Coverage for pygeodesy/ellipsoidalVincenty.py: 99%

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1 

2# -*- coding: utf-8 -*- 

3 

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

5 

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

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

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

9 

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

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

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

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

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

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

16 

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

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

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

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

21 

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

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

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

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

26 

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

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

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

306,371,009 meter (for WGS-84, resulting in an error of up to about 0.5%). 

31 

32Here'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 

40To 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 

46or by converting to anothor datum: 

47 

48 >>> p = p.toDatum(Datums.OSGB36) 

49''' 

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

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

52 

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

54from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, _nearestOn 

55from pygeodesy.ellipsoidalBaseDI import _intersection3, _intersections2, \ 

56 LatLonEllipsoidalBaseDI, _TOL_M 

57from pygeodesy.errors import _and, _ValueError, _xkwds 

58from pygeodesy.fmath import Fpolynomial, hypot, hypot1 

59from pygeodesy.interns import _ambiguous_, _antipodal_, _COLONSPACE_, \ 

60 _to_, _SPACE_, _limit_ # PYCHOK used! 

61from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _ALL_OTHER 

62from pygeodesy.namedTuples import Destination2Tuple, Destination3Tuple, \ 

63 Distance3Tuple 

64from pygeodesy.points import Fmt, ispolar # PYCHOK exported 

65from pygeodesy.props import deprecated_function, deprecated_method, \ 

66 Property_RO, property_doc_ 

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

68from pygeodesy.units import Number_, Scalar_ 

69from pygeodesy.utily import atan2b, atan2d, sincos2, sincos2d, unroll180, wrap180 

70 

71from math import atan2, cos, degrees, fabs, radians, tan 

72 

73__all__ = _ALL_LAZY.ellipsoidalVincenty 

74__version__ = '23.05.30' 

75 

76_antipodal_to_ = _SPACE_(_antipodal_, _to_) 

77 

78 

79class 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 

86class 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 

114class 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 # 5, 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 = _sincostan3r(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 r._iteration = i 

247 return r 

248 

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

250 '''(INTERNAL) Inverse Vincenty method. 

251 

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

253 

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

255 ellipsoids are not compatible. 

256 

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

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

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

260 point are coincident or near-antipodal. 

261 ''' 

262 E = self.ellipsoids(other) 

263 f = E.f 

264 

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

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

267 

268 c1c2, s1c2 = c1 * c2, s1 * c2 

269 c1s2, s1s2 = c1 * s2, s1 * s2 

270 

271 eps = self.epsilon 

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

273 dl = ll = radians(d) 

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

275 sll, cll = sincos2(ll) 

276 

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

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

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

280 t = self._is_to(other, True) 

281 raise VincentyError(_ambiguous_, txt=t) 

282 self._iteration = i 

283 # return zeros like Karney, unlike Veness 

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

285 

286 cs = s1s2 + c1c2 * cll 

287 s, e = atan2(ss, cs), ll 

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

289 if ca2: 

290 c2sm = cs - _2_0 * s1s2 / ca2 

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

292 else: # equatorial line 

293 ll = dl + f * sa * s 

294 e = fabs(ll - e) 

295 if e < eps: 

296 self._iteration = i 

297 break 

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

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

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

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

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

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

304 else: 

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

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

307 

308 if ca2: # e22 == (a / b)**2 - 1 

309 A, B = _AB2(ca2 * E.e22) 

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

311 

312 b = E.b 

313# if self.height or other.height: 

314# b += self._havg(other) 

315 d = b * s 

316 

317 if azis: # forward and reverse azimuth 

318 s, c = sincos2(ll) 

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

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

321 else: 

322 f = r = _0_0 

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

324 

325 def _is_to(self, other, anti): 

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

327 ''' 

328 t = _antipodal_to_ if anti else _to_ 

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

330 

331 def _no_convergence(self, e): 

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

333 ''' 

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

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

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

337 

338 

339def _AB2(u2): # WGS84 e22 = 0.00673949674227643 

340 # 2-Tuple C{(A, B)} polynomials 

341 if u2: 

