Coverage for pygeodesy/rhumb/solve.py: 93%

96 statements  

« prev     ^ index     » next       coverage.py v7.6.1, created at 2025-01-10 16:55 -0500

1 

2# -*- coding: utf-8 -*- 

3 

4u'''Wrapper to invoke I{Karney}'s U{RhumbSolve 

5<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>} utility 

6as an (exact) rhumb or rhumb line from I{either GeographicLib 2.0 or 2.2+}. 

7 

8@note: Set env variable C{PYGEODESY_RHUMBSOLVE} to the (fully qualified) 

9 path of the C{RhumbSolve} executable. 

10''' 

11from pygeodesy.basics import _xinstanceof 

12from pygeodesy.constants import _0_0, _180_0, _N_180_0, _over, _90_0 # PYCHOK used! 

13from pygeodesy.errors import RhumbError # PYCHOK used! 

14from pygeodesy.interns import NN, _a12_, _azi12_, _lat2_, _lon2_, _s12_, _S12_, _UNDER_ 

15from pygeodesy.karney import Caps, GDict, _norm180, Rhumb8Tuple, _sincos2d, _Xables 

16from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

17from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple 

18from pygeodesy.props import deprecated_method, Property, Property_RO 

19from pygeodesy.solveBase import _SolveGDictBase, _SolveGDictLineBase 

20from pygeodesy.utily import _unrollon, _Wrap, wrap360 

21 

22__all__ = _ALL_LAZY.rhumb_solve 

23__version__ = '24.11.07' 

24 

25 

26class _RhumbSolveBase(_SolveGDictBase): 

27 '''(INTERNAL) Base class for L{RhumbSolve} and L{RhumbLineSolve}. 

28 ''' 

29 _Error = RhumbError 

30 _Names_Direct = _lat2_, _lon2_, _S12_ 

31 _Names_Inverse = _azi12_, _s12_, _S12_ 

32 _Xable_name = _Xables.RhumbSolve.__name__ 

33 _Xable_path = _Xables.RhumbSolve() 

34 

35 @Property_RO 

36 def _cmdBasic(self): 

37 '''(INTERNAL) Get the basic C{RhumbSolve} cmd (C{tuple}). 

38 ''' 

39 return (self.RhumbSolve,) + (self._e_option + 

40 self._p_option + 

41 self._s_option) 

42 

43 @Property 

44 def RhumbSolve(self): 

45 '''Get the U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>} 

46 executable (C{filename}). 

47 ''' 

48 return self._Xable_path 

49 

50 @RhumbSolve.setter # PYCHOK setter! 

51 def RhumbSolve(self, path): 

52 '''Set the U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>} 

53 executable (C{filename}), the (fully qualified) path to the C{RhumbSolve} executable. 

54 

55 @raise RhumbError: Invalid B{C{path}}, B{C{path}} doesn't exist or isn't 

56 the C{RhumbSolve} executable. 

57 ''' 

58 self._setXable(path) 

59 

60 @Property_RO 

61 def _s_option(self): # == not -E for GeodSolve 

62 return () if self.Exact else ('-s',) 

63 

64 def toStr(self, **prec_sep): # PYCHOK signature 

65 '''Return this C{RhumbSolve} as string. 

66 

67 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=", "} 

68 for the C{float} C{prec}ision, number of decimal digits 

69 (0..9) and the C{sep}arator string to join. Trailing 

70 zero decimals are stripped for B{C{prec}} values of 1 

71 and above, but kept for negative B{C{prec}} values. 

72 

73 @return: RhumbSolve items (C{str}). 

74 ''' 

75 return self._toStr(RhumbSolve=self.RhumbSolve, **prec_sep) 

76 

77# @Property_RO 

78# def _u_option(self): 

79# return '-u' if self.unroll else () 

80 

81 

82class RhumbSolve(_RhumbSolveBase): 

83 '''Wrapper to invoke I{Karney}'s U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>} 

84 like a class, similar to L{pygeodesy.Rhumb} and L{pygeodesy.RhumbAux}. 

85 

86 @note: Use property C{RhumbSolve} or env variable C{PYGEODESY_RHUMBSOLVE} to specify the (fully 

87 qualified) path to the C{RhumbSolve} executable. 

88 

89 @note: This C{rhumb} is intended I{for testing purposes only}, it invokes the C{RhumbSolve} 

90 executable for I{every} method call. 

91 ''' 

92# def Area(self, polyline=False, **name): 

93# '''Set up a L{RhumbArea} to compute area and 

94# perimeter of a polygon. 

