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 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, _ALL_OTHER

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 atan2b, atan2d, sincos2, sincos2d, unroll180, wrap180

71

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

73

74__all__ = _ALL_LAZY.ellipsoidalVincenty

75__version__ = '23.12.18'

76

77_antipodal_to_ = _SPACE_(_antipodal_, _to_)

78

79

80 class VincentyError(_ValueError):

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

82 for coincident points or lack of convergence.

83 '''

84 pass

85

86

87 class Cartesian(CartesianEllipsoidalBase):

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

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

90 '''

91 @property_RO

92 def Ecef(self):

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

94 '''

95 return _Ecef()

96

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

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

99

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

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

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

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

104

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

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

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

108

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

110 '''

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

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

113

114

115 class LatLon(LatLonEllipsoidalBaseDI):

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

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

118 (1975) to compute geodesic distances, bearings (azimuths), etc.

119

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

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

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

123

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

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

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

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

128 '''

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

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

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

132

133 @deprecated_method

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

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

136 '''

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

138

139 @property_RO

140 def Ecef(self):

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

142 '''

143 return _Ecef()

144

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

146 def epsilon(self):

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

148 '''

149 return self._epsilon

150

151 @epsilon.setter # PYCHOK setter!

152 def epsilon(self, epsilon):

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

154

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

156

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

158 '''

159 self._epsilon = Scalar_(epsilon=epsilon)

160

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

162 def iterations(self):

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

164 '''

165 return self._iterations - 1

166

167 @iterations.setter # PYCHOK setter!

168 def iterations(self, limit):

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

170

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

172

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

174 '''

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

176

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

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

179 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 B{C{Cartesian}}

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

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

189

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

191 B{C{Cartesian_datum_kwds}}.

192 '''

193 kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian,

194 datum=self.datum)

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

196

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

198 '''(INTERNAL) Direct Vincenty method.

199

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

201

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

203 ellipsoids are not compatible.

204

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

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

207 limits.

208 '''

209 E = self.ellipsoid()

210 f = E.f

211

212 sb, cb = sincos2d(bearing)

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

214

215 eps = self.epsilon

216 s12 = atan2(t1, cb) * _2_0

217 sa, ca2 = _sincos22(c1 * sb)

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

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

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

221 ss, cs = sincos2(s)

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

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

224 e = fabs(s - e)

225 if e < eps:

226 self._iteration = i

227 break

228 else:

229 t = self._no_convergence(e)

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

231

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

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

234 d = atan2b(sa, -t)

235 if llr:

236 b = cb * ss

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

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

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

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

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

242 else:

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

244 r._iteration = i

245 return r

246

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

248 '''(INTERNAL) Inverse Vincenty method.

249

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

251

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

253 ellipsoids are not compatible.

254

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

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

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

258 point are coincident or near-antipodal.

259 '''

260 E = self.ellipsoids(other)

261 f = E.f

262

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

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

265

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

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

268

269 eps = self.epsilon

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

271 dl = ll = radians(d)

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

273 sll, cll = sincos2(ll)

274

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

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

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

278 t = self._is_to(other, True)

279 raise VincentyError(_ambiguous_, txt=t)

280 self._iteration = i

281 # return zeros like Karney, unlike Veness

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

283

284 cs = s1s2 + c1c2 * cll

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

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

287 if ca2:

288 c2sm = cs - _2_0 * s1s2 / ca2

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

290 else: # equatorial line

291 ll = dl + f * sa * s

292 e = fabs(ll - e)

293 if e < eps:

294 self._iteration = i

295 break

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

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

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

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

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

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

302 else:

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

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

305

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

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

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

309

310 b = E.b

311# if self.height or other.height:

312# b += self._havg(other)

313 d = b * s

314

315 if azis: # forward and reverse azimuth

316 s, c = sincos2(ll)

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

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

319 else:

320 f = r = _0_0 # NAN

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

322

323 def _is_to(self, other, anti):

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

325 '''

326 t = _antipodal_to_ if anti else _to_

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

328

329 def _no_convergence(self, e):

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

331 '''

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

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

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

335

336

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

338 # 2-Tuple C{(A, B)} polynomials

339 if u2:

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

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

342 return A, B

343 return _1_0, _0_0

344

345

346 def _c2sm2(c2sm):

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

348 return c2sm**2 * _2_0 - _1_0

349

350

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

352 # C{Dl}

353 if f and sa:

354 C = f * ca2 / _4_0

355 C *= f - C * _3_0 + _1_0

356 if C and ss:

357 s += C * ss * (c2sm +

358 C * cs * _c2sm2(c2sm))

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

360 return dl

361

362

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

364 # C{Ds - d}

365 if B and ss:

366 c2sm2 = _c2sm2(c2sm)

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

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

369 B / _6_0 * c2sm * ss2))

370 d += B

371 return d

372

373

374 def _Ecef():

375 # get the Ecef class and overwrite property_RO

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

377 return E

378

379

380 def _sincos22(sa):

381 # 2-Tuple C{(sin(a), cos(a)**2)}

382 ca2 = _1_0 - sa**2

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

384

385

386 def _sincostan3r(a, f):

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

388 if a: # see L{sincostan3}

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

390 if t:

391 c = _1_0 / hypot1(t)

392 s = c * t

393 return s, c, t

394 return _0_0, _1_0, _0_0

395

396

397@deprecated_function

398 def areaOf(points, **datum_wrap):

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

400 '''

401 try:

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

403 except ImportError:

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

405

406

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

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

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

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

411 (initial) bearing from North.

412

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

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

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

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

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

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

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

420 or C{None} for the mean height.

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

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

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

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

425 C{B{start1}.Equidistant}.

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

427 (C{meter}, conventionally).

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

429 or C{None}.

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

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

432

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

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

435 lon, height, datum)}.

436

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

438 non-intersecting lines or no convergence

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

440

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

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

443

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

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

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

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

448 earth perimeter).

449

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

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

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

453 BOUNDARIES} for more details about the iteration algorithm.

454 '''

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

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

457

458

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

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

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

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

463

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

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

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

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

468 B{C{radius1}}).

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

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

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

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

473 (C{bool}).

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

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

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

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

478 and B{C{radius2}}).

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

480 or C{None}.

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

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

483

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

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

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

487 aka the I{radical center}.

488

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

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

491

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

493 or invalid B{C{equidistant}}.

494

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

496

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

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

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

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

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

502 intersections.

503 '''

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

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

506

507

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

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

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

511 two other (ellipsoidal) points.

512

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

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

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

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

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

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

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

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

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

522 takes the heights of the points into account.

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

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

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

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

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

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

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

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

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

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

533

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

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

536

537 @raise ImportError: Package U{geographiclib

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

539 not installed or not found, but only if

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

541

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

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

544

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

546

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

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

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

550 BOUNDARIES} for more details about the iteration algorithm.

551 '''

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

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

554

555

556@deprecated_function

557 def perimeterOf(points, **closed_datum_wrap):

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

559 '''

560 try:

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

562 except ImportError:

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

564

565

566__all__ += _ALL_OTHER(Cartesian, LatLon, intersecant2, # from .ellipsoidalBaseDI

567 intersection3, intersections2, ispolar, # from .points

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

569

570# **) MIT License

571#

572# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

573#

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

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

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

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

580#

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

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583#

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