Coverage for pygeodesy/geodesicw.py: 91%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''Wrapper around Python classes C{geodesic.Geodesic} and C{geodesicline.GeodesicLine} from 

5I{Karney}'s Python package U{geographiclib<https://PyPI.org/project/geographiclib>}, provided 

6that package is installed. 

7 

8The I{wrapped} class methods return a L{GDict} instance offering access to the C{dict} items 

9either by C{key} or by C{attribute} name. 

10 

11With env variable C{PYGEODESY_GEOGRAPHICLIB} left undefined or set to C{"2"}, this module and modules 

12L{pygeodesy.geodesici}, L{pygeodesy.geodesicx} and L{pygeodesy.karney} will use U{GeographicLib 2.0 

13<https://GeographicLib.SourceForge.io/C++/doc/>} transcoding, otherwise C{1.52} or older. 

14''' 

15 

16from pygeodesy.basics import _copysign, _xinstanceof 

17from pygeodesy.constants import EPS, NAN, _EPSqrt as _TOL, _0_5 

18from pygeodesy.datums import _earth_datum, _WGS84, _EWGS84 

19# from pygeodesy.dms import F_D # from .latlonBase 

20# from pygeodesy.ellipsoids import _EWGS84 # from .datums 

21from pygeodesy.errors import _AssertionError, GeodesicError, \ 

22 IntersectionError 

23from pygeodesy.fsums import Fsum, Fmt, unstr 

24from pygeodesy.internals import typename, _under 

25from pygeodesy.interns import NN, _DOT_, _SPACE_, _to_, _too_ 

26from pygeodesy.karney import _atan2d, Caps, Direct9Tuple, GDict, \ 

27 Inverse10Tuple, _kWrapped 

28from pygeodesy.latlonBase import LatLonBase as _LLB, F_D, Radius_ 

29from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS 

30from pygeodesy.named import callername, classname, _name1__, _name2__ 

31from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple 

32from pygeodesy.props import Property, Property_RO, property_RO, \ 

33 property_ROver 

34# from pygeodesy.streprs import Fmt, unstr # from .fsums 

35# from pygeodesy.units import Radius_ # from .latlonBase 

36from pygeodesy.utily import _unrollon, _Wrap, wrap360, fabs # PYCHOK used! 

37 

38from contextlib import contextmanager 

39# from math import fabs # from .utily 

40 

41__all__ = _ALL_LAZY.geodesicw 

42__version__ = '25.04.14' 

43 

44_plumb_ = 'plumb' 

45_TRIPS = 65 

46 

47 

48class _gWrapped(_kWrapped): 

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

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

51 ''' 

52 

53 @property_ROver # MCCABE 24 

54 def Geodesic(self): 

55 '''Get the I{wrapped} C{geodesic.Geodesic} class from I{Karney}'s Python 

56 U{geographiclib<https://GitHub.com/geographiclib/geographiclib-python>}, 

57 provided the latter is installed. 

58 ''' 

59 _Geodesic = self.geographiclib.Geodesic 

60 if not (Caps.LATITUDE == _Geodesic.LATITUDE and 

61 Caps.LONGITUDE == _Geodesic.LONGITUDE and 

62 Caps.AZIMUTH == _Geodesic.AZIMUTH and 

63 Caps.DISTANCE == _Geodesic.DISTANCE and 

64 Caps.DISTANCE_IN == _Geodesic.DISTANCE_IN and 

65 Caps.REDUCEDLENGTH == _Geodesic.REDUCEDLENGTH and 

66 Caps.GEODESICSCALE == _Geodesic.GEODESICSCALE and 

67 Caps.AREA == _Geodesic.AREA and 

68 Caps.STANDARD == _Geodesic.STANDARD and 

69 Caps.ALL == _Geodesic.ALL): 

70 raise _AssertionError(Caps=bin(Caps.ALL), 

71 Geodesic=bin(_Geodesic.ALL)) 

72 

73 class Geodesic(_Geodesic): 

74 '''I{Wrapper} for I{Karney}'s Python U{geodesic.Geodesic 

75 <https://PyPI.org/project/geographiclib>} class. 

