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, _0_0, _1_0, _180_0, \

41 _2__PI, _copysign_1_0

42 from pygeodesy.fsums import _COMMASPACE_, fsumf_, fsum1f_

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

44 _sincos12, _sin1cos2

45# from pygeodesy.interns import _COMMASPACE_ # from .fsums

46 from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS

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

48 _K_2_0, _norm2, _norm180, _sincos2, \

49 _sincos2d, _xinstanceof

50 from pygeodesy.props import Property_RO, _update_all

51# from pygeodesy.streprs import pairs # _MODS

52 from pygeodesy.utily import atan2d as _atan2d_reverse, sincos2

53

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

55

56__all__ = ()

57__version__ = '23.09.29'

58

59_glXs = [] # instances of C{[_]GeodesicLineExact} to be updated

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

61_TINY = _EPSmin

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

63

64

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

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

67 any L{GeodesicLineExact} instances tied to the given

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

69 '''

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

71 for glX in _glXs: # PYCHOK use weakref?

72 if glX._gX is gX:

73 _update_all(glX)

74

75

76 class _GeodesicLineExact(_GeodesicBase):

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

78 '''

79 _a13 = _s13 = NAN

80 _azi1 = _0_0

81 _cchi1 = NAN

82 _dn1 = NAN

83 _gX = None # Exact only

84 _k2 = NAN

85 _lat1 = _lon1 = _0_0

86 _salp0 = _calp0 = NAN

87 _salp1 = _calp1 = NAN

88 _somg1 = _comg1 = NAN

89 _ssig1 = _csig1 = NAN

90

91 def __init__(self, gX, lat1, lon1, azi1, caps, _debug, *salp1_calp1, **name):

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

93 '''

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

95 Cs = Caps

96 if _debug: # PYCHOK no cover

97 self._debug |= _debug & Cs._DEBUG_ALL

98 # _CapsBase.debug._update(self)

99 if salp1_calp1:

100 salp1, calp1 = salp1_calp1

101 else:

102 azi1 = _norm180(azi1)

103 # guard against salp0 underflow,

104 # also -0 is converted to +0

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 | Cs._LINE

117

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

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 & Cs.LINE_OFF):

142 _glXs.append(self)

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

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

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

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

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

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

297 return r # Uninitialized or impossible distance requested

298

299 Cs = Caps

300 if self._debug: # PYCHOK no cover

301 outmask |= self._debug & Cs._DEBUG_DIRECT_LINE

302 outmask &= self._caps & Cs._OUT_MASK

303

304 eF = self._eF

305 gX = self.geodesic # ._gX

306

307 if arcmode:

308 # s12_a12 is spherical arc length

309 E2 = _0_0

310 sig12 = radians(s12_a12)

311 if _K_2_0:

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

313 else: # PYCHOK no cover

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

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

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

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

318 else: # s12_a12 is distance

319 t = s12_a12 / self._E0b

320 s, c = _sincos2(t) # tau12

321 # tau2 = tau1 + tau12

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

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

324 ssig12, csig12 = _sincos2(sig12)

325

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

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

328

329 # sig2 = sig1 + sig12

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

331 dn2 = eF.fDelta(ssig2, csig2)

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

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

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

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

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

337 cbet2 = csig2 = _TINY

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

339 salp2 = salp0

340 calp2 = calp0 * csig2 # no need to normalize

341

342 if (outmask & Cs.DISTANCE):

343 if arcmode: # or f_0_01

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

345 # AB1 = _E0 * (E2 - _E1)

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

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

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

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

350 else:

351 s12 = s12_a12

352 r.set_(s12=s12)

353

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

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

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

357

358 if (outmask & Cs.LONGITUDE):

359 schi1 = self._somg1

360 cchi1 = self._cchi1

361 schi2 = ssig2 * salp0

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

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

364 -self._H1, sig12)

365 if (outmask & Cs.LONG_UNROLL):

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

367 tchi1 = t * schi1

368 tchi2 = t * schi2

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

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

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

372 else:

