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 2005-2024}

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 LatLonEllipsoidalBaseDI, \

56 _intersection3, _intersections2, \

57 _TOL_M, intersecant2

58 from pygeodesy.errors import _and, _ValueError, _xkwds

59 from pygeodesy.fmath import Fpolynomial, hypot, hypot1

60 from pygeodesy.interns import _ambiguous_, _antipodal_, _COLONSPACE_, \

61 _to_, _SPACE_, _limit_ # PYCHOK used!

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

63 from pygeodesy.namedTuples import Destination2Tuple, Destination3Tuple, \

64 Distance3Tuple

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

66 from pygeodesy.props import deprecated_function, deprecated_method, \

67 property_doc_, property_RO

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

69 from pygeodesy.units import Number_, Scalar_

70 from pygeodesy.utily import atan2, atan2b, atan2d, sincos2, sincos2d, \

71 unroll180, wrap180

72

73 from math import cos, degrees, fabs, radians, tan as _tan

74

75__all__ = _ALL_LAZY.ellipsoidalVincenty

76__version__ = '24.11.26'

77

78_antipodal_to_ = _SPACE_(_antipodal_, _to_)

79

80

81 class VincentyError(_ValueError):

82 '''Error raised by I{Vincenty}'s C{Direct} and C{Inverse} methods

83 for coincident points or lack of convergence.

84 '''

85 pass

86

87

88 class Cartesian(CartesianEllipsoidalBase):

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

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

91 '''

92 @property_RO

93 def Ecef(self):

94 '''Get the ECEF I{class} (L{EcefVeness}), I{once}.

95 '''

96 return _Ecef()

97

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

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

100

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

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

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

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

105

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

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

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

109

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

111 '''

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

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

114

115

116 class LatLon(LatLonEllipsoidalBaseDI):

117 '''New point on an (oblate) ellipsoidal earth model, using the formulae devised

118 by U{I{Thaddeus Vincenty}<https://WikiPedia.org/wiki/Vincenty's_formulae>}

119 (1975) to compute geodesic distances, bearings (azimuths), etc.

120

121 Set the earth model to be used with the keyword argument datum. The default

122 is C{Datums.WGS84}, which is the most globally accurate. For other models,

123 see the L{Datums<pygeodesy.datums>}.

124

125 @note: This implementation of I{Vincenty} methods may not converge for some

126 valid points, raising a L{VincentyError}. In that case, a result may

127 be obtained by increasing the tolerance C{epsilon} and/or iteration

128 C{limit}, see properties L{LatLon.epsilon} and L{LatLon.iterations}.

129 '''

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

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

132 _iterations = 201 # 5, default max, 200 vs Veness' 1,000

133

134 @deprecated_method

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

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

137 '''

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

139

140 @property_RO

141 def Ecef(self):

142 '''Get the ECEF I{class} (L{EcefVeness}), I{once}.

143 '''

144 return _Ecef()

145

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

147 def epsilon(self):

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

149 '''

150 return self._epsilon

151

152 @epsilon.setter # PYCHOK setter!

153 def epsilon(self, epsilon):

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

155

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

157

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

159 '''

160 self._epsilon = Scalar_(epsilon=epsilon)

161

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

163 def iterations(self):

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

165 '''

166 return self._iterations - 1

167

168 @iterations.setter # PYCHOK setter!

169 def iterations(self, limit):

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

171

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

173

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

175 '''

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

177

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

179 '''Convert this point to C{Vincenty}-based cartesian (ECEF) coordinates.

180

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

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

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

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

185

186 @return: The cartesian point (L{Cartesian}) or if C{B{Cartesian} is None},

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

188 C{C} and C{M} if available.

189

190 @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other B{C{Cartesian_datum_kwds}}.

191 '''

192 kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian,

193 datum=self.datum)

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

195

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

197 '''(INTERNAL) Direct Vincenty method.

198

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

200

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

202 not compatible.

203

204 @raise VincentyError: Vincenty fails to converge for the current limits, see

205 L{epsilon<LatLon.epsilon>} and L{iterations<LatLon.iterations>}.

206 '''

207 E = self.ellipsoid()

208 f = E.f

209

210 sb, cb = sincos2d(bearing)

211 s1, c1, t1 = _sincostan3r(self.phi, f)

212

213 eps = self.epsilon

214 s12 = atan2(t1, cb) * _2_0

215 sa, ca2 = _sincos22(c1 * sb)

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

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

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

219 ss, cs = sincos2(s)

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

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

222 e = fabs(s - e)

223 if e < eps:

224 self._iteration = i

225 break

226 else:

227 t = self._no_convergence(e)

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

229

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

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

232 d = atan2b(sa, -t)

233 if llr:

234 b = cb * ss

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

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

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

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

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

240 else:

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

242 r._iteration = i

243 return r

244

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

246 '''(INTERNAL) Inverse Vincenty method.

247

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

249

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

251 ellipsoids are not compatible.

252

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

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

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

256 point are coincident or near-antipodal.

