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, _xkwds_pop2

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

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__ = '24.05.14'

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=NN): # 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}), ignored if B{C{a_ellipsoid})

75 is not C{meter}.

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

77 '''

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

79 with _wargs(self, *self.ellipsoid.a_f, name=name) as args:

80 _Geodesic.__init__(self, *args)

81 if name:

82 self._name = str(name)

83

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

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

86 '''

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

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

89 return GDict(d)

90

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

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

93 '''

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

95

96 Area = _Geodesic.Polygon # like GeodesicExact.Area

97

98 @property_RO

99 def datum(self):

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

101 '''

102 return self._datum

103

104 @Property

105 def debug(self):

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

107 '''

108 return bool(self._debug)

109

110 @debug.setter # PYCHOK setter!

111 def debug(self, debug):

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

113 details in L{GDict} results.

114 '''

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

116

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

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

119 '''

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

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

122 return GDict(d)

123

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

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

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

127 '''

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

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

130

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

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

133 '''

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

135

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

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

138 '''

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

140

141 @Property_RO

142 def ellipsoid(self):

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

144 '''

145 return self.datum.ellipsoid

146

147 @property_RO

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

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

150 '''

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

152

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

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

155 '''

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

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

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

159

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

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

162 '''

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

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

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

166

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

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

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

170 '''

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

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

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

174

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

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

177 '''

178 if wrap:

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

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

181

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

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

184 '''

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

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

187 return GDict(d)

188

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

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

191

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

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

194 '''

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

196 # and .HeightIDWkarney._distances

197 if wrap:

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

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

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

201 return fabs(r.a12)

202

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

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

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

206 '''

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

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

209

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

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

212 '''

213 if wrap:

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

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

216

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

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

219 '''

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

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

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

223

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

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

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

227 '''

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

229

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

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

232 to reference point 3.

233 '''

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

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

236 gl.a13, gl.s13 = t.a13, t.s13

237 return gl

238

239 @property_RO

240 def name(self):

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

242 '''

243 return self._name

244

245# Polygon = _Geodesic.Polygon

246

247 # Geodesic.ArcDirect.__doc__ = _Geodesic.ArcDirect.__doc__

248 # Geodesic.Direct.__doc__ = _Geodesic.Direct.__doc__

249 # Geodesic.Inverse.__doc__ = _Geodesic.Inverse.__doc__

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

251 # Geodesic.Line.__doc__ = _Geodesic.Line.__doc__

252 return Geodesic

253

254 @Property_RO # MCCABE 16

255 def GeodesicLine(self):

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

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

258 provided the latter is installed.

259 '''

260 _GeodesicLine = self.geographiclib.GeodesicLine

261

262 class GeodesicLine(_GeodesicLine):

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

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

265 '''

266 _geodesic = None

267 _name = NN

268

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

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

271

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

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

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

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

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

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

278 capabilities the C{GeodesicLine} instance should possess,

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

280 for I{INTERNAL} use.

281 '''

282 _xinstanceof(_wrapped.Geodesic, geodesic=geodesic)

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

284 name, caps_ = _xkwds_pop2(caps_name_, name=geodesic.name)

285 _GeodesicLine.__init__(self, *args, **caps_)

286 if name:

287 self._name = str(name)

288 self._geodesic = geodesic

289

290 @Property_RO

291 def a1(self):

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

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

294

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

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

297 '''

298 try:

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

300 except AttributeError:

301 return NAN # see .geodesicx.gxline._GeodesicLineExact

302

303 equatorarc = a1

304

305 def Arc(self):

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

307 '''

308 return self.a13

309

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

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

312

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

314 (C{degrees}).

315

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

317 '''

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

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

320 return GDict(d)

321

322 @Property_RO

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

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

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

326

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

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

329 '''

330 try:

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

332 except AttributeError:

333 return NAN # see .geodesicx.gxline._GeodesicLineExact

334

335 equatorazimuth = azi0

336

337 def Distance(self):

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

339 '''

340 return self.s13

341

342 @property_RO

343 def geodesic(self):

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

345 '''

346 return self._geodesic

347

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

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

350

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

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

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

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

355

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

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

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

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

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

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

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

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

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

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

366 intersections are the same L{GDict} instance.

367

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

369 intersect.

370

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

372 '''

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

374

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

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

377 with a geodesic from the given point.

378

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

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

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

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

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

384

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

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

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

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

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

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

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

392 geodesic and this line at the intersection point. The

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

394 See method L{Position} for further details.

395

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

397 '''

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

399

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

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

402

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

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

405 the quantities to be returned.

406

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

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

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

410 except when C{a12=NAN}.

411 '''

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

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

414 return GDict(d)

415

416 # GeodesicLine.ArcPosition.__doc__ = _GeodesicLine.ArcPosition.__doc__

417 # GeodesicLine.Position.__doc__ = _GeodesicLine.Position.__doc__

418 return GeodesicLine

419

420 @Property_RO

421 def Geodesic_WGS84(self):

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

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

424 is installed, otherwise an C{ImportError}.

425 '''

426 return _EWGS84.geodesic

427

428_wrapped = _gWrapped() # PYCHOK singleton, .ellipsoids, .test/base.py

429

430

431 def Geodesic(a_ellipsoid, f=None, name=NN):

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

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

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

435

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

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

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

439 B{C{a_ellipsoid}}) is not specified as C{meter}.

440 @kwarg name: Optional ellipsoid name (C{str}), ignored like B{C{f}}.

441 '''

442 return _wrapped.Geodesic(a_ellipsoid, f=f, name=name)

443

444

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

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

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

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

449

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

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

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

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

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

455 specifying the capabilities the C{GeodesicLine}

456 instance should possess, i.e., which quantities can

457 be returned by calls to C{GeodesicLine.Position}

458 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 n = _DOT_(classname(inst), callername(up=2, underOK=True))

483 raise GeodesicError(unstr(n, *args, **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.