Coverage for pygeodesy/geodesicx/gxline.py: 92%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''A pure Python version of I{Karney}'s C++ class U{GeodesicLineExact 

5<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1GeodesicLineExact.html>}. 

6 

7Class L{GeodesicLineExact} follows the naming, methods and return 

8values from class C{GeodesicLine} from I{Karney}'s Python U{geographiclib 

9<https://GeographicLib.SourceForge.io/1.52/python/index.html>}. 

10 

11Copyright (C) U{Charles Karney<mailto:Karney@Alum.MIT.edu>} (2008-2023) 

12and licensed under the MIT/X11 License. For more information, see the 

13U{GeographicLib<https://GeographicLib.SourceForge.io>} documentation. 

14''' 

15# make sure int/int division yields float quotient 

16from __future__ import division as _; del _ # PYCHOK semicolon 

17 

18# A copy of comments from Karney's C{GeodesicLineExact.cpp}: 

19# 

20# This is a reformulation of the geodesic problem. The 

21# notation is as follows: 

22# - at a general point (no suffix or 1 or 2 as suffix) 

23# - phi = latitude 

24# - lambda = longitude 

25# - beta = latitude on auxiliary sphere 

26# - omega = longitude on auxiliary sphere 

27# - alpha = azimuth of great circle 

28# - sigma = arc length along great circle 

29# - s = distance 

30# - tau = scaled distance (= sigma at multiples of PI/2) 

31# - at northwards equator crossing 

32# - beta = phi = 0 

33# - omega = lambda = 0 

34# - alpha = alpha0 

35# - sigma = s = 0 

36# - a 12 suffix means a difference, e.g., s12 = s2 - s1. 

37# - s and c prefixes mean sin and cos 

38 

39# from pygeodesy.basics import _xinstanceof # _MODS 

40from pygeodesy.constants import NAN, _EPSqrt as _TOL, _0_0, _1_0, \ 

41 _180_0, _2__PI, _copysign_1_0, isfinite 

42from pygeodesy.errors import _xError, _xkwds_pop2 

43from pygeodesy.fsums import fsumf_, fsum1f_ 

44from pygeodesy.geodesicx.gxbases import _cosSeries, _GeodesicBase, \ 

45 _sincos12, _sin1cos2, \ 

46 _sinf1cos2d, _TINY 

47# from pygeodesy.geodesicw import _Intersecant2 # _MODS 

48from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS 

49from pygeodesy.karney import _around, _atan2d, Caps, GDict, _fix90, \ 

50 _K_2_0, _llz2gl, _norm2, _norm180, \ 

51 _sincos2, _sincos2d 

52from pygeodesy.props import Property_RO, property_ROver, _update_all 

53from pygeodesy.utily import atan2, atan2d as _atan2d_reverse, sincos2 

54 

55from math import cos, degrees, fabs, floor, radians, sin 

56 

57__all__ = () 

58__version__ = '24.11.24' 

59 

60_glXs = [] # instances of C{[_]GeodesicLineExact} to be updated 

61 

62 

63def _update_glXs(gX): # see GeodesicExact.C4order and -._ef_reset_k2 

64 '''(INTERNAL) Zap cached/memoized C{Property[_RO]}s of 

65 any L{GeodesicLineExact} instances tied to the given 

66 L{GeodesicExact} instance B{C{gX}}. 

67 ''' 

68 _xGeodesicExact(gX=gX) 

69 for glX in _glXs: # PYCHOK use weakref? 

70 if glX._gX is gX: 

71 _update_all(glX) 

72 

73 

74def _xGeodesicExact(**gX): 

75 '''(INTERNAL) Check a L{GeodesicExact} instance. 

76 ''' 

77 _MODS.basics._xinstanceof(_MODS.geodesicx.GeodesicExact, **gX) 

78 

79 

80class _GeodesicLineExact(_GeodesicBase): 

81 '''(INTERNAL) Base class for L{GeodesicLineExact}. 

