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 2005-2024}' 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 _isin, 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.ecefLocals import _EcefLocal 

21from pygeodesy.errors import _AttributeError, IntersectionError, \ 

22 _incompatible, _IsnotError, _TypeError, \ 

23 _ValueError, _xattr, _xdatum, _xError, \ 

24 _xkwds, _xkwds_get, _xkwds_item2, _xkwds_not 

25# from pygeodesy.fmath import favg # _MODS 

26# from pygeodesy import formy as _formy # _MODS.into 

27from pygeodesy.internals import _passarg, typename 

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

29 _intersection_, _LatLon_, _m_, _negative_, \ 

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

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

32# from pygeodesy.karney import Caps # _MODS 

33from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

34from pygeodesy.named import _name2__, _NamedBase, 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.streprs import Fmt, hstr # from .named, _MODS 

41from pygeodesy.units import _isDegrees, _isRadius, Distance_, Lat, Lon, \ 

42 Height, Radius, Radius_, Scalar, Scalar_ 

43from pygeodesy.utily import sincos2d_, _unrollon, _unrollon3, _Wrap 

44# from pygeodesy.vector2d import _circin6, Circin6Tuple, _circum3, circum4_, \ 

45# Circum3Tuple, _radii11ABC4 # _MODS 

46# from pygeodesy.vector3d import nearestOn6, Vector3d # _MODS 

47 

48from contextlib import contextmanager 

49from math import asin, cos, degrees, fabs, radians 

50 

51__all__ = _ALL_LAZY.latlonBase 

52__version__ = '25.04.28' 

53 

54_formy = _MODS.into(formy=__name__) 

55 

56 

57class LatLonBase(_NamedBase, _EcefLocal): 

58 '''(INTERNAL) Base class for ellipsoidal and spherical C{satLon}s. 

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, lat_llh, lon=None, height=0, datum=None, **wrap_name): 

67 '''New C{LatLon}. 

68 

69 @arg lat_llh: 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), 

72 required if B{C{lat_llh}} is C{degrees} or C{str}. 

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

74 (C{meter}, conventionally). 

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

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

77 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword 

78 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize} 

79 B{C{lat}} and B{C{lon}} (C{bool}). 

80 

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

82 

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

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

85 

86 @raise TypeError: If B{C{lat_llh}} is not a C{LatLon}. 

87 

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

89 ''' 

90 w, n = self._wrap_name2(**wrap_name) 

91 if n: 

92 self.name = n 

93 

94 if lon is None: 

95 lat, lon, height = _latlonheight3(lat_llh, height, w) 

96 elif w: 

97 lat, lon = _Wrap.latlonDMS2(lat_llh, lon) 

98 else: 

99 lat = lat_llh 

100 

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

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

103 if height: # elevation 

104 self._height = Height(height) 

105 if datum is not None: 

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

107 

108 def __eq__(self, other): 

109 return self.isequalTo(other) 

110 

111 def __ne__(self, other): 

112 return not self.isequalTo(other) 

113 

114 def __str__(self): 

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

116 

117 def antipode(self, height=None): 

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

119 this point. 

120 

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

122 this point's height otherwise. 

123 

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

125 ''' 

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

127 h = self._heigHt(height) 

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

129 

130 @deprecated_method 

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

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

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

134 

135 def boundsOf(self, wide, tall, radius=R_M, height=None, **name): 

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

137 bounding box centered at this location. 

138 

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

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

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

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

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

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

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

146 overriding the point's height. 

147 @kwarg name: Optional C{B{name}=NN} (C{str}). 

148 

149 @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)}, the lower-left 

150 and upper-right corner (C{LatLon}). 

151 

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

153 ''' 

154 w = Scalar_(wide=wide) * _0_5 

155 t = Scalar_(tall=tall) * _0_5 

156 if radius is not None: 

157 r = Radius_(radius) 

158 c = cos(self.phi) 

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

160 t = degrees(t / r) 

161 y, t = self.lat, fabs(t) 

162 x, w = self.lon, fabs(w) 

163 

164 h = self._heigHt(height) 

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

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

167 return Bounds2Tuple(sw, ne, name=self._name__(name)) 

168 

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

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

171 this and an other point. 

172 

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

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

175 or if C{None}, use each point's height. 

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

177 point (C{bool}). 

178 

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

180 

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

182 ''' 

183 def _v3d(ll, V3d=_MODS.vector3d.Vector3d): 

184 t = ll.toEcef(height=height) # .toVector(Vector=V3d) 

185 return V3d(t.x, t.y, t.z) 

186 

187 p = self.others(other) 

188 if wrap: 

189 p = _Wrap.point(p) 

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

191 

192 def circin6(self, point2, point3, eps=EPS4, **wrap_name): 

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

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

195 

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

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

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

199 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword 

200 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize} 

201 the B{C{points}} (C{bool}). 

202 

203 @return: A 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 w, n = self._wrap_name2(**wrap_name) 

229 

230 with _toCartesian3(self, point2, point3, w) as cs: 

231 m = _MODS.vector2d 

232 r, c, d, A, B, C = m._circin6(*cs, eps=eps, useZ=True, dLL3=True, 

233 datum=self.datum) # PYCHOK unpack 

234 return m.Circin6Tuple(r, c.toLatLon(), d, A.toLatLon(), 

235 B.toLatLon(), 

236 C.toLatLon(), name=n) 

237 

238 def circum3(self, point2, point3, circum=True, eps=EPS4, **wrap_name): 

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

240 this and two other points. 

241 

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

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

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

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

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

247 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword 

248 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize} 

249 the B{C{points}} (C{bool}). 

250 

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

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

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

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

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

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

257 

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

259 version 1.10. 

260 

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

262 incompatible C{Ecef} classes or a trilateration 

263 or C{numpy} issue. 

264 

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

266 

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

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

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

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

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

272 height)} representing the difference between both results from 

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

274 

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

276 ''' 

277 w, n = self._wrap_name2(**wrap_name) 

278 

279 with _toCartesian3(self, point2, point3, w, circum=circum) as cs: 

280 m = _MODS.vector2d 

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

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

283 return m.Circum3Tuple(r, c.toLatLon(), d, name=n) 

284 

285 def circum4_(self, *points, **wrap_name): 

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

287 

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

289 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument 

290 C{B{wrap}=False}, if C{True}, wrap or I{normalize} the B{C{points}} 

291 (C{bool}). 

292 

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

294 instance of this (sub-)class. 

295 

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

297 version 1.10. 

298 

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

300 

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

302 

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

304 

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

306 ''' 

307 w, n = self._wrap_name2(**wrap_name) 

308 

309 def _cs(ps, C, w): 

310 _wp = _Wrap.point if w else _passarg 

311 for i, p in enumerate(ps): 

312 yield C(i=i, points=_wp(p)) 

313 

314 C = self._toCartesianEcef 

315 c = C(point=self) 

316 t = _MODS.vector2d.circum4_(c, Vector=c.classof, *_cs(points, C, w)) 

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

318 return t.dup(center=c, name=n) 

319 

320 @property 

321 def clipid(self): 

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

323 ''' 

324 return self._clipid 

325 

326 @clipid.setter # PYCHOK setter! 

