Coverage for pygeodesy/geodesicx/gxline.py: 97%

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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, _EPSmin, _EPSqrt as _TOL, _0_0, \ 

41 _1_0, _180_0, _2__PI, _copysign_1_0 

42from pygeodesy.errors import _xError, _COMMASPACE_ 

43from pygeodesy.fsums import fsumf_, fsum1f_ 

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

45 _sincos12, _sin1cos2 

46# from pygeodesy.geodesicw import _Intersecant2 # _MODS 

47# from pygeodesy.interns import _COMMASPACE_ # from .errors 

48from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS 

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

50 _K_2_0, _norm2, _norm180, _sincos2, _sincos2d 

51from pygeodesy.props import Property_RO, _update_all 

52# from pygeodesy.streprs import pairs # _MODS 

53from pygeodesy.utily import atan2d as _atan2d_reverse, sincos2 

54 

55from math import atan2, cos, degrees, fabs, floor, radians, sin 

56 

57__all__ = () 

58__version__ = '24.05.19' 

59 

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

61# underflow guard, we require _TINY * EPS > 0, _TINY + EPS == EPS 

62_TINY = _EPSmin 

63# assert (_TINY * EPS) > 0 and (_TINY + EPS) == EPS 

64 

65 

66def _update_glXs(gX): # see GeodesicExact.C4order and -._ef_reset_k2 

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

68 any L{GeodesicLineExact} instances tied to the given 

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

70 ''' 

71 _xGeodesicExact(gX=gX) 

72 for glX in _glXs: # PYCHOK use weakref? 

73 if glX._gX is gX: 

74 _update_all(glX) 

75 

76 

77def _xGeodesicExact(**gX): 

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

79 ''' 

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

81 

82 

83class _GeodesicLineExact(_GeodesicBase): 

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

85 ''' 

86 _a13 = _s13 = NAN 

87# _azi1 = _0_0 

88# _cchi1 = NAN 

89# _dn1 = NAN 

90 _gX = None # Exact only 

91# _k2 = NAN 

92# _lat1 = _lon1 = _0_0 

93# _salp0 = _calp0 = NAN 

94# _salp1 = _calp1 = NAN 

95# _somg1 = _comg1 = NAN 

96# _ssig1 = _csig1 = NAN 

97 

98 def __init__(self, gX, lat1, lon1, azi1, caps, _debug, *salp1_calp1, **name): 

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

100 ''' 

101 _xGeodesicExact(gX=gX) 

102 Cs = Caps 

103 if _debug: # PYCHOK no cover 

104 self._debug |= _debug & Cs._DEBUG_ALL 

105 # _CapsBase.debug._update(self) 

106 if salp1_calp1: 

107 salp1, calp1 = salp1_calp1 

108 else: 

109 azi1 = _norm180(azi1) 

110 # guard against salp0 underflow, 

111 # also -0 is converted to +0 

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

113 if name: 

114 self.name = name 

115 

116 self._gX = gX # GeodesicExact only 

117 self._lat1 = lat1 = _fix90(lat1) 

118 self._lon1 = lon1 

119 self._azi1 = azi1 

120 self._salp1 = salp1 

121 self._calp1 = calp1 

122 # allow lat, azimuth and unrolling of lon 

123 self._caps = caps | Cs._LINE 

124 

125 sbet1, cbet1 = gX._sinf1cos2d(_around(lat1)) 

126 self._dn1 = gX._dn(sbet1, cbet1) 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

141 self._somg1 = sbet1 * self._salp0 

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

143 # Without normalization we have schi1 = somg1. 

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

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

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

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

148 if not (caps & Cs.LINE_OFF): 

149 _glXs.append(self) 

150 # no need to pre-compute other attrs based on _Caps.X. All are 

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

152 # when C4order is changed or Elliptic function reset is invoked. 

153 

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

155 if _glXs: # may be empty or None 

156 try: # PYCHOK no cover 

157 _glXs.remove(self) 

158 except (TypeError, ValueError): 

159 pass 

160 self._gX = None 

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

162 

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

164 if updated: 

165 _update_all(self, *attrs) 

166 

167 @Property_RO 

168 def a1(self): 

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

170 the northward equatorial crossing and the first point. 

171 ''' 

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

173 

174 equatorarc = a1 

175 

176 @Property_RO 

177 def a13(self): 

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

179 

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

181 ''' 

182 return self._a13 

183 

184 def Arc(self): 

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

186 

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

188 ''' 

189 return self.a13 

190 

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

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

193 

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

195 second point (C{degrees}). 

