Coverage for pygeodesy/latlonBase.py: 93%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''(INTERNAL) Base class L{LatLonBase} for all elliposiodal, spherical and N-vectorial C{LatLon} classes. 

5 

6@see: I{(C) Chris Veness}' U{latlong<https://www.Movable-Type.co.UK/scripts/latlong.html>}, 

7 U{-ellipsoidal<https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>} and 

8 U{-vectors<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>} and I{Charles Karney}'s 

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

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

11''' 

12 

13from pygeodesy.basics import isscalar, isstr, map1, _xinstanceof 

14from pygeodesy.constants import EPS, EPS0, EPS1, EPS4, INT0, R_M, \ 

15 _0_0, _0_5, _1_0 

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

17from pygeodesy.dms import F_D, F_DMS, latDMS, lonDMS, parse3llh 

18# from pygeodesy.ecef import EcefKarney # _MODS 

19from pygeodesy.errors import _incompatible, IntersectionError, _IsnotError, \ 

20 _TypeError, _ValueError, _xdatum, _xError, \ 

21 _xkwds, _xkwds_not 

22# from pygeodesy.fmath import favg # _MODS 

23from pygeodesy.formy import antipode, compassAngle, cosineAndoyerLambert_, \ 

24 cosineForsytheAndoyerLambert_, cosineLaw, \ 

25 equirectangular, euclidean, flatLocal_, \ 

26 flatPolar, _hartzell, haversine, isantipode, \ 

27 _isequalTo, isnormal, normal, philam2n_xyz, \ 

28 thomas_, vincentys, _spherical_datum 

29from pygeodesy.interns import NN, _COMMASPACE_, _concentric_, _height_, \ 

30 _intersection_, _LatLon_, _m_, _negative_, \ 

31 _no_, _overlap_, _point_ # PYCHOK used! 

32# from pygeodesy.iters import PointsIter, points2 # from .vector3d, _MODS 

33# from pygeodesy.karney import Caps # _MODS 

34from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

35# from pygeodesy.ltp import Ltp, _xLtp # _MODS 

36from pygeodesy.named import _NamedBase, notOverloaded, Fmt 

37from pygeodesy.namedTuples import Bounds2Tuple, LatLon2Tuple, PhiLam2Tuple, \ 

38 Trilaterate5Tuple, Vector3Tuple 

39# from pygeodesy.nvectorBase import _N_vector_ # _MODS 

40from pygeodesy.props import deprecated_method, Property, Property_RO, \ 

41 property_RO, _update_all 

42# from pygeodesy.streprs import Fmt, hstr # from .named, _MODS 

43from pygeodesy.units import Distance_, Lat, Lon, Height, Radius, Radius_, \ 

44 Scalar, Scalar_ 

45from pygeodesy.utily import _unrollon, _unrollon3, _Wrap 

46from pygeodesy.vector2d import _circin6, Circin6Tuple, _circum3, circum4_, \ 

47 Circum3Tuple, _radii11ABC 

48from pygeodesy.vector3d import nearestOn6, Vector3d, PointsIter 

49 

50from contextlib import contextmanager 

51from math import asin, cos, degrees, fabs, radians 

52 

53__all__ = _ALL_LAZY.latlonBase 

54__version__ = '23.10.04' 

55 

56 

57class LatLonBase(_NamedBase): 

58 '''(INTERNAL) Base class for C{LatLon} points on spherical or 

59 ellipsoidal earth models. 

60 ''' 

61 _clipid = INT0 # polygonal clip, see .booleans 

62 _datum = None # L{Datum}, to be overriden 

63 _height = INT0 # height (C{meter}), default 

64 _lat = 0 # latitude (C{degrees}) 

65 _lon = 0 # longitude (C{degrees}) 

66 

67 def __init__(self, latlonh, lon=None, height=0, wrap=False, name=NN): 

68 '''New C{LatLon}. 

69 

70 @arg latlonh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or 

71 a previous C{LatLon} instance provided C{B{lon}=None}. 

72 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or 

73 C(None), indicating B{C{latlonh}} is a C{LatLon}. 

74 @kwarg height: Optional height above (or below) the earth surface 

75 (C{meter}, conventionally). 

76 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}} 

77 (C{bool}). 

78 @kwarg name: Optional name (C{str}). 

79 

80 @return: New instance (C{LatLon}). 

81 

82 @raise RangeError: A B{C{lon}} or C{lat} value outside the valid 

83 range and L{rangerrors} set to C{True}. 

84 

85 @raise TypeError: If B{C{latlonh}} is not a C{LatLon}. 

86 

87 @raise UnitError: Invalid B{C{lat}}, B{C{lon}} or B{C{height}}. 

88 

89 @example: 

90 

91 >>> p = LatLon(50.06632, -5.71475) 

92 >>> q = LatLon('50°03′59″N', """005°42'53"W""") 

93 >>> r = LatLon(p) 

94 ''' 

95 if name: 

96 self.name = name 

97 

98 if lon is None: 

99 try: 

100 lat, lon = latlonh.lat, latlonh.lon 

101 height = latlonh.get(_height_, height) 

102 except AttributeError: 

103 raise _IsnotError(_LatLon_, latlonh=latlonh) 

104 if wrap: 

105 lat, lon = _Wrap.latlon(lat, lon) 

106 elif wrap: 

107 lat, lon = _Wrap.latlonDMS2(latlonh, lon) 

108 else: 

109 lat = latlonh 

110 

111 self._lat = Lat(lat) # parseDMS2(lat, lon) 

112 self._lon = Lon(lon) # PYCHOK LatLon2Tuple 

113 if height: # elevation 

114 self._height = Height(height) 

115 

116 def __eq__(self, other): 

117 return self.isequalTo(other) 

118 

119 def __ne__(self, other): 

120 return not self.isequalTo(other) 

121 

122 def __str__(self): 

123 return self.toStr(form=F_D, prec=6) 

124 

125 def antipode(self, height=None): 

126 '''Return the antipode, the point diametrically opposite 

127 to this point. 

128 

129 @kwarg height: Optional height of the antipode (C{meter}), 

130 this point's height otherwise. 

131 

132 @return: The antipodal point (C{LatLon}). 

133 ''' 

134 h = self._heigHt(height) 

135 return self.classof(*antipode(*self.latlon), height=h) 

136 

137 @deprecated_method 

138 def bounds(self, wide, tall, radius=R_M): # PYCHOK no cover 

139 '''DEPRECATED, use method C{boundsOf}.''' 

140 return self.boundsOf(wide, tall, radius=radius) 

141 

142 def boundsOf(self, wide, tall, radius=R_M, height=None): 

143 '''Return the SW and NE lat-/longitude of a great circle 

144 bounding box centered at this location. 

145 

146 @arg wide: Longitudinal box width (C{meter}, same units as 

147 B{C{radius}} or C{degrees} if B{C{radius}} is C{None}). 

148 @arg tall: Latitudinal box size (C{meter}, same units as 

149 B{C{radius}} or C{degrees} if B{C{radius}} is C{None}). 

150 @kwarg radius: Mean earth radius (C{meter}) or C{None} if I{both} 

151 B{C{wide}} and B{C{tall}} are in C{degrees}. 

152 @kwarg height: Height for C{latlonSW} and C{latlonNE} (C{meter}), 

153 overriding the point's height. 

154 

155 @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)}, the 

156 lower-left and upper-right corner (C{LatLon}). 

157 

158 @see: U{https://www.Movable-Type.co.UK/scripts/latlong-db.html} 

159 ''' 

160 w = Scalar_(wide=wide) * _0_5 

161 t = Scalar_(tall=tall) * _0_5 

162 if radius is not None: 

163 r = Radius_(radius) 

164 c = cos(self.phi) 

165 w = degrees(asin(w / r) / c) if fabs(c) > EPS0 else _0_0 # XXX 

166 t = degrees(t / r) 

167 y, t = self.lat, fabs(t) 

168 x, w = self.lon, fabs(w) 

169 

170 h = self._heigHt(height) 

171 sw = self.classof(y - t, x - w, height=h) 

172 ne = self.classof(y + t, x + w, height=h) 

173 return Bounds2Tuple(sw, ne, name=self.name) 

174 

175 def chordTo(self, other, height=None, wrap=False): 

176 '''Compute the length of the chord through the earth between 

177 this and an other point. 

178 

179 @arg other: The other point (C{LatLon}). 

180 @kwarg height: Overriding height for both points (C{meter}) 

181 or C{None} for each point's height. 

182 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{other}} 

183 point (C{bool}). 

184 

185 @return: The chord length (conventionally C{meter}). 

