Coverage for pygeodesy/latlonBase.py: 94%

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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 isstr, map1, _xinstanceof 

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

15 _EPSqrt as _TOL, _0_0, _0_5, _1_0, \ 

16 _360_0, _umod_360 

17from pygeodesy.datums import _spherical_datum 

18from pygeodesy.dms import F_D, F_DMS, latDMS, lonDMS, parse3llh 

19# from pygeodesy.ecef import EcefKarney # _MODS 

20from pygeodesy.errors import _AttributeError, IntersectionError, \ 

21 _incompatible, _IsnotError, _TypeError, \ 

22 _ValueError, _xattr, _xdatum, _xError, \ 

23 _xkwds, _xkwds_not 

24# from pygeodesy.fmath import favg # _MODS 

25# from pygeodesy.formy import antipode, compassAngle, cosineAndoyerLambert_, \ 

26# cosineForsytheAndoyerLambert_, cosineLaw, \ 

27# equirectangular, euclidean, flatLocal_, \ 

28# flatPolar, _hartzell, haversine, isantipode, \ 

29# _isequalTo, isnormal, normal, philam2n_xyz, \ 

30# thomas_, vincentys # as _formy 

31from pygeodesy.interns import NN, _COMMASPACE_, _concentric_, _height_, \ 

32 _intersection_, _LatLon_, _m_, _negative_, \ 

33 _no_, _overlap_, _too_, _point_ # PYCHOK used! 

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

35# from pygeodesy.karney import Caps # _MODS 

36from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

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

38from pygeodesy.named import _NamedBase, notImplemented, notOverloaded, Fmt 

39from pygeodesy.namedTuples import Bounds2Tuple, LatLon2Tuple, PhiLam2Tuple, \ 

40 Trilaterate5Tuple 

41# from pygeodesy.nvectorBase import _N_vector_ # _MODS 

42from pygeodesy.props import deprecated_method, Property, Property_RO, \ 

43 property_RO, _update_all 

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

45from pygeodesy.units import _isDegrees, _isRadius, Distance_, Lat, Lon, \ 

46 Height, Radius, Radius_, Scalar, Scalar_ 

47from pygeodesy.utily import _unrollon, _unrollon3, _Wrap 

48from pygeodesy.vector2d import _circin6, Circin6Tuple, _circum3, circum4_, \ 

49 Circum3Tuple, _radii11ABC 

50from pygeodesy.vector3d import nearestOn6, Vector3d, PointsIter 

51 

52from contextlib import contextmanager 

53from math import asin, cos, degrees, fabs, radians 

54 

55__all__ = _ALL_LAZY.latlonBase 

56__version__ = '24.01.18' 

57 

58 

59class LatLonBase(_NamedBase): 

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

61 ellipsoidal earth models. 

62 ''' 

63 _clipid = INT0 # polygonal clip, see .booleans 

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

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

66 _lat = 0 # latitude (C{degrees}) 

67 _lon = 0 # longitude (C{degrees}) 

68 

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

70 '''New C{LatLon}. 

71 

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

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

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

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

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

77 (C{meter}, conventionally). 

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

79 (C{bool}). 

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

81 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, 

82 L{a_f2Tuple} or I{scalar} radius) or C{None}. 

83 

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

85 

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

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

88 

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

90 

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

92 ''' 

93 if name: 

94 self.name = name 

95 

96 if lon is None: 

97 lat, lon, height = _latlonheight3(latlonh, height, wrap) 

98 elif wrap: 

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

100 else: 

101 lat = latlonh 

102 

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

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

105 if height: # elevation 

106 self._height = Height(height) 

107 if datum is not None: 

108 self._datum = _spherical_datum(datum, name=self.name) 

109 

110 def __eq__(self, other): 

111 return self.isequalTo(other) 

112 

113 def __ne__(self, other): 

114 return not self.isequalTo(other) 

115 

116 def __str__(self): 

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

118 

119 def antipode(self, height=None): 

120 '''Return the antipode, the point diametrically opposite to 

121 this point. 

122 

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

124 this point's height otherwise. 

125 

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

127 ''' 

128 a = self._formy.antipode(*self.latlon) 

129 h = self._heigHt(height) 

130 return self.classof(*a, height=h) 

131 

132 @deprecated_method 

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

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

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

136 

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

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

139 bounding box centered at this location. 

140 

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

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

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

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

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

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

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

148 overriding the point's height. 

149 

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

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

152 

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

154 ''' 

155 w = Scalar_(wide=wide) * _0_5 

156 t = Scalar_(tall=tall) * _0_5 

157 if radius is not None: 

158 r = Radius_(radius) 

159 c = cos(self.phi) 

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

161 t = degrees(t / r) 

162 y, t = self.lat, fabs(t) 

163 x, w = self.lon, fabs(w) 

164 

165 h = self._heigHt(height) 

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

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

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

169 

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

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

172 this and an other point. 

173 

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

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

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

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

178 point (C{bool}). 

179 

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

181 

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

183 ''' 

184 def _v3d(ll): 

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

186 return Vector3d(t.x, t.y, t.z) 

187 

188 p = self.others(other) 

189 if wrap: 

190 p = _Wrap.point(p) 

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

192 

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

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

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

196 

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

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

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

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

201 B{C{point3}} (C{bool}). 

202 

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

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

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

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

207 

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

209 than version 1.10. 

210 

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

212 a trilateration or C{numpy} issue. 

213 

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

215 

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

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

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

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

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

221 height)} representing the differences between both results from 

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

223 

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

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

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

227 ''' 

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

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

230 datum=self.datum) # PYCHOK unpack 

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

232 

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

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

235 this and two other points. 

236 

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

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

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

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

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

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

243 B{C{point3}} (C{bool}). 

244 

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

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

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

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

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

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

251 

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

253 version 1.10. 

254 

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

256 incompatible C{Ecef} classes or a trilateration 

257 or C{numpy} issue. 

258 

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

260 

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

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

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

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

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

266 height)} representing the difference between both results from 

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

268 

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

270 ''' 

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

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

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

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

275 

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

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

278 

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

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

281 (C{bool}), default C{False}. 

282 

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

284 an instance of this (sub-)class. 

285 

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

287 version 1.10. 

288 

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

290 

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

292 

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

294 

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

296 ''' 

297 def _cs(ps, C, wrap=False): 

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

299 for i, p in enumerate(ps): 

300 yield C(i=i, points=_wp(p)) 

301 

302 C = self._toCartesianEcef 

303 c = C(point=self) 

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

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

306 return t.dup(center=c) 

307 

308 @property 

309 def clipid(self): 

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

311 ''' 

312 return self._clipid 

313 

314 @clipid.setter # PYCHOK setter! 