95# 

96# @kwarg polyline: If C{True}, compute the perimeter only, 

97# otherwise perimeter and area (C{bool}). 

98# @kwarg name: Optional C{B{name}=NN} (C{str}). 

99# 

100# @return: A L{RhumbArea} instance. 

101# 

102# @note: The B{C{debug}} setting is passed as C{verbose} 

103# to the returned L{RhumbAreaExact} instance. 

104# ''' 

105# rA = _MODS.rhumbs.rhumb*.RhumbArea(self, polyline=polyline, 

106# name=self._name__(name)) 

107# if self.verbose or self.debug: # PYCHOK no cover 

108# rA.verbose = True 

109# return rA 

110 

111# Polygon = Area # for C{geographiclib} compatibility 

112 

113 def _azimuth_reverse(self, azimuth): 

114 '''(INTERNAL) Reverse final azimuth C{azimuth}. 

115 ''' 

116 z = _norm180(float(azimuth)) 

117 if self.reverse2: # like .utils.atan2d 

118 z += _180_0 if z < 0 else _N_180_0 

119 return z 

120 

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

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

123 ''' 

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

125 

126 def Direct3(self, lat1, lon1, azi1, s12): # PYCHOK outmask 

127 '''Return the destination lat, lon and reverse azimuth 

128 (final bearing) in C{degrees}. 

129 

130 @return: L{Destination3Tuple}C{(lat, lon, final)}. 

131 ''' 

132 r = self._GDictDirect(lat1, lon1, azi1, False, s12, floats=False) 

133 z = self._azimuth_reverse(r.azi12) 

134 return Destination3Tuple(float(r.lat2), float(r.lon2), wrap360(z), 

135 iteration=r._iteration) 

136 

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

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

139 ''' 

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

141 

142 def DirectLine(self, lat1, lon1, azi1, caps=Caps.STANDARD, **name): 

143 '''Set up a L{RhumbLineSolve} 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{degrees}). 

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

148 @arg azi1: Azimuth at the first point (compass C{degrees}). 

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

150 the capabilities the L{RhumbLineSolve} instance 

151 should possess, always C{Caps.ALL}. 

152 @kwarg name: Optional C{B{name}=NN} (C{str}). 

153 

154 @return: A L{RhumbLineSolve} instance. 

155 

156 @note: If the point is at a pole, the azimuth is defined by keeping 

157 B{C{lon1}} fixed, writing C{B{lat1} = ±(90 − ε)}, and taking 

158 the limit C{ε → 0+}. 

159 

160 @see: C++ U{RhumbExact.Line 

161 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbExact.html>} 

162 and Python U{Rhumb.Line<https://GeographicLib.SourceForge.io/Python/doc/code.html>}. 

163 ''' 

164 return RhumbLineSolve(self, lat1, lon1, azi1, caps=caps, name=self._name__(name)) 

165 

166 def _GDictDirect(self, lat, lon, azi1, arcmode, s12_a12, *unused, **floats): # PYCHOK signature 

167 '''(INTERNAL) Get C{_GenDirect}-like result as an 8-item C{GDict}. 

168 ''' 

169 d = _RhumbSolveBase._GDictDirect(self, lat, lon, azi1, arcmode, s12_a12, **floats) 

170 r = GDict(lat1=lat, lon1=lon, azi12=azi1, s12=s12_a12) # a12=_over(s12_a12, self._mpd) 

171 r.update(d) 

172 return r 

173 

174 def _GDictInverse(self, lat1, lon1, lat2, lon2, *unused, **floats): # PYCHOK signature 

175 '''(INTERNAL) Get C{_GenInverse}-like result as an 8-item C{GDict}, but I{without} C{_SALP_CALPs_}. 

176 ''' 

177 i = _RhumbSolveBase._GDictInverse(self, lat1, lon1, lat2, lon2, **floats) 

178 a = _over(float(i.s12), self._mpd) # for .Inverse1 

179 r = GDict(lat1=lat1, lon1=lon1, lat2=lat2, lon2=lon2, a12=a) 

180 r.update(i) 

181 return r 

182 

183 def _Inverse(self, ll1, ll2, wrap, **unused): 

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

185 ''' 

186 if wrap: # PYCHOK no cover 

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

188 return self._GDictInverse(ll1.lat, ll1.lon, ll2.lat, ll2.lon) 

189 

190 def Inverse3(self, lat1, lon1, lat2, lon2): # PYCHOK outmask 

191 '''Return the distance in C{meter} and the forward and 

192 reverse azimuths (initial and final bearing) in C{degrees}. 