327 def clipid(self, clipid): 

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

329 ''' 

330 self._clipid = int(clipid) 

331 

332 @deprecated_method 

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

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

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

336 

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

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

339 this and an other point. 

340 

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

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

343 larger distances. 

344 

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

346 @kwarg adjust_wrap: Optional keyword arguments for function 

347 L{pygeodesy.compassAngle}. 

348 

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

350 

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

352 

353 @note: Courtesy of Martin Schultz. 

354 

355 @see: U{Local, flat earth approximation 

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

357 ''' 

358 p = self.others(other) 

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

360 

361 @deprecated_method 

362 def cosineAndoyerLambertTo(self, other, **wrap): 

363 '''DEPRECATED on 2024.12.31, use method L{cosineLawTo} with C{B{corr}=1}.''' 

364 return self.cosineLawTo(other, corr=1, **wrap) 

365 

366 @deprecated_method 

367 def cosineForsytheAndoyerLambertTo(self, other, **wrap): 

368 '''DEPRECATED on 2024.12.31, use method L{cosineLawTo} with C{B{corr}=2}.''' 

369 return self.cosineLawTo(other, corr=2, **wrap) 

370 

371 def cosineLawTo(self, other, **radius__corr_wrap): 

372 '''Compute the distance between this and an other point using the U{Law of 

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

374 formula, optionally corrected. 

375 

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

377 @kwarg radius__corr_wrap: Optional earth C{B{radius}=None} (C{meter}), 

378 overriding the equatorial or mean radius of this point's 

379 datum's ellipsoid and keyword arguments for function 

380 L{pygeodesy.cosineLaw}. 

381 

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

383 

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

385 

386 @see: Function L{pygeodesy.cosineLaw} and methods C{distanceTo*}, 

387 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo} / 

388 L{hubenyTo}, L{flatPolarTo}, L{haversineTo}, L{thomasTo} and 

389 L{vincentysTo}. 

390 ''' 

391 c = _xkwds_get(radius__corr_wrap, corr=0) 

392 return self._distanceTo_(_formy.cosineLaw_, other, **radius__corr_wrap) if c else \ 

393 self._distanceTo( _formy.cosineLaw, other, **radius__corr_wrap) 

394 

395 @property_RO 

396 def datum(self): # PYCHOK no cover 

397 '''I{Must be overloaded}.''' 

398 self._notOverloaded() 

399 

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

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

402 

403 @arg delta: Local delta to the destination (L{XyzLocal}, L{Aer}, L{Enu}, L{Ned} 

404 or L{Local9Tuple}). 

405 @kwarg LatLon: Optional (geodetic) class to return the destination or C{None}. 

406 @kwarg LatLon_kwds: Optionally, additional B{C{LatLon}} keyword arguments, 

407 ignored if C{B{LatLon} is None}. 

408 

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

410 L{LatLon4Tuple}C{(lat, lon, height, datum)} or L{LatLon3Tuple}C{(lat, 

411 lon, height)} if a C{datum} keyword is specified or not. 

412 

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

414 ''' 

415 t = self._ltp._local2ecef(delta, nine=True) # _EcefLocal._ltp 

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

417 

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

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

420 ''' 

421 p = self.others(other, up=2) 

422 R = radius or (self._datum.ellipsoid.R1 if self._datum else R_M) 

423 return func(self.lat, self.lon, p.lat, p.lon, radius=R, **kwds) 

424 

425 def _distanceTo_(self, func_, other, wrap=False, radius=None, **kwds): 

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

427 ''' 

428 p = self.others(other, up=2) 

429 D = self.datum or _spherical_datum(radius or R_M, func_) 

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

431 r = func_(phi2, self.phi, lam21, datum=D, **kwds) 

432 return r * (radius or D.ellipsoid.a) 

433 

434 @Property_RO 

435 def _Ecef_forward(self): 

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

437 ''' 

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

439 

440 @Property_RO 

441 def _ecef9(self): 

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

443 ''' 

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

445 

446 @property_RO 

447 def ellipsoidalLatLon(self): 

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

449 ''' 

450 return False 

451 

452 @deprecated_method 

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

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

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

456 

457 @deprecated_method 

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

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

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

461 

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

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

464 using the U{Equirectangular Approximation / Projection 

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

466 

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

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

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

470 

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

472 @kwarg radius_adjust_limit_wrap: Optional keyword arguments 

473 for function L{pygeodesy.equirectangular}, 

474 overriding the default mean C{radius} of this 

475 point's datum ellipsoid. 

476 

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

478 

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

480 

481 @see: Function L{pygeodesy.equirectangular} and methods L{cosineLawTo}, 

482 C{distanceTo*}, C{euclideanTo}, L{flatLocalTo} / L{hubenyTo}, 

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

484 ''' 

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

486 

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

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

489 an other point. 

490 

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

492 

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

494 @kwarg radius_adjust_wrap: Optional keyword arguments for function 

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

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

497 

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

499 

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

501 

502 @see: Function L{pygeodesy.euclidean} and methods L{cosineLawTo}, C{distanceTo*}, 

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

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

505 ''' 

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

507 

508 def flatLocalTo(self, other, radius=None, **wrap): 

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

510 U{ellipsoidal Earth to plane projection 

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

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

513 

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

515 @kwarg radius: Mean earth radius (C{meter}) or C{None} for the I{equatorial 

516 radius} of this point's datum ellipsoid. 

517 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, wrap 

518 or I{normalize} and unroll the B{C{other}} point (C{bool}). 

519 

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

521 

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

523 

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

525 

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

527 C{distanceTo*}, L{equirectangularTo}, L{euclideanTo}, L{flatPolarTo}, 

528 L{haversineTo}, L{thomasTo} and L{vincentysTo} and U{local, flat Earth 

529 approximation<https://www.edwilliams.org/avform.htm#flat>}. 

530 ''' 

531 r = radius if _isin(radius, None, R_M, _1_0, 1) else Radius(radius) 

532 return self._distanceTo_(_formy.flatLocal_, other, radius=r, **wrap) # PYCHOK kwargs 

533 

534 hubenyTo = flatLocalTo # for Karl Hubeny 

535 

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

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

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

539 Geographical_distance#Polar_coordinate_flat-Earth_formula>} formula. 

540 

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

542 @kwarg radius_wrap: Optional C{B{radius}=R_M} and C{B{wrap}=False} for 

543 function L{pygeodesy.flatPolar}, overriding the default 

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

545 

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

547 

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

549 

550 @see: Function L{pygeodesy.flatPolar} and methods L{cosineLawTo}, C{distanceTo*}, 

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

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

553 ''' 

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

555 

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

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

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

559 

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

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

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

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

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

565 ellipsoid. 

566 

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

568 to this C{pov}. 

569 

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

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

572 the ellipsoid. 

573 

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

575 

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

577 ''' 

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

579 

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

581 '''Compute the distance between this and an other point using the U{Haversine 

582 <https://www.Movable-Type.co.UK/scripts/latlong.html>} formula. 

