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# - beta = latitude on auxiliary sphere

25# - omega = longitude on auxiliary sphere

26# - lambda = longitude

27# - alpha = azimuth of great circle

28# - sigma = arc length along great circle

29# - s = distance

30# - tau = scaled distance (= sigma at multiples of PI/2)

31# - at northwards equator crossing

32# - beta = phi = 0

33# - omega = lambda = 0

34# - alpha = alpha0

35# - sigma = s = 0

36# - a 12 suffix means a difference, e.g., s12 = s2 - s1.

37# - s and c prefixes mean sin and cos

38

39# from pygeodesy.basics import _xinstanceof # from .karney

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

41 _0_0, _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, \

51 _sincos2d, _xinstanceof

52 from pygeodesy.props import Property_RO, _update_all

53# from pygeodesy.streprs import pairs # _MODS

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__ = '23.11.09'

60

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

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

63_TINY = _EPSmin

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

65

66

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

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

69 any L{GeodesicLineExact} instances tied to the given

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

71 '''

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

73 for glX in _glXs: # PYCHOK use weakref?

74 if glX._gX is gX:

75 _update_all(glX)

76

77

78 class _GeodesicLineExact(_GeodesicBase):

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

80 '''

81 _a13 = _s13 = NAN

82 _azi1 = _0_0

83 _cchi1 = NAN

84 _dn1 = NAN

85 _gX = None # Exact only

86 _k2 = NAN

87 _lat1 = _lon1 = _0_0

88 _salp0 = _calp0 = NAN

89 _salp1 = _calp1 = NAN

90 _somg1 = _comg1 = NAN

91 _ssig1 = _csig1 = NAN

92

93 def __init__(self, gX, lat1, lon1, azi1, caps, _debug, *salp1_calp1, **name): # name=NN

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

95 '''

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

97 Cs = Caps

98 if _debug: # PYCHOK no cover

99 self._debug |= _debug & Cs._DEBUG_ALL

100 # _CapsBase.debug._update(self)

101 if salp1_calp1:

102 salp1, calp1 = salp1_calp1

103 else:

104 azi1 = _norm180(azi1)

105 # guard against salp0 underflow,

106 # also -0 is converted to +0

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

108 if name: # *args, name=NN): Python3

109 name = _xkwds_get(name, name=NN)

110 if name:

111 self.name = name

112

113 self._gX = gX # GeodesicExact only

114 self._lat1 = lat1 = _fix90(lat1)

115 self._lon1 = lon1

116 self._azi1 = azi1

117 self._salp1 = salp1

118 self._calp1 = calp1

119 # allow lat, azimuth and unrolling of lon

120 self._caps = caps | Cs._LINE

121

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

138 self._somg1 = sbet1 * self._salp0

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

140 # Without normalization we have schi1 = somg1.

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

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

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

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

145 if not (caps & Cs.LINE_OFF):

146 _glXs.append(self)

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

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

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

150

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

152 if _glXs: # may be empty or None

153 try: # PYCHOK no cover

154 _glXs.remove(self)

155 except (TypeError, ValueError):

156 pass

157 self._gX = None

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

159

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

161 if updated:

162 _update_all(self, *attrs)

163

164 @Property_RO

165 def a1(self):

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

167 the northward equatorial crossing and the first point.

168 '''

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

170

171 equatorarc = a1

172

173 @Property_RO

174 def a13(self):

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

176

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

178 '''

179 return self._a13

180

181 def Arc(self):

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

183

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

185 '''

186 return self.a13

187

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

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

190

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

192 second point (C{degrees}).

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

194 the quantities to be returned.

195

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

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

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

199 except when C{a12=NAN}.

200

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

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

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

204 '''

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

206

207 @Property_RO

208 def azi0(self):

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

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

211 '''

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

213

214 equatorazimuth = azi0

215

216 @Property_RO

217 def azi0_sincos2(self):

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

219 '''

220 return self._salp0, self._calp0

221

222 @Property_RO

223 def azi1(self):

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

225 '''

226 return self._azi1

227

228 @Property_RO

229 def azi1_sincos2(self):

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

231 '''

232 return self._salp1, self._calp1

233

234 @Property_RO

235 def _B41(self):

236 '''(INTERNAL) Cached/memoized.

237 '''

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

239

240 @Property_RO

241 def _C4a(self):

242 '''(INTERNAL) Cached/memoized.

243 '''

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

245

246 @Property_RO

247 def _caps_DISTANCE_IN(self):

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

249 '''

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

251

252 @Property_RO

253 def _D0k2(self):

254 '''(INTERNAL) Cached/memoized.

255 '''

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

257

258 @Property_RO

259 def _D1(self):

260 '''(INTERNAL) Cached/memoized.

261 '''

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

263

264 def Distance(self):

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

266

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

268 '''

269 return self.s13

270

271 @Property_RO

272 def _E0b(self):

273 '''(INTERNAL) Cached/memoized.

274 '''

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

276

277 @Property_RO

278 def _E1(self):

279 '''(INTERNAL) Cached/memoized.

280 '''

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

282

283 @Property_RO

284 def _eF(self):

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

286 '''

287 # see .gx.GeodesicExact._ef_reset_k2

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

289

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

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

292

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

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

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

296 except when C{a12=NAN}.

