1

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

3

4 u'''Base classes C{RhumbBase} and C{RhumbLineBase}, pure Python version of I{Karney}'s C++

5 classes U{Rhumb<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>}

6 and U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>}

7 from I{GeographicLib versions 2.0} and I{2.2} and I{Karney}'s C++ example U{Rhumb intersect

8<https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/>}.

9

10 Class L{RhumbLine} has been enhanced with methods C{intersection2} and C{nearestOn4} to iteratively

11 find the intersection of two rhumb lines, respectively the nearest point on a rumb line along a

12 geodesic or perpendicular rhumb line from an other point.

13

14 For more details, see the C++ U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/index.html>}

15 documentation, especially the U{Class List<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>},

16 the background information on U{Rhumb lines<https://GeographicLib.SourceForge.io/C++/doc/rhumb.html>},

17 the utily U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>} and U{Online

18 rhumb line calculations<https://GeographicLib.SourceForge.io/cgi-bin/RhumbSolve>}.

19

20 Copyright (C) U{Charles Karney<mailto:Karney@Alum.MIT.edu>} (2014-2023) and licensed under the MIT/X11

21 License. For more information, see the U{GeographicLib<https://GeographicLib.SourceForge.io>} documentation.

22'''

23# make sure int/int division yields float quotient

24 from __future__ import division as _; del _ # PYCHOK semicolon

25

26# from pygeodesy.basics import unsigned0, _xinstanceof # from .karney

27 from pygeodesy.constants import EPS, EPS1, INT0, _EPSqrt as _TOL, NAN, \

28 _0_0, _0_01, _1_0, _90_0, _over

29# from pygeodesy.datums import _spherical_datum # from .formy

30# from pygeodesy.ellipsoids import _EWGS84 # from .karney

31 from pygeodesy.errors import IntersectionError, itemsorted, RhumbError, \

32 _xdatum, _xkwds, _Xorder

33# from pygeodesy.etm import ExactTransverseMercator # _MODS

34 from pygeodesy.fmath import euclid, favg, fabs, Fsum

35 from pygeodesy.formy import opposing, _spherical_datum

36# from pygeodesy.fsums import Fsum # from .fmath

37 from pygeodesy.interns import NN, _coincident_, _COMMASPACE_, _Dash, \

38 _intersection_, _no_, _parallel_, _under

39 from pygeodesy.karney import _atan2d, Caps, _CapsBase, _diff182, _fix90, \

40 GDict, _norm180, _EWGS84, unsigned0, _xinstanceof

41# from pygeodesy.ktm import KTransverseMercator, _AlpCoeffs # _MODS

42 from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS

43# from pygeodesy.named import notOverloaded # _MODS

44 from pygeodesy.namedTuples import Distance2Tuple, LatLon2Tuple, NearestOn4Tuple

45 from pygeodesy.props import deprecated_method, Property, Property_RO, property_RO, \

46 _update_all

47 from pygeodesy.streprs import Fmt, pairs, unstr

48 from pygeodesy.units import Float_, Lat, Lon, Meter, Int # PYCHOK shared

49 from pygeodesy.utily import atan2d, _azireversed, _loneg, sincos2d, sincos2d_, \

50 _unrollon, _Wrap, sincos2_ # PYCHOK shared

51 from pygeodesy.vector3d import _intersect3d3, Vector3d # in .intersection2 below

52

53# from math import fabs # from .fmath

54

55__all__ = ()

56__version__ = '23.09.20'

57

58_anti_ = _Dash('anti')

59_rls = [] # instances of C{RbumbLine...} to be updated

60_TRIPS = 65 # .intersection2, .nearestOn4, 19+

61

62

63 class _Lat(Lat):

64 '''(INTERNAL) Latitude B{C{lat}}.

65 '''

66 def __init__(self, *lat, **Error_name):

67 kwds = _xkwds(Error_name, clip=0, Error=RhumbError)

68 Lat.__new__(_Lat, *lat, **kwds)

69

70

71 class _Lon(Lon):

72 '''(INTERNAL) Longitude B{C{lon}}.

73 '''

74 def __init__(self, *lon, **Error_name):

75 kwds = _xkwds(Error_name, clip=0, Error=RhumbError)

76 Lon.__new__(_Lon, *lon, **kwds)

77

78

79 def _update_all_rls(r):

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

81 of any C{RhumbLine} instances tied to the given

82 C{Rhumb} instance B{C{r}}.

83 '''

84 # _xinstanceof(_MODS.rhumbaux.RhumbAux, _MODS.rhumbx.Rhumb, r=r)

85 _update_all(r)

86 for rl in _rls: # PYCHOK use weakref?

87 if rl._rhumb is r:

88 _update_all(rl)

89

90

91 class RhumbBase(_CapsBase):

92 '''(INTERNAL) Base class for C{rhumbaux.RhumbAux} and C{rhumbx.Rhumb}.

93 '''

94 _E = _EWGS84

95 _exact = True

96 _f_max = _0_01

97 _mTM = 6 # see .TMorder

98

99 def __init__(self, a_earth, f, exact, name):

100 '''New C{rhumbaux.RhumbAux} or C{rhumbx.Rhum}.

101 '''

102 if f is not None:

103 self.ellipsoid = a_earth, f

104 elif a_earth not in (_EWGS84, None):

105 self.ellipsoid = a_earth

106 if not exact:

107 self.exact = False

108 if name:

109 self.name = name

110

111 @Property_RO

112 def a(self):

113 '''Get the C{ellipsoid}'s equatorial radius, semi-axis (C{meter}).