583 

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

585 @kwarg radius_wrap: Optional C{B{radius}=R_M} and C{B{wrap}=False} for function 

586 L{pygeodesy.haversine}, overriding the default C{mean radius} of 

587 this point's datum ellipsoid. 

588 

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

590 

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

592 

593 @see: Function L{pygeodesy.haversine} and methods L{cosineLawTo}, C{distanceTo*}, 

594 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo} / L{hubenyTo}, \ 

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

596 ''' 

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

598 

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

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

601 

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

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

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

605 

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

607 overriding height B{C{h}} (C{Height}). 

608 ''' 

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

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

611 

612 @Property 

613 def height(self): 

614 '''Get the height (C{meter}). 

615 ''' 

616 return self._height 

617 

618 @height.setter # PYCHOK setter! 

619 def height(self, height): 

620 '''Set the height (C{meter}). 

621 

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

623 

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

625 ''' 

626 h = Height(height) 

627 if self._height != h: 

628 _update_all(self) 

629 self._height = h 

630 

631 def _heigHt(self, height): 

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

633 ''' 

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

635 

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

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

638 this datum's ellipsoid surface. 

639 

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

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

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

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

644 @kwarg normal: If C{True}, the projection is the normal to this ellipsoid's 

645 surface, otherwise the intersection of the I{radial} line to 

646 this ellipsoid's center (C{bool}). 

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

648 (C{LatLon}) or C{None}. 

649 @kwarg LatLon_kwds: Optionally, additional B{C{LatLon}} keyword arguments, 

650 ignored if C{B{LatLon} is None}. 

651 

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

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

654 

655 @return: A B{C{LatLon}} instance or if C{B{LatLon} is None}, a L{Vector4Tuple}C{(x, 

656 y, z, h)} with the I{projection} C{x}, C{y} and C{z} coordinates and 

657 height C{h} in C{meter}, conventionally. 

658 

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

660 

661 @raise TypeError: Invalid B{C{LatLon}}, B{C{LatLon_kwds}} item, B{C{earth}} 

662 or triaxial B{C{earth}} couldn't be converted to biaxial 

663 B{C{LatLon}} datum. 

664 

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

666 ''' 

667 c = self.toCartesian() 

668 if LatLon is None: 

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

670 else: 

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

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

673 if r.datum != c.datum: 

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

675 return r 

676 

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

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

679 

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

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

682 

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

684 ''' 

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

686 

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

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

689 self._notImplemented(*args, **kwds) 

690 

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

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

693 line and return the 2 intersecant points accordingly. 

694 ''' 

695 if height is None: 

696 hp = hq = _xattr(p, height=INT0) 

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

698 if h != hp: 

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

700 if s: # fmath.fidw? 

701 s = (h - hp) / s # slope 

702 hq += s * Q.s12 

703 hp += s * P.s12 

704 else: 

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

706 else: 

707 hp = hq = Height(height) 

708 

709# n = self.name or typename(unused) 

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

711 p._iteration = P.iteration 

712 if P is not Q: 

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

714 q._iteration = Q.iteration 

715 return p, q 

716 

717 @deprecated_method 

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

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

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

721 

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

723 '''Check whether this and an other point are antipodal, on diametrically 

724 opposite sides of the earth. 

725 

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

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

728 

729 @return: C{True} if points are antipodal within the given tolerance, 

730 C{False} otherwise. 

731 ''' 

732 p = self.others(other) 

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

734 

735 @Property_RO 

736 def isEllipsoidal(self): 

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

738 ''' 

739 return _xattr(self.datum, isEllipsoidal=None) 

740 

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

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

743 

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

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

746 

747 @return: C{True} if both points are identical, I{ignoring} height, 

748 C{False} otherwise. 

749 

750 @raise TypeError: The B{C{other}} point is not C{LatLon} or mismatch 

751 of the B{C{other}} and this C{class} or C{type}. 

752 

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

754 

755 @see: Method L{isequalTo3}. 

756 ''' 

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

758 

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

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

761 

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

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

764 

765 @return: C{True} if both points are identical I{including} height, 

766 C{False} otherwise. 

767 

768 @raise TypeError: The B{C{other}} point is not C{LatLon} or mismatch 

769 of the B{C{other}} and this C{class} or C{type}. 

770 

771 @see: Method L{isequalTo}. 

772 ''' 

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

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

775 

776 @Property_RO 

777 def isnormal(self): 

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

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

780 

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

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

783 ''' 

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

785 

786 @Property_RO 

787 def isSpherical(self): 

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

789 ''' 

790 return _xattr(self.datum, isSpherical=None) 

791 

792 @Property_RO 

793 def lam(self): 

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

795 ''' 

796 return radians(self.lon) 

797 

798 @Property 

799 def lat(self): 

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

801 ''' 

802 return self._lat 

803 

804 @lat.setter # PYCHOK setter! 

805 def lat(self, lat): 

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

807 

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

809 ''' 

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

811 if self._lat != lat: 

812 _update_all(self) 

813 self._lat = lat 

814 

815 @Property 

816 def latlon(self): 

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

818 ''' 

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

820 

821 @latlon.setter # PYCHOK setter! 

822 def latlon(self, latlonh): 

823 '''Set the lat- and longitude and optionally the height (2- or 3-tuple 

824 or comma- or space-separated C{str} of C{degrees90}, C{degrees180} 

825 and C{meter}). 

826 

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

828 not C{list} or C{tuple}. 

829 

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

831 

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

833 into a 3-tuple C{(lat, lon, h)}. 

834 ''' 

835 if isstr(latlonh): 

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

837 else: 

838 _xinstanceof(list, tuple, latlonh=latlonh) 

839 if len(latlonh) == 3: 

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

841 elif len(latlonh) != 2: 

842 raise _ValueError(latlonh=latlonh) 

843 else: 

844 h = self.height 

845 

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

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

848 _update_all(self) 

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

850 

851 def latlon2(self, ndigits=0): 

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

853 

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

855 

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

857 away from zero. 

858 

859 @note: The C{round}ed values are always C{float}, also if B{C{ndigits}} 

860 is omitted. 

861 ''' 

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

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

864 

865 @deprecated_method 

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

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

868 return self.latlon2(ndigits=ndigits) 

869 

870 latlon2round = latlon_ # PYCHOK no cover 

871 

872 @Property 

873 def latlonheight(self): 

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

875 ''' 

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

877 

878 @latlonheight.setter # PYCHOK setter! 

879 def latlonheight(self, latlonh): 

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

881 (2- or 3-tuple or comma- or space-separated C{str} of 

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

883 

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

885 ''' 

886 self.latlon = latlonh 

887 

888 @Property 

889 def lon(self): 

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

891 ''' 

892 return self._lon 

893 

894 @lon.setter # PYCHOK setter! 

895 def lon(self, lon): 

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

897 

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

899 ''' 

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

901 if self._lon != lon: 

902 _update_all(self) 

903 self._lon = lon 

904 

905# _ltp = _EcefLocal._ltp(self) 

906 

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

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

909 

910 Points are converted to and distances are computed in I{geocentric}, 

911 cartesian space. 

