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.internals import _dunder_nameof, _under 

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

38 _parallel_, _too_ 

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

40 _norm180, GDict 

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

42from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS 

43from pygeodesy.namedTuples import Distance2Tuple, LatLon2Tuple 

44from pygeodesy.props import deprecated_method, Property, Property_RO, \ 

45 property_RO, _update_all 

46from pygeodesy.streprs import Fmt, pairs 

47from pygeodesy.units import Float_, Lat, Lon, Meter, Radius_, Int # PYCHOK shared 

48from pygeodesy.utily import acos1, _azireversed, _loneg, sincos2d, sincos2d_, \ 

49 _unrollon, _Wrap 

50from pygeodesy.vector3d import _intersect3d3, Vector3d # in .Intersection below 

51 

52from math import cos, fabs 

53 

54__all__ = () 

55__version__ = '24.05.13' 

56 

57_anti_ = _Dash('anti') 

58_rls = [] # instances of C{RbumbLine...} to be updated 

59_TRIPS = 65 # .Intersection, .PlumbTo, 19+ 

60 

61 

62class _Lat(Lat): 

63 '''(INTERNAL) Latitude B{C{lat}}. 

64 ''' 

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

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

67 Lat.__new__(_Lat, *lat, **kwds) 

68 

69 

70class _Lon(Lon): 

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

72 ''' 

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

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

75 Lon.__new__(_Lon, *lon, **kwds) 

76 

77 

78def _update_all_rls(r): 

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

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

81 C{Rhumb} instance B{C{r}}. 

82 ''' 

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

84 _update_all(r) 

85 for rl in _rls: # PYCHOK use weakref? 

86 if rl._rhumb is r: 

87 _update_all(rl) 

88 

89 

90class RhumbBase(_CapsBase): 

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

92 ''' 

93 _datum = _WGS84 

94 _exact = True 

95 _f_max = _0_01 

96 _mTM = 6 # see .TMorder 

97 

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

99 '''New C{RhumbAux} or C{Rhumb}. 

100 ''' 

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

102 if not exact: 

103 self.exact = False 

104 if name: 

105 self.name = name 

106 

107 @Property_RO 

108 def a(self): 

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

110 ''' 

111 return self.ellipsoid.a 

112 

113 equatoradius = a 

114 

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

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

117 

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

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

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

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

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

123 

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

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

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

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

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

129 

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

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

132 is True} and L{RhumbAux}. 

133 

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

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

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

137 

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

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

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

141 carried out in finite terms. 

142 ''' 

143 s12 = a12 * self._mpd 

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

145 

146 @Property_RO 

147 def b(self): 

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

149 ''' 

150 return self.ellipsoid.b 

151 

152 polaradius = b 

153 

154 @property 

155 def datum(self): 

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

157 ''' 

158 return self._datum 

159 

160 @datum.setter # PYCHOK setter! 

161 def datum(self, datum): 

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

163 

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

165 ''' 

166 _xinstanceof(Datum, datum=datum) 

167 if self._datum != datum: 

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

169 _update_all_rls(self) 

170 self._datum = datum 

171 

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

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

174 ''' 

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

176 

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

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

179 

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

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

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

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

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

185 

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

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

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

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

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

191 

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

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

194 is True} and L{RhumbAux}. 

195 

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

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

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

199 

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

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

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

203 carried out in finite terms. 

204 ''' 

205 a12 = _over(s12, self._mpd) 

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

207 

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

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

210 ''' 

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

212 

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

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

215 ''' 

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

217 

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

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

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

221 

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

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

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

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

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

227 L{Caps} values specifying the required capabilities. 

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

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

230 

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

232 C{.Position} to compute each point. 

233 

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

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

236 ''' 

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

238 

239 Line = DirectLine # synonyms 

240 

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

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

243 ''' 

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

245 name=self.name) 

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

247 

248 @Property 

249 def ellipsoid(self): 

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

251 ''' 

252 return self.datum.ellipsoid 

253 

254 @ellipsoid.setter # PYCHOK setter! 

255 def ellipsoid(self, a_earth_f): 

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

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

258 

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

260 ''' 

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

262 

263 @Property 

264 def exact(self): 

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

266 ''' 

267 return self._exact 

268 

269 @exact.setter # PYCHOK setter! 