114 '''

115 return self.ellipsoid.a

116

117 equatoradius = a

118

119 def ArcDirect(self, lat1, lon1, azi12, a12, outmask=Caps.LATITUDE_LONGITUDE):

120 '''Solve the I{direct rhumb} problem, optionally with area.

121

122 @arg lat1: Latitude of the first point (C{degrees90}).

123 @arg lon1: Longitude of the first point (C{degrees180}).

124 @arg azi12: Azimuth of the rhumb line (compass C{degrees}).

125 @arg a12: Angle along the rhumb line from the given to the

126 destination point (C{degrees}), can be negative.

127

128 @return: L{GDict} with 2 up to 8 items C{lat2, lon2, a12, S12,

129 lat1, lon1, azi12, s12} with the destination point's

130 latitude C{lat2} and longitude C{lon2} in C{degrees},

131 the rhumb angle C{a12} in C{degrees} and area C{S12}

132 under the rhumb line in C{meter} I{squared}.

133

134 @raise ImportError: Package C{numpy} not found or not installed,

135 only required for area C{S12} when C{B{exact}

136 is True} and L{RhumbAux}.

137

138 @note: If B{C{a12}} is large enough that the rhumb line crosses

139 a pole, the longitude of the second point is indeterminate

140 and C{NAN} is returned for C{lon2} and area C{S12}.

141

142 @note: If the given point is a pole, the cosine of its latitude is

143 taken to be C{sqrt(L{EPS})}. This position is extremely

144 close to the actual pole and allows the calculation to be

145 carried out in finite terms.

146 '''

147 s12 = a12 * self._mpd

148 return self._DirectRhumb(lat1, lon1, azi12, a12, s12, outmask)

149

150 @Property_RO

151 def b(self):

152 '''Get the C{ellipsoid}'s polar radius, semi-axis (C{meter}).

153 '''

154 return self.ellipsoid.b

155

156 polaradius = b

157

158 def _Direct(self, ll1, azi12, s12, **outmask):

159 '''(INTERNAL) Short-cut version, see .latlonBase.

160 '''

161 return self.Direct(ll1.lat, ll1.lon, azi12, s12, **outmask)

162

163 def Direct(self, lat1, lon1, azi12, s12, outmask=Caps.LATITUDE_LONGITUDE):

164 '''Solve the I{direct rhumb} problem, optionally with area.

165

166 @arg lat1: Latitude of the first point (C{degrees90}).

167 @arg lon1: Longitude of the first point (C{degrees180}).

168 @arg azi12: Azimuth of the rhumb line (compass C{degrees}).

169 @arg s12: Distance along the rhumb line from the given to

170 the destination point (C{meter}), can be negative.

171

172 @return: L{GDict} with 2 up to 8 items C{lat2, lon2, a12, S12,

173 lat1, lon1, azi12, s12} with the destination point's

174 latitude C{lat2} and longitude C{lon2} in C{degrees},

175 the rhumb angle C{a12} in C{degrees} and area C{S12}

176 under the rhumb line in C{meter} I{squared}.

177

178 @raise ImportError: Package C{numpy} not found or not installed,

179 only required for area C{S12} when C{B{exact}

180 is True} and L{RhumbAux}.

181

182 @note: If B{C{s12}} is large enough that the rhumb line crosses

183 a pole, the longitude of the second point is indeterminate

184 and C{NAN} is returned for C{lon2} and area C{S12}.

185

186 @note: If the given point is a pole, the cosine of its latitude is

187 taken to be C{sqrt(L{EPS})}. This position is extremely

188 close to the actual pole and allows the calculation to be

189 carried out in finite terms.

190 '''

191 a12 = _over(s12, self._mpd)

192 return self._DirectRhumb(lat1, lon1, azi12, a12, s12, outmask)

193

194 def Direct8(self, lat1, lon1, azi12, s12, outmask=Caps.LATITUDE_LONGITUDE_AREA):

195 '''Like method L{Rhumb.Direct} but returning a L{Rhumb8Tuple} with area C{S12}.

196 '''

197 return self.Direct(lat1, lon1, azi12, s12, outmask=outmask).toRhumb8Tuple()

198

199 def _DirectLine(self, ll1, azi12, **caps_name):

200 '''(INTERNAL) Short-cut version, see .latlonBase.

201 '''

202 return self.DirectLine(ll1.lat, ll1.lon, azi12, **caps_name)

203

204 def DirectLine(self, lat1, lon1, azi12, **caps_name):

205 '''Define a C{RhumbLine} in terms of the I{direct} rhumb

206 problem to compute several points on a single rhumb line.

207

208 @arg lat1: Latitude of the first point (C{degrees90}).

209 @arg lon1: Longitude of the first point (C{degrees180}).

210 @arg azi12: Azimuth of the rhumb line (compass C{degrees}).

211 @kwarg caps_name: Optional keyword arguments C{B{name}=NN} and

212 C{B{caps}=Caps.STANDARD}, a bit-or'ed combination of

213 L{Caps} values specifying the required capabilities.

214 Include C{Caps.LINE_OFF} if updates to the B{C{rhumb}}

215 should I{not} be reflected in this rhumb line.

216

217 @return: A C{RhumbLine...} instance and invoke its method

218 C{.Position} to compute each point.

219

220 @note: Updates to this rhumb are reflected in the returned

221 rhumb line, unless C{B{caps} |= Caps.LINE_OFF}.

