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

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

8U{Rhumb<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>} 

9and U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>} classes. 

10''' 

11 

12from pygeodesy.basics import isscalar, isstr, map1, _xinstanceof 

13from pygeodesy.constants import EPS, EPS0, EPS1, EPS4, INT0, R_M, \ 

14 _0_0, _0_5, _1_0 

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

16from pygeodesy.dms import F_D, F_DMS, latDMS, lonDMS, parse3llh 

17# from pygeodesy.ecef import EcefKarney # _MODS 

18from pygeodesy.errors import _incompatible, IntersectionError, _IsnotError, \ 

19 _TypeError, _ValueError, _xdatum, _xError, \ 

20 _xkwds, _xkwds_not 

21# from pygeodesy.fmath import favg # _MODS 

22from pygeodesy.formy import antipode, compassAngle, cosineAndoyerLambert_, \ 

23 cosineForsytheAndoyerLambert_, cosineLaw, \ 

24 equirectangular, euclidean, flatLocal_, \ 

25 flatPolar, hartzell, haversine, isantipode, \ 

26 _isequalTo, isnormal, normal, philam2n_xyz, \ 

27 thomas_, vincentys, _spherical_datum 

28from pygeodesy.interns import NN, _COMMASPACE_, _concentric_, _height_, \ 

29 _intersection_, _m_, _LatLon_, _no_, \ 

30 _overlap_, _point_ # PYCHOK used! 

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

32from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

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

34from pygeodesy.named import _NamedBase, notOverloaded, Fmt 

35from pygeodesy.namedTuples import Bounds2Tuple, LatLon2Tuple, PhiLam2Tuple, \ 

36 Trilaterate5Tuple, Vector3Tuple 

37# from pygeodesy.nvectorBase import _N_vector_ # _MODS 

38from pygeodesy.props import deprecated_method, Property, Property_RO, \ 

39 property_RO, _update_all 

40# from pygeodesy.rhumbx import Caps, Rhumb # _MODS 

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

42from pygeodesy.units import Distance_, Lat, Lon, Height, Radius, Radius_, \ 

43 Scalar, Scalar_ 

44from pygeodesy.utily import _unrollon, _unrollon3, _Wrap 

45from pygeodesy.vector2d import _circin6, Circin6Tuple, _circum3, circum4_, \ 

46 Circum3Tuple, _radii11ABC 

47from pygeodesy.vector3d import nearestOn6, Vector3d, PointsIter 

48 

49from contextlib import contextmanager 

50from math import asin, cos, degrees, fabs, radians 

51 

52__all__ = _ALL_LAZY.latlonBase 

53__version__ = '23.06.12' 

54 

55 

56class LatLonBase(_NamedBase): 

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

58 ellipsoidal earth models. 

59 ''' 

60 _clipid = INT0 # polygonal clip, see .booleans 

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

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

63 _lat = 0 # latitude (C{degrees}) 

64 _lon = 0 # longitude (C{degrees}) 

65 

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

67 '''New C{LatLon}. 

68 

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

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

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

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

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

74 (C{meter}, conventionally). 

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

76 (C{bool}). 

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

78 

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

80 

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

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

83 

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

85 

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

87 

88 @example: 

89 

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

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

92 >>> r = LatLon(p) 

93 ''' 

94 if name: 

95 self.name = name 

96 

97 if lon is None: 

98 try: 

99 lat, lon = latlonh.lat, latlonh.lon 

100 height = latlonh.get(_height_, height) 

101 except AttributeError: 

102 raise _IsnotError(_LatLon_, latlonh=latlonh) 

103 if wrap: 

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

105 elif wrap: 

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

107 else: 

108 lat = latlonh 

109 

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

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

112 if height: # elevation 

113 self._height = Height(height) 

114 

115 def __eq__(self, other): 

116 return self.isequalTo(other) 

117 

118 def __ne__(self, other): 

119 return not self.isequalTo(other) 

120 

121 def __str__(self): 

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

123 

124 def antipode(self, height=None): 

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

126 to this point. 

127 

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

129 this point's height otherwise. 

130 

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

132 ''' 

133 h = self._heigHt(height) 

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

135 

136 @deprecated_method 

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

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

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

140 

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

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

143 bounding box centered at this location. 

144 

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

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

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

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

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

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

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

152 overriding the point's height. 

153 

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

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

156 

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

158 ''' 

159 w = Scalar_(wide=wide) * _0_5 

160 t = Scalar_(tall=tall) * _0_5 

161 if radius is not None: 

162 r = Radius_(radius) 

163 c = cos(self.phi) 

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

165 t = degrees(t / r) 

166 y, t = self.lat, fabs(t) 

167 x, w = self.lon, fabs(w) 

168 

169 h = self._heigHt(height) 

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

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

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

173 

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

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

176 this and an other point. 

177 

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

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

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

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

182 point (C{bool}). 

183 

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

185 

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

187 ''' 

188 def _v3d(ll): 

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

190 return Vector3d(t.x, t.y, t.z) 

191 

192 p = self.others(other) 

193 if wrap: 

194 p = _Wrap.point(p) 

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

196 

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

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

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

200 

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

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

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

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

205 B{C{point3}} (C{bool}). 

206 

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

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

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

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

211 

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

213 than version 1.10. 

214 

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

216 a trilateration or C{numpy} issue. 