193 

194 @return: L{Distance3Tuple}C{(distance, initial, final)}. 

195 ''' 

196 r = self._GDictInverse(lat1, lon1, lat2, lon2, floats=False) 

197 z = self._azimuth_reverse(r.azi12) 

198 return Distance3Tuple(float(r.s12), wrap360(r.azi12), wrap360(z), 

199 iteration=r._iteration) 

200 

201 def _InverseLine(self, ll1, ll2, wrap, **name_caps): 

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

203 ''' 

204 if wrap: # PYCHOK no cover 

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

206 return self.InverseLine(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **name_caps) 

207 

208 def InverseLine(self, lat1, lon1, lat2, lon2, caps=Caps.STANDARD, **name): 

209 '''Define a L{RhumbLineSolve} in terms of the I{inverse} 

210 rhumb problem. 

211 

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

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

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

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

216 @kwarg caps: Optional C{caps}, see L{RhumbLine} C{B{caps}}. 

217 @kwarg name: Optional C{B{name}=NN} (C{str}). 

218 

219 @return: A L{RhumbLineSolve} instance and invoke its method 

220 L{RhumbLine.Position} to compute each point. 

221 

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

223 rhumb line. 

224 ''' 

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

226 return RhumbLineSolve(self, lat1, lon1, r.azi12, caps=caps, 

227 name=self._name__(name)) 

228 

229 Line = DirectLine 

230 

231 

232class RhumbLineSolve(_RhumbSolveBase, _SolveGDictLineBase): 

233 '''Wrapper to invoke I{Karney}'s U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>} 

234 like a class, similar to L{pygeodesy.RhumbLine} and L{pygeodesy.RhumbLineAux}. 

235 

236 @note: Use property C{RhumbSolve} or env variable C{PYGEODESY_RHUMBSOLVE} to specify the (fully 

237 qualified) path to the C{RhumbSolve} executable. 

238 

239 @note: This C{rhumb line} is intended I{for testing purposes only}, it invokes the C{RhumbSolve} 

240 executable for I{every} method call. 

241 ''' 

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

243 '''New L{RhumbLineSolve} instance, allowing points to be found along 

244 a rhumb starting at C{(B{lat1}, B{lon1})} with azimuth B{C{azi12}}. 

245 

246 @arg rhumb: The rhumb to use (L{RhumbSolve}). 

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

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

249 @arg azi12: Azimuth of the rhumb line (compass C{degrees180}). 

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

251 the capabilities the L{RhumbLineSolve} instance should 

252 possess, always C{Caps.ALL}. Use C{Caps.LINE_OFF} 

253 if updates to the B{C{rhumb}} should I{not} be 

254 reflected in this L{RhumbLineSolve} instance. 

255 @kwarg name: Optional C{B{name}=NN} (C{str}). 

256 

257 @kwarg name: Optional name (C{str}). 

258 

259 @raise RhumbError: Invalid path for C{RhumbSolve} executable or 

260 isn't the C{RhumbSolve} executable, see 

261 property C{B{rhumb}.RhumbSolve}. 

262 

263 @raise TypeError: Invalid B{C{rhumb}}. 

264 ''' 

265 _xinstanceof(RhumbSolve, rhumb=rhumb) 

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

267 rhumb = rhumb.copy(deep=False, name=NN(_UNDER_, rhumb.name)) 

268 _SolveGDictLineBase.__init__(self, rhumb, lat1, lon1, caps, azi12=azi12, **name) 

269 try: 

270 self.RhumbSolve = rhumb.RhumbSolve # rhumb or copy of rhumb 

271 except RhumbError: 

272 pass 

273 

274# def ArcPosition(self, a12, *unused): 

275# '''Find the position on the line given B{C{a12}}. 

276# 

277# @arg a12: Spherical arc length from the first point to the 

278# second point (C{degrees}). 

279# 

280# @return: A C{dict} with 8 items C{lat1, lon1, lat2, lon2, 

281# azi12, a12, s12, S12}. 

282# ''' 

283# s = a12 * self._mpd 

284# a = self._GDictInvoke(self._cmdArc, self._Names_Direct, s) 

285# r = GDict(a12=a12, s12=s, **self._lla1) 

286# r.updated(a) 

287# return r 

288 

289 @Property_RO 

290 def azi12(self): 

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

292 ''' 

293 return self._lla1.azi12 

294 

295 azi1 = azi12 # like GeodesicLineSolve 

296 

297 @Property_RO 

298 def azi12_sincos2(self): # PYCHOK no cover 

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

300 ''' 

301 return _sincos2d(self.azi12) 

302 

303 azi1_sincos2 = azi12_sincos2 

304 

305# @Property_RO 

306# def _cmdArc(self): 

307# '''(INTERNAL) Get the C{RhumbSolve} I{-a -L} cmd (C{tuple}). 

