ValueError(wrap=wrap)

616

617 if _MODS.booleans.isBoolean(points):

618 # recursive call for each boolean clip

619

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

621 return _polygon(geodesic, clip, *args)

622

623 if not closed: # closed only

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

625

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

627

628 gP = geodesic.Polygon(line)

629 _A = gP.AddPoint

630

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

632 p0 = Ps[0]

633

634 # note, lon deltas are unrolled, by default

635 _A(p0.lat, p0.lon)

636 for p in Ps.iterate(closed=closed):

637 _A(p.lat, p.lon)

638 if closed and line and p != p0:

639 _A(p0.lat, p0.lon)

640

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

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

643

644

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

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

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

648

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

650 '''

651 s, t = cs[i], _0_0

652 _s2_ = _sum2_

653 for c in cs[i+1:j]:

654 s, t = _s2_(s * x, t * x, c)

655 return s # + t

656

657

658 def _remainder(x, y):

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

660

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

662 '''

663 try:

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

665 except AttributeError:

666 return fremainder(x, y)

667

668

669 if _K_2_0:

670 from pygeodesy.basics import signBit as _signBit

671 from math import cos as _cos, sin as _sin

672

673 def _sincos2(rad):

674 return _sin(rad), _cos(rad)

675

676 else:

677 from pygeodesy.utily import sincos2 as _sincos2 # PYCHOK shared

678

679 def _signBit(x):

680 '''(INTERNAL) GeographicLin 1.52-.

681 '''

682 return x < 0

683

684

685 def _sincos2d(deg):

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

687

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

689 '''

690 try:

691 return _wrapped.Math.sincosd(deg)

692 except AttributeError:

693 return sincos2d(deg)

694

695

696 def _sincos2de(deg, t):

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

698

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

700 '''

701 try:

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

703 except AttributeError:

704 return sincos2d(deg, adeg=t)

705

706

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

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

709

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

711

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

713

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

715 '''

716 try:

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

718 except AttributeError:

719 pass

720 s = u + v

721 r = s - v

722 t = s - r

723 # if Algorithm_3_1:

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

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

726 # r -= u

727 # t -= v

728 # t += r

729 # t = -t

730 # else:

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

732 return s, t

733

734

735 def _sum2_(s, t, *vs):

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

737

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

739

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

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

742 function C{_sum2} above.

743

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

745 '''

746 _s2, _u0 = _sum2, unsigned0

747 for v in vs:

748 if v:

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

750 if s:

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

752 if s:

753 t += u # accumulate u into t

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

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

756 else:

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

758 else:

759 s, t = _u0(t), u

760 return s, t

761

762

763 def _tand(x):

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

765 '''

766 try:

767 return _wrapped.Math.tand(x)

768 except AttributeError:

769 return tand(x)

770

771

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

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

774

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

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

777 '''

778 if wrap:

779 d, t = _diff182(lon1, lon2)

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

781 else:

782 lon2 = _norm180(lon2)

783 return (lon2 - lon1), lon2

784

785

786 def _unsigned2(x):

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

788 '''

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

790

791

792__all__ += _ALL_DOCS(_CapsBase)

793

794# **) MIT License

795#

796# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

797#

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

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

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

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

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

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

804#

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

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

807#

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

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

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

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

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

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

814# OTHER DEALINGS IN THE SOFTWARE.