222 '''

223 return self._RhumbLine(self, lat1, lon1, azi12, **caps_name)

224

225 Line = DirectLine # synonyms

226

227 def _DirectRhumb(self, lat1, lon1, azi12, a12, s12, outmask):

228 '''(INTERNAL) See methods C{.ArcDirect} and C{.Direct}.

229 '''

230 rl = self._RhumbLine(self, lat1, lon1, azi12, caps=Caps.LINE_OFF,

231 name=self.name)

232 return rl._Position(a12, s12, outmask | self._debug) # lat2, lon2, S12

233

234 @Property

235 def ellipsoid(self):

236 '''Get this rhumb's ellipsoid (L{Ellipsoid}).

237 '''

238 return self._E

239

240 @ellipsoid.setter # PYCHOK setter!

241 def ellipsoid(self, a_earth_f):

242 '''Set this rhumb's ellipsoid (L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or

243 L{a_f2Tuple}) or (equatorial) radius and flattening (2-tuple C{(a, f)}).

244

245 @raise RhumbError: If C{abs(B{f}} exceeds non-zero C{f_max} and C{exact=False}.

246 '''

247 E = _spherical_datum(a_earth_f, Error=RhumbError).ellipsoid

248 if self._E != E:

249 self._exactest(self.exact, E, self.f_max)

250 _update_all_rls(self)

251 self._E = E

252

253 @Property

254 def exact(self):

255 '''Get the I{exact} option (C{bool}).

256 '''

257 return self._exact

258

259 @exact.setter # PYCHOK setter!

260 def exact(self, exact):

261 '''Set the I{exact} option (C{bool}). If C{True}, use I{exact} rhumb

262 expressions, otherwise a series expansion (accurate for oblate or

263 prolate ellipsoids with C{abs(flattening)} below C{f_max}.

264

265 @raise RhumbError: If C{B{exact}=False} and C{abs(flattening})

266 exceeds non-zero C{f_max}.

267

268 @see: Option U{B{-s}<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}

269 and U{ACCURACY<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html#ACCURACY>}.

270 '''

271 x = bool(exact)

272 if self._exact != x:

273 self._exactest(x, self.ellipsoid, self.f_max)

274 _update_all_rls(self)

275 self._exact = x

276

277 def _exactest(self, exact, ellipsoid, f_max):

278 # Helper for property setters C{ellipsoid}, C{exact} and C{f_max}

279 if fabs(ellipsoid.f) > f_max > 0 and not exact:

280 raise RhumbError(exact=exact, f=ellipsoid.f, f_max=f_max)

281

282 @Property_RO

283 def f(self):

284 '''Get the C{ellipsoid}'s flattening (C{float}).

285 '''

286 return self.ellipsoid.f

287

288 flattening = f

289

290 @property

291 def f_max(self):

292 '''Get the I{max.} flattening (C{float}).

293 '''

294 return self._f_max

295

296 @f_max.setter # PYCHOK setter!

297 def f_max(self, f_max): # PYCHOK no cover

298 '''Set the I{max.} flattening, not to exceed (C{float}).

299

300 @raise RhumbError: If C{exact=False} and C{abs(flattening})

301 exceeds non-zero C{f_max}.

302 '''

303 f = Float_(f_max=f_max, low=_0_0, high=EPS1)

304 if self._f_max != f:

305 self._exactest(self.exact, self.ellipsoid, f)

306 self._f_max = f

307

308 def _Inverse(self, ll1, ll2, wrap, **outmask):

309 '''(INTERNAL) Short-cut version, see .latlonBase.

310 '''

311 if wrap:

312 ll2 = _unrollon(ll1, _Wrap.point(ll2))

313 return self.Inverse(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **outmask)

314

315 def Inverse(self, lat1, lon1, lat2, lon2, outmask=Caps.AZIMUTH_DISTANCE):

316 '''Solve the I{inverse rhumb} problem.

317

318 @arg lat1: Latitude of the first point (C{degrees90}).

319 @arg lon1: Longitude of the first point (C{degrees180}).

320 @arg lat2: Latitude of the second point (C{degrees90}).

321 @arg lon2: Longitude of the second point (C{degrees180}).

322

323 @return: L{GDict} with 4 to 8 items C{lat1, lon1, lat2, lon2,

324 azi12, s12, a12, S12, }, the rhumb line's azimuth

325 C{azi12} in compass C{degrees} between C{-180} and

326 C{+180}, the rhumb distance C{s12} and rhumb angle

327 C{a12} between both points in C{meter} respectively

328 C{degrees} and the area C{S12} under the rhumb line

329 in C{meter} I{squared}.

330

331 @raise ImportError: Package C{numpy} not found or not installed,

332 only required for L{RhumbAux} area C{S12}

333 when C{B{exact} is True}.

334

335 @note: The shortest rhumb line is found. If the end points are

336 on opposite meridians, there are two shortest rhumb lines

337 and the East-going one is chosen.

338

339 @note: If either point is a pole, the cosine of its latitude is

340 taken to be C{sqrt(L{EPS})}. This position is extremely

341 close to the actual pole and allows the calculation to be

342 carried out in finite terms.

343 '''

344 r = GDict(lat1=lat1, lon1=lon1, lat2=lat2, lon2=lon2, name=self.name)

345 Cs = Caps

346 if (outmask & Cs.AZIMUTH_DISTANCE_AREA):

347 lon12, _ = _diff182(lon1, lon2, K_2_0=True)

348 y, x, s1, s2 = self._Inverse4(lon12, r, outmask)

349 if (outmask & Cs.AZIMUTH):

350 r.set_(azi12=_atan2d(y, x))

351 if (outmask & Cs.AREA):

352 S12 = self._S12d(s1, s2, lon12)

353 r.set_(S12=unsigned0(S12)) # like .gx

354 return r

355

356 def _Inverse4(self, lon12, r, outmask): # PYCHOK no cover

357 '''I{Must be overloaded}, see function C{notOverloaded}.