308# ''' 

309# return self._cmdDistance + ('-a',) 

310 

311 def Position(self, s12, **unused): 

312 '''Find the position on the line given B{C{s12}}. 

313 

314 @arg s12: Distance from the first point to the second (C{meter}). 

315 

316 @return: A L{GDict} with 7 items C{lat1, lon1, lat2, lon2, 

317 azi12, s12, S12}. 

318 ''' 

319 d = self._GDictInvoke(self._cmdDistance, self._Names_Direct, s12) 

320 r = GDict(s12=s12, **self._lla1) # a12=_over(s12, self._mpd) 

321 r.update(d) 

322 return r 

323 

324 def toStr(self, **prec_sep): # PYCHOK signature 

325 '''Return this C{RhumbLineSolve} as string. 

326 

327 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=", "} 

328 for the C{float} C{prec}ision, number of decimal digits 

329 (0..9) and the C{sep}arator string to join. Trailing 

330 zero decimals are stripped for B{C{prec}} values of 1 

331 and above, but kept for negative B{C{prec}} values. 

332 

333 @return: RhumbLineSolve items (C{str}). 

334 ''' 

335 return _SolveGDictLineBase._toStr(self, azi12=self.azi12, rhumb=self._solve, 

336 RhumbSolve=self.RhumbSolve, **prec_sep) 

337 

338 

339class RhumbSolve7Tuple(Rhumb8Tuple): 

340 '''7-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12)} with lat- C{lat1}, 

341 C{lat2} and longitudes C{lon1}, C{lon2} of both points, the azimuth of 

342 the rhumb line C{azi12}, the distance C{s12} and the area C{S12} under 

343 the rhumb line between both points. 

344 ''' 

345 assert Rhumb8Tuple._Names_.index(_a12_) == 7 

346 _Names_ = Rhumb8Tuple._Names_[:7] # drop a12 

347 _Units_ = Rhumb8Tuple._Units_[:7] 

348 

349 @deprecated_method 

350 def _to7Tuple(self): # PYCHOK no cover 

351 '''DEPRECATED, I{don't use!} 

352 ''' 

353 return _MODS.deprecated.classes.Rhumb7Tuple(self[:7]) 

354 

355 

356__all__ += _ALL_DOCS(_RhumbSolveBase) 

357 

358if __name__ == '__main__': 

359 

360 from pygeodesy import printf 

361 from sys import argv 

362 

363 def rhumb_intercept(rS, lat1, lon1, lat2, lon2, azi2, s23): 

364 # using RhumbSolve and GeodesicExact for I{Karney}'s C++ U{rhumb-intercept.cpp 

365 # <https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/> 

366 from pygeodesy.constants import EPS4 as _TOL 

367 from pygeodesy.karney import _diff182 

368 

369 E = rS.ellipsoid 

370 gX = E.geodesicx # == GeodesicExact(E) 

371 m = gX.STANDARD | gX.REDUCEDLENGTH | gX.GEODESICSCALE 

372 

373 rlS = rS.Line(lat2, lon2, azi2) 

374 sa, _ = rlS.azi12_sincos2 # aka _salp, _calp 

375 for i in range(1, 16): 

376 p = rlS.Position(s23) # outmask=gX.LATITUDE_LONGITUDE 

377 r = gX.Inverse(lat1, lon1, p.lat2, p.lon2, outmask=m) 

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

379 s, c = _sincos2d(d) 

380 printf('%2d %.3f %.8f, %.8f, %.8e', 

381 i, s23, r.lat2, r.lon2, c) 

382 s2, c2 = _sincos2d(r.lat2) 

383 c2 *= E.rocTransverse(r.lat2) 

384 if c2 and r.m12: 

385 s *= (s2 * sa) / c2 - s * r.M21 / r.m12 

386 t = (c / s) if s else _0_0 

387 if abs(t) < _TOL: 

388 break 

389 s23 += t 

390 else: 

391 break 

392 

393 rS = RhumbSolve(name='Test') 