297 '''

298

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

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

301 return r # Uninitialized or impossible distance requested

302

303 Cs = Caps

304 if self._debug: # PYCHOK no cover

305 outmask |= self._debug & Cs._DEBUG_DIRECT_LINE

306 outmask &= self._caps & Cs._OUT_MASK

307

308 eF = self._eF

309 gX = self.geodesic # ._gX

310

311 if arcmode:

312 # s12_a12 is spherical arc length

313 E2 = _0_0

314 sig12 = radians(s12_a12)

315 if _K_2_0:

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

317 else: # PYCHOK no cover

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

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

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

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

322 else: # s12_a12 is distance

323 t = s12_a12 / self._E0b

324 s, c = _sincos2(t) # tau12

325 # tau2 = tau1 + tau12

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

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

328 ssig12, csig12 = _sincos2(sig12)

329

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

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

332

333 # sig2 = sig1 + sig12

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

335 dn2 = eF.fDelta(ssig2, csig2)

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

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

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

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

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

341 cbet2 = csig2 = _TINY

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

343 salp2 = salp0

344 calp2 = calp0 * csig2 # no need to normalize

345

346 if (outmask & Cs.DISTANCE):

347 if arcmode: # or f_0_01

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

349 # AB1 = _E0 * (E2 - _E1)

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

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

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

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

354 else:

355 s12 = s12_a12

356 r.set_(s12=s12)

357

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

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

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

361

362 if (outmask & Cs.LONGITUDE):

363 schi1 = self._somg1

364 cchi1 = self._cchi1

365 schi2 = ssig2 * salp0

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

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

368 -self._H1, sig12)

369 if (outmask & Cs.LONG_UNROLL):

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

371 tchi1 = t * schi1

372 tchi2 = t * schi2

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

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

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

376 else:

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

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

379 r.set_(lon2=lon2)

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

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

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

383

384 if (outmask & Cs.LATITUDE):

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

386

387 if (outmask & Cs.AZIMUTH):

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

389

390 if (outmask & Cs._REDUCEDLENGTH_GEODESICSCALE):

391 dn1 = self._dn1

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

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

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

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

396 if (outmask & Cs.REDUCEDLENGTH):

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

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

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

400 -dn1 * (ssig1 * csig2),

401 -J12 * (csig1 * csig2)))

402 if (outmask & Cs.GEODESICSCALE):

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

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

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

406

407 if (outmask & Cs.AREA):

408 A4 = salp0 * calp0

409 if A4:

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

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

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

413 # If csig12 > 0, write

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

415 # else

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

417 # No need to normalize

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

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

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

421 A4 *= gX._e2a2

422 B41 = self._B41

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

424 S12 = (B42 - B41) * A4

425 else:

426 S12 = A4 = B41 = B42 = _0_0

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

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

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

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

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

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

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

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

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

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

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

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

439 r.set_(S12=S12)

440

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

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

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

444 azi1=_norm180(self.azi1))

445 return r

446

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

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

449

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

451 s12, m12, M12, M21, S12)}.

452 '''

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

454 return r.toDirect9Tuple()

455

456 def _GenSet(self, arcmode, s13_a13):

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

458 '''

459 if arcmode:

460 self.SetArc(s13_a13)

461 else:

462 self.SetDistance(s13_a13)

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

464

465 @Property_RO

466 def geodesic(self):

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

468 '''

469 _xinstanceof(_MODS.geodesicx.GeodesicExact, geodesic=self._gX)

470 return self._gX

471

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

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

474

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

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

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

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

479

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

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

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

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

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

485 along the geodesic from the circle center to the intersection

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

487 and this line at the intersection. The geodesic azimuth

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

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

490 L{GDict} instance.

491

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

493 intersect, no I{perpencular} geodetic

494 intersection or no convergence.

495

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

497 '''

498 try:

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

500 except (TypeError, ValueError) as x:

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

502

503 @Property_RO

504 def _H0e2_f1(self):

505 '''(INTERNAL) Cached/memoized.

506 '''

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

508

509 @Property_RO

510 def _H1(self):

511 '''(INTERNAL) Cached/memoized.

512 '''

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

514

515 @Property_RO

516 def lat1(self):

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

518 '''

519 return self._lat1

520

521 @Property_RO

522 def lon1(self):

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

524 '''

525 return self._lon1

526

527 @Property_RO

528 def _lon1_norm180(self):

529 '''(INTERNAL) Cached/memoized.

530 '''

531 return _norm180(self._lon1)

532

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

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

535 and a geodesic from the given point.

536

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

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

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

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

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

542

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

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

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

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

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

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

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

550 geodesic and this line at the intersection. The geodesic

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

552 L{Position} for further details.

553

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

555 '''

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

557

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

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

560

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

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

563 the quantities to be returned.

564

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

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

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

568 except when C{a12=NAN}.

569

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

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

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

573

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

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

576 '''

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

578

579 @Property_RO

580 def s13(self):

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

582

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

584 '''

585 return self._s13

586

587 def SetArc(self, a13):

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

589

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

591 point (C{degrees}).

592

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

594 the reference point or C{NAN}.

595 '''

596 if self._a13 != a13:

597 self._a13 = a13

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

599 _update_all(self)

600 return self._s13

601

602 def SetDistance(self, s13):

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

604

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

606

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

608 and the reference point or C{NAN}.

609 '''

610 if self._s13 != s13:

611 self._s13 = s13

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

613 _update_all(self)

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

615

616 @Property_RO

617 def _stau1_ctau1(self):

618 '''(INTERNAL) Cached/memoized.

619 '''

620 s, c = _sincos2(self._E1)

621 # tau1 = sig1 + B11

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

623 # unnecessary because Einv inverts E

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

625

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

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

628

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

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

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

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

633

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

635 '''

636 d = dict(geodesic=self.geodesic,

637 lat1=self.lat1, lon1=self.lon1, azi1=self.azi1,

638 a13=self.a13, s13=self.s13)

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

640

641

642__all__ += _ALL_DOCS(_GeodesicLineExact)

643

644# **) MIT License

645#

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

647#

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

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

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

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

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

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

654#

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

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

657#

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

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

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

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

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

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

664# OTHER DEALINGS IN THE SOFTWARE.