217 

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

219 

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

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

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

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

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

225 height)} representing the differences between both results from 

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

227 

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

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

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

231 ''' 

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

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

234 datum=self.datum) # PYCHOK unpack 

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

236 

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

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

239 this and two other points. 

240 

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

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

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

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

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

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

247 B{C{point3}} (C{bool}). 

248 

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

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

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

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

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

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

255 

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

257 version 1.10. 

258 

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

260 incompatible C{Ecef} classes or a trilateration 

261 or C{numpy} issue. 

262 

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

264 

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

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

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

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

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

270 height)} representing the difference between both results from 

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

272 

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

274 ''' 

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

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

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

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

279 

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

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

282 

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

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

285 (C{bool}), default C{False}. 

286 

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

288 an instance of this (sub-)class. 

289 

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

291 version 1.10. 

292 

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

294 

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

296 

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

298 

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

300 ''' 

301 def _cs(ps, C, wrap=False): 

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

303 for i, p in enumerate(ps): 

304 yield C(i=i, points=_wp(p)) 

305 

306 C = self._toCartesianEcef 

307 c = C(point=self) 

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

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

310 return t.dup(center=c) 

311 

312 @property 

313 def clipid(self): 

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

315 ''' 

316 return self._clipid 

317 

318 @clipid.setter # PYCHOK setter! 

319 def clipid(self, clipid): 

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

321 ''' 

322 self._clipid = int(clipid) 

323 

324 @deprecated_method 

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

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

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

328 

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

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

331 this and an other point. 

332 

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

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

335 larger distances. 

336 

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

338 @kwarg adjust_wrap: Optional keyword arguments for function 

339 L{pygeodesy.compassAngle}. 

340 

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

342 

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

344 

345 @note: Courtesy of Martin Schultz. 

346 

347 @see: U{Local, flat earth approximation 

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

349 ''' 

350 p = self.others(other) 

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

352 

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

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

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

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

357 

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

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

360 the B{C{other}} point (C{bool}). 

361 

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

363 point's datum ellipsoid). 

364 

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

366 

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

368 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, 

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

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

371 L{thomasTo} and L{vincentysTo}. 

372 ''' 

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

374 

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

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

377 the U{Forsythe-Andoyer-Lambert correction 

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

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

380 formula. 

381 

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

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

384 the B{C{other}} point (C{bool}). 

385 

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

387 this point's datum ellipsoid). 

388 

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

390 

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

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

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

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

395 ''' 

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

397 

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

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

400 U{spherical Law of Cosines 

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

402 formula. 

403 

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

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

406 for the mean radius of this point's datum 

407 ellipsoid. 

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

409 the B{C{other}} point (C{bool}). 

410 

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

412 

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

414 

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

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

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

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

419 ''' 

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

421 

422 @property_RO 

423 def datum(self): # PYCHOK no cover 

424 '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. 

425 ''' 

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{Vector3d}) or 

599 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}) or this very instance 

605 if this C{pov's height} is C{0}. 

606 

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

608 C{pov's height} is negative or B{C{los}} 

609 points outside the ellipsoid or in an 

610 opposite direction. 

611 

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

613 

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

615 ''' 

616 h = self.height 

617 if not h: 

618 r = self 

619 elif h < 0: 

620 raise IntersectionError(pov=self, los=los, height=h, txt=_no_(_height_)) 

621 elif los is None: 

622 d = self.datum if earth is None else _spherical_datum(earth) 

623 r = self.dup(datum=d, height=0, name=self.hartzell.__name__) 

624 else: 

625 c = self.toCartesian() 

626 r = hartzell(c, los=los, earth=earth or self.datum, LatLon=self.classof) 

627 return r 

628 

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

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

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

632 formula. 

633 

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

635 @kwarg radius_wrap: Optional keyword arguments for function 

636 L{pygeodesy.haversine}, overriding the 

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

638 datum ellipsoid. 

639 

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

641 

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

643 

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

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

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

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

648 ''' 

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

650 

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

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

653 

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

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

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

657 

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

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

660 ''' 

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

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

663 

664 @Property 

665 def height(self): 

666 '''Get the height (C{meter}). 

667 ''' 

668 return self._height 

669 

670 @height.setter # PYCHOK setter! 

671 def height(self, height): 

672 '''Set the height (C{meter}). 

673 

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

675 

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

677 ''' 

678 h = Height(height) 

679 if self._height != h: 

680 _update_all(self) 

681 self._height = h 

682 

683 def _heigHt(self, height): 

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

685 ''' 

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

687 

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

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

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

691 

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

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

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

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

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

697 ellipsoid's surface, otherwise the intersection of the 

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

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

700 (C{LatLon}) or C{None}. 

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

702 ignored if C{B{LatLon} is None}. 

703 

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

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

706 

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

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

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

710 

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

712 

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

714 

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

716 ''' 

717 c = self.toCartesian() 

718 if LatLon is None: 

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

720 else: 

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

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

723 return r 

724 

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

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

727 

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

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

730 

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

732 ''' 

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

734 

735 @deprecated_method 

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

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

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

739 

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

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

742 on diametrically opposite sides of the earth. 

743 

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

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

746 

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

748 tolerance, C{False} otherwise. 

749 ''' 

750 p = self.others(other) 

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

752 

753 @Property_RO 

754 def isEllipsoidal(self): 

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

756 ''' 

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

758 

759 @Property_RO 

760 def isEllipsoidalLatLon(self): 

761 '''Get C{LatLon} base. 