394 rS.verbose = '--verbose' in argv # or '-v' in argv 

395 

396 if not _Xables.X_OK(rS.RhumbSolve): # not set 

397 rS.RhumbSolve = _Xables.RhumbSolve(_Xables.bin_) 

398 printf('version: %s', rS.version) 

399 

400 if len(argv) > 6: # 60 0 30 0 45 1e6 

401 t = (14, 's23'), (7, 'lat3'), (11, 'lon3'), (13, 'cos()') 

402 printf(' '.join('%*s' % _ for _ in t)) 

403 rhumb_intercept(rS, *map(float, argv[-6:])) 

404 exit() 

405 

406 r = rS.Direct(40.6, -73.8, 51, 5.5e6) 

407 printf('Direct: %r', r, nl=1) 

408 printf('Direct3: %r', rS.Direct3(40.6, -73.8, 51, 5.5e6)) 

409 

410 printf('Inverse: %r', rS.Inverse( 40.6, -73.8, 51.6, -0.5), nl=1) 

411 printf('Inverse1: %r', rS.Inverse1(40.6, -73.8, 51.6, -0.5)) 

412 printf('Inverse3: %r', rS.Inverse3(40.6, -73.8, 51.6, -0.5)) 

413 

414 printf('Inverse: %r', rS.Inverse( 40.6, -73.8, 35.8, 140.3), nl=1) 

415 printf('Inverse1: %r', rS.Inverse1(40.6, -73.8, 35.8, 140.3)) 

416 printf('Inverse3: %r', rS.Inverse3(40.6, -73.8, 35.8, 140.3)) 

417 

418 rlS = RhumbLineSolve(rS, 40.6, -73.8, 51, name='LineTest') 

419 p = rlS.Position(5.5e6) 

420 printf('Position: %s %r', p == r, p, nl=1) 

421# p = rlS.ArcPosition(49.475527) 

422# printf('ArcPosition: %s %r', p == r, p) 

423 

424 

425# % python3 -m pygeodesy.rhumb.solve 

426 

427# version: /opt/local/bin/RhumbSolve: GeographicLib version 2.2 

428 

429# Direct: GDict(azi12=51, lat1=40.6, lat2=71.6889, lon1=-73.8, lon2=0.25552, s12=5500000.0, S12=44095641862956.109375) 

430# Direct3: Destination3Tuple(lat=71.6889, lon=0.25552, final=51.0) 

431 

432# Inverse: GDict(a12=51.929543, azi12=77.76839, lat1=40.6, lat2=51.6, lon1=-73.8, lon2=-0.5, s12=5771083.383328, S12=37395209100030.390625) 

433# Inverse1: 51.929542507561905 

434# Inverse3: Distance3Tuple(distance=5771083.383328, initial=77.76839, final=77.76839) 

435 

436# Inverse: GDict(a12=115.02062, azi12=-92.388888, lat1=40.6, lat2=35.8, lon1=-73.8, lon2=140.3, s12=12782581.067684, S12=-63760642939072.5) 

437# Inverse1: 115.02061966879248 

438# Inverse3: Distance3Tuple(distance=12782581.067684, initial=267.611112, final=267.611112) 

439 

440# Position: True GDict(azi12=51, lat1=40.6, lat2=71.6889, lon1=-73.8, lon2=0.25552, s12=5500000.0, S12=44095641862956.109375) 

441 

442 

443# % python3 -m pygeodesy.rhumb.solve --verbose 

444 

445# RhumbSolve 'Test' 1: /opt/local/bin/RhumbSolve --version (invoke) 

446# RhumbSolve 'Test' 1: /opt/local/bin/RhumbSolve: GeographicLib version 2.2 (0) 

447# version: /opt/local/bin/RhumbSolve: GeographicLib version 2.2 

448# RhumbSolve 'Test' 2: /opt/local/bin/RhumbSolve -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct) 

449# RhumbSolve 'Test' 2: lat2=71.688899882813018, lon2=0.255519824423402, S12=44095641862956.109 (0) 

450 

451# Direct: GDict(azi12=51, lat1=40.6, lat2=71.6889, lon1=-73.8, lon2=0.25552, s12=5500000.0, S12=44095641862956.109375) 

452# RhumbSolve 'Test' 3: /opt/local/bin/RhumbSolve -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct3) 

453# RhumbSolve 'Test' 3: lat2=71.688899882813018, lon2=0.255519824423402, S12=44095641862956.109 (0) 

454# Direct3: Destination3Tuple(lat=71.6889, lon=0.25552, final=51.0) 

455# RhumbSolve 'Test' 4: /opt/local/bin/RhumbSolve -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse) 

