Coverage for pygeodesy/rhumb/solve.py: 89%

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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 

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

17 _PYGEODESY_RHUMBSOLVE_ 

18from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple 

19from pygeodesy.props import deprecated_method, Property, Property_RO 

20from pygeodesy.solveBase import _SolveBase, _SolveLineBase 

21from pygeodesy.utily import _unrollon, _Wrap, wrap360 

22 

23__all__ = _ALL_LAZY.rhumb_solve 

24__version__ = '24.04.13' 

25 

26 

27class _RhumbSolveBase(_SolveBase): 

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

29 ''' 

30 _Error = RhumbError 

31 _Names_Direct = _lat2_, _lon2_, _S12_ 

32 _Names_Inverse = _azi12_, _s12_, _S12_ 

33 _Solve_name = 'RhumbSolve' 

34 _Solve_path = _getenv(_PYGEODESY_RHUMBSOLVE_, _PYGEODESY_RHUMBSOLVE_) 

35 

36 @Property_RO 

37 def _cmdBasic(self): 

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

39 ''' 

40 return (self.RhumbSolve,) + self._e_option \ 

41 + self._p_option \ 

42 + self._s_option 

43 

44 @Property 

45 def RhumbSolve(self): 

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

47 executable (C{filename}). 

48 ''' 

49 return self._Solve_path 

50 

51 @RhumbSolve.setter # PYCHOK setter! 

52 def RhumbSolve(self, path): 

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

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

55 

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

57 the C{RhumbSolve} executable. 

58 ''' 

59 self._setSolve(path) 

60 

61 @Property_RO 

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

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

64 

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

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

67 

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

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

70 (0..9) and the C{sep}arator string to join. Trailing 

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

72 1 and above, but kept for negative B{C{prec}} values. 

73 

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

75 ''' 

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

77 

78# @Property_RO 

79# def _u_option(self): 

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

81 

82 

83class RhumbSolve(_RhumbSolveBase): 

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

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

86 

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

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

89 

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

91 executable for I{every} method call. 

92 ''' 

93# def Area(self, polyline=False, name=NN): 

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

95# perimeter of a polygon. 

96# 

97# @kwarg polyline: If C{True} perimeter only, otherwise 

98# area and perimeter (C{bool}). 

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

100# 

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

102# 

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

104# to the returned L{RhumbAreaExact} instance. 

105# ''' 

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

107# name=name or self.name) 

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

109# rA.verbose = True 

110# return rA 

111 

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

113 

114 def _azimuth_reverse(self, azimuth): 

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

116 ''' 

117 z = _norm180(float(azimuth)) 

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

119 z += _180_0 if z < 0 else _N_180_0 

120 return z 

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

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

129 (final bearing) in C{degrees}. 

130 

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

132 ''' 

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

134 z = self._azimuth_reverse(r.azi12) 

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

136 iteration=r._iteration) 

137 

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

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

140 ''' 

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

142 

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

144 '''Set up a L{RhumbLineSolve} in terms of the I{direct} rhumb 

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

146 

147 @arg lat1: Latitude of the first point (C{degrees}). 

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

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

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

151 the capabilities the L{RhumbLineSolve} instance 

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

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=name or self.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 

176 I{without} C{_SALPs_CALPs_}. 

177 ''' 

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

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

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

181 r.update(i) 

182 return r 

183 

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

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

186 ''' 

187 if wrap: 

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

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

190 

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

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

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

194 

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

196 ''' 

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

198 z = self._azimuth_reverse(r.azi12) 

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

200 iteration=r._iteration) 

201 

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

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

204 ''' 

205 if wrap: 

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

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

208 

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

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

211 rhumb problem. 

212 

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

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

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

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

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

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=name or self.name) 

228 

229 Line = DirectLine 

230 

231 

232class RhumbLineSolve(_RhumbSolveBase, _SolveLineBase): 

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=NN): 

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 

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

257 

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

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

260 property C{B{rhumb}.RhumbSolve}. 

261 

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

263 ''' 

264 _xinstanceof(RhumbSolve, rhumb=rhumb) 

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

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

267 _SolveLineBase.__init__(self, rhumb, lat1, lon1, caps, name, azi12=azi12) 

268 try: 

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

270 except RhumbError: 

271 pass 

272 

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

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

275# 

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

277# second point (C{degrees}). 

278# 

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

280# azi12, a12, s12, S12}. 

