Coverage for pygeodesy/rhumb/bases.py: 94%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''(INTERNAL) base classes C{RhumbBase} and C{RhumbLineBase}, pure Python version of I{Karney}'s 

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

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

7from 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 

10Class L{RhumbLineBase} has been enhanced with methods C{Intersecant2}, C{Intersection} and C{PlumbTo} 

11to iteratively find the intersection of a rhumb line and a circle or an other rhumb line, respectively 

12a perpendicular geodesic or other rhumb line. 

13 

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

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

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

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

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

19 

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

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

22''' 

23# make sure int/int division yields float quotient 

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

25 

26from pygeodesy.basics import _copysign, itemsorted, unsigned0, _xinstanceof 

27from pygeodesy.constants import EPS, EPS0, EPS1, INT0, NAN, _over, \ 

28 _EPSqrt as _TOL, _0_0, _0_01, _1_0, _90_0 

29from pygeodesy.datums import Datum, _earth_datum, _spherical_datum, _WGS84 

30from pygeodesy.errors import IntersectionError, RhumbError, _xdatum, \ 

31 _xkwds, _xkwds_pop2, _Xorder 

32# from pygeodesy.etm import ExactTransverseMercator # _MODS 

33from pygeodesy.fmath import euclid, favg, sqrt_a, Fsum 

34# from pygeodesy.formy import opposing # _MODS 

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

36from pygeodesy.interns import NN, _coincident_, _COMMASPACE_, _Dash, \ 

37 _dunder_nameof, _parallel_, _too_, _under 

38from pygeodesy.karney import _atan2d, Caps, _CapsBase, _diff182, _fix90, \ 

39 _norm180, GDict 

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

41from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS 

42from pygeodesy.namedTuples import Distance2Tuple, LatLon2Tuple 

43from pygeodesy.props import deprecated_method, Property, Property_RO, \ 

44 property_RO, _update_all 

45from pygeodesy.streprs import Fmt, pairs 

46from pygeodesy.units import Float_, Lat, Lon, Meter, Radius_, Int # PYCHOK shared 

47from pygeodesy.utily import acos1, _azireversed, _loneg, sincos2d, sincos2d_, \ 

48 _unrollon, _Wrap 

49from pygeodesy.vector3d import _intersect3d3, Vector3d # in .Intersection below 

50 

51from math import cos, fabs 

52 

53__all__ = () 

54__version__ = '24.04.07' 

55 

56_anti_ = _Dash('anti') 

57_rls = [] # instances of C{RbumbLine...} to be updated 

58_TRIPS = 65 # .Intersection, .PlumbTo, 19+ 

59 

60 

61class _Lat(Lat): 

62 '''(INTERNAL) Latitude B{C{lat}}. 

63 ''' 

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

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

66 Lat.__new__(_Lat, *lat, **kwds) 

67 

68 

69class _Lon(Lon): 

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

71 ''' 

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

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

74 Lon.__new__(_Lon, *lon, **kwds) 

75 

76 

77def _update_all_rls(r): 

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

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

80 C{Rhumb} instance B{C{r}}. 

81 ''' 

82 # _xinstanceof(_MODS.rhumb.aux_.RhumbAux, _MODS.rhumb.ekx.Rhumb, r=r) 

83 _update_all(r) 

84 for rl in _rls: # PYCHOK use weakref? 

85 if rl._rhumb is r: 

86 _update_all(rl) 

87 

88 

89class RhumbBase(_CapsBase): 

90 '''(INTERNAL) Base class for C{rhumb.aux_.RhumbAux} and C{rhumb.ekx.Rhumb}. 

91 ''' 

92 _datum = _WGS84 

93 _exact = True 

94 _f_max = _0_01 

95 _mTM = 6 # see .TMorder 

96 

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

98 '''New C{RhumbAux} or C{Rhumb}. 

99 ''' 

100 _earth_datum(self, a_earth, f=f, name=name) 

101 if not exact: 

102 self.exact = False 

103 if name: 

104 self.name = name 

105 

106 @Property_RO 

107 def a(self): 

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

109 ''' 

110 return self.ellipsoid.a 

111 

112 equatoradius = a 

113 

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

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

116 

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

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

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

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

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

122 

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

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

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

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

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

128 

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

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

131 is True} and L{RhumbAux}. 

132 

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

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

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

136 

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

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

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

140 carried out in finite terms. 

141 ''' 

142 s12 = a12 * self._mpd 

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

144 

145 @Property_RO 

146 def b(self): 

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

148 ''' 

149 return self.ellipsoid.b 

150 

151 polaradius = b 

152 

153 @property 

154 def datum(self): 

155 '''Get this rhumb's datum (L{Datum}). 

156 ''' 

157 return self._datum 

158 

159 @datum.setter # PYCHOK setter! 

160 def datum(self, datum): 

161 '''Set this rhumb's datum (L{Datum}). 

