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 isstr, map1, _xinstanceof, _passarg 

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_get, _xkwds_item2, _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 

31# from pygeodesy.internals import _passarg # from .basics 

32from pygeodesy.interns import NN, _COMMASPACE_, _concentric_, _height_, \ 

33 _intersection_, _LatLon_, _m_, _negative_, \ 

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

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

36# from pygeodesy.karney import Caps # _MODS 

37from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

38from pygeodesy.named import _name2__, _NamedBase, _NamedLocal, Fmt 

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

40 Trilaterate5Tuple, Vector3Tuple 

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 sincos2d_, _unrollon, _unrollon3, _Wrap 

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

49# Circum3Tuple, _radii11ABC4 # _MODS 

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

51 

52from contextlib import contextmanager 

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

54 

55__all__ = _ALL_LAZY.latlonBase 

56__version__ = '24.12.31' 

57 

58_formy = _MODS.into(formy=__name__) 

59 

60 

61class LatLonBase(_NamedBase, _NamedLocal): 

62 '''(INTERNAL) Base class for ellipsoidal and spherical C{LatLon}s. 

63 ''' 

64 _clipid = INT0 # polygonal clip, see .booleans 

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

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

67 _lat = 0 # latitude (C{degrees}) 

68 _lon = 0 # longitude (C{degrees}) 

69 

70 def __init__(self, lat_llh, lon=None, height=0, datum=None, **wrap_name): 

71 '''New C{LatLon}. 

72 

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

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

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

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

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

78 (C{meter}, conventionally). 

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

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

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

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

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

84 

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

86 

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

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

89 

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

91 

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

93 ''' 

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

95 if n: 

96 self.name = n 

97 

98 if lon is None: 

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

100 elif w: 

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

102 else: 

103 lat = lat_llh 

104 

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

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

107 if height: # elevation 

108 self._height = Height(height) 

109 if datum is not None: 

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

111 

112 def __eq__(self, other): 

113 return self.isequalTo(other) 

114 

115 def __ne__(self, other): 

116 return not self.isequalTo(other) 

117 

118 def __str__(self): 

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

120 

121 def antipode(self, height=None): 

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

123 this point. 

124 

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

126 this point's height otherwise. 

127 

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

129 ''' 

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

131 h = self._heigHt(height) 

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

133 

134 @deprecated_method 

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

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

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

138 

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

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

141 bounding box centered at this location. 

142 

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

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

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

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

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

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

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

150 overriding the point's height. 

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

152 

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

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

155 

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

157 ''' 

158 w = Scalar_(wide=wide) * _0_5 

159 t = Scalar_(tall=tall) * _0_5 

160 if radius is not None: 

161 r = Radius_(radius) 

162 c = cos(self.phi) 

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

164 t = degrees(t / r) 

165 y, t = self.lat, fabs(t) 

166 x, w = self.lon, fabs(w) 

167 

168 h = self._heigHt(height) 

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

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

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

172 

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

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

175 this and an other point. 

176 

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

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

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

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

181 point (C{bool}). 

182 

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

184 

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

186 ''' 

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

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

189 return V3d(t.x, t.y, t.z) 

190 

191 p = self.others(other) 

192 if wrap: 

193 p = _Wrap.point(p) 

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

195 

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

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

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

199 

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

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

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

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

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

205 the B{C{points}} (C{bool}). 

206 

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

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

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

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

211 

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

213 than version 1.10. 

214 

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

216 a trilateration or C{numpy} issue. 

217 

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

219 

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

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

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

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

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

225 height)} representing the differences between both results from 

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

227 

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

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

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

231 ''' 

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

233 

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

235 m = _MODS.vector2d 

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

237 datum=self.datum) # PYCHOK unpack 

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

239 B.toLatLon(), 

240 C.toLatLon(), name=n) 

241 

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

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

244 this and two other points. 

245 

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

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

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

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

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

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

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

253 the B{C{points}} (C{bool}). 

254 

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

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

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

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

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

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

261 

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

263 version 1.10. 

264 

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

266 incompatible C{Ecef} classes or a trilateration 

267 or C{numpy} issue. 

268 

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

270 

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

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

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

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

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

276 height)} representing the difference between both results from 

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

278 

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

280 ''' 

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

282 

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

284 m = _MODS.vector2d 

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

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

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

288 

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

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

291 

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

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

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

295 (C{bool}). 