270 def exact(self, exact): 

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

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

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

274 

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

276 exceeds non-zero C{f_max}. 

277 

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

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

280 ''' 

281 x = bool(exact) 

282 if self._exact != x: 

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

284 _update_all_rls(self) 

285 self._exact = x 

286 

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

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

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

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

291 

292 @Property_RO 

293 def f(self): 

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

295 ''' 

296 return self.ellipsoid.f 

297 

298 flattening = f 

299 

300 @property 

301 def f_max(self): 

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

303 ''' 

304 return self._f_max 

305 

306 @f_max.setter # PYCHOK setter! 

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

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

309 

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

311 exceeds non-zero C{f_max}. 

312 ''' 

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

314 if self._f_max != f: 

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

316 self._f_max = f 

317 

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

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

320 ''' 

321 if wrap: 

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

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

324 

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

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

327 

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

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

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

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

332 

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

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

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

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

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

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

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

340 I{squared}. 

341 

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

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

344 when C{B{exact} is True}. 

345 

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

347 on opposite meridians, there are two shortest rhumb lines 

348 and the East-going one is chosen. 

349 

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

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

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

353 carried out in finite terms. 

354 ''' 

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

356 Cs = Caps 

357 if (outmask & Cs.AZIMUTH_DISTANCE_AREA): 

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

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

360 if (outmask & Cs.AZIMUTH): 

361 z = _atan2d(y, x) 

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

363 if (outmask & Cs.AREA): 

364 S12 = self._S12d(s1, s2, lon12) 

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

366 return r 

367 

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

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

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

371 

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

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

374 ''' 

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

376 

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

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

379 ''' 

380 if wrap: 

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

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

383 

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

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

386 

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

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

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

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

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

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

393 L{Caps} values specifying the required capabilities. 

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

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

396 

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

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

399 

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

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

402 ''' 

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

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

405 

406 @Property_RO 

407 def _mpd(self): # PYCHOK no cover 

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

409 _MODS.named.notOverloaded(self) 

410 

411 @property_RO 

412 def RAorder(self): 

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

414 ''' 

415 return None 

416 

417 @property_RO 

418 def _RhumbLine(self): # PYCHOK no cover 

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

420 self._notOverloaded(underOK=True) 

421 

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

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

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

425 

426 @Property 

427 def TMorder(self): 

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

429 ''' 

430 return self._mTM 

431 

432 @TMorder.setter # PYCHOK setter! 

433 def TMorder(self, order): 

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

435 

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

437 for L{Rhumb} instances. 

438 ''' 

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

440 if self._mTM != m: 

441 _update_all_rls(self) 

442 self._mTM = m 

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

444 self.exact = False 

445 

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

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

448 

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

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

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

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

453 

454 @return: Tuple items (C{str}). 

455 ''' 

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

457 exact=self.exact, TMorder=self.TMorder) 

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

459 

460 

461class RhumbLineBase(_CapsBase): 

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

463 ''' 

464 _azi12 = _0_0 

465 _calp = _1_0 

466# _caps = \ 

467# _debug = 0 

468# _lat1 = \ 

469# _lon1 = \ 

470# _lon12 = _0_0 

471 _Rhumb = RhumbBase # compatible C{Rhumb} class 

472 _rhumb = None # C{Rhumb} instance 

473 _salp = \ 

474 _talp = _0_0 

475 

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

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

478 ''' 

479 _xinstanceof(self._Rhumb, rhumb=rhumb) 

480 

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

482 self._lon1 = _Lon(lon1= lon1) 

483 self._lon12 = _norm180(self._lon1) 

484 if azi12: # non-zero, non-None 

485 self.azi12 = _norm180(azi12) 

486 

487 n = name or rhumb.name 

488 if n: 

489 self.name=n 

490 

491 self._caps = caps 

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

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

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

495 else: 

496 self._rhumb = rhumb 

497 _rls.append(self) 

498 

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

500 if _rls: # may be empty or None 

501 try: # PYCHOK no cover 

502 _rls.remove(self) 

503 except (TypeError, ValueError): 

504 pass 

505 self._rhumb = None 

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

507 

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

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

510 

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

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

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

514 the quantities to be returned. 

515 

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

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

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

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

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

521 

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

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

524 when C{B{exact} is True}. 