186 

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

188 ''' 

189 def _v3d(ll): 

190 t = ll.toEcef(height=height) # .toVector(Vector=Vector3d) 

191 return Vector3d(t.x, t.y, t.z) 

192 

193 p = self.others(other) 

194 if wrap: 

195 p = _Wrap.point(p) 

196 return _v3d(self).minus(_v3d(p)).length 

197 

198 def circin6(self, point2, point3, eps=EPS4, wrap=False): 

199 '''Return the radius and center of the I{inscribed} aka I{In-}circle 

200 of the (planar) triangle formed by this and two other points. 

201 

202 @arg point2: Second point (C{LatLon}). 

203 @arg point3: Third point (C{LatLon}). 

204 @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}. 

205 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and 

206 B{C{point3}} (C{bool}). 

207 

208 @return: L{Circin6Tuple}C{(radius, center, deltas, cA, cB, cC)}. The 

209 C{center} and contact points C{cA}, C{cB} and C{cC}, each an 

210 instance of this (sub-)class, are co-planar with this and the 

211 two given points, see the B{Note} below. 

212 

213 @raise ImportError: Package C{numpy} not found, not installed or older 

214 than version 1.10. 

215 

216 @raise IntersectionError: Near-coincident or -colinear points or 

217 a trilateration or C{numpy} issue. 

218 

219 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. 

220 

221 @note: The C{center} is trilaterated in cartesian (ECEF) space and converted 

222 back to geodetic lat-, longitude and height. The latter, conventionally 

223 in C{meter} indicates whether the C{center} is above, below or on the 

224 surface of the earth model. If C{deltas} is C{None}, the C{center} is 

225 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon, 

226 height)} representing the differences between both results from 

227 L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof. 

228 

229 @see: Function L{pygeodesy.circin6}, method L{circum3}, U{Incircle 

230 <https://MathWorld.Wolfram.com/Incircle.html>} and U{Contact Triangle 

231 <https://MathWorld.Wolfram.com/ContactTriangle.html>}. 

232 ''' 

233 with _toCartesian3(self, point2, point3, wrap) as cs: 

234 r, c, d, cA, cB, cC = _circin6(*cs, eps=eps, useZ=True, dLL3=True, 

235 datum=self.datum) # PYCHOK unpack 

236 return Circin6Tuple(r, c.toLatLon(), d, cA.toLatLon(), cB.toLatLon(), cC.toLatLon()) 

237 

238 def circum3(self, point2, point3, circum=True, eps=EPS4, wrap=False): 

239 '''Return the radius and center of the smallest circle I{through} or I{containing} 

240 this and two other points. 

241 

242 @arg point2: Second point (C{LatLon}). 

243 @arg point3: Third point (C{LatLon}). 

244 @kwarg circum: If C{True} return the C{circumradius} and C{circumcenter}, 

245 always, ignoring the I{Meeus}' Type I case (C{bool}). 

246 @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}. 

247 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and 

248 B{C{point3}} (C{bool}). 

249 

250 @return: A L{Circum3Tuple}C{(radius, center, deltas)}. The C{center}, an 

251 instance of this (sub-)class, is co-planar with this and the two 

252 given points. If C{deltas} is C{None}, the C{center} is 

253 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, 

254 lon, height)} representing the difference between both results 

255 from L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof. 

256 

257 @raise ImportError: Package C{numpy} not found, not installed or older than 

258 version 1.10. 

259 

260 @raise IntersectionError: Near-concentric, -coincident or -colinear points, 

261 incompatible C{Ecef} classes or a trilateration 

262 or C{numpy} issue. 

263 

264 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. 

265 

266 @note: The C{center} is trilaterated in cartesian (ECEF) space and converted 

267 back to geodetic lat-, longitude and height. The latter, conventionally 

268 in C{meter} indicates whether the C{center} is above, below or on the 

269 surface of the earth model. If C{deltas} is C{None}, the C{center} is 

270 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon, 

271 height)} representing the difference between both results from 

272 L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof. 

273 

274 @see: Function L{pygeodesy.circum3} and methods L{circin6} and L{circum4_}. 

275 ''' 

276 with _toCartesian3(self, point2, point3, wrap, circum=circum) as cs: 

277 r, c, d = _circum3(*cs, circum=circum, eps=eps, useZ=True, dLL3=True, # XXX -3d2 

278 clas=cs[0].classof, datum=self.datum) # PYCHOK unpack 

279 return Circum3Tuple(r, c.toLatLon(), d) 

280 

281 def circum4_(self, *points, **wrap): 

282 '''Best-fit a sphere through this and two or more other points. 

283 

284 @arg points: The other points (each a C{LatLon}). 

285 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{points}} 

286 (C{bool}), default C{False}. 

287 

288 @return: L{Circum4Tuple}C{(radius, center, rank, residuals)} with C{center} 

289 an instance of this (sub-)class. 

290 

291 @raise ImportError: Package C{numpy} not found, not installed or older than 

292 version 1.10. 

293 

294 @raise NumPyError: Some C{numpy} issue. 

295 

296 @raise TypeError: One of the B{C{points}} invalid. 

297 

298 @raise ValueError: Too few B{C{points}}. 

299 

300 @see: Function L{pygeodesy.circum4_} and L{circum3}. 

301 ''' 

302 def _cs(ps, C, wrap=False): 

303 _wp = _Wrap.point if wrap else (lambda p: p) 

304 for i, p in enumerate(ps): 

305 yield C(i=i, points=_wp(p)) 

306 

307 C = self._toCartesianEcef 

308 c = C(point=self) 

309 t = circum4_(c, Vector=c.classof, *_cs(points, C, **wrap)) 

310 c = t.center.toLatLon(LatLon=self.classof) 

311 return t.dup(center=c) 

312 

313 @property 

314 def clipid(self): 

315 '''Get the (polygonal) clip (C{int}). 

316 ''' 

317 return self._clipid 

318 

319 @clipid.setter # PYCHOK setter! 

320 def clipid(self, clipid): 

321 '''Get the (polygonal) clip (C{int}). 

322 ''' 

323 self._clipid = int(clipid) 

324 

325 @deprecated_method 

326 def compassAngle(self, other, **adjust_wrap): # PYCHOK no cover 

327 '''DEPRECATED, use method L{compassAngleTo}.''' 

328 return self.compassAngleTo(other, **adjust_wrap) 

329 

330 def compassAngleTo(self, other, **adjust_wrap): 

331 '''Return the angle from North for the direction vector between 

332 this and an other point. 

333 

334 Suitable only for short, non-near-polar vectors up to a few 

335 hundred Km or Miles. Use method C{initialBearingTo} for 

336 larger distances. 

337 

338 @arg other: The other point (C{LatLon}). 

339 @kwarg adjust_wrap: Optional keyword arguments for function 

340 L{pygeodesy.compassAngle}. 

341 

342 @return: Compass angle from North (C{degrees360}). 

343 

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

345 

346 @note: Courtesy of Martin Schultz. 

347 

348 @see: U{Local, flat earth approximation 

349 <https://www.EdWilliams.org/avform.htm#flat>}. 

350 ''' 

351 p = self.others(other) 

352 return compassAngle(self.lat, self.lon, p.lat, p.lon, **adjust_wrap) 

353 

354 def cosineAndoyerLambertTo(self, other, wrap=False): 

355 '''Compute the distance between this and an other point using the U{Andoyer-Lambert correction<https:// 

356 navlib.net/wp-content/uploads/2013/10/admiralty-manual-of-navigation-vol-1-1964-english501c.pdf>} 

357 of the U{Law of Cosines<https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>} formula. 

358 

359 @arg other: The other point (C{LatLon}). 

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

361 the B{C{other}} point (C{bool}). 

362 

363 @return: Distance (C{meter}, same units as the axes of this 

364 point's datum ellipsoid). 

365 

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

367 

368 @see: Function L{pygeodesy.cosineAndoyerLambert} and methods 

369 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, 

370 C{distanceTo*}, L{equirectangularTo}, L{euclideanTo}, 

371 L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, L{haversineTo}, 

372 L{thomasTo} and L{vincentysTo}. 

373 ''' 

374 return self._distanceTo_(cosineAndoyerLambert_, other, wrap=wrap) 

375 

376 def cosineForsytheAndoyerLambertTo(self, other, wrap=False): 

377 '''Compute the distance between this and an other point using 

378 the U{Forsythe-Andoyer-Lambert correction 

379 <https://www2.UNB.Ca/gge/Pubs/TR77.pdf>} of the U{Law of Cosines 

380 <https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>} 

381 formula. 

382 

383 @arg other: The other point (C{LatLon}). 

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

385 the B{C{other}} point (C{bool}). 

386 

387 @return: Distance (C{meter}, same units as the axes of 

388 this point's datum ellipsoid). 