162 

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

164 ''' 

165 _xinstanceof(Datum, datum=datum) 

166 if self._datum != datum: 

167 self._exactest(self.exact, datum.ellipsoid, self.f_max) 

168 _update_all_rls(self) 

169 self._datum = datum 

170 

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

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

173 ''' 

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

175 

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

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

178 

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

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

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

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

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

184 

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

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

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

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

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

190 

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

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

193 is True} and L{RhumbAux}. 

194 

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

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

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

198 

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

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

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

202 carried out in finite terms. 

203 ''' 

204 a12 = _over(s12, self._mpd) 

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

206 

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

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

209 ''' 

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

211 

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

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

214 ''' 

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

216 

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

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

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

220 

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

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

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

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

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

226 L{Caps} values specifying the required capabilities. 

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

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

229 

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

231 C{.Position} to compute each point. 

232 

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

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

235 ''' 

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

237 

238 Line = DirectLine # synonyms 

239 

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

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

242 ''' 

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

244 name=self.name) 

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

246 

247 @Property 

248 def ellipsoid(self): 

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

250 ''' 

251 return self.datum.ellipsoid 

252 

253 @ellipsoid.setter # PYCHOK setter! 

254 def ellipsoid(self, a_earth_f): 

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

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

257 

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

259 ''' 

260 self.datum = _spherical_datum(a_earth_f, Error=RhumbError) 

261 

262 @Property 

263 def exact(self): 

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

265 ''' 

266 return self._exact 

267 

268 @exact.setter # PYCHOK setter! 

269 def exact(self, exact): 

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

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

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

273 

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

275 exceeds non-zero C{f_max}. 

276 

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

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

279 ''' 

280 x = bool(exact) 

281 if self._exact != x: 

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

283 _update_all_rls(self) 

284 self._exact = x 

285 

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

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

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

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

290 

291 @Property_RO 

292 def f(self): 

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

294 ''' 

295 return self.ellipsoid.f 

296 

297 flattening = f 

298 

299 @property 

300 def f_max(self): 

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

302 ''' 

303 return self._f_max 

304 

305 @f_max.setter # PYCHOK setter! 

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

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

308 

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

310 exceeds non-zero C{f_max}. 

311 ''' 

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

313 if self._f_max != f: 

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

315 self._f_max = f 

316 

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

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

319 ''' 

320 if wrap: 

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

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

323 

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

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

326 

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

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

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

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

331 

332 @return: L{GDict} with 4 to 9 items C{lat1, lon1, lat2, lon2, 

333 azi12, azi21, s12, a12, S12}, the rhumb line's azimuth 

334 C{azi12} and I{reverse} azimuth C{azi21}, both in 

335 compass C{degrees} between C{-180} and C{+180}, the 

336 rhumb distance C{s12} and rhumb angle C{a12} between 

337 both points in C{meter} respectively C{degrees} and 

338 the area C{S12} under the rhumb line in C{meter} 

339 I{squared}. 

340 

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

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

343 when C{B{exact} is True}. 

344 

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

346 on opposite meridians, there are two shortest rhumb lines 

347 and the East-going one is chosen. 

348 

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

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

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

352 carried out in finite terms. 

353 ''' 

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

355 Cs = Caps 

356 if (outmask & Cs.AZIMUTH_DISTANCE_AREA): 

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

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

359 if (outmask & Cs.AZIMUTH): 

360 z = _atan2d(y, x) 

361 r.set_(azi12=z, azi21=_azireversed(z)) 

362 if (outmask & Cs.AREA): 

363 S12 = self._S12d(s1, s2, lon12) 

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

365 return r 

366 

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

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

369 self._notOverloaded(lon12, r, Caps.toStr(outmask)) # underOK=True 

370 

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

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

373 ''' 

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

375 

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

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

378 ''' 

379 if wrap: 

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

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

382 

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

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

385 

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

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

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

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

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

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

392 L{Caps} values specifying the required capabilities. 

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

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

395 

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

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

398 

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

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

401 ''' 

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

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

404 

405 @Property_RO 

406 def _mpd(self): # PYCHOK no cover 

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

408 _MODS.named.notOverloaded(self) 

409 

410 @property_RO 

411 def RAorder(self): 

412 '''Get the I{Rhumb Area} order, C{None} always. 

413 ''' 

414 return None 

415 

416 @property_RO 

417 def _RhumbLine(self): # PYCHOK no cover 

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

419 self._notOverloaded(underOK=True) 

420 

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

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

423 self._notOverloaded(s1, s2, lon) # underOK=True 

424 

425 @Property 

426 def TMorder(self): 

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

428 ''' 

429 return self._mTM 

430 

431 @TMorder.setter # PYCHOK setter! 

432 def TMorder(self, order): 

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

434 

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

436 for L{Rhumb} instances. 