296 

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

298 instance of this (sub-)class. 

299 

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

301 version 1.10. 

302 

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

304 

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

306 

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

308 

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

310 ''' 

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

312 

313 def _cs(ps, C, w): 

314 _wp = _Wrap.point if w else _passarg 

315 for i, p in enumerate(ps): 

316 yield C(i=i, points=_wp(p)) 

317 

318 C = self._toCartesianEcef 

319 c = C(point=self) 

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

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

322 return t.dup(center=c, name=n) 

323 

324 @property 

325 def clipid(self): 

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

327 ''' 

328 return self._clipid 

329 

330 @clipid.setter # PYCHOK setter! 

331 def clipid(self, clipid): 

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

333 ''' 

334 self._clipid = int(clipid) 

335 

336 @deprecated_method 

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

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

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

340 

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

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

343 this and an other point. 

344 

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

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

347 larger distances. 

348 

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

350 @kwarg adjust_wrap: Optional keyword arguments for function 

351 L{pygeodesy.compassAngle}. 

352 

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

354 

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

356 

357 @note: Courtesy of Martin Schultz. 

358 

359 @see: U{Local, flat earth approximation 

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

361 ''' 

362 p = self.others(other) 

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

364 

365 @deprecated_method 

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

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

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

369 

370 @deprecated_method 

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

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

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

374 

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

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

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

378 formula, optionally corrected. 

379 

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

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

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

383 datum's ellipsoid and keyword arguments for function 

384 L{pygeodesy.cosineLaw}. 

385 

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

387 

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

389 

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

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

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

393 L{vincentysTo}. 

394 ''' 

395 c = _xkwds_get(radius__corr_wrap, corr=0) 

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

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

398 

399 @property_RO 

400 def datum(self): # PYCHOK no cover 

401 '''I{Must be overloaded}.''' 

402 self._notOverloaded() 

403 

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

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

406 

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

408 or L{Local9Tuple}). 

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

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

411 ignored if C{B{LatLon} is None}. 

412 

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

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

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

416 

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

418 ''' 

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

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

421 

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

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

424 ''' 

425 p = self.others(other, up=2) 

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

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

428 

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

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

431 ''' 

432 p = self.others(other, up=2) 

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

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

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

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

437 

438 @Property_RO 

439 def _Ecef_forward(self): 

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

441 ''' 

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

443 

444 @Property_RO 

445 def _ecef9(self): 

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

447 ''' 

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

449 

450 @property_RO 

451 def ellipsoidalLatLon(self): 

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

453 ''' 

454 return False 

455 

456 @deprecated_method 

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

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

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

460 

461 @deprecated_method 

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

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

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

465 

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

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

468 using the U{Equirectangular Approximation / Projection 

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

470 

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

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

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

474 

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

476 @kwarg radius_adjust_limit_wrap: Optional keyword arguments 

477 for function L{pygeodesy.equirectangular}, 

478 overriding the default mean C{radius} of this 

479 point's datum ellipsoid. 

480 

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

482 

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

484 

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

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

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

488 ''' 

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

490 

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

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

493 an other point. 

494 

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

496 

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

498 @kwarg radius_adjust_wrap: Optional keyword arguments for function 

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

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

501 

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

503 

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

505 

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

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

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

509 ''' 

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

511 

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

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

514 U{ellipsoidal Earth to plane projection 

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

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

517 

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

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

520 radius} of this point's datum ellipsoid. 

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

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

523 

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

525 

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

527 

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

529 

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

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

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

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

534 ''' 

535 r = radius if radius in (None, R_M, _1_0, 1) else Radius(radius) 

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

537 

538 hubenyTo = flatLocalTo # for Karl Hubeny 

539 

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

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

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

543 Geographical_distance#Polar_coordinate_flat-Earth_formula>} formula. 

544 

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

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

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

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

549 

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

551 

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

553 

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

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

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

557 ''' 

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

559 

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

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

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

563 

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

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

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

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

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

569 ellipsoid. 

570 

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

572 to this C{pov}. 

573 

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

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

576 the ellipsoid. 

577 

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

579 

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

581 ''' 

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

583 

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

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

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

587 

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

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

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

591 this point's datum ellipsoid. 

