1

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

3

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

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

6 that package is installed.

7

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

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

10

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

12 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

16 from pygeodesy.basics import _copysign, _xinstanceof

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

18 from pygeodesy.datums import _earth_datum, _WGS84, _EWGS84

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

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

21 from pygeodesy.errors import IntersectionError, GeodesicError

22 from pygeodesy.fsums import Fsum, Fmt, unstr

23 from pygeodesy.internals import _dunder_nameof, _under

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

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

26 _kWrapped, Inverse10Tuple

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

28 from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS

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

30 from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple

31 from pygeodesy.props import Property, Property_RO, property_RO

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

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

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

35

36 from contextlib import contextmanager

37# from math import fabs # from .utily

38

39__all__ = _ALL_LAZY.geodesicw

40__version__ = '24.06.24'

41

42_plumb_ = 'plumb'

43_TRIPS = 65

44

45

46 class _gWrapped(_kWrapped):

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

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

49 '''

50

51 @Property_RO # MCCABE 24

52 def Geodesic(self):

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

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

55 provided the latter is installed.

56 '''

57 _Geodesic = self.geographiclib.Geodesic

58 # assert Caps._STD == _Geodesic.STANDARD

59

60 class Geodesic(_Geodesic):

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

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

63 '''

64 _datum = _WGS84

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

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

67 _name = NN

68

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

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

71

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

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

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

75 is C{meter}, ignored otherwise.

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

77 '''

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

79 E = self.ellipsoid

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

81 _Geodesic.__init__(self, *args)

82 if name:

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

84

85 def ArcDirect(self, lat1, lon1, azi1, a12, outmask=Caps._STD):

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

87 '''

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

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

90 return GDict(d)

91

92 def ArcDirectLine(self, lat1, lon1, azi1, a12, caps=Caps._STD_LINE, **name):

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

94 '''

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

96

97 Area = _Geodesic.Polygon # like GeodesicExact.Area

98

99 @property_RO

100 def datum(self):

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

102 '''

103 return self._datum

104

105 @Property

106 def debug(self):

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

108 '''

109 return bool(self._debug)

110

111 @debug.setter # PYCHOK setter!

112 def debug(self, debug):

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

114 details in L{GDict} results.

115 '''

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

117

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

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

120 '''

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

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

123 return GDict(d)

124

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

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

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

128 '''

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

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

131

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

133 '''(INTERNAL) Short-cut version.

134 '''

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

136

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

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

139 '''

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

141

142 @Property_RO

143 def ellipsoid(self):

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

145 '''

146 return self.datum.ellipsoid

147

148 @property_RO

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

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

151 '''

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

153

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

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

156 '''

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

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

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

160

161 def _GDictInverse(self, lat1, lon1, lat2, lon2, outmask=Caps._STD):

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

163 '''

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

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

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

167

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

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

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

171 '''

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

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

174 return self._Line13(t, **name)

175

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

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

178 '''

179 if wrap:

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

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

182

183 def Inverse(self, lat1, lon1, lat2, lon2, outmask=Caps._STD):

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

185 '''

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

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

188 return GDict(d)

189

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

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

192

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

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

195 '''

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

197 # and .HeightIDWkarney._distances

198 if wrap:

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

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

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

202 return fabs(r.a12)

203

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

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

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

207 '''

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

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

210

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

212 '''(INTERNAL) Short-cut version.

213 '''

214 if wrap:

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

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

217

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

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

220 '''

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

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

223 return self._Line13(t, **name)

224

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

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

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

228 '''

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

230

231 def _Line13(self, t, **name):

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

233 to reference point 3.

234 '''

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

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

237 gl.a13, gl.s13 = t.a13, t.s13

238 return gl

239

240 @property_RO

241 def name(self):

242 '''Get the name (C{str}).

243 '''

244 return self._name

245

246# Polygon = _Geodesic.Polygon

247

248 # Geodesic.ArcDirect.__doc__ = _Geodesic.ArcDirect.__doc__

249 # Geodesic.Direct.__doc__ = _Geodesic.Direct.__doc__

250 # Geodesic.Inverse.__doc__ = _Geodesic.Inverse.__doc__

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

252 # Geodesic.Line.__doc__ = _Geodesic.Line.__doc__

253 return Geodesic

254

255 @Property_RO # MCCABE 16

256 def GeodesicLine(self):

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

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

259 provided the latter is installed.

260 '''

261 _GeodesicLine = self.geographiclib.GeodesicLine

262

263 class GeodesicLine(_GeodesicLine):

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

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

266 '''

267 _geodesic = None

268 _name = NN

269

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

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

272

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

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

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

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

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

278 a bit-or'ed combination of L{Caps} values specifying the

279 capabilities the C{GeodesicLine} instance should possess,

280 an optional C{B{name}=NN} plus C{salp1=NAN} and C{calp1=NAN}

281 for I{INTERNAL} use.