389 

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

391 

392 @see: Function L{pygeodesy.cosineForsytheAndoyerLambert} and methods 

393 L{cosineAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

394 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

395 L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo}. 

396 ''' 

397 return self._distanceTo_(cosineForsytheAndoyerLambert_, other, wrap=wrap) 

398 

399 def cosineLawTo(self, other, radius=None, wrap=False): 

400 '''Compute the distance between this and an other point using the 

401 U{spherical Law of Cosines 

402 <https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>} 

403 formula. 

404 

405 @arg other: The other point (C{LatLon}). 

406 @kwarg radius: Mean earth radius (C{meter}) or C{None} 

407 for the mean radius of this point's datum 

408 ellipsoid. 

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

410 the B{C{other}} point (C{bool}). 

411 

412 @return: Distance (C{meter}, same units as B{C{radius}}). 

413 

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

415 

416 @see: Function L{pygeodesy.cosineLaw} and methods L{cosineAndoyerLambertTo}, 

417 L{cosineForsytheAndoyerLambertTo}, C{distanceTo*}, L{equirectangularTo}, 

418 L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, 

419 L{haversineTo}, L{thomasTo} and L{vincentysTo}. 

420 ''' 

421 return self._distanceTo(cosineLaw, other, radius, wrap=wrap) 

422 

423 @property_RO 

424 def datum(self): # PYCHOK no cover 

425 '''I{Must be overloaded}.''' 

426 notOverloaded(self) 

427 

428 def destinationXyz(self, delta, LatLon=None, **LatLon_kwds): 

429 '''Calculate the destination using a I{local} delta from this point. 

430 

431 @arg delta: Local delta to the destination (L{XyzLocal}, L{Enu}, 

432 L{Ned} or L{Local9Tuple}). 

433 @kwarg LatLon: Optional (geodetic) class to return the destination 

434 or C{None}. 

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

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

437 

438 @return: Destination as a C{B{LatLon}(lat, lon, **B{LatLon_kwds})} 

439 instance or if C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, 

440 lon, height)} respectively L{LatLon4Tuple}C{(lat, lon, 

441 height, datum)} depending on whether a C{datum} keyword 

442 is un-/specified. 

443 

444 @raise TypeError: Invalid B{C{delta}}, B{C{LatLon}} or B{C{LatLon_kwds}}. 

445 ''' 

446 t = self._ltp._local2ecef(delta, nine=True) 

447 return t.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, name=self.name)) 

448 

449 def _distanceTo(self, func, other, radius=None, **kwds): 

450 '''(INTERNAL) Helper for distance methods C{<func>To}. 

451 ''' 

452 p, r = self.others(other, up=2), radius 

453 if r is None: 

454 r = self._datum.ellipsoid.R1 if self._datum else R_M 

455 return func(self.lat, self.lon, p.lat, p.lon, radius=r, **kwds) 

456 

457 def _distanceTo_(self, func_, other, wrap=False, radius=None): 

458 '''(INTERNAL) Helper for (ellipsoidal) methods C{<func>To}. 

459 ''' 

460 p = self.others(other, up=2) 

461 D = self.datum 

462 lam21, phi2, _ = _Wrap.philam3(self.lam, p.phi, p.lam, wrap) 

463 r = func_(phi2, self.phi, lam21, datum=D) 

464 return r * (D.ellipsoid.a if radius is None else radius) 

465 

466 @Property_RO 

467 def Ecef(self): 

468 '''Get the ECEF I{class} (L{EcefKarney}), I{lazily}. 

469 ''' 

470 return _MODS.ecef.EcefKarney # default 

471 

472 @Property_RO 

473 def _Ecef_forward(self): 

474 '''(INTERNAL) Helper for L{_ecef9} and L{toEcef} (C{callable}). 

475 ''' 

476 return self.Ecef(self.datum, name=self.name).forward 

477 

478 @Property_RO 

479 def _ecef9(self): 

480 '''(INTERNAL) Helper for L{toCartesian}, L{toEcef} and L{toCartesian} (L{Ecef9Tuple}). 

481 ''' 

482 return self._Ecef_forward(self, M=True) 

483 

484 @deprecated_method 

485 def equals(self, other, eps=None): # PYCHOK no cover 

486 '''DEPRECATED, use method L{isequalTo}.''' 

487 return self.isequalTo(other, eps=eps) 

488 

489 @deprecated_method 

490 def equals3(self, other, eps=None): # PYCHOK no cover 

491 '''DEPRECATED, use method L{isequalTo3}.''' 

492 return self.isequalTo3(other, eps=eps) 

493 

494 def equirectangularTo(self, other, **radius_adjust_limit_wrap): 

495 '''Compute the distance between this and an other point 

496 using the U{Equirectangular Approximation / Projection 

497 <https://www.Movable-Type.co.UK/scripts/latlong.html#equirectangular>}. 

498 

499 Suitable only for short, non-near-polar distances up to a 

500 few hundred Km or Miles. Use method L{haversineTo} or 

501 C{distanceTo*} for more accurate and/or larger distances. 

502 

503 @arg other: The other point (C{LatLon}). 

504 @kwarg radius_adjust_limit_wrap: Optional keyword arguments 

505 for function L{pygeodesy.equirectangular}, 

506 overriding the default mean C{radius} of this 

507 point's datum ellipsoid. 

508 

509 @return: Distance (C{meter}, same units as B{C{radius}}). 

510 

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

512 

513 @see: Function L{pygeodesy.equirectangular} and methods L{cosineAndoyerLambertTo}, 

514 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

515 C{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, 

516 L{haversineTo}, L{thomasTo} and L{vincentysTo}. 

517 ''' 

518 return self._distanceTo(equirectangular, other, **radius_adjust_limit_wrap) 

519 

520 def euclideanTo(self, other, **radius_adjust_wrap): 

521 '''Approximate the C{Euclidian} distance between this and 

522 an other point. 

523 

524 See function L{pygeodesy.euclidean} for the available B{C{options}}. 

525 

526 @arg other: The other point (C{LatLon}). 

527 @kwarg radius_adjust_wrap: Optional keyword arguments for function 

528 L{pygeodesy.euclidean}, overriding the default mean 

529 C{radius} of this point's datum ellipsoid. 

530 

531 @return: Distance (C{meter}, same units as B{C{radius}}). 

532 

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

534 

535 @see: Function L{pygeodesy.euclidean} and methods L{cosineAndoyerLambertTo}, 

536 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

537 L{equirectangularTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, 

538 L{haversineTo}, L{thomasTo} and L{vincentysTo}. 

539 ''' 

540 return self._distanceTo(euclidean, other, **radius_adjust_wrap) 

541 

542 def flatLocalTo(self, other, radius=None, wrap=False): 

543 '''Compute the distance between this and an other point using the 

544 U{ellipsoidal Earth to plane projection 

545 <https://WikiPedia.org/wiki/Geographical_distance#Ellipsoidal_Earth_projected_to_a_plane>} 

546 aka U{Hubeny<https://www.OVG.AT/de/vgi/files/pdf/3781/>} formula. 

547 

548 @arg other: The other point (C{LatLon}). 

549 @kwarg radius: Mean earth radius (C{meter}) or C{None} for 

550 the I{equatorial radius} of this point's 

551 datum ellipsoid. 

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

553 the B{C{other}} point (C{bool}). 

554 

555 @return: Distance (C{meter}, same units as B{C{radius}}). 

556 

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

558 

559 @raise ValueError: Invalid B{C{radius}}. 

560 

561 @see: Function L{pygeodesy.flatLocal}/L{pygeodesy.hubeny}, methods 

562 L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo}, 

563 L{cosineLawTo}, C{distanceTo*}, L{equirectangularTo}, L{euclideanTo}, 

564 L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo} and 

565 U{local, flat Earth approximation<https://www.edwilliams.org/avform.htm#flat>}. 

566 ''' 

567 return self._distanceTo_(flatLocal_, other, wrap=wrap, radius= 

568 radius if radius in (None, R_M, _1_0, 1) else Radius(radius)) # PYCHOK kwargs 

569 

570 hubenyTo = flatLocalTo # for Karl Hubeny 

571 

572 def flatPolarTo(self, other, **radius_wrap): 

573 '''Compute the distance between this and an other point using 

574 the U{polar coordinate flat-Earth<https://WikiPedia.org/wiki/ 

575 Geographical_distance#Polar_coordinate_flat-Earth_formula>} formula. 

576 

577 @arg other: The other point (C{LatLon}). 

578 @kwarg radius_wrap: Optional keyword arguments for function 

579 L{pygeodesy.flatPolar}, overriding the 

580 default mean C{radius} of this point's 

581 datum ellipsoid. 

582 

583 @return: Distance (C{meter}, same units as B{C{radius}}). 