525 

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

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

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

529 

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

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

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

533 carried out in finite terms. 

534 ''' 

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

536 

537 @Property 

538 def azi12(self): 

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

540 ''' 

541 return self._azi12 

542 

543 @azi12.setter # PYCHOK setter! 

544 def azi12(self, azi12): 

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

546 ''' 

547 z = _norm180(azi12) 

548 if self._azi12 != z: 

549 if self._rhumb: 

550 _update_all(self) 

551 self._azi12 = z 

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

553 self._talp = _over(*t) 

554 

555 @property_RO 

556 def azi12_sincos2(self): # PYCHOK no cover 

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

558 ''' 

559 return self._scalp, self._calp 

560 

561 @property_RO 

562 def datum(self): 

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

564 ''' 

565 return self.rhumb.datum 

566 

567 def degrees2m(self, angle): 

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

569 

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

571 

572 @return: Distance (C{meter}). 

573 ''' 

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

575 

576 @deprecated_method 

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

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

579 

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

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

582 ''' 

583 r = self.Inverse(lat, lon) 

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

585 

586 @property_RO 

587 def ellipsoid(self): 

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

589 ''' 

590 return self.rhumb.ellipsoid 

591 

592 @property_RO 

593 def exact(self): 

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

595 ''' 

596 return self.rhumb.exact 

597 

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

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

600 

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

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

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

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

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

606 @kwarg tol_eps: Optional keyword arguments, see method 

607 method L{Intersection} for further details. 

608 

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

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

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

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

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

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

615 rhumb line is tangential to the circle, both points 

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

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

618 

619 @raise IntersectionError: The circle and this rhumb line 

620 do not intersect. 

621 

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

623 ''' 

624 r = Radius_(radius) 

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

626 a = q.s02 

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

628 if a < r: 

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

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

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

632 d, h = _0_0, r 

633 else: 

634 d = q.s12 

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

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

637 m = self.rhumb._mpr 

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

639 else: 

640 h = _copysign(sqrt_a(r, a), a) 

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

642 if h: 

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

644 elif a > r: 

645 t = _too_(Fmt.distant(a)) 

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

647 txt=t, **tol_eps) 

648 else: # tangential 

649 q.set_(**t) # == p.set(_**t) 

650 return p, q 

651 

652 @deprecated_method 

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

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

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

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

657 r._iteration = p.iteration 

658 return r 

659 

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

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

662 

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

664 @kwarg tol: Tolerance for longitudinal convergence and parallel 

665 error (C{degrees}). 

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

667 

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

669 13 items C{lat1, lon1, azi12, a12, s12, lat2, lon2, lat0, 

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

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

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

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

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

675 See method L{Position} for further details. 

676 

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

678 no intersection for an other reason. 

679 

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

681 L{pygeodesy.intersection3d3}. 

682 

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

684 L{ExactTransverseMercator} or L{KTransverseMercator} 

685 projection and function L{pygeodesy.intersection3d3} in 

686 that domain. 

687 ''' 

688 _xinstanceof(RhumbLineBase, other=other) 

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

690 try: 

691 if self.others(other) is self: 

692 raise ValueError(_coincident_) 

693 # make invariants and globals locals 

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

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

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

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

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

699 _diff = euclid # approximate length 

700 _i3d3 = _intersect3d3 # NOT .vector3d.intersection3d3 

701 _LL2T = LatLon2Tuple 

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

703 # use halfway point as initial estimate 

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

705 favg(self.lon1, other.lon1)) 

706 for i in range(1, _TRIPS): 

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

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

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

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

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

712 if d < tol: # 19 trips 

713 break 

714 else: 

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

716 

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

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

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

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

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

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

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

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

725 except Exception as x: 

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

727 eps=eps, cause=x) 

728 return P 

729 

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

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

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

733 

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

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

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

737 and B{C{lon2}} (C{bool}). 

