Coverage for pygeodesy/rhumbBase.py: 96%

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1 

2# -*- coding: utf-8 -*- 

3 

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

5classes 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{RhumbLine} has been enhanced with methods C{intersection2} and C{nearestOn4} to iteratively 

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

12geodesic or perpendicular 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:Charles@Karney.com>} (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 

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

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

28 _0_0, _0_01, _1_0, _90_0, _180_0 

29# from pygeodesy.datums import _spherical_datum # _MODS 

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

31 _xdatum, _xkwds, _Xorder 

32# from pygeodesy.etm import ExactTransverseMercator # _MODS 

33from pygeodesy.fmath import euclid, favg, fabs 

34# from pygeodesy.fsums import Fsum # _MODS 

35from pygeodesy.interns import NN, _coincident_, _COMMASPACE_, _intersection_, \ 

36 _no_, _parallel_, _under 

37from pygeodesy.karney import Caps, _CapsBase, _diff182, _EWGS84, _fix90, \ 

38 _norm180, _xinstanceof 

39from pygeodesy.ktm import KTransverseMercator, _AlpCoeffs # PYCHOK used! 

40from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS 

41# from pygeodesy.named import notOverloaded # _MODS 

42from pygeodesy.namedTuples import Distance2Tuple, LatLon2Tuple, NearestOn4Tuple 

43from pygeodesy.props import Property, Property_RO, property_RO, _update_all 

44from pygeodesy.streprs import Fmt, pairs, unstr 

45from pygeodesy.units import Float_, Lat, Lon, Meter 

46from pygeodesy.utily import sincos2d, sincos2d_, _unrollon, _Wrap 

47from pygeodesy.vector3d import _intersect3d3, Vector3d # in .intersection2 below 

48 

49# from math import fabs # from .fmath 

50 

51__all__ = () 

52__version__ = '23.08.09' 

53 

54_rls = [] # instances of C{RbumbLine} to be updated 

55_TRIPS = 65 # .intersection2, .nearestOn4, 18+ 

56 

57 

58class _Lat(Lat): 

59 '''(INTERNAL) Latitude B{C{lat}}. 

60 ''' 

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

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

63 Lat.__new__(_Lat, *lat, **kwds) 

64 

65 

66class _Lon(Lon): 

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

68 ''' 

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

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

71 Lon.__new__(_Lon, *lon, **kwds) 

72 

73 

74def _update_all_rls(r): 

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

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

77 C{Rhumb} instance B{C{r}}. 

78 ''' 

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

80 _update_all(r) 

81 for rl in _rls: # PYCHOK use weakref? 

82 if rl._rhumb is r: 

83 _update_all(rl) 

84 

85 

86class RhumbBase(_CapsBase): 

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

88 ''' 

89 _E = _EWGS84 

90 _exact = True 

91 _f_max = _0_01 

92 _mTM = 6 # see .TMorder 

93 

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

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

96 ''' 

97 if f is not None: 

98 self.ellipsoid = a_earth, f 

99 elif a_earth not in (_EWGS84, None): 

100 self.ellipsoid = a_earth 

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 @Property_RO 

115 def b(self): 

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

117 ''' 

118 return self.ellipsoid.b 

119 

120 polaradius = b 

121 

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

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

124 ''' 

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

126 

127 def Direct(self, lat1, lon1, azi12, s12, outmask=0): # PYCHOK no cover 

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

129 ''' 

130 _MODS.named.notOverloaded(self, lat1, lon1, azi12, s12, outmask=outmask) 

131 

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

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

134 ''' 

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

136 

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

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

139 ''' 

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

141 

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

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

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

145 

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

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

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

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

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

151 L{Caps} values specifying the required capabilities. 

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

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

154 

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

156 C{.Position} to compute each point. 

157 

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

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

160 ''' 

161 return self._RhumbLine(self, lat1=lat1, lon1=lon1, azi12=azi12, 

162 **caps_name) 

163 

164 Line = DirectLine # synonyms 

165 

166 @Property 

167 def ellipsoid(self): 

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

169 ''' 

170 return self._E 

171 

172 @ellipsoid.setter # PYCHOK setter! 

