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

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

17 _PYGEODESY_RHUMBSOLVE_

18 from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple

19 from pygeodesy.props import deprecated_method, Property, Property_RO

20 from pygeodesy.solveBase import _SolveGDictBase, _SolveGDictLineBase

21 from pygeodesy.utily import _unrollon, _Wrap, wrap360

22

23__all__ = _ALL_LAZY.rhumb_solve

24__version__ = '24.07.11'

25

26

27 class _RhumbSolveBase(_SolveGDictBase):

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 _Xable_name = 'RhumbSolve'

34 _Xable_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._Xable_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._setXable(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 1

72 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

83 class 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):

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 C{B{name}=NN} (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=self._name__(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):

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

154

155 @return: A L{RhumbLineSolve} instance.

156

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

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

159 the limit C{ε → 0+}.

160

161 @see: C++ U{RhumbExact.Line

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

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

164 '''

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

166

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

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

169 '''

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

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

172 r.update(d)

173 return r

174

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

176 '''(INTERNAL) Get C{_GenInverse}-like result as an 8-item C{GDict}, but I{without} C{_SALP_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):

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

219

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

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

222

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

224 rhumb line.

225 '''

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

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

228 name=self._name__(name))

229

230 Line = DirectLine

231

232

233 class RhumbLineSolve(_RhumbSolveBase, _SolveGDictLineBase):

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

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

236

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

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

239

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

241 executable for I{every} method call.

242 '''

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

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

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

246

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

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

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

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

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

252 the capabilities the L{RhumbLineSolve} instance should

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

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

255 reflected in this L{RhumbLineSolve} instance.

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

257

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

259

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

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

262 property C{B{rhumb}.RhumbSolve}.

263

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

265 '''

266 _xinstanceof(RhumbSolve, rhumb=rhumb)

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

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

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

270 try:

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

272 except RhumbError:

273 pass

274

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

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

277#

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

279# second point (C{degrees}).

280#

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

282# azi12, a12, s12, S12}.

283# '''

284# s = a12 * self._mpd

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

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

287# r.updated(a)

288# return r

289

290 @Property_RO

291 def azi12(self):

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

293 '''

294 return self._lla1.azi12

295

296 azi1 = azi12 # like GeodesicLineSolve

297

298 @Property_RO

299 def azi12_sincos2(self): # PYCHOK no cover

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

301 '''

302 return _sincos2d(self.azi12)

303

304 azi1_sincos2 = azi12_sincos2

305

306# @Property_RO

307# def _cmdArc(self):

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

309# '''

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

311

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

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

314

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

316

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

318 azi12, s12, S12}.

319 '''

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

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

322 r.update(d)

323 return r

324

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

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

327

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

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

330 (0..9) and the C{sep}arator string to join. Trailing

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

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

333

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

335 '''

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

337 RhumbSolve=self.RhumbSolve, **prec_sep)

338

339

340 class RhumbSolve7Tuple(Rhumb8Tuple):

341 '''7-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12)} with lat- C{lat1},

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

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

344 the rhumb line between both points.

345 '''

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

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

348 _Units_ = Rhumb8Tuple._Units_[:7]

349

350 @deprecated_method

351 def _to7Tuple(self): # PYCHOK no cover

352 '''DEPRECATED, I{don't use!}

353 '''

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

355

356

357__all__ += _ALL_DOCS(_RhumbSolveBase)

358

359 if __name__ == '__main__':

360

361 from pygeodesy import printf

362 from sys import argv

363

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

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

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

367 from pygeodesy.constants import EPS4 as _TOL

368 from pygeodesy.karney import _diff182

369

370 E = rS.ellipsoid

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

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

373

374 rlS = rS.Line(lat2, lon2, azi2)

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

376 for i in range(1, 16):

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

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

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

380 s, c = _sincos2d(d)

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

382 i, s23, r.lat2, r.lon2, c)

383 s2, c2 = _sincos2d(r.lat2)

384 c2 *= E.rocTransverse(r.lat2)

385 if c2 and r.m12:

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

387 t = (c / s) if s else _0_0

388 if abs(t) < _TOL:

389 break

390 s23 += t

391 else:

392 break

393

394 rS = RhumbSolve(name='Test')

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

396

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

398 rS.RhumbSolve = '/opt/local/bin/RhumbSolve' # '/opt/local/Cellar/geographiclib/2.3/bin/RhumbSolve' # HomeBrew

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

400

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

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

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

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

405 exit()

406

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

408 printf('Direct: %r', r, nl=1)

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

410

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

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

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

414

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

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

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

418

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

420 p = rlS.Position(5.5e6)

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

422# p = rlS.ArcPosition(49.475527)

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

424

425

426# % python3 -m pygeodesy.rhumb.solve

427

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

429

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

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

432

433# 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)

434# Inverse1: 51.929542507561905

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

436

437# 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)

438# Inverse1: 115.02061966879248

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

440

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

442

443

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

445

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

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

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

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

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

451

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

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

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

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

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

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

458

459# 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)

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

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

462# Inverse1: 51.929542507561905

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

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

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

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

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

468

469# 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)

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

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

472# Inverse1: 115.02061966879248

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

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

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

476

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

478

479

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

481

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

483# s23 lat3 lon3 cos()

484# 1 1000000.000 36.37559999, 7.58982303, -5.83098638e-01

485# 2 4532573.097 58.84251798, 41.57078946, 4.05349594e-01

486# 3 2233216.895 44.22871762, 17.86660260, -2.91432608e-01

487# 4 3168401.173 50.17678842, 26.60741388, 3.00555188e-02

488# 5 3082690.347 49.63189746, 25.76374255, -1.49446251e-04

489# 6 3083112.629 49.63458216, 25.76787599, -2.59865190e-09

490# 7 3083112.636 49.63458221, 25.76787606, 4.96052409e-16

491# 8 3083112.636 49.63458221, 25.76787606, -4.96052409e-16

492# 9 3083112.636 49.63458221, 25.76787606, 4.96052409e-16

493# 10 3083112.636 49.63458221, 25.76787606, -4.96052409e-16

494# 11 3083112.636 49.63458221, 25.76787606, 4.96052409e-16

495# 12 3083112.636 49.63458221, 25.76787606, -4.96052409e-16

496# 13 3083112.636 49.63458221, 25.76787606, 4.96052409e-16

497# 14 3083112.636 49.63458221, 25.76787606, -4.96052409e-16

498# 15 3083112.636 49.63458221, 25.76787606, 4.96052409e-16

499

500

501# **) MIT License

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

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511#

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

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