592 

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

594 

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

596 

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

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

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

600 ''' 

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

602 

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

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

605 

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

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

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

609 

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

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

612 ''' 

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

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

615 

616 @Property 

617 def height(self): 

618 '''Get the height (C{meter}). 

619 ''' 

620 return self._height 

621 

622 @height.setter # PYCHOK setter! 

623 def height(self, height): 

624 '''Set the height (C{meter}). 

625 

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

627 

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

629 ''' 

630 h = Height(height) 

631 if self._height != h: 

632 _update_all(self) 

633 self._height = h 

634 

635 def _heigHt(self, height): 

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

637 ''' 

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

639 

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

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

642 this datum's ellipsoid surface. 

643 

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

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

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

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

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

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

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

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

652 (C{LatLon}) or C{None}. 

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

654 ignored if C{B{LatLon} is None}. 

655 

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

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

658 

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

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

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

662 

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

664 

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

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

667 B{C{LatLon}} datum. 

668 

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

670 ''' 

671 c = self.toCartesian() 

672 if LatLon is None: 

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

674 else: 

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

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

677 if r.datum != c.datum: 

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

679 return r 

680 

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

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

683 

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

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

686 

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

688 ''' 

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

690 

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

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

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

694 

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

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

697 line and return the 2 intersecant points accordingly. 

698 ''' 

699 if height is None: 

700 hp = hq = _xattr(p, height=INT0) 

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

702 if h != hp: 

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

704 if s: # fmath.fidw? 

705 s = (h - hp) / s # slope 

706 hq += s * Q.s12 

707 hp += s * P.s12 

708 else: 

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

710 else: 

711 hp = hq = Height(height) 

712 

713# n = self.name or unused.__name__ 

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

715 p._iteration = P.iteration 

716 if P is not Q: 

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

718 q._iteration = Q.iteration 

719 return p, q 

720 

721 @deprecated_method 

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

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

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

725 

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

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

728 opposite sides of the earth. 

729 

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

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

732 

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

734 C{False} otherwise. 

735 ''' 

736 p = self.others(other) 

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

738 

739 @Property_RO 

740 def isEllipsoidal(self): 

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

742 ''' 

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

744 

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

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

747 

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

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

750 

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

752 C{False} otherwise. 

753 

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

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

756 

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

758 

759 @see: Method L{isequalTo3}. 

760 ''' 

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

762 

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

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

765 

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

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

768 

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

770 C{False} otherwise. 

771 

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

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

774 

775 @see: Method L{isequalTo}. 

776 ''' 

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

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

779 

780 @Property_RO 

781 def isnormal(self): 

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

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

784 

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

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

787 ''' 

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

789 

790 @Property_RO 

791 def isSpherical(self): 

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

793 ''' 

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

795 

796 @Property_RO 

797 def lam(self): 

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

799 ''' 

800 return radians(self.lon) 

801 

802 @Property 

803 def lat(self): 

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

805 ''' 

806 return self._lat 

807 

808 @lat.setter # PYCHOK setter! 

809 def lat(self, lat): 

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

811 

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

813 ''' 

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

815 if self._lat != lat: 

816 _update_all(self) 

817 self._lat = lat 

818 

819 @Property 

820 def latlon(self): 

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

822 ''' 

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

824 

825 @latlon.setter # PYCHOK setter! 

826 def latlon(self, latlonh): 

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

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

829 and C{meter}). 

830 

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

832 not C{list} or C{tuple}. 

833 

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

835 

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

837 into a 3-tuple C{(lat, lon, h)}. 

838 ''' 

839 if isstr(latlonh): 

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

841 else: 

842 _xinstanceof(list, tuple, latlonh=latlonh) 

843 if len(latlonh) == 3: 

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

845 elif len(latlonh) != 2: 

846 raise _ValueError(latlonh=latlonh) 

847 else: 

848 h = self.height 

849 

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

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

852 _update_all(self) 

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

854 

855 def latlon2(self, ndigits=0): 

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

857 

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

859 

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

861 away from zero. 

862 

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

864 is omitted. 

865 ''' 

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

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

868 

869 @deprecated_method 

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

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

872 return self.latlon2(ndigits=ndigits) 

873 

874 latlon2round = latlon_ # PYCHOK no cover 

875 

876 @Property 

877 def latlonheight(self): 

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

879 ''' 

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

881 

882 @latlonheight.setter # PYCHOK setter! 