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

197 the quantities to be returned. 

198 

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

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

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

202 except when C{a12=NAN}. 

203 

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

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

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

207 ''' 

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

209 

210 @Property_RO 

211 def azi0(self): 

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

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

214 ''' 

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

216 

217 equatorazimuth = azi0 

218 

219 @Property_RO 

220 def azi0_sincos2(self): 

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

222 ''' 

223 return self._salp0, self._calp0 

224 

225 @Property_RO 

226 def azi1(self): 

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

228 ''' 

229 return self._azi1 

230 

231 @Property_RO 

232 def azi1_sincos2(self): 

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

234 ''' 

235 return self._salp1, self._calp1 

236 

237 @Property_RO 

238 def _B41(self): 

239 '''(INTERNAL) Cached/memoized. 

240 ''' 

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

242 

243 @Property_RO 

244 def _C4a(self): 

245 '''(INTERNAL) Cached/memoized. 

246 ''' 

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

248 

249 @Property_RO 

250 def _caps_DISTANCE_IN(self): 

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

252 ''' 

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

254 

255 @Property_RO 

256 def _D0k2(self): 

257 '''(INTERNAL) Cached/memoized. 

258 ''' 

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

260 

261 @Property_RO 

262 def _D1(self): 

263 '''(INTERNAL) Cached/memoized. 

264 ''' 

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

266 

267 def Distance(self): 

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

269 

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

271 ''' 

272 return self.s13 

273 

274 @Property_RO 

275 def _E0b(self): 

276 '''(INTERNAL) Cached/memoized. 

277 ''' 

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

279 

280 @Property_RO 

281 def _E1(self): 

282 '''(INTERNAL) Cached/memoized. 

283 ''' 

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

285 

286 @Property_RO 

287 def _eF(self): 

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

289 ''' 

290 # see .gx.GeodesicExact._ef_reset_k2 

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

292 

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

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

295 

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

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

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

299 except when C{a12=NAN}. 

300 ''' 

301 

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

303 if not (arcmode or self._caps_DISTANCE_IN): # PYCHOK no cover 

304 return r # Uninitialized or impossible distance requested 

305 

306 Cs = Caps 

307 if self._debug: # PYCHOK no cover 

308 outmask |= self._debug & Cs._DEBUG_DIRECT_LINE 

309 outmask &= self._caps & Cs._OUT_MASK 

310 

311 eF = self._eF 

312 gX = self.geodesic # ._gX 

313 

314 if arcmode: 

315 # s12_a12 is spherical arc length 

316 E2 = _0_0 

317 sig12 = radians(s12_a12) 

318 if _K_2_0: 

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

320 else: # PYCHOK no cover 

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

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

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

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

325 else: # s12_a12 is distance 

326 t = s12_a12 / self._E0b 

327 s, c = _sincos2(t) # tau12 

328 # tau2 = tau1 + tau12 

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

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

331 ssig12, csig12 = _sincos2(sig12) 

332 

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

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

335 

336 # sig2 = sig1 + sig12 

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

338 dn2 = eF.fDelta(ssig2, csig2) 

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

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

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

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

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

344 cbet2 = csig2 = _TINY 

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

346 salp2 = salp0 

347 calp2 = calp0 * csig2 # no need to normalize 

348 

349 if (outmask & Cs.DISTANCE): 

350 if arcmode: # or f_0_01 

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

352 # AB1 = _E0 * (E2 - _E1) 

353 # s12 = _b * (_E0 * sig12 + AB1) 

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

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

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

357 else: 

358 s12 = s12_a12 

359 r.set_(s12=s12) 

360 

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

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

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

364 

365 if (outmask & Cs.LONGITUDE): 

366 schi1 = self._somg1 

367 cchi1 = self._cchi1 

368 schi2 = ssig2 * salp0 

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

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

371 -self._H1, sig12) 

372 if (outmask & Cs.LONG_UNROLL): 

373 _a, t = atan2, _copysign_1_0(salp0) # east-going? 

374 tchi1 = t * schi1 

375 tchi2 = t * schi2 

376 chi12 = t * fsum1f_(_a(ssig1, csig1), -_a(ssig2, csig2), 

377 _a(tchi2, cchi2), -_a(tchi1, cchi1), sig12) 

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

379 else: 

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

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

382 r.set_(lon2=lon2) 

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

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

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

386 

387 if (outmask & Cs.LATITUDE): 

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

389 

390 if (outmask & Cs.AZIMUTH): 

391 r.set_(azi2=_atan2d_reverse(salp2, calp2, reverse=outmask & Cs.REVERSE2)) 

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_(a12=s12_a12 if arcmode else degrees(sig12), 

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

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

447 azi1=_norm180(self.azi1)) 

448 return r 

449 

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

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

452 

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

454 s12, m12, M12, M21, S12)}. 