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

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

375 r.set_(lon2=lon2)

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

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

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

379

380 if (outmask & Cs.LATITUDE):

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

382

383 if (outmask & Cs.AZIMUTH):

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

385

386 if (outmask & Cs._REDUCEDLENGTH_GEODESICSCALE):

387 dn1 = self._dn1

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

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

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

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

392 if (outmask & Cs.REDUCEDLENGTH):

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

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

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

396 -dn1 * (ssig1 * csig2),

397 -J12 * (csig1 * csig2)))

398 if (outmask & Cs.GEODESICSCALE):

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

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

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

402

403 if (outmask & Cs.AREA):

404 A4 = salp0 * calp0

405 if A4:

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

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

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

409 # If csig12 > 0, write

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

411 # else

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

413 # No need to normalize

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

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

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

417 A4 *= gX._e2a2

418 B41 = self._B41

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

420 S12 = (B42 - B41) * A4

421 else:

422 S12 = A4 = B41 = B42 = _0_0

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

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

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

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

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

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

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

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

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

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

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

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

435 r.set_(S12=S12)

436

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

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

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

440 azi1=_norm180(self.azi1))

441 return r

442

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

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

445

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

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

448 '''

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

450 return r.toDirect9Tuple()

451

452 def _GenSet(self, arcmode, s13_a13):

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

454 '''

455 if arcmode:

456 self.SetArc(s13_a13)

457 else:

458 self.SetDistance(s13_a13)

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

460

461 @Property_RO

462 def geodesic(self):

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

464 '''

465 assert isinstance(self._gX, _MODS.geodesicx.GeodesicExact)

466 return self._gX

467

468 @Property_RO

469 def _H0e2_f1(self):

470 '''(INTERNAL) Cached/memoized.

471 '''

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

473

474 @Property_RO

475 def _H1(self):

476 '''(INTERNAL) Cached/memoized.

477 '''

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

479

480 @Property_RO

481 def lat1(self):

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

483 '''

484 return self._lat1

485

486 @Property_RO

487 def lon1(self):

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

489 '''

490 return self._lon1

491

492 @Property_RO

493 def _lon1_norm180(self):

494 '''(INTERNAL) Cached/memoized.

495 '''

496 return _norm180(self._lon1)

497

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

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

500

501 @arg s12: Distance from the first point to the second (C{meter}).

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

503 the quantities to be returned.

504

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

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

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

508 except when C{a12=NAN}.

509

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

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

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

513

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

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

516 '''

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

518

519 @Property_RO

520 def s13(self):

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

522

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

524 '''

525 return self._s13

526

527 def SetArc(self, a13):

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

529

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

531 point (C{degrees}).

532

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

534 the reference point or C{NAN}.

535 '''

536 self._a13 = a13

537 self._s13 = s13 = self._GDictPosition(True, a13, Caps.DISTANCE).s12

538 _update_all(self)

539 return s13

540

541 def SetDistance(self, s13):

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

543

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

545

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

547 and the reference point or C{NAN}.

548 '''

549 self._s13 = s13

550 self._a13 = a13 = self._GDictPosition(False, s13, 0).a12

551 _update_all(self)

552 return a13 # NAN for GeodesicLineExact without Cap.DISTANCE_IN

553

554 @Property_RO

555 def _stau1_ctau1(self):

556 '''(INTERNAL) Cached/memoized.

557 '''

558 s, c = _sincos2(self._E1)

559 # tau1 = sig1 + B11

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

561 # unnecessary because Einv inverts E

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

563

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

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

566

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

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

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

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

571

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

573 '''

574 d = dict(geodesic=self.geodesic,

575 lat1=self.lat1, lon1=self.lon1, azi1=self.azi1,

576 a13=self.a13, s13=self.s13)

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

578

579

580__all__ += _ALL_DOCS(_GeodesicLineExact)

581

582# **) MIT License

583#

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

585#

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

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

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

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

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

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

592#

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

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

595#

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

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

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

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

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

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

602# OTHER DEALINGS IN THE SOFTWARE.