Coverage for pygeodesy/geodesicw.py: 90%

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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, 

12L{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 IntersectionError, GeodesicError 

22from pygeodesy.fsums import Fsum, Fmt, unstr 

23from pygeodesy.interns import NN, _DOT_, _dunder_nameof, _SPACE_, \ 

24 _to_, _too_,_under 

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

26 _kWrapped, Inverse10Tuple 

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

28from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS 

29from pygeodesy.named import callername, classname 

30from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple 

31from 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 

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

35 

36from contextlib import contextmanager 

37# from math import fabs # from .utily 

38 

39__all__ = _ALL_LAZY.geodesicw 

40__version__ = '24.02.21' 

41 

42_plumb_ = 'plumb' 

43_TRIPS = 65 

44 

45 

46class _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 

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

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

70 

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

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

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

74 B{C{a_ellipsoid}) is not specified as C{scalar}. 

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

76 ''' 

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

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

79 _Geodesic.__init__(self, *args) 

80 

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

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

83 ''' 

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

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

86 return GDict(d) 

87 

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

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

90 ''' 

91 return self._GenDirectLine(lat1, lon1, azi1, True, a12, caps) 

92 

93 Area = _Geodesic.Polygon # like GeodesicExact.Area 

94 

95 @property_RO 

96 def datum(self): 

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

98 ''' 

99 return self._datum 

100 

101 @Property 

102 def debug(self): 

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

104 ''' 

105 return bool(self._debug) 

106 

107 @debug.setter # PYCHOK setter! 

108 def debug(self, debug): 

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

110 details in L{GDict} results. 

111 ''' 

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

113 

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

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

116 ''' 

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

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

119 return GDict(d) 

120 

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

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

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

124 ''' 

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

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

127 

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

129 '''(INTERNAL) Short-cut version. 

130 ''' 

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

132 

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

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

135 ''' 

136 return self._GenDirectLine(lat1, lon1, azi1, False, s12, caps) 

137 

138 @Property_RO 

139 def ellipsoid(self): 

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

141 ''' 

142 return self.datum.ellipsoid 

143 

144 @property_RO 

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

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

147 ''' 

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

149 

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

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

152 ''' 

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

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

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

156 

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

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

159 ''' 

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

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

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

163 

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

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

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

167 ''' 

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

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

170 return self._Line13(t) 

171 

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

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

174 ''' 

175 if wrap: 

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

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

178 

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

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

181 ''' 

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

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

184 return GDict(d) 

185 

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

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

188 

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

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

191 ''' 

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

193 # and .HeightIDWkarney._distances 

194 if wrap: 

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

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

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

198 return fabs(r.a12) 

199 

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

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

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

203 ''' 

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

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

206 

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

208 '''(INTERNAL) Short-cut version. 

209 ''' 

210 if wrap: 

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

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

213 

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

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

216 ''' 

217 with _wargs(self, lat1, lon1, lat2, lon2, caps) as args: 

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

219 return self._Line13(t) 

220 

221 def Line(self, lat1, lon1, azi1, caps=Caps._STD_LINE): 

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

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

224 ''' 

225 return _wrapped.GeodesicLine(self, lat1, lon1, azi1, caps=caps) 

226 

227 def _Line13(self, t): 

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

229 to reference point 3. 

230 ''' 

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

232 salp1=t.salp1, calp1=t.calp1) 

233 gl.a13, gl.s13 = t.a13, t.s13 

234 return gl 

235 

236# Polygon = _Geodesic.Polygon 

237 

238 # Geodesic.ArcDirect.__doc__ = _Geodesic.ArcDirect.__doc__ 

239 # Geodesic.Direct.__doc__ = _Geodesic.Direct.__doc__ 

240 # Geodesic.Inverse.__doc__ = _Geodesic.Inverse.__doc__ 

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

242 # Geodesic.Line.__doc__ = _Geodesic.Line.__doc__ 

243 return Geodesic 

244 

245 @Property_RO # MCCABE 16 

246 def GeodesicLine(self): 

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

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

249 provided the latter is installed. 

250 ''' 

251 _GeodesicLine = self.geographiclib.GeodesicLine 

252 

253 class GeodesicLine(_GeodesicLine): 

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

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

256 ''' 

257 _geodesic = None 

258 

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

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

261 

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

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

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

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

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

267 specifying the capabilities the C{GeodesicLine} 

268 instance should possess (plus optional keyword 

269 arguments C{salp1=NAN} and C{calp1=NAN}). 

270 ''' 

271 _xinstanceof(_wrapped.Geodesic, geodesic=geodesic) 

272 with _wargs(self, geodesic, lat1, lon1, azi1, **caps_) as args: 

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

274 self._geodesic = geodesic 

275 

276 @Property_RO 

277 def a1(self): 

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

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

280 

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

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

283 ''' 

284 try: 

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

286 except AttributeError: 

287 return NAN # see .geodesicx.gxline._GeodesicLineExact 

288 

289 equatorarc = a1 

290 

291 def Arc(self): 

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

293 ''' 

294 return self.a13 

295 

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

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

298 

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

300 (C{degrees}). 

