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, _xkwds_get 

43from pygeodesy.fsums import fsumf_, fsum1f_ 

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

45 _sincos12, _sin1cos2 

46# from pygeodesy.geodesicw import _Intersecant2 # _MODS 

47from pygeodesy.interns import NN, _COMMASPACE_ 

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__ = '24.02.21' 

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): # name=NN 

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: # *args, name=NN): Python3 

114 name = _xkwds_get(name, name=NN) 

115 if name: 

116 self.name = name 

117 

118 self._gX = gX # GeodesicExact only 

119 self._lat1 = lat1 = _fix90(lat1) 

120 self._lon1 = lon1 

121 self._azi1 = azi1 

122 self._salp1 = salp1 

123 self._calp1 = calp1 

124 # allow lat, azimuth and unrolling of lon 

125 self._caps = caps | Cs._LINE 

126 

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

128 self._dn1 = gX._dn(sbet1, cbet1) 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

143 self._somg1 = sbet1 * self._salp0 

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

145 # Without normalization we have schi1 = somg1. 

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

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

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

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

150 if not (caps & Cs.LINE_OFF): 

151 _glXs.append(self) 

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

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

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

155 

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

157 if _glXs: # may be empty or None 

158 try: # PYCHOK no cover 

159 _glXs.remove(self) 

160 except (TypeError, ValueError): 

161 pass 

162 self._gX = None 

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

164 

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

166 if updated: 

167 _update_all(self, *attrs) 

168 

169 @Property_RO 

170 def a1(self): 

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

172 the northward equatorial crossing and the first point. 

173 ''' 

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

175 

176 equatorarc = a1 

177 

178 @Property_RO 

179 def a13(self): 

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

181 

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

183 ''' 

184 return self._a13 

185 

186 def Arc(self): 

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

188 

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

190 ''' 

191 return self.a13 

192 

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

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

195 

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

197 second point (C{degrees}). 

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

199 the quantities to be returned. 

200 

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

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

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

204 except when C{a12=NAN}. 

205 

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

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

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

209 ''' 

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

211 

212 @Property_RO 

213 def azi0(self): 

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

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

216 ''' 

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

218 

219 equatorazimuth = azi0 

220 

221 @Property_RO 

222 def azi0_sincos2(self): 

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

224 ''' 

225 return self._salp0, self._calp0 

226 

227 @Property_RO 

228 def azi1(self): 

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

230 ''' 

231 return self._azi1 

232 

233 @Property_RO 

234 def azi1_sincos2(self): 

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

236 ''' 

237 return self._salp1, self._calp1 

238 

239 @Property_RO 

240 def _B41(self): 

241 '''(INTERNAL) Cached/memoized. 

242 ''' 

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

244 

245 @Property_RO 

246 def _C4a(self): 

247 '''(INTERNAL) Cached/memoized. 

248 ''' 

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

250 

251 @Property_RO 

252 def _caps_DISTANCE_IN(self): 

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

254 ''' 

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

256 

257 @Property_RO 

258 def _D0k2(self): 

259 '''(INTERNAL) Cached/memoized. 

260 ''' 

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

262 

263 @Property_RO 

264 def _D1(self): 

265 '''(INTERNAL) Cached/memoized. 

266 ''' 

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

268 

269 def Distance(self): 

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

271 

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

273 ''' 

274 return self.s13 

275 

276 @Property_RO 

277 def _E0b(self): 

278 '''(INTERNAL) Cached/memoized. 

279 ''' 

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

281 

282 @Property_RO 

283 def _E1(self): 

284 '''(INTERNAL) Cached/memoized. 

285 ''' 

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

287 

288 @Property_RO 

289 def _eF(self): 

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

291 ''' 

292 # see .gx.GeodesicExact._ef_reset_k2 

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

294 

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

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

297 

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

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

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

301 except when C{a12=NAN}. 

302 ''' 

303 

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

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

306 return r # Uninitialized or impossible distance requested 

307 

308 Cs = Caps 

309 if self._debug: # PYCHOK no cover 

310 outmask |= self._debug & Cs._DEBUG_DIRECT_LINE 

311 outmask &= self._caps & Cs._OUT_MASK 

312 

313 eF = self._eF 

314 gX = self.geodesic # ._gX 

315 

316 if arcmode: 

317 # s12_a12 is spherical arc length 

318 E2 = _0_0 

319 sig12 = radians(s12_a12) 

320 if _K_2_0: 

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

322 else: # PYCHOK no cover 

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

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

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

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

327 else: # s12_a12 is distance 

328 t = s12_a12 / self._E0b 

329 s, c = _sincos2(t) # tau12 

330 # tau2 = tau1 + tau12 

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

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

333 ssig12, csig12 = _sincos2(sig12) 

334 

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

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

337 

338 # sig2 = sig1 + sig12 

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

340 dn2 = eF.fDelta(ssig2, csig2) 

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

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

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

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

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

346 cbet2 = csig2 = _TINY 

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

348 salp2 = salp0 

349 calp2 = calp0 * csig2 # no need to normalize 

350 

351 if (outmask & Cs.DISTANCE): 

352 if arcmode: # or f_0_01 

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

354 # AB1 = _E0 * (E2 - _E1) 

355 # s12 = _b * (_E0 * sig12 + AB1) 

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

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

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

359 else: 

