1

2# -*- coding: utf-8 -*-

3

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

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

6

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

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

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

10

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

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

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

14'''

15# make sure int/int division yields float quotient

16 from __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

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

41 _180_0, _2__PI, _copysign_1_0, isfinite

42 from pygeodesy.errors import _xError, _xkwds_pop2

43 from pygeodesy.fsums import fsumf_, fsum1f_

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

45 _sincos12, _sin1cos2, \

46 _sinf1cos2d, _TINY

47# from pygeodesy.geodesicw import _Intersecant2 # _MODS

48 from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS

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

50 _K_2_0, _llz2gl, _norm2, _norm180, \

51 _sincos2, _sincos2d

52 from pygeodesy.named import Property_RO, _update_all

53# from pygeodesy.props import Property_RO, _update_all # from .named

54 from pygeodesy.utily import atan2d as _atan2d_reverse, sincos2

55

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

57

58__all__ = ()

59__version__ = '24.07.12'

60

61_glXs = [] # instances of C{[_]GeodesicLineExact} to be updated

62

63

64 def _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 _xGeodesicExact(gX=gX)

70 for glX in _glXs: # PYCHOK use weakref?

71 if glX._gX is gX:

72 _update_all(glX)

73

74

75 def _xGeodesicExact(**gX):

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

77 '''

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

79

80

81 class _GeodesicLineExact(_GeodesicBase):

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

83 '''

84 _a13 = _s13 = NAN

85# _azi1 = _0_0

86# _cchi1 = NAN

87# _dn1 = NAN

88 _gX = None # Exact only

89# _k2 = NAN

90# _lat1 = _lon1 = _0_0

91# _salp0 = _calp0 = NAN

92# _salp1 = _calp1 = NAN

93# _somg1 = _comg1 = NAN

94# _ssig1 = _csig1 = NAN

95

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

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

98 '''

99# _xGeodesicExact(gX=gX)

100 if azi1 is None: # see GeodesicExact.InverseLine

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

102 azi1 = _atan2d(salp1, calp1)

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

104 azi1 = _norm180(azi1)

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

106 if name_:

107 self.name = name_

108

109 self._gX = gX # GeodesicExact only

110 self._lat1 = lat1 = _fix90(lat1)

111 self._lon1 = lon1

112 self._azi1 = azi1

113 self._salp1 = salp1

114 self._calp1 = calp1

115 # allow lat, azimuth and unrolling of lon

116 self._caps = caps | Caps._AZIMUTH_LATITUDE_LONG_UNROLL

117

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

119 self._dn1 = gX._dn(sbet1, cbet1)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

134 self._somg1 = sbet1 * self._salp0

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

136 # Without normalization we have schi1 = somg1.

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

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

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

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

141 if not (caps & Caps.LINE_OFF):

142 _glXs.append(self)

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

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

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

146

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

148 if _glXs: # may be empty or None

149 try: # PYCHOK no cover

150 _glXs.remove(self)

151 except (TypeError, ValueError):

152 pass

153 self._gX = None

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

155

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

157 if updated:

158 _update_all(self, *attrs)

159

160 @Property_RO

161 def a1(self):

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

163 the northward equatorial crossing and the first point.

164 '''

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

166

167 equatorarc = a1

168

169 @Property_RO

170 def a13(self):

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

172

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

174 '''

175 return self._a13

176

177 def Arc(self):

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

179

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

181 '''

182 return self.a13

183

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

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

186

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

188 second point (C{degrees}).

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

190 the quantities to be returned.

191

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

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

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

195 except when C{a12=NAN}.

196

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

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

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

200 '''

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

202

203 @Property_RO

204 def azi0(self):

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

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

207 '''

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

209

210 equatorazimuth = azi0

211

212 @Property_RO

213 def azi0_sincos2(self):

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

215 '''

216 return self._salp0, self._calp0

217

218 @Property_RO

219 def azi1(self):

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

221 '''

222 return self._azi1

223

224 @Property_RO

225 def azi1_sincos2(self):

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

227 '''

228 return self._salp1, self._calp1

229

230 @Property_RO

231 def _B41(self):

232 '''(INTERNAL) Cached/memoized.