738 

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

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

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

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

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

744 ''' 

745 if wrap: 

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

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

748 return r 

749 

750 @Property_RO 

751 def isLoxodrome(self): 

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

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

754 

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

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

757 ''' 

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

759 

760 @Property_RO 

761 def lat1(self): 

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

763 ''' 

764 return self._lat1 

765 

766 @Property_RO 

767 def lon1(self): 

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

769 ''' 

770 return self._lon1 

771 

772 @Property_RO 

773 def latlon1(self): 

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

775 ''' 

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

777 

778 def m2degrees(self, distance): 

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

780 

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

782 

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

784 ''' 

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

786 

787 @property_RO 

788 def _mu1(self): # PYCHOK no cover 

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

790 self._notOverloaded(underOK=True) 

791 

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

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

794 self._notOverloaded(mu2) # underOK=True 

795 

796 @deprecated_method 

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

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

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

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

801 name=self.nearestOn4.__name__) 

802 r._iteration = P.iteration 

803 return r 

804 

805 @deprecated_method 

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

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

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

809 

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

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

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

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

814 

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

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

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

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

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

820 see method L{Ellipsoid.geodesic_}. 

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

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

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

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

825 C{B{exact} is not None}. 

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

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

828 C{not None}. 

829 

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

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

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

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

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

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

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

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

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

839 method L{Position} for further details. 

840 

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

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

843 package not found or not installed. 

844 

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

846 intersection for some other reason. 

847 

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

849 and function L{pygeodesy.intersection3d3}. 

850 ''' 

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

852 

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

854# if p: 

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

856# return p 

857 

858 if exact is None: 

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

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

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

862 

863 else: # C{rhumb-intercept} 

864 E = self.ellipsoid 

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

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

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

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

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

870 _, s12 = sincos2d(d) 

871 s12 *= r.s12 # signed 

872 else: 

873 s12 = Meter(est=est) 

874 try: 

875 _abs = fabs 

876 _d2 = _diff182 

877 _ErT = E.rocPrimeVertical # aka rocTransverse 

878 _ovr = _over 

879 _S12 = Fsum(s12).fsum2f_ 

880 _scd = sincos2d_ 

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

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

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

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

885 s, c, s2, c2 = _scd(d, r.lat2) 

886 c2 *= _ErT(r.lat2) 

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

888 s12, t = _S12(c / s) # XXX _ovr? 

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

890 break 

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

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

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

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

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

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

897 

898 return P 

899 

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

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

902 

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

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

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

906 the quantities to be returned. 

907 

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

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

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

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

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

913 

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

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

916 when C{B{exact} is True}. 

917 

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

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

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

921 

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

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

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

925 carried out in finite terms. 

926 ''' 

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

928 

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

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

931 ''' 

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

933 Cs = Caps 

934 if (outmask & Cs.LATITUDE_LONGITUDE_AREA): 

935 if a12 or s12: 

936 mu12 = self._calp * a12 

937 mu2 = self._mu1 + mu12 

938 if fabs(mu2) > 90: # past pole 

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

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

941 mu2 = _norm180(_loneg(mu2)) 

942 lat2 = self._mu2lat(mu2) 

943 lon2 = S12 = NAN 

944 else: 

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

946 if (outmask & Cs.AREA): 

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

948 S12 = unsigned0(S12) # like .gx 

949# else: 

950# S12 = None # unused 

951 if (outmask & Cs.LONGITUDE): 

952 if (outmask & Cs.LONG_UNROLL): 

953 lon2 += self.lon1 

954 else: 

955 lon2 = _norm180(self._lon12 + lon2) 

956 else: # coincident 

957 lat2, lon2 = self.latlon1 

958 S12 = _0_0 

959 

960 if (outmask & Cs.AREA): 

961 r.set_(S12=S12) 

962 if (outmask & Cs.LATITUDE): 

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

964 if (outmask & Cs.LONGITUDE): 

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

966 return r 

967 

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

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

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

971 

972 @Property_RO 

973 def rhumb(self): 

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

975 ''' 

976 return self._rhumb 

977 

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

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

980 

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

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

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

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

985 

986 @return: C{RhumbLine} (C{str}). 

987 ''' 

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

989 azi12=self.azi12, exact=self.exact, 

990 TMorder=self.TMorder, xTM=self.xTM) 

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

992 

993 @property_RO 

994 def TMorder(self): 

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

996 ''' 

997 return self.rhumb.TMorder 

998 

999 @Property_RO 

1000 def xTM(self): 

1001 '''Get this rhumb line's I{Transverse Mercator} projection (L{ExactTransverseMercator} 

1002 if I{exact} and I{ellipsoidal}, otherwise L{KTransverseMercator} for C{TMorder}). 