762 ''' 

763 return False 

764 

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

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

767 

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

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

770 

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

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

773 

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

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

776 this C{class} or C{type}. 

777 

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

779 

780 @see: Method L{isequalTo3}. 

781 ''' 

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

783 

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

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

786 

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

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

789 

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

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

792 

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

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

795 this C{class} or C{type}. 

796 

797 @see: Method L{isequalTo}. 

798 ''' 

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

800 _isequalTo(self, other, eps=eps) 

801 

802 @Property_RO 

803 def isnormal(self): 

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

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

806 

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

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

809 ''' 

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

811 

812 @Property_RO 

813 def isSpherical(self): 

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

815 ''' 

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

817 

818 @Property_RO 

819 def lam(self): 

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

821 ''' 

822 return radians(self.lon) 

823 

824 @Property 

825 def lat(self): 

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

827 ''' 

828 return self._lat 

829 

830 @lat.setter # PYCHOK setter! 

831 def lat(self, lat): 

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

833 

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

835 ''' 

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

837 if self._lat != lat: 

838 _update_all(self) 

839 self._lat = lat 

840 

841 @Property 

842 def latlon(self): 

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

844 ''' 

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

846 

847 @latlon.setter # PYCHOK setter! 

848 def latlon(self, latlonh): 

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

850 (2- or 3-tuple or comma- or space-separated C{str} 

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

852 

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

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

855 

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

857 

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

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

860 ''' 

861 if isstr(latlonh): 

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

863 else: 

864 _xinstanceof(list, tuple, latlonh=latlonh) 

865 if len(latlonh) == 3: 

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

867 elif len(latlonh) != 2: 

868 raise _ValueError(latlonh=latlonh) 

869 else: 

870 h = self.height 

871 

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

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

874 _update_all(self) 

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

876 

877 def latlon2(self, ndigits=0): 

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

879 

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

881 

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

883 and rounded away from zero. 

884 

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

886 if B{C{ndigits}} is omitted. 

887 ''' 

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

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

890 

891 @deprecated_method 

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

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

894 return self.latlon2(ndigits=ndigits) 

895 

896 latlon2round = latlon_ # PYCHOK no cover 

897 

898 @Property 

899 def latlonheight(self): 

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

901 ''' 

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

903 

904 @latlonheight.setter # PYCHOK setter! 

905 def latlonheight(self, latlonh): 

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

907 (2- or 3-tuple or comma- or space-separated C{str} 

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

909 

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

911 ''' 

912 self.latlon = latlonh 

913 

914 @Property 

915 def lon(self): 

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

917 ''' 

918 return self._lon 

919 

920 @lon.setter # PYCHOK setter! 

921 def lon(self, lon): 

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

923 

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

925 ''' 

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

927 if self._lon != lon: 

928 _update_all(self) 

929 self._lon = lon 

930 

931 @Property_RO 

932 def _ltp(self): 

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

934 ''' 

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

936 

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

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

939 

940 Points are converted to and distances are computed in 

941 I{geocentric}, cartesian space. 

942 

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

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

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

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

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

948 account for distances. 

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

950 the B{C{points}} (C{bool}). 

951 

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

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

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

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

956 units as the cartesian axes. 

957 

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

959 

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

961 C{Ecef} invalid. 

962 

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

964 

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

966 ''' 

967 def _cs(Ps, h, w, C): 

968 p = None # not used 

969 for i, q in Ps.enumerate(): 

970 if w and i: 

971 q = _unrollon(p, q) 

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

973 p = q 

974 

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

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

977 

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

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

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

981 

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

983 height=height) 

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

985 p = _r(c).toLatLon(**kwds) 

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

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

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

989 

990 def normal(self): 

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

992 C{abs(lon) <= 180}. 

993 

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

995 wasn't (but is now). 

996 

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

998 ''' 

999 n = self.isnormal 

1000 if not n: 

1001 self.latlon = normal(*self.latlon) 

1002 return n 

1003 

1004 @Property_RO 

1005 def _N_vector(self): 

1006 '''(INTERNAL) Get the (C{nvectorBase._N_vector_}) 

1007 ''' 

1008 return _MODS.nvectorBase._N_vector_(*self.xyzh) 

1009 

1010 @Property_RO 

1011 def phi(self): 

1012 '''Get the latitude (B{C{radians}}). 

1013 ''' 

1014 return radians(self.lat) 

1015 

1016 @Property_RO 

1017 def philam(self): 

1018 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}). 

1019 ''' 

1020 return PhiLam2Tuple(self.phi, self.lam, name=self.name) 

1021 

1022 def philam2(self, ndigits=0): 

1023 '''Return this point's lat- and longitude in C{radians}, rounded. 

1024 

1025 @kwarg ndigits: Number of (decimal) digits (C{int}). 

1026 

1027 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float} 

1028 and rounded away from zero. 

1029 

1030 @note: The C{round}ed values are always C{float}, also 

1031 if B{C{ndigits}} is omitted. 

1032 ''' 

1033 return PhiLam2Tuple(round(self.phi, ndigits), 

1034 round(self.lam, ndigits), name=self.name) 

1035 

1036 @Property_RO 

1037 def philamheight(self): 

1038 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). 