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

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

344 return A, B 

345 return _1_0, _0_0 

346 

347 

348def _c2sm2(c2sm): 

349 # C{2 * c2sm**2 - 1} 

350 return c2sm**2 * _2_0 - _1_0 

351 

352 

353def _Dl(f, ca2, sa, s, cs, ss, c2sm, dl=_0_0): 

354 # C{Dl} 

355 if f and sa: 

356 C = f * ca2 / _4_0 

357 C *= f - C * _3_0 + _1_0 

358 if C and ss: 

359 s += C * ss * (c2sm + 

360 C * cs * _c2sm2(c2sm)) 

361 dl += (_1_0 - C) * f * sa * s 

362 return dl 

363 

364 

365def _Ds(B, cs, ss, c2sm, d): 

366 # C{Ds - d} 

367 if B and ss: 

368 c2sm2 = _c2sm2(c2sm) 

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

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

371 B / _6_0 * c2sm * ss2)) 

372 d += B 

373 return d 

374 

375 

376def _sincos22(sa): 

377 # 2-Tuple C{(sin(a), cos(a)**2)} 

378 ca2 = _1_0 - sa**2 

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

380 

381 

382def _sincostan3r(a, f): 

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

384 if a: # see L{sincostan3} 

385 t = (_1_0 - f) * tan(a) 

386 if t: 

387 c = _1_0 / hypot1(t) 

388 s = t * c 

389 return s, c, t 

390 return _0_0, _1_0, _0_0 

391 

392 

393@deprecated_function 

394def areaOf(points, **datum_wrap): 

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

396 ''' 

397 try: 

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

399 except ImportError: 

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

401 

402 

403def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True 

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

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

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

407 (initial) bearing from North. 

408 

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

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

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

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

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

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

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

416 or C{None} for the mean height. 

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

418 and B{C{end*}} points (C{bool}). 

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

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

421 C{B{start1}.Equidistant}. 

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

423 (C{meter}, conventionally). 

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

425 or C{None}. 

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

427 ignored if C{B{LatLon} is None}. 

428 

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

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

431 lon, height, datum)}. 

432 

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

434 non-intersecting lines or no convergence 

435 for the given B{C{tol}}. 

436 

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

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

439 

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

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

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

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

444 earth perimeter). 

445 

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

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

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

449 BOUNDARIES} for more details about the iteration algorithm. 

450 ''' 

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

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

453 

454 

455def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True 

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

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

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

459 

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

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

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

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

464 B{C{radius1}}). 

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

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

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

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

469 (C{bool}). 

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

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

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

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

474 and B{C{radius2}}). 

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

476 or C{None}. 

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

478 ignored if C{B{LatLon} is None}. 

479 

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

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

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

483 aka the I{radical center}. 

484 

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

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

487 

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

489 or invalid B{C{equidistant}}. 

490 

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

492 

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

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

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

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

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

498 intersections. 

499 ''' 

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

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

502 

503 

504def nearestOn(point, point1, point2, within=True, height=None, wrap=False, 

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

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

507 two other (ellipsoidal) points. 

508 

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

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

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

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

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

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

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

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

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

518 takes the heights of the points into account. 

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

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

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

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

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

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

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

526 (L{LatLon}) or C{None}. 

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

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

529 

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

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

532 

533 @raise ImportError: Package U{geographiclib 

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

535 not installed or not found, but only if 

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

537 

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

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

540 

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

542 

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

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

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

546 BOUNDARIES} for more details about the iteration algorithm. 

547 ''' 

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

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

550 

551 

552@deprecated_function 

553def perimeterOf(points, **closed_datum_wrap): 

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

555 ''' 

556 try: 

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

558 except ImportError: 

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

560 

561 

562__all__ += _ALL_OTHER(Cartesian, LatLon, 

563 intersection3, intersections2, ispolar, # from .points 

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

565 

566# **) MIT License 

567# 

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

569# 

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

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

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

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

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

576# 

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

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

579# 

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

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

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