233 '''

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

235

236 @Property_RO

237 def _C4a(self):

238 '''(INTERNAL) Cached/memoized.

239 '''

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

241

242 @Property_RO

243 def _caps_DISTANCE_IN(self):

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

245 '''

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

247

248 @Property_RO

249 def _D0k2(self):

250 '''(INTERNAL) Cached/memoized.

251 '''

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

253

254 @Property_RO

255 def _D1(self):

256 '''(INTERNAL) Cached/memoized.

257 '''

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

259

260 def Distance(self):

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

262

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

264 '''

265 return self.s13

266

267 @Property_RO

268 def _E0b(self):

269 '''(INTERNAL) Cached/memoized.

270 '''

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

272

273 @Property_RO

274 def _E1(self):

275 '''(INTERNAL) Cached/memoized.

276 '''

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

278

279 @Property_RO

280 def _eF(self):

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

282 '''

283 # see .gx.GeodesicExact._ef_reset_k2

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

285

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

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

288

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

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

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

292 except when C{a12=NAN}.

293 '''

294 Cs = Caps

295 if outmask:

296 outmask &= self._caps & Cs._OUT_MASK

297 eF = self._eF

298 gX = self.geodesic # ._gX

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

300

301 if not isfinite(s12_a12):

302 # E2 = sig12 = ssig12 = csig12 = NAN

303 return r._toNAN(outmask)

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

305 r.set_(a12=s12_a12)

306 sig12 = radians(s12_a12)

307 if _K_2_0:

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

309 else: # PYCHOK no cover

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

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

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

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

314 E2 = _0_0

315 elif self._caps_DISTANCE_IN: # s12_a12 is distance

316 t = s12_a12 / self._E0b

317 s, c = _sincos2(t) # tau12

318 # tau2 = tau1 + tau12

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

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

321 ssig12, csig12 = _sincos2(sig12)

322 r.set_(a12=degrees(sig12))

323 else: # uninitialized or impossible distance requested

324 return r

325

326 # sig2 = sig1 + sig12

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

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

329 dn2 = eF.fDelta(*t)

330

331 if (outmask & Cs.DISTANCE):

332 outmask ^= Cs.DISTANCE

333 if arcmode: # or f_0_01

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

335 # AB1 = _E0 * (E2 - _E1)

336 # s12 = _b * (_E0 * sig12 + AB1)

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

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

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

340 else:

341 s12 = s12_a12

342 r.set_(s12=s12)

343

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

345 return r

346

347 if self._debug: # PYCHOK no cover

348 outmask |= self._debug & Cs._DEBUG_DIRECT_LINE

349

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

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

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

353

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

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

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

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

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

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

360 cbet2 = csig2 = _TINY

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

362 salp2 = salp0

363 calp2 = calp0 * csig2 # no need to normalize

364

365 if (outmask & Cs.AZIMUTH):

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

367 reverse=outmask & Cs.REVERSE2))

368

369 if (outmask & Cs.LATITUDE):

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

371

372 if (outmask & Cs.LONGITUDE):

373 schi1 = self._somg1

374 cchi1 = self._cchi1

375 schi2 = ssig2 * salp0

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

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

378 -self._H1, sig12)

379 if (outmask & Cs.LONG_UNROLL):

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

381 tchi1 = t * schi1

382 tchi2 = t * schi2

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

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

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

386 else:

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

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

389 r.set_(lon2=lon2)

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

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

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

393

394 if (outmask & Cs._REDUCEDLENGTH_GEODESICSCALE):

395 dn1 = self._dn1

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

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

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

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

400 if (outmask & Cs.REDUCEDLENGTH):

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

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

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

404 -dn1 * (ssig1 * csig2),

405 -J12 * (csig1 * csig2)))

406 if (outmask & Cs.GEODESICSCALE):

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

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

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

410

411 if (outmask & Cs.AREA):