358 '''

359 _MODS.named.notOverloaded(self, lon12, r, outmask)

360

361 def Inverse8(self, lat1, lon1, azi12, s12, outmask=Caps.AZIMUTH_DISTANCE_AREA):

362 '''Like method L{Rhumb.Inverse} but returning a L{Rhumb8Tuple} with area C{S12}.

363 '''

364 return self.Inverse(lat1, lon1, azi12, s12, outmask=outmask).toRhumb8Tuple()

365

366 def _InverseLine(self, ll1, ll2, wrap, **caps_name):

367 '''(INTERNAL) Short-cut version, see .latlonBase.

368 '''

369 if wrap:

370 ll2 = _unrollon(ll1, _Wrap.point(ll2))

371 return self.InverseLine(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **caps_name)

372

373 def InverseLine(self, lat1, lon1, lat2, lon2, **caps_name):

374 '''Define a C{RhumbLine} in terms of the I{inverse} rhumb problem.

375

376 @arg lat1: Latitude of the first point (C{degrees90}).

377 @arg lon1: Longitude of the first point (C{degrees180}).

378 @arg lat2: Latitude of the second point (C{degrees90}).

379 @arg lon2: Longitude of the second point (C{degrees180}).

380 @kwarg caps_name: Optional keyword arguments C{B{name}=NN} and

381 C{B{caps}=Caps.STANDARD}, a bit-or'ed combination of

382 L{Caps} values specifying the required capabilities.

383 Include C{Caps.LINE_OFF} if updates to the B{C{rhumb}}

384 should I{not} be reflected in this rhumb line.

385

386 @return: A C{RhumbLine...} instance and invoke its method

387 C{ArcPosition} or C{Position} to compute points.

388

389 @note: Updates to this rhumb are reflected in the returned

390 rhumb line, unless C{B{caps} |= Caps.LINE_OFF}.

391 '''

392 r = self.Inverse(lat1, lon1, lat2, lon2, outmask=Caps.AZIMUTH)

393 return self._RhumbLine(self, lat1, lon1, r.azi12, **caps_name)

394

395 @Property_RO

396 def _mpd(self): # PYCHOK no cover

397 '''I{Must be overloaded}, see function C{notOverloaded}.

398 '''

399 _MODS.named.notOverloaded(self)

400

401 @property_RO

402 def _RhumbLine(self): # PYCHOK no cover

403 '''I{Must be overloaded}, see function C{notOverloaded}.

404 '''

405 _MODS.named.notOverloaded(self)

406

407 def _S12d(self, s1, s2, lon): # PYCHOK no cover

408 '''I{Must be overloaded}, see function C{notOverloaded}.

409 '''

410 _MODS.named.notOverloaded(self, s1, s2, lon)

411

412 @Property

413 def TMorder(self):

414 '''Get the I{Transverse Mercator} order (C{int}, 4, 5, 6, 7 or 8).

415 '''

416 return self._mTM

417

418 @TMorder.setter # PYCHOK setter!

419 def TMorder(self, order):

420 '''Set the I{Transverse Mercator} order (C{int}, 4, 5, 6, 7 or 8).

421

422 @note: Setting C{TMorder} turns property C{exact} off, but only

423 for L{Rhumb} instances.

424 '''

425 m = _Xorder(_MODS.ktm._AlpCoeffs, RhumbError, TMorder=order)

426 if self._mTM != m:

427 _update_all_rls(self)

428 self._mTM = m

429 if self.exact and isinstance(self, _MODS.rhumbx.Rhumb):

430 self.exact = False

431

432 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK no cover

433 '''I{Must be overloaded}, see function C{notOverloaded}.

434 '''

435 _MODS.named.notOverloaded(self, prec=prec, sep=sep)

436

437

438 class RhumbLineBase(_CapsBase):

439 '''(INTERNAL) Base class for C{rhumbaux.RhumbLineAux} and C{rhumbx.RhumbLine}.

440 '''

441 _azi12 = _0_0

442 _calp = _1_0

443# _caps = 0

444# _debug = 0

445# _lat1 = _0_0

446# _lon1 = _0_0

447# _lon12 = _0_0

448 _Rhumb = RhumbBase # compatible C{Rhumb} class

449 _rhumb = None # C{Rhumb} instance

450 _salp = _0_0

451 _talp = _0_0

452

453 def __init__(self, rhumb, lat1, lon1, azi12, caps=Caps.STANDARD, name=NN):

454 '''New C{RhumbLine}.

455 '''

456 _xinstanceof(self._Rhumb, rhumb=rhumb)

457

458 self._lat1 = _Lat(lat1=_fix90(lat1))

459 self._lon1 = _Lon(lon1= lon1)

460 self._lon12 = _norm180(self._lon1)

461 if azi12: # non-zero, non-None

462 self.azi12 = _norm180(azi12)

463

464 n = name or rhumb.name

465 if n:

466 self.name=n

467

468 self._caps = caps

469 self._debug |= (caps | rhumb._debug) & Caps._DEBUG_DIRECT_LINE

470 if (caps & Caps.LINE_OFF): # copy to avoid updates

471 self._rhumb = rhumb.copy(deep=False, name=_under(rhumb.name))

472 else:

473 self._rhumb = rhumb

474 _rls.append(self)

475

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

477 if _rls: # may be empty or None

478 try: # PYCHOK no cover

479 _rls.remove(self)

480 except (TypeError, ValueError):

481 pass

482 self._rhumb = None

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

484

485 def ArcPosition(self, a12, outmask=Caps.LATITUDE_LONGITUDE):

486 '''Compute a point at a given angular distance on this rhumb line.