912 

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

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

915 @kwarg height: Optional height, overriding the height of this and all 

916 other points (C{meter}). If C{None}, take the height 

917 of points into account for distances. 

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

919 (C{bool}). 

920 

921 @return: A L{NearestOn6Tuple}C{(closest, distance, fi, j, start, end)} 

922 with the C{closest}, the C{start} and the C{end} point each an 

923 instance of this C{LatLon} and C{distance} in C{meter}, same 

924 units as the cartesian axes. 

925 

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

927 

928 @raise TypeError: Some B{C{points}} or some B{C{points}}' C{Ecef} invalid. 

929 

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

931 

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

933 ''' 

934 def _cs(Ps, h, w, C): 

935 p = None # not used 

936 for i, q in Ps.enumerate(): 

937 if w and i: 

938 q = _unrollon(p, q) 

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

940 p = q 

941 

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

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

944 

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

946 t = _MODS.vector3d.nearestOn6(c, _cs(Ps, height, wrap, C), closed=closed) 

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

948 

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

950 height=height) 

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

952 p = _r(c).toLatLon(**kwds) 

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

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

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

956 

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

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

959 self._notImplemented(*args, **kwds) 

960 

961 def normal(self): 

962 '''Normalize this point I{in-place} to C{abs(lat) <= 90} and C{abs(lon) <= 180}. 

963 

964 @return: C{True} if this point was I{normal}, C{False} if it wasn't (but is now). 

965 

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

967 ''' 

968 n = self.isnormal 

969 if not n: 

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

971 return n 

972 

973 @property_RO 

974 def _N_vector(self): 

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

976 ''' 

977 _N = _MODS.nvectorBase._N_vector_ 

978 return _N(*self._n_xyz3, h=self.height, name=self.name) 

979 

980 @Property_RO 

981 def _n_xyz3(self): 

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

983 ''' 

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

985 

986 @Property_RO 

987 def phi(self): 

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

989 ''' 

990 return radians(self.lat) 

991 

992 @Property_RO 

993 def philam(self): 

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

995 ''' 

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

997 

998 def philam2(self, ndigits=0): 

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

1000 

1001 @kwarg ndigits: Number of (decimal) digits (C{int}). 

1002 

1003 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float} and rounded 

1004 away from zero. 

1005 

1006 @note: The C{round}ed values are C{float}, always. 

1007 ''' 

1008 return PhiLam2Tuple(round(self.phi, ndigits), 

1009 round(self.lam, ndigits), name=self.name) 

1010 

1011 @Property_RO 

1012 def philamheight(self): 

1013 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). 

1014 ''' 

1015 return self.philam.to3Tuple(self.height) 

1016 

1017 @deprecated_method 

1018 def points(self, points, **closed): # PYCHOK no cover 

1019 '''DEPRECATED, use method L{points2}.''' 

1020 return self.points2(points, **closed) 

1021 

1022 def points2(self, points, closed=True): 

1023 '''Check a path or polygon represented by points. 

1024 

1025 @arg points: The path or polygon points (C{LatLon}[]) 

1026 @kwarg closed: Optionally, consider the polygon closed, ignoring any 

1027 duplicate or closing final B{C{points}} (C{bool}). 

1028 

1029 @return: A L{Points2Tuple}C{(number, points)}, an C{int} and a C{list} 

1030 or C{tuple}. 

1031 

1032 @raise PointsError: Insufficient number of B{C{points}}. 

1033 

1034 @raise TypeError: Some B{C{points}} are not C{LatLon}. 

1035 ''' 

1036 return _MODS.iters.points2(points, closed=closed, base=self) 

1037 

1038 def PointsIter(self, points, loop=0, dedup=False, wrap=False): 

1039 '''Return a C{PointsIter} iterator. 

1040 

1041 @arg points: The path or polygon points (C{LatLon}[]) 

1042 @kwarg loop: Number of loop-back points (non-negative C{int}). 

1043 @kwarg dedup: If C{True}, skip duplicate points (C{bool}). 

1044 @kwarg wrap: If C{True}, wrap or I{normalize} the enum-/iterated 

1045 B{C{points}} (C{bool}). 

1046 

1047 @return: A new C{PointsIter} iterator. 

1048 

1049 @raise PointsError: Insufficient number of B{C{points}}. 

1050 ''' 

1051 return _MODS.iters.PointsIter(points, base=self, loop=loop, 

1052 dedup=dedup, wrap=wrap) 

1053 

1054 def radii11(self, point2, point3, wrap=False): 

1055 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent} 

1056 circles of a (planar) triangle formed by this and two other points. 

1057 

1058 @arg point2: Second point (C{LatLon}). 

1059 @arg point3: Third point (C{LatLon}). 

1060 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and 

1061 B{C{point3}} (C{bool}). 

1062 

1063 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}. 

1064 

1065 @raise IntersectionError: Near-coincident or -colinear points. 

1066 

1067 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. 

1068 

1069 @see: Function L{pygeodesy.radii11}, U{Incircle 

1070 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles 

1071 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent 

1072 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}. 

1073 ''' 

1074 with _toCartesian3(self, point2, point3, wrap) as cs: 

1075 return _MODS.vector2d._radii11ABC4(*cs, useZ=True)[0] 

1076 

1077 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3 

1078 '''(INTERNAL) Get the C{rhumb} for this point's datum or for 

1079 the B{C{radius}}' earth model iff non-C{None}. 

1080 ''' 

1081 try: 

1082 d = self._rhumb3dict 

1083 t = d[(exact, radius)] 

1084 except KeyError: 

1085 D = self.datum if radius is None else \ 

1086 _spherical_datum(radius) # ellipsoidal OK 

1087 try: 

1088 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical 

1089 except AttributeError as x: 

1090 raise _AttributeError(datum=D, radius=radius, cause=x) 

1091 t = r, D, _MODS.karney.Caps 

1092 if len(d) > 2: 

1093 d.clear() # d[:] = {} 

1094 d[(exact, radius)] = t # cache 3-tuple 

1095 return t 

1096 

1097 @Property_RO 

1098 def _rhumb3dict(self): # in ._update 

1099 return {} # 3-item cache 

1100 

1101 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False, b360=False): 

1102 '''Return the azimuth (bearing) of a rhumb line (loxodrome) between this and 

1103 an other (ellipsoidal) point. 

1104 

1105 @arg other: The other point (C{LatLon}). 

1106 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see method 

1107 L{Ellipsoid.rhumb_}. 

1108 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, L{Ellipsoid}, 

1109 L{Ellipsoid2} or L{a_f2Tuple}), overriding this point's datum. 

1110 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}} point (C{bool}). 

1111 @kwarg b360: If C{True}, return the azimuth as bearing in compass degrees (C{bool}). 

1112 

1113 @return: Rhumb azimuth (C{degrees180} or compass C{degrees360}). 

1114 

1115 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}} is invalid. 