76 ''' 

77 _datum = _WGS84 

78 _debug = 0 # like .geodesicx.bases._GeodesicBase 

79 LINE_OFF = 0 # in .azimuthal._GnomonicBase and .css.CassiniSoldner 

80 _name = NN 

81 STANDARD_LINE = Caps.STANDARD_LINE 

82 

83 def __init__(self, a_ellipsoid=_EWGS84, f=None, **name): # PYCHOK signature 

84 '''New I{wrapped} C{geodesic.Geodesic} instance. 

85 

86 @arg a_ellipsoid: The equatorial radius I{a} (C{meter}, conventionally), 

87 an ellipsoid (L{Ellipsoid}) or a datum (L{Datum}). 

88 @arg f: The ellipsoid's flattening (C{scalar}), required if B{C{a_ellipsoid}) 

89 is C{meter}, ignored otherwise. 

90 @kwarg name: Optional C{B{name}=NN} (C{str}). 

91 ''' 

92 _earth_datum(self, a_ellipsoid, f=f, **name) # raiser=NN 

93 E = self.ellipsoid 

94 with _wargs(self, *E.a_f, **name) as args: 

95 _Geodesic.__init__(self, *args) 

96 if name: 

97 self._name, _ = _name2__(name, _or_nameof=E) 

98 

99 def ArcDirect(self, lat1, lon1, azi1, a12, outmask=Caps.STANDARD): # PYCHOK no cover 

100 '''Return the C{_Geodesic.ArcDirect} result as L{GDict}. 

101 ''' 

102 with _wargs(self, lat1, lon1, azi1, a12, outmask) as args: 

103 d = _Geodesic.ArcDirect(self, *args) 

104 return GDict(d) 

105 

106 def ArcDirectLine(self, lat1, lon1, azi1, a12, caps=Caps.STANDARD_LINE, **name): # PYCHOK no cover 

107 '''Return the C{_Geodesic.ArcDirectLine} as I{wrapped} C{GeodesicLine}. 

108 ''' 

109 return self._GenDirectLine(lat1, lon1, azi1, True, a12, caps, **name) 

110 

111 Area = _Geodesic.Polygon # like GeodesicExact.Area 

112 

113 @property_RO 

114 def datum(self): 

115 '''Get this geodesic's datum (C{Datum}). 

116 ''' 

117 return self._datum 

118 

119 @Property 

120 def debug(self): 

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

122 ''' 

123 return bool(self._debug) 

124 

125 @debug.setter # PYCHOK setter! 

126 def debug(self, debug): 

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

128 details in L{GDict} results. 

129 ''' 

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

131 

132 def Direct(self, lat1, lon1, azi1, s12=0, outmask=Caps.STANDARD): 

133 '''Return the C{_Geodesic.Direct} result as L{GDict}. 

134 ''' 

135 with _wargs(self, lat1, lon1, azi1, s12, outmask) as args: 

136 d = _Geodesic.Direct(self, *args) 

137 return GDict(d) 

138 

139 def Direct3(self, lat1, lon1, azi1, s12): # PYCHOK outmask 

140 '''Return the destination lat, lon and reverse azimuth 

141 in C{degrees} as L{Destination3Tuple}. 

142 ''' 

143 d = self.Direct(lat1, lon1, azi1, s12, outmask=Caps._DIRECT3) 

144 return Destination3Tuple(d.lat2, d.lon2, d.azi2) 

145 

146 def _DirectLine(self, ll1, azi12, s12=0, **caps_name): 

147 '''(INTERNAL) Short-cut version. 