281# ''' 

282# s = a12 * self._mpd 

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

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

285# r.updated(a) 

286# return r 

287 

288 @Property_RO 

289 def azi12(self): 

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

291 ''' 

292 return self._lla1.azi12 

293 

294 azi1 = azi12 # like GeodesicLineSolve 

295 

296 @Property_RO 

297 def azi12_sincos2(self): # PYCHOK no cover 

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

299 ''' 

300 return _sincos2d(self.azi12) 

301 

302 azi1_sincos2 = azi12_sincos2 

303 

304# @Property_RO 

305# def _cmdArc(self): 

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

307# ''' 

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

309 

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

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

312 

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

314 

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

316 azi12, s12, S12}. 

317 ''' 

318 d = self._GDictInvoke(self._cmdDistance, True, self._Names_Direct, s12) 

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

320 r.update(d) 

321 return r 

322 

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

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

325 

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

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

328 (0..9) and the C{sep}arator string to join. Trailing 

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

330 1 and above, but kept for negative B{C{prec}} values. 

331 

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

333 ''' 

334 return _SolveLineBase._toStr(self, azi12=self.azi12, rhumb=self._solve, 

335 RhumbSolve=self.RhumbSolve, **prec_sep) 

336 

337 

338class RhumbSolve7Tuple(Rhumb8Tuple): 

339 '''7-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12)} with lat- C{lat1}, 

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

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

342 the rhumb line between both points. 

343 ''' 

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

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

346 _Units_ = Rhumb8Tuple._Units_[:7] 

347 

348 @deprecated_method 

349 def _to7Tuple(self): # PYCHOK no cover 

350 '''DEPRECATED, I{don't use!} 

351 ''' 

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

353 

354 

355__all__ += _ALL_DOCS(_RhumbSolveBase) 

356 

357if __name__ == '__main__': 

358 

359 from pygeodesy import printf 

360 from sys import argv 

361 

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

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

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

365 from pygeodesy.constants import EPS4 as _TOL 

366 from pygeodesy.karney import _diff182 

367 

368 E = rS.ellipsoid 

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

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

371 

372 rlS = rS.Line(lat2, lon2, azi2) 

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

374 for i in range(1, 16): 

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

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

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

378 s, c = _sincos2d(d) 

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

380 i, s23, r.lat2, r.lon2, c) 

381 s2, c2 = _sincos2d(r.lat2) 

382 c2 *= E.rocTransverse(r.lat2) 

383 if c2 and r.m12: 

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

385 t = (c / s) if s else _0_0 

386 if abs(t) < _TOL: 

387 break 

388 s23 += t 

389 else: 

390 break 

391 

392 rS = RhumbSolve(name='Test') 

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

394 

395 if rS.RhumbSolve in (_PYGEODESY_RHUMBSOLVE_, None): # not set 

396 rS.RhumbSolve = '/opt/local/bin/RhumbSolve' # '/opt/local/Cellar/geographiclib/2.2/bin/RhumbSolve' # HomeBrew 

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

398 

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

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

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

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

403 exit() 

404 

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

406 printf('Direct: %r', r, nl=1) 

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

408 

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

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

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

412 

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

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

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

416 

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

418 p = rlS.Position(5.5e6) 

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

420# p = rlS.ArcPosition(49.475527) 

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

422 

423# % python3 -m pygeodesy.rhumb.solve 

424 

425# version: /opt/local/bin/RhumbSolve: GeographicLib version 1.51 

426# 

427# Direct: GDict(S12=44095641862956.148438, azi12=51, lat1=40.6, lat2=71.6889, lon1=-73.8, lon2=0.25552, s12=5500000.0) 

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

429# 

430# Inverse: GDict(S12=37395209100030.367188, a12=51.929543, azi12=77.76839, lat1=40.6, lat2=51.6, lon1=-73.8, lon2=-0.5, s12=5771083.383328) 

431# Inverse1: 51.92954250756195 

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

433# 

434# Inverse: GDict(S12=-63760642939072.492188, a12=115.02062, azi12=-92.388888, lat1=40.6, lat2=35.8, lon1=-73.8, lon2=140.3, s12=12782581.067684) 

435# Inverse1: 115.02061966879258 

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

437# 

438# Position: True GDict(S12=44095641862956.148438, azi12=51, lat1=40.6, lat2=71.6889, lon1=-73.8, lon2=0.25552, s12=5500000.0) 

439 

440 

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

442 

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

444# RhumbSolve 'Test' 1: /opt/local/bin/RhumbSolve: GeographicLib version 1.51 (0) 