1039 ''' 

1040 return self.philam.to3Tuple(self.height) 

1041 

1042 @deprecated_method 

1043 def points(self, points, closed=True): # PYCHOK no cover 

1044 '''DEPRECATED, use method L{points2}.''' 

1045 return self.points2(points, closed=closed) 

1046 

1047 def points2(self, points, closed=True): 

1048 '''Check a path or polygon represented by points. 

1049 

1050 @arg points: The path or polygon points (C{LatLon}[]) 

1051 @kwarg closed: Optionally, consider the polygon closed, 

1052 ignoring any duplicate or closing final 

1053 B{C{points}} (C{bool}). 

1054 

1055 @return: A L{Points2Tuple}C{(number, points)}, an C{int} 

1056 and C{list} or C{tuple}. 

1057 

1058 @raise PointsError: Insufficient number of B{C{points}}. 

1059 

1060 @raise TypeError: Some B{C{points}} are not C{LatLon}. 

1061 ''' 

1062 return _MODS.iters.points2(points, closed=closed, base=self) 

1063 

1064 def PointsIter(self, points, loop=0, dedup=False, wrap=False): 

1065 '''Return a C{PointsIter} iterator. 

1066 

1067 @arg points: The path or polygon points (C{LatLon}[]) 

1068 @kwarg loop: Number of loop-back points (non-negative C{int}). 

1069 @kwarg dedup: Skip duplicate points (C{bool}). 

1070 @kwarg wrap: If C{True}, wrap or I{normalize} the 

1071 enum-/iterated B{C{points}} (C{bool}). 

1072 

1073 @return: A new C{PointsIter} iterator. 

1074 

1075 @raise PointsError: Insufficient number of B{C{points}}. 

1076 ''' 

1077 return PointsIter(points, base=self, loop=loop, dedup=dedup, wrap=wrap) 

1078 

1079 def radii11(self, point2, point3, wrap=False): 

1080 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent} 

1081 circles of a (planar) triangle formed by this and two other points. 

1082 

1083 @arg point2: Second point (C{LatLon}). 

1084 @arg point3: Third point (C{LatLon}). 

1085 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and 

1086 B{C{point3}} (C{bool}). 

1087 

1088 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}. 

1089 

1090 @raise IntersectionError: Near-coincident or -colinear points. 

1091 

1092 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. 

1093 

1094 @see: Function L{pygeodesy.radii11}, U{Incircle 

1095 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles 

1096 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent 

1097 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}. 

1098 ''' 

1099 with _toCartesian3(self, point2, point3, wrap) as cs: 

1100 return _radii11ABC(*cs, useZ=True)[0] 

1101 

1102 def _rhumbx3(self, exact, radius): # != .sphericalBase._rhumbs3 

1103 '''(INTERNAL) Get the C{rhumb} for this point's datum or for 

1104 the earth model or earth B{C{radius}} if not C{None}. 

1105 ''' 

1106 D = self.datum if radius is None else _spherical_datum(radius) # ellipsoidal OK 

1107 x = _MODS.rhumbx # XXX Property_RO? 

1108 r = D.ellipsoid.rhumbx if exact else \ 

1109 x.Rhumb(D, exact=False, name=D.name) 

1110 return r, D, x.Caps 

1111 

1112 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False): 

1113 '''Return the azimuth (bearing) of a rhumb line (loxodrome) 

1114 between this and an other (ellipsoidal) point. 

1115 

1116 @arg other: The other point (C{LatLon}). 

1117 @kwarg exact: If C{True}, use the I{exact} L{Rhumb} (C{bool}), 

1118 default C{False}. 

1119 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1120 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

1121 L{a_f2Tuple}), overriding this point's datum. 

1122 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1123 B{C{other}} point (C{bool}). 

1124 

1125 @return: Rhumb azimuth (compass C{degrees360}). 

1126 

1127 @raise TypeError: The B{C{other}} point is incompatible or 

1128 B{C{radius}} is invalid. 

1129 ''' 

1130 r, _, C = self._rhumbx3(exact, radius) 

1131 return r._Inverse(self, other, wrap, outmask=C.AZIMUTH).azi12 

1132 

1133 def rhumbDestination(self, distance, azimuth, exact=False, radius=None, height=None): 

1134 '''Return the destination point having travelled the given distance 

1135 from this point along a rhumb line (loxodrome) at the given azimuth. 

1136 

1137 @arg distance: Distance travelled (C{meter}, same units as this 

1138 point's datum (ellipsoid) axes or B{C{radius}}, 

1139 may be negative. 

1140 @arg azimuth: Azimuth (bearing) at this point (compass C{degrees}). 

1141 @kwarg exact: If C{True}, use the I{exact} L{Rhumb} (C{bool}), 

1142 default C{False}. 

1143 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1144 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

1145 L{a_f2Tuple}), overriding this point's datum. 

1146 @kwarg height: Optional height, overriding the default height 

1147 (C{meter}). 

1148 

1149 @return: The destination point (ellipsoidal C{LatLon}). 

1150 

1151 @raise TypeError: Invalid B{C{radius}}. 

1152 

1153 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, 

1154 B{C{radius}} or B{C{height}}. 

1155 ''' 

1156 r, D, _ = self._rhumbx3(exact, radius) 

1157 d = r._Direct(self, azimuth, distance) 

1158 h = self._heigHt(height) 

1159 return self.classof(d.lat2, d.lon2, datum=D, height=h) 

1160 

1161 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False): 

1162 '''Return the distance from this to an other point along 

1163 a rhumb line (loxodrome). 

