1

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

3

4 u'''Ellipsoidal, I{Vincenty}-based geodesy.

5

6 I{Thaddeus Vincenty}'s geodetic (lat-/longitude) L{LatLon}, geocentric

7(ECEF) L{Cartesian} and L{VincentyError} classes and functions L{areaOf},

8 L{intersections2}, L{nearestOn} and L{perimeterOf}.

9

10 Pure Python implementation of geodesy tools for ellipsoidal earth models,

11 transcoded from JavaScript originals by I{(C) Chris Veness 2005-2016}

12 and published under the same MIT Licence**, see U{Vincenty geodesics

13<https://www.Movable-Type.co.UK/scripts/LatLongVincenty.html>}. More

14 at U{geographiclib<https://PyPI.org/project/geographiclib>} and

15 U{GeoPy<https://PyPI.org/project/geopy>}.

16

17 Calculate geodesic distance between two points using the U{Vincenty

18<https://WikiPedia.org/wiki/Vincenty's_formulae>} formulae and one of

19 several ellipsoidal earth models. The default model is WGS-84, the

20 most widely used globally-applicable model for the earth ellipsoid.

21

22 Other ellipsoids offering a better fit to the local geoid include Airy

23(1830) in the UK, Clarke (1880) in Africa, International 1924 in much

24 of Europe, and GRS-67 in South America. North America (NAD83) and

25 Australia (GDA) use GRS-80, which is equivalent to the WGS-84 model.

26

27 Great-circle distance uses a I{spherical} model of the earth with the

28 mean earth radius defined by the International Union of Geodesy and

29 Geophysics (IUGG) as M{(2 * a + b) / 3 = 6371008.7714150598} or about

30 6,371,009 meter (for WGS-84, resulting in an error of up to about 0.5%).

31

32 Here's an example usage of C{ellipsoidalVincenty}:

33

34 >>> from pygeodesy.ellipsoidalVincenty import LatLon

35 >>> Newport_RI = LatLon(41.49008, -71.312796)

36 >>> Cleveland_OH = LatLon(41.499498, -81.695391)

37 >>> Newport_RI.distanceTo(Cleveland_OH)

38 866,455.4329158525 # meter

39

40 To change the ellipsoid model used by the Vincenty formulae use:

41

42 >>> from pygeodesy import Datums

43 >>> from pygeodesy.ellipsoidalVincenty import LatLon

44 >>> p = LatLon(0, 0, datum=Datums.OSGB36)

45

46 or by converting to anothor datum:

47

48 >>> p = p.toDatum(Datums.OSGB36)

49'''

50# make sure int/int division yields float quotient, see .basics

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

52

53 from pygeodesy.constants import EPS, EPS0, _0_0, _1_0, _2_0, _3_0, _4_0, _6_0

54 from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, _nearestOn

55 from pygeodesy.ellipsoidalBaseDI import _intersection3, _intersections2, \

56 LatLonEllipsoidalBaseDI, _TOL_M

57 from pygeodesy.errors import _and, _ValueError, _xkwds

58 from pygeodesy.fmath import Fpolynomial, hypot, hypot1

59 from pygeodesy.interns import _ambiguous_, _antipodal_, _COLONSPACE_, _to_, _SPACE_

60 from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _ALL_OTHER

61 from pygeodesy.namedTuples import Destination2Tuple, Destination3Tuple, \

62 Distance3Tuple

63 from pygeodesy.points import Fmt, ispolar # PYCHOK exported

64 from pygeodesy.props import deprecated_function, deprecated_method, \

65 Property_RO, property_doc_

66# from pygeodesy.streprs import Fmt # from .points

67 from pygeodesy.units import Number_, Scalar_

68 from pygeodesy.utily import atan2b, atan2d, sincos2, sincos2d, unroll180, wrap180

69

70 from math import atan2, cos, degrees, fabs, radians, tan

71

72__all__ = _ALL_LAZY.ellipsoidalVincenty

73__version__ = '23.03.20'

74

75_antipodal_to_ = _SPACE_(_antipodal_, _to_)

76_limit_ = 'limit' # PYCHOK used!