487

488 @arg a12: The angle along this rhumb line from its origin to the

489 point (C{degrees}), can be negative.

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

491 the quantities to be returned.

492

493 @return: L{GDict} with 4 to 8 items C{azi12, a12, s12, S12, lat2,

494 lon2, lat1, lon1} with latitude C{lat2} and longitude

495 C{lon2} of the point in C{degrees}, the rhumb distance

496 C{s12} in C{meter} from the start point of and the area

497 C{S12} under this rhumb line in C{meter} I{squared}.

498

499 @raise ImportError: Package C{numpy} not found or not installed,

500 only required for L{RhumbLineAux} area C{S12}

501 when C{B{exact} is True}.

502

503 @note: If B{C{a12}} is large enough that the rhumb line crosses a

504 pole, the longitude of the second point is indeterminate and

505 C{NAN} is returned for C{lon2} and area C{S12}.

506

507 If the first point is a pole, the cosine of its latitude is

508 taken to be C{sqrt(L{EPS})}. This position is extremely

509 close to the actual pole and allows the calculation to be

510 carried out in finite terms.

511 '''

512 return self._Position(a12, self.degrees2m(a12), outmask)

513

514 @Property

515 def azi12(self):

516 '''Get this rhumb line's I{azimuth} (compass C{degrees}).

517 '''

518 return self._azi12

519

520 @azi12.setter # PYCHOK setter!

521 def azi12(self, azi12):

522 '''Set this rhumb line's I{azimuth} (compass C{degrees}).

523 '''

524 z = _norm180(azi12)

525 if self._azi12 != z:

526 if self._rhumb:

527 _update_all(self)

528 self._azi12 = z

529 self._salp, self._calp = t = sincos2d(z) # no NEG0

530 self._talp = _over(*t)

531

532 @property_RO

533 def azi12_sincos2(self): # PYCHOK no cover

534 '''Get the sine and cosine of this rhumb line's I{azimuth} (2-tuple C{(sin, cos)}).

535 '''

536 return self._scalp, self._calp

537

538 def degrees2m(self, angle):

539 '''Convert an angular distance along this rhumb line to C{meter}.

540

541 @arg angle: Angular distance (C{degrees}).

542

543 @return: Distance (C{meter}).

544 '''

545 return float(angle) * self.rhumb._mpd

546

547 @deprecated_method

548 def distance2(self, lat, lon): # PYCHOK no cover

549 '''DEPRECATED, use method L{RhumbLineAux.Inverse} or L{RhumbLine.Inverse}.

550

551 @return: A L{Distance2Tuple}C{(distance, initial)} with the C{distance}

552 in C{meter} and C{initial} bearing (azimuth) in C{degrees}.

553 '''

554 r = self.Inverse(lat, lon)

555 return Distance2Tuple(r.s12, r.azi12)

556

557 @property_RO

558 def ellipsoid(self):

559 '''Get this rhumb line's ellipsoid (L{Ellipsoid}).

560 '''

561 return self.rhumb.ellipsoid

562

563 @property_RO

564 def exact(self):

565 '''Get this rhumb line's I{exact} option (C{bool}).

566 '''

567 return self.rhumb.exact

568

569 def intersection2(self, other, tol=_TOL, **eps):

570 '''I{Iteratively} find the intersection of this and an other rhumb line.

571

572 @arg other: The other rhumb line (C{RhumbLine}).

573 @kwarg tol: Tolerance for longitudinal convergence and parallel

574 error (C{degrees}).

575 @kwarg eps: Tolerance for L{pygeodesy.intersection3d3} (C{EPS}).

576

577 @return: A L{LatLon2Tuple}{(lat, lon)} with the C{lat}- and

578 C{lon}gitude of the intersection point.

579

580 @raise IntersectionError: No convergence for this B{C{tol}} or

581 no intersection for an other reason.

582

583 @see: Methods C{distance2} and C{nearestOn4} and function

584 L{pygeodesy.intersection3d3}.

585

586 @note: Each iteration involves a round trip to this rhumb line's

587 L{ExactTransverseMercator} or L{KTransverseMercator}

588 projection and invoking function L{pygeodesy.intersection3d3}

589 in that domain.

590 '''

591 _xinstanceof(RhumbLineBase, other=other)

592 _xdatum(self.rhumb, other.rhumb, Error=RhumbError)

593 try:

594 if other is self:

595 raise ValueError(_coincident_)

596 # make invariants and globals locals

597 _s_3d, s_az = self._xTM3d, self.azi12

598 _o_3d, o_az = other._xTM3d, other.azi12

599 p = opposing(s_az, o_az, margin=tol)

600 if p is not None: # == t in (True, False)

601 raise ValueError(_anti_(_parallel_) if p else _parallel_)

602 _diff = euclid # approximate length

603 _i3d3 = _intersect3d3 # NOT .vector3d.intersection3d3

604 _LL2T = LatLon2Tuple

605 _xTMr = self.xTM.reverse # ellipsoidal or spherical

606 # use halfway point as initial estimate

607 p = _LL2T(favg(self.lat1, other.lat1),

608 favg(self.lon1, other.lon1))

609 for i in range(1, _TRIPS):

610 v = _i3d3(_s_3d(p), s_az, # point + bearing

611 _o_3d(p), o_az, useZ=False, **eps)[0]

612 t = _xTMr(v.x, v.y, lon0=p.lon) # PYCHOK Reverse4Tuple

613 d = _diff(t.lon - p.lon, t.lat) # PYCHOK t.lat + p.lat - p.lat

614 p = _LL2T(t.lat + p.lat, t.lon) # PYCHOK t.lon + p.lon = lon0

615 if d < tol: # 19 trips

616 return _LL2T(p.lat, p.lon, iteration=i, # PYCHOK p...