1116 ''' 

1117 r, _, Cs = self._rhumb3(exact, radius) 

1118 z = r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12 

1119 return _umod_360(z + _360_0) if b360 else z 

1120 

1121 def rhumbDestination(self, distance, azimuth, radius=None, height=None, exact=False, **name): 

1122 '''Return the destination point having travelled the given distance from this point along 

1123 a rhumb line (loxodrome) of the given azimuth. 

1124 

1125 @arg distance: Distance travelled (C{meter}, same units as this point's datum (ellipsoid) 

1126 axes or B{C{radius}}, may be negative. 

1127 @arg azimuth: Azimuth (bearing) of the rhumb line (compass C{degrees}). 

1128 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, L{Ellipsoid}, 

1129 L{Ellipsoid2} or L{a_f2Tuple}), overriding this point's datum. 

1130 @kwarg height: Optional height, overriding the default height (C{meter}). 

1131 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see method L{Ellipsoid.rhumb_}. 

1132 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1133 

1134 @return: The destination point (ellipsoidal C{LatLon}). 

1135 

1136 @raise TypeError: Invalid B{C{radius}}. 

1137 

1138 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, B{C{radius}} or B{C{height}}. 

1139 ''' 

1140 r, D, _ = self._rhumb3(exact, radius) 

1141 d = r._Direct(self, azimuth, distance) 

1142 h = self._heigHt(height) 

1143 return self.classof(d.lat2, d.lon2, datum=D, height=h, **name) 

1144 

1145 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False): 

1146 '''Return the distance from this to an other point along a rhumb line (loxodrome). 

1147 

1148 @arg other: The other point (C{LatLon}). 

1149 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see method L{Ellipsoid.rhumb_}. 

1150 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, L{Ellipsoid}, 

1151 L{Ellipsoid2} or L{a_f2Tuple}), overriding this point's datum. 

1152 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}} point (C{bool}). 

1153 

1154 @return: Distance (C{meter}, the same units as this point's datum (ellipsoid) axes or B{C{radius}}. 

1155 

1156 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}} is invalid. 

1157 

1158 @raise ValueError: Invalid B{C{radius}}. 

1159 ''' 

1160 r, _, Cs = self._rhumb3(exact, radius) 

1161 return r._Inverse(self, other, wrap, outmask=Cs.DISTANCE).s12 

1162 

1163 def rhumbIntersecant2(self, circle, point, other, height=None, 

1164 **exact_radius_wrap_eps_tol): 

1165 '''Compute the intersections of a circle and a rhumb line given as two points or as a 

1166 point and azimuth. 

1167 

1168 @arg circle: Radius of the circle centered at this location (C{meter}), or a point 

1169 on the circle (same C{LatLon} class). 

1170 @arg point: The start point of the rhumb line (same C{LatLon} class). 

1171 @arg other: An other point I{on} (same C{LatLon} class) or the azimuth I{of} (compass 

1172 C{degrees}) the rhumb line. 

1173 @kwarg height: Optional height for the intersection points (C{meter}, conventionally) 

1174 or C{None} for interpolated heights. 

1175 @kwarg exact_radius_wrap_eps_tol: Optional keyword arguments, see methods L{rhumbLine} 

1176 and L{RhumbLineAux.Intersecant2} or L{RhumbLine.Intersecant2}. 

1177 

1178 @return: 2-Tuple of the intersection points (representing a chord), each an instance of 

1179 this class. Both points are the same instance if the rhumb line is tangent to 

1180 the circle. 

1181 

1182 @raise IntersectionError: The circle and rhumb line do not intersect. 

1183 

1184 @raise TypeError: Invalid B{C{point}}, B{C{circle}} or B{C{other}}. 

1185 

1186 @raise ValueError: Invalid B{C{circle}}, B{C{other}}, B{C{height}} or B{C{exact_radius_wrap}}. 

1187 

1188 @see: Methods L{RhumbLineAux.Intersecant2} and L{RhumbLine.Intersecant2}. 

1189 ''' 

1190 def _kwds3(eps=EPS, tol=_TOL, wrap=False, **kwds): 

1191 return kwds, wrap, dict(eps=eps, tol=tol) 

1192 

1193 exact_radius, w, eps_tol = _kwds3(**exact_radius_wrap_eps_tol) 

1194 

1195 p = _unrollon(self, self.others(point=point), wrap=w) 

1196 try: 

1197 r = Radius_(circle=circle) if _isRadius(circle) else \ 

1198 self.rhumbDistanceTo(self.others(circle=circle), wrap=w, **exact_radius) 

1199 rl = p.rhumbLine(other, wrap=w, **exact_radius) 

1200 P, Q = rl.Intersecant2(self.lat, self.lon, r, **eps_tol) 

1201 

1202 return self._intersecend2(p, other, w, height, rl.rhumb, P, Q, 

1203 self.rhumbIntersecant2) 

1204 except (TypeError, ValueError) as x: 

1205 raise _xError(x, center=self, circle=circle, point=point, other=other, 

1206 **exact_radius_wrap_eps_tol) 

1207 

1208 def rhumbLine(self, other, exact=False, radius=None, wrap=False, **name_caps): 

1209 '''Get a rhumb line through this point at a given azimuth or through this and an other point. 

1210 

1211 @arg other: The azimuth I{of} (compass C{degrees}) or an other point I{on} (same 

1212 C{LatLon} class) the rhumb line. 

1213 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see method L{Ellipsoid.rhumb_}. 

1214 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, L{Ellipsoid}, 

1215 L{Ellipsoid2} or L{a_f2Tuple}), overriding this point's C{datum}. 

1216 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}} point (C{bool}). 

1217 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see L{RhumbLine} or L{RhumbLineAux} C{B{caps}}. 

1218 

1219 @return: A C{RhumbLine} instance (C{RhumbLine} or C{RhumbLineAux}). 

1220 

1221 @raise TypeError: Invalid B{C{radius}} or B{C{other}} not C{scalar} nor same C{LatLon} class. 

1222 

1223 @see: Modules L{rhumb.aux_} and L{rhumb.ekx}. 

1224 ''' 

1225 r, _, Cs = self._rhumb3(exact, radius) 

1226 kwds = _xkwds(name_caps, name=self.name, caps=Cs.LINE_OFF) 

1227 rl = r._DirectLine( self, other, **kwds) if _isDegrees(other) else \ 

1228 r._InverseLine(self, self.others(other), wrap, **kwds) 

1229 return rl 

1230 

1231 def rhumbMidpointTo(self, other, exact=False, radius=None, height=None, fraction=_0_5, **wrap_name): 

1232 '''Return the (loxodromic) midpoint on the rhumb line between this and an other point. 

1233 

1234 @arg other: The other point (same C{LatLon} class). 

1235 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see method L{Ellipsoid.rhumb_}. 

1236 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, L{Ellipsoid}, 

1237 L{Ellipsoid2} or L{a_f2Tuple}), overriding this point's datum. 

1238 @kwarg height: Optional height, overriding the mean height (C{meter}). 

1239 @kwarg fraction: Midpoint location from this point (C{scalar}), 0 for this, 1 for the B{C{other}}, 

1240 0.5 for halfway between this and the B{C{other}} point, may be negative or 

1241 greater than 1. 