77

78

79 class VincentyError(_ValueError):

80 '''Error raised from I{Vincenty}'s C{direct} and C{inverse} methods

81 for coincident points or lack of convergence.

82 '''

83 pass

84

85

86 class Cartesian(CartesianEllipsoidalBase):

87 '''Extended to convert geocentric, L{Cartesian} points to

88 Vincenty-based, ellipsoidal, geodetic L{LatLon}.

89 '''

90 @Property_RO

91 def Ecef(self):

92 '''Get the ECEF I{class} (L{EcefVeness}), I{lazily}.

93 '''

94 return _MODS.ecef.EcefVeness

95

96 def toLatLon(self, **LatLon_and_kwds): # PYCHOK LatLon=LatLon, datum=None

97 '''Convert this cartesian point to a C{Vincenty}-based geodetic point.

98

99 @kwarg LatLon_and_kwds: Optional L{LatLon} and L{LatLon} keyword

100 arguments as C{datum}. Use C{B{LatLon}=...,

101 B{datum}=...} to override this L{LatLon}

102 class or specify C{B{LatLon}=None}.

103

104 @return: The geodetic point (L{LatLon}) or if B{C{LatLon}} is C{None},

105 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}

106 with C{C} and C{M} if available.

107

108 @raise TypeError: Invalid B{C{LatLon_and_kwds}} argument.

109 '''

110 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon, datum=self.datum)

111 return CartesianEllipsoidalBase.toLatLon(self, **kwds)

112

113

114 class LatLon(LatLonEllipsoidalBaseDI):

115 '''Using the formulae devised by U{I{Thaddeus Vincenty (1975)}

116 <https://WikiPedia.org/wiki/Vincenty's_formulae>} for an (oblate)

117 ellipsoidal model of the earth to compute the geodesic distance

118 and bearings between two given points or the destination point

119 given an start point and (initial) bearing.

120

121 Set the earth model to be used with the keyword argument

122 datum. The default is Datums.WGS84, which is the most globally

123 accurate. For other models, see the Datums in module datum.

124

125 Note: This implementation of I{Vincenty} methods may not converge

126 for some valid points, raising a L{VincentyError}. In that case,

127 a result may be obtained by increasing the tolerance C{epsilon}

128 and/or iteration C{limit}, see properties L{LatLon.epsilon} and

129 L{LatLon.iterations}.

130 '''

131 _epsilon = 1e-12 # radians, about 6 um

132# _iteration = None # iteration number from .named._NamedBase

133 _iterations = 201 # default max, 200 vs Veness' 1,000

134

135 @deprecated_method

136 def bearingTo(self, other, wrap=False): # PYCHOK no cover

137 '''DEPRECATED, use method L{initialBearingTo} or L{bearingTo2}.

138 '''

139 return self.initialBearingTo(other, wrap=wrap)

140

141 @Property_RO

142 def Ecef(self):

143 '''Get the ECEF I{class} (L{EcefVeness}), I{lazily}.

144 '''

145 return _MODS.ecef.EcefVeness

146

147 @property_doc_(''' the convergence epsilon (C{radians}).''')

148 def epsilon(self):

149 '''Get the convergence epsilon (C{radians}).

150 '''

151 return self._epsilon

152

153 @epsilon.setter # PYCHOK setter!

154 def epsilon(self, epsilon):

155 '''Set the convergence epsilon (C{radians}).

156

157 @raise TypeError: Non-scalar B{C{epsilon}}.

158

159 @raise ValueError: Out of bounds B{C{epsilon}}.

160 '''

161 self._epsilon = Scalar_(epsilon=epsilon)

162

163 @property_doc_(''' the iteration limit (C{int}).''')

164 def iterations(self):

165 '''Get the iteration limit (C{int}).

166 '''

167 return self._iterations - 1

168

169 @iterations.setter # PYCHOK setter!