584 

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

586 

587 @see: Function L{pygeodesy.flatPolar} and methods L{cosineAndoyerLambertTo}, 

588 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

589 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

590 L{haversineTo}, L{thomasTo} and L{vincentysTo}. 

591 ''' 

592 return self._distanceTo(flatPolar, other, **radius_wrap) 

593 

594 def hartzell(self, los=None, earth=None): 

595 '''Compute the intersection of a Line-Of-Sight (los) from this Point-Of-View 

596 (pov) with this point's ellipsoid surface. 

597 

598 @kwarg los: Line-Of-Sight, I{direction} to earth (L{Los}, L{Vector3d}) 

599 or C{None} to point to the ellipsoid's center. 

600 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, 

601 L{a_f2Tuple} or C{scalar} radius in C{meter}) overriding 

602 this point's C{datum} ellipsoid. 

603 

604 @return: The ellipsoid intersection (C{LatLon}) with C{.height} set 

605 to the distance to this C{pov}. 

606 

607 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov} 

608 is inside the ellipsoid or B{C{los}} points 

609 outside or away from the ellipsoid. 

610 

611 @raise TypeError: Invalid B{C{los}}. 

612 

613 @see: Function C{hartzell} for further details. 

614 ''' 

615 return _hartzell(self, los, earth, LatLon=self.classof) 

616 

617 def haversineTo(self, other, **radius_wrap): 

618 '''Compute the distance between this and an other point using the 

619 U{Haversine<https://www.Movable-Type.co.UK/scripts/latlong.html>} 

620 formula. 

621 

622 @arg other: The other point (C{LatLon}). 

623 @kwarg radius_wrap: Optional keyword arguments for function 

624 L{pygeodesy.haversine}, overriding the 

625 default mean C{radius} of this point's 

626 datum ellipsoid. 

627 

628 @return: Distance (C{meter}, same units as B{C{radius}}). 

629 

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

631 

632 @see: Function L{pygeodesy.haversine} and methods L{cosineAndoyerLambertTo}, 

633 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

634 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

635 L{flatPolarTo}, L{thomasTo} and L{vincentysTo}. 

636 ''' 

637 return self._distanceTo(haversine, other, **radius_wrap) 

638 

639 def _havg(self, other, f=_0_5, h=None): 

640 '''(INTERNAL) Weighted, average height. 

641 

642 @arg other: An other point (C{LatLon}). 

643 @kwarg f: Optional fraction (C{float}). 

644 @kwarg h: Overriding height (C{meter}). 

645 

646 @return: Average, fractional height (C{float}) or 

647 the overriding B{C{height}} (C{Height}). 

648 ''' 

649 return Height(h) if h is not None else \ 

650 _MODS.fmath.favg(self.height, other.height, f=f) 

651 

652 @Property 

653 def height(self): 

654 '''Get the height (C{meter}). 

655 ''' 

656 return self._height 

657 

658 @height.setter # PYCHOK setter! 

659 def height(self, height): 

660 '''Set the height (C{meter}). 

661 

662 @raise TypeError: Invalid B{C{height}} C{type}. 

663 

664 @raise ValueError: Invalid B{C{height}}. 

665 ''' 

666 h = Height(height) 

667 if self._height != h: 

668 _update_all(self) 

669 self._height = h 

670 

671 def _heigHt(self, height): 

672 '''(INTERNAL) Overriding this C{height}. 

673 ''' 

674 return self.height if height is None else Height(height) 

675 

676 def height4(self, earth=None, normal=True, LatLon=None, **LatLon_kwds): 

677 '''Compute the height above or below and the projection of this point 

678 on this datum's or on an other earth's ellipsoid surface. 

679 

680 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius 

681 I{overriding} this datum (L{Datum}, L{Ellipsoid}, 

682 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_}, 

683 L{JacobiConformal} or C{meter}, conventionally). 

684 @kwarg normal: If C{True} the projection is the nearest point on the 

685 ellipsoid's surface, otherwise the intersection of the 

686 radial line to the center and the ellipsoid's surface. 

687 @kwarg LatLon: Optional class to return the height and projection 

688 (C{LatLon}) or C{None}. 

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

690 ignored if C{B{LatLon} is None}. 

691 

692 @note: Use keyword argument C{height=0} to override C{B{LatLon}.height} 

693 to {0} or any other C{scalar}, conventionally in C{meter}. 

694 

695 @return: An instance of B{C{LatLon}} or if C{B{LatLon} is None}, a 

696 L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y} 

697 and C{z} coordinates and height C{h} in C{meter}, conventionally. 

698 

699 @raise TriaxialError: No convergence in triaxial root finding. 

700 

701 @raise TypeError: Invalid B{C{earth}}. 

702 

703 @see: L{Ellipsoid.height4} and L{Triaxial_.height4} for more information. 

704 ''' 

705 c = self.toCartesian() 

706 if LatLon is None: 

707 r = c.height4(earth=earth, normal=normal) 

708 else: 

709 r = c.height4(earth=earth, normal=normal, Cartesian=c.classof, height=0) 

710 r = r.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, height=r.height)) 

711 return r 

712 

713 def heightStr(self, prec=-2, m=_m_): 

714 '''Return this point's B{C{height}} as C{str}ing. 

715 

716 @kwarg prec: Number of (decimal) digits, unstripped (C{int}). 

717 @kwarg m: Optional unit of the height (C{str}). 

718 

719 @see: Function L{pygeodesy.hstr}. 

720 ''' 

721 return _MODS.streprs.hstr(self.height, prec=prec, m=m) 

722 

723 @deprecated_method 

724 def isantipode(self, other, eps=EPS): # PYCHOK no cover 

725 '''DEPRECATED, use method L{isantipodeTo}.''' 

726 return self.isantipodeTo(other, eps=eps) 

727 

728 def isantipodeTo(self, other, eps=EPS): 

729 '''Check whether this and an other point are antipodal, 

730 on diametrically opposite sides of the earth. 

731 

732 @arg other: The other point (C{LatLon}). 

733 @kwarg eps: Tolerance for near-equality (C{degrees}). 

734 

735 @return: C{True} if points are antipodal within the given 

736 tolerance, C{False} otherwise. 

737 ''' 

738 p = self.others(other) 

739 return isantipode(*(self.latlon + p.latlon), eps=eps) 

740 

741 @Property_RO 

742 def isEllipsoidal(self): 

743 '''Check whether this point is ellipsoidal (C{bool} or C{None} if unknown). 

744 ''' 

745 return self.datum.isEllipsoidal if self._datum else None 

746 

747 @Property_RO 

748 def isEllipsoidalLatLon(self): 

749 '''Get C{LatLon} base. 

750 ''' 

751 return False 

752 

753 def isequalTo(self, other, eps=None): 

754 '''Compare this point with an other point, I{ignoring} height. 

755 

756 @arg other: The other point (C{LatLon}). 

757 @kwarg eps: Tolerance for equality (C{degrees}). 

758 

759 @return: C{True} if both points are identical, 

760 I{ignoring} height, C{False} otherwise. 

761 

762 @raise TypeError: The B{C{other}} point is not C{LatLon} 

763 or mismatch of the B{C{other}} and 

764 this C{class} or C{type}. 

765 

766 @raise UnitError: Invalid B{C{eps}}. 

767 

768 @see: Method L{isequalTo3}. 

769 ''' 

770 return _isequalTo(self, self.others(other), eps=eps) 

771 

772 def isequalTo3(self, other, eps=None): 

773 '''Compare this point with an other point, I{including} height. 

774 

775 @arg other: The other point (C{LatLon}). 

776 @kwarg eps: Tolerance for equality (C{degrees}). 

777 

778 @return: C{True} if both points are identical 

779 I{including} height, C{False} otherwise. 

780 

781 @raise TypeError: The B{C{other}} point is not C{LatLon} 

782 or mismatch of the B{C{other}} and 

783 this C{class} or C{type}. 

784 

785 @see: Method L{isequalTo}. 

786 ''' 

787 return self.height == self.others(other).height and \ 

788 _isequalTo(self, other, eps=eps) 

789 

790 @Property_RO 

791 def isnormal(self): 

792 '''Return C{True} if this point is normal (C{bool}), 

793 meaning C{abs(lat) <= 90} and C{abs(lon) <= 180}. 

794 

795 @see: Methods L{normal}, L{toNormal} and functions 

796 L{pygeodesy.isnormal} and L{pygeodesy.normal}. 

797 ''' 

798 return isnormal(self.lat, self.lon, eps=0) 

799 

800 @Property_RO 

801 def isSpherical(self): 

802 '''Check whether this point is spherical (C{bool} or C{None} if unknown). 

803 ''' 

804 return self.datum.isSpherical if self._datum else None 

805 

806 @Property_RO 

807 def lam(self): 

808 '''Get the longitude (B{C{radians}}). 