148 ''' 

149 return self.DirectLine(ll1.lat, ll1.lon, azi12, s12, **caps_name) 

150 

151 def DirectLine(self, lat1, lon1, azi1, s12, caps=Caps.STANDARD_LINE, **name): 

152 '''Return the C{_Geodesic.DirectLine} as I{wrapped} C{GeodesicLine}. 

153 ''' 

154 return self._GenDirectLine(lat1, lon1, azi1, False, s12, caps, **name) 

155 

156 @Property_RO 

157 def ellipsoid(self): 

158 '''Get this geodesic's ellipsoid (C{Ellipsoid}). 

159 ''' 

160 return self.datum.ellipsoid 

161 

162 @property_RO 

163 def f1(self): # in .css.CassiniSoldner.reset 

164 '''Get the geodesic's ellipsoid's I{1 - flattening} (C{float}). 

165 ''' 

166 return getattr(self, _under(Geodesic.f1.name), self.ellipsoid.f1) 

167 

168 def _GDictDirect(self, lat, lon, azi, arcmode, s12_a12, outmask=Caps.STANDARD): 

169 '''(INTERNAL) Get C{_Geodesic._GenDirect} result as C{GDict}. 

170 ''' 

171 with _wargs(self, lat, lon, azi, arcmode, s12_a12, outmask) as args: 

172 t = _Geodesic._GenDirect(self, *args) 

173 return Direct9Tuple(t).toGDict() # *t 

174 

175 def _GDictInverse(self, lat1, lon1, lat2, lon2, outmask=Caps.STANDARD): 

176 '''(INTERNAL) Get C{_Geodesic._GenInverse} result as L{Inverse10Tuple}. 

177 ''' 

178 with _wargs(self, lat1, lon1, lat2, lon2, outmask) as args: 

179 t = _Geodesic._GenInverse(self, *args) 

180 return Inverse10Tuple(t).toGDict(lon1=lon1, lon2=lon2) # *t 

181 

182 def _GenDirectLine(self, lat1, lon1, azi1, arcmode, s12_a12, *caps, **name): 

183 '''(INTERNAL) Invoked by C{_Geodesic.DirectLine} and C{-.ArcDirectLine}, 

184 returning the result as a I{wrapped} C{GeodesicLine}. 

185 ''' 

186 with _wargs(self, lat1, lon1, azi1, arcmode, s12_a12, *caps, **name) as args: 

187 t = _Geodesic._GenDirectLine(self, *args) 

188 return self._Line13(t, **name) 

189 

190 def _Inverse(self, ll1, ll2, wrap, **outmask): 

191 '''(INTERNAL) Short-cut version, see .ellipsoidalBaseDI.intersecant2. 

192 ''' 

193 if wrap: 

194 ll2 = _unrollon(ll1, _Wrap.point(ll2)) 

195 return self.Inverse(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **outmask) 

196 

197 def Inverse(self, lat1, lon1, lat2, lon2, outmask=Caps.STANDARD): 

198 '''Return the C{_Geodesic.Inverse} result as L{GDict}. 

199 ''' 

200 with _wargs(self, lat1, lon1, lat2, lon2, outmask) as args: 

201 d = _Geodesic.Inverse(self, *args) 

202 return GDict(d) 

203 

204 def Inverse1(self, lat1, lon1, lat2, lon2, wrap=False): 

205 '''Return the non-negative, I{angular} distance in C{degrees}. 

206 

207 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll 

208 B{C{lat2}} and BC{lon2}} (C{bool}). 

209 ''' 

210 # see .FrechetKarney.distance, .HausdorffKarney._distance 

211 # and .HeightIDWkarney._distances 

212 if wrap: 

213 _, lat2, lon2 = _Wrap.latlon3(lat1, lat2, lon2, True) # _Geodesic.LONG_UNROLL 

214 r = self.Inverse(lat1, lon1, lat2, lon2) 

215 # XXX _Geodesic.DISTANCE needed for 'a12'? 