1164 

1165 @arg other: The other point (C{LatLon}). 

1166 @kwarg exact: If C{True}, use the I{exact} L{Rhumb} (C{bool}), 

1167 default C{False}. 

1168 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1169 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

1170 L{a_f2Tuple}), overriding this point's datum. 

1171 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1172 B{C{other}} point (C{bool}). 

1173 

1174 @return: Distance (C{meter}, the same units as this point's 

1175 datum (ellipsoid) axes or B{C{radius}}. 

1176 

1177 @raise TypeError: The B{C{other}} point is incompatible or 

1178 B{C{radius}} is invalid. 

1179 

1180 @raise ValueError: Invalid B{C{radius}}. 

1181 ''' 

1182 r, _, C = self._rhumbx3(exact, radius) 

1183 return r._Inverse(self, other, wrap, outmask=C.DISTANCE).s12 

1184 

1185 def rhumbLine(self, azimuth_other, exact=False, radius=None, wrap=False, 

1186 **name_caps): 

1187 '''Get a rhumb line through this point at a given azimuth or 

1188 through this and an other point. 

1189 

1190 @arg azimuth_other: The azimuth of the rhumb line (compass 

1191 C{degrees}) or the other point (C{LatLon}). 

1192 @kwarg exact: If C{True}, use the I{exact} L{Rhumb} (C{bool}), 

1193 default C{False}. 

1194 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1195 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

1196 L{a_f2Tuple}), overriding this point's datum. 

1197 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1198 C{azimuth_B{other}} point (C{bool}). 

1199 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see 

1200 L{RhumbLine} C{B{caps}}. 

1201 

1202 @return: A L{RhumbLine} instance. 

1203 

1204 @raise TypeError: Invalid B{C{radius}} or BC{C{azimuth_other}} 

1205 not a C{scalar} nor a C{LatLon}. 

1206 

1207 @see: Classes L{RhumbLine} and L{Rhumb}, property L{Rhumb.exact} 

1208 and methods L{Rhumb.DirectLine} and L{Rhumb.InverseLine}. 

1209 ''' 

1210 r, _, _ = self._rhumbx3(exact, radius) 

1211 a, kwds = azimuth_other, _xkwds(name_caps, name=self.name) 

1212 if isscalar(a): 

1213 r = r._DirectLine(self, a, **kwds) 

1214 elif isinstance(a, LatLonBase): 

1215 r = r._InverseLine(self, a, wrap, **kwds) 

1216 else: 

1217 raise _TypeError(azimuth_other=a) 

1218 return r 

1219 

1220 def rhumbMidpointTo(self, other, exact=False, radius=None, 

1221 height=None, fraction=_0_5, wrap=False): 

1222 '''Return the (loxodromic) midpoint on the rhumb line between 

1223 this and an other point. 

1224 

1225 @arg other: The other point (C{LatLon}). 

1226 @kwarg exact: If C{True}, use the I{exact} L{Rhumb} (C{bool}), 

1227 default C{False}. 

1228 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1229 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

1230 L{a_f2Tuple}), overriding this point's datum. 

1231 @kwarg height: Optional height, overriding the mean height 

1232 (C{meter}). 

1233 @kwarg fraction: Midpoint location from this point (C{scalar}), 

1234 may be negative or greater than 1.0. 

1235 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1236 B{C{other}} point (C{bool}). 

1237 

1238 @return: The midpoint at the given B{C{fraction}} along the 

1239 rhumb line (C{LatLon}). 

1240 

1241 @raise TypeError: The B{C{other}} point is incompatible or 

1242 B{C{radius}} is invalid. 

1243 

1244 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}. 

1245 ''' 

1246 r, D, _ = self._rhumbx3(exact, radius) 

1247 f = Scalar(fraction=fraction) 

1248 d = r._Inverse(self, other, wrap) # C.AZIMUTH_DISTANCE 

1249 d = r._Direct( self, d.azi12, d.s12 * f) 

1250 h = self._havg(other, f=f, h=height) 

1251 return self.classof(d.lat2, d.lon2, datum=D, height=h) 

1252 

1253 def thomasTo(self, other, wrap=False): 

1254 '''Compute the distance between this and an other point using 

1255 U{Thomas'<https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>} 

1256 formula. 

1257 

1258 @arg other: The other point (C{LatLon}). 

1259 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll 

1260 the B{C{other}} point (C{bool}). 

1261 

1262 @return: Distance (C{meter}, same units as the axes of 

1263 this point's datum ellipsoid). 

1264 

1265 @raise TypeError: The B{C{other}} point is not C{LatLon}. 

1266 

1267 @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo}, 

1268 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

1269 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

1270 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}. 

1271 ''' 

1272 return self._distanceTo_(thomas_, other, wrap=wrap) 

1273 

1274 @deprecated_method 

1275 def to2ab(self): # PYCHOK no cover 

1276 '''DEPRECATED, use property L{philam}.''' 

1277 return self.philam 

1278 

1279 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds): 

1280 '''Convert this point to cartesian, I{geocentric} coordinates, 

1281 also known as I{Earth-Centered, Earth-Fixed} (ECEF). 