809 ''' 

810 return radians(self.lon) 

811 

812 @Property 

813 def lat(self): 

814 '''Get the latitude (C{degrees90}). 

815 ''' 

816 return self._lat 

817 

818 @lat.setter # PYCHOK setter! 

819 def lat(self, lat): 

820 '''Set the latitude (C{str[N|S]} or C{degrees}). 

821 

822 @raise ValueError: Invalid B{C{lat}}. 

823 ''' 

824 lat = Lat(lat) # parseDMS(lat, suffix=_NS_, clip=90) 

825 if self._lat != lat: 

826 _update_all(self) 

827 self._lat = lat 

828 

829 @Property 

830 def latlon(self): 

831 '''Get the lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}). 

832 ''' 

833 return LatLon2Tuple(self._lat, self._lon, name=self.name) 

834 

835 @latlon.setter # PYCHOK setter! 

836 def latlon(self, latlonh): 

837 '''Set the lat- and longitude and optionally the height 

838 (2- or 3-tuple or comma- or space-separated C{str} 

839 of C{degrees90}, C{degrees180} and C{meter}). 

840 

841 @raise TypeError: Height of B{C{latlonh}} not C{scalar} or 

842 B{C{latlonh}} not C{list} or C{tuple}. 

843 

844 @raise ValueError: Invalid B{C{latlonh}} or M{len(latlonh)}. 

845 

846 @see: Function L{pygeodesy.parse3llh} to parse a B{C{latlonh}} 

847 string into a 3-tuple C{(lat, lon, h)}. 

848 ''' 

849 if isstr(latlonh): 

850 latlonh = parse3llh(latlonh, height=self.height) 

851 else: 

852 _xinstanceof(list, tuple, latlonh=latlonh) 

853 if len(latlonh) == 3: 

854 h = Height(latlonh[2], name=Fmt.SQUARE(latlonh=2)) 

855 elif len(latlonh) != 2: 

856 raise _ValueError(latlonh=latlonh) 

857 else: 

858 h = self.height 

859 

860 llh = Lat(latlonh[0]), Lon(latlonh[1]), h # parseDMS2(latlonh[0], latlonh[1]) 

861 if (self._lat, self._lon, self._height) != llh: 

862 _update_all(self) 

863 self._lat, self._lon, self._height = llh 

864 

865 def latlon2(self, ndigits=0): 

866 '''Return this point's lat- and longitude in C{degrees}, rounded. 

867 

868 @kwarg ndigits: Number of (decimal) digits (C{int}). 

869 

870 @return: A L{LatLon2Tuple}C{(lat, lon)}, both C{float} 

871 and rounded away from zero. 

872 

873 @note: The C{round}ed values are always C{float}, also 

874 if B{C{ndigits}} is omitted. 

875 ''' 

876 return LatLon2Tuple(round(self.lat, ndigits), 

877 round(self.lon, ndigits), name=self.name) 

878 

879 @deprecated_method 

880 def latlon_(self, ndigits=0): # PYCHOK no cover 

881 '''DEPRECATED, use method L{latlon2}.''' 

882 return self.latlon2(ndigits=ndigits) 

883 

884 latlon2round = latlon_ # PYCHOK no cover 

885 

886 @Property 

887 def latlonheight(self): 

888 '''Get the lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}). 

889 ''' 

890 return self.latlon.to3Tuple(self.height) 

891 

892 @latlonheight.setter # PYCHOK setter! 

893 def latlonheight(self, latlonh): 

894 '''Set the lat- and longitude and optionally the height 

895 (2- or 3-tuple or comma- or space-separated C{str} 

896 of C{degrees90}, C{degrees180} and C{meter}). 

897 

898 @see: Property L{latlon} for more details. 

899 ''' 

900 self.latlon = latlonh 

901 

902 @Property 

903 def lon(self): 

904 '''Get the longitude (C{degrees180}). 

905 ''' 

906 return self._lon 

907 

908 @lon.setter # PYCHOK setter! 

909 def lon(self, lon): 

910 '''Set the longitude (C{str[E|W]} or C{degrees}). 

911 

912 @raise ValueError: Invalid B{C{lon}}. 

913 ''' 

914 lon = Lon(lon) # parseDMS(lon, suffix=_EW_, clip=180) 

915 if self._lon != lon: 

916 _update_all(self) 

917 self._lon = lon 

918 

919 @Property_RO 

920 def _ltp(self): 

921 '''(INTERNAL) Cache for L{toLtp}. 

922 ''' 

923 return _MODS.ltp.Ltp(self, ecef=self.Ecef(self.datum), name=self.name) 

924 

925 def nearestOn6(self, points, closed=False, height=None, wrap=False): 

926 '''Locate the point on a path or polygon closest to this point. 

927 

928 Points are converted to and distances are computed in 

929 I{geocentric}, cartesian space. 

930 

931 @arg points: The path or polygon points (C{LatLon}[]). 

932 @kwarg closed: Optionally, close the polygon (C{bool}). 

933 @kwarg height: Optional height, overriding the height of 

934 this and all other points (C{meter}). If 

935 C{None}, take the height of points into 

936 account for distances. 

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

938 the B{C{points}} (C{bool}). 

939 

940 @return: A L{NearestOn6Tuple}C{(closest, distance, fi, j, 

941 start, end)} with the C{closest}, the C{start} 

942 and the C{end} point each an instance of this 

943 C{LatLon} and C{distance} in C{meter}, same 

944 units as the cartesian axes. 

945 

946 @raise PointsError: Insufficient number of B{C{points}}. 

947 

948 @raise TypeError: Some B{C{points}} or some B{C{points}}' 

949 C{Ecef} invalid. 

950 

951 @raise ValueError: Some B{C{points}}' C{Ecef} is incompatible. 

952 

953 @see: Function L{pygeodesy.nearestOn6}. 

954 ''' 

955 def _cs(Ps, h, w, C): 

956 p = None # not used 

957 for i, q in Ps.enumerate(): 

958 if w and i: 

959 q = _unrollon(p, q) 

960 yield C(height=h, i=i, up=3, points=q) 

961 p = q 

962 

963 C = self._toCartesianEcef # to verify datum and Ecef 

964 Ps = self.PointsIter(points, wrap=wrap) 

965 

966 c = C(height=height, this=self) # this Cartesian 

967 t = nearestOn6(c, _cs(Ps, height, wrap, C), closed=closed) 

968 c, s, e = t.closest, t.start, t.end 

969 

970 kwds = _xkwds_not(None, LatLon=self.classof, # this LatLon 

971 height=height) 

972 _r = self.Ecef(self.datum).reverse 

973 p = _r(c).toLatLon(**kwds) 

974 s = _r(s).toLatLon(**kwds) if s is not c else p 

975 e = _r(e).toLatLon(**kwds) if e is not c else p 

976 return t.dup(closest=p, start=s, end=e) 

977 

978 def normal(self): 

979 '''Normalize this point I{in-place} to C{abs(lat) <= 90} and 

980 C{abs(lon) <= 180}. 

981 

982 @return: C{True} if this point was I{normal}, C{False} if it 

983 wasn't (but is now). 

984 

985 @see: Property L{isnormal} and method L{toNormal}. 

986 ''' 

987 n = self.isnormal 

988 if not n: 

989 self.latlon = normal(*self.latlon) 

990 return n 

991 

992 @Property_RO 

993 def _N_vector(self): 

994 '''(INTERNAL) Get the (C{nvectorBase._N_vector_}) 

995 ''' 

996 return _MODS.nvectorBase._N_vector_(*self.xyzh) 

997 

998 @Property_RO 

999 def phi(self): 

1000 '''Get the latitude (B{C{radians}}). 

1001 ''' 

1002 return radians(self.lat) 

1003 

1004 @Property_RO 

1005 def philam(self): 

1006 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}). 

1007 ''' 

1008 return PhiLam2Tuple(self.phi, self.lam, name=self.name) 

1009 

1010 def philam2(self, ndigits=0): 

1011 '''Return this point's lat- and longitude in C{radians}, rounded. 

1012 

1013 @kwarg ndigits: Number of (decimal) digits (C{int}). 

1014 

1015 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float} 

1016 and rounded away from zero. 

1017 

1018 @note: The C{round}ed values are always C{float}, also 

1019 if B{C{ndigits}} is omitted. 

1020 ''' 

1021 return PhiLam2Tuple(round(self.phi, ndigits), 

1022 round(self.lam, ndigits), name=self.name) 

1023 

1024 @Property_RO 

1025 def philamheight(self): 

1026 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). 

1027 ''' 

1028 return self.philam.to3Tuple(self.height) 

1029 

1030 @deprecated_method 

1031 def points(self, points, closed=True): # PYCHOK no cover 

1032 '''DEPRECATED, use method L{points2}.''' 