617 name=self.intersection2.__name__)

618 except Exception as x:

619 raise IntersectionError(_no_(_intersection_), cause=x)

620 t = unstr(self.intersection2, other, **eps)

621 raise IntersectionError(Fmt.no_convergence(d, tol), txt=t)

622

623 def Inverse(self, lat2, lon2, wrap=False):

624 '''Return the rhumb angle, distance, azimuth, I{reverse} azimuth, etc. of

625 a rhumb line between the given point and this rhumb line's start point.

626

627 @arg lat2: Latitude of the point (C{degrees}).

628 @arg lon2: Longitude of the points (C{degrees}).

629 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{lat2}}

630 and B{C{lon2}} (C{bool}).

631

632 @return: L{GDict} with 8 items C{a12, s12, azi12, azi21, lat1, lon1,

633 lat2, lon2}, the rhumb angle C{a12} and rhumb distance C{s12}

634 between both points in C{degrees} respectively C{meter}, the

635 rhumb line's azimuth C{azi12} and I{reverse} azimuth C{azi21}

636 both in compass C{degrees} between C{-180} and C{+180}.

637 '''

638 if wrap:

639 _, lat2, lon2 = _Wrap.latlon3(self.lon1, _fix90(lat2), lon2)

640 r = self.rhumb.Inverse(self.lat1, self.lon1, lat2, lon2)

641 r.set_(azi21=_azireversed(r.azi12))

642 return r

643

644 @Property_RO

645 def isLoxodrome(self):

646 '''Is this rhumb line a loxodrome (C{True} if non-meridional and

647 non-parallel, C{False} if parallel or C{None} if meridional)?

648

649 @see: I{Osborne's} U{2.5 Rumb lines and loxodromes

650 <https://Zenodo.org/record/35392>}, page 37.

651 '''

652 return bool(self._salp) if self._calp else None

653

654 @Property_RO

655 def lat1(self):

656 '''Get this rhumb line's latitude (C{degrees90}).

657 '''

658 return self._lat1

659

660 @Property_RO

661 def lon1(self):

662 '''Get this rhumb line's longitude (C{degrees180}).

663 '''

664 return self._lon1

665

666 @Property_RO

667 def latlon1(self):

668 '''Get this rhumb line's lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}).

669 '''

670 return LatLon2Tuple(self.lat1, self.lon1)

671

672 def m2degrees(self, distance):

673 '''Convert a distance along this rhumb line to an angular distance.

674

675 @arg distance: Distance (C{meter}).

676

677 @return: Angular distance (C{degrees}).

678 '''

679 return _over(float(distance), self.rhumb._mpd)

680

681 @property_RO

682 def _mu1(self): # PYCHOK no cover

683 '''I{Must be overloaded}, see function C{notOverloaded}.

684 '''

685 _MODS.named.notOverloaded(self)

686

687 def _mu2lat(self, mu2): # PYCHOK no cover

688 '''I{Must be overloaded}, see function C{notOverloaded}.

689 '''

690 _MODS.named.notOverloaded(self, mu2)

691

692 def nearestOn4(self, lat, lon, tol=_TOL, exact=None, eps=EPS, est=None):

693 '''I{Iteratively} locate the point on this rhumb line nearest to the

694 given point, in part transcoded from I{Karney}'s C++ U{rhumb-intercept

695 <https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/>}.

696

697 @arg lat: Latitude of the point (C{degrees}).

698 @arg lon: Longitude of the point (C{degrees}).

699 @kwarg tol: Longitudinal convergence tolerance (C{degrees}) or the

700 distance tolerance (C(meter)) when C{B{exact} is None},

701 respectively C{not None}.

702 @kwarg exact: If C{None}, use a rhumb line perpendicular to this rhumb

703 line, otherwise use an I{exact} C{Geodesic...} from the

704 given point perpendicular to this rhumb line (C{bool} or

705 C{Geodesic...}), see method L{Ellipsoid.geodesic_}.

706 @kwarg eps: Optional tolerance for L{pygeodesy.intersection3d3}

707 (C{EPS}), used only if C{B{exact} is None}.

708 @kwarg est: Optional, initial estimate for the distance C{s13} of

709 the intersection I{along} this rhumb line (C{meter}),

710 used only if C{B{exact} is not None}.

711

712 @return: A L{NearestOn4Tuple}C{(lat, lon, distance, normal)} with

713 the C{lat}- and C{lon}gitude of the nearest point on and

714 the C{distance} in C{meter} to this rhumb line and the

715 C{normal} azimuth at the intersection.

716

717 @raise ImportError: I{Karney}'s U{geographiclib

718 <https://PyPI.org/project/geographiclib>}

719 package not found or not installed.

720

721 @raise IntersectionError: No convergence for this B{C{eps}} or

722 no intersection for an other reason.