360 s12 = s12_a12 

361 r.set_(s12=s12) 

362 

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

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

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

366 

367 if (outmask & Cs.LONGITUDE): 

368 schi1 = self._somg1 

369 cchi1 = self._cchi1 

370 schi2 = ssig2 * salp0 

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

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

373 -self._H1, sig12) 

374 if (outmask & Cs.LONG_UNROLL): 

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

376 tchi1 = t * schi1 

377 tchi2 = t * schi2 

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

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

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

381 else: 

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

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

384 r.set_(lon2=lon2) 

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

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

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

388 

389 if (outmask & Cs.LATITUDE): 

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

391 

392 if (outmask & Cs.AZIMUTH): 

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

394 

395 if (outmask & Cs._REDUCEDLENGTH_GEODESICSCALE): 

396 dn1 = self._dn1 

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

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

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

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

401 if (outmask & Cs.REDUCEDLENGTH): 

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

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

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

405 -dn1 * (ssig1 * csig2), 

406 -J12 * (csig1 * csig2))) 

407 if (outmask & Cs.GEODESICSCALE): 

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

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

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

411 

412 if (outmask & Cs.AREA): 

413 A4 = salp0 * calp0 

414 if A4: 

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

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

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

418 # If csig12 > 0, write 

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

420 # else 

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

422 # No need to normalize 

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

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

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

426 A4 *= gX._e2a2 

427 B41 = self._B41 

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

429 S12 = (B42 - B41) * A4 

430 else: 

431 S12 = A4 = B41 = B42 = _0_0 

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

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

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

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

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

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

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

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

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

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

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

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

444 r.set_(S12=S12) 

445 

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

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

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

449 azi1=_norm180(self.azi1)) 

450 return r 

451 

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

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

454 

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

456 s12, m12, M12, M21, S12)}. 

457 ''' 

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

459 return r.toDirect9Tuple() 

460 

461 def _GenSet(self, arcmode, s13_a13): 

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

463 ''' 

464 if arcmode: 

465 self.SetArc(s13_a13) 

466 else: 

467 self.SetDistance(s13_a13) 

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

469 

470 @Property_RO 

471 def geodesic(self): 

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

473 ''' 

474 _xGeodesicExact(geodesic=self._gX) 

475 return self._gX 

476 

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

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

479 

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

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

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

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

484 

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

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

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

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

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

490 along the geodesic from the circle center to the intersection 

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

492 and this line at the intersection. The geodesic azimuth 

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

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

495 L{GDict} instance. 

496 

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

498 intersect, no I{perpencular} geodetic 

499 intersection or no convergence. 

500 

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

502 ''' 

503 try: 

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

505 except (TypeError, ValueError) as x: 

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

507 

508 @Property_RO 

509 def _H0e2_f1(self): 

510 '''(INTERNAL) Cached/memoized. 

511 ''' 

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

513 

514 @Property_RO 

515 def _H1(self): 

516 '''(INTERNAL) Cached/memoized. 

517 ''' 

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

519 

520 @Property_RO 

521 def lat1(self): 

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

523 ''' 

524 return self._lat1 

525 

526 @Property_RO 

527 def lon1(self): 

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

529 ''' 

530 return self._lon1 

531 

532 @Property_RO 

533 def _lon1_norm180(self): 

534 '''(INTERNAL) Cached/memoized. 

535 ''' 

536 return _norm180(self._lon1) 

537 

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

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

540 and a geodesic from the given point. 

541 

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

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

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

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

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

547 

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

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

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

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

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

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

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

555 geodesic and this line at the intersection. The geodesic 

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

557 L{Position} for further details. 

558 

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

560 ''' 

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

562 

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

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

565 

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

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

568 the quantities to be returned. 

569 

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

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

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

573 except when C{a12=NAN}. 

574 

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

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

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

578 

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

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

581 ''' 

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

583 

584 @Property_RO 

585 def s13(self): 

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

587 

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

589 ''' 

590 return self._s13 

591 

592 def SetArc(self, a13): 

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

594 

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

596 point (C{degrees}). 

597 

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

599 the reference point or C{NAN}. 

600 ''' 

601 if self._a13 != a13: 

602 self._a13 = a13 

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

604 _update_all(self) 

605 return self._s13 

606 

607 def SetDistance(self, s13): 

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

609 

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

611 

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

613 and the reference point or C{NAN}. 

614 ''' 

615 if self._s13 != s13: 

616 self._s13 = s13 

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

618 _update_all(self) 

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

620 

621 @Property_RO 

622 def _stau1_ctau1(self): 

623 '''(INTERNAL) Cached/memoized. 

624 ''' 

625 s, c = _sincos2(self._E1) 

626 # tau1 = sig1 + B11 

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

628 # unnecessary because Einv inverts E 

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

630 

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

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

633 

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

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

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

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

638 

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

640 ''' 

641 d = dict(geodesic=self.geodesic, 

642 lat1=self.lat1, lon1=self.lon1, azi1=self.azi1, 

643 a13=self.a13, s13=self.s13) 

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

645 

646 

647__all__ += _ALL_DOCS(_GeodesicLineExact) 

648 

649# **) MIT License 

650# 

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

652# 

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

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

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

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

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

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

659# 

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

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

662# 

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

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

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

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

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

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

669# OTHER DEALINGS IN THE SOFTWARE.