883 def latlonheight(self, latlonh): 

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

885 (2- or 3-tuple or comma- or space-separated C{str} of 

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

887 

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

889 ''' 

890 self.latlon = latlonh 

891 

892 @Property 

893 def lon(self): 

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

895 ''' 

896 return self._lon 

897 

898 @lon.setter # PYCHOK setter! 

899 def lon(self, lon): 

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

901 

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

903 ''' 

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

905 if self._lon != lon: 

906 _update_all(self) 

907 self._lon = lon 

908 

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

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

911 

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

913 cartesian space. 

914 

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

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

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

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

919 of points into account for distances. 

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

921 (C{bool}). 

922 

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

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

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

926 units as the cartesian axes. 

927 

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

929 

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

931 

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

933 

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

935 ''' 

936 def _cs(Ps, h, w, C): 

937 p = None # not used 

938 for i, q in Ps.enumerate(): 

939 if w and i: 

940 q = _unrollon(p, q) 

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

942 p = q 

943 

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

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

946 

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

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

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

950 

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

952 height=height) 

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

954 p = _r(c).toLatLon(**kwds) 

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

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

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

958 

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

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

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

962 

963 def normal(self): 

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

965 

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

967 

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

969 ''' 

970 n = self.isnormal 

971 if not n: 

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

973 return n 

974 

975 @property_RO 

976 def _N_vector(self): 

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

978 ''' 

979 _N = _MODS.nvectorBase._N_vector_ 

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

981 

982 @Property_RO 

983 def _n_xyz3(self): 

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

985 ''' 

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

987 

988 @Property_RO 

989 def phi(self): 

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

991 ''' 

992 return radians(self.lat) 

993 

994 @Property_RO 

995 def philam(self): 

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

997 ''' 

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

999 

1000 def philam2(self, ndigits=0): 

1001 '''Return this point's lat- and longitude in C{radians}, rounded. 

1002 

1003 @kwarg ndigits: Number of (decimal) digits (C{int}). 

1004 

1005 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float} and rounded 

1006 away from zero. 

1007 

1008 @note: The C{round}ed values are C{float}, always. 

1009 ''' 

1010 return PhiLam2Tuple(round(self.phi, ndigits), 

1011 round(self.lam, ndigits), name=self.name) 

1012 

1013 @Property_RO 

1014 def philamheight(self): 

1015 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). 

1016 ''' 

1017 return self.philam.to3Tuple(self.height) 

1018 

1019 @deprecated_method 

1020 def points(self, points, **closed): # PYCHOK no cover 

1021 '''DEPRECATED, use method L{points2}.''' 

1022 return self.points2(points, **closed) 

1023 

1024 def points2(self, points, closed=True): 

1025 '''Check a path or polygon represented by points. 

1026 

1027 @arg points: The path or polygon points (C{LatLon}[]) 

1028 @kwarg closed: Optionally, consider the polygon closed, ignoring any 

1029 duplicate or closing final B{C{points}} (C{bool}). 

1030 

1031 @return: A L{Points2Tuple}C{(number, points)}, an C{int} and a C{list} 

1032 or C{tuple}. 

1033 

1034 @raise PointsError: Insufficient number of B{C{points}}. 

1035 

1036 @raise TypeError: Some B{C{points}} are not C{LatLon}. 

1037 ''' 

1038 return _MODS.iters.points2(points, closed=closed, base=self) 

1039 

1040 def PointsIter(self, points, loop=0, dedup=False, wrap=False): 

1041 '''Return a C{PointsIter} iterator. 

1042 

1043 @arg points: The path or polygon points (C{LatLon}[]) 

1044 @kwarg loop: Number of loop-back points (non-negative C{int}). 

1045 @kwarg dedup: If C{True}, skip duplicate points (C{bool}). 

1046 @kwarg wrap: If C{True}, wrap or I{normalize} the enum-/iterated 

1047 B{C{points}} (C{bool}). 

1048 

1049 @return: A new C{PointsIter} iterator. 

1050 

1051 @raise PointsError: Insufficient number of B{C{points}}. 

1052 ''' 

1053 return _MODS.iters.PointsIter(points, base=self, loop=loop, 

1054 dedup=dedup, wrap=wrap) 

1055 

1056 def radii11(self, point2, point3, wrap=False): 

1057 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent} 

1058 circles of a (planar) triangle formed by this and two other points. 