437 ''' 

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

439 if self._mTM != m: 

440 _update_all_rls(self) 

441 self._mTM = m 

442 if self.exact and isinstance(self, _MODS.rhumb.ekx.Rhumb): 

443 self.exact = False 

444 

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

446 '''Return this C{Rhumb} as string. 

447 

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

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

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

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

452 

453 @return: Tuple items (C{str}). 

454 ''' 

455 d = dict(ellipsoid=self.ellipsoid, RAorder=self.RAorder, 

456 exact=self.exact, TMorder=self.TMorder) 

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

458 

459 

460class RhumbLineBase(_CapsBase): 

461 '''(INTERNAL) Base class for C{rhumb.aux_.RhumbLineAux} and C{rhumb.ekx.RhumbLine}. 

462 ''' 

463 _azi12 = _0_0 

464 _calp = _1_0 

465# _caps = \ 

466# _debug = 0 

467# _lat1 = \ 

468# _lon1 = \ 

469# _lon12 = _0_0 

470 _Rhumb = RhumbBase # compatible C{Rhumb} class 

471 _rhumb = None # C{Rhumb} instance 

472 _salp = \ 

473 _talp = _0_0 

474 

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

476 '''New C{RhumbLine} or C{RhumbLineAux}. 

477 ''' 

478 _xinstanceof(self._Rhumb, rhumb=rhumb) 

479 

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

481 self._lon1 = _Lon(lon1= lon1) 

482 self._lon12 = _norm180(self._lon1) 

483 if azi12: # non-zero, non-None 

484 self.azi12 = _norm180(azi12) 

485 

486 n = name or rhumb.name 

487 if n: 

488 self.name=n 

489 

490 self._caps = caps 

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

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

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

494 else: 

495 self._rhumb = rhumb 

496 _rls.append(self) 

497 

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

499 if _rls: # may be empty or None 

500 try: # PYCHOK no cover 

501 _rls.remove(self) 

502 except (TypeError, ValueError): 

503 pass 

504 self._rhumb = None 

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

506 

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

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

509 

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

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

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

513 the quantities to be returned. 

514 

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

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

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

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

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

520 

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

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

523 when C{B{exact} is True}. 

524 

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

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

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

528 

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

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

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

532 carried out in finite terms. 

533 ''' 

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

535 

536 @Property 

537 def azi12(self): 

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

539 ''' 

540 return self._azi12 

541 

542 @azi12.setter # PYCHOK setter! 

543 def azi12(self, azi12): 

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

545 ''' 

546 z = _norm180(azi12) 

547 if self._azi12 != z: 

548 if self._rhumb: 

549 _update_all(self) 

550 self._azi12 = z 

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

552 self._talp = _over(*t) 

553 

554 @property_RO 

555 def azi12_sincos2(self): # PYCHOK no cover 

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

557 ''' 

558 return self._scalp, self._calp 

559 

560 @property_RO 

561 def datum(self): 

562 '''Get this rhumb line's datum (L{Datum}). 

563 ''' 

564 return self.rhumb.datum 

565 

566 def degrees2m(self, angle): 

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

568 

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

570 

571 @return: Distance (C{meter}). 

572 ''' 

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

574 

575 @deprecated_method 

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

577 '''DEPRECATED on 23.09.23, use method L{RhumbLineAux.Inverse} or L{RhumbLine.Inverse}. 

578 

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

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

581 ''' 

582 r = self.Inverse(lat, lon) 

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

584 

585 @property_RO 

586 def ellipsoid(self): 

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

588 ''' 

589 return self.rhumb.ellipsoid 

590 

591 @property_RO 

592 def exact(self): 

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

594 ''' 

595 return self.rhumb.exact 

596 

597 def Intersecant2(self, lat0, lon0, radius, napier=True, **tol_eps): 

598 '''Compute the intersection(s) of this rhumb line and a circle. 

599 

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

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

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

603 @kwarg napier: If C{True}, apply I{Napier}'s spherical triangle 

604 instead of planar trigonometry (C{bool}). 

605 @kwarg tol_eps: Optional keyword arguments, see method 

606 method L{Intersection} for further details. 

607 

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

609 a rhumb chord), each a L{GDict} from method L{Intersection} 

610 extended to 18 items by C{lat3, lon3, azi03, a03, s03} 

611 with azimuth C{azi03} of, distance C{a03} in C{degrees} 

612 and C{s03} in C{meter} along the rhumb line from the circle 

613 C{lat0, lon0} to the chord center C{lat3, lon3}. If this 

614 rhumb line is tangential to the circle, both points 

615 are the same L{GDict} instance with distances C{s02} and 

616 C{s03} near-equal to the B{C{radius}}. 

617 

618 @raise IntersectionError: The circle and this rhumb line 

619 do not intersect. 