170 def iterations(self, limit):

171 '''Set the iteration limit (C{int}).

172

173 @raise TypeError: Non-scalar B{C{limit}}.

174

175 @raise ValueError: Out-of-bounds B{C{limit}}.

176 '''

177 self._iterations = Number_(limit, name=_limit_, low=4, high=1000) + 1

178

179 def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, datum=None

180 '''Convert this point to C{Vincenty}-based cartesian (ECEF)

181 coordinates.

182

183 @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} and other

184 keyword arguments, ignored if C{B{Cartesian}=None}. Use

185 C{B{Cartesian}=...} to override this L{Cartesian} class

186 or specify C{B{Cartesian}=None}.

187

188 @return: The cartesian point (L{Cartesian}) or if B{C{Cartesian}}

189 is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height,

190 C, M, datum)} with C{C} and C{M} if available.

191

192 @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other

193 B{C{Cartesian_datum_kwds}}.

194 '''

195 kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian,

196 datum=self.datum)

197 return LatLonEllipsoidalBaseDI.toCartesian(self, **kwds)

198

199 def _Direct(self, distance, bearing, llr, height):

200 '''(INTERNAL) Direct Vincenty method.

201

202 @raise TypeError: The B{C{other}} point is not L{LatLon}.

203

204 @raise ValueError: If this and the B{C{other}} point's L{Datum}

205 ellipsoids are not compatible.

206

207 @raise VincentyError: Vincenty fails to converge for the current

208 L{LatLon.epsilon} and L{LatLon.iterations}

209 limits.

210 '''

211 E = self.ellipsoid()

212 f = E.f

213

214 sb, cb = sincos2d(bearing)

215 s1, c1, t1 = _sincostan3(self.phi, f)

216

217 eps = self.epsilon

218 s12 = atan2(t1, cb) * _2_0

219 sa, ca2 = _sincos22(c1 * sb)

220 A, B = _AB2(ca2 * E.e22) # e22 == (a / b)**2 - 1

221 s = d = distance / (A * E.b)

222 for i in range(1, self._iterations): # 1-origin

223 ss, cs = sincos2(s)

224 c2sm, e = cos(s12 + s), s

225 s = _Ds(B, cs, ss, c2sm, d)

226 e = fabs(s - e)

227 if e < eps:

228 self._iteration = i

229 break

230 else:

231 t = self._no_convergence(e)

232 raise VincentyError(t, txt=repr(self)) # self.toRepr()

233

234 t = s1 * ss - c1 * cs * cb

235 # final bearing (reverse azimuth +/- 180)

236 d = atan2b(sa, -t)

237 if llr:

238 b = cb * ss

239 a = atan2d(s1 * cs + c1 * b, hypot(sa, t) * E.b_a)

240 b = atan2d(sb * ss, -s1 * b + c1 * cs) + self.lon \

241 - degrees(_Dl(f, ca2, sa, s, cs, ss, c2sm))

242 t = Destination3Tuple(a, wrap180(b), d)

243 r = self._Direct2Tuple(self.classof, height, t)

244 else:

245 r = Destination2Tuple(None, d, name=self.name)

246 return r

247

248 def _Inverse(self, other, wrap, azis=True): # PYCHOK signature

249 '''(INTERNAL) Inverse Vincenty method.

250

251 @raise TypeError: The B{C{other}} point is not L{LatLon}.

252

253 @raise ValueError: If this and the B{C{other}} point's L{Datum}

254 ellipsoids are not compatible.

255

256 @raise VincentyError: Vincenty fails to converge for the current

257 L{LatLon.epsilon} and L{LatLon.iterations}

258 limits and/or if this and the B{C{other}}

259 point are coincident or near-antipodal.

