1

2# -*- coding: utf-8 -*-

3

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

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

6 as 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'''

11 from pygeodesy.basics import _xinstanceof

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

13 from pygeodesy.errors import RhumbError # PYCHOK used!

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

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

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

17 from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple

18 from pygeodesy.props import deprecated_method, Property, Property_RO

19 from pygeodesy.solveBase import _SolveGDictBase, _SolveGDictLineBase

20 from pygeodesy.utily import _unrollon, _Wrap, wrap360

21

22__all__ = _ALL_LAZY.rhumb_solve

23__version__ = '24.11.07'

24

25

26 class _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

82 class 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

232 class 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

339 class 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

358 if __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

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

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

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