82 ''' 

83 _a13 = _s13 = NAN 

84# _azi1 = _0_0 

85# _cchi1 = NAN 

86# _dn1 = NAN 

87 _gX = None # Exact only 

88# _k2 = NAN 

89# _lat1 = _lon1 = _0_0 

90# _salp0 = _calp0 = NAN 

91# _salp1 = _calp1 = NAN 

92# _somg1 = _comg1 = NAN 

93# _ssig1 = _csig1 = NAN 

94 

95 def __init__(self, gX, lat1, lon1, azi1, caps, **name_): 

96 '''(INTERNAL) New C{[_]GeodesicLineExact} instance. 

97 ''' 

98# _xGeodesicExact(gX=gX) 

99 if azi1 is None: # see GeodesicExact.InverseLine 

100 (salp1, calp1), name_ = _xkwds_pop2(name_, _s_calp1=(_0_0, _1_0)) 

101 azi1 = _atan2d(salp1, calp1) 

102 else: # guard against salp0 underflow, convert -0 to +0 

103 azi1 = _norm180(azi1) 

104 salp1, calp1 = _sincos2d(_around(azi1)) 

105 if name_: 

106 self.name = name_ 

107 

108 self._gX = gX # GeodesicExact only 

109 self._lat1 = lat1 = _fix90(lat1) 

110 self._lon1 = lon1 

111 self._azi1 = azi1 

112 self._salp1 = salp1 

113 self._calp1 = calp1 

114 # allow lat, azimuth and unrolling of lon 

115 self._caps = caps | Caps._AZIMUTH_LATITUDE_LONG_UNROLL 

116 

117 sbet1, cbet1 = _sinf1cos2d(_around(lat1), gX.f1) 

118 self._dn1 = gX._dn(sbet1, cbet1) 

119 # Evaluate alp0 from sin(alp1) * cos(bet1) = sin(alp0), with alp0 

120 # in [0, pi/2 - |bet1|]. Alt: calp0 = hypot(sbet1, calp1 * cbet1), 

121 # but the following is slightly better, consider the case salp1 = 0. 

122 self._salp0, self._calp0 = _sin1cos2(salp1, calp1, sbet1, cbet1) 

123 self._k2 = self._calp0**2 * gX.ep2 

124 # Evaluate sig with tan(bet1) = tan(sig1) * cos(alp1). 

125 # sig = 0 is nearest northward crossing of equator. 

126 # With bet1 = 0, alp1 = pi/2, we have sig1 = 0 (equatorial line). 

127 # With bet1 = pi/2, alp1 = -pi, sig1 = pi/2 

128 # With bet1 = -pi/2, alp1 = 0 , sig1 = -pi/2 

129 # Evaluate omg1 with tan(omg1) = sin(alp0) * tan(sig1). 

130 # With alp0 in (0, pi/2], quadrants for sig and omg coincide. 

131 # No atan2(0,0) ambiguity at poles since cbet1 = +epsilon. 

132 # With alp0 = 0, omg1 = 0 for alp1 = 0, omg1 = pi for alp1 = pi. 

133 self._somg1 = sbet1 * self._salp0 

134 self._comg1 = c = (cbet1 * calp1) if (sbet1 or calp1) else _1_0 

135 # Without normalization we have schi1 = somg1. 

136 self._cchi1 = gX.f1 * self._dn1 * c 

137 self._ssig1, self._csig1 = _norm2(sbet1, c) # sig1 in (-pi, pi] 

138 # _norm2(somg1, comg1) # no need to normalize! 

139 # _norm2(schi1?, cchi1) # no need to normalize! 

140 if not (caps & Caps.LINE_OFF): 

141 _glXs.append(self) 

142 # no need to pre-compute other attrs for (caps & Caps.X). All are 

143 # Property_RO's, computed once and cached/memoized until reset when 

144 # arc, distance, C4order is changed or Elliptic function is reset. 

145 

146 def __del__(self): # XXX use weakref? 

147 if _glXs: # may be empty or None 

148 try: # PYCHOK no cover 

149 _glXs.remove(self) 

150 except (TypeError, ValueError): 

151 pass 

152 self._gX = None 

153 # _update_all(self) # throws TypeError during Python 2 cleanup 

154 

155 def _update(self, updated, *attrs, **unused): 

156 if updated: 

157 _update_all(self, *attrs) 

158 

159 @Property_RO 

160 def a1(self): 

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

162 the northward equatorial crossing and the first point. 