282 '''

283 _xinstanceof(_wrapped.Geodesic, geodesic=geodesic)

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

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

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

287 if name:

288 self._name = name

289 self._geodesic = geodesic

290

291 @Property_RO

292 def a1(self):

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

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

295

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

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

298 '''

299 try:

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

301 except AttributeError:

302 return NAN # see .geodesicx.gxline._GeodesicLineExact

303

304 equatorarc = a1

305

306 def Arc(self):

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

308 '''

309 return self.a13

310

311 def ArcPosition(self, a12, outmask=Caps._STD):

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

313

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

315 (C{degrees}).

316

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

318 '''

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

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

321 return GDict(d)

322

323 @Property_RO

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

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

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

327

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

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

330 '''

331 try:

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

333 except AttributeError:

334 return NAN # see .geodesicx.gxline._GeodesicLineExact

335

336 equatorazimuth = azi0

337

338 def Distance(self):

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

340 '''

341 return self.s13

342

343 @property_RO

344 def geodesic(self):

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

346 '''

347 return self._geodesic

348

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

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

351

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

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

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

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

356

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

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

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

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

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

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

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

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

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

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

367 intersections are the same L{GDict} instance.

368

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

370 intersect.

371

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

373 '''

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

375

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

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

378 with a geodesic from the given point.

379

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

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

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

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

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

385

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

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

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

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

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

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

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

393 geodesic and this line at the intersection point. The

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

395 See method L{Position} for further details.

396

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

398 '''

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

400

401 def Position(self, s12, outmask=Caps._STD):

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

403

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

405 @kwarg outmask: Bit-or'ed combination of L{Caps} values specifying

406 the quantities to be returned.

407

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

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

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

411 except when C{a12=NAN}.

412 '''

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

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

415 return GDict(d)

416

417 # GeodesicLine.ArcPosition.__doc__ = _GeodesicLine.ArcPosition.__doc__

418 # GeodesicLine.Position.__doc__ = _GeodesicLine.Position.__doc__

419 return GeodesicLine

420

421 @Property_RO

422 def Geodesic_WGS84(self):

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

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

425 is installed, otherwise an C{ImportError}.

426 '''

427 return _EWGS84.geodesic

428

429_wrapped = _gWrapped() # PYCHOK singleton, .ellipsoids, .test/base.py

430

431

432 def Geodesic(a_ellipsoid=_EWGS84, f=None, **name):

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

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

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

436

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

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

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

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

441 @kwarg name: Optional C{B{name}=NN} (C{str}), ignored like B{C{f}}.

442 '''

443 return _wrapped.Geodesic(a_ellipsoid, f=f, **name)

444

445

446 def GeodesicLine(geodesic, lat1, lon1, azi1, caps=Caps._STD_LINE):

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

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

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

450

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

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

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

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

455 @kwarg caps: Optional, bit-or'ed combination of L{Caps} values specifying

456 the capabilities the C{GeodesicLine} instance should possess,

457 i.e., which quantities can be returned by methods

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

459 '''

460 return _wrapped.GeodesicLine(geodesic, lat1, lon1, azi1, caps=caps)

461

462

463 def Geodesic_WGS84():

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

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

466 installed, otherwise an C{ImportError}.

467 '''

468 return _wrapped.Geodesic_WGS84

469

470

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

472 '''(INTERNAL) C{geographiclib} caller and exception mapper.

473 '''

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

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

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

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

478 '''

479 try:

480 yield args

481 except Exception as x:

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

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

484

485_wargs = _wargs() # PYCHOK singleton

486

487

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

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

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

491 r = Radius_(radius)

492 n = _dunder_nameof(_Intersecant2)[1:]

493 _P = gl.Position

494 _I = gl.geodesic.Inverse

495 _a = fabs

496

497 def _R3(s):

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

499 P = _P(s)

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

501 return _a(d.s12), P, d

502

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

504 _s = Fsum(c).fsumf_

505 for i in range(_TRIPS):

506 b = _s(s)

507 Rb, P, d = _R3(b)

508 if Rb > r:

509 break

510 else: # b >>> s and c >>> s

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

512 __2 = _0_5 # Rb > r > Rc

513 for i in range(_TRIPS): # 47-48

514 s = (b + c) * __2

515 R, P, d = _R3(s)

516 if Rb > R > r:

517 b, Rb = s, R

518 elif Rc < R < r:

519 c, Rc = s, R

520 t = _a(b - c)

521 if t < tol: # or _a(R - r) < tol:

522 break

523 else: # t = min(t, _a(R - r))

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

525 i += C.iteration # combine iterations

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

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

528 return P, s

529

530 # get the perpendicular intersection of 2 geodesics,

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

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

533 try:

534 a = _a(C.s02) # distance between centers

535 if a < r:

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

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

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

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

540 if _a(p - q) < max(EPS, tol):

541 Q = P

542 elif a > r:

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

544 else: # tangential

545 P = Q = C

546 except Exception as x:

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

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

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

550

551 return P, Q

552

553

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

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

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

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

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

559 est=est, tol=tol)

560

561# **) MIT License

562#

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

564#

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

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

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

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

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

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

571#

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

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

574#

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

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

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

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

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

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

581# OTHER DEALINGS IN THE SOFTWARE.