1059 

1060 @arg point2: Second point (C{LatLon}). 

1061 @arg point3: Third point (C{LatLon}). 

1062 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and 

1063 B{C{point3}} (C{bool}). 

1064 

1065 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}. 

1066 

1067 @raise IntersectionError: Near-coincident or -colinear points. 

1068 

1069 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. 

1070 

1071 @see: Function L{pygeodesy.radii11}, U{Incircle 

1072 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles 

1073 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent 

1074 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}. 

1075 ''' 

1076 with _toCartesian3(self, point2, point3, wrap) as cs: 

1077 return _MODS.vector2d._radii11ABC4(*cs, useZ=True)[0] 

1078 

1079 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3 

1080 '''(INTERNAL) Get the C{rhumb} for this point's datum or for 

1081 the B{C{radius}}' earth model iff non-C{None}. 

1082 ''' 

1083 try: 

1084 d = self._rhumb3dict 

1085 t = d[(exact, radius)] 

1086 except KeyError: 

1087 D = self.datum if radius is None else \ 

1088 _spherical_datum(radius) # ellipsoidal OK 

1089 try: 

1090 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical 

1091 except AttributeError as x: 

1092 raise _AttributeError(datum=D, radius=radius, cause=x) 

1093 t = r, D, _MODS.karney.Caps 

1094 if len(d) > 2: 

1095 d.clear() # d[:] = {} 

1096 d[(exact, radius)] = t # cache 3-tuple 

1097 return t 

1098 

1099 @Property_RO 

1100 def _rhumb3dict(self): # in ._update 

1101 return {} # 3-item cache 

1102 

1103 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False, b360=False): 

1104 '''Return the azimuth (bearing) of a rhumb line (loxodrome) between this and 

1105 an other (ellipsoidal) point. 

1106 

1107 @arg other: The other point (C{LatLon}). 

1108 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see method 

1109 L{Ellipsoid.rhumb_}. 

1110 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, L{Ellipsoid}, 

1111 L{Ellipsoid2} or L{a_f2Tuple}), overriding this point's datum. 

1112 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}} point (C{bool}). 

1113 @kwarg b360: If C{True}, return the azimuth as bearing in compass degrees (C{bool}). 

1114 

1115 @return: Rhumb azimuth (C{degrees180} or compass C{degrees360}). 

1116 

1117 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}} is invalid. 

1118 ''' 

1119 r, _, Cs = self._rhumb3(exact, radius) 

1120 z = r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12 

1121 return _umod_360(z + _360_0) if b360 else z 

1122 

1123 def rhumbDestination(self, distance, azimuth, radius=None, height=None, exact=False, **name): 

1124 '''Return the destination point having travelled the given distance from this point along 

1125 a rhumb line (loxodrome) of the given azimuth. 

1126 

1127 @arg distance: Distance travelled (C{meter}, same units as this point's datum (ellipsoid) 

1128 axes or B{C{radius}}, may be negative. 

1129 @arg azimuth: Azimuth (bearing) of the rhumb line (compass C{degrees}). 

1130 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, L{Ellipsoid}, 

1131 L{Ellipsoid2} or L{a_f2Tuple}), overriding this point's datum. 

1132 @kwarg height: Optional height, overriding the default height (C{meter}). 

1133 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see method L{Ellipsoid.rhumb_}. 

1134 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1135 

1136 @return: The destination point (ellipsoidal C{LatLon}). 

1137 

1138 @raise TypeError: Invalid B{C{radius}}. 

1139 

1140 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, B{C{radius}} or B{C{height}}. 

1141 ''' 

1142 r, D, _ = self._rhumb3(exact, radius) 

1143 d = r._Direct(self, azimuth, distance) 

1144 h = self._heigHt(height) 

1145 return self.classof(d.lat2, d.lon2, datum=D, height=h, **name) 

1146 

1147 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False): 

1148 '''Return the distance from this to an other point along a rhumb line (loxodrome). 

1149 

1150 @arg other: The other point (C{LatLon}). 

1151 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see method L{Ellipsoid.rhumb_}. 

1152 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, L{Ellipsoid}, 

1153 L{Ellipsoid2} or L{a_f2Tuple}), overriding this point's datum. 

1154 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}} point (C{bool}). 