620 

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

622 ''' 

623 r = Radius_(radius) 

624 p = q = self.PlumbTo(lat0, lon0, exact=None, **tol_eps) 

625 a = q.s02 

626 t = dict(lat3=q.lat2, lon3=q.lon2, azi03=q.azi02, a03=q.a02, s03=a) 

627 if a < r: 

628 t.update(iteration=q.iteration, lat0=q.lat1, lon0=q.lon1, # or lat0, lon0 

629 name=_dunder_nameof(self.Intersecant2, self.name)) 

630 if fabs(a) < EPS0: # coincident centers 

631 d, h = _0_0, r 

632 else: 

633 d = q.s12 

634 if napier: # Napier rule (R1) cos(b) = cos(c) / cos(a) 

635 # <https://WikiPedia.org/wiki/Spherical_trigonometry> 

636 m = self.rhumb._mpr 

637 h = (acos1(cos(r / m) / cos(a / m)) * m) if m else _0_0 

638 else: 

639 h = _copysign(sqrt_a(r, a), a) 

640 p = q = self.Position(d + h).set_(**t) 

641 if h: 

642 q = self.Position(d - h).set_(**t) 

643 elif a > r: 

644 t = _too_(Fmt.distant(a)) 

645 raise IntersectionError(self, lat0, lon0, radius, 

646 txt=t, **tol_eps) 

647 else: # tangential 

648 q.set_(**t) # == p.set(_**t) 

649 return p, q 

650 

651 @deprecated_method 

652 def intersection2(self, other, **tol_eps): # PYCHOK no cover 

653 '''DEPRECATED on 23.10.10, use method L{Intersection}.''' 

654 p = self.Intersection(other, **tol_eps) 

655 r = LatLon2Tuple(p.lat2, p.lon2, name=self.intersection2.__name__) 

656 r._iteration = p.iteration 

657 return r 

658 

659 def Intersection(self, other, tol=_TOL, **eps): 

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

661 

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

663 @kwarg tol: Tolerance for longitudinal convergence and parallel 

664 error (C{degrees}). 

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

666 

667 @return: The intersection point, a L{Position}-like L{GDict} with 

668 13 items C{lat1, lon1, azi12, a12, s12, lat2, lon2, lat0, 

669 lon0, azi02, a02, s02, at} with the rhumb angle C{a02} 

670 and rhumb distance C{s02} between the start point C{lat0, 

671 lon0} of the B{C{other}} rhumb line and the intersection 

672 C{lat2, lon2}, the azimuth C{azi02} of the B{C{other}} 

673 rhumb line and the angle C{at} between both rhumb lines. 

674 See method L{Position} for further details. 

675 

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

677 no intersection for an other reason. 

678 

679 @see: Methods C{distance2} and C{PlumbTo} and function 

680 L{pygeodesy.intersection3d3}. 

681 

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

683 L{ExactTransverseMercator} or L{KTransverseMercator} 

684 projection and function L{pygeodesy.intersection3d3} in 

685 that domain. 

686 ''' 

687 _xinstanceof(RhumbLineBase, other=other) 

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

689 try: 

690 if self.others(other) is self: 

691 raise ValueError(_coincident_) 

692 # make invariants and globals locals 

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

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

695 p = _MODS.formy.opposing(s_az, o_az, margin=tol) 

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

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

698 _diff = euclid # approximate length 

699 _i3d3 = _intersect3d3 # NOT .vector3d.intersection3d3 

700 _LL2T = LatLon2Tuple 

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

702 # use halfway point as initial estimate 

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

704 favg(self.lon1, other.lon1)) 

705 for i in range(1, _TRIPS): 

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

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

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

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

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

711 if d < tol: # 19 trips 

712 break 

713 else: 

714 raise ValueError(Fmt.no_convergence(d, tol)) 

715 

716 P = GDict(lat1=self.lat1, lat2=p.lat, lat0=other.lat1, 

717 lon1=self.lon1, lon2=p.lon, lon0=other.lon1, 

718 name=_dunder_nameof(self.Intersection, self.name)) 

719 r = self.Inverse( p.lat, p.lon, outmask=Caps.DISTANCE) 

720 t = other.Inverse(p.lat, p.lon, outmask=Caps.DISTANCE) 

721 P.set_(azi12= self.azi12, a12=r.a12, s12=r.s12, 

722 azi02=other.azi12, a02=t.a12, s02=t.s12, 

723 at=other.azi12 - self.azi12, iteration=i) 

724 except Exception as x: 

725 raise IntersectionError(self, other, tol=tol, 

726 eps=eps, cause=x) 

727 return P 

728 

729 def Inverse(self, lat2, lon2, wrap=False, **outmask): 

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

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

732 

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

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

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

736 and B{C{lon2}} (C{bool}). 

737 

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

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

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

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

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

743 ''' 

744 if wrap: 

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

746 r = self.rhumb.Inverse(self.lat1, self.lon1, lat2, lon2, **outmask) 

747 return r 

748 

749 @Property_RO 

750 def isLoxodrome(self): 

751 '''Is this rhumb line a meridional (C{None}), a parallel 

752 (C{False}) or a C{True} loxodrome? 