216 return fabs(r.a12) 

217 

218 def Inverse3(self, lat1, lon1, lat2, lon2): # PYCHOK outmask 

219 '''Return the distance in C{meter} and the forward and reverse 

220 azimuths in C{degrees} as L{Distance3Tuple}. 

221 ''' 

222 r = self.Inverse(lat1, lon1, lat2, lon2, outmask=Caps._INVERSE3) 

223 return Distance3Tuple(r.s12, wrap360(r.azi1), wrap360(r.azi2)) 

224 

225 def _InverseLine(self, ll1, ll2, wrap, **caps_name): 

226 '''(INTERNAL) Short-cut version. 

227 ''' 

228 if wrap: 

229 ll2 = _unrollon(ll1, _Wrap.point(ll2)) 

230 return self.InverseLine(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **caps_name) 

231 

232 def InverseLine(self, lat1, lon1, lat2, lon2, caps=Caps.STANDARD_LINE, **name): 

233 '''Return the C{_Geodesic.InverseLine} as I{wrapped} C{GeodesicLine}. 

234 ''' 

235 with _wargs(self, lat1, lon1, lat2, lon2, caps, **name) as args: 

236 t = _Geodesic.InverseLine(self, *args) 

237 return self._Line13(t, **name) 

238 

239 def Line(self, lat1, lon1, azi1, caps=Caps.STANDARD_LINE, **name): 

240 '''Set up a I{wrapped} C{GeodesicLine} to compute several points 

241 along a single, I{wrapped} (this) geodesic. 

242 ''' 

243 return _wrapped.GeodesicLine(self, lat1, lon1, azi1, caps=caps, **name) 

244 

245 def _Line13(self, t, **name): 

246 '''(INTERNAL) Wrap C{_GeodesicLine}, add distance and arc length 

247 to reference point 3. 

248 ''' 

249 gl = _wrapped.GeodesicLine(self, t.lat1, t.lon1, t.azi1, caps=t.caps, 

250 salp1=t.salp1, calp1=t.calp1, **name) 

251 gl.a13, gl.s13 = t.a13, t.s13 

252 return gl 

253 

254 @property_RO 

255 def name(self): 

256 '''Get the name (C{str}). 

257 ''' 

258 return self._name 

259 

260# Polygon = _Geodesic.Polygon 

261 

262 WGS84 = None # _EWGS84.geodesicw recusion 

263 

264 # Geodesic.ArcDirect.__doc__ = _Geodesic.ArcDirect.__doc__ 

265 # Geodesic.Direct.__doc__ = _Geodesic.Direct.__doc__ 

266 # Geodesic.Inverse.__doc__ = _Geodesic.Inverse.__doc__ 

267 # Geodesic.InverseLine.__doc__ = _Geodesic.InverseLinr.__doc__ 

268 # Geodesic.Line.__doc__ = _Geodesic.Line.__doc__ 

269 return Geodesic # overwrite property_ROver 

270 

271 @property_ROver # MCCABE 16 

272 def GeodesicLine(self): 

273 '''Get the I{wrapped} C{geodesicline.GeodesicLine} class from I{Karney}'s 

274 Python U{geographiclib<https://GitHub.com/geographiclib/geographiclib-python>}, 

275 provided the latter is installed. 

276 ''' 

277 _GeodesicLine = self.geographiclib.GeodesicLine 

278 

279 class GeodesicLine(_GeodesicLine): 

280 '''I{Wrapper} for I{Karney}'s Python U{geodesicline.GeodesicLine 

281 <https://PyPI.org/project/geographiclib>} class. 

282 ''' 

283 _geodesic = None 

284 _name = NN 

285 

286 def __init__(self, geodesic, lat1, lon1, azi1, **caps_name_): # salp1=NAN, calp1=NAN 

287 '''New I{wrapped} C{geodesicline.GeodesicLine} instance. 

288 

289 @arg geodesic: A I{wrapped} C{Geodesic} instance. 