1033 return self.points2(points, closed=closed) 

1034 

1035 def points2(self, points, closed=True): 

1036 '''Check a path or polygon represented by points. 

1037 

1038 @arg points: The path or polygon points (C{LatLon}[]) 

1039 @kwarg closed: Optionally, consider the polygon closed, 

1040 ignoring any duplicate or closing final 

1041 B{C{points}} (C{bool}). 

1042 

1043 @return: A L{Points2Tuple}C{(number, points)}, an C{int} 

1044 and C{list} or C{tuple}. 

1045 

1046 @raise PointsError: Insufficient number of B{C{points}}. 

1047 

1048 @raise TypeError: Some B{C{points}} are not C{LatLon}. 

1049 ''' 

1050 return _MODS.iters.points2(points, closed=closed, base=self) 

1051 

1052 def PointsIter(self, points, loop=0, dedup=False, wrap=False): 

1053 '''Return a C{PointsIter} iterator. 

1054 

1055 @arg points: The path or polygon points (C{LatLon}[]) 

1056 @kwarg loop: Number of loop-back points (non-negative C{int}). 

1057 @kwarg dedup: Skip duplicate points (C{bool}). 

1058 @kwarg wrap: If C{True}, wrap or I{normalize} the 

1059 enum-/iterated B{C{points}} (C{bool}). 

1060 

1061 @return: A new C{PointsIter} iterator. 

1062 

1063 @raise PointsError: Insufficient number of B{C{points}}. 

1064 ''' 

1065 return PointsIter(points, base=self, loop=loop, dedup=dedup, wrap=wrap) 

1066 

1067 def radii11(self, point2, point3, wrap=False): 

1068 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent} 

1069 circles of a (planar) triangle formed by this and two other points. 

1070 

1071 @arg point2: Second point (C{LatLon}). 

1072 @arg point3: Third point (C{LatLon}). 

1073 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and 

1074 B{C{point3}} (C{bool}). 

1075 

1076 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}. 

1077 

1078 @raise IntersectionError: Near-coincident or -colinear points. 

1079 

1080 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. 

1081 

1082 @see: Function L{pygeodesy.radii11}, U{Incircle 

1083 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles 

1084 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent 

1085 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}. 

1086 ''' 

1087 with _toCartesian3(self, point2, point3, wrap) as cs: 

1088 return _radii11ABC(*cs, useZ=True)[0] 

1089 

1090 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3 

1091 '''(INTERNAL) Get the C{rhumb} for this point's datum or for 

1092 the B{C{radius}}' earth model iff non-C{None}. 

1093 ''' 

1094 try: 

1095 d = self._rhumb3dict 

1096 t = d[(exact, radius)] 

1097 except KeyError: 

1098 D = self.datum if radius is None else _spherical_datum(radius) # ellipsoidal OK 

1099 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical) 

1100 t = r, D, _MODS.karney.Caps 

1101 while d: 

1102 d.popitem() 

1103 d[(exact, radius)] = t # cache 3-tuple 

1104 return t 

1105 

1106 @Property_RO 

1107 def _rhumb3dict(self): 

1108 return {} # single-item cache 

1109 

1110 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False): 

1111 '''Return the azimuth (bearing) of a rhumb line (loxodrome) 

1112 between this and an other (ellipsoidal) point. 

1113 

1114 @arg other: The other point (C{LatLon}). 

1115 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), 

1116 see method L{Ellipsoid.rhumb_}. 

1117 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1118 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

1119 L{a_f2Tuple}), overriding this point's datum. 

1120 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1121 B{C{other}} point (C{bool}). 

1122 

1123 @return: Rhumb azimuth (compass C{degrees360}). 

1124 

1125 @raise TypeError: The B{C{other}} point is incompatible or 

1126 B{C{radius}} is invalid. 

1127 ''' 

1128 r, _, Cs = self._rhumb3(exact, radius) 

1129 return r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12 

1130 

1131 def rhumbDestination(self, distance, azimuth, exact=False, radius=None, height=None): 

1132 '''Return the destination point having travelled the given distance 

1133 from this point along a rhumb line (loxodrome) at the given azimuth. 

1134 

1135 @arg distance: Distance travelled (C{meter}, same units as this 

1136 point's datum (ellipsoid) axes or B{C{radius}}, 

1137 may be negative. 

1138 @arg azimuth: Azimuth (bearing) at this point (compass C{degrees}). 

1139 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), 

1140 see method L{Ellipsoid.rhumb_}. 

1141 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1142 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

1143 L{a_f2Tuple}), overriding this point's datum. 

1144 @kwarg height: Optional height, overriding the default height 

1145 (C{meter}). 

1146 

1147 @return: The destination point (ellipsoidal C{LatLon}). 

1148 

1149 @raise TypeError: Invalid B{C{radius}}. 

1150 

1151 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, 

1152 B{C{radius}} or B{C{height}}. 

1153 ''' 

1154 r, D, _ = self._rhumb3(exact, radius) 

1155 d = r._Direct(self, azimuth, distance) 

1156 h = self._heigHt(height) 

1157 return self.classof(d.lat2, d.lon2, datum=D, height=h) 

1158 

1159 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False): 

1160 '''Return the distance from this to an other point along 

1161 a rhumb line (loxodrome). 

1162 

1163 @arg other: The other point (C{LatLon}). 

1164 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), 

1165 see method L{Ellipsoid.rhumb_}. 

1166 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1167 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

1168 L{a_f2Tuple}), overriding this point's datum. 

1169 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1170 B{C{other}} point (C{bool}). 

1171 

1172 @return: Distance (C{meter}, the same units as this point's 

1173 datum (ellipsoid) axes or B{C{radius}}. 

1174 

1175 @raise TypeError: The B{C{other}} point is incompatible or 

1176 B{C{radius}} is invalid. 

1177 

1178 @raise ValueError: Invalid B{C{radius}}. 

1179 ''' 

1180 r, _, Cs = self._rhumb3(exact, radius) 

1181 return r._Inverse(self, other, wrap, outmask=Cs.DISTANCE).s12 

1182 

1183 def rhumbLine(self, azimuth_other, exact=False, radius=None, wrap=False, 

1184 **name_caps): 

1185 '''Get a rhumb line through this point at a given azimuth or 

1186 through this and an other point. 

1187 

1188 @arg azimuth_other: The azimuth of the rhumb line (compass 

1189 C{degrees}) or the other point (C{LatLon}). 

1190 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), 

1191 see method L{Ellipsoid.rhumb_}. 

1192 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1193 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

1194 L{a_f2Tuple}), overriding this point's datum. 

1195 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1196 C{azimuth_B{other}} point (C{bool}). 

1197 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see 

1198 L{RhumbLine} C{B{caps}}. 

1199 

1200 @return: A C{RhumbLine} instance. 

1201 

1202 @raise TypeError: Invalid B{C{radius}} or BC{C{azimuth_other}} 

1203 not a C{scalar} nor a C{LatLon}. 

1204 

1205 @see: Modules L{rhumbaux} and L{rhumbx}. 

1206 ''' 

1207 r, _, _ = self._rhumb3(exact, radius) 

1208 a, kwds = azimuth_other, _xkwds(name_caps, name=self.name) 

1209 if isscalar(a): 

1210 r = r._DirectLine(self, a, **kwds) 

1211 elif isinstance(a, LatLonBase): 

1212 r = r._InverseLine(self, a, wrap, **kwds) 

1213 else: 

1214 raise _TypeError(azimuth_other=a) 

1215 return r 

1216 

1217 def rhumbMidpointTo(self, other, exact=False, radius=None, 

1218 height=None, fraction=_0_5, wrap=False): 

1219 '''Return the (loxodromic) midpoint on the rhumb line between 

1220 this and an other point. 

1221 

1222 @arg other: The other point (C{LatLon}). 

1223 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), 

1224 see method L{Ellipsoid.rhumb_}. 

1225 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1226 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

1227 L{a_f2Tuple}), overriding this point's datum. 

1228 @kwarg height: Optional height, overriding the mean height 

1229 (C{meter}). 

1230 @kwarg fraction: Midpoint location from this point (C{scalar}), 0 

1231 for this, 1 for the B{C{other}}, 0.5 for halfway 

1232 between this and the B{C{other}} point, may be 

1233 negative or greater than 1. 

1234 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1235 B{C{other}} point (C{bool}). 

1236 

1237 @return: The midpoint at the given B{C{fraction}} along the 

1238 rhumb line (C{LatLon}). 

1239 

1240 @raise TypeError: The B{C{other}} point is incompatible or 

1241 B{C{radius}} is invalid. 

1242 

1243 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}. 