1242 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and C{B{wrap}=False}, if C{True}, wrap or 

1243 I{normalize} and unroll the B{C{other}} point (C{bool}). 

1244 

1245 @return: The midpoint at the given B{C{fraction}} along the rhumb line (same C{LatLon} class). 

1246 

1247 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}} is invalid. 

1248 

1249 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}. 

1250 ''' 

1251 w, n = self._wrap_name2(**wrap_name) 

1252 r, D, _ = self._rhumb3(exact, radius) 

1253 f = Scalar(fraction=fraction) 

1254 d = r._Inverse(self, self.others(other), w) # C.AZIMUTH_DISTANCE 

1255 d = r._Direct( self, d.azi12, d.s12 * f) 

1256 h = self._havg(other, f=f, h=height) 

1257 return self.classof(d.lat2, d.lon2, datum=D, height=h, name=n) 

1258 

1259 @property_RO 

1260 def sphericalLatLon(self): 

1261 '''Get the C{LatLon type} iff spherical, overloaded in L{LatLonSphericalBase}. 

1262 ''' 

1263 return False 

1264 

1265 def thomasTo(self, other, **wrap): 

1266 '''Compute the distance between this and an other point using U{Thomas' 

1267 <https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>} formula. 

1268 

1269 @arg other: The other point (C{LatLon}). 

1270 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, wrap 

1271 or I{normalize} and unroll the B{C{other}} point (C{bool}). 

1272 

1273 @return: Distance (C{meter}, same units as the axes of this point's datum ellipsoid). 

1274 

1275 @raise TypeError: The B{C{other}} point is not C{LatLon}. 

1276 

1277 @see: Function L{pygeodesy.thomas} and methods L{cosineLawTo}, C{distanceTo*}, 

1278 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo} / L{hubenyTo}, 

1279 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}. 

1280 ''' 

1281 return self._distanceTo_(_formy.thomas_, other, **wrap) 

1282 

1283 @deprecated_method 

1284 def to2ab(self): # PYCHOK no cover 

1285 '''DEPRECATED, use property L{philam}.''' 

1286 return self.philam 

1287 

1288 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds): 

1289 '''Convert this point to cartesian, I{geocentric} coordinates, also known as 

1290 I{Earth-Centered, Earth-Fixed} (ECEF). 

1291 

1292 @kwarg height: Optional height, overriding this point's height (C{meter}, 

1293 conventionally). 

1294 @kwarg Cartesian: Optional class to return the geocentric coordinates 

1295 (C{Cartesian}) or C{None}. 

1296 @kwarg Cartesian_kwds: Optionally, additional B{C{Cartesian}} keyword 

1297 arguments, ignored if C{B{Cartesian} is None}. 

1298 

1299 @return: A B{C{Cartesian}} instance or if B{C{Cartesian} is None}, an 

1300 L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with 

1301 C{C=0} and C{M} if available. 

1302 

1303 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}} item. 

1304 

1305 @see: Methods C{toNvector}, C{toVector} and C{toVector3d}. 

1306 ''' 

1307 r = self._ecef9 if height is None else self.toEcef(height=height) 

1308 if Cartesian is not None: # class or .classof 

1309 r = Cartesian(r, **self._name1__(Cartesian_kwds)) 

1310 _xdatum(r.datum, self.datum) 

1311 return r 

1312 

1313 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point): 

1314 '''(INTERNAL) Convert to cartesian and check Ecef's before and after. 

1315 ''' 

1316 p = self.others(up=up, **name_point) 

1317 c = p.toCartesian(height=height) 

1318 E = self.Ecef 

1319 if E: 

1320 for p in (p, c): 

1321 e = _xattr(p, Ecef=None) 

1322 if not _isin(e, None, E): # PYCHOK no cover 

1323 n, _ = _xkwds_item2(name_point) 

1324 n = Fmt.INDEX(n, i) 

1325 t = _incompatible(typename(E)) 

1326 raise _ValueError(n, e, txt=t) # txt__ 

1327 return c 

1328 

1329 def toDatum(self, datum2, height=None, **name): 

1330 '''I{Must be overloaded}.''' 

1331 self._notOverloaded(datum2, height=height, **name) 

1332 

1333 def toEcef(self, height=None, M=False): 

1334 '''Convert this point to I{geocentric} coordinates, also known as 

1335 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}). 

1336 

1337 @kwarg height: Optional height, overriding this point's height (C{meter}, 

1338 conventionally). 

1339 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}). 

1340 

1341 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with 

1342 C{C=0} and C{M} if available. 

1343 

1344 @raise EcefError: A C{.datum} or an ECEF issue. 

1345 ''' 

1346 return self._ecef9 if _isin(height, None, self.height) else \ 

1347 self._Ecef_forward(self.lat, self.lon, height=height, M=M) 

1348 

1349 @deprecated_method 

1350 def to3llh(self, height=None): # PYCHOK no cover 

1351 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.''' 

1352 return self.latlonheight if _isin(height, None, self.height) else \ 

1353 self.latlon.to3Tuple(height) 

1354 

1355 def toNormal(self, deep=False, **name): 

1356 '''Get this point I{normalized} to C{abs(lat) <= 90} and C{abs(lon) <= 180}. 

1357 

1358 @kwarg deep: If C{True}, make a deep, otherwise a shallow copy (C{bool}). 

1359 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1360 

1361 @return: A copy of this point, I{normalized} (C{LatLon}), optionally renamed. 

1362 

1363 @see: Property L{isnormal}, method L{normal} and function L{pygeodesy.normal}. 

1364 ''' 

1365 ll = self.copy(deep=deep) 

1366 _ = ll.normal() 

1367 if name: 

1368 ll.rename(name) 

1369 return ll 

1370 

1371 def toNvector(self, h=None, Nvector=None, **name_Nvector_kwds): 

1372 '''Convert this point to C{n-vector} (normal to the earth's surface) components, 

1373 I{including height}. 

1374 

1375 @kwarg h: Optional height, overriding this point's height (C{meter}). 

1376 @kwarg Nvector: Optional class to return the C{n-vector} components (C{Nvector}) 

1377 or C{None}. 

1378 @kwarg name_Nvector_kwds: Optional C{B{name}=NN} (C{str}) and optionally, 

1379 additional B{C{Nvector}} keyword arguments, ignored if C{B{Nvector} 

1380 is None}. 

1381 

1382 @return: An B{C{Nvector}} instance or a L{Vector4Tuple}C{(x, y, z, h)} if 

1383 C{B{Nvector} is None}. 

1384 

1385 @raise TypeError: Invalid B{C{h}}, B{C{Nvector}} or B{C{name_Nvector_kwds}}. 

1386 

1387 @see: Methods C{toCartesian}, C{toVector} and C{toVector3d}. 