753 

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

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

756 ''' 

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

758 

759 @Property_RO 

760 def lat1(self): 

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

762 ''' 

763 return self._lat1 

764 

765 @Property_RO 

766 def lon1(self): 

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

768 ''' 

769 return self._lon1 

770 

771 @Property_RO 

772 def latlon1(self): 

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

774 ''' 

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

776 

777 def m2degrees(self, distance): 

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

779 

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

781 

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

783 ''' 

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

785 

786 @property_RO 

787 def _mu1(self): # PYCHOK no cover 

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

789 self._notOverloaded(underOK=True) 

790 

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

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

793 self._notOverloaded(mu2) # underOK=True 

794 

795 @deprecated_method 

796 def nearestOn4(self, lat0, lon0, **exact_eps_est_tol): # PYCHOK no cover 

797 '''DEPRECATED on 23.10.10, use method L{PlumbTo}.''' 

798 P = self.PlumbTo(lat0, lon0, **exact_eps_est_tol) 

799 r = _MODS.deprecated.classes.NearestOn4Tuple(P.lat2, P.lon2, P.s12, P.azi02, 

800 name=self.nearestOn4.__name__) 

801 r._iteration = P.iteration 

802 return r 

803 

804 @deprecated_method 

805 def NearestOn(self, lat0, lon0, **exact_eps_est_tol): # PYCHOK no cover 

806 '''DEPRECATED on 23.10.30, use method L{PlumbTo}.''' 

807 return self.PlumbTo(lat0, lon0, **exact_eps_est_tol) 

808 

809 def PlumbTo(self, lat0, lon0, exact=None, eps=EPS, est=None, tol=_TOL): 

810 '''Compute the I{perpendicular} intersection of this rhumb line with a geodesic 

811 from the given point (transcoded from I{Karney}'s C++ U{rhumb-intercept 

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

813 

814 @arg lat0: Latitude of the point on the geodesic (C{degrees}). 

815 @arg lon0: Longitude of the point on the geodesic (C{degrees}). 

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

817 otherwise use an I{exact} C{Geodesic...} from the given point 

818 perpendicular to this rhumb line (C{bool} or C{Geodesic...}), 

819 see method L{Ellipsoid.geodesic_}. 

820 @kwarg eps: Optional tolerance for L{pygeodesy.intersection3d3} (C{EPS}), 

821 used only if C{B{exact} is None}. 

822 @kwarg est: Optionally, an initial estimate for the distance C{s12} of the 

823 intersection I{along} this rhumb line (C{meter}), used only if 

824 C{B{exact} is not None}. 

825 @kwarg tol: Longitudinal convergence tolerance (C{degrees}) or distance 

826 tolerance (C(meter)) when C{B{exact} is None}, respectively 

827 C{not None}. 

828 

829 @return: The intersection point on this rhumb line, a L{GDict} from method 

830 L{Intersection} if B{C{exact}=None}. If C{B{exact} is not None}, 

831 a L{Position}-like L{GDict} of 13 items C{azi12, a12, s12, lat2, 

832 lat1, lat0, lon2, lon1, lon0, azi0, a02, s02, at} with distance 

833 C{a02} in C{degrees} and C{s02} in C{meter} between the given point 

834 C{lat0, lon0} and the intersection C{lat2, lon2}, geodesic azimuth 

835 C{azi0} at the given point and the (perpendicular) angle C{at} 

836 between the geodesic and this rhumb line at the intersection. The 

837 I{geodesic} azimuth at the intersection is C{(at + azi12)}. See 

838 method L{Position} for further details. 

839 

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

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

842 package not found or not installed. 

843 

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

845 intersection for some other reason. 

846 

847 @see: Methods C{distance2}, C{Intersecant2} and C{Intersection} 

848 and function L{pygeodesy.intersection3d3}. 

849 ''' 

850 Cs, tol = Caps, Float_(tol=tol, low=EPS, high=None) 

851 

852# def _over(p, q): # see @note at method C{.Position} 

853# if p: 

854# p = (p / (q or _copysign(tol, q))) if isfinite(q) else NAN 

855# return p 

856 

857 if exact is None: 

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

859 rl = RhumbLineBase(self.rhumb, lat0, lon0, z, caps=Cs.LINE_OFF) 

860 P = self.Intersection(rl, tol=tol, eps=eps) 

861 

862 else: # C{rhumb-intercept} 

863 E = self.ellipsoid 

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

865 gm = Cs.STANDARD | Cs._REDUCEDLENGTH_GEODESICSCALE # ^ Cs.DISTANCE_IN 

866 if est is None: # get an estimate from the "perpendicular" geodesic 

867 r = _gI(self.lat1, self.lon1, lat0, lon0, outmask=Cs.AZIMUTH_DISTANCE) 

868 d, _ = _diff182(r.azi2, self.azi12, K_2_0=True) 

869 _, s12 = sincos2d(d) 