315 def clipid(self, clipid): 

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

317 ''' 

318 self._clipid = int(clipid) 

319 

320 @deprecated_method 

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

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

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

324 

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

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

327 this and an other point. 

328 

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

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

331 larger distances. 

332 

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

334 @kwarg adjust_wrap: Optional keyword arguments for function 

335 L{pygeodesy.compassAngle}. 

336 

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

338 

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

340 

341 @note: Courtesy of Martin Schultz. 

342 

343 @see: U{Local, flat earth approximation 

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

345 ''' 

346 p = self.others(other) 

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

348 

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

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

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

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

353 

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

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

356 the B{C{other}} point (C{bool}). 

357 

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

359 point's datum ellipsoid). 

360 

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

362 

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

364 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, 

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

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

367 L{thomasTo} and L{vincentysTo}. 

368 ''' 

369 return self._distanceTo_(self._formy.cosineAndoyerLambert_, other, wrap=wrap) 

370 

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

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

373 the U{Forsythe-Andoyer-Lambert correction 

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

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

376 formula. 

377 

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

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

380 the B{C{other}} point (C{bool}). 

381 

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

383 this point's datum ellipsoid). 

384 

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

386 

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

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

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

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

391 ''' 

392 return self._distanceTo_(self._formy.cosineForsytheAndoyerLambert_, other, wrap=wrap) 

393 

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

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

396 U{spherical Law of Cosines 

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

398 formula. 

399 

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

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

402 for the mean radius of this point's datum 

403 ellipsoid. 

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

405 the B{C{other}} point (C{bool}). 

406 

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

408 

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

410 

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

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

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

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

415 ''' 

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

417 

418 @property_RO 

419 def datum(self): # PYCHOK no cover 

420 '''I{Must be overloaded}.''' 

421 notOverloaded(self) 

422 

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

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

425 

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

427 L{Ned} or L{Local9Tuple}). 

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

429 or C{None}. 

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

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

432 

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

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

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

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

437 is un-/specified. 

438 

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

440 ''' 

441 t = self._Ltp._local2ecef(delta, nine=True) 

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

443 

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

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

446 ''' 

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

448 if r is None: 

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

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

451 

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

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

454 ''' 

455 p = self.others(other, up=2) 

456 D = self.datum 

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

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

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

460 

461 @property_RO 

462 def Ecef(self): 

463 '''Get the ECEF I{class} (L{EcefKarney}), I{once}. 

464 ''' 

465 LatLonBase.Ecef = E = _MODS.ecef.EcefKarney # overwrite property_RO 

466 return E 

467 

468 @Property_RO 

469 def _Ecef_forward(self): 

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

471 ''' 

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

473 

474 @Property_RO 

475 def _ecef9(self): 

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

477 ''' 

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

479 

480 @property_RO 

481 def ellipsoidalLatLon(self): 

482 '''Get the C{LatLon type} iff ellipsoidal, overloaded in L{LatLonEllipsoidalBase}. 

483 ''' 

484 return False 

485 

486 @deprecated_method 

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

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

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

490 

491 @deprecated_method 

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

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

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

495 

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

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

498 using the U{Equirectangular Approximation / Projection 

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

500 

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

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

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

504 

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

506 @kwarg radius_adjust_limit_wrap: Optional keyword arguments 

507 for function L{pygeodesy.equirectangular}, 

508 overriding the default mean C{radius} of this 

509 point's datum ellipsoid. 

510 

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

512 

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

514 

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

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

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

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

519 ''' 

520 return self._distanceTo(self._formy.equirectangular, other, **radius_adjust_limit_wrap) 

521 

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

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

524 an other point. 

525 

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

527 

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

529 @kwarg radius_adjust_wrap: Optional keyword arguments for function 

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

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

532 

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

534 

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

536 

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

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

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

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

541 ''' 

542 return self._distanceTo(self._formy.euclidean, other, **radius_adjust_wrap) 

543 

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

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

546 U{ellipsoidal Earth to plane projection 

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

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

549 

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

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

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

553 datum ellipsoid. 

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

555 the B{C{other}} point (C{bool}). 

556 

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

558 

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

560 

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

562 

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

564 L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo}, 

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

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

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

568 ''' 

569 return self._distanceTo_(self._formy.flatLocal_, other, wrap=wrap, radius= 

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

571 

572 hubenyTo = flatLocalTo # for Karl Hubeny 

573 

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

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

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

577 Geographical_distance#Polar_coordinate_flat-Earth_formula>} formula. 

578 

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

580 @kwarg radius_wrap: Optional keyword arguments for function 

581 L{pygeodesy.flatPolar}, overriding the 

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

583 datum ellipsoid. 

584 

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

586 

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

588 

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

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

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

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

593 ''' 

594 return self._distanceTo(self._formy.flatPolar, other, **radius_wrap) 

595 

596 @property_RO 

597 def _formy(self): 

598 '''(INTERNAL) Import module C{distance.formy}, I{once} and I{lazily} 

599 to avoid circular imports. 

600 ''' 

601 LatLonBase._formy = f = _MODS.formy # overwrite property_RO 

602 return f 

603 

604 def hartzell(self, los=False, earth=None): 

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

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

607 

608 @kwarg los: Line-Of-Sight, I{direction} to the ellipsoid (L{Los}, L{Vector3d}), 

609 C{True} for the I{normal, plumb} onto the surface or I{False} or 

610 C{None} to point to the center of the ellipsoid. 

611 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} 

612 or C{scalar} radius in C{meter}), overriding this point's C{datum} 

613 ellipsoid. 

614 

615 @return: The intersection (C{LatLon}) with C{.height} set to the distance to 

616 this C{pov}. 

617 

618 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov} is inside 

619 the ellipsoid or B{C{los}} points outside or away from 

620 the ellipsoid. 

621 

622 @raise TypeError: Invalid B{C{los}} or invalid or undefined B{C{earth}} or C{datum}. 

623 

624 @see: Function L{hartzell<pygeodesy.formy.hartzell>} for further details. 

625 ''' 

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

627 

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

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

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

631 formula. 

632 

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

634 @kwarg radius_wrap: Optional keyword arguments for function 

635 L{pygeodesy.haversine}, overriding the 

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

637 datum ellipsoid. 

638 

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

640 

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

642 

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

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

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

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

647 ''' 

648 return self._distanceTo(self._formy.haversine, other, **radius_wrap) 

649 

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

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

652 

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

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

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

656 

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

658 the overriding height B{C{h}} (C{Height}). 

659 ''' 

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

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

662 

663 @Property 

664 def height(self): 

665 '''Get the height (C{meter}). 