723

724 @see: Methods C{distance2} and C{intersection2} and function

725 L{pygeodesy.intersection3d3}.

726 '''

727 if exact is None:

728 z = _norm180(self.azi12 + _90_0) # perpendicular azimuth

729 rl = RhumbLineBase(self.rhumb, lat, lon, z, caps=Caps.LINE_OFF)

730 p = self.intersection2(rl, tol=tol, eps=eps)

731 r = rl.Inverse(p.lat, p.lon)

732 r = NearestOn4Tuple(p.lat, p.lon, r.s12, z,

733 iteration=p.iteration)

734 else: # C{rhumb-intercept}

735 azi = self.azi12

736 szi = self._salp

737 E = self.ellipsoid

738 _gI = E.geodesic_(exact=exact).Inverse

739 Cs = Caps

740 gm = Cs._AZIMUTH_LATITUDE_LONGITUDE | Cs._REDUCEDLENGTH_GEODESICSCALE

741 if est is None: # get an estimate from the perpendicular

742 r = _gI(self.lat1, self.lon1, lat, lon, outmask=Cs.AZIMUTH_DISTANCE)

743 d, _ = _diff182(r.azi2, azi, K_2_0=True)

744 _, c = sincos2d(d)

745 s12 = c * r.s12 # signed

746 else:

747 s12 = Meter(est=est)

748 try:

749 tol = Float_(tol=tol, low=EPS, high=None)

750 # def _over(p, q): # see @note at RhumbLine[Aux].Position

751 # return (p / (q or _copysign(tol, q))) if isfinite(q) else NAN

752

753 _S12 = Fsum(s12).fsum2_

754 for i in range(1, _TRIPS): # suffix 1 == C++ 2, 2 == C++ 3

755 p = self.Position(s12) # outmask=Cs.LATITUDE_LONGITUDE

756 r = _gI(lat, lon, p.lat2, p.lon2, outmask=gm)

757 d, _ = _diff182(azi, r.azi2, K_2_0=True)

758 s, c, s2, c2 = sincos2d_(d, r.lat2)

759 c2 *= E.rocPrimeVertical(r.lat2) # aka rocTransverse

760 s *= _over(s2 * szi, c2) - _over(s * r.M21, r.m12)

761 s12, t = _S12(c / s) # XXX _over?

762 if fabs(t) < tol: # or fabs(c) < EPS

763 break

764 r = NearestOn4Tuple(r.lat2, r.lon2, s12, r.azi2,

765 iteration=i)

766 except Exception as x: # Fsum(NAN) Value-, ZeroDivisionError

767 t = unstr(self.nearestOn4, lat, lon, tol=tol, exact=exact,

768 iteration=i, eps=eps, est=est)

769 raise IntersectionError(t, cause=x)

770 return r

771

772 def Position(self, s12, outmask=Caps.LATITUDE_LONGITUDE):

773 '''Compute a point at a given distance on this rhumb line.

774

775 @arg s12: The distance along this rhumb line from its origin to

776 the point (C{meters}), can be negative.

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

778 the quantities to be returned.

779

780 @return: L{GDict} with 4 to 8 items C{azi12, a12, s12, S12, lat2,

781 lon2, lat1, lon1} with latitude C{lat2} and longitude

782 C{lon2} of the point in C{degrees}, the rhumb angle C{a12}

783 in C{degrees} from the start point of and the area C{S12}

784 under this rhumb line in C{meter} I{squared}.

785

786 @raise ImportError: Package C{numpy} not found or not installed,

787 only required for L{RhumbLineAux} area C{S12}

788 when C{B{exact} is True}.

789

790 @note: If B{C{s12}} is large enough that the rhumb line crosses a

791 pole, the longitude of the second point is indeterminate and

792 C{NAN} is returned for C{lon2} and area C{S12}.

793

794 If the first point is a pole, the cosine of its latitude is

795 taken to be C{sqrt(L{EPS})}. This position is extremely

796 close to the actual pole and allows the calculation to be

797 carried out in finite terms.

798 '''

799 return self._Position(self.m2degrees(s12), s12, outmask)

800

801 def _Position(self, a12, s12, outmask):

802 '''(INTERNAL) C{Arc-/Position} helper.

803 '''

804 r = GDict(azi12=self.azi12, a12=a12, s12=s12, name=self.name)

805 Cs = Caps

806 if (outmask & Cs.LATITUDE_LONGITUDE_AREA):

807 if a12 or s12:

808 mu12 = self._calp * a12

809 mu2 = self._mu1 + mu12

810 if fabs(mu2) > 90: # past pole

811 mu2 = _norm180(mu2) # reduce to [-180, 180)

812 if fabs(mu2) > 90: # point on anti-meridian

813 mu2 = _norm180(_loneg(mu2))

814 lat2 = self._mu2lat(mu2)

815 lon2 = S12 = NAN

816 else:

817 lat2, lon2, S1, S2 = self._Position4(a12, mu2, s12, mu12)

818 if (outmask & Cs.AREA):

819 S12 = self.rhumb._S12d(S1, S2, lon2)

820 S12 = unsigned0(S12) # like .gx

821# else:

822# S12 = None # unused

823 if (outmask & Cs.LONGITUDE):

824 if (outmask & Cs.LONG_UNROLL):

825 lon2 += self.lon1

826 else:

827 lon2 = _norm180(self._lon12 + lon2)

828 else: # coincident or outmask 0

829 lat2, lon2 = self.latlon1

830 S12 = _0_0

831

832 if (outmask & Cs.LATITUDE):

833 r.set_(lat2=lat2, lat1=self.lat1)

834 if (outmask & Cs.LONGITUDE):

835 r.set_(lon2=lon2, lon1=self.lon1)

836 if (outmask & Cs.AREA):

837 r.set_(S12=S12)

838 return r

839

840 def _Position4(self, a12, mu2, s12, mu12): # PYCHOK no cover

841 '''I{Must be overloaded}, see function C{notOverloaded}.

