1

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

3

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

5 classes U{Rhumb<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>}

6 and U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>}

7 from I{GeographicLib versions 2.0} and I{2.2} and I{Karney}'s C++ example U{Rhumb intersect

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

9

10 Class L{RhumbLine} has been enhanced with methods C{intersection2} and C{nearestOn4} to iteratively

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

12 geodesic or perpendicular rhumb line.

13

14 For more details, see the C++ U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/index.html>}

15 documentation, especially the U{Class List<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>},

16 the background information on U{Rhumb lines<https://GeographicLib.SourceForge.io/C++/doc/rhumb.html>},

17 the utily U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>} and U{Online

18 rhumb line calculations<https://GeographicLib.SourceForge.io/cgi-bin/RhumbSolve>}.

19

20 Copyright (C) U{Charles Karney<mailto:Karney@Alum.MIT.edu>} (2014-2023) and licensed under the MIT/X11

21 License. For more information, see the U{GeographicLib<https://GeographicLib.SourceForge.io>} documentation.

22'''

23# make sure int/int division yields float quotient

24 from __future__ import division as _; del _ # PYCHOK semicolon

25

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

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

28 _0_0, _0_01, _1_0, _90_0

29# from pygeodesy.datums import _spherical_datum # from .formy

30# from pygeodesy.ellipsoids import _EWGS84 # from .karney

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

32 _xdatum, _xkwds, _Xorder

33# from pygeodesy.etm import ExactTransverseMercator # _MODS

34 from pygeodesy.fmath import euclid, favg, fabs, Fsum

35 from pygeodesy.formy import opposing, _spherical_datum

36# from pygeodesy.fsums import Fsum # from .fmath

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

38 _no_, _parallel_, _under

39 from pygeodesy.karney import Caps, _CapsBase, _diff182, _fix90, _norm180, \

40 _EWGS84, _xinstanceof

41# from pygeodesy.ktm import KTransverseMercator, _AlpCoeffs # _MODS

42 from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS

43# from pygeodesy.named import notOverloaded # _MODS

44 from pygeodesy.namedTuples import Distance2Tuple, LatLon2Tuple, NearestOn4Tuple

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

46 from pygeodesy.streprs import Fmt, pairs, unstr

47 from pygeodesy.units import Float_, Lat, Lon, Meter, Int # PYCHOK shared

48 from pygeodesy.utily import _loneg, sincos2d, sincos2d_, _unrollon, _Wrap, \

49 sincos2_ # PYCHOK shared

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

51

52# from math import fabs # from .fmath

53

54__all__ = ()

55__version__ = '23.09.15'

56

57_rls = [] # instances of C{RbumbLine...} to be updated

58_TRIPS = 65 # .intersection2, .nearestOn4, 19+

59

60

61 class _Lat(Lat):

62 '''(INTERNAL) Latitude B{C{lat}}.

63 '''

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

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

66 Lat.__new__(_Lat, *lat, **kwds)

67

68

69 class _Lon(Lon):

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

71 '''

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

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

74 Lon.__new__(_Lon, *lon, **kwds)

75

76

77 def _update_all_rls(r):

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

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

80 C{Rhumb} instance B{C{r}}.

81 '''

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

83 _update_all(r)

84 for rl in _rls: # PYCHOK use weakref?

85 if rl._rhumb is r:

86 _update_all(rl)

87

88

89 class RhumbBase(_CapsBase):

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

91 '''

92 _E = _EWGS84

93 _exact = True

94 _f_max = _0_01

95 _mTM = 6 # see .TMorder

96

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

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

99 '''

100 if f is not None:

101 self.ellipsoid = a_earth, f

102 elif a_earth not in (_EWGS84, None):

103 self.ellipsoid = a_earth

104 if not exact:

105 self.exact = False

106 if name:

107 self.name = name

108

109 @Property_RO

110 def a(self):

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

112 '''

113 return self.ellipsoid.a

114

115 equatoradius = a

116

117 @Property_RO

118 def b(self):

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

120 '''

121 return self.ellipsoid.b

122

123 polaradius = b

124

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

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

127 '''

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

129

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

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

132 '''

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

134

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

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

137 '''

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

139

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

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

142 '''

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

144

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

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

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

148

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

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

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

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

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

154 L{Caps} values specifying the required capabilities.

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

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

157

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

159 C{.Position} to compute each point.

160

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

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

163 '''

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

165 **caps_name)

166

167 Line = DirectLine # synonyms

168

169 @Property

170 def ellipsoid(self):

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

172 '''

173 return self._E

174

175 @ellipsoid.setter # PYCHOK setter!

176 def ellipsoid(self, a_earth_f):

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

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

179

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

181 '''

182 E = _spherical_datum(a_earth_f, Error=RhumbError).ellipsoid

183 if self._E != E:

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

185 _update_all_rls(self)

186 self._E = E

187

188 @Property

189 def exact(self):

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

191 '''

192 return self._exact

193

194 @exact.setter # PYCHOK setter!