163 ''' 

164 return _atan2d(self._ssig1, self._csig1) # or NAN 

165 

166 equatorarc = a1 

167 

168 @Property_RO 

169 def a13(self): 

170 '''Get the arc length to reference point 3 (C{degrees}). 

171 

172 @see: Methods L{Arc} and L{SetArc}. 

173 ''' 

174 return self._a13 

175 

176 def Arc(self): 

177 '''Return the arc length to reference point 3 (C{degrees} or C{NAN}). 

178 

179 @see: Method L{SetArc} and property L{a13}. 

180 ''' 

181 return self.a13 

182 

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

184 '''Find the position on the line given B{C{a12}}. 

185 

186 @arg a12: Spherical arc length from the first point to the 

187 second point (C{degrees}). 

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

189 the quantities to be returned. 

190 

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

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

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

194 except when C{a12=NAN}. 

195 

196 @note: By default, C{B{outmask}=STANDARD}, meaning thc C{lat1}, 

197 C{lon1}, C{azi1}, C{lat2}, C{lon2}, C{azi2}, C{s12} and 

198 C{a12} entries are returned, except when C{a12=NAN}. 

199 ''' 

200 return self._GDictPosition(True, a12, outmask) 

201 

202 @Property_RO 

203 def azi0(self): 

204 '''Get the I{equatorial azimuth}, the azimuth of this geodesic line 

205 as it crosses the equator in a northward direction (C{degrees90}). 

206 ''' 

207 return _atan2d(*self.azi0_sincos2) # or NAN 

208 

209 equatorazimuth = azi0 

210 

211 @Property_RO 

212 def azi0_sincos2(self): 

213 '''Get the sine and cosine of the I{equatorial azimuth} (2-tuple C{(sin, cos)}). 

214 ''' 

215 return self._salp0, self._calp0 

216 

217 @Property_RO 

218 def azi1(self): 

219 '''Get the azimuth at the first point (compass C{degrees}). 

220 ''' 

221 return self._azi1 

222 

223 @Property_RO 

224 def azi1_sincos2(self): 

225 '''Get the sine and cosine of the first point's azimuth (2-tuple C{(sin, cos)}). 

226 ''' 

227 return self._salp1, self._calp1 

228 

229 @Property_RO 

230 def _B41(self): 

231 '''(INTERNAL) Cached/memoized. 

232 ''' 

233 return _cosSeries(self._C4a, self._ssig1, self._csig1) 

234 

235 @Property_RO 

236 def _C4a(self): 

237 '''(INTERNAL) Cached/memoized. 

238 ''' 

239 return self.geodesic._C4f_k2(self._k2) 

240 

241 @Property_RO 

242 def _caps_DISTANCE_IN(self): 

243 '''(INTERNAL) Get C{Caps.DISTANCE_IN} and C{_OUT}. 

244 ''' 

245 return self.caps & (Caps.DISTANCE_IN & Caps._OUT_MASK) 

246 

247 @Property_RO 

248 def _D0k2(self): 

249 '''(INTERNAL) Cached/memoized. 

250 ''' 

251 return self._eF.cD * _2__PI * self._k2 

252 

253 @Property_RO 

254 def _D1(self): 

255 '''(INTERNAL) Cached/memoized. 

256 ''' 

257 return self._eF.deltaD(self._ssig1, self._csig1, self._dn1) 

258 

259 def Distance(self): 

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

261 

262 @see: Method L{SetDistance} and property L{s13}. 

263 ''' 

264 return self.s13 

265 

266 @Property_RO 

267 def _E0b(self): 

268 '''(INTERNAL) Cached/memoized. 

269 ''' 

270 return self._eF.cE * _2__PI * self.geodesic.b 

271 

272 @Property_RO 

273 def _E1(self): 

274 '''(INTERNAL) Cached/memoized. 

275 ''' 

276 return self._eF.deltaE(self._ssig1, self._csig1, self._dn1) 

277 

278 @Property_RO 

279 def _eF(self): 

280 '''(INTERNAL) Cached/memoized C{Elliptic} function. 