1282 

1283 @kwarg height: Optional height, overriding this point's height 

1284 (C{meter}, conventionally). 

1285 @kwarg Cartesian: Optional class to return the geocentric 

1286 coordinates (C{Cartesian}) or C{None}. 

1287 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} 

1288 keyword arguments, ignored if 

1289 C{B{Cartesian} is None}. 

1290 

1291 @return: A B{C{Cartesian}} or if B{C{Cartesian}} is C{None}, 

1292 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, 

1293 datum)} with C{C=0} and C{M} if available. 

1294 

1295 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}. 

1296 ''' 

1297 r = self._ecef9 if height is None else self.toEcef(height=height) 

1298 if Cartesian is not None: # class or .classof 

1299 r = self._xnamed(Cartesian(r, **Cartesian_kwds)) 

1300 _xdatum(r.datum, self.datum) 

1301 return r 

1302 

1303 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point): 

1304 '''(INTERNAL) Convert to cartesian and check Ecef's before and after. 

1305 ''' 

1306 p = self.others(up=up, **name_point) 

1307 c = p.toCartesian(height=height) 

1308 E = self.Ecef 

1309 if E: 

1310 for p in (p, c): 

1311 e = getattr(p, LatLonBase.Ecef.name, None) 

1312 if e not in (None, E): # PYCHOK no cover 

1313 n, _ = name_point.popitem() 

1314 if i is not None: 

1315 Fmt.SQUARE(n, i) 

1316 raise _ValueError(n, e, txt=_incompatible(E.__name__)) 

1317 return c 

1318 

1319 def toEcef(self, height=None, M=False): 

1320 '''Convert this point to I{geocentric} coordinates, also known as 

1321 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}). 

1322 

1323 @kwarg height: Optional height, overriding this point's height 

1324 (C{meter}, conventionally). 

1325 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}). 

1326 

1327 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} 

1328 with C{C=0} and C{M} if available. 

1329 

1330 @raise EcefError: A C{.datum} or an ECEF issue. 

1331 ''' 

1332 return self._ecef9 if height in (None, self.height) else \ 

1333 self._Ecef_forward(self.lat, self.lon, height=height, M=M) 

1334 

1335 @deprecated_method 

1336 def to3llh(self, height=None): # PYCHOK no cover 

1337 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.''' 

1338 return self.latlonheight if height in (None, self.height) else \ 

1339 self.latlon.to3Tuple(height) 

1340 

1341 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds): 

1342 '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}. 

1343 

1344 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z} 

1345 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}. 

1346 @kwarg ltp: The I{local tangent plane} (LTP) to use, 

1347 overriding this point's LTP (L{Ltp}). 

1348 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword 

1349 arguments, ignored if C{B{Xyz} is None}. 

1350 

1351 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None}, 

1352 a L{Local9Tuple}C{(x, y, z, lat, lon, height, 

1353 ltp, ecef, M)} with C{M=None}, always. 

1354 

1355 @raise TypeError: Invalid B{C{ltp}}. 

1356 ''' 

1357 p = _MODS.ltp._xLtp(ltp, self._ltp) 

1358 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds) 

1359 

1360 def toLtp(self, Ecef=None): 

1361 '''Return the I{local tangent plane} (LTP) for this point. 

1362 

1363 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ... 

1364 L{EcefYou}), overriding this point's C{Ecef}. 

1365 ''' 

1366 return self._ltp if Ecef in (None, self.Ecef) else _MODS.ltp.Ltp( 

1367 self, ecef=Ecef(self.datum), name=self.name) 

1368 

1369 def toNormal(self, deep=False, name=NN): 

1370 '''Get this point I{normalized} to C{abs(lat) <= 90} 

1371 and C{abs(lon) <= 180}. 

1372 

1373 @kwarg deep: If C{True} make a deep, otherwise a 

1374 shallow copy (C{bool}). 

1375 @kwarg name: Optional name of the copy (C{str}). 

1376 

1377 @return: A copy of this point, I{normalized} and 

1378 optionally renamed (C{LatLon}). 

1379 

1380 @see: Property L{isnormal}, method L{normal} and function 

1381 L{pygeodesy.normal}. 

1382 ''' 

1383 ll = self.copy(deep=deep) 

1384 _ = ll.normal() 

1385 if name: 

1386 ll.rename(name) 

1387 return ll 

1388 

1389 def toNvector(self, h=None, Nvector=None, **Nvector_kwds): 

1390 '''Convert this point to C{n-vector} (normal to the earth's surface) 

1391 components, I{including height}. 

1392 

1393 @kwarg h: Optional height, overriding this point's 

1394 height (C{meter}). 

1395 @kwarg Nvector: Optional class to return the C{n-vector} 

1396 components (C{Nvector}) or C{None}. 

1397 @kwarg Nvector_kwds_wrap: Optional, additional B{C{Nvector}} 

1398 keyword arguments, ignored if C{B{Nvector} 

1399 is None}. 

1400 

1401 @return: A B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} 

1402 if B{C{Nvector}} is C{None}. 

1403 

1404 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}. 

1405 ''' 

1406 return self.toVector(Vector=Nvector, h=self.height if h is None else h, 

1407 ll=self, **Nvector_kwds) 

1408 

1409 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected 

1410 '''Convert this point to a "lat, lon[, +/-height]" string, formatted 

1411 in the given C{B{form}at}. 