666 ''' 

667 return self._height 

668 

669 @height.setter # PYCHOK setter! 

670 def height(self, height): 

671 '''Set the height (C{meter}). 

672 

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

674 

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

676 ''' 

677 h = Height(height) 

678 if self._height != h: 

679 _update_all(self) 

680 self._height = h 

681 

682 def _heigHt(self, height): 

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

684 ''' 

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

686 

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

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

689 this datum's ellipsoid surface. 

690 

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

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

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

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

695 @kwarg normal: If C{True} the projection is the normal to this 

696 ellipsoid's surface, otherwise the intersection of the 

697 I{radial} line to this ellipsoid's center (C{bool}). 

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

699 datum (C{LatLon}) or C{None}. 

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

701 ignored if C{B{LatLon} is None}. 

702 

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

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

705 

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

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

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

709 

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

711 

712 @raise TypeError: Invalid B{C{earth}} or triaxial B{C{earth}} couldn't be 

713 converted to biaxial B{C{LatLon}} datum. 

714 

715 @see: Methods 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 c = c.height4(earth=earth, normal=normal, Cartesian=c.classof, height=0) 

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

723 if r.datum != c.datum: 

724 raise _TypeError(earth=earth, datum=r.datum) 

725 return r 

726 

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

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

729 

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

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

732 

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

734 ''' 

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

736 

737 def intersecant2(self, *args, **kwds): # PYCHOK no cover 

738 '''B{Not implemented}, throws a C{NotImplementedError} always.''' 

739 notImplemented(self, *args, **kwds) 

740 

741 def _intersecend2(self, p, q, wrap, height, g_or_r, P, Q, unused): # in .LatLonEllipsoidalBaseDI.intersecant2 

742 '''(INTERNAL) Interpolate 2 heights along a geodesic or rhumb 

743 line and return the 2 intercant points accordingly. 

744 ''' 

745 if height is None: 

746 hp = hq = _xattr(p, height=INT0) 

747 h = _xattr(q, height=hp) # if isLatLon(q) else hp 

748 if h != hp: 

749 s = g_or_r._Inverse(p, q, wrap).s12 

750 if s: # fmath.fidw? 

751 s = (h - hp) / s # slope 

752 hq += s * Q.s12 

753 hp += s * P.s12 

754 else: 

755 hp = hq = _MODS.fmath.favg(hp, h) 

756 else: 

757 hp = hq = Height(height) 

758 

759# n = self.name or unused.__name__ 

760 p = q = self.classof(P.lat2, P.lon2, datum=g_or_r.datum, height=hp) # name=n 

761 p._iteration = P.iteration 

762 if P is not Q: 

763 q = self.classof(Q.lat2, Q.lon2, datum=g_or_r.datum, height=hq) # name=n 

764 q._iteration = Q.iteration 

765 return p, q 

766 

767 @deprecated_method 

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

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

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

771 

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

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

774 on diametrically opposite sides of the earth. 

775 

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

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

778 

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

780 tolerance, C{False} otherwise. 

781 ''' 

782 p = self.others(other) 

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

784 

785 @Property_RO 

786 def isEllipsoidal(self): 

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

788 ''' 

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

790 

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

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

793 

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

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

796 

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

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

799 

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

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

802 this C{class} or C{type}. 

803 

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

805 

806 @see: Method L{isequalTo3}. 

807 ''' 

808 return self._formy._isequalTo(self, self.others(other), eps=eps) 

809 

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

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

812 

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

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

815 

816 @return: C{True} if both points are identical I{including} 

817 height, C{False} otherwise. 

818 

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

820 or mismatch of the B{C{other}} and this 

821 C{class} or C{type}. 

822 

823 @see: Method L{isequalTo}. 

824 ''' 

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

826 self._formy._isequalTo(self, other, eps=eps) 

827 

828 @Property_RO 

829 def isnormal(self): 

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

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

832 

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

834 <pygeodesy.isnormal>} and L{normal<pygeodesy.normal>}. 

835 ''' 

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

837 

838 @Property_RO 

839 def isSpherical(self): 

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

841 ''' 

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

843 

844 @Property_RO 

845 def lam(self): 

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

847 ''' 

848 return radians(self.lon) 

849 

850 @Property 

851 def lat(self): 

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

853 ''' 

854 return self._lat 

855 

856 @lat.setter # PYCHOK setter! 

857 def lat(self, lat): 

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

859 

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

861 ''' 

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

863 if self._lat != lat: 

864 _update_all(self) 

865 self._lat = lat 

866 

867 @Property 

868 def latlon(self): 

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

870 ''' 

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

872 

873 @latlon.setter # PYCHOK setter! 

874 def latlon(self, latlonh): 

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

876 (2- or 3-tuple or comma- or space-separated C{str} 

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

878 

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

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

881 

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

883 

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

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

886 ''' 

887 if isstr(latlonh): 

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

889 else: 

890 _xinstanceof(list, tuple, latlonh=latlonh) 

891 if len(latlonh) == 3: 

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

893 elif len(latlonh) != 2: 

894 raise _ValueError(latlonh=latlonh) 

895 else: 

896 h = self.height 

897 

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

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

900 _update_all(self) 

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

902 

903 def latlon2(self, ndigits=0): 

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

905 

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

907 

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

909 and rounded away from zero. 

910 

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

912 if B{C{ndigits}} is omitted. 

913 ''' 

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

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

916 

917 @deprecated_method 

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

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

920 return self.latlon2(ndigits=ndigits) 

921 

922 latlon2round = latlon_ # PYCHOK no cover 

923 

924 @Property 

925 def latlonheight(self): 

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

927 ''' 

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

929 

930 @latlonheight.setter # PYCHOK setter! 

931 def latlonheight(self, latlonh): 

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

933 (2- or 3-tuple or comma- or space-separated C{str} of 

934 C{degrees90}, C{degrees180} and C{meter}). 

935 

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

937 ''' 

938 self.latlon = latlonh 

939 

940 @Property 

941 def lon(self): 

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

943 ''' 

944 return self._lon 

945 

946 @lon.setter # PYCHOK setter! 

947 def lon(self, lon): 

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

949 

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

951 ''' 

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

953 if self._lon != lon: 

954 _update_all(self) 

955 self._lon = lon 

956 

957 @property_RO 

958 def _ltp(self): 

959 '''(INTERNAL) Get the C{.ltp} module, I{once}. 

960 ''' 

961 LatLonBase._ltp = m = _MODS.ltp # overwrite property_RO 

962 return m 

963 

964 @Property_RO 

965 def _Ltp(self): 

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

967 ''' 

968 return self._ltp.Ltp(self, ecef=self.Ecef(self.datum), name=self.name) 

969 

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

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

972 

973 Points are converted to and distances are computed in 

974 I{geocentric}, cartesian space. 

975 

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

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

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

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

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

981 account for distances. 