195 def exact(self, exact):

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

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

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

199

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

201 exceeds non-zero C{f_max}.

202

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

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

205 '''

206 x = bool(exact)

207 if self._exact != x:

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

209 _update_all_rls(self)

210 self._exact = x

211

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

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

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

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

216

217 @Property_RO

218 def f(self):

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

220 '''

221 return self.ellipsoid.f

222

223 flattening = f

224

225 @property

226 def f_max(self):

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

228 '''

229 return self._f_max

230

231 @f_max.setter # PYCHOK setter!

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

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

234

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

236 exceeds non-zero C{f_max}.

237 '''

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

239 if self._f_max != f:

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

241 self._f_max = f

242

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

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

245 '''

246 if wrap:

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

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

249

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

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

252 '''

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

254

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

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

257 '''

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

259

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

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

262 '''

263 if wrap:

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

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

266

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

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

269

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

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

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

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

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

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

276 L{Caps} values specifying the required capabilities.

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

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

279

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

281 C{.Position} to compute each point.

282

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

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

285 '''

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

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

288 **caps_name)

289

290 @Property_RO

291 def _RhumbLine(self): # PYCHOK no cover

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

293 '''

294 _MODS.named.notOverloaded(self)

295

296 def _TMorder(self, order):

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

298

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

300 '''

301 x = self.exact

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

303 if self._mTM != n:

304 _update_all_rls(self)

305 self._mTM = n

306 x = False

307 return x

308

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

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

311 '''

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

313

314

315 class RhumbLineBase(RhumbBase):

316 '''(INTERNAL) Class C{RhumbLine}

317 '''

318 _azi12 = _0_0

319# _caps = 0

320# _debug = 0

321# _lat1 = _0_0

322# _lon1 = _0_0

323# _lon12 = _0_0

324 _salp = _0_0

325 _calp = _1_0

326 _Rhumb = RhumbBase # compatible C{Rhumb} class

327 _rhumb = None # C{Rhumb} instance

328

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

330 '''New C{RhumbLine}.

331 '''

332 _xinstanceof(self._Rhumb, rhumb=rhumb)

333

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

335 self._lon1 = _Lon(lon1= lon1)

336 self._lon12 = _norm180(self._lon1)

337 if azi12: # non-zero, non-None

338 self.azi12 = _norm180(azi12)

339

340 n = name or rhumb.name

341 if n:

342 self.name=n

343

344 self._caps = caps

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

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

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

348 else:

349 self._rhumb = rhumb

350 _rls.append(self)

351

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

353 if _rls: # may be empty or None

354 try: # PYCHOK no cover

355 _rls.remove(self)

356 except (TypeError, ValueError):

357 pass

358 self._rhumb = None

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

360

361 @Property

362 def azi12(self):

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

364 '''

365 return self._azi12

366

367 @azi12.setter # PYCHOK setter!

368 def azi12(self, azi12):

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

370 '''

371 z = _norm180(azi12)

372 if self._azi12 != z:

373 if self._rhumb:

374 _update_all(self)

375 self._azi12 = z

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

377

378 @property_RO

379 def azi12_sincos2(self): # PYCHOK no cover

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

381 '''

382 return self._scalp, self._calp

383

384 def distance2(self, lat, lon):

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

386 point to this rhumb line's start point.

387

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

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

390

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

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

393

394 @see: Methods C{intersection2} and C{nearestOn4} of L{RhumbLineAux} and

395 L{RhumbLine}.

396 '''

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

398# outmask=Caps.AZIMUTH_DISTANCE)

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

400

401 @property_RO

402 def ellipsoid(self):

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

404 '''

405 return self.rhumb.ellipsoid

406

407 @property_RO

408 def exact(self):

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

410 '''

411 return self.rhumb.exact

412

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

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

415

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

417 @kwarg tol: Tolerance for longitudinal convergence and parallel

418 error (C{degrees}).

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

420

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

422 C{lon}gitude of the intersection point.

423

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

425 no intersection for an other reason.

426

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

428 L{pygeodesy.intersection3d3}.

429

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

431 L{ExactTransverseMercator} or L{KTransverseMercator}

432 projection and invoking function L{pygeodesy.intersection3d3}

433 in that domain.

434 '''

435 _xinstanceof(RhumbLineBase, other=other)

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

437 try:

438 if other is self:

439 raise ValueError(_coincident_)

440 # make invariants and globals locals

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

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

443 t = opposing(s_az, o_az, margin=tol)

444 if t is not None: # == t in (True, False)

445 raise ValueError(_parallel_)

446 _diff = euclid # approximate length

447 _i3d3 = _intersect3d3 # NOT .vector3d.intersection3d3

448 _LL2T = LatLon2Tuple

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

450 # use halfway point as initial estimate

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

452 favg(self.lon1, other.lon1))

453 for i in range(1, _TRIPS):

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

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

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

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

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

459 if d < tol: # 19 trips

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

461 name=self.intersection2.__name__)

462 except Exception as x:

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

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

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

466

467 @Property_RO

468 def isLoxodrome(self):

469 '''Is this rhumb line a loxodrome (C{True} if non-meridional and

470 non-parallel, C{False} if parallel or C{None} if meridional)?