1244 ''' 

1245 r, D, _ = self._rhumb3(exact, radius) 

1246 f = Scalar(fraction=fraction) 

1247 d = r._Inverse(self, other, wrap) # C.AZIMUTH_DISTANCE 

1248 d = r._Direct( self, d.azi12, d.s12 * f) 

1249 h = self._havg(other, f=f, h=height) 

1250 return self.classof(d.lat2, d.lon2, datum=D, height=h) 

1251 

1252 def thomasTo(self, other, wrap=False): 

1253 '''Compute the distance between this and an other point using 

1254 U{Thomas'<https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>} 

1255 formula. 

1256 

1257 @arg other: The other point (C{LatLon}). 

1258 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll 

1259 the B{C{other}} point (C{bool}). 

1260 

1261 @return: Distance (C{meter}, same units as the axes of 

1262 this point's datum ellipsoid). 

1263 

1264 @raise TypeError: The B{C{other}} point is not C{LatLon}. 

1265 

1266 @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo}, 

1267 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

1268 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

1269 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}. 

1270 ''' 

1271 return self._distanceTo_(thomas_, other, wrap=wrap) 

1272 

1273 @deprecated_method 

1274 def to2ab(self): # PYCHOK no cover 

1275 '''DEPRECATED, use property L{philam}.''' 

1276 return self.philam 

1277 

1278 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds): 

1279 '''Convert this point to cartesian, I{geocentric} coordinates, 

1280 also known as I{Earth-Centered, Earth-Fixed} (ECEF). 

1281 

1282 @kwarg height: Optional height, overriding this point's height 

1283 (C{meter}, conventionally). 

1284 @kwarg Cartesian: Optional class to return the geocentric 

1285 coordinates (C{Cartesian}) or C{None}. 

1286 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} 

1287 keyword arguments, ignored if 

1288 C{B{Cartesian} is None}. 

1289 

1290 @return: A B{C{Cartesian}} or if B{C{Cartesian}} is C{None}, 

1291 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, 

1292 datum)} with C{C=0} and C{M} if available. 

1293 

1294 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}. 

1295 ''' 

1296 r = self._ecef9 if height is None else self.toEcef(height=height) 

1297 if Cartesian is not None: # class or .classof 

1298 r = self._xnamed(Cartesian(r, **Cartesian_kwds)) 

1299 _xdatum(r.datum, self.datum) 

1300 return r 

1301 

1302 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point): 

1303 '''(INTERNAL) Convert to cartesian and check Ecef's before and after. 

1304 ''' 

1305 p = self.others(up=up, **name_point) 

1306 c = p.toCartesian(height=height) 

1307 E = self.Ecef 

1308 if E: 

1309 for p in (p, c): 

1310 e = getattr(p, LatLonBase.Ecef.name, None) 

1311 if e not in (None, E): # PYCHOK no cover 

1312 n, _ = name_point.popitem() 

1313 if i is not None: 

1314 Fmt.SQUARE(n, i) 

1315 raise _ValueError(n, e, txt=_incompatible(E.__name__)) 

1316 return c 

1317 

1318 def toDatum(self, datum2, height=None, name=NN): 

1319 '''I{Must be overloaded}.''' 

1320 notOverloaded(self, datum2, height=height, name=name) 

1321 

1322 def toEcef(self, height=None, M=False): 

1323 '''Convert this point to I{geocentric} coordinates, also known as 

1324 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}). 

1325 

1326 @kwarg height: Optional height, overriding this point's height 

1327 (C{meter}, conventionally). 

1328 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}). 

1329 

1330 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} 

1331 with C{C=0} and C{M} if available. 

1332 

1333 @raise EcefError: A C{.datum} or an ECEF issue. 

1334 ''' 

1335 return self._ecef9 if height in (None, self.height) else \ 

1336 self._Ecef_forward(self.lat, self.lon, height=height, M=M) 

1337 

1338 @deprecated_method 

1339 def to3llh(self, height=None): # PYCHOK no cover 

1340 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.''' 

1341 return self.latlonheight if height in (None, self.height) else \ 

1342 self.latlon.to3Tuple(height) 

1343 

1344 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds): 

1345 '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}. 

1346 

1347 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z} 

1348 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}. 

1349 @kwarg ltp: The I{local tangent plane} (LTP) to use, 

1350 overriding this point's LTP (L{Ltp}). 

1351 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword 

1352 arguments, ignored if C{B{Xyz} is None}. 

1353 

1354 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None}, 

1355 a L{Local9Tuple}C{(x, y, z, lat, lon, height, 

1356 ltp, ecef, M)} with C{M=None}, always. 

1357 

1358 @raise TypeError: Invalid B{C{ltp}}. 

1359 ''' 

1360 p = _MODS.ltp._xLtp(ltp, self._ltp) 

1361 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds) 

1362 

1363 def toLtp(self, Ecef=None): 

1364 '''Return the I{local tangent plane} (LTP) for this point. 

1365 

1366 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ... 

1367 L{EcefYou}), overriding this point's C{Ecef}. 

1368 ''' 

1369 return self._ltp if Ecef in (None, self.Ecef) else _MODS.ltp.Ltp( 

1370 self, ecef=Ecef(self.datum), name=self.name) 

1371 

1372 def toNormal(self, deep=False, name=NN): 

1373 '''Get this point I{normalized} to C{abs(lat) <= 90} 

1374 and C{abs(lon) <= 180}. 

1375 

1376 @kwarg deep: If C{True} make a deep, otherwise a 

1377 shallow copy (C{bool}). 

1378 @kwarg name: Optional name of the copy (C{str}). 

1379 

1380 @return: A copy of this point, I{normalized} and 

1381 optionally renamed (C{LatLon}). 

1382 

1383 @see: Property L{isnormal}, method L{normal} and function 

1384 L{pygeodesy.normal}. 

1385 ''' 

1386 ll = self.copy(deep=deep) 

1387 _ = ll.normal() 

1388 if name: 

1389 ll.rename(name) 

1390 return ll 

1391 

1392 def toNvector(self, h=None, Nvector=None, **Nvector_kwds): 

1393 '''Convert this point to C{n-vector} (normal to the earth's surface) 

1394 components, I{including height}. 

1395 

1396 @kwarg h: Optional height, overriding this point's 

1397 height (C{meter}). 

1398 @kwarg Nvector: Optional class to return the C{n-vector} 

1399 components (C{Nvector}) or C{None}. 

1400 @kwarg Nvector_kwds_wrap: Optional, additional B{C{Nvector}} 

1401 keyword arguments, ignored if C{B{Nvector} 

1402 is None}. 

1403 

1404 @return: A B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} 

1405 if B{C{Nvector}} is C{None}. 

1406 

1407 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}. 

1408 ''' 

1409 return self.toVector(Vector=Nvector, h=self.height if h is None else h, 

1410 ll=self, **Nvector_kwds) 

1411 

1412 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected 

1413 '''Convert this point to a "lat, lon[, +/-height]" string, formatted 

1414 in the given C{B{form}at}. 

1415 

1416 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see 

1417 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}. 

1418 @kwarg joined: Separator to join the lat-, longitude and heigth 

1419 strings (C{str} or C{None} or C{NN} for non-joined). 

1420 @kwarg m: Optional unit of the height (C{str}), use C{None} to 

1421 exclude height from the returned string. 

1422 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator}, 

1423 B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword 

1424 arguments, see function L{pygeodesy.latDMS} or 

1425 L{pygeodesy.lonDMS}. 

1426 

1427 @return: This point in the specified C{B{form}at}, etc. (C{str} or 

1428 a 2- or 3-tuple C{(lat_str, lon_str[, height_str])} if 

1429 C{B{joined}=NN} or C{B{joined}=None}). 

1430 

1431 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more 

1432 details about keyword arguments C{B{form}at}, C{B{prec}ision}, 

1433 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}. 

1434 

1435 @example: 

1436 

1437 >>> LatLon(51.4778, -0.0016).toStr() # 51°28′40″N, 000°00′06″W 

1438 >>> LatLon(51.4778, -0.0016).toStr(F_D) # 51.4778°N, 000.0016°W 

1439 >>> LatLon(51.4778, -0.0016, 42).toStr() # 51°28′40″N, 000°00′06″W, +42.00m 

1440 ''' 

1441 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S), 

1442 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S)) 

1443 if self.height and m is not None: 

1444 t += (self.heightStr(m=m),) 

1445 return joined.join(t) if joined else t 

1446 

1447 def toVector(self, Vector=None, **Vector_kwds): 

1448 '''Convert this point to C{n-vector} (normal to the earth's 

1449 surface) components, I{ignoring height}. 

1450 

1451 @kwarg Vector: Optional class to return the C{n-vector} 

1452 components (L{Vector3d}) or C{None}. 