1155 

1156 @return: Distance (C{meter}, the same units as this point's datum (ellipsoid) axes or B{C{radius}}. 

1157 

1158 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}} is invalid. 

1159 

1160 @raise ValueError: Invalid B{C{radius}}. 

1161 ''' 

1162 r, _, Cs = self._rhumb3(exact, radius) 

1163 return r._Inverse(self, other, wrap, outmask=Cs.DISTANCE).s12 

1164 

1165 def rhumbIntersecant2(self, circle, point, other, height=None, 

1166 **exact_radius_wrap_eps_tol): 

1167 '''Compute the intersections of a circle and a rhumb line given as two points or as a 

1168 point and azimuth. 

1169 

1170 @arg circle: Radius of the circle centered at this location (C{meter}), or a point 

1171 on the circle (same C{LatLon} class). 

1172 @arg point: The start point of the rhumb line (same C{LatLon} class). 

1173 @arg other: An other point I{on} (same C{LatLon} class) or the azimuth I{of} (compass 

1174 C{degrees}) the rhumb line. 

1175 @kwarg height: Optional height for the intersection points (C{meter}, conventionally) 

1176 or C{None} for interpolated heights. 

1177 @kwarg exact_radius_wrap_eps_tol: Optional keyword arguments, see methods L{rhumbLine} 

1178 and L{RhumbLineAux.Intersecant2} or L{RhumbLine.Intersecant2}. 

1179 

1180 @return: 2-Tuple of the intersection points (representing a chord), each an instance of 

1181 this class. Both points are the same instance if the rhumb line is tangent to 

1182 the circle. 

1183 

1184 @raise IntersectionError: The circle and rhumb line do not intersect. 

1185 

1186 @raise TypeError: Invalid B{C{point}}, B{C{circle}} or B{C{other}}. 

1187 

1188 @raise ValueError: Invalid B{C{circle}}, B{C{other}}, B{C{height}} or B{C{exact_radius_wrap}}. 

1189 

1190 @see: Methods L{RhumbLineAux.Intersecant2} and L{RhumbLine.Intersecant2}. 

1191 ''' 

1192 def _kwds3(eps=EPS, tol=_TOL, wrap=False, **kwds): 

1193 return kwds, wrap, dict(eps=eps, tol=tol) 

1194 

1195 exact_radius, w, eps_tol = _kwds3(**exact_radius_wrap_eps_tol) 

1196 

1197 p = _unrollon(self, self.others(point=point), wrap=w) 

1198 try: 

1199 r = Radius_(circle=circle) if _isRadius(circle) else \ 

1200 self.rhumbDistanceTo(self.others(circle=circle), wrap=w, **exact_radius) 

1201 rl = p.rhumbLine(other, wrap=w, **exact_radius) 

1202 P, Q = rl.Intersecant2(self.lat, self.lon, r, **eps_tol) 

1203 

1204 return self._intersecend2(p, other, w, height, rl.rhumb, P, Q, 

1205 self.rhumbIntersecant2) 

1206 except (TypeError, ValueError) as x: 

1207 raise _xError(x, center=self, circle=circle, point=point, other=other, 

1208 **exact_radius_wrap_eps_tol) 

1209 

1210 def rhumbLine(self, other, exact=False, radius=None, wrap=False, **name_caps): 

1211 '''Get a rhumb line through this point at a given azimuth or through this and an other point. 

1212 

1213 @arg other: The azimuth I{of} (compass C{degrees}) or an other point I{on} (same 

1214 C{LatLon} class) the rhumb line. 

1215 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see method L{Ellipsoid.rhumb_}. 

1216 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, L{Ellipsoid}, 

1217 L{Ellipsoid2} or L{a_f2Tuple}), overriding this point's C{datum}. 

1218 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}} point (C{bool}). 

1219 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see L{RhumbLine} or L{RhumbLineAux} C{B{caps}}. 

1220 

1221 @return: A C{RhumbLine} instance (C{RhumbLine} or C{RhumbLineAux}). 

1222 

1223 @raise TypeError: Invalid B{C{radius}} or B{C{other}} not C{scalar} nor same C{LatLon} class. 

1224 

1225 @see: Modules L{rhumb.aux_} and L{rhumb.ekx}. 