281 ''' 

282 # see .gx.GeodesicExact._ef_reset_k2 

283 return _MODS.elliptic.Elliptic(k2=-self._k2, alpha2=-self.geodesic.ep2) 

284 

285 def _GDictPosition(self, arcmode, s12_a12, outmask=Caps.STANDARD): # MCCABE 17 

286 '''(INTERNAL) Generate a new position along the geodesic. 

287 

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

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

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

291 except when C{a12=NAN}. 

292 ''' 

293 Cs = Caps 

294 if outmask: 

295 outmask &= self._caps & Cs._OUT_MASK 

296 eF = self._eF 

297 gX = self.geodesic # ._gX 

298 r = GDict(a12=NAN, s12=NAN) # both a12 and s12, always 

299 

300 if not isfinite(s12_a12): 

301 # E2 = sig12 = ssig12 = csig12 = NAN 

302 return r._toNAN(outmask) 

303 elif arcmode: # s12_a12 is (spherical) arc length 

304 r.set_(a12=s12_a12) 

305 sig12 = radians(s12_a12) 

306 if _K_2_0: 

307 ssig12, csig12 = sincos2(sig12) # utily, no NEG0 

308 else: # PYCHOK no cover 

309 a = fabs(s12_a12) # 0 <= fabs(_remainder(s12_a12, _180_0)) <= 90 

310 a -= floor(a / _180_0) * _180_0 # 0 <= 0 < 180 

311 ssig12 = _0_0 if a == 0 else sin(sig12) 

312 csig12 = _0_0 if a == 90 else cos(sig12) 

313 E2 = _0_0 

314 elif self._caps_DISTANCE_IN: # s12_a12 is distance 

315 t = s12_a12 / self._E0b 

316 s, c = _sincos2(t) # tau12 

317 # tau2 = tau1 + tau12 

318 E2 = -eF.deltaEinv(*_sincos12(-s, c, *self._stau1_ctau1)) 

319 sig12 = fsum1f_(self._E1, -E2, t) # == t - (E2 - E1) 

320 ssig12, csig12 = _sincos2(sig12) 

321 r.set_(a12=degrees(sig12)) 

322 else: # uninitialized or impossible distance requested 

323 return r 

324 

325 # sig2 = sig1 + sig12 

326 ssig1, csig1 = self._ssig1, self._csig1 

327 ssig2, csig2 = t = _sincos12(-ssig12, csig12, ssig1, csig1) 

328 dn2 = eF.fDelta(*t) 

329 

330 if (outmask & Cs.DISTANCE): 

331 outmask ^= Cs.DISTANCE 

332 if arcmode: # or f_0_01 

333 E2 = eF.deltaE(ssig2, csig2, dn2) 

334 # AB1 = _E0 * (E2 - _E1) 

335 # s12 = _b * (_E0 * sig12 + AB1) 

336 # = _b * _E0 * (sig12 + (E2 - _E1)) 

337 # = _b * _E0 * (E2 - _E1 + sig12) 

338 s12 = self._E0b * fsum1f_(E2, -self._E1, sig12) 

339 else: 

340 s12 = s12_a12 

341 r.set_(s12=s12) 

342 

343 if not outmask: # all done, see ._GenSet 

344 return r 

345 

346 if self._debug: # PYCHOK no cover 

347 outmask |= self._debug & Cs._DEBUG_DIRECT_LINE 

348 

349 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover 

350 r.set_(sig12=sig12, dn2=dn2, b=gX.b, e2=gX.e2, f1=gX.f1, 

351 E0b=self._E0b, E1=self._E1, E2=E2, eFk2=eF.k2, eFa2=eF.alpha2) 

352 

353 # sin(bet2) = cos(alp0) * sin(sig2) and 

354 # cbet2 = hypot(salp0, calp0 * csig2). Alt: 

355 # cbet2 = hypot(csig2, salp0 * ssig2) 

356 salp0, calp0 = self._salp0, self._calp0 

357 sbet2, cbet2 = _sin1cos2(calp0, salp0, csig2, ssig2) 

358 if cbet2 == 0: # salp0 = 0, csig2 = 0, break degeneracy 

359 cbet2 = csig2 = _TINY 

360 # tan(alp0) = cos(sig2) * tan(alp2) 