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

983 the B{C{points}} (C{bool}). 

984 

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

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

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

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

989 units as the cartesian axes. 

990 

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

992 

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

994 C{Ecef} invalid. 

995 

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

997 

998 @see: Function L{nearestOn6<pygeodesy.nearestOn6>}. 

999 ''' 

1000 def _cs(Ps, h, w, C): 

1001 p = None # not used 

1002 for i, q in Ps.enumerate(): 

1003 if w and i: 

1004 q = _unrollon(p, q) 

1005 yield C(height=h, i=i, up=3, points=q) 

1006 p = q 

1007 

1008 C = self._toCartesianEcef # to verify datum and Ecef 

1009 Ps = self.PointsIter(points, wrap=wrap) 

1010 

1011 c = C(height=height, this=self) # this Cartesian 

1012 t = nearestOn6(c, _cs(Ps, height, wrap, C), closed=closed) 

1013 c, s, e = t.closest, t.start, t.end 

1014 

1015 kwds = _xkwds_not(None, LatLon=self.classof, # this LatLon 

1016 height=height) 

1017 _r = self.Ecef(self.datum).reverse 

1018 p = _r(c).toLatLon(**kwds) 

1019 s = _r(s).toLatLon(**kwds) if s is not c else p 

1020 e = _r(e).toLatLon(**kwds) if e is not c else p 

1021 return t.dup(closest=p, start=s, end=e) 

1022 

1023 def nearestTo(self, *args, **kwds): # PYCHOK no cover 

1024 '''B{Not implemented}, throws a C{NotImplementedError} always.''' 

1025 notImplemented(self, *args, **kwds) 

1026 

1027 def normal(self): 

1028 '''Normalize this point I{in-place} to C{abs(lat) <= 90} and 

1029 C{abs(lon) <= 180}. 

1030 

1031 @return: C{True} if this point was I{normal}, C{False} if it 

1032 wasn't (but is now). 

1033 

1034 @see: Property L{isnormal} and method L{toNormal}. 

1035 ''' 

1036 n = self.isnormal 

1037 if not n: 

1038 self.latlon = self._formy.normal(*self.latlon) 

1039 return n 

1040 

1041 @property_RO 

1042 def _N_vector(self): 

1043 '''(INTERNAL) Get the C{Nvector} (C{nvectorBase._N_vector_}) 

1044 ''' 

1045 x, y, z = self._n_xyz3 

1046 return _MODS.nvectorBase._N_vector_(x, y, z, h=self.height, name=self.name) 

1047 

1048 @Property_RO 

1049 def _n_xyz3(self): 

1050 '''(INTERNAL) Get the n-vector components as L{Vector3Tuple}. 

1051 ''' 

1052 return self._formy.philam2n_xyz(self.phi, self.lam, name=self.name) 

1053 

1054 @Property_RO 

1055 def phi(self): 

1056 '''Get the latitude (B{C{radians}}). 

1057 ''' 

1058 return radians(self.lat) 

1059 

1060 @Property_RO 

1061 def philam(self): 

1062 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}). 

1063 ''' 

1064 return PhiLam2Tuple(self.phi, self.lam, name=self.name) 

1065 

1066 def philam2(self, ndigits=0): 

1067 '''Return this point's lat- and longitude in C{radians}, rounded. 

1068 

1069 @kwarg ndigits: Number of (decimal) digits (C{int}). 

1070 

1071 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float} 

1072 and rounded away from zero. 

1073 

1074 @note: The C{round}ed values are always C{float}, also 

1075 if B{C{ndigits}} is omitted. 

1076 ''' 

1077 return PhiLam2Tuple(round(self.phi, ndigits), 

1078 round(self.lam, ndigits), name=self.name) 

1079 

1080 @Property_RO 

1081 def philamheight(self): 

1082 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). 

1083 ''' 

1084 return self.philam.to3Tuple(self.height) 

1085 

1086 @deprecated_method 

1087 def points(self, points, closed=True): # PYCHOK no cover 

1088 '''DEPRECATED, use method L{points2}.''' 

1089 return self.points2(points, closed=closed) 

1090 

1091 def points2(self, points, closed=True): 

1092 '''Check a path or polygon represented by points. 

1093 

1094 @arg points: The path or polygon points (C{LatLon}[]) 

1095 @kwarg closed: Optionally, consider the polygon closed, 

1096 ignoring any duplicate or closing final 

1097 B{C{points}} (C{bool}). 

1098 

1099 @return: A L{Points2Tuple}C{(number, points)}, an C{int} 

1100 and C{list} or C{tuple}. 

1101 

1102 @raise PointsError: Insufficient number of B{C{points}}. 

1103 

1104 @raise TypeError: Some B{C{points}} are not C{LatLon}. 

1105 ''' 

1106 return _MODS.iters.points2(points, closed=closed, base=self) 

1107 

1108 def PointsIter(self, points, loop=0, dedup=False, wrap=False): 

1109 '''Return a C{PointsIter} iterator. 

1110 

1111 @arg points: The path or polygon points (C{LatLon}[]) 

1112 @kwarg loop: Number of loop-back points (non-negative C{int}). 

1113 @kwarg dedup: Skip duplicate points (C{bool}). 

1114 @kwarg wrap: If C{True}, wrap or I{normalize} the 

1115 enum-/iterated B{C{points}} (C{bool}). 

1116 

1117 @return: A new C{PointsIter} iterator. 

1118 

1119 @raise PointsError: Insufficient number of B{C{points}}. 

1120 ''' 

1121 return PointsIter(points, base=self, loop=loop, dedup=dedup, wrap=wrap) 

1122 

1123 def radii11(self, point2, point3, wrap=False): 

1124 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent} 

1125 circles of a (planar) triangle formed by this and two other points. 

1126 

1127 @arg point2: Second point (C{LatLon}). 

1128 @arg point3: Third point (C{LatLon}). 

1129 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and 

1130 B{C{point3}} (C{bool}). 

1131 

1132 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}. 

1133 

1134 @raise IntersectionError: Near-coincident or -colinear points. 

1135 

1136 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. 

1137 

1138 @see: Function L{pygeodesy.radii11}, U{Incircle 

1139 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles 

1140 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent 

1141 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}. 

1142 ''' 

1143 with _toCartesian3(self, point2, point3, wrap) as cs: 

1144 return _radii11ABC(*cs, useZ=True)[0] 

1145 

1146 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3 

1147 '''(INTERNAL) Get the C{rhumb} for this point's datum or for 

1148 the B{C{radius}}' earth model iff non-C{None}. 