1388 ''' 

1389 h = self._heigHt(h) 

1390 if Nvector is None: 

1391 r = self._n_xyz3.to4Tuple(h) 

1392 n, _ = _name2__(name_Nvector_kwds, _or_nameof=self) 

1393 if n: 

1394 r.rename(n) 

1395 else: 

1396 x, y, z = self._n_xyz3 

1397 r = Nvector(x, y, z, h=h, ll=self, **self._name1__(name_Nvector_kwds)) 

1398 return r 

1399 

1400 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected 

1401 '''Convert this point to a "lat, lon[, +/-height]" string, formatted in the 

1402 given C{B{form}at}. 

1403 

1404 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see functions 

1405 L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}. 

1406 @kwarg joined: Separator to join the lat-, longitude and height strings (C{str} 

1407 or C{None} or C{NN} for non-joined). 

1408 @kwarg m: Optional unit of the height (C{str}), use C{None} to exclude height 

1409 from the returned string. 

1410 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator}, B{C{s_D}}, 

1411 B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword arguments, see function 

1412 L{pygeodesy.toDMS} for details. 

1413 

1414 @return: This point in the specified C{B{form}at}, etc. (C{str} or a 2- or 3-tuple 

1415 C{(lat_str, lon_str[, height_str])} if B{C{joined}} is C{NN} or C{None}). 

1416 

1417 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more details about 

1418 keyword arguments C{B{form}at}, C{B{prec}ision}, C{B{sep}arator}, B{C{s_D}}, 

1419 B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}. 

1420 ''' 

1421 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S), 

1422 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S)) 

1423 if self.height and m is not None: 

1424 t += (self.heightStr(m=m),) 

1425 return joined.join(t) if joined else t 

1426 

1427 def toVector(self, Vector=None, **Vector_kwds): 

1428 '''Convert this point to a C{Vector} with the I{geocentric} C{(x, y, z)} (ECEF) 

1429 coordinates, I{ignoring height}. 

1430 

1431 @kwarg Vector: Optional class to return the I{geocentric} components (L{Vector3d}) 

1432 or C{None}. 

1433 @kwarg Vector_kwds: Optionally, additional B{C{Vector}} keyword arguments, 

1434 ignored if C{B{Vector} is None}. 

1435 

1436 @return: A B{C{Vector}} instance or a L{Vector3Tuple}C{(x, y, z)} if C{B{Vector} 

1437 is None}. 

1438 

1439 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}. 

1440 

1441 @see: Methods C{toCartesian}, C{toNvector} and C{toVector3d}. 

1442 ''' 

1443 return self._ecef9.toVector(Vector=Vector, **self._name1__(Vector_kwds)) 

1444 

1445 def toVector3d(self, norm=True, **Vector3d_kwds): 

1446 '''Convert this point to a L{Vector3d} with the I{geocentric} C{(x, y, z)} 

1447 (ECEF) coordinates, I{ignoring height}. 

1448 

1449 @kwarg norm: If C{False}, don't normalize the coordinates (C{bool}). 

1450 @kwarg Vector3d_kwds: Optional L{Vector3d} keyword arguments. 

1451 

1452 @return: Named, unit vector or vector (L{Vector3d}). 

1453 

1454 @raise TypeError: Invalid B{C{Vector3d_kwds}}. 

1455 

1456 @see: Methods C{toCartesian}, C{toNvector} and C{toVector}. 

1457 ''' 

1458 r = self.toVector(Vector=_MODS.vector3d.Vector3d, **Vector3d_kwds) 

1459 if norm: 

1460 r = r.unit(ll=self) 

1461 return r 

1462 

1463 def toWm(self, **toWm_kwds): 

1464 '''Convert this point to a WM coordinate. 

1465 

1466 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments. 

1467 

1468 @return: The WM coordinate (L{Wm}). 

1469 

1470 @see: Function L{pygeodesy.toWm}. 

1471 ''' 

1472 return _MODS.webmercator.toWm(self, **self._name1__(toWm_kwds)) 

1473 

1474 @deprecated_method 

1475 def to3xyz(self): # PYCHOK no cover 

1476 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector}, 

1477 L{toVector3d} or perhaps (geocentric) L{toEcef}.''' 

1478 return self.xyz # self.toVector() 

1479 

1480# def _update(self, updated, *attrs, **setters): 

1481# '''(INTERNAL) See C{_NamedBase._update}. 

1482# ''' 

1483# if updated: 

1484# self._rhumb3dict.clear() 

1485# return _NamedBase._update(self, updated, *attrs, **setters) 

1486 

1487 def vincentysTo(self, other, **radius_wrap): 

1488 '''Compute the distance between this and an other point using U{Vincenty's 

1489 <https://WikiPedia.org/wiki/Great-circle_distance>} spherical formula. 

1490 

1491 @arg other: The other point (C{LatLon}). 

1492 @kwarg radius_wrap: Optional C{B{radius}=R_M} and C{B{wrap}=False} for 

1493 function L{pygeodesy.vincentys}, overriding the default 

1494 C{mean radius} of this point's datum ellipsoid. 

1495 

1496 @return: Distance (C{meter}, same units as B{C{radius}}). 

1497 

1498 @raise TypeError: The B{C{other}} point is not C{LatLon}. 

1499 

1500 @see: Function L{pygeodesy.vincentys} and methods L{cosineLawTo}, C{distanceTo*}, 

1501 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo} / L{hubenyTo}, 

1502 L{flatPolarTo}, L{haversineTo} and L{thomasTo}. 

1503 ''' 

1504 return self._distanceTo(_formy.vincentys, other, **_xkwds(radius_wrap, radius=None)) 

1505 

1506 def _wrap_name2(self, wrap=False, **name): 

1507 '''(INTERNAL) Return the C{wrap} and C{name} value. 

1508 ''' 

1509 return wrap, (self._name__(name) if name else NN) 

1510 

1511 @property_RO 

1512 def xyz(self): 

1513 '''Get the I{geocentric} C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)}) 

1514 ''' 

1515 return self._ecef9.xyz 

1516 

1517 @property_RO 

1518 def xyz3(self): 

1519 '''Get the I{geocentric} C{(x, y, z)} coordinates as C{3-tuple}. 

1520 ''' 

1521 return tuple(self.xyz) 

1522 

1523 @Property_RO 

1524 def xyzh(self): 

1525 '''Get the I{geocentric} C{(x, y, z)} coordinates and height (L{Vector4Tuple}C{(x, y, z, h)}) 

1526 ''' 

1527 return self.xyz.to4Tuple(self.height) 

1528 

1529 

1530class _toCartesian3(object): # see also .formy._idllmn6, .geodesicw._wargs, .vector2d._numpy 

1531 '''(INTERNAL) Wrapper to convert 2 other points. 

1532 ''' 

1533 @contextmanager # <https://www.Python.org/dev/peps/pep-0343/> Examples 

1534 def __call__(self, p, p2, p3, wrap, **kwds): 

1535 try: 

1536 if wrap: 

1537 p2, p3 = map1(_Wrap.point, p2, p3) 

1538 kwds = _xkwds(kwds, wrap=wrap) 

1539 yield (p. toCartesian().copy(name=_point_), # copy to rename 

1540 p._toCartesianEcef(up=4, point2=p2), 

1541 p._toCartesianEcef(up=4, point3=p3)) 

1542 except (AssertionError, TypeError, ValueError) as x: # Exception? 