412 A4 = salp0 * calp0

413 if A4:

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

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

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

417 # If csig12 > 0, write

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

419 # else

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

421 # No need to normalize

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

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

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

425 A4 *= gX._e2a2

426 B41 = self._B41

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

428 S12 = (B42 - B41) * A4

429 else:

430 S12 = A4 = B41 = B42 = _0_0

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

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

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

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

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

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

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

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

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

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

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

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

443 r.set_(S12=S12)

444

445 r.set_(azi1=_norm180(self.azi1),

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

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

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, debug, s12=None, a12=None, **llz2):

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

461 '''

462 Cs = Caps

463 if debug: # PYCHOK no cover

464 self._debug |= debug & Cs._DEBUG_ALL

465 # _CapsBase.debug._update(self)

466 if s12 is None:

467 if a12 is None: # see GeodesicExact.Line

468 return self

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

470 elif a12 is None:

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

472 self._s13 = s12

473 self._a13 = a12

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

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

476 return _llz2gl(self, **llz2)

477

478 @Property_RO

479 def geodesic(self):

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

481 '''

482 _xGeodesicExact(geodesic=self._gX)

483 return self._gX

484

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

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

487

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

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

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

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

492

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

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

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

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

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

498 along the geodesic from the circle center to the intersection

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

500 and this line at the intersection. The geodesic azimuth

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

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

503 L{GDict} instance.

504

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

506 intersect, no I{perpencular} geodetic

507 intersection or no convergence.

508

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

510 '''

511 try:

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

513 except (TypeError, ValueError) as x:

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

515

516 @Property_RO

517 def _H0e2_f1(self):

518 '''(INTERNAL) Cached/memoized.

519 '''

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

521

522 @Property_RO

523 def _H1(self):

524 '''(INTERNAL) Cached/memoized.

525 '''

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

527

528 @Property_RO

529 def lat1(self):

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

531 '''

532 return self._lat1

533

534 @Property_RO

535 def lon1(self):

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

537 '''

538 return self._lon1

539

540 @Property_RO

541 def _lon1_norm180(self):

542 '''(INTERNAL) Cached/memoized.

543 '''

544 return _norm180(self._lon1)

545

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

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

548 and a geodesic from the given point.

549

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

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

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

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

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

555

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

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

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

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

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

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

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

563 geodesic and this line at the intersection. The geodesic

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

565 L{Position} for further details.

566

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

568 '''

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

570

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

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

573

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

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

576 the quantities to be returned.

577

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

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

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

581 except when C{a12=NAN}.

582

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

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

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

586

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

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

589 '''

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

591

592 @Property_RO

593 def s13(self):

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

595

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

597 '''

598 return self._s13

599

600 def SetArc(self, a13):

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

602

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

604 point (C{degrees}).

605

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

607 the reference point or C{NAN}.

608 '''

609 if self._a13 != a13:

610 self._GenSet(0, a12=a13)

611 _update_all(self)

612 return self._s13

613

614 def SetDistance(self, s13):

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

616

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

618

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

620 and the reference point or C{NAN}.

621 '''

622 if self._s13 != s13:

623 self._GenSet(0, s12=s13)

624 _update_all(self)

625 return self._a13

626

627 @Property_RO

628 def _stau1_ctau1(self):

629 '''(INTERNAL) Cached/memoized.

630 '''

631 s, c = _sincos2(self._E1)

632 # tau1 = sig1 + B11

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

634 # unnecessary because Einv inverts E

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

636

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

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

639

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

641 for further details.

642

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

644 '''

645 C = _GeodesicLineExact

646 t = C.lat1, C.lon1, C.azi1, C.a13, C.s13, C.caps, C.geodesic

647 return self._instr(props=t, **prec_sep_name)

648

649

650__all__ += _ALL_DOCS(_GeodesicLineExact)

651

652# **) MIT License

653#

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

655#

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

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

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

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

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

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

662#

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

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

665#

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

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

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

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

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

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

672# OTHER DEALINGS IN THE SOFTWARE.