1453 @kwarg Vector_kwds: Optional, additional B{C{Vector}} 

1454 keyword arguments, ignored if 

1455 C{B{Vector} is None}. 

1456 

1457 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)} 

1458 if B{C{Vector}} is C{None}. 

1459 

1460 @raise TypeError: Invalid B{C{Vector}} or B{C{kwds}}. 

1461 

1462 @note: These are C{n-vector} x, y and z components, 

1463 I{NOT} geocentric (ECEF) x, y and z coordinates! 

1464 ''' 

1465 r = self._vector3tuple 

1466 if Vector is not None: 

1467 r = Vector(*r, **_xkwds(Vector_kwds, name=self.name)) 

1468 return r 

1469 

1470 def toVector3d(self): 

1471 '''Convert this point to C{n-vector} (normal to the earth's 

1472 surface) components, I{ignoring height}. 

1473 

1474 @return: Unit vector (L{Vector3d}). 

1475 

1476 @note: These are C{n-vector} x, y and z components, 

1477 I{NOT} geocentric (ECEF) x, y and z coordinates! 

1478 ''' 

1479 return self._vector3d # XXX .unit() 

1480 

1481 def toWm(self, **toWm_kwds): 

1482 '''Convert this point to a WM coordinate. 

1483 

1484 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments. 

1485 

1486 @return: The WM coordinate (L{Wm}). 

1487 

1488 @see: Function L{pygeodesy.toWm}. 

1489 ''' 

1490 return self._wm if not toWm_kwds else _MODS.webmercator.toWm( 

1491 self, **_xkwds(toWm_kwds, name=self.name)) 

1492 

1493 @deprecated_method 

1494 def to3xyz(self): # PYCHOK no cover 

1495 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector}, 

1496 L{toVector3d} or perhaps (geocentric) L{toEcef}.''' 

1497 return self.xyz # self.toVector() 

1498 

1499 @Property_RO 

1500 def _vector3d(self): 

1501 '''(INTERNAL) Cache for L{toVector3d}. 

1502 ''' 

1503 return self.toVector(Vector=Vector3d) # XXX .unit() 

1504 

1505 @Property_RO 

1506 def _vector3tuple(self): 

1507 '''(INTERNAL) Cache for L{toVector}. 

1508 ''' 

1509 return philam2n_xyz(self.phi, self.lam, name=self.name) 

1510 

1511 def vincentysTo(self, other, **radius_wrap): 

1512 '''Compute the distance between this and an other point using 

1513 U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>} 

1514 spherical formula. 

1515 

1516 @arg other: The other point (C{LatLon}). 

1517 @kwarg radius_wrap: Optional keyword arguments for function 

1518 L{pygeodesy.vincentys}, overriding the 

1519 default mean C{radius} of this point's 

1520 datum ellipsoid. 

1521 

1522 @return: Distance (C{meter}, same units as B{C{radius}}). 

1523 

1524 @raise TypeError: The B{C{other}} point is not C{LatLon}. 

1525 

1526 @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo}, 

1527 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

1528 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

1529 L{flatPolarTo}, L{haversineTo} and L{thomasTo}. 

1530 ''' 

1531 return self._distanceTo(vincentys, other, **_xkwds(radius_wrap, radius=None)) 

1532 

1533 @Property_RO 

1534 def _wm(self): 

1535 '''(INTERNAL) Get this point as webmercator (L{Wm}). 

1536 ''' 

1537 return _MODS.webmercator.toWm(self) 

1538 

1539 @Property_RO 

1540 def xyz(self): 

1541 '''Get the C{n-vector} X, Y and Z components (L{Vector3Tuple}C{(x, y, z)}) 

1542 

1543 @note: These are C{n-vector} x, y and z components, I{NOT} 

1544 geocentric (ECEF) x, y and z coordinates! 

1545 ''' 

1546 return self.toVector(Vector=Vector3Tuple) 

1547 

1548 @Property_RO 

1549 def xyzh(self): 

1550 '''Get the C{n-vector} X, Y, Z and H components (L{Vector4Tuple}C{(x, y, z, h)}) 

1551 

1552 @note: These are C{n-vector} x, y and z components, I{NOT} 

1553 geocentric (ECEF) x, y and z coordinates! 

1554 ''' 

1555 return self.xyz.to4Tuple(self.height) 

1556 

1557 

1558class _toCartesian3(object): # see also .geodesicw._wargs, .vector2d._numpy 

1559 '''(INTERNAL) Wrapper to convert 2 other points. 

1560 ''' 

1561 @contextmanager # <https://www.python.org/dev/peps/pep-0343/> Examples 

1562 def __call__(self, p, p2, p3, wrap, **kwds): 

1563 try: 

1564 if wrap: 

1565 p2, p3 = map1(_Wrap.point, p2, p3) 

1566 kwds = _xkwds(kwds, wrap=wrap) 

1567 yield (p. toCartesian().copy(name=_point_), # copy to rename 

1568 p._toCartesianEcef(up=4, point2=p2), 

1569 p._toCartesianEcef(up=4, point3=p3)) 

1570 except (AssertionError, TypeError, ValueError) as x: 

1571 raise _xError(x, point=p, point2=p2, point3=p3, **kwds) 

1572 

1573_toCartesian3 = _toCartesian3() # PYCHOK singleton 

1574 

1575 

1576def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, # MCCABE 13 

1577 radius=R_M, wrap=False): 

1578 '''(INTERNAL) Trilaterate three points by I{area overlap} or by 

1579 I{perimeter intersection} of three circles. 

1580 

1581 @note: The B{C{radius}} is only needed for both the n-vectorial 

1582 and C{sphericalTrigonometry.LatLon.distanceTo} methods and 

1583 silently ignored by the C{ellipsoidalExact}, C{-GeodSolve}, 

1584 C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods. 

1585 ''' 

1586 p2, p3, w = _unrollon3(p1, p2, p3, wrap) 

1587 

1588 r1 = Distance_(distance1=d1) 

1589 r2 = Distance_(distance2=d2) 

1590 r3 = Distance_(distance3=d3) 

1591 m = 0 if area else (r1 + r2 + r3) 

1592 pc = 0 

1593 t = [] 

1594 for _ in range(3): 

1595 try: # intersection of circle (p1, r1) and (p2, r2) 

1596 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w) 

1597 

1598 if area: # check overlap 

1599 if c1 is c2: # abutting 

1600 c = c1 

1601 else: # nearest point on radical 

1602 c = p3.nearestOn(c1, c2, within=True, wrap=w) 

1603 d = r3 - p3.distanceTo(c, radius=radius, wrap=w) 

1604 if d > eps: # sufficient overlap 

1605 t.append((d, c)) 

1606 m = max(m, d) 

1607 

1608 else: # check intersection 

1609 for c in ((c1,) if c1 is c2 else (c1, c2)): 

1610 d = fabs(r3 - p3.distanceTo(c, radius=radius, wrap=w)) 

1611 if d < eps: # below margin 

1612 t.append((d, c)) 

1613 m = min(m, d) 

1614 

1615 except IntersectionError as x: 

1616 if _concentric_ in str(x): # XXX ConcentricError? 

1617 pc += 1 

1618 

1619 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate 

1620 

1621 if t: # get min, max, points and count ... 

1622 t = tuple(sorted(t)) 

1623 n = len(t), # as 1-tuple 

1624 # ... or for a single trilaterated result, 

1625 # min *is* max, min- *is* maxPoint and n=1, 2 or 3 

1626 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...) 

1627 

1628 elif area and pc == 3: # all pairwise concentric ... 

1629 r, p = min((r1, p1), (r2, p2), (r3, p3)) 

1630 m = max(r1, r2, r3) 

1631 # ... return "smallest" point twice, the smallest 

1632 # and largest distance and n=0 for concentric 

1633 return Trilaterate5Tuple(float(r), p, float(m), p, 0) 

1634 

1635 n, f = (_overlap_, max) if area else (_intersection_, min) 

1636 t = _COMMASPACE_(_no_(n), '%s %.3g' % (f.__name__, m)) 

1637 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t) 

1638 

1639 

1640__all__ += _ALL_DOCS(LatLonBase) 

1641 

1642# **) MIT License 

1643# 

1644# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved. 

1645# 

1646# Permission is hereby granted, free of charge, to any person obtaining a 

1647# copy of this software and associated documentation files (the "Software"), 

1648# to deal in the Software without restriction, including without limitation 

1649# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1650# and/or sell copies of the Software, and to permit persons to whom the 

1651# Software is furnished to do so, subject to the following conditions: 

1652# 

1653# The above copyright notice and this permission notice shall be included 

1654# in all copies or substantial portions of the Software. 

1655# 

1656# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1657# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1658# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1659# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1660# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1661# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1662# OTHER DEALINGS IN THE SOFTWARE.