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, _EPSmin, _EPSqrt as _TOL, _0_0, \

41 _1_0, _180_0, _2__PI, _copysign_1_0

42 from pygeodesy.errors import _xError, _COMMASPACE_

43 from pygeodesy.fsums import fsumf_, fsum1f_

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

45 _sincos12, _sin1cos2

46# from pygeodesy.geodesicw import _Intersecant2 # _MODS

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

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, _norm2, _norm180, _sincos2, _sincos2d

51 from pygeodesy.props import Property_RO, _update_all

52# from pygeodesy.streprs import pairs # _MODS

53 from pygeodesy.utily import atan2d as _atan2d_reverse, sincos2

54

55 from 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

66 def _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

77 def _xGeodesicExact(**gX):

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

79 '''

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

81

82

83 class _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.