257 '''

258 E = self.ellipsoids(other)

259 f = E.f

260

261 s1, c1, _ = _sincostan3r( self.phi, f)

262 s2, c2, _ = _sincostan3r(other.phi, f)

263

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

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

266

267 eps = self.epsilon

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

269 dl = ll = radians(d)

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

271 sll, cll = sincos2(ll)

272

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

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

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

276 t = self._is_to(other, True)

277 raise VincentyError(_ambiguous_, txt=t)

278 self._iteration = i

279 # return zeros like Karney, unlike Veness

280 return Distance3Tuple(_0_0, 0, 0, iteration=i)

281

282 cs = s1s2 + c1c2 * cll

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

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

285 if ca2:

286 c2sm = cs - _2_0 * s1s2 / ca2

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

288 else: # equatorial line

289 ll = dl + f * sa * s

290 e = fabs(ll - e)

291 if e < eps:

292 self._iteration = i

293 break

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

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

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

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

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

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

300 else:

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

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

303

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

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

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

307

308 b = E.b

309# if self.height or other.height:

310# b += self._havg(other)

311 d = b * s

312

313 if azis: # forward and reverse azimuth

314 s, c = sincos2(ll)

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

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

317 else:

318 f = r = _0_0 # NAN

319 return Distance3Tuple(d, f, r, name=self.name, iteration=i)

320

321 def _is_to(self, other, anti):

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

323 '''

324 t = _antipodal_to_ if anti else _to_

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

326

327 def _no_convergence(self, e):

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

329 '''

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

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

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

333

334

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

336 # 2-Tuple C{(A, B)} polynomials

337 if u2:

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

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

340 return A, B

341 return _1_0, _0_0

342

343

344 def _c2sm2(c2sm):

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

346 return c2sm**2 * _2_0 - _1_0

347

348

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

350 # C{Dl}

351 if f and sa:

352 C = f * ca2 / _4_0

353 C *= f - C * _3_0 + _1_0

354 if C and ss:

355 s += C * ss * (c2sm +

356 C * cs * _c2sm2(c2sm))

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

358 return dl

359

360

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

362 # C{Ds - d}

363 if B and ss:

364 c2sm2 = _c2sm2(c2sm)

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

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

367 B / _6_0 * c2sm * ss2))

368 d += B

369 return d

370

371

372 def _Ecef():

373 # get the Ecef class and overwrite property_RO

374 Cartesian.Ecef = LatLon.Ecef = E = _MODS.ecef.EcefVeness

375 return E

376

377

378 def _sincos22(sa):

379 # 2-Tuple C{(sin(a), cos(a)**2)}

380 ca2 = _1_0 - sa**2

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

382

383

384 def _sincostan3r(a, f):

385 # I{Reduced} 3-tuple C{(sin(B{a}), cos(B{a}), tan(B{a}))}

386 if a: # see L{sincostan3}

387 t = (_1_0 - f) * _tan(a)

388 if t:

389 c = _1_0 / hypot1(t)

390 s = c * t

391 return s, c, t

392 return _0_0, _1_0, _0_0

393

394

395@deprecated_function

396 def areaOf(points, **datum_wrap):

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

398 '''

399 try:

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

401 except ImportError:

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

403

404

405 def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True

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

407 '''I{Iteratively} compute the intersection point of two lines, each defined

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

409 (initial) bearing from North.

410

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

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

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

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

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

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

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

418 or C{None} for the mean height.

419 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{start2}}

420 and B{C{end*}} points (C{bool}).

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

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

423 C{B{start1}.Equidistant}.

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

425 (C{meter}, conventionally).

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

427 or C{None}.

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

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

430

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

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

433 lon, height, datum)}.

434

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

436 non-intersecting lines or no convergence

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

438

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

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

441

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

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

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

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

446 earth perimeter).

447

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

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

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

451 BOUNDARIES} for more details about the iteration algorithm.

452 '''

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

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

455

456

457 def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True

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

459 '''I{Iteratively} compute the intersection points of two circles, each defined

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

461

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

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

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

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

466 B{C{radius1}}).

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

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

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

470 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{center2}}

471 (C{bool}).

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

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

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

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

476 and B{C{radius2}}).

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

478 or C{None}.

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

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

481

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

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

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

485 aka the I{radical center}.

486

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

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

489

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

491 or invalid B{C{equidistant}}.

492

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

494

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

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

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

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

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

500 intersections.

501 '''

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

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

504

505

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

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

508 '''I{Iteratively} locate the closest point on the geodesic between

509 two other (ellipsoidal) points.

510

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

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

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

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

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

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

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

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

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

520 takes the heights of the points into account.

521 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both

522 B{C{point1}} and B{C{point2}} (C{bool}).

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

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

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

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

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

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

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

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

531

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

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

534

535 @raise ImportError: Package U{geographiclib

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

537 not installed or not found, but only if

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

539

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

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

542

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

544

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

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

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

548 BOUNDARIES} for more details about the iteration algorithm.

549 '''

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

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

552

553

554@deprecated_function

555 def perimeterOf(points, **closed_datum_wrap):

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

557 '''

558 try:

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

560 except ImportError:

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

562

563

564__all__ += _ALL_DOCS(Cartesian, LatLon, intersecant2, # from .ellipsoidalBaseDI

565 intersection3, intersections2, ispolar, # from .points

566 nearestOn,

567 areaOf, perimeterOf) # DEPRECATED

568

569# **) MIT License

570#

571# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.

572#

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

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

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

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

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

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

579#

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

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

582#

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

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

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

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

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

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