1149 ''' 

1150 try: 

1151 d = self._rhumb3dict 

1152 t = d[(exact, radius)] 

1153 except KeyError: 

1154 D = self.datum if radius is None else \ 

1155 _spherical_datum(radius) # ellipsoidal OK 

1156 try: 

1157 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical 

1158 except AttributeError as x: 

1159 raise _AttributeError(datum=D, radius=radius, cause=x) 

1160 t = r, D, _MODS.karney.Caps 

1161 while d: 

1162 d.popitem() 

1163 d[(exact, radius)] = t # cache 3-tuple 

1164 return t 

1165 

1166 @Property_RO 

1167 def _rhumb3dict(self): # in rhumbIntersecant2 below 

1168 return {} # single-item cache 

1169 

1170 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False, b360=False): 

1171 '''Return the azimuth (bearing) of a rhumb line (loxodrome) between this 

1172 and an other (ellipsoidal) point. 

1173 

1174 @arg other: The other point (C{LatLon}). 

1175 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see 

1176 method L{Ellipsoid.rhumb_}. 

1177 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, 

1178 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding 

1179 this point's datum. 

1180 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}} 

1181 point (C{bool}). 

1182 @kwarg b360: If C{True}, return the azimuth in the bearing range. 

1183 

1184 @return: Rhumb azimuth (compass C{degrees180} or C{degrees360}). 

1185 

1186 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}} 

1187 is invalid. 

1188 ''' 

1189 r, _, Cs = self._rhumb3(exact, radius) 

1190 z = r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12 

1191 return _umod_360(z + _360_0) if b360 else z 

1192 

1193 def rhumbDestination(self, distance, azimuth, exact=False, radius=None, height=None): 

1194 '''Return the destination point having travelled the given distance from 

1195 this point along a rhumb line (loxodrome) of the given azimuth. 

1196 

1197 @arg distance: Distance travelled (C{meter}, same units as this point's 

1198 datum (ellipsoid) axes or B{C{radius}}, may be negative. 

1199 @arg azimuth: Azimuth (bearing) of the rhumb line (compass C{degrees}). 

1200 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see 

1201 method L{Ellipsoid.rhumb_}. 

1202 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, 

1203 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding 

1204 this point's datum. 

1205 @kwarg height: Optional height, overriding the default height (C{meter}). 

1206 

1207 @return: The destination point (ellipsoidal C{LatLon}). 

1208 

1209 @raise TypeError: Invalid B{C{radius}}. 

1210 

1211 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, B{C{radius}} 

1212 or B{C{height}}. 

1213 ''' 

1214 r, D, _ = self._rhumb3(exact, radius) 

1215 d = r._Direct(self, azimuth, distance) 

1216 h = self._heigHt(height) 

1217 return self.classof(d.lat2, d.lon2, datum=D, height=h) 

1218 

1219 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False): 

1220 '''Return the distance from this to an other point along a rhumb line 

1221 (loxodrome). 

1222 

1223 @arg other: The other point (C{LatLon}). 

1224 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see 

1225 method L{Ellipsoid.rhumb_}. 

1226 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, 

1227 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding 

1228 this point's datum. 

1229 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}} 

1230 point (C{bool}). 

1231 

1232 @return: Distance (C{meter}, the same units as this point's datum 

1233 (ellipsoid) axes or B{C{radius}}. 

1234 

1235 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}} 

1236 is invalid. 

1237 

1238 @raise ValueError: Invalid B{C{radius}}. 

1239 ''' 

1240 r, _, Cs = self._rhumb3(exact, radius) 

1241 return r._Inverse(self, other, wrap, outmask=Cs.DISTANCE).s12 

1242 

1243 def rhumbIntersecant2(self, circle, point, other, height=None, 

1244 **exact_radius_wrap_eps_tol): 

1245 '''Compute the intersections of a circle and a rhumb line given as two 

1246 points or as a point and azimuth. 

1247 

1248 @arg circle: Radius of the circle centered at this location (C{meter}), 

1249 or a point on the circle (this C{LatLon}). 

1250 @arg point: The start point of the rhumb line (this C{LatLon}). 

1251 @arg other: An other point I{on} (this C{LatLon}) or the azimuth I{of} 

1252 (compass C{degrees}) the rhumb line. 

1253 @kwarg height: Optional height for the intersection points (C{meter}, 

1254 conventionally) or C{None} for interpolated heights. 

1255 @kwarg exact_radius_wrap_eps_tol: Optional keyword arguments, see 

1256 methods L{rhumbLine} and L{RhumbLineAux.Intersecant2} 

1257 or L{RhumbLine.Intersecant2}. 

1258 

1259 @return: 2-Tuple of the intersection points (representing a chord), 

1260 each an instance of this class. Both points are the same 

1261 instance if the rhumb line is tangent to the circle. 

1262 

1263 @raise IntersectionError: The circle and rhumb line do not intersect. 

1264 

1265 @raise TypeError: If B{C{point}} is not this C{LatLon} or B{C{circle}} 

1266 or B{C{other}} invalid. 

1267 

1268 @raise ValueError: Invalid B{C{circle}}, B{C{other}}, B{C{height}} 

1269 or B{C{exact_radius_wrap}}. 

1270 

1271 @see: Methods L{RhumbLineAux.Intersecant2} and L{RhumbLine.Intersecant2}. 

1272 ''' 

1273 def _kwds3(eps=EPS, tol=_TOL, wrap=False, **kwds): 

1274 return kwds, wrap, dict(eps=eps, tol=tol) 

1275 

1276 exact_radius, w, eps_tol = _kwds3(**exact_radius_wrap_eps_tol) 

1277 

1278 p = _unrollon(self, self.others(point=point), wrap=w) 

1279 try: 

1280 r = Radius_(circle=circle) if _isRadius(circle) else \ 

1281 self.rhumbDistanceTo(self.others(circle=circle), wrap=w, **exact_radius) 

1282 rl = p.rhumbLine(other, wrap=w, **exact_radius) 

1283 P, Q = rl.Intersecant2(self.lat, self.lon, r, **eps_tol) 

1284 

1285 return self._intersecend2(p, other, w, height, rl.rhumb, P, Q, 

1286 self.rhumbIntersecant2) 

1287 

1288 except (TypeError, ValueError) as x: 

1289 raise _xError(x, center=self, circle=circle, point=point, other=other, 

1290 **exact_radius_wrap_eps_tol) 

1291 

1292 def rhumbLine(self, other, exact=False, radius=None, wrap=False, **name_caps): 

1293 '''Get a rhumb line through this point at a given azimuth or through 

1294 this and an other point. 