290 @arg lat1: Latitude of the first points (C{degrees}). 

291 @arg lon1: Longitude of the first points (C{degrees}). 

292 @arg azi1: Azimuth at the first points (compass C{degrees360}). 

293 @kwarg caps_name_: Optional keyword arguments C{B{caps}=Caps.STANDARD}, 

294 a bit-or'ed combination of L{Caps<pygeodesy.karney.Caps>} 

295 values specifying the capabilities the C{GeodesicLine} instance 

296 should possess, an optional C{B{name}=NN} plus C{salp1=NAN} and 

297 C{calp1=NAN} for I{INTERNAL} use. 

298 ''' 

299 _xinstanceof(_wrapped.Geodesic, geodesic=geodesic) 

300 with _wargs(self, geodesic, lat1, lon1, azi1, **caps_name_) as args: 

301 name, caps_ = _name2__(caps_name_, _or_nameof=geodesic) 

302 _GeodesicLine.__init__(self, *args, **caps_) # XXX avoid updates? 

303 if name: 

304 self._name = name 

305 self._geodesic = geodesic 

306 

307 @Property_RO 

308 def a1(self): 

309 '''Get the I{equatorial arc} (C{degrees}), the arc length between 

310 the northward equatorial crossing and point C{(lat1, lon1)}. 

311 

312 @see: U{EquatorialArc<https://GeographicLib.SourceForge.io/ 

313 C++/doc/classGeographicLib_1_1GeodesicLine.html>} 

314 ''' 

315 try: 

316 return _atan2d(self._ssig1, self._csig1) 

317 except AttributeError: 

318 return NAN # see .geodesicx.gxline._GeodesicLineExact 

319 

320 equatorarc = a1 

321 

322 def Arc(self): 

323 '''Return the angular distance to point 3 (C{degrees} or C{NAN}). 

324 ''' 

325 return self.a13 

326 

327 def ArcPosition(self, a12, outmask=Caps.STANDARD): 

328 '''Return the position at C{B{a12} degrees} on this line. 

329 

330 @arg a12: Angular distance from this line's first point 

331 (C{degrees}). 

332 

333 @see: Method L{Position} for further details. 

334 ''' 

335 with _wargs(self, a12, outmask) as args: 

336 d = _GeodesicLine.ArcPosition(self, *args) 

337 return GDict(d) 

338 

339 @Property_RO 

340 def azi0(self): # see .css.CassiniSoldner.forward4 

341 '''Get the I{equatorial azimuth} (C{degrees}), the azimuth of the 

342 geodesic line as it crosses the equator in a northward direction. 

343 

344 @see: U{EquatorialAzimuth<https://GeographicLib.SourceForge.io/ 

345 C++/doc/classGeographicLib_1_1GeodesicLine.html>} 

346 ''' 

347 try: 

348 return _atan2d(self._salp0, self._calp0) 

349 except AttributeError: 

350 return NAN # see .geodesicx.gxline._GeodesicLineExact 

351 

352 equatorazimuth = azi0 

353 

354 def Distance(self): 

355 '''Return the distance to reference point 3 (C{meter} or C{NAN}). 

356 ''' 

357 return self.s13 

358 

359 @property_RO 

360 def geodesic(self): 

361 '''Get the I{wrapped} geodesic (L{Geodesic}). 

362 ''' 

363 return self._geodesic 

364 

365 def Intersecant2(self, lat0, lon0, radius, tol=_TOL): 

366 '''Compute the intersection(s) of this geodesic line and a circle. 

367 

368 @arg lat0: Latitude of the circle center (C{degrees}). 

369 @arg lon0: Longitude of the circle center (C{degrees}). 

370 @arg radius: Radius of the circle (C{meter}, conventionally). 

371 @kwarg tol: Convergence tolerance (C{scalar}). 