173 def ellipsoid(self, a_earth_f): 

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

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

176 

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

178 ''' 

179 E = _MODS.datums._spherical_datum(a_earth_f, Error=RhumbError).ellipsoid 

180 if self._E != E: 

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

182 _update_all_rls(self) 

183 self._E = E 

184 

185 @Property 

186 def exact(self): 

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

188 ''' 

189 return self._exact 

190 

191 @exact.setter # PYCHOK setter! 

192 def exact(self, exact): 

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

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

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

196 

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

198 exceeds non-zero C{f_max}. 

199 

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

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

202 ''' 

203 x = bool(exact) 

204 if self._exact != x: 

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

206 _update_all_rls(self) 

207 self._exact = x 

208 

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

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

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

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

213 

214 @Property_RO 

215 def f(self): 

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

217 ''' 

218 return self.ellipsoid.f 

219 

220 flattening = f 

221 

222 @property 

223 def f_max(self): 

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

225 ''' 

226 return self._f_max 

227 

228 @f_max.setter # PYCHOK setter! 

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

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

231 

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

233 exceeds non-zero C{f_max}. 

234 ''' 

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

236 if self._f_max != f: 

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

238 self._f_max = f 

239 

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

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

242 ''' 

243 if wrap: 

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

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

246 

247 def Inverse(self, lat1, lon1, lat2, lon2, outmask=0): # PYCHOK no cover 

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

249 ''' 

250 _MODS.named.notOverloaded(self, lat1, lon1, lat2, lon2, outmask=outmask) 

251 

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

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

254 ''' 

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

256 

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

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

259 ''' 

260 if wrap: 

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

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

263 

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

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

266 

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

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

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

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

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

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

273 L{Caps} values specifying the required capabilities. 

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

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

276 

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

278 C{.Position} to compute each point. 

279 

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

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

282 ''' 

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

284 return self._RhumbLine(self, lat1=lat1, lon1=lon1, azi12=r.azi12, 

285 **caps_name) 

286 

287 @Property_RO 

288 def _RhumbLine(self): # PYCHOK no cover 

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

290 ''' 

291 _MODS.named.notOverloaded(self) 

292 

293 def _TMorder(self, order): 

294 '''(INTERNAL) Set the I{Transverse Mercator} order (C{int}). 

295 

296 @note: Setting C{TMorder} turns property C{exact} off. 

297 ''' 

298 x = self.exact 

299 n = _Xorder(_MODS.ktm._AlpCoeffs, RhumbError, TMorder=order) 

300 if self._mTM != n: 

301 _update_all_rls(self) 

302 self._mTM = n 

303 x = False 

304 return x 

305 

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

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

308 ''' 

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

310 

311 

312class RhumbLineBase(RhumbBase): 

313 '''(INTERNAL) Class C{RhumbLine} 

314 ''' 

315 _azi12 = _0_0 

316# _caps = 0 

317# _debug = 0 

318# _lat1 = _0_0 

319# _lon1 = _0_0 

320# _lon12 = _0_0 

321 _salp = _0_0 

322 _calp = _1_0 

323 _Rhumb = RhumbBase # compatible C{Rhumb} class 

324 _rhumb = None # C{Rhumb} instance 

325 

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

327 '''New C{RhumbLine}. 

328 ''' 

329 _xinstanceof(self._Rhumb, rhumb=rhumb) 

330 

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

332 self._lon1 = _Lon(lon1= lon1) 

333 self._lon12 = _norm180(self._lon1) 

334 if azi12: # non-zero, non-None 

335 self.azi12 = _norm180(azi12) 

336 

337 n = name or rhumb.name 

338 if n: 

339 self.name=n 

340 

341 self._caps = caps 

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

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

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

345 else: 

346 self._rhumb = rhumb 

347 _rls.append(self) 

348 

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

350 if _rls: # may be empty or None 

351 try: # PYCHOK no cover 

352 _rls.remove(self) 

353 except (TypeError, ValueError): 

354 pass 

355 self._rhumb = None 

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

357 

358 @Property 

359 def azi12(self): 

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

361 ''' 

362 return self._azi12 

363 

364 @azi12.setter # PYCHOK setter! 