1295 

1296 @arg other: The azimuth I{of} (compass C{degrees}) or an other point 

1297 I{on} (this C{LatLon}) the rhumb line. 

1298 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see 

1299 method L{Ellipsoid.rhumb_}. 

1300 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1301 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), 

1302 overriding this point's datum. 

1303 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}} 

1304 point (C{bool}). 

1305 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see L{RhumbLine} 

1306 or L{RhumbLineAux} C{B{caps}}. 

1307 

1308 @return: A C{RhumbLine} instance. 

1309 

1310 @raise TypeError: Invalid B{C{radius}} or B{C{other}} not C{scalar} nor 

1311 this C{LatLon}. 

1312 

1313 @see: Modules L{rhumb.aux_} and L{rhumb.ekx}. 

1314 ''' 

1315 r, _, Cs = self._rhumb3(exact, radius) 

1316 kwds = _xkwds(name_caps, name=self.name, caps=Cs.LINE_OFF) 

1317 rl = r._DirectLine( self, other, **kwds) if _isDegrees(other) else \ 

1318 r._InverseLine(self, self.others(other), wrap, **kwds) 

1319 return rl 

1320 

1321 def rhumbMidpointTo(self, other, exact=False, radius=None, 

1322 height=None, fraction=_0_5, wrap=False): 

1323 '''Return the (loxodromic) midpoint on the rhumb line between this and 

1324 an other point. 

1325 

1326 @arg other: The other point (this C{LatLon}). 

1327 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see 

1328 method L{Ellipsoid.rhumb_}. 

1329 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, 

1330 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding 

1331 this point's datum. 

1332 @kwarg height: Optional height, overriding the mean height (C{meter}). 

1333 @kwarg fraction: Midpoint location from this point (C{scalar}), 0 for this, 

1334 1 for the B{C{other}}, 0.5 for halfway between this and 

1335 the B{C{other}} point, may be negative or greater than 1. 

1336 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}} 

1337 point (C{bool}). 

1338 

1339 @return: The midpoint at the given B{C{fraction}} along the rhumb line 

1340 (this C{LatLon}). 

1341 

1342 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}} 

1343 is invalid. 

1344 

1345 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}. 

1346 ''' 

1347 r, D, _ = self._rhumb3(exact, radius) 

1348 f = Scalar(fraction=fraction) 

1349 d = r._Inverse(self, self.others(other), wrap) # C.AZIMUTH_DISTANCE 

1350 d = r._Direct( self, d.azi12, d.s12 * f) 

1351 h = self._havg(other, f=f, h=height) 

1352 return self.classof(d.lat2, d.lon2, datum=D, height=h) 

1353 

1354 @property_RO 

1355 def sphericalLatLon(self): 

1356 '''Get the C{LatLon type} iff spherical, overloaded in L{LatLonSphericalBase}. 

1357 ''' 

1358 return False 

1359 

1360 def thomasTo(self, other, wrap=False): 

1361 '''Compute the distance between this and an other point using 

1362 U{Thomas'<https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>} 

1363 formula. 

1364 

1365 @arg other: The other point (C{LatLon}). 

1366 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll 

1367 the B{C{other}} point (C{bool}). 

1368 

1369 @return: Distance (C{meter}, same units as the axes of 

1370 this point's datum ellipsoid). 

1371 

1372 @raise TypeError: The B{C{other}} point is not C{LatLon}. 

1373 

1374 @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo}, 

1375 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

1376 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

1377 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}. 

1378 ''' 

1379 return self._distanceTo_(self._formy.thomas_, other, wrap=wrap) 

1380 

1381 @deprecated_method 

1382 def to2ab(self): # PYCHOK no cover 

1383 '''DEPRECATED, use property L{philam}.''' 

1384 return self.philam 

1385 

1386 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds): 

1387 '''Convert this point to cartesian, I{geocentric} coordinates, 

1388 also known as I{Earth-Centered, Earth-Fixed} (ECEF). 

1389 

1390 @kwarg height: Optional height, overriding this point's height 

1391 (C{meter}, conventionally). 

1392 @kwarg Cartesian: Optional class to return the geocentric 

1393 coordinates (C{Cartesian}) or C{None}. 

1394 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} 

1395 keyword arguments, ignored if 

1396 C{B{Cartesian} is None}. 

1397 

1398 @return: A B{C{Cartesian}} or if B{C{Cartesian}} is C{None}, 

1399 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, 

1400 datum)} with C{C=0} and C{M} if available. 

1401 

1402 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}. 

1403 

1404 @see: Methods C{toNvector}, C{toVector} and C{toVector3d}. 

1405 ''' 

1406 r = self._ecef9 if height is None else self.toEcef(height=height) 

1407 if Cartesian is not None: # class or .classof 

1408 r = Cartesian(r, **_xkwds(Cartesian_kwds, name=self.name)) 

1409 _xdatum(r.datum, self.datum) 

1410 return r 

1411 

1412 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point): 

1413 '''(INTERNAL) Convert to cartesian and check Ecef's before and after. 

1414 ''' 

1415 p = self.others(up=up, **name_point) 

1416 c = p.toCartesian(height=height) 

1417 E = self.Ecef 

1418 if E: 

1419 for p in (p, c): 

1420 e = _xattr(p, Ecef=None) 

1421 if e not in (None, E): # PYCHOK no cover 

1422 n, _ = name_point.popitem() 

1423 if i is not None: 

1424 n = Fmt.SQUARE(n, i) 

1425 raise _ValueError(n, e, txt=_incompatible(E.__name__)) 

1426 return c 

1427 

1428 def toDatum(self, datum2, height=None, name=NN): 

1429 '''I{Must be overloaded}.''' 

1430 notOverloaded(self, datum2, height=height, name=name) 

1431 

1432 def toEcef(self, height=None, M=False): 

1433 '''Convert this point to I{geocentric} coordinates, also known as 

1434 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}). 

1435 

1436 @kwarg height: Optional height, overriding this point's height 

1437 (C{meter}, conventionally). 

1438 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}). 

1439 

1440 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} 

1441 with C{C=0} and C{M} if available. 

1442 

1443 @raise EcefError: A C{.datum} or an ECEF issue. 

1444 ''' 

1445 return self._ecef9 if height in (None, self.height) else \ 

1446 self._Ecef_forward(self.lat, self.lon, height=height, M=M) 

1447 

1448 @deprecated_method 

1449 def to3llh(self, height=None): # PYCHOK no cover 

1450 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.''' 

1451 return self.latlonheight if height in (None, self.height) else \ 

1452 self.latlon.to3Tuple(height) 

1453 

1454 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds): 

1455 '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}. 

1456 

1457 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z} 

1458 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}. 

