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__ = '23.09.22'

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 '''(INTERNAL) I{Must be overloaded}.'''

358 _MODS.named.notOverloaded(self, lon12, r, Caps.toStr(outmask))

359

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

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

362 '''

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

364

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

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

367 '''

368 if wrap:

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

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

371

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

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

374

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

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

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

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

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

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

381 L{Caps} values specifying the required capabilities.

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

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

384

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

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

387

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

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

390 '''

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

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

393

394 @Property_RO

395 def _mpd(self): # PYCHOK no cover

396 '''(INTERNAL) I{Must be overloaded}.'''

397 _MODS.named.notOverloaded(self)

398

399 @property_RO

400 def _RhumbLine(self): # PYCHOK no cover

401 '''(INTERNAL) I{Must be overloaded}.'''

402 _MODS.named.notOverloaded(self, underOK=True)

403

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

405 '''(INTERNAL) I{Must be overloaded}.'''

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

407

408 @Property

409 def TMorder(self):

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

411 '''

412 return self._mTM

413

414 @TMorder.setter # PYCHOK setter!

415 def TMorder(self, order):

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

417

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

419 for L{Rhumb} instances.

420 '''

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

422 if self._mTM != m:

423 _update_all_rls(self)

424 self._mTM = m

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

426 self.exact = False

427

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

429 '''I{Must be overloaded}.'''

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

431

432

433 class RhumbLineBase(_CapsBase):

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

435 '''

436 _azi12 = _0_0

437 _calp = _1_0

438# _caps = 0

439# _debug = 0

440# _lat1 = _0_0

441# _lon1 = _0_0

442# _lon12 = _0_0

443 _Rhumb = RhumbBase # compatible C{Rhumb} class

444 _rhumb = None # C{Rhumb} instance

445 _salp = _0_0

446 _talp = _0_0

447

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

449 '''New C{RhumbLine}.

450 '''

451 _xinstanceof(self._Rhumb, rhumb=rhumb)

452

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

454 self._lon1 = _Lon(lon1= lon1)

455 self._lon12 = _norm180(self._lon1)

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

457 self.azi12 = _norm180(azi12)

458

459 n = name or rhumb.name

460 if n:

461 self.name=n

462

463 self._caps = caps

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

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

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

467 else:

468 self._rhumb = rhumb

469 _rls.append(self)

470

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

472 if _rls: # may be empty or None

473 try: # PYCHOK no cover

474 _rls.remove(self)

475 except (TypeError, ValueError):

476 pass

477 self._rhumb = None

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

479

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

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

482

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

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

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

486 the quantities to be returned.

487

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

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

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

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

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

493

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

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

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

497

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

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

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

501

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

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

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

505 carried out in finite terms.

506 '''

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

508

509 @Property

510 def azi12(self):

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

512 '''

513 return self._azi12

514

515 @azi12.setter # PYCHOK setter!

516 def azi12(self, azi12):

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

518 '''

519 z = _norm180(azi12)

520 if self._azi12 != z:

521 if self._rhumb:

522 _update_all(self)

523 self._azi12 = z

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

525 self._talp = _over(*t)

526

527 @property_RO

528 def azi12_sincos2(self): # PYCHOK no cover

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

530 '''

531 return self._scalp, self._calp

532

533 def degrees2m(self, angle):

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

535

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

537

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

539 '''

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

541

542 @deprecated_method

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

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

545

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

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

548 '''

549 r = self.Inverse(lat, lon)

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

551

552 @property_RO

553 def ellipsoid(self):

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

555 '''

556 return self.rhumb.ellipsoid

557

558 @property_RO

559 def exact(self):

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

561 '''

562 return self.rhumb.exact

563

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

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

566

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

568 @kwarg tol: Tolerance for longitudinal convergence and parallel

569 error (C{degrees}).

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

571

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

573 C{lon}gitude of the intersection point.

574

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

576 no intersection for an other reason.

577

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

579 L{pygeodesy.intersection3d3}.

580

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

582 L{ExactTransverseMercator} or L{KTransverseMercator}

583 projection and invoking function L{pygeodesy.intersection3d3}

584 in that domain.

585 '''

586 _xinstanceof(RhumbLineBase, other=other)

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

588 try:

589 if other is self:

590 raise ValueError(_coincident_)

591 # make invariants and globals locals

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

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

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

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

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

597 _diff = euclid # approximate length

598 _i3d3 = _intersect3d3 # NOT .vector3d.intersection3d3

599 _LL2T = LatLon2Tuple

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

601 # use halfway point as initial estimate

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

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

604 for i in range(1, _TRIPS):

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

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

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

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

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

610 if d < tol: # 19 trips

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

612 name=self.intersection2.__name__)

613 except Exception as x:

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

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

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

617

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

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

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

621

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

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

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

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

626

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

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

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

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

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

632 '''

633 if wrap:

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

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

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

637 return r

638

639 @Property_RO

640 def isLoxodrome(self):

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

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

643

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

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

646 '''

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

648

649 @Property_RO

650 def lat1(self):

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

652 '''

653 return self._lat1

654

655 @Property_RO

656 def lon1(self):

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

658 '''

659 return self._lon1

660

661 @Property_RO

662 def latlon1(self):

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

664 '''

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

666

667 def m2degrees(self, distance):

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

669

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

671

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

673 '''

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

675

676 @property_RO

677 def _mu1(self): # PYCHOK no cover

678 '''(INTERNAL) I{Must be overloaded}.'''