455 ''' 

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

457 return r.toDirect9Tuple() 

458 

459 def _GenSet(self, arcmode, s13_a13): 

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

461 ''' 

462 if arcmode: 

463 self.SetArc(s13_a13) 

464 else: 

465 self.SetDistance(s13_a13) 

466 return self # for gx.GeodesicExact.InverseLine and -._GenDirectLine 

467 

468 @Property_RO 

469 def geodesic(self): 

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

471 ''' 

472 _xGeodesicExact(geodesic=self._gX) 

473 return self._gX 

474 

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

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

477 

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

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

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

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

482 

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

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

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

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

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

488 along the geodesic from the circle center to the intersection 

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

490 and this line at the intersection. The geodesic azimuth 

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

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

493 L{GDict} instance. 

494 

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

496 intersect, no I{perpencular} geodetic 

497 intersection or no convergence. 

498 

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

500 ''' 

501 try: 

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

503 except (TypeError, ValueError) as x: 

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

505 

506 @Property_RO 

507 def _H0e2_f1(self): 

508 '''(INTERNAL) Cached/memoized. 

509 ''' 

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

511 

512 @Property_RO 

513 def _H1(self): 

514 '''(INTERNAL) Cached/memoized. 

515 ''' 

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

517 

518 @Property_RO 

519 def lat1(self): 

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

521 ''' 

522 return self._lat1 

523 

524 @Property_RO 

525 def lon1(self): 

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

527 ''' 

528 return self._lon1 

529 

530 @Property_RO 

531 def _lon1_norm180(self): 

532 '''(INTERNAL) Cached/memoized. 

533 ''' 

534 return _norm180(self._lon1) 

535 

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

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

538 and a geodesic from the given point. 

539 

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

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

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

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

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

545 

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

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

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

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

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

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

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

553 geodesic and this line at the intersection. The geodesic 

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

555 L{Position} for further details. 

556 

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

558 ''' 

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

560 

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

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

563 

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

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

566 the quantities to be returned. 

567 

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

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

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

571 except when C{a12=NAN}. 

572 

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

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

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

576 

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

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

579 ''' 

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

581 

582 @Property_RO 

583 def s13(self): 

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

585 

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

587 ''' 

588 return self._s13 

589 

590 def SetArc(self, a13): 

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

592 

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

594 point (C{degrees}). 

595 

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

597 the reference point or C{NAN}. 

598 ''' 

599 if self._a13 != a13: 

600 self._a13 = a13 

601 self._s13 = self._GDictPosition(True, a13, Caps.DISTANCE).s12 # if a13 else _0_0 

602 _update_all(self) 

603 return self._s13 

604 

605 def SetDistance(self, s13): 

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

607 

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

609 

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

611 and the reference point or C{NAN}. 

612 ''' 

613 if self._s13 != s13: 

614 self._s13 = s13 

615 self._a13 = self._GDictPosition(False, s13, 0).a12 if s13 else _0_0 

616 _update_all(self) 

617 return self._a13 # NAN for GeodesicLineExact without Cap.DISTANCE_IN 

618 

619 @Property_RO 

620 def _stau1_ctau1(self): 

621 '''(INTERNAL) Cached/memoized. 

622 ''' 

623 s, c = _sincos2(self._E1) 

624 # tau1 = sig1 + B11 

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

626 # unnecessary because Einv inverts E 

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

628 

629 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature 

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

631 

632 @kwarg prec: The C{float} precision, number of decimal digits (0..9). 

633 Trailing zero decimals are stripped for B{C{prec}} values 

634 of 1 and above, but kept for negative B{C{prec}} values. 

635 @kwarg sep: Separator to join (C{str}). 

636 

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

638 ''' 

639 d = dict(geodesic=self.geodesic, 

640 lat1=self.lat1, lon1=self.lon1, azi1=self.azi1, 

641 a13=self.a13, s13=self.s13) 

642 return sep.join(_MODS.streprs.pairs(d, prec=prec)) 

643 

644 

645__all__ += _ALL_DOCS(_GeodesicLineExact) 

646 

647# **) MIT License 

648# 

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

650# 

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

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

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

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

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

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

657# 

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

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

660# 

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

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

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

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

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

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

667# OTHER DEALINGS IN THE SOFTWARE.