1459 @kwarg ltp: The I{local tangent plane} (LTP) to use, 

1460 overriding this point's LTP (L{Ltp}). 

1461 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword 

1462 arguments, ignored if C{B{Xyz} is None}. 

1463 

1464 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None}, 

1465 a L{Local9Tuple}C{(x, y, z, lat, lon, height, 

1466 ltp, ecef, M)} with C{M=None}, always. 

1467 

1468 @raise TypeError: Invalid B{C{ltp}}. 

1469 ''' 

1470 p = self._ltp._xLtp(ltp, self._Ltp) 

1471 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds) 

1472 

1473 def toLtp(self, Ecef=None): 

1474 '''Return the I{local tangent plane} (LTP) for this point. 

1475 

1476 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ... 

1477 L{EcefYou}), overriding this point's C{Ecef}. 

1478 ''' 

1479 return self._Ltp if Ecef in (None, self.Ecef) else self._ltp.Ltp( 

1480 self, ecef=Ecef(self.datum), name=self.name) 

1481 

1482 def toNormal(self, deep=False, name=NN): 

1483 '''Get this point I{normalized} to C{abs(lat) <= 90} 

1484 and C{abs(lon) <= 180}. 

1485 

1486 @kwarg deep: If C{True} make a deep, otherwise a 

1487 shallow copy (C{bool}). 

1488 @kwarg name: Optional name of the copy (C{str}). 

1489 

1490 @return: A copy of this point, I{normalized} and 

1491 optionally renamed (C{LatLon}). 

1492 

1493 @see: Property L{isnormal}, method L{normal} and function 

1494 L{pygeodesy.normal}. 

1495 ''' 

1496 ll = self.copy(deep=deep) 

1497 _ = ll.normal() 

1498 if name: 

1499 ll.rename(name) 

1500 return ll 

1501 

1502 def toNvector(self, h=None, Nvector=None, **Nvector_kwds): 

1503 '''Convert this point to C{n-vector} (normal to the earth's surface) 

1504 components, I{including height}. 

1505 

1506 @kwarg h: Optional height, overriding this point's height (C{meter}). 

1507 @kwarg Nvector: Optional class to return the C{n-vector} components 

1508 (C{Nvector}) or C{None}. 

1509 @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword 

1510 arguments, ignored if C{B{Nvector} is None}. 

1511 

1512 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if 

1513 B{C{Nvector}} is C{None}. 

1514 

1515 @raise TypeError: Invalid B{C{h}}, B{C{Nvector}} or B{C{Nvector_kwds}} 

1516 item. 

1517 

1518 @see: Methods C{toCartesian}, C{toVector} and C{toVector3d}. 

1519 ''' 

1520 h = self._heigHt(h) 

1521 if Nvector is None: 

1522 r = self._n_xyz3.to4Tuple(h) 

1523 else: 

1524 x, y, z = self._n_xyz3 

1525 r = Nvector(x, y, z, h=h, ll=self, **_xkwds(Nvector_kwds, name=self.name)) 

1526 return r 

1527 

1528 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected 

1529 '''Convert this point to a "lat, lon[, +/-height]" string, formatted 

1530 in the given C{B{form}at}. 

1531 

1532 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see 

1533 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}. 

1534 @kwarg joined: Separator to join the lat-, longitude and heigth 

1535 strings (C{str} or C{None} or C{NN} for non-joined). 

1536 @kwarg m: Optional unit of the height (C{str}), use C{None} to 

1537 exclude height from the returned string. 

1538 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator}, 

1539 B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword 

1540 arguments, see function L{pygeodesy.latDMS} or 

1541 L{pygeodesy.lonDMS}. 

1542 

1543 @return: This point in the specified C{B{form}at}, etc. (C{str} or 

1544 a 2- or 3-tuple C{(lat_str, lon_str[, height_str])} if 

1545 C{B{joined}=NN} or C{B{joined}=None}). 

1546 

1547 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more 

1548 details about keyword arguments C{B{form}at}, C{B{prec}ision}, 

1549 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}. 

1550 ''' 

1551 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S), 

1552 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S)) 

1553 if self.height and m is not None: 

1554 t += (self.heightStr(m=m),) 

1555 return joined.join(t) if joined else t 

1556 

1557 def toVector(self, Vector=None, **Vector_kwds): 

1558 '''Convert this point to a C{Vector} with the I{geocentric} C{(x, 

1559 y, z)} (ECEF) coordinates, I{ignoring height}. 

1560 

1561 @kwarg Vector: Optional class to return the I{geocentric} 

1562 components (L{Vector3d}) or C{None}. 

1563 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword 

1564 arguments, ignored if C{B{Vector} is None}. 

1565 

1566 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)} 

1567 if B{C{Vector}} is C{None}. 

1568 

1569 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}} item. 

1570 

1571 @see: Methods C{toCartesian}, C{toNvector} and C{toVector3d}. 

1572 ''' 

1573 return self._ecef9.toVector(Vector=Vector, **Vector_kwds) 

1574 

1575 def toVector3d(self, norm=True, **Vector3d_kwds): 

1576 '''Convert this point to a L{Vector3d} with the I{geocentric} C{(x, 

1577 y, z)} (ECEF) I{unit} coordinates, I{ignoring height}. 

1578 

1579 @kwarg norm: Normalize the 3-D vector (C{bool}). 

1580 @kwarg Vector3d_kwds: Optional L{Vector3d} keyword arguments. 

1581 

1582 @return: Unit vector (L{Vector3d}). 

1583 

1584 @raise TypeError: Invalid B{C{Vector3d_kwds}} item. 

1585 

1586 @see: Methods C{toCartesian}, C{toNvector} and C{toVector}. 

1587 ''' 

1588 r = self.toVector(Vector=Vector3d, **Vector3d_kwds) 

1589 if norm: 

1590 r = r.unit(ll=self) 

1591 return r 

1592 

1593 def toWm(self, **toWm_kwds): 

1594 '''Convert this point to a WM coordinate. 

1595 

1596 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments. 

1597 

1598 @return: The WM coordinate (L{Wm}). 

1599 

1600 @see: Function L{pygeodesy.toWm}. 

1601 ''' 

1602 return self._wm if not toWm_kwds else _MODS.webmercator.toWm( 

1603 self, **_xkwds(toWm_kwds, name=self.name)) 

1604 

1605 @deprecated_method 

1606 def to3xyz(self): # PYCHOK no cover 

1607 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector}, 

1608 L{toVector3d} or perhaps (geocentric) L{toEcef}.''' 

1609 return self.xyz # self.toVector() 

1610 

1611 def vincentysTo(self, other, **radius_wrap): 

1612 '''Compute the distance between this and an other point using 

1613 U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>} 

1614 spherical formula. 