842 '''

843 _MODS.named.notOverloaded(self, a12, s12, mu2, mu12)

844

845 @Property_RO

846 def rhumb(self):

847 '''Get this rhumb line's rhumb (L{RhumbAux} or L{Rhumb}).

848 '''

849 return self._rhumb

850

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

852 '''Return this C{RhumbLine} as string.

853

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

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

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

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

858

859 @return: C{RhumbLine} (C{str}).

860 '''

861 d = dict(rhumb=self.rhumb, lat1=self.lat1, lon1=self.lon1,

862 azi12=self.azi12, exact=self.exact,

863 TMorder=self.TMorder, xTM=self.xTM)

864 return sep.join(pairs(itemsorted(d, asorted=False), prec=prec))

865

866 @property_RO

867 def TMorder(self):

868 '''Get this rhumb line's I{Transverse Mercator} order (C{int}, 4, 5, 6, 7 or 8).

869 '''

870 return self.rhumb.TMorder

871

872 @Property_RO

873 def xTM(self):

874 '''Get this rhumb line's I{Transverse Mercator} projection (L{ExactTransverseMercator}

875 if I{exact} and I{ellipsoidal}, otherwise L{KTransverseMercator} for C{TMorder}).

876 '''

877 E = self.ellipsoid

878 # ExactTransverseMercator doesn't handle spherical earth models

879 return _MODS.etm.ExactTransverseMercator(E) if self.exact and E.isEllipsoidal else \

880 _MODS.ktm.KTransverseMercator(E, TMorder=self.TMorder)

881

882 def _xTM3d(self, latlon0, z=INT0, V3d=Vector3d):

883 '''(INTERNAL) C{xTM.forward} this C{latlon1} to C{V3d} with B{C{latlon0}}

884 as current intersection estimate and central meridian.

885 '''

886 t = self.xTM.forward(self.lat1 - latlon0.lat, self.lon1, lon0=latlon0.lon)

887 return V3d(t.easting, t.northing, z)

888

889

890__all__ += _ALL_DOCS(RhumbBase, RhumbLineBase)

891

892 if __name__ == '__main__':

893

894 from pygeodesy import printf, Rhumb as R, RhumbAux as A

895

896 A = A(_EWGS84).Line(30, 0, 45)

897 R = R(_EWGS84).Line(30, 0, 45)

898

899 for i in range(1, 10):

900 s = .5e6 + 1e6 / i

901 a = A.Position(s).lon2

902 r = R.Position(s).lon2

903 e = (fabs(a - r) / a) if a else 0

904 printf('Position.lon2 %.14f vs %.14f, diff %g', r, a, e)

905

906 for exact in (None, False, True):

907 for est in (None, 1e6):

908 a = A.nearestOn4(60, 0, exact=exact, est=est)

909 r = R.nearestOn4(60, 0, exact=exact, est=est)

910 printf('%s, iteration=%s, exact=%s, est=%s\n%s, iteration=%s',

911 a.toRepr(), a.iteration, exact, est,

912 r.toRepr(), r.iteration, nl=1)

913

914# % python3 -m pygeodesy.rhumbBase

915

916# Position.lon2 11.61455846901637 vs 11.61455846901637, diff 1.52942e-16

917# Position.lon2 7.58982302826842 vs 7.58982302826842, diff 2.34045e-16

918# Position.lon2 6.28526067416369 vs 6.28526067416369, diff 2.82623e-16

919# Position.lon2 5.63938995325146 vs 5.63938995325146, diff 1.57495e-16

920# Position.lon2 5.25385527435707 vs 5.25385527435707, diff 0

921# Position.lon2 4.99764604290380 vs 4.99764604290380, diff 8.88597e-16

922# Position.lon2 4.81503363740473 vs 4.81503363740473, diff 1.84459e-16

923# Position.lon2 4.67828821748836 vs 4.67828821748835, diff 5.69553e-16

924# Position.lon2 4.57205667906283 vs 4.57205667906283, diff 1.94262e-16

925

926# NearestOn4Tuple(lat=45.0, lon=15.830286, distance=1977981.142985, normal=135.0), iteration=9, exact=None, est=None

927# NearestOn4Tuple(lat=45.0, lon=15.830286, distance=3278714.911694, normal=135.0), iteration=9

928

929# NearestOn4Tuple(lat=45.0, lon=15.830286, distance=1977981.142985, normal=135.0), iteration=9, exact=None, est=1000000.0

930# NearestOn4Tuple(lat=45.0, lon=15.830286, distance=3278714.911694, normal=135.0), iteration=9

931

932# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=5, exact=False, est=None

933# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=5

934

935# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=7, exact=False, est=1000000.0

936# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=7

937

938# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=5, exact=True, est=None

939# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=5

940

941# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=7, exact=True, est=1000000.0

942# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=7

943

944# **) MIT License

945#

946# Copyright (C) 2022-2023 -- mrJean1 at Gmail -- All Rights Reserved.

947#

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

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

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

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

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

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

954#

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

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

957#

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

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

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

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

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

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

964# OTHER DEALINGS IN THE SOFTWARE.