260 '''

261 E = self.ellipsoids(other)

262 f = E.f

263

264 s1, c1, _ = _sincostan3( self.phi, f)

265 s2, c2, _ = _sincostan3(other.phi, f)

266

267 c1c2, s1c2 = c1 * c2, s1 * c2

268 c1s2, s1s2 = c1 * s2, s1 * s2

269

270 eps = self.epsilon

271 d, _ = unroll180(self.lon, other.lon, wrap=wrap)

272 dl = ll = radians(d)

273 for i in range(1, self._iterations): # 1-origin

274 sll, cll = sincos2(ll)

275

276 ss = hypot(c2 * sll, c1s2 - s1c2 * cll)

277 if ss < EPS: # coincident or antipodal, ...

278 if self.isantipodeTo(other, eps=eps):

279 t = self._is_to(other, True)

280 raise VincentyError(_ambiguous_, txt=t)

281 self._iteration = i

282 # return zeros like Karney, unlike Veness

283 return Distance3Tuple(_0_0, 0, 0)

284

285 cs = s1s2 + c1c2 * cll

286 s, e = atan2(ss, cs), ll

287 sa, ca2 = _sincos22(c1c2 * sll / ss)

288 if ca2:

289 c2sm = cs - _2_0 * s1s2 / ca2

290 ll = _Dl(f, ca2, sa, s, cs, ss, c2sm, dl)

291 else: # equatorial line

292 ll = dl + f * sa * s

293 e = fabs(ll - e)

294 if e < eps:

295 self._iteration = i

296 break

297# elif abs(ll) > PI and self.isantipodeTo(other, eps=eps):

298# # omitted and applied *after* failure to converge below,

299# # see footnote under Inverse <https://WikiPedia.org/wiki/

300# # Vincenty's_formulae> and <https://GitHub.com/chrisveness/

301# # geodesy/blob/master/latlon-ellipsoidal-vincenty.js>

302# raise VincentyError(_ambiguous_, self._is_to(other, True))

303 else:

304 t = self._is_to(other, self.isantipodeTo(other, eps=eps))

305 raise VincentyError(self._no_convergence(e), txt=t)

306

307 if ca2: # e22 == (a / b)**2 - 1

308 A, B = _AB2(ca2 * E.e22)

309 s = -A * _Ds(B, cs, ss, c2sm, -s)

310

311 b = E.b

312# if self.height or other.height:

313# b += self._havg(other)

314 d = b * s

315

316 if azis: # forward and reverse azimuth

317 s, c = sincos2(ll)

318 f = atan2b(c2 * s, c1s2 - s1c2 * c)

319 r = atan2b(c1 * s, -s1c2 + c1s2 * c)

320 else:

321 f = r = _0_0

322 return Distance3Tuple(d, f, r, name=self.name)

323

324 def _is_to(self, other, anti):

325 '''(INTERNAL) Return I{'<self> [antipodal] to <other>'} text (C{str}).

326 '''

327 t = _antipodal_to_ if anti else _to_

328 return _SPACE_(repr(self), t, repr(other))

329

330 def _no_convergence(self, e):

331 '''(INTERNAL) Return I{'no convergence (..): ...'} text (C{str}).

332 '''

333 t = (Fmt.PARENSPACED(*t) for t in ((LatLon.epsilon.name, self.epsilon),

334 (LatLon.iterations.name, self.iterations)))

335 return _COLONSPACE_(Fmt.no_convergence(e), _and(*t))

336

337

338 def _AB2(u2): # WGS84 e22 = 0.00673949674227643

339 # 2-Tuple C{(A, B)} polynomials

340 if u2:

341 A = Fpolynomial(u2, 16384, 4096, -768, 320, -175).fover(16384)

342 B = Fpolynomial(u2, 0, 256, -128, 74, -47).fover( 1024)

343 return A, B

344 return _1_0, _0_0

345

346

347 def _c2sm2(c2sm):

348 # C{2 * c2sm**2 - 1}

349 return c2sm**2 * _2_0 - _1_0

350

351

352 def _Dl(f, ca2, sa, s, cs, ss, c2sm, dl=_0_0):

353 # C{Dl}

354 if f and sa:

355 C = f * ca2 / _4_0

356 C *= f - C * _3_0 + _1_0

357 if C and ss:

358 s += C * ss * (c2sm +

359 C * cs * _c2sm2(c2sm))

360 dl += (_1_0 - C) * f * sa * s

361 return dl

362

363

364 def _Ds(B, cs, ss, c2sm, d):

365 # C{Ds - d}

366 if B and ss:

367 c2sm2 = _c2sm2(c2sm)

368 ss2 = (ss**2 * _4_0 - _3_0) * (c2sm2 * _2_0 - _1_0)

369 B *= ss * (c2sm + B / _4_0 * (c2sm2 * cs -

370 B / _6_0 * c2sm * ss2))

371 d += B

372 return d

373

374

375 def _sincos22(sa):

376 # 2-Tuple C{(sin(a), cos(a)**2)}

377 ca2 = _1_0 - sa**2

378 return sa, (_0_0 if ca2 < EPS0 else ca2) # XXX EPS?

379

380

381 def _sincostan3(a, f):

382 # I{Reduced} C{(sin(B{a}), cos(B{a}), tan(B{a}))}

383 if a: # see L{sincostan3}

384 t = (_1_0 - f) * tan(a)

385 if t:

386 c = _1_0 / hypot1(t)

387 s = t * c

388 return s, c, t

389 return _0_0, _1_0, _0_0

390

391

392@deprecated_function

393 def areaOf(points, **datum_wrap):

394 '''DEPRECATED, use function L{ellipsoidalExact.areaOf} or L{ellipsoidalKarney.areaOf}.

395 '''

396 try:

397 return _MODS.ellipsoidalKarney.areaOf(points, **datum_wrap)

398 except ImportError:

399 return _MODS.ellipsoidalExact.areaOf(points, **datum_wrap)

400

401

402 def intersection3(start1, end1, start2, end2, height=None, wrap=True,

403 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):

404 '''Iteratively compute the intersection point of two paths, each defined

405 by two (ellipsoidal) points or by an (ellipsoidal) start point and an

406 initial bearing from North.

407

408 @arg start1: Start point of the first path (L{LatLon}).

409 @arg end1: End point of the first path (L{LatLon}) or the initial bearing

410 at the first point (compass C{degrees360}).

411 @arg start2: Start point of the second path (L{LatLon}).

412 @arg end2: End point of the second path (L{LatLon}) or the initial bearing

413 at the second point (compass C{degrees360}).

414 @kwarg height: Optional height at the intersection (C{meter}, conventionally)

415 or C{None} for the mean height.

416 @kwarg wrap: Wrap and unroll longitudes (C{bool}).

417 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function

418 L{pygeodesy.equidistant}) or C{None} for the preferred

419 C{B{start1}.Equidistant}.

420 @kwarg tol: Tolerance for convergence and for skew line distance and length

421 (C{meter}, conventionally).

422 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})

423 or C{None}.

424 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,

425 ignored if C{B{LatLon} is None}.

426

427 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}

428 a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat,

429 lon, height, datum)}.

430

431 @raise IntersectionError: Skew, colinear, parallel or otherwise

432 non-intersecting paths or no convergence

433 for the given B{C{tol}}.

434

435 @raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}},

436 B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.

437

438 @note: For each path specified with an initial bearing, a pseudo-end point

439 is computed as the C{destination} along that bearing at about 1.5

440 times the distance from the start point to an initial gu-/estimate

441 of the intersection point (and between 1/8 and 3/8 of the authalic

442 earth perimeter).

443

444 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/

445 calculating-intersection-of-two-circles>} and U{Karney's paper

446 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME

447 BOUNDARIES} for more details about the iteration algorithm.

448 '''

449 return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap,

450 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)

451

452

453 def intersections2(center1, radius1, center2, radius2, height=None, wrap=True,

454 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):

455 '''Iteratively compute the intersection points of two circles, each defined

456 by an (ellipsoidal) center point and a radius.

457

458 @arg center1: Center of the first circle (L{LatLon}).

