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:Charles@Karney.com>} (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# - beta = latitude on auxiliary sphere 

25# - omega = longitude on auxiliary sphere 

26# - lambda = longitude 

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 # from .karney 

40from pygeodesy.constants import NAN, _EPSmin, _0_0, _1_0, _180_0, _2__PI 

41from pygeodesy.fsums import _COMMASPACE_, fsumf_, fsum1f_ 

42from pygeodesy.geodesicx.gxbases import _cosSeries, _GeodesicBase, \ 

43 _sincos12, _sin1cos2 

44# from pygeodesy.interns import _COMMASPACE_ # from .fsums 

45from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS 

46from pygeodesy.karney import _around, _atan2d, Caps, _copysign, GDict, \ 

47 _fix90, _K_2_0, _norm2, _norm180, \ 

48 _sincos2, _sincos2d, _xinstanceof 

49from pygeodesy.props import Property_RO, _update_all 

50# from pygeodesy.streprs import pairs # _MODS 

51from pygeodesy.utily import atan2d as _atan2d_reverse, sincos2 

52 

53from math import atan2, cos, degrees, fabs, floor, radians, sin 

54 

55__all__ = () 

56__version__ = '23.06.23' 

57 

58_glXs = [] # instances of C{[_]GeodesicLineExact} to be updated 

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

60_TINY = _EPSmin 

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

62 

63 

64def _update_glXs(gX): # see GeodesicExact.C4order and -._ef_reset_k2 

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

66 any L{GeodesicLineExact} instances tied to the given 

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

68 ''' 

69 _xinstanceof(_MODS.geodesicx.GeodesicExact, gX=gX) 

70 for glX in _glXs: # PYCHOK use weakref? 

71 if glX._gX is gX: 

72 _update_all(glX) 

73 

74 

75class _GeodesicLineExact(_GeodesicBase): 

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

77 ''' 

78 _a13 = _s13 = NAN 

79 _azi1 = _0_0 

80 _cchi1 = NAN 

81 _dn1 = NAN 

82 _gX = None # Exact only 

83 _k2 = NAN 

84 _lat1 = _lon1 = _0_0 

85 _salp0 = _calp0 = NAN 

86 _salp1 = _calp1 = NAN 

87 _somg1 = _comg1 = NAN 

88 _ssig1 = _csig1 = NAN 

89 

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

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

92 ''' 

93 _xinstanceof(_MODS.geodesicx.GeodesicExact, gX=gX) 

94 Cs = Caps 

95 if _debug: # PYCHOK no cover 

96 self._debug |= _debug & Cs._DEBUG_ALL 

97 # _CapsBase.debug._update(self) 

98 if salp1_calp1: 

99 salp1, calp1 = salp1_calp1 

100 else: 

101 azi1 = _norm180(azi1) 

102 # guard against salp0 underflow, 

103 # also -0 is converted to +0 

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 | Cs._LINE 

116 

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

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 & Cs.LINE_OFF): 

141 _glXs.append(self) 

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

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

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

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_OUT 

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 

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

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

296 return r # Uninitialized or impossible distance requested 

297 

298 Cs = Caps 

299 if self._debug: # PYCHOK no cover 

300 outmask |= self._debug & Cs._DEBUG_DIRECT_LINE 

301 outmask &= self._caps & Cs._OUT_MASK 

302 

303 eF = self._eF 

304 gX = self.geodesic # ._gX 

305 

306 if arcmode: 

307 # s12_a12 is spherical arc length 

308 E2 = _0_0 

309 sig12 = radians(s12_a12) 

310 if _K_2_0: 

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

312 else: # PYCHOK no cover 

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

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

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

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

317 else: # s12_a12 is distance 

318 t = s12_a12 / self._E0b 

319 s, c = _sincos2(t) # tau12 

320 # tau2 = tau1 + tau12 

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

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

323 ssig12, csig12 = _sincos2(sig12) 

324 

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

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

327 

328 # sig2 = sig1 + sig12 

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

330 dn2 = eF.fDelta(ssig2, csig2) 

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

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

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

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

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

336 cbet2 = csig2 = _TINY 

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

338 salp2 = salp0 

339 calp2 = calp0 * csig2 # no need to normalize 

340 

341 if (outmask & Cs.DISTANCE): 

342 if arcmode: # or f_0_01 

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

344 # AB1 = _E0 * (E2 - _E1) 

345 # s12 = _b * (_E0 * sig12 + AB1) 

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

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

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

349 else: 

350 s12 = s12_a12 

351 r.set_(s12=s12) 

352 

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

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

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

356 

357 if (outmask & Cs.LONGITUDE): 

358 schi1 = self._somg1 

359 cchi1 = self._cchi1 

360 schi2 = ssig2 * salp0 

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

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

363 -self._H1, sig12) 

364 if (outmask & Cs.LONG_UNROLL): 

365 t = _copysign(_1_0, salp0) # east-going? 