361 salp2 = salp0 

362 calp2 = calp0 * csig2 # no need to normalize 

363 

364 if (outmask & Cs.AZIMUTH): 

365 r.set_(azi2=_atan2d_reverse(salp2, calp2, 

366 reverse=outmask & Cs.REVERSE2)) 

367 

368 if (outmask & Cs.LATITUDE): 

369 r.set_(lat2=_atan2d(sbet2, gX.f1 * cbet2)) 

370 

371 if (outmask & Cs.LONGITUDE): 

372 schi1 = self._somg1 

373 cchi1 = self._cchi1 

374 schi2 = ssig2 * salp0 

375 cchi2 = gX.f1 * dn2 * csig2 # schi2 = somg2 without normalization 

376 lam12 = salp0 * self._H0e2_f1 * fsum1f_(eF.deltaH(ssig2, csig2, dn2), 

377 -self._H1, sig12) 

378 if (outmask & Cs.LONG_UNROLL): 

379 t = _copysign_1_0(salp0) # east-going? 

380 tchi1 = t * schi1 

381 tchi2 = t * schi2 

382 chi12 = t * fsum1f_(atan2(ssig1, csig1), -atan2(ssig2, csig2), 

383 atan2(tchi2, cchi2), -atan2(tchi1, cchi1), sig12) 

384 lon2 = self.lon1 + degrees(chi12 - lam12) 

385 else: 

386 chi12 = atan2(*_sincos12(schi1, cchi1, schi2, cchi2)) 

387 lon2 = _norm180(self._lon1_norm180 + _norm180(degrees(chi12 - lam12))) 

388 r.set_(lon2=lon2) 

389 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover 

390 r.set_(ssig2=ssig2, chi12=chi12, H0e2_f1=self._H0e2_f1, 

391 csig2=csig2, lam12=lam12, H1=self._H1) 

392 

393 if (outmask & Cs._REDUCEDLENGTH_GEODESICSCALE): 

394 dn1 = self._dn1 

395 J12 = self._D0k2 * fsumf_(eF.deltaD(ssig2, csig2, dn2), -self._D1, sig12) 

396 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover 

397 r.set_(ssig1=ssig1, dn1=dn1, D0k2=self._D0k2, 

398 csig1=csig1, J12=J12, D1=self._D1) 

399 if (outmask & Cs.REDUCEDLENGTH): 

400 # Add parens around (csig1 * ssig2) and (ssig1 * csig2) to 

401 # ensure accurate cancellation in the case of coincident points. 

402 r.set_(m12=gX.b * fsum1f_(dn2 * (csig1 * ssig2), 

403 -dn1 * (ssig1 * csig2), 

404 -J12 * (csig1 * csig2))) 

405 if (outmask & Cs.GEODESICSCALE): 

406 t = self._k2 * (ssig2 - ssig1) * (ssig2 + ssig1) / (dn2 + dn1) 

407 r.set_(M12=csig12 + ssig1 * (t * ssig2 - csig2 * J12) / dn1, 

408 M21=csig12 - ssig2 * (t * ssig1 - csig1 * J12) / dn2) 

409 

410 if (outmask & Cs.AREA): 

411 A4 = salp0 * calp0 

412 if A4: 

413 # tan(alp) = tan(alp0) * sec(sig) 

414 # tan(alp2-alp1) = (tan(alp2) - tan(alp1)) / (tan(alp2) * tan(alp1) + 1) 

415 # = calp0 * salp0 * (csig1 - csig2) / (salp0^2 + calp0^2 * csig1 * csig2) 

416 # If csig12 > 0, write 

417 # csig1 - csig2 = ssig12 * (csig1 * ssig12 / (1 + csig12) + ssig1) 

418 # else 

419 # csig1 - csig2 = csig1 * (1 - csig12) + ssig12 * ssig1 

420 # No need to normalize 

421 salp12 = (((ssig12 * csig1 / (_1_0 + csig12) + ssig1) * ssig12) if csig12 > 0 else 

422 (csig1 * (_1_0 - csig12) + ssig1 * ssig12)) * A4 

423 calp12 = salp0**2 + calp0**2 * csig1 * csig2 

424 A4 *= gX._e2a2 

425 B41 = self._B41 

426 B42 = _cosSeries(self._C4a, ssig2, csig2) 

427 S12 = (B42 - B41) * A4 

428 else: 

429 S12 = A4 = B41 = B42 = _0_0 

430 # alp12 = alp2 - alp1, used in atan2 so no need to normalize 

431 salp12, calp12 = _sincos12(self._salp1, self._calp1, salp2, calp2) 

432 # We used to include some patch up code that purported to deal 

433 # with nearly meridional geodesics properly. However, this turned 

434 # out to be wrong once salp1 = -0 was allowed (via InverseLine). 