459 @arg radius1: Radius of the first circle (C{meter}, conventionally).

460 @arg center2: Center of the second circle (L{LatLon}).

461 @arg radius2: Radius of the second circle (C{meter}, same units as

462 B{C{radius1}}).

463 @kwarg height: Optional height for the intersection points (C{meter},

464 conventionally) or C{None} for the I{"radical height"}

465 at the I{radical line} between both centers.

466 @kwarg wrap: Wrap and unroll longitudes (C{bool}).

467 @kwarg equidistant: An azimuthal equidistant projection (I{class} or

468 function L{pygeodesy.equidistant}) or C{None} for

469 the preferred C{B{center1}.Equidistant}.

470 @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}}

471 and B{C{radius2}}).

472 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})

473 or C{None}.

474 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,

475 ignored if C{B{LatLon} is None}.

476

477 @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance

478 or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is

479 None}. For abutting circles, both points are the same instance,

480 aka the I{radical center}.

481

482 @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting

483 circles or no convergence for the B{C{tol}}.

484

485 @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}}

486 or invalid B{C{equidistant}}.

487

488 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.

489

490 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/

491 calculating-intersection-of-two-circles>}, U{Karney's paper

492 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},

493 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and

494 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}

495 intersections.

496 '''

497 return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap,

498 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)

499

500

501 def nearestOn(point, point1, point2, within=True, height=None, wrap=False,

502 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):

503 '''Iteratively locate the closest point on the geodesic between

504 two other (ellipsoidal) points.

505

506 @arg point: Reference point (C{LatLon}).

507 @arg point1: Start point of the geodesic (C{LatLon}).

508 @arg point2: End point of the geodesic (C{LatLon}).

509 @kwarg within: If C{True} return the closest point I{between}

510 B{C{point1}} and B{C{point2}}, otherwise the

511 closest point elsewhere on the geodesic (C{bool}).

512 @kwarg height: Optional height for the closest point (C{meter},

513 conventionally) or C{None} or C{False} for the

514 interpolated height. If C{False}, the closest

515 takes the heights of the points into account.

516 @kwarg wrap: Wrap and unroll longitudes (C{bool}).

517 @kwarg equidistant: An azimuthal equidistant projection (I{class}

518 or function L{pygeodesy.equidistant}) or C{None}

519 for the preferred C{B{point}.Equidistant}.

520 @kwarg tol: Convergence tolerance (C{meter}).

521 @kwarg LatLon: Optional class to return the closest point

522 (L{LatLon}) or C{None}.

523 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword

524 arguments, ignored if C{B{LatLon} is None}.

525

526 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon}

527 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.

528

529 @raise ImportError: Package U{geographiclib

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

531 not installed or not found, but only if

532 C{B{equidistant}=}L{EquidistantKarney}.

533

534 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}}

535 or B{C{point2}} or invalid B{C{equidistant}}.

536

537 @raise ValueError: No convergence for the B{C{tol}}.

538

539 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/

540 calculating-intersection-of-two-circles>} and U{Karney's paper

541 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME

542 BOUNDARIES} for more details about the iteration algorithm.

543 '''

544 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap,

545 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)

546

547

548@deprecated_function

549 def perimeterOf(points, **closed_datum_wrap):

550 '''DEPRECATED, use function L{ellipsoidalExact.perimeterOf} or L{ellipsoidalKarney.perimeterOf}.

551 '''

552 try:

553 return _MODS.ellipsoidalKarney.perimeterOf(points, **closed_datum_wrap)

554 except ImportError:

555 return _MODS.ellipsoidalExact.perimeterOf(points, **closed_datum_wrap)

556

557

558__all__ += _ALL_OTHER(Cartesian, LatLon,

559 intersection3, intersections2, ispolar, # from .points

560 nearestOn) + _ALL_DOCS(areaOf, perimeterOf) # deprecated

561

562# **) MIT License

563#

564# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

565#

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

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

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

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

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

572#

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

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

575#

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

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