870 s12 *= r.s12 # signed 

871 else: 

872 s12 = Meter(est=est) 

873 try: 

874 _abs = fabs 

875 _d2 = _diff182 

876 _ErT = E.rocPrimeVertical # aka rocTransverse 

877 _ovr = _over 

878 _S12 = Fsum(s12).fsum2f_ 

879 _scd = sincos2d_ 

880 for i in range(1, _TRIPS): # 9+, suffix 1 == C++ 2, 2 == C++ 3 

881 P = self.Position(s12) # outmask=Cs.LATITUDE_LONGITUDE 

882 r = _gI(lat0, lon0, P.lat2, P.lon2, outmask=gm) 

883 d, _ = _d2(self.azi12, r.azi2, K_2_0=True) 

884 s, c, s2, c2 = _scd(d, r.lat2) 

885 c2 *= _ErT(r.lat2) 

886 s *= _ovr(s2 * self._salp, c2) - _ovr(s * r.M21, r.m12) 

887 s12, t = _S12(c / s) # XXX _ovr? 

888 if _abs(t) < tol: # or _abs(c) < EPS 

889 break 

890 P.set_(azi0=r.azi1, a02=r.a12, s02=r.s12, # azi2=r.azi2, 

891 lat0=lat0, lon0=lon0, iteration=i, at=r.azi2 - self.azi12, 

892 name=_dunder_nameof(self.PlumbTo, self.name)) 

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

894 raise IntersectionError(lat0, lon0, tol=tol, exact=exact, 

895 eps=eps, est=est, iteration=i, cause=x) 

896 

897 return P 

898 

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

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

901 

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

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

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

905 the quantities to be returned. 

906 

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

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

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

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

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

912 

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

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

915 when C{B{exact} is True}. 

916 

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

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

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

920 

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

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

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

924 carried out in finite terms. 

925 ''' 

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

927 

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

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

930 ''' 

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

932 Cs = Caps 

933 if (outmask & Cs.LATITUDE_LONGITUDE_AREA): 

934 if a12 or s12: 

935 mu12 = self._calp * a12 

936 mu2 = self._mu1 + mu12 

937 if fabs(mu2) > 90: # past pole 

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

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

940 mu2 = _norm180(_loneg(mu2)) 

941 lat2 = self._mu2lat(mu2) 

942 lon2 = S12 = NAN 

943 else: 

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

945 if (outmask & Cs.AREA): 

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

947 S12 = unsigned0(S12) # like .gx 

948# else: 

949# S12 = None # unused 

950 if (outmask & Cs.LONGITUDE): 

951 if (outmask & Cs.LONG_UNROLL): 

952 lon2 += self.lon1 

953 else: 

954 lon2 = _norm180(self._lon12 + lon2) 

955 else: # coincident 

956 lat2, lon2 = self.latlon1 

957 S12 = _0_0 

958 

959 if (outmask & Cs.AREA): 

960 r.set_(S12=S12) 

961 if (outmask & Cs.LATITUDE): 

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

963 if (outmask & Cs.LONGITUDE): 

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

965 return r 

966 

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

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

969 self._notOverloaded(a12, s12, mu2, mu12) # underOK=True 

970 

971 @Property_RO 

972 def rhumb(self): 

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

974 ''' 

975 return self._rhumb 

976 

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

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

979 

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

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

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

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

984 

985 @return: C{RhumbLine} (C{str}). 

986 ''' 

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

988 azi12=self.azi12, exact=self.exact, 

989 TMorder=self.TMorder, xTM=self.xTM) 

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

991 

992 @property_RO 

993 def TMorder(self): 

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

995 ''' 

996 return self.rhumb.TMorder 

997 

998 @Property_RO 

999 def xTM(self): 

1000 '''Get this rhumb line's I{Transverse Mercator} projection (L{ExactTransverseMercator} 

1001 if I{exact} and I{ellipsoidal}, otherwise L{KTransverseMercator} for C{TMorder}). 

1002 ''' 

1003 E = self.ellipsoid 

1004 # ExactTransverseMercator doesn't handle spherical earth models 

1005 return _MODS.etm.ExactTransverseMercator(E) if self.exact and E.isEllipsoidal else \ 

1006 _MODS.ktm.KTransverseMercator(E, TMorder=self.TMorder) 

1007 

1008 def _xTM3d(self, latlon0, z=INT0, V3d=Vector3d): 

1009 '''(INTERNAL) C{xTM.forward} this C{latlon1} to C{V3d} with B{C{latlon0}} 

1010 as current intersection estimate and central meridian. 

1011 ''' 

1012 t = self.xTM.forward(self.lat1 - latlon0.lat, self.lon1, lon0=latlon0.lon) 

1013 return V3d(t.easting, t.northing, z) 

1014 

1015 

1016class _PseudoRhumbLine(RhumbLineBase): 

1017 '''(INTERNAL) Pseudo-rhumb line for a geodesic (line), see C{geodesicw._PlumbTo}. 