435 # In fact, the calculation of {s,c}alp12 was already correct 

436 # (following the IEEE rules for handling signed zeros). So, 

437 # the patch up code was unnecessary (as well as dangerous). 

438 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover 

439 r.set_(salp12=salp12, salp0=salp0, B41=B41, A4=A4, 

440 calp12=calp12, calp0=calp0, B42=B42, c2=gX.c2) 

441 S12 += gX.c2 * atan2(salp12, calp12) 

442 r.set_(S12=S12) 

443 

444 r.set_(azi1=_norm180(self.azi1), 

445 lat1=self.lat1, # == _fix90(lat1) 

446 lon1=self.lon1 if (outmask & Cs.LONG_UNROLL) else self._lon1_norm180) 

447 return r 

448 

449 def _GenPosition(self, arcmode, s12_a12, outmask): 

450 '''(INTERNAL) Generate a new position along the geodesic. 

451 

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

453 s12, m12, M12, M21, S12)}. 

454 ''' 

455 r = self._GDictPosition(arcmode, s12_a12, outmask) 

456 return r.toDirect9Tuple() 

457 

458 def _GenSet(self, debug, s12=None, a12=None, **llz2): 

459 '''(INTERNAL) Aka C++ C{GenSetDistance}. 

460 ''' 

461 Cs = Caps 

462 if debug: # PYCHOK no cover 

463 self._debug |= debug & Cs._DEBUG_ALL 

464 # _CapsBase.debug._update(self) 

465 if s12 is None: 

466 if a12 is None: # see GeodesicExact.Line 

467 return self 

468 s12 = self._GDictPosition(True, a12, outmask=Cs.DISTANCE).s12 if a12 else _0_0 

469 elif a12 is None: 

470 a12 = self._GDictPosition(False, s12, 0).a12 if s12 else _0_0 

471 self._s13 = s12 

472 self._a13 = a12 

473 self._caps |= Cs.DISTANCE | Cs.DISTANCE_IN 

474 # _update_all(self) # new, from GeodesicExact.*Line 

475 return _llz2gl(self, **llz2) 

476 

477 @Property_RO 

478 def geodesic(self): 

479 '''Get the I{exact} geodesic (L{GeodesicExact}). 

480 ''' 

481 _xGeodesicExact(geodesic=self._gX) 

482 return self._gX 

483 

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

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

486 

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

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

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

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

491 

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

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

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

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

496 at, distance C{a02} in C{degrees} and C{s02} in C{meter} 

497 along the geodesic from the circle center to the intersection 

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

499 and this line at the intersection. The geodesic azimuth 

500 at the intersection is C{(at + azi2)}. If this geodesic 

501 line is tangential to the circle, both points are the same 

502 L{GDict} instance. 

503 

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

505 intersect, no I{perpencular} geodetic 

506 intersection or no convergence. 

507 

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

509 ''' 

510 try: 

511 return _MODS.geodesicw._Intersecant2(self, lat0, lon0, radius, tol=tol) 

512 except (TypeError, ValueError) as x: 

513 raise _xError(x, lat0, lon0, radius, tol=_TOL) 

514 

515 @Property_RO 

516 def _H0e2_f1(self): 

517 '''(INTERNAL) Cached/memoized. 

518 ''' 

519 return self._eF.cH * _2__PI * self.geodesic._e2_f1 

520 

521 @Property_RO 

522 def _H1(self): 

523 '''(INTERNAL) Cached/memoized. 

524 ''' 

525 return self._eF.deltaH(self._ssig1, self._csig1, self._dn1) 

526 

527 @Property_RO 

528 def lat1(self): 

529 '''Get the latitude of the first point (C{degrees}). 