1003 ''' 

1004 E = self.ellipsoid 

1005 # ExactTransverseMercator doesn't handle spherical earth models 

1006 return _MODS.etm.ExactTransverseMercator(E) if self.exact and E.isEllipsoidal else \ 

1007 _MODS.ktm.KTransverseMercator(E, TMorder=self.TMorder) 

1008 

1009 def _xTM3d(self, latlon0, z=INT0, V3d=Vector3d): 

1010 '''(INTERNAL) C{xTM.forward} this C{latlon1} to C{V3d} with B{C{latlon0}} 

1011 as current intersection estimate and central meridian. 

1012 ''' 

1013 t = self.xTM.forward(self.lat1 - latlon0.lat, self.lon1, lon0=latlon0.lon) 

1014 return V3d(t.easting, t.northing, z) 

1015 

1016 

1017class _PseudoRhumbLine(RhumbLineBase): 

1018 '''(INTERNAL) Pseudo-rhumb line for a geodesic (line), see C{geodesicw._PlumbTo}. 

1019 ''' 

1020 def __init__(self, gl, name=NN): 

1021 R = RhumbBase(gl.geodesic.ellipsoid, None, True, name) 

1022 RhumbLineBase.__init__(self, R, gl.lat1, gl.lon1, 0, caps=Caps.LINE_OFF) 

1023 self._azi1 = self.azi12 = gl.azi1 

1024 self._gl = gl 

1025 self._gD = gl.geodesic.Direct 

1026 

1027 def PlumbTo(self, lat0, lon0, **exact_eps_est_tol): # PYCHOK signature 

1028 P = RhumbLineBase.PlumbTo(self, lat0, lon0, **exact_eps_est_tol) 

1029 z, P = _xkwds_pop2(P, azi12=None) 

1030 P.set_(azi1=self._gl.azi1, azi2=z) 

1031 return P # geodesic L{Position} 

1032 

1033 def Position(self, s12, **unused): # PYCHOK signature 

1034 r = self._gD(self.lat1, self.lon1, self._azi1, s12) 

1035 self._azi1 = r.azi1 

1036 self.azi12 = z = r.azi2 

1037 self._salp, _ = sincos2d(z) 

1038 return r.set_(azi12=z) 

1039 

1040 

1041__all__ += _ALL_DOCS(RhumbBase, RhumbLineBase) 

1042 

1043if __name__ == '__main__': 

1044 

1045 from pygeodesy import printf, Rhumb as Rh, RhumbAux as Ah 

1046 from pygeodesy.basics import _zip 

1047 from pygeodesy.ellipsoids import _EWGS84 

1048 

1049 Al = Ah(_EWGS84).Line(30, 0, 45) 

1050 Rl = Rh(_EWGS84).Line(30, 0, 45) 

1051 

1052 for i in range(1, 10): 

1053 s = .5e6 + 1e6 / i 

1054 a = Al.Position(s).lon2 

1055 r = Rl.Position(s).lon2 

1056 e = (fabs(a - r) / a) if a else 0 

1057 printf('# Position.lon2 %.14f vs %.14f, diff %g', r, a, e) 

1058 

1059 for exact in (None, False, True): 

1060 for est in (None, 1e6): 

1061 a = Al.PlumbTo(60, 0, exact=exact, est=est) 

1062 r = Rl.PlumbTo(60, 0, exact=exact, est=est) 

1063 printf('# %s, iteration=%s, exact=%s, est=%s\n# %s, iteration=%s', 

1064 a.toRepr(), a.iteration, exact, est, 

1065 r.toRepr(), r.iteration, nl=1) 

1066 

1067 NE_=(71.688899882813, 0.2555198244234, 44095641862956.11) 

1068 LHR=(77.7683897102557, 5771083.38332803, 37395209100030.39) 

1069 NRT=(-92.38888798169965, 12782581.067684170, -63760642939072.50) 

1070 

1071 def _ref(fmt, r3, x3): 

1072 e3 = [] 

1073 for r, x in _zip(r3, x3): # strict=True 

1074 e = fabs(r - x) / fabs(x) 

1075 e3.append('%.g' % (e,)) 