1412 

1413 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see 

1414 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}. 

1415 @kwarg joined: Separator to join the lat-, longitude and heigth 

1416 strings (C{str} or C{None} or C{NN} for non-joined). 

1417 @kwarg m: Optional unit of the height (C{str}), use C{None} to 

1418 exclude height from the returned string. 

1419 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator}, 

1420 B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword 

1421 arguments, see function L{pygeodesy.latDMS} or 

1422 L{pygeodesy.lonDMS}. 

1423 

1424 @return: This point in the specified C{B{form}at}, etc. (C{str} or 

1425 a 2- or 3-tuple C{(lat_str, lon_str[, height_str])} if 

1426 C{B{joined}=NN} or C{B{joined}=None}). 

1427 

1428 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more 

1429 details about keyword arguments C{B{form}at}, C{B{prec}ision}, 

1430 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}. 

1431 

1432 @example: 

1433 

1434 >>> LatLon(51.4778, -0.0016).toStr() # 51°28′40″N, 000°00′06″W 

1435 >>> LatLon(51.4778, -0.0016).toStr(F_D) # 51.4778°N, 000.0016°W 

1436 >>> LatLon(51.4778, -0.0016, 42).toStr() # 51°28′40″N, 000°00′06″W, +42.00m 

1437 ''' 

1438 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S), 

1439 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S)) 

1440 if self.height and m is not None: 

1441 t += (self.heightStr(m=m),) 

1442 return joined.join(t) if joined else t 

1443 

1444 def toVector(self, Vector=None, **Vector_kwds): 

1445 '''Convert this point to C{n-vector} (normal to the earth's 

1446 surface) components, I{ignoring height}. 

1447 

1448 @kwarg Vector: Optional class to return the C{n-vector} 

1449 components (L{Vector3d}) or C{None}. 

1450 @kwarg Vector_kwds: Optional, additional B{C{Vector}} 

1451 keyword arguments, ignored if 

1452 C{B{Vector} is None}. 

1453 

1454 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)} 

1455 if B{C{Vector}} is C{None}. 

1456 

1457 @raise TypeError: Invalid B{C{Vector}} or B{C{kwds}}. 

1458 

1459 @note: These are C{n-vector} x, y and z components, 

1460 I{NOT} geocentric (ECEF) x, y and z coordinates! 

1461 ''' 

1462 r = self._vector3tuple 

1463 if Vector is not None: 

1464 r = Vector(*r, **_xkwds(Vector_kwds, name=self.name)) 

1465 return r 

1466 

1467 def toVector3d(self): 

1468 '''Convert this point to C{n-vector} (normal to the earth's 

1469 surface) components, I{ignoring height}. 

1470 

1471 @return: Unit vector (L{Vector3d}). 

1472 

1473 @note: These are C{n-vector} x, y and z components, 

1474 I{NOT} geocentric (ECEF) x, y and z coordinates! 

1475 ''' 

1476 return self._vector3d # XXX .unit() 

1477 

1478 def toWm(self, **toWm_kwds): 

1479 '''Convert this point to a WM coordinate. 

1480 

1481 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments. 

1482 

1483 @return: The WM coordinate (L{Wm}). 

1484 

1485 @see: Function L{pygeodesy.toWm}. 

1486 ''' 

1487 return self._wm if not toWm_kwds else _MODS.webmercator.toWm( 

1488 self, **_xkwds(toWm_kwds, name=self.name)) 

1489 

1490 @deprecated_method 

1491 def to3xyz(self): # PYCHOK no cover 

1492 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector}, 

1493 L{toVector3d} or perhaps (geocentric) L{toEcef}.''' 

1494 return self.xyz # self.toVector() 

1495 

1496 @Property_RO 

1497 def _vector3d(self): 

1498 '''(INTERNAL) Cache for L{toVector3d}. 

1499 ''' 

1500 return self.toVector(Vector=Vector3d) # XXX .unit() 

1501 

1502 @Property_RO 

1503 def _vector3tuple(self): 

1504 '''(INTERNAL) Cache for L{toVector}. 

1505 ''' 

1506 return philam2n_xyz(self.phi, self.lam, name=self.name) 

1507 

1508 def vincentysTo(self, other, **radius_wrap): 

1509 '''Compute the distance between this and an other point using 

1510 U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>} 

1511 spherical formula. 

1512 

1513 @arg other: The other point (C{LatLon}). 

1514 @kwarg radius_wrap: Optional keyword arguments for function 

1515 L{pygeodesy.vincentys}, overriding the 

1516 default mean C{radius} of this point's 

1517 datum ellipsoid. 

1518 

1519 @return: Distance (C{meter}, same units as B{C{radius}}). 

1520 

1521 @raise TypeError: The B{C{other}} point is not C{LatLon}. 

1522 

1523 @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo}, 

1524 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

1525 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

1526 L{flatPolarTo}, L{haversineTo} and L{thomasTo}. 

1527 ''' 

1528 return self._distanceTo(vincentys, other, **_xkwds(radius_wrap, radius=None)) 

1529 

1530 @Property_RO 

1531 def _wm(self): 

1532 '''(INTERNAL) Get this point as webmercator (L{Wm}). 