372 

373 @return: 2-Tuple C{(P, Q)} with both intersections points (representing 

374 a geodesic chord), each a L{GDict} from method L{Position} and 

375 extended to 14 items C{lat1, lon1, azi1, lat2, lon2, azi2, a12, 

376 s12, lat0, lon0, azi0, a02, s02, at} with the circle center 

377 C{lat0}, C{lon0}, azimuth C{azi0} at the intersection, distance 

378 C{a02} in C{degrees} and C{s02} in C{meter} along the geodesic 

379 from the circle center to the intersection C{lat2, lon2} and 

380 the angle C{at} between the geodesic and this line at the 

381 intersection. The I{geodesic} azimuth at the intersection is 

382 C{(at + azi2)}. If this line is tangential to the circle, both 

383 intersections are the same L{GDict} instance. 

384 

385 @raise IntersectionError: The circle and this geodesic line do not 

386 intersect. 

387 

388 @raise UnitError: Invalid B{C{radius}}. 

389 ''' 

390 return _Intersecant2(self, lat0, lon0, radius, tol=tol) 

391 

392 def PlumbTo(self, lat0, lon0, est=None, tol=_TOL): 

393 '''Compute the I{perpendicular} intersection of this geodesic line 

394 with a geodesic from the given point. 

395 

396 @arg lat0: Latitude of the point (C{degrees}). 

397 @arg lon0: Longitude of the point (C{degrees}). 

398 @kwarg est: Optional, initial estimate for the distance C{s12} of 

399 the intersection I{along} this geodesic line (C{meter}). 

400 @kwarg tol: Convergence tolerance (C(meter)). 

401 

402 @return: The intersection point on this geodesic line, a L{GDict} 

403 from method L{Position} extended to 14 items C{lat1, lon1, 

404 azi1, lat2, lon2, azi2, a12, s12, lat0, lon0, azi0, a02, 

405 s02, at} with C{a02} and C{s02} the distance in C{degrees} 

406 and C{meter} from the given point C{lat0, lon0} to the 

407 intersection C{lat2, lon2}, azimuth C{azi0} at the given 

408 point and the (perpendicular) angle C{at} between the 

409 geodesic and this line at the intersection point. The 

410 geodesic azimuth at the intersection is C{(at + azi2)}. 

411 See method L{Position} for further details. 

412 

413 @see: Methods C{Intersecant2}, C{Intersection} and C{Position}. 

414 ''' 

415 return _PlumbTo(self, lat0, lon0, est=est, tol=tol) 

416 

417 def Position(self, s12, outmask=Caps.STANDARD): 

418 '''Return the position at distance C{B{s12} meter} on this line. 

419 

420 @arg s12: Distance from this line's first point (C{meter}). 

421 @kwarg outmask: Bit-or'ed combination of L{Caps<pygeodesy.karney.Caps>} 

422 values specifying the quantities to be returned. 

423 

424 @return: A L{GDict} with up to 12 items C{lat1, lon1, azi1, lat2, 

425 lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1}, 

426 C{lon1}, C{azi1} and arc length C{a12} always included, 

427 except when C{a12=NAN}. 

428 ''' 

429 with _wargs(self, s12, outmask) as args: 

430 d = _GeodesicLine.Position(self, *args) 

431 return GDict(d) 

432 

433 # GeodesicLine.ArcPosition.__doc__ = _GeodesicLine.ArcPosition.__doc__ 

434 # GeodesicLine.Position.__doc__ = _GeodesicLine.Position.__doc__ 

435 return GeodesicLine # overwrite property_ROver 

436 

437 @property_ROver 

438 def Geodesic_WGS84(self): 

439 '''Get the I{wrapped} C{Geodesic(WGS84)} singleton, provided the 

440 U{geographiclib<https://PyPI.org/project/geographiclib>} package 

441 is installed, otherwise an C{ImportError}. 