1076 printf((fmt % r3) + ', rel errors: ' + ', '.join(e3)) 

1077 

1078 for R in (Ah, Rh): # <https://GeographicLib.SourceForge.io/cgi-bin/RhumbSolve -p 9> version 2.2 

1079 rh = R(exact=True) # WGS84 default 

1080 printf('# %r', rh, nl=1) 

1081 r = rh.Direct8(40.6, -73.8, 51, 5.5e6) # from JFK about NE 

1082 _ref('# JFK NE lat2=%.12f, lon2=%.12f, S12=%.1f', (r.lat2, r.lon2, r.S12), NE_) 

1083 r = rh.Inverse8(40.6, -73.8, 51.6, -0.5) # JFK to LHR 

1084 _ref('# JFK-LHR azi12=%.12f, s12=%.3f S12=%.1f', (r.azi12, r.s12, r.S12), LHR) 

1085 r = rh.Inverse8(40.6, -73.8, 35.8, 140.3) # JFK to Tokyo Narita 

1086 _ref('# JFK-NRT azi12=%.12f, s12=%.3f S12=%.1f', (r.azi12, r.s12, r.S12), NRT) 

1087 

1088# % python3.10 -m pygeodesy3.rhumb.Bases 

1089 

1090# Position.lon2 11.61455846901637 vs 11.61455846901637, diff 3.05885e-16 

1091# Position.lon2 7.58982302826842 vs 7.58982302826842, diff 2.34045e-16 

1092# Position.lon2 6.28526067416369 vs 6.28526067416369, diff 2.82623e-16 

1093# Position.lon2 5.63938995325146 vs 5.63938995325146, diff 1.57495e-16 

1094# Position.lon2 5.25385527435707 vs 5.25385527435707, diff 0 

1095# Position.lon2 4.99764604290380 vs 4.99764604290380, diff 8.88597e-16 

1096# Position.lon2 4.81503363740473 vs 4.81503363740473, diff 1.84459e-16 

1097# Position.lon2 4.67828821748836 vs 4.67828821748835, diff 5.69553e-16 

1098# Position.lon2 4.57205667906283 vs 4.57205667906283, diff 5.82787e-16 

1099 

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, exact=None, est=None 

1101# 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 

1102 

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, exact=None, est=1000000.0 

1104# 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 

1105 

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, exact=False, est=None 

1107# 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 

1108 

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, exact=False, est=1000000.0 

1110# 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 

1111 

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, exact=True, est=None 

1113# 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 

1114 

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, exact=True, est=1000000.0 

1116# 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 

1117 

1118# 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) 

1119# JFK NE lat2=71.688899882813, lon2=0.255519824423, S12=44095641862956.1, rel errors: 4e-16, 2e-13, 4e-16 

1120# JFK-LHR azi12=77.768389710256, s12=5771083.383 S12=37395209100030.4, rel errors: 5e-16, 3e-16, 8e-16 

1121# JFK-NRT azi12=-92.388887981700, s12=12782581.068 S12=-63760642939072.5, rel errors: 0, 1e-16, 7e-16 

1122 

1123# 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) 

1124# JFK NE lat2=71.688899882813, lon2=0.255519824423, S12=44095641862956.1, rel errors: 2e-16, 1e-13, 5e-16 

1125# JFK-LHR azi12=77.768389710256, s12=5771083.383 S12=37395209100030.4, rel errors: 4e-16, 3e-16, 6e-16 

1126# JFK-NRT azi12=-92.388887981700, s12=12782581.068 S12=-63760642939072.5, rel errors: 0, 1e-16, 1e-16 

1127 

1128# **) MIT License 

1129# 

1130# Copyright (C) 2022-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1131# 

1132# Permission is hereby granted, free of charge, to any person obtaining a 

1133# copy of this software and associated documentation files (the "Software"), 

1134# to deal in the Software without restriction, including without limitation 

1135# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1136# and/or sell copies of the Software, and to permit persons to whom the 

1137# Software is furnished to do so, subject to the following conditions: 

1138# 

1139# The above copyright notice and this permission notice shall be included 

1140# in all copies or substantial portions of the Software. 

1141# 

1142# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1143# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1144# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1145# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1146# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1147# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1148# OTHER DEALINGS IN THE SOFTWARE.