365 def azi12(self, azi12): 

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

367 ''' 

368 z = _norm180(azi12) 

369 if self._azi12 != z: 

370 if self._rhumb: 

371 _update_all(self) 

372 self._azi12 = z 

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

374 

375 @Property_RO 

376 def azi12_sincos2(self): # PYCHOK no cover 

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

378 ''' 

379 return self._scalp, self._calp 

380 

381 def distance2(self, lat, lon): 

382 '''Return the distance from and (initial) bearing at the given 

383 point to this rhumb line's start point. 

384 

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

386 @arg lon: Longitude of the points (C{degrees}). 

387 

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

389 in C{meter} and C{initial} bearing in C{degrees}. 

390 

391 @see: Methods C{intersection2} and C{nearestOn4} of L{RhumbLine} and 

392 L{RhumbLineAux}. 

393 ''' 

394 r = self.rhumb.Inverse(self.lat1, self.lon1, lat, lon) 

395# outmask=Caps.AZIMUTH_DISTANCE) 

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

397 

398 @property_RO 

399 def ellipsoid(self): 

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

401 ''' 

402 return self.rhumb.ellipsoid 

403 

404 @property_RO 

405 def exact(self): 

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

407 ''' 

408 return self.rhumb.exact 

409 

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

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

412 

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

414 @kwarg tol: Tolerance for longitudinal convergence (C{degrees}). 

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

416 

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

418 C{lon}gitude of the intersection point. 

419 

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

421 no intersection for an other reason. 

422 

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

424 L{pygeodesy.intersection3d3}. 

425 

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

427 L{ExactTransverseMercator} or L{KTransverseMercator} 

428 projection and invoking function L{pygeodesy.intersection3d3} 

429 in that domain. 

430 ''' 

431 _xinstanceof(RhumbLineBase, other=other) 

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

433 try: 

434 if other is self: 

435 raise ValueError(_coincident_) 

436 # make globals and invariants locals 

437 _diff = euclid # approximate length 

438 _i3d3 = _intersect3d3 # NOT .vector3d.intersection3d3 

439 _LL2T = LatLon2Tuple 

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

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

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

443 t = fabs(s_az - o_az) 

444 if t < EPS or fabs(t - _180_0) < EPS: 

445 raise ValueError(_parallel_) 

446 # use halfway point as initial estimate 

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

448 favg(self.lon1, other.lon1)) 

449 for i in range(1, _TRIPS): 

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

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

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

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

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

455 if d < tol: 

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

457 name=self.intersection2.__name__) 

458 except Exception as x: 

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

460 t = unstr(self.intersection2, tol=tol, **eps) 

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

462 

463 @Property_RO 

464 def lat1(self): 

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

466 ''' 

467 return self._lat1 

468 

469 @Property_RO 

470 def lon1(self): 

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

472 ''' 

473 return self._lon1 

474 

475 @Property_RO 

476 def latlon1(self): 

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

478 ''' 

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

480 

481 def _mu22(self, mu12, mu1): 

482 mu2 = mu12 + mu1 

483 x90 = fabs(mu2) > 90 

484 if x90: # reduce to [-180, 180) 

485 mu2 = _norm180(mu2) 

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

487 mu2 = _norm180(_180_0 - mu2) 

488 return mu2, x90 

489 

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

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

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

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

494 

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

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

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

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

499 respectively C{B{exact} is not None}. 

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

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

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

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

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

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

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

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

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

509 

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

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

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

513 C{normal} azimuth at the intersection. 

514 

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

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

517 package not found or not installed. 

518 

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

520 no intersection for an other reason. 