301 

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

303 ''' 

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

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

306 return GDict(d) 

307 

308 @Property_RO 

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

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

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

312 

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

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

315 ''' 

316 try: 

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

318 except AttributeError: 

319 return NAN # see .geodesicx.gxline._GeodesicLineExact 

320 

321 equatorazimuth = azi0 

322 

323 def Distance(self): 

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

325 ''' 

326 return self.s13 

327 

328 @property_RO 

329 def geodesic(self): 

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

331 ''' 

332 return self._geodesic 

333 

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

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

336 

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

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

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

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

341 

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

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

344 extended to 14 items by C{lon0, lat0, azi0, a02, s02, at} 

345 with the circle center C{lat0}, C{lon0}, azimuth C{azi0} at, 

346 distance C{a02} in C{degrees} and C{s02} in C{meter} along 

347 the geodesic from the circle center to the intersection 

348 C{lat2}, C{lon2} and the angle C{at} between the geodesic 

349 and this line at the intersection. The I{geodesic} azimuth 

350 at the intersection is C{(at + azi2)}. If this line is 

351 tangential to the circle, both intersections are the same 

352 L{GDict} instance. 

353 

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

355 intersect. 

356 

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

358 ''' 

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

360 

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

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

363 with a geodesic from the given point. 

364 

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

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

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

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

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

370 

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

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

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

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

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

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

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

378 geodesic and this line at the intersection point. The 

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

380 See method L{Position} for further details. 

381 

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

383 ''' 

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

385 

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

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

388 

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

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

391 the quantities to be returned. 

392 

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

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

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

396 except when C{a12=NAN}. 

397 ''' 

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

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

400 return GDict(d) 

401 

402 # GeodesicLine.ArcPosition.__doc__ = _GeodesicLine.ArcPosition.__doc__ 

403 # GeodesicLine.Position.__doc__ = _GeodesicLine.Position.__doc__ 

404 return GeodesicLine 

405 

406 @Property_RO 

407 def Geodesic_WGS84(self): 

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

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

410 is installed, otherwise an C{ImportError}. 

411 ''' 

412 return _EWGS84.geodesic 

413 

414_wrapped = _gWrapped() # PYCHOK singleton, .ellipsoids, .test/base.py 

415 

416 

417def Geodesic(a_ellipsoid, f=None, name=NN): 

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

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

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

421 

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

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

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

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

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

427 ''' 

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

429 

430 

431def GeodesicLine(geodesic, lat1, lon1, azi1, caps=Caps._STD_LINE): 

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

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

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

435 

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

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

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

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

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

441 specifying the capabilities the C{GeodesicLine} 

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

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

444 and C{GeodesicLine.ArcPosition}. 

445 ''' 

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

447 

448 

449def Geodesic_WGS84(): 

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

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

452 installed, otherwise an C{ImportError}. 

453 ''' 

454 return _wrapped.Geodesic_WGS84 

455 

456 

457class _wargs(object): # see also .formy._idllmn6, .latlonBase._toCartesian3, .vector2d._numpy 

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

459 ''' 

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

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

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

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

464 ''' 

465 try: 

466 yield args 

467 except (AttributeError, TypeError, ValueError) as x: 

468 n = _DOT_(classname(inst), callername(up=3, underOK=True)) 

469 raise GeodesicError(unstr(n, *args, **kwds), cause=x) 

470 

471_wargs = _wargs() # PYCHOK singleton 

472 

473 

474def _Intersecant2(gl, lat0, lon0, radius, tol=_TOL, form=F_D): # MCCABE in LatLonEllipsoidalBaseDI.intersecant2, .geodesicx.gxline.Intersecant2 

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

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

477 r = Radius_(radius) 

478 n = _dunder_nameof(_Intersecant2)[1:] 

479 _P = gl.Position 

480 _I = gl.geodesic.Inverse 

481 _a = fabs 

482 

483 def _R3(s): 

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

485 P = _P(s) 

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

487 return _a(d.s12), P, d 

488 

489 def _bisect2(s, c, Rc, r, tol): 

490 _s = Fsum(c).fsumf_ 

491 for i in range(_TRIPS): 

492 b = _s(s) 

493 Rb, P, d = _R3(b) 

494 if Rb > r: 

495 break 

496 else: # b >>> s and c >>> s 

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

498 __2 = _0_5 # Rb > r > Rc 

499 for i in range(_TRIPS): # 47-48 

500 s = (b + c) * __2 

501 R, P, d = _R3(s) 

502 if Rb > R > r: 

503 b, Rb = s, R 

504 elif Rc < R < r: 

505 c, Rc = s, R 

506 t = _a(b - c) 

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

508 break 

509 else: # t = min(t, _a(R - r)) 

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

511 i += C.iteration # combine iterations 

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

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

514 return P, s 

515 

516 # get the perpendicular intersection of 2 geodesics, 

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

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

519 try: 

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

521 if a < r: 

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

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

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

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

526 if _a(p - q) < max(EPS, tol): 

527 Q = P 

528 elif a > r: 

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

530 else: # tangential 

531 P = Q = C 

532 except Exception as x: 

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

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

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

536 

537 return P, Q 

538 

539 

540def _PlumbTo(gl, lat0, lon0, est=None, tol=_TOL): 

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

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

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

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

545 est=est, tol=tol) 

546 

547# **) MIT License 

548# 

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

550# 

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

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

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

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

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

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

557# 

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

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

560# 

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

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

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

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

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

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

567# OTHER DEALINGS IN THE SOFTWARE.