1543 raise _xError(x, point=p, point2=p2, point3=p3, **kwds) 

1544 

1545_toCartesian3 = _toCartesian3() # PYCHOK singleton 

1546 

1547 

1548def _latlonheight3(latlonh, height, wrap): # in .points.LatLon_.__init__ 

1549 '''(INTERNAL) Get 3-tuple C{(lat, lon, height)}. 

1550 ''' 

1551 try: 

1552 lat, lon = latlonh.lat, latlonh.lon 

1553 height = _xattr(latlonh, height=height) 

1554 except AttributeError: 

1555 raise _IsnotError(_LatLon_, latlonh=latlonh) 

1556 if wrap: 

1557 lat, lon = _Wrap.latlon(lat, lon) 

1558 return lat, lon, height 

1559 

1560 

1561def latlon2n_xyz(lat_ll, lon=None, **name): 

1562 '''Convert lat-, longitude to C{n-vector} (I{normal} to the earth's surface) X, Y and Z components. 

1563 

1564 @arg lat_ll: Latitude (C{degrees}) or a C{LatLon} instance, L{LatLon2Tuple} or other C{LatLon*Tuple}. 

1565 @kwarg lon: Longitude (C{degrees}), required if C{B{lon_ll} is degrees}, ignored otherwise. 

1566 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1567 

1568 @return: A L{Vector3Tuple}C{(x, y, z)}. 

1569 

1570 @see: Function L{philam2n_xyz}. 

1571 

1572 @note: These are C{n-vector} x, y and z components, I{NOT geocentric} x, y and z (ECEF) coordinates! 

1573 ''' 

1574 lat = lat_ll 

1575 if lon is None: 

1576 try: 

1577 lat, lon = lat_ll.latlon 

1578 except AttributeError: 

1579 lat = lat_ll.lat 

1580 lon = lat_ll.lon 

1581 # Kenneth Gade eqn 3, but using right-handed 

1582 # vector x -> 0°E,0°N, y -> 90°E,0°N, z -> 90°N 

1583 sa, ca, sb, cb = sincos2d_(lat, lon) 

1584 return Vector3Tuple(ca * cb, ca * sb, sa, **name) 

1585 

1586 

1587def philam2n_xyz(phi_ll, lam=None, **name): 

1588 '''Convert lat-, longitude to C{n-vector} (I{normal} to the earth's surface) X, Y and Z components. 

1589 

1590 @arg phi_ll: Latitude (C{radians}) or a C{LatLon} instance with C{phi}, C{lam} or C{philam} attributes. 

1591 @kwarg lam: Longitude (C{radians}), required if C{B{phi_ll} is radians}, ignored otherwise. 

1592 @kwarg name: Optional name (C{str}). 

1593 

1594 @return: A L{Vector3Tuple}C{(x, y, z)}. 

1595 

1596 @see: Function L{latlon2n_xyz}. 

1597 

1598 @note: These are C{n-vector} x, y and z components, I{NOT geocentric} x, y and z (ECEF) coordinates! 

1599 ''' 

1600 phi = phi_ll 

1601 if lam is None: 

1602 try: 

1603 phi, lam = phi_ll.philam 

1604 except AttributeError: 

1605 phi = phi_ll.phi 

1606 lam = phi_ll.lam 

1607 return latlon2n_xyz(degrees(phi), degrees(lam), **name) 

1608 

1609 

1610def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, radius=R_M, wrap=False): # MCCABE 13 

1611 '''(INTERNAL) Trilaterate three points by I{area overlap} or by I{perimeter intersection} of three circles. 

1612 

1613 @note: The B{C{radius}} is needed only for C{n-vectorial} and C{sphericalTrigonometry.LatLon.distanceTo} 

1614 methods and silently ignored by the C{ellipsoidalExact}, C{-GeodSolve}, C{-Karney} and 

1615 C{-Vincenty.LatLon.distanceTo} methods. 

1616 ''' 

1617 p2, p3, w = _unrollon3(p1, p2, p3, wrap) 

1618 rw = dict(radius=radius, wrap=w) 

1619 

1620 r1 = Distance_(distance1=d1) 

1621 r2 = Distance_(distance2=d2) 

1622 r3 = Distance_(distance3=d3) 

1623 m = 0 if area else (r1 + r2 + r3) 

1624 pc = 0 

1625 t = [] 

1626 for _ in range(3): 

1627 try: # intersection of circle (p1, r1) and (p2, r2) 

1628 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w) 

1629 

1630 if area: # check overlap 

1631 if c1 is c2: # abutting 

1632 c = c1 

1633 else: # nearest point on radical 

1634 c = p3.nearestOn(c1, c2, within=True, wrap=w) 

1635 d = r3 - p3.distanceTo(c, **rw) 

1636 if d > eps: # sufficient overlap 

1637 t.append((d, c)) 

1638 m = max(m, d) 

1639 

1640 else: # check intersection 

1641 for c in ((c1,) if c1 is c2 else (c1, c2)): 

1642 d = fabs(r3 - p3.distanceTo(c, **rw)) 

1643 if d < eps: # below margin 

1644 t.append((d, c)) 

1645 m = min(m, d) 

1646 

1647 except IntersectionError as x: 

1648 if _concentric_ in str(x): # XXX ConcentricError? 

1649 pc += 1 

1650 

1651 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate 

1652 

1653 if t: # get min, max, points and count ... 

1654 t = tuple(sorted(t)) 

1655 n = len(t), # as 1-tuple 

1656 # ... or for a single trilaterated result, 

1657 # min *is* max, min- *is* maxPoint and n=1, 2 or 3 

1658 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...) 

1659 

1660 elif area and pc == 3: # all pairwise concentric ... 

1661 r, p = min((r1, p1), (r2, p2), (r3, p3)) 

1662 m = max(r1, r2, r3) 

1663 # ... return "smallest" point twice, the smallest 

1664 # and largest distance and n=0 for concentric 

1665 return Trilaterate5Tuple(float(r), p, float(m), p, 0) 

1666 

1667 n, f = (_overlap_, max) if area else (_intersection_, min) 

1668 t = _COMMASPACE_(_no_(n), '%s %.3g' % (typename(f), m)) 

1669 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t) 

1670 

1671 

1672__all__ += _ALL_DOCS(LatLonBase) 

1673 

1674# **) MIT License 

1675# 

1676# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

1677# 

1678# Permission is hereby granted, free of charge, to any person obtaining a 

1679# copy of this software and associated documentation files (the "Software"), 

1680# to deal in the Software without restriction, including without limitation 

1681# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1682# and/or sell copies of the Software, and to permit persons to whom the 

1683# Software is furnished to do so, subject to the following conditions: 

1684# 

1685# The above copyright notice and this permission notice shall be included 

1686# in all copies or substantial portions of the Software. 

1687# 

1688# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1689# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1690# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1691# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1692# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1693# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1694# OTHER DEALINGS IN THE SOFTWARE.