1615 

1616 @arg other: The other point (C{LatLon}). 

1617 @kwarg radius_wrap: Optional keyword arguments for function 

1618 L{pygeodesy.vincentys}, overriding the 

1619 default mean C{radius} of this point's 

1620 datum ellipsoid. 

1621 

1622 @return: Distance (C{meter}, same units as B{C{radius}}). 

1623 

1624 @raise TypeError: The B{C{other}} point is not C{LatLon}. 

1625 

1626 @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo}, 

1627 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

1628 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

1629 L{flatPolarTo}, L{haversineTo} and L{thomasTo}. 

1630 ''' 

1631 return self._distanceTo(self._formy.vincentys, other, **_xkwds(radius_wrap, radius=None)) 

1632 

1633 @Property_RO 

1634 def _wm(self): 

1635 '''(INTERNAL) Get this point as webmercator (L{Wm}). 

1636 ''' 

1637 return _MODS.webmercator.toWm(self) 

1638 

1639 @property_RO 

1640 def xyz(self): 

1641 '''Get the I{geocentric} C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)}) 

1642 ''' 

1643 return self._ecef9.xyz 

1644 

1645 @Property_RO 

1646 def xyzh(self): 

1647 '''Get the I{geocentric} C{(x, y, z)} coordinates and height (L{Vector4Tuple}C{(x, y, z, h)}) 

1648 ''' 

1649 return self.xyz.to4Tuple(self.height) 

1650 

1651 

1652class _toCartesian3(object): # see also .formy._idllmn6, .geodesicw._wargs, .vector2d._numpy 

1653 '''(INTERNAL) Wrapper to convert 2 other points. 

1654 ''' 

1655 @contextmanager # <https://www.Python.org/dev/peps/pep-0343/> Examples 

1656 def __call__(self, p, p2, p3, wrap, **kwds): 

1657 try: 

1658 if wrap: 

1659 p2, p3 = map1(_Wrap.point, p2, p3) 

1660 kwds = _xkwds(kwds, wrap=wrap) 

1661 yield (p. toCartesian().copy(name=_point_), # copy to rename 

1662 p._toCartesianEcef(up=4, point2=p2), 

1663 p._toCartesianEcef(up=4, point3=p3)) 

1664 except (AssertionError, TypeError, ValueError) as x: # Exception? 

1665 raise _xError(x, point=p, point2=p2, point3=p3, **kwds) 

1666 

1667_toCartesian3 = _toCartesian3() # PYCHOK singleton 

1668 

1669 

1670def _latlonheight3(latlonh, height, wrap): # in .points.LatLon_.__init__ 

1671 '''(INTERNAL) Get 3-tuple C{(lat, lon, height)}. 

1672 ''' 

1673 try: 

1674 lat, lon = latlonh.lat, latlonh.lon 

1675 height = _xattr(latlonh, height=height) 

1676 except AttributeError: 

1677 raise _IsnotError(_LatLon_, latlonh=latlonh) 

1678 if wrap: 

1679 lat, lon = _Wrap.latlon(lat, lon) 

1680 return lat, lon, height 

1681 

1682 

1683def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, # MCCABE 13 

1684 radius=R_M, wrap=False): 

1685 '''(INTERNAL) Trilaterate three points by I{area overlap} or by 

1686 I{perimeter intersection} of three circles. 

1687 

1688 @note: The B{C{radius}} is only needed for the n-vectorial and 

1689 C{sphericalTrigonometry.LatLon.distanceTo} methods and 

1690 silently ignored by the C{ellipsoidalExact}, C{-GeodSolve}, 

1691 C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods. 

1692 ''' 

1693 p2, p3, w = _unrollon3(p1, p2, p3, wrap) 

1694 

1695 r1 = Distance_(distance1=d1) 

1696 r2 = Distance_(distance2=d2) 

1697 r3 = Distance_(distance3=d3) 

1698 m = 0 if area else (r1 + r2 + r3) 

1699 pc = 0 

1700 t = [] 

1701 for _ in range(3): 

1702 try: # intersection of circle (p1, r1) and (p2, r2) 

1703 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w) 

1704 

1705 if area: # check overlap 

1706 if c1 is c2: # abutting 

1707 c = c1 

1708 else: # nearest point on radical 

1709 c = p3.nearestOn(c1, c2, within=True, wrap=w) 

1710 d = r3 - p3.distanceTo(c, radius=radius, wrap=w) 

1711 if d > eps: # sufficient overlap 

1712 t.append((d, c)) 

1713 m = max(m, d) 

1714 

1715 else: # check intersection 

1716 for c in ((c1,) if c1 is c2 else (c1, c2)): 

1717 d = fabs(r3 - p3.distanceTo(c, radius=radius, wrap=w)) 

1718 if d < eps: # below margin 

1719 t.append((d, c)) 

1720 m = min(m, d) 

1721 

1722 except IntersectionError as x: 

1723 if _concentric_ in str(x): # XXX ConcentricError? 

1724 pc += 1 

1725 

1726 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate 

1727 

1728 if t: # get min, max, points and count ... 

1729 t = tuple(sorted(t)) 

1730 n = len(t), # as 1-tuple 

1731 # ... or for a single trilaterated result, 

1732 # min *is* max, min- *is* maxPoint and n=1, 2 or 3 

1733 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...) 

1734 

1735 elif area and pc == 3: # all pairwise concentric ... 

1736 r, p = min((r1, p1), (r2, p2), (r3, p3)) 

1737 m = max(r1, r2, r3) 

1738 # ... return "smallest" point twice, the smallest 

1739 # and largest distance and n=0 for concentric 

1740 return Trilaterate5Tuple(float(r), p, float(m), p, 0) 

1741 

1742 n, f = (_overlap_, max) if area else (_intersection_, min) 

1743 t = _COMMASPACE_(_no_(n), '%s %.3g' % (f.__name__, m)) 

1744 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t) 

1745 

1746 

1747__all__ += _ALL_DOCS(LatLonBase) 

1748 

1749# **) MIT License 

1750# 

1751# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1752# 

1753# Permission is hereby granted, free of charge, to any person obtaining a 

1754# copy of this software and associated documentation files (the "Software"), 

1755# to deal in the Software without restriction, including without limitation 

1756# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1757# and/or sell copies of the Software, and to permit persons to whom the 

1758# Software is furnished to do so, subject to the following conditions: 

1759# 

1760# The above copyright notice and this permission notice shall be included 

1761# in all copies or substantial portions of the Software. 

1762# 

1763# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1764# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1765# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1766# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1767# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1768# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1769# OTHER DEALINGS IN THE SOFTWARE.