366 tchi1 = t * schi1 

367 tchi2 = t * schi2 

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

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

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

371 else: 

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

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

374 r.set_(lon2=lon2) 

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

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

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

378 

379 if (outmask & Cs.LATITUDE): 

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

381 

382 if (outmask & Cs.AZIMUTH): 

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

384 

385 if (outmask & Cs._REDUCEDLENGTH_GEODESICSCALE): 

386 dn1 = self._dn1 

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

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

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

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

391 if (outmask & Cs.REDUCEDLENGTH): 

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

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

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

395 -dn1 * (ssig1 * csig2), 

396 -J12 * (csig1 * csig2))) 

397 if (outmask & Cs.GEODESICSCALE): 

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

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

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

401 

402 if (outmask & Cs.AREA): 

403 A4 = salp0 * calp0 

404 if A4: 

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

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

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

408 # If csig12 > 0, write 

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

410 # else 

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

412 # No need to normalize 

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

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

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

416 A4 *= gX._e2a2 

417 B41 = self._B41 

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

419 S12 = (B42 - B41) * A4 

420 else: 

421 S12 = A4 = B41 = B42 = _0_0 

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

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

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

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

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

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

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

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

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

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

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

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

434 r.set_(S12=S12) 

435 

436 r.set_(a12=s12_a12 if arcmode else degrees(sig12), 

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

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

439 azi1=_norm180(self.azi1)) 

440 return r 

441 

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

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

444 

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

446 s12, m12, M12, M21, S12)}. 

447 ''' 

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

449 return r.toDirect9Tuple() 

450 

451 def _GenSet(self, arcmode, s13_a13): 

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

453 ''' 

454 if arcmode: 

455 self.SetArc(s13_a13) 

456 else: 

457 self.SetDistance(s13_a13) 

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

459 

460 @Property_RO 

461 def geodesic(self): 

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

463 ''' 

464 assert isinstance(self._gX, _MODS.geodesicx.GeodesicExact) 

465 return self._gX 

466 

467 @Property_RO 

468 def _H0e2_f1(self): 

469 '''(INTERNAL) Cached/memoized. 

470 ''' 

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

472 

473 @Property_RO 

474 def _H1(self): 

475 '''(INTERNAL) Cached/memoized. 

476 ''' 

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

478 

479 @Property_RO 

480 def lat1(self): 

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

482 ''' 

483 return self._lat1 

484 

485 @Property_RO 

486 def lon1(self): 

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

488 ''' 

489 return self._lon1 

490 

491 @Property_RO 

492 def _lon1_norm180(self): 

493 '''(INTERNAL) Cached/memoized. 

494 ''' 

495 return _norm180(self._lon1) 

496 

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

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

499 

500 @arg s12: Distance from the first point to the second (C{meter}). 

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

502 the quantities to be returned. 

503 

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

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

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

507 except when C{a12=NAN}. 

508 

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

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

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

512 

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

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

515 ''' 

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

517 

518 @Property_RO 

519 def s13(self): 

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

521 

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

523 ''' 

524 return self._s13 

525 

526 def SetArc(self, a13): 

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

528 

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

530 point (C{degrees}). 

531 

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

533 the reference point or C{NAN}. 

534 ''' 

535 self._a13 = a13 

536 self._s13 = s13 = self._GDictPosition(True, a13, Caps.DISTANCE).s12 

537 _update_all(self) 

538 return s13 

539 

540 def SetDistance(self, s13): 

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

542 

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

544 

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

546 and the reference point or C{NAN}. 

547 ''' 

548 self._s13 = s13 

549 self._a13 = a13 = self._GDictPosition(False, s13, 0).a12 

550 _update_all(self) 

551 return a13 # NAN for GeodesicLineExact without Cap.DISTANCE_IN 

552 

553 @Property_RO 

554 def _stau1_ctau1(self): 

555 '''(INTERNAL) Cached/memoized. 

556 ''' 

557 s, c = _sincos2(self._E1) 

558 # tau1 = sig1 + B11 

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

560 # unnecessary because Einv inverts E 

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

562 

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

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

565 

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

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

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

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

570 

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

572 ''' 

573 d = dict(geodesic=self.geodesic, 

574 lat1=self.lat1, lon1=self.lon1, azi1=self.azi1, 

575 a13=self.a13, s13=self.s13) 

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

577 

578 

579__all__ += _ALL_DOCS(_GeodesicLineExact) 

580 

581# **) MIT License 

582# 

583# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved. 

584# 

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

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

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

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

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

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

591# 

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

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

594# 

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

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

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

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

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

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

601# OTHER DEALINGS IN THE SOFTWARE.