1018 ''' 

1019 def __init__(self, gl, name=NN): 

1020 R = RhumbBase(gl.geodesic.ellipsoid, None, True, name) 

1021 RhumbLineBase.__init__(self, R, gl.lat1, gl.lon1, 0, caps=Caps.LINE_OFF) 

1022 self._azi1 = self.azi12 = gl.azi1 

1023 self._gl = gl 

1024 self._gD = gl.geodesic.Direct 

1025 

1026 def PlumbTo(self, lat0, lon0, **exact_eps_est_tol): # PYCHOK signature 

1027 P = RhumbLineBase.PlumbTo(self, lat0, lon0, **exact_eps_est_tol) 

1028 z, P = _xkwds_pop2(P, azi12=None) 

1029 P.set_(azi1=self._gl.azi1, azi2=z) 

1030 return P # geodesic L{Position} 

1031 

1032 def Position(self, s12, **unused): # PYCHOK signature 

1033 r = self._gD(self.lat1, self.lon1, self._azi1, s12) 

1034 self._azi1 = r.azi1 

1035 self.azi12 = z = r.azi2 

1036 self._salp, _ = sincos2d(z) 

1037 return r.set_(azi12=z) 

1038 

1039 

1040__all__ += _ALL_DOCS(RhumbBase, RhumbLineBase) 

1041 

1042if __name__ == '__main__': 

1043 

1044 from pygeodesy import printf, Rhumb as Rh, RhumbAux as Ah 

1045 from pygeodesy.basics import _zip 

1046 from pygeodesy.ellipsoids import _EWGS84 

1047 

1048 Al = Ah(_EWGS84).Line(30, 0, 45) 

1049 Rl = Rh(_EWGS84).Line(30, 0, 45) 

1050 

1051 for i in range(1, 10): 

1052 s = .5e6 + 1e6 / i 

1053 a = Al.Position(s).lon2 

1054 r = Rl.Position(s).lon2 

1055 e = (fabs(a - r) / a) if a else 0 

1056 printf('# Position.lon2 %.14f vs %.14f, diff %g', r, a, e) 

1057 

1058 for exact in (None, False, True): 

1059 for est in (None, 1e6): 

1060 a = Al.PlumbTo(60, 0, exact=exact, est=est) 

1061 r = Rl.PlumbTo(60, 0, exact=exact, est=est) 

1062 printf('# %s, iteration=%s, exact=%s, est=%s\n# %s, iteration=%s', 

1063 a.toRepr(), a.iteration, exact, est, 

1064 r.toRepr(), r.iteration, nl=1) 

1065 

1066 NE_=(71.688899882813, 0.2555198244234, 44095641862956.11) 

1067 LHR=(77.7683897102557, 5771083.38332803, 37395209100030.39) 

1068 NRT=(-92.38888798169965, 12782581.067684170, -63760642939072.50) 

1069 

1070 def _ref(fmt, r3, x3): 

1071 e3 = [] 

1072 for r, x in _zip(r3, x3): # strict=True 

1073 e = fabs(r - x) / fabs(x) 

1074 e3.append('%.g' % (e,)) 

1075 printf((fmt % r3) + ', rel errors: ' + ', '.join(e3)) 

1076 

1077 for R in (Ah, Rh): # <https://GeographicLib.SourceForge.io/cgi-bin/RhumbSolve -p 9> version 2.2 

1078 rh = R(exact=True) # WGS84 default 

1079 printf('# %r', rh, nl=1) 

1080 r = rh.Direct8(40.6, -73.8, 51, 5.5e6) # from JFK about NE 

1081 _ref('# JFK NE lat2=%.12f, lon2=%.12f, S12=%.1f', (r.lat2, r.lon2, r.S12), NE_) 

1082 r = rh.Inverse8(40.6, -73.8, 51.6, -0.5) # JFK to LHR 

1083 _ref('# JFK-LHR azi12=%.12f, s12=%.3f S12=%.1f', (r.azi12, r.s12, r.S12), LHR) 

1084 r = rh.Inverse8(40.6, -73.8, 35.8, 140.3) # JFK to Tokyo Narita 

1085 _ref('# JFK-NRT azi12=%.12f, s12=%.3f S12=%.1f', (r.azi12, r.s12, r.S12), NRT) 