679 _MODS.named.notOverloaded(self, underOK=True)

680

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

682 '''(INTERNAL) I{Must be overloaded}.'''

683 _MODS.named.notOverloaded(self, mu2, underOK=True)

684

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

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

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

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

689

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

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

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

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

694 respectively C{not None}.

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

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

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

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

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

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

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

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

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

704

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

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

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

708 C{normal} azimuth at the intersection.

709

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

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

712 package not found or not installed.

713

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

715 no intersection for an other reason.

716

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

718 L{pygeodesy.intersection3d3}.

719 '''

720 if exact is None:

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

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

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

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

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

726 iteration=p.iteration)

727 else: # C{rhumb-intercept}

728 azi = self.azi12

729 szi = self._salp

730 E = self.ellipsoid

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

732 Cs = Caps

733 gm = Cs._AZIMUTH_LATITUDE_LONGITUDE | Cs._REDUCEDLENGTH_GEODESICSCALE

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

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

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

737 _, c = sincos2d(d)

738 s12 = c * r.s12 # signed

739 else:

740 s12 = Meter(est=est)

741 try:

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

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

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

745

746 _S12 = Fsum(s12).fsum2_

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

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

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

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

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

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

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

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

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

756 break

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

758 iteration=i)

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

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

761 iteration=i, eps=eps, est=est)

762 raise IntersectionError(t, cause=x)

763 return r

764

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

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

767

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

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

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

771 the quantities to be returned.

772

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

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

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

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

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

778

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

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

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

782

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

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

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

786

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

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

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

790 carried out in finite terms.

791 '''

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

793

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

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

796 '''

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

798 Cs = Caps

799 if (outmask & Cs.LATITUDE_LONGITUDE_AREA):

800 if a12 or s12:

801 mu12 = self._calp * a12

802 mu2 = self._mu1 + mu12

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

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

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

806 mu2 = _norm180(_loneg(mu2))

807 lat2 = self._mu2lat(mu2)

808 lon2 = S12 = NAN

809 else:

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

811 if (outmask & Cs.AREA):

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

813 S12 = unsigned0(S12) # like .gx

814# else:

815# S12 = None # unused

816 if (outmask & Cs.LONGITUDE):

817 if (outmask & Cs.LONG_UNROLL):

818 lon2 += self.lon1

819 else:

820 lon2 = _norm180(self._lon12 + lon2)

821 else: # coincident or outmask 0

822 lat2, lon2 = self.latlon1

823 S12 = _0_0

824

825 if (outmask & Cs.LATITUDE):

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

827 if (outmask & Cs.LONGITUDE):

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

829 if (outmask & Cs.AREA):

830 r.set_(S12=S12)

831 return r

832

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

834 '''(INTERNAL) I{Must be overloaded}.'''

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

836

837 @Property_RO

838 def rhumb(self):

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

840 '''

841 return self._rhumb

842

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

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

845

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

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

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

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

850

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

852 '''

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

854 azi12=self.azi12, exact=self.exact,

855 TMorder=self.TMorder, xTM=self.xTM)

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

857

858 @property_RO

859 def TMorder(self):

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

861 '''

862 return self.rhumb.TMorder

863

864 @Property_RO

865 def xTM(self):

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

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

868 '''

869 E = self.ellipsoid

870 # ExactTransverseMercator doesn't handle spherical earth models

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

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

873

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

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

876 as current intersection estimate and central meridian.

877 '''

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

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

880

881

882__all__ += _ALL_DOCS(RhumbBase, RhumbLineBase)

883

884 if __name__ == '__main__':

885

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

887

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

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

890

891 for i in range(1, 10):

892 s = .5e6 + 1e6 / i

893 a = A.Position(s).lon2

894 r = R.Position(s).lon2

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

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

897

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

899 for est in (None, 1e6):

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

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

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

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

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

905

906# % python3 -m pygeodesy.rhumbBase

907

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

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

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

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

912# Position.lon2 5.25385527435707 vs 5.25385527435707, diff 0

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

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

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

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

917

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

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

920

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

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

923

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

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

926

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

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

929

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

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

932

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

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

935

936# **) MIT License

937#

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

939#

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

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

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

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

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

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

946#

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

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

949#

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

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

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

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

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

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

956# OTHER DEALINGS IN THE SOFTWARE.