530 ''' 

531 return self._lat1 

532 

533 @Property_RO 

534 def lon1(self): 

535 '''Get the longitude of the first point (C{degrees}). 

536 ''' 

537 return self._lon1 

538 

539 @Property_RO 

540 def _lon1_norm180(self): 

541 '''(INTERNAL) Cached/memoized. 

542 ''' 

543 return _norm180(self._lon1) 

544 

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

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

547 and a geodesic from the given point. 

548 

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

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

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

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

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

554 

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

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

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

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

559 C{meter} between the given C{lat0, lon0} point and the 

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

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

562 geodesic and this line at the intersection. The geodesic 

563 azimuth at the intersection is C{(at + azi2)}. See method 

564 L{Position} for further details. 

565 

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

567 ''' 

568 return _MODS.geodesicw._PlumbTo(self, lat0, lon0, est=est, tol=tol) 

569 

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

571 '''Find the position on the line given B{C{s12}}. 

572 

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

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

575 the quantities to be returned. 

576 

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

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

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

580 except when C{a12=NAN}. 

581 

582 @note: By default, C{B{outmask}=STANDARD}, meaning thc C{lat1}, 

583 C{lon1}, C{azi1}, C{lat2}, C{lon2}, C{azi2}, C{s12} and 

584 C{a12} entries are returned, except when C{a12=NAN}. 

585 

586 @note: This L{GeodesicLineExact} instance must have been 

587 constructed with capability C{Caps.DISTANCE_IN} set. 

588 ''' 

589 return self._GDictPosition(False, s12, outmask) 

590 

591 @Property_RO 

592 def s13(self): 

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

594 

595 @see: Methods L{Distance} and L{SetDistance}. 

596 ''' 

597 return self._s13 

598 

599 def SetArc(self, a13): 

600 '''Set reference point 3 in terms relative to the first point. 

601 

602 @arg a13: Spherical arc length from the first to the reference 

603 point (C{degrees}). 

604 

605 @return: The distance C{s13} (C{meter}) between the first and 

606 the reference point or C{NAN}. 

607 ''' 

608 if self._a13 != a13: 

609 self._GenSet(0, a12=a13) 

610 _update_all(self) 

611 return self._s13 

612 

613 def SetDistance(self, s13): 

614 '''Set reference point 3 in terms relative to the first point. 

615 

616 @arg s13: Distance from the first to the reference point (C{meter}). 

617 

618 @return: The arc length C{a13} (C{degrees}) between the first 

619 and the reference point or C{NAN}. 

620 ''' 

621 if self._s13 != s13: 

622 self._GenSet(0, s12=s13) 

623 _update_all(self) 

624 return self._a13 

625 

626 @Property_RO 

627 def _stau1_ctau1(self): 

628 '''(INTERNAL) Cached/memoized. 

629 ''' 

630 s, c = _sincos2(self._E1) 

631 # tau1 = sig1 + B11 

632 return _sincos12(-s, c, self._ssig1, self._csig1) 

633 # unnecessary because Einv inverts E 

634 # return -self._eF.deltaEinv(stau1, ctau1) 

635 

636 @property_ROver 

637 def _toProps7(self): 

638 '''(INTERNAL) 7-Tuple of C{toStr} properties. 

639 ''' 

640 C = _GeodesicLineExact 

641 return C.lat1, C.lon1, C.azi1, C.a13, C.s13, C.caps, C.geodesic 

642 

643 def toStr(self, **prec_sep_name): # PYCHOK signature 

644 '''Return this C{GeodesicLineExact} as string. 

645 

646 @see: L{Ellipsoid.toStr<pygeodesy.ellipsoids.Ellipsoid.toStr>} 

647 for further details. 

648 

649 @return: C{GeodesicLineExact} (C{str}). 

650 ''' 

651 return self._instr(props=self._toProps7, **prec_sep_name) 

652 

653 

654__all__ += _ALL_DOCS(_GeodesicLineExact) 

655 

656# **) MIT License 

657# 

658# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

659# 

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

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

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

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

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

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

666# 

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

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

669# 

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

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

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

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

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

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

676# OTHER DEALINGS IN THE SOFTWARE.