471

472 @see: I{Osborne's} U{2.5 Rumb lines and loxodromes

473 <https://Zenodo.org/record/35392>}, page 37.

474 '''

475 return bool(self._salp) if self._calp else None

476

477 @Property_RO

478 def lat1(self):

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

480 '''

481 return self._lat1

482

483 @Property_RO

484 def lon1(self):

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

486 '''

487 return self._lon1

488

489 @Property_RO

490 def latlon1(self):

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

492 '''

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

494

495 def _mu22(self, mu12, mu1):

496 mu2 = mu12 + mu1

497 x90 = fabs(mu2) > 90

498 if x90: # reduce to [-180, 180)

499 mu2 = _norm180(mu2)

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

501 mu2 = _norm180(_loneg(mu2))

502 return mu2, x90

503

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

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

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

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

508

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

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

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

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

513 respectively C{not None}.

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

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

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

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

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

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

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

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

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

523

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

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

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

527 C{normal} azimuth at the intersection.

528

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

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

531 package not found or not installed.

532

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

534 no intersection for an other reason.

535

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

537 L{pygeodesy.intersection3d3}.

538 '''

539 if exact is None:

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

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

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

543 t = rl.distance2(p.lat, p.lon)

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

545 iteration=p.iteration)

546 else: # C{rhumb-intercept}

547 azi = self.azi12

548 szi = self._salp

549 E = self.ellipsoid

550 gX = E.geodesic_(exact=exact)

551 Cs = Caps

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

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

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

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

556 _, c = sincos2d(d)

557 s12 = c * r.s12 # signed

558 else:

559 s12 = Meter(est=est)

560 try:

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

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

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

564

565 _s12 = Fsum(s12).fsum2_

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

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

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

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

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

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

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

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

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

575 break

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

577 iteration=i)

578 except Exception as x: # Fsum(NAN) Value-, ZeroDivisionError

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

580 return r

581

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

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

584 '''

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

586

587 @Property_RO

588 def rhumb(self):

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

590 '''

591 return self._rhumb

592

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

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

595

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

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

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

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

600

601 @return: C{RhumbLine} (C{str}).

602 '''

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

604 azi12=self.azi12, exact=self.exact,

605 TMorder=self.TMorder, xTM=self.xTM)

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

607

608 @property_RO

609 def TMorder(self):

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

611 '''

612 return self.rhumb.TMorder

613

614 @Property_RO

615 def xTM(self):

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

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

618 '''

619 E = self.ellipsoid

620 # ExactTransverseMercator doesn't handle spherical earth models

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

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

623

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

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

626 as current intersection estimate and central meridian.

627 '''

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

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

630

631

632__all__ += _ALL_DOCS(RhumbBase, RhumbLineBase)

633

634

635 if __name__ == '__main__':

636

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

638

639 A = A(_EWGS84).Line(30, 0, 45)

640 R = R(_EWGS84).Line(30, 0, 45)

641

642 for i in range(1, 10):

643 s = .5e6 + 1e6 / i

644 a = A.Position(s).lon2

645 r = R.Position(s).lon2

646 e = (fabs(a - r) / a) if a else 0

647 printf('Position.lon2 %.14f vs %.14f, diff %g', r, a, e)

648

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

650 for est in (None, 1e6):

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

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

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

654 a.toRepr(), a.iteration, exact, est,

655 r.toRepr(), r.iteration, nl=1)

656

657# % python3 -m pygeodesy.rhumbBase

658

659# Position.lon2 11.61455846901637 vs 11.61455846901637, diff 3.05885e-16

660# Position.lon2 7.58982302826842 vs 7.58982302826842, diff 2.34045e-16

661# Position.lon2 6.28526067416369 vs 6.28526067416369, diff 1.41311e-16

662# Position.lon2 5.63938995325146 vs 5.63938995325146, diff 1.57495e-16

663# Position.lon2 5.25385527435707 vs 5.25385527435707, diff 3.38105e-16

664# Position.lon2 4.99764604290380 vs 4.99764604290380, diff 8.88597e-16

665# Position.lon2 4.81503363740473 vs 4.81503363740473, diff 1.84459e-16

666# Position.lon2 4.67828821748836 vs 4.67828821748835, diff 5.69553e-16

667# Position.lon2 4.57205667906283 vs 4.57205667906283, diff 1.94262e-16

668

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

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

671

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

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

674

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

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

677

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

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

680

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

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

683

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

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

686

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

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

689

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

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

692

693# **) MIT License

694#

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

696#

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

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

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

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

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

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

703#

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

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

706#

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

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

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

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

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

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

713# OTHER DEALINGS IN THE SOFTWARE.