1533 ''' 

1534 return _MODS.webmercator.toWm(self) 

1535 

1536 @Property_RO 

1537 def xyz(self): 

1538 '''Get the C{n-vector} X, Y and Z components (L{Vector3Tuple}C{(x, y, z)}) 

1539 

1540 @note: These are C{n-vector} x, y and z components, I{NOT} 

1541 geocentric (ECEF) x, y and z coordinates! 

1542 ''' 

1543 return self.toVector(Vector=Vector3Tuple) 

1544 

1545 @Property_RO 

1546 def xyzh(self): 

1547 '''Get the C{n-vector} X, Y, Z and H components (L{Vector4Tuple}C{(x, y, z, h)}) 

1548 

1549 @note: These are C{n-vector} x, y and z components, I{NOT} 

1550 geocentric (ECEF) x, y and z coordinates! 

1551 ''' 

1552 return self.xyz.to4Tuple(self.height) 

1553 

1554 

1555class _toCartesian3(object): # see also .geodesicw._wargs, .vector2d._numpy 

1556 '''(INTERNAL) Wrapper to convert 2 other points. 

1557 ''' 

1558 @contextmanager # <https://www.python.org/dev/peps/pep-0343/> Examples 

1559 def __call__(self, p, p2, p3, wrap, **kwds): 

1560 try: 

1561 if wrap: 

1562 p2, p3 = map1(_Wrap.point, p2, p3) 

1563 kwds = _xkwds(kwds, wrap=wrap) 

1564 yield (p. toCartesian().copy(name=_point_), # copy to rename 

1565 p._toCartesianEcef(up=4, point2=p2), 

1566 p._toCartesianEcef(up=4, point3=p3)) 

1567 except (AssertionError, TypeError, ValueError) as x: 

1568 raise _xError(x, point=p, point2=p2, point3=p3, **kwds) 

1569 

1570_toCartesian3 = _toCartesian3() # PYCHOK singleton 

1571 

1572 

1573def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, # MCCABE 13 

1574 radius=R_M, wrap=False): 

1575 '''(INTERNAL) Trilaterate three points by area overlap or by 

1576 perimeter intersection of three circles. 

1577 

1578 @note: The B{C{radius}} is only needed for both the n-vectorial 

1579 and C{sphericalTrigonometry.LatLon.distanceTo} methods and 

1580 silently ignored by the C{ellipsoidalExact}, C{-GeodSolve}, 

1581 C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods. 

1582 ''' 

1583 p2, p3, w = _unrollon3(p1, p2, p3, wrap) 

1584 

1585 r1 = Distance_(distance1=d1) 

1586 r2 = Distance_(distance2=d2) 

1587 r3 = Distance_(distance3=d3) 

1588 m = 0 if area else (r1 + r2 + r3) 

1589 pc = 0 

1590 t = [] 

1591 for _ in range(3): 

1592 try: # intersection of circle (p1, r1) and (p2, r2) 

1593 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w) 

1594 

1595 if area: # check overlap 

1596 if c1 is c2: # abutting 

1597 c = c1 

1598 else: # nearest point on radical 

1599 c = p3.nearestOn(c1, c2, within=True, wrap=w) 

1600 d = r3 - p3.distanceTo(c, radius=radius, wrap=w) 

1601 if d > eps: # sufficient overlap 

1602 t.append((d, c)) 

1603 m = max(m, d) 

1604 

1605 else: # check intersection 

1606 for c in ((c1,) if c1 is c2 else (c1, c2)): 

1607 d = fabs(r3 - p3.distanceTo(c, radius=radius, wrap=w)) 

1608 if d < eps: # below margin 

1609 t.append((d, c)) 

1610 m = min(m, d) 

1611 

1612 except IntersectionError as x: 

1613 if _concentric_ in str(x): # XXX ConcentricError? 

1614 pc += 1 

1615 

1616 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate 

1617 

1618 if t: # get min, max, points and count ... 

1619 t = tuple(sorted(t)) 

1620 n = len(t), # as 1-tuple 

1621 # ... or for a single trilaterated result, 

1622 # min *is* max, min- *is* maxPoint and n=1, 2 or 3 

1623 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...) 

1624 

1625 elif area and pc == 3: # all pairwise concentric ... 

1626 r, p = min((r1, p1), (r2, p2), (r3, p3)) 

1627 m = max(r1, r2, r3) 

1628 # ... return "smallest" point twice, the smallest 

1629 # and largest distance and n=0 for concentric 

1630 return Trilaterate5Tuple(float(r), p, float(m), p, 0) 

1631 

1632 n, f = (_overlap_, max) if area else (_intersection_, min) 

1633 t = _COMMASPACE_(_no_(n), '%s %.3g' % (f.__name__, m)) 

1634 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t) 

1635 

1636 

1637__all__ += _ALL_DOCS(LatLonBase) 

1638 

1639# **) MIT License 

1640# 

1641# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved. 

1642# 

1643# Permission is hereby granted, free of charge, to any person obtaining a 

1644# copy of this software and associated documentation files (the "Software"), 

1645# to deal in the Software without restriction, including without limitation 

1646# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1647# and/or sell copies of the Software, and to permit persons to whom the 

1648# Software is furnished to do so, subject to the following conditions: 

1649# 

1650# The above copyright notice and this permission notice shall be included 

1651# in all copies or substantial portions of the Software. 

1652# 

1653# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1654# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1655# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1656# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1657# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1658# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1659# OTHER DEALINGS IN THE SOFTWARE.