442 ''' 

443 return _EWGS84.geodesicw # overwrite property_ROver 

444 

445_wrapped = _gWrapped() # PYCHOK singleton, .ellipsoids, .test/base.py 

446 

447 

448class Geodesic(_gWrapped): # overwritten by 1st instance 

449 '''I{Wrapper} around I{Karney}'s class U{geographiclib.geodesic.Geodesic 

450 <https://GeographicLib.SourceForge.io/Python/doc/code.html>}. 

451 ''' 

452 def __new__(unused, a_ellipsoid=_EWGS84, f=None, **name): 

453 '''Return a I{wrapped} C{geodesic.Geodesic} instance from I{Karney}'s 

454 Python U{geographiclib<https://PyPI.org/project/geographiclib>}, 

455 provide the latter is installed, otherwise an C{ImportError}. 

456 

457 @arg a_ellipsoid: An ellipsoid (L{Ellipsoid}) or datum (L{Datum}) 

458 or the equatorial radius I{a} of the ellipsoid (C{meter}). 

459 @arg f: The flattening of the ellipsoid (C{scalar}), required if 

460 B{C{a_ellipsoid}}) is C{meter}, ignored otherwise. 

461 @kwarg name: Optional C{B{name}=NN} (C{str}). 

462 ''' 

463 g = _wrapped.Geodesic(a_ellipsoid, f=f, **name) 

464 _MODS.geodesicw.Geodesic = g.__class__ # overwrite class 

465 return g 

466 

467 

468class GeodesicLine(_gWrapped): # overwritten by 1st instance 

469 '''I{Wrapper} around I{Karney}'s class U{geographiclib.geodesicline.GeodesicLine 

470 <https://GeographicLib.SourceForge.io/Python/doc/code.html>}. 

471 ''' 

472 def __new__(unused, geodesic, lat1, lon1, azi1, caps=Caps.STANDARD_LINE, **name): 

473 '''Return a I{wrapped} C{geodesicline.GeodesicLine} instance from I{Karney}'s 

474 Python U{geographiclib<https://PyPI.org/project/geographiclib>}, provided 

475 the latter is installed, otherwise an C{ImportError}. 

476 

477 @arg geodesic: A I{wrapped} L{Geodesic} instance. 

478 @arg lat1: Latitude of the first points (C{degrees}). 

479 @arg lon1: Longitude of the first points (C{degrees}). 

480 @arg azi1: Azimuth at the first points (compass C{degrees360}). 

481 @kwarg caps: Optional, bit-or'ed combination of L{Caps<pygeodesy.karney.Caps>} 

482 values specifying the capabilities the C{GeodesicLine} instance 

483 should possess, i.e., which quantities can be returned by methods 

484 C{GeodesicLine.Position} and C{GeodesicLine.ArcPosition}. 

485 @kwarg name: Optional C{B{name}=NN} (C{str}). 

486 ''' 

487 gl = _wrapped.GeodesicLine(geodesic, lat1, lon1, azi1, caps=caps, **name) 

488 _MODS.geodesicw.GeodesicLine = gl.__class__ # overwrite class 

489 return gl 

490 

491 

492def Geodesic_WGS84(): 

493 '''Get the I{wrapped} L{Geodesic}C{(WGS84)} singleton, provided 

494 U{geographiclib<https://PyPI.org/project/geographiclib>} is 

495 installed, otherwise an C{ImportError}. 

496 ''' 

497 return _wrapped.Geodesic_WGS84 

498 

499 

500class _wargs(object): # see also .formy._idllmn6, .latlonBase._toCartesian3, .vector2d._numpy 

501 '''(INTERNAL) C{geographiclib} arguments and exception handler. 

502 ''' 

503 @contextmanager # <https://www.Python.org/dev/peps/pep-0343/> Examples 

504 def __call__(self, inst, *args, **kwds): 

505 '''(INTERNAL) Yield C{tuple(B{args})} with any errors raised 

506 as L{GeodesicError} embellished with all B{C{kwds}}. 