1086 

1087# % python3.10 -m pygeodesy3.rhumb.Bases 

1088 

1089# Position.lon2 11.61455846901637 vs 11.61455846901637, diff 3.05885e-16 

1090# Position.lon2 7.58982302826842 vs 7.58982302826842, diff 2.34045e-16 

1091# Position.lon2 6.28526067416369 vs 6.28526067416369, diff 2.82623e-16 

1092# Position.lon2 5.63938995325146 vs 5.63938995325146, diff 1.57495e-16 

1093# Position.lon2 5.25385527435707 vs 5.25385527435707, diff 0 

1094# Position.lon2 4.99764604290380 vs 4.99764604290380, diff 8.88597e-16 

1095# Position.lon2 4.81503363740473 vs 4.81503363740473, diff 1.84459e-16 

1096# Position.lon2 4.67828821748836 vs 4.67828821748835, diff 5.69553e-16 

1097# Position.lon2 4.57205667906283 vs 4.57205667906283, diff 5.82787e-16 

1098 

1099# Intersection(a02=17.798332, a12=19.521356, at=90.0, azi02=135.0, azi12=45.0, lat0=60.0, lat1=30.0, lat2=45.0, lon0=0.0, lon1=0.0, lon2=15.830286, name='Intersection', s02=1977981.142985, s12=2169465.957531), iteration=9, exact=None, est=None 

1100# Intersection(a02=17.798332, a12=19.521356, at=90.0, azi02=135.0, azi12=45.0, lat0=60.0, lat1=30.0, lat2=45.0, lon0=0.0, lon1=0.0, lon2=15.830286, name='Intersection', s02=1977981.142985, s12=2169465.957531), iteration=9 

1101 

1102# Intersection(a02=17.798332, a12=19.521356, at=90.0, azi02=135.0, azi12=45.0, lat0=60.0, lat1=30.0, lat2=45.0, lon0=0.0, lon1=0.0, lon2=15.830286, name='Intersection', s02=1977981.142985, s12=2169465.957531), iteration=9, exact=None, est=1000000.0 

1103# Intersection(a02=17.798332, a12=19.521356, at=90.0, azi02=135.0, azi12=45.0, lat0=60.0, lat1=30.0, lat2=45.0, lon0=0.0, lon1=0.0, lon2=15.830286, name='Intersection', s02=1977981.142985, s12=2169465.957531), iteration=9 

1104 

1105# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=5, exact=False, est=None 

1106# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=5 

1107 

1108# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=7, exact=False, est=1000000.0 

1109# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=7 

1110 

1111# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=5, exact=True, est=None 

1112# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=5 

1113 

1114# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=7, exact=True, est=1000000.0 

1115# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=7 

1116 

1117# RhumbAux(RAorder=None, TMorder=6, ellipsoid=Ellipsoid(name='WGS84', a=6378137, b=6356752.31424518, f_=298.25722356, f=0.00335281, f2=0.00336409, n=0.00167922, e=0.08181919, e2=0.00669438, e21=0.99330562, e22=0.0067395, e32=0.00335843, A=6367449.14582341, L=10001965.72931272, R1=6371008.77141506, R2=6371007.18091847, R3=6371000.79000916, Rbiaxial=6367453.63451633, Rtriaxial=6372797.5559594), exact=True) 

1118# JFK NE lat2=71.688899882813, lon2=0.255519824423, S12=44095641862956.1, rel errors: 4e-16, 2e-13, 4e-16 

1119# JFK-LHR azi12=77.768389710256, s12=5771083.383 S12=37395209100030.4, rel errors: 5e-16, 3e-16, 8e-16 

1120# JFK-NRT azi12=-92.388887981700, s12=12782581.068 S12=-63760642939072.5, rel errors: 0, 1e-16, 7e-16 

1121 

1122# Rhumb(RAorder=6, TMorder=6, ellipsoid=Ellipsoid(name='WGS84', a=6378137, b=6356752.31424518, f_=298.25722356, f=0.00335281, f2=0.00336409, n=0.00167922, e=0.08181919, e2=0.00669438, e21=0.99330562, e22=0.0067395, e32=0.00335843, A=6367449.14582341, L=10001965.72931272, R1=6371008.77141506, R2=6371007.18091847, R3=6371000.79000916, Rbiaxial=6367453.63451633, Rtriaxial=6372797.5559594), exact=True) 

1123# JFK NE lat2=71.688899882813, lon2=0.255519824423, S12=44095641862956.1, rel errors: 2e-16, 1e-13, 5e-16 

1124# JFK-LHR azi12=77.768389710256, s12=5771083.383 S12=37395209100030.4, rel errors: 4e-16, 3e-16, 6e-16 

1125# JFK-NRT azi12=-92.388887981700, s12=12782581.068 S12=-63760642939072.5, rel errors: 0, 1e-16, 1e-16 

1126 

1127# **) MIT License 

1128# 

1129# Copyright (C) 2022-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1130# 

1131# Permission is hereby granted, free of charge, to any person obtaining a 

1132# copy of this software and associated documentation files (the "Software"), 

1133# to deal in the Software without restriction, including without limitation 

1134# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1135# and/or sell copies of the Software, and to permit persons to whom the 

1136# Software is furnished to do so, subject to the following conditions: 

1137# 

1138# The above copyright notice and this permission notice shall be included 

1139# in all copies or substantial portions of the Software. 

1140# 

1141# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1142# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1143# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1144# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1145# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1146# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1147# OTHER DEALINGS IN THE SOFTWARE.