456# RhumbSolve 'Test' 4: azi12=77.768389710255661, s12=5771083.383328028, S12=37395209100030.391 (0) 

457 

458# Inverse: GDict(a12=51.929543, azi12=77.76839, lat1=40.6, lat2=51.6, lon1=-73.8, lon2=-0.5, s12=5771083.383328, S12=37395209100030.390625) 

459# RhumbSolve 'Test' 5: /opt/local/bin/RhumbSolve -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse1) 

460# RhumbSolve 'Test' 5: azi12=77.768389710255661, s12=5771083.383328028, S12=37395209100030.391 (0) 

461# Inverse1: 51.929542507561905 

462# RhumbSolve 'Test' 6: /opt/local/bin/RhumbSolve -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse3) 

463# RhumbSolve 'Test' 6: azi12=77.768389710255661, s12=5771083.383328028, S12=37395209100030.391 (0) 

464# Inverse3: Distance3Tuple(distance=5771083.383328, initial=77.76839, final=77.76839) 

465# RhumbSolve 'Test' 7: /opt/local/bin/RhumbSolve -p 10 -i \ 40.600000000000001 -73.799999999999997 35.799999999999997 140.300000000000011 (Inverse) 

466# RhumbSolve 'Test' 7: azi12=-92.388887981699654, s12=12782581.0676841699, S12=-63760642939072.5 (0) 

467 

468# Inverse: GDict(a12=115.02062, azi12=-92.388888, lat1=40.6, lat2=35.8, lon1=-73.8, lon2=140.3, s12=12782581.067684, S12=-63760642939072.5) 

469# RhumbSolve 'Test' 8: /opt/local/bin/RhumbSolve -p 10 -i \ 40.600000000000001 -73.799999999999997 35.799999999999997 140.300000000000011 (Inverse1) 

470# RhumbSolve 'Test' 8: azi12=-92.388887981699654, s12=12782581.0676841699, S12=-63760642939072.5 (0) 

471# Inverse1: 115.02061966879248 

472# RhumbSolve 'Test' 9: /opt/local/bin/RhumbSolve -p 10 -i \ 40.600000000000001 -73.799999999999997 35.799999999999997 140.300000000000011 (Inverse3) 

473# RhumbSolve 'Test' 9: azi12=-92.388887981699654, s12=12782581.0676841699, S12=-63760642939072.5 (0) 

474# Inverse3: Distance3Tuple(distance=12782581.067684, initial=267.611112, final=267.611112) 

475 

476# Position: True GDict(azi12=51, lat1=40.6, lat2=71.6889, lon1=-73.8, lon2=0.25552, s12=5500000.0, S12=44095641862956.109375) 

477 

478 

479# % python3 -m pygeodesy.rhumb.solve 60 0 30 0 45 1e6 

480 

481# version: /opt/local/bin/RhumbSolve: GeographicLib version 2.2 

482# s23 lat3 lon3 cos() 

483# 1 1000000.000 36.37559999, 7.58982303, -5.83098638e-01 

484# 2 4532573.097 58.84251798, 41.57078946, 4.05349594e-01 

485# 3 2233216.895 44.22871762, 17.86660260, -2.91432608e-01 

486# 4 3168401.173 50.17678842, 26.60741388, 3.00555188e-02 

487# 5 3082690.347 49.63189746, 25.76374255, -1.49446251e-04 

488# 6 3083112.629 49.63458216, 25.76787599, -2.59865190e-09 

489# 7 3083112.636 49.63458221, 25.76787606, 4.96052409e-16 

490# 8 3083112.636 49.63458221, 25.76787606, -4.96052409e-16 

491# 9 3083112.636 49.63458221, 25.76787606, 4.96052409e-16 

492# 10 3083112.636 49.63458221, 25.76787606, -4.96052409e-16 

493# 11 3083112.636 49.63458221, 25.76787606, 4.96052409e-16 

494# 12 3083112.636 49.63458221, 25.76787606, -4.96052409e-16 

495# 13 3083112.636 49.63458221, 25.76787606, 4.96052409e-16 

496# 14 3083112.636 49.63458221, 25.76787606, -4.96052409e-16 

497# 15 3083112.636 49.63458221, 25.76787606, 4.96052409e-16 

498 

499 

500# **) MIT License 

501# 

502# Copyright (C) 2022-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

503# 

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

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

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

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

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

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

510# 

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

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

513# 

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

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

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

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

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

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

520# OTHER DEALINGS IN THE SOFTWARE.