507 ''' 

508 try: 

509 yield args 

510 except Exception as x: 

511 u = _DOT_(classname(inst), callername(up=2, underOK=True)) 

512 raise GeodesicError(unstr(u, *args, **_name1__(kwds)), cause=x) 

513 

514_wargs = _wargs() # PYCHOK singleton 

515 

516 

517def _Intersecant2(gl, lat0, lon0, radius, tol=_TOL, form=F_D): # MCCABE in LatLonEllipsoidalBaseDI.intersecant2, .geodesicx.gxline.Intersecant2 

518 # (INTERNAL) Return the intersections of a circle at C{lat0, lon0} 

519 # and a geodesic line as a 2-Tuple C{(P, Q)}, each a C{GDict}. 

520 r = Radius_(radius) 

521 n = typename(_Intersecant2)[1:] 

522 _P = gl.Position 

523 _I = gl.geodesic.Inverse 

524 

525 def _R3(s): 

526 # radius, intersection, etc. at distance C{s} 

527 P = _P(s) 

528 d = _I(lat0, lon0, P.lat2, P.lon2) 

529 return fabs(d.s12), P, d 

530 

531 def _bisect2(s, c, Rc, r, tol, _R3): 

532 _s = Fsum(c).fsumf_ 

533 for i in range(_TRIPS): 

534 b = _s(s) 

535 Rb, P, d = _R3(b) 

536 if Rb > r: 

537 break 

538 else: # b >>> s and c >>> s 

539 raise ValueError(Fmt.no_convergence(b, s)) 

540 # Rb > r > Rc 

541 for i in range(_TRIPS): # 47-48 

542 s = (b + c) * _0_5 

543 R, P, d = _R3(s) 

544 if Rb > R > r: 

545 b, Rb = s, R 

546 elif Rc < R < r: 

547 c, Rc = s, R 

548# else: 

549# break 

550 t = fabs(b - c) 

551 if t < tol: # or fabs(R - r) < tol: 

552 break 

553 else: # t = min(t, fabs(R - r)) 

554 raise ValueError(Fmt.no_convergence(t, tol)) 

555 i += C.iteration # combine iterations 

556 P.set_(lat0=lat0, lon0=lon0, azi0=d.azi1, iteration=i, 

557 a02=d.a12, s02=d.s12, at=d.azi2 - P.azi2, name=n) 

558 return P, s 

559 

560 # get the perpendicular intersection of 2 geodesics, 

561 # one the plumb, pseudo-rhumb line to the other 

562 C = _PlumbTo(gl, lat0, lon0, tol=tol) 

563 try: 

564 a = fabs(C.s02) # distance between centers 

565 if a < r: 

566 c = C.s12 # distance along pseudo-rhumb line 

567 h = _copysign(r, c) # past half chord length 

568 P, p = _bisect2( h, c, a, r, tol, _R3) 

569 Q, q = _bisect2(-h, c, a, r, tol, _R3) 

570 if fabs(p - q) < max(EPS, tol): 

571 Q = P 

572 elif a > r: 

573 raise ValueError(_too_(Fmt.distant(a))) 

574 else: # tangential 

575 P = Q = C 

576 except Exception as x: 

577 t = _LLB(C.lat2, C.lon2).toStr(form=form) 

578 t = _SPACE_(x, _plumb_, _to_, Fmt.PAREN(t)) 

579 raise IntersectionError(t, txt=None, cause=x) 

580 

581 return P, Q 

582 

583 

584def _PlumbTo(gl, lat0, lon0, est=None, tol=_TOL): 

585 # (INTERNAL) Return the I{perpendicular} intersection of 

586 # a geodesic line C{gl} and geodesic from C{(lat0, lon0)}. 

587 pl = _MODS.rhumb.bases._PseudoRhumbLine(gl) 

588 return pl.PlumbTo(lat0, lon0, exact=gl.geodesic, 

589 est=est, tol=tol) 

590 

591# **) MIT License 

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