445# version: /opt/local/bin/RhumbSolve: GeographicLib version 1.51 

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

447# RhumbSolve 'Test' 2: lat2=71.688899882813047, lon2=0.255519824423445, S12=44095641862956.148 (0) 

448 

449# Direct: GDict(S12=44095641862956.148438, azi12=51, lat1=40.6, lat2=71.6889, lon1=-73.8, lon2=0.25552, s12=5500000.0) 

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

451# RhumbSolve 'Test' 3: lat2=71.688899882813047, lon2=0.255519824423445, S12=44095641862956.148 (0) 

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

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

454# RhumbSolve 'Test' 4: azi12=77.768389710255661, s12=5771083.3833280317, S12=37395209100030.367 (0) 

455 

456# Inverse: GDict(S12=37395209100030.367188, a12=51.929543, azi12=77.76839, lat1=40.6, lat2=51.6, lon1=-73.8, lon2=-0.5, s12=5771083.383328) 

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

458# RhumbSolve 'Test' 5: azi12=77.768389710255661, s12=5771083.3833280317, S12=37395209100030.367 (0) 

459# Inverse1: 51.92954250756195 

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

461# RhumbSolve 'Test' 6: azi12=77.768389710255661, s12=5771083.3833280317, S12=37395209100030.367 (0) 

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

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

464# RhumbSolve 'Test' 7: azi12=-92.388887981699639, s12=12782581.0676841792, S12=-63760642939072.492 (0) 

465 

466# Inverse: GDict(S12=-63760642939072.492188, a12=115.02062, azi12=-92.388888, lat1=40.6, lat2=35.8, lon1=-73.8, lon2=140.3, s12=12782581.067684) 

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

468# RhumbSolve 'Test' 8: azi12=-92.388887981699639, s12=12782581.0676841792, S12=-63760642939072.492 (0) 

469# Inverse1: 115.02061966879258 

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

471# RhumbSolve 'Test' 9: azi12=-92.388887981699639, s12=12782581.0676841792, S12=-63760642939072.492 (0) 

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

473 

474# Position: True GDict(S12=44095641862956.148438, azi12=51, lat1=40.6, lat2=71.6889, lon1=-73.8, lon2=0.25552, s12=5500000.0) 

475 

476 

477# % python3 -m pygeodesy.rhumb.solve 

478 

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

480 

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

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

483 

484# 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) 

485# Inverse1: 51.92954250756191 

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

487 

488# 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) 

489# Inverse1: 115.02061966879249 

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

491 

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

493 

494 

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

496 

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

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

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

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

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

502 

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

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

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

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

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

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

509 

510# 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) 

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

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

513# Inverse1: 51.92954250756191 

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

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

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

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

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

519 

520# 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) 

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

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

523# Inverse1: 115.02061966879249 

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

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

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

527 

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

529 

530 

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

532 

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

534# s23 lat3 lon3 cos() 

535# 1 1000000.000 36.37559999, 7.58982303, -5.83098638e-01 

536# 2 4532573.097 58.84251798, 41.57078946, 4.05349594e-01 

537# 3 2233216.895 44.22871762, 17.86660260, -2.91432608e-01 

538# 4 3168401.173 50.17678842, 26.60741388, 3.00555188e-02 

539# 5 3082690.347 49.63189746, 25.76374255, -1.49446251e-04 

540# 6 3083112.629 49.63458216, 25.76787599, -2.59865190e-09 

541# 7 3083112.636 49.63458221, 25.76787606, 4.96052409e-16 

542# 8 3083112.636 49.63458221, 25.76787606, -4.96052409e-16 

543# 9 3083112.636 49.63458221, 25.76787606, 4.96052409e-16 

544# 10 3083112.636 49.63458221, 25.76787606, -4.96052409e-16 

545# 11 3083112.636 49.63458221, 25.76787606, 4.96052409e-16 

546# 12 3083112.636 49.63458221, 25.76787606, -4.96052409e-16 

547# 13 3083112.636 49.63458221, 25.76787606, 4.96052409e-16 

548# 14 3083112.636 49.63458221, 25.76787606, -4.96052409e-16 

549# 15 3083112.636 49.63458221, 25.76787606, 4.96052409e-16 

550 

551 

552# **) MIT License 

553# 

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

555# 

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

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

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

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

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

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

562# 

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

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

565# 

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

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

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

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

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

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

572# OTHER DEALINGS IN THE SOFTWARE.