521 

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

523 L{pygeodesy.intersection3d3}. 

524 ''' 

525 if exact is None: 

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

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

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

529 t = rl.distance2(p.lat, p.lon) 

530 r = NearestOn4Tuple(p.lat, p.lon, t.distance, z, 

531 iteration=p.iteration) 

532 else: # C{rhumb-intercept} 

533 azi = self.azi12 

534 szi = self._salp 

535 E = self.ellipsoid 

536 gX = E.geodesic_(exact=exact) 

537 Cs = Caps 

538 gm = Cs.AZIMUTH | Cs.LATITUDE_LONGITUDE | Cs.REDUCEDLENGTH | Cs.GEODESICSCALE 

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

540 r = gX.Inverse(self.lat1, self.lon1, lat, lon, outmask=Cs.AZIMUTH_DISTANCE) 

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

542 _, c = sincos2d(d) 

543 s12 = c * r.s12 # signed 

544 else: 

545 s12 = Meter(est=est) 

546 try: 

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

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

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

550 

551 _s12 = _MODS.fsums.Fsum(s12).fsum2_ 

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

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

554 r = gX.Inverse(lat, lon, p.lat2, p.lon2, outmask=gm) 

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

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

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

558 s *= (s2 * szi / c2) - (s * r.M21 / r.m12) # XXX _over? 

559 s12, t = _s12(c / s) # XXX _over? 

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

561 break 

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

563 iteration=i) 

564 except Exception as x: # Fsum Value-, ZeroDivisionError 

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

566 return r 

567 

568 def Position(self, s12, outmask=0): # PYCHOK no cover 

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

570 ''' 

571 _MODS.named.notOverloaded(self, s12, outmask=outmask) 

572 

573 @Property_RO 

574 def rhumb(self): 

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

576 ''' 

577 return self._rhumb 

578 

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

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

581 

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

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

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

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

586 

587 @return: C{RhumbLine} (C{str}). 

588 ''' 

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

590 azi12=self.azi12, exact=self.exact, 

591 TMorder=self.TMorder, xTM=self.xTM) 

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

593 

594 @property_RO 

595 def TMorder(self): 

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

597 ''' 

598 return self.rhumb.TMorder 

599 

600 @Property_RO 

601 def xTM(self): 

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

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

604 ''' 

605 E = self.ellipsoid 

606 # ExactTransverseMercator doesn't handle spherical earth models 

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

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

609 

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

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

612 as current intersection estimate and central meridian. 

613 ''' 

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

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

616 

617 

618__all__ += _ALL_DOCS(RhumbBase, RhumbLineBase) 

619 

620 

621if __name__ == '__main__': 

622 

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

624 

625 A = A(_EWGS84).Line(30, 0, 45) 

626 R = R(_EWGS84).Line(30, 0, 45) 

627 

628 n = 1 

629 for i in range(1, 10): 

630 s = .5e6 + 1e6 / i 

631 a = A.Position(s).lon2 

632 r = R.Position(s).lon2 

633 e = (fabs(a - r) * 100.0 / a) if a else 0 

634 printf('Positions %s vs %s, diff %.2f%%', r, a, e, nl=n) 

635 n = 0 

636 

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

638 for est in (None, 1e6): 

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

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

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

642 a.toRepr(), a.iteration, exact, est, r.toRepr(), r.iteration, nl=1) 

643 

644# % python3 -m pygeodesy.rhumbBase 

645 

646# Positions 11.614558469016366 vs 11.61455846901637, diff 0.00% 

647# Positions 7.589823028268422 vs 7.589823028268423, diff 0.00% 

648# Positions 6.285260674163688 vs 6.285260674163687, diff 0.00% 

649# Positions 5.639389953251457 vs 5.6393899532514595, diff 0.00% 

650# Positions 5.253855274357075 vs 5.253855274357073, diff 0.00% 

651# Positions 4.9976460429038 vs 4.9976460429038045, diff 0.00% 

652# Positions 4.815033637404729 vs 4.81503363740473, diff 0.00% 

653# Positions 4.678288217488354 vs 4.678288217488353, diff 0.00% 

654# Positions 4.572056679062825 vs 4.572056679062826, diff 0.00% 

655 

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

657# NearestOn4Tuple(lat=45.0, lon=15.830286, distance=1977981.142985, normal=135.0), iteration=9 

658 

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

660# NearestOn4Tuple(lat=45.0, lon=15.830286, distance=1977981.142985, normal=135.0), iteration=9 

661 

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

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

664 

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

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

667 

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

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

670 

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

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

673 

674# **) MIT License 

675# 

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

677# 

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

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

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

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

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

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

684# 

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

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

687# 

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

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

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

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

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

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

694# OTHER DEALINGS IN THE SOFTWARE.