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, _xkwds_get

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 NN, _COMMASPACE_

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__ = '24.02.21'

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

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): # 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.