1226 ''' 

1227 r, _, Cs = self._rhumb3(exact, radius) 

1228 kwds = _xkwds(name_caps, name=self.name, caps=Cs.LINE_OFF) 

1229 rl = r._DirectLine( self, other, **kwds) if _isDegrees(other) else \ 

1230 r._InverseLine(self, self.others(other), wrap, **kwds) 

1231 return rl 

1232 

1233 def rhumbMidpointTo(self, other, exact=False, radius=None, height=None, fraction=_0_5, **wrap_name): 

1234 '''Return the (loxodromic) midpoint on the rhumb line between this and an other point. 

1235 

1236 @arg other: The other point (same C{LatLon} class). 

1237 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see method L{Ellipsoid.rhumb_}. 

1238 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, L{Ellipsoid}, 

1239 L{Ellipsoid2} or L{a_f2Tuple}), overriding this point's datum. 

1240 @kwarg height: Optional height, overriding the mean height (C{meter}). 

1241 @kwarg fraction: Midpoint location from this point (C{scalar}), 0 for this, 1 for the B{C{other}}, 

1242 0.5 for halfway between this and the B{C{other}} point, may be negative or 

1243 greater than 1. 

1244 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and C{B{wrap}=False}, if C{True}, wrap or 

1245 I{normalize} and unroll the B{C{other}} point (C{bool}). 

1246 

1247 @return: The midpoint at the given B{C{fraction}} along the rhumb line (same C{LatLon} class). 

1248 

1249 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}} is invalid. 

1250 

1251 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}. 

1252 ''' 

1253 w, n = self._wrap_name2(**wrap_name) 

1254 r, D, _ = self._rhumb3(exact, radius) 

1255 f = Scalar(fraction=fraction) 

1256 d = r._Inverse(self, self.others(other), w) # C.AZIMUTH_DISTANCE 

1257 d = r._Direct( self, d.azi12, d.s12 * f) 

1258 h = self._havg(other, f=f, h=height) 

1259 return self.classof(d.lat2, d.lon2, datum=D, height=h, name=n) 

1260 

1261 @property_RO 

1262 def sphericalLatLon(self): 

1263 '''Get the C{LatLon type} iff spherical, overloaded in L{LatLonSphericalBase}. 

1264 ''' 

1265 return False 

1266 

1267 def thomasTo(self, other, **wrap): 

1268 '''Compute the distance between this and an other point using U{Thomas' 

1269 <https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>} formula. 

1270 

1271 @arg other: The other point (C{LatLon}). 

1272 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, wrap 

1273 or I{normalize} and unroll the B{C{other}} point (C{bool}). 

1274 

1275 @return: Distance (C{meter}, same units as the axes of this point's datum ellipsoid). 

1276 

1277 @raise TypeError: The B{C{other}} point is not C{LatLon}. 

1278 

1279 @see: Function L{pygeodesy.thomas} and methods L{cosineLawTo}, C{distanceTo*}, 

1280 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo} / L{hubenyTo}, 

1281 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}. 

1282 ''' 

1283 return self._distanceTo_(_formy.thomas_, other, **wrap) 

1284 

1285 @deprecated_method 

1286 def to2ab(self): # PYCHOK no cover 

1287 '''DEPRECATED, use property L{philam}.''' 

1288 return self.philam 

1289 

1290 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds): 

1291 '''Convert this point to cartesian, I{geocentric} coordinates, also known as 

1292 I{Earth-Centered, Earth-Fixed} (ECEF). 

1293 

1294 @kwarg height: Optional height, overriding this point's height (C{meter}, 

1295 conventionally). 

1296 @kwarg Cartesian: Optional class to return the geocentric coordinates 

1297 (C{Cartesian}) or C{None}. 

1298 @kwarg Cartesian_kwds: Optionally, additional B{C{Cartesian}} keyword 

1299 arguments, ignored if C{B{Cartesian} is None}. 

1300 

1301 @return: A B{C{Cartesian}} instance or if B{C{Cartesian} is None}, an 

1302 L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with 

1303 C{C=0} and C{M} if available. 

1304 

1305 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}} item. 

1306 

1307 @see: Methods C{toNvector}, C{toVector} and C{toVector3d}. 

1308 ''' 

1309 r = self._ecef9 if height is None else self.toEcef(height=height) 

1310 if Cartesian is not None: # class or .classof 

1311 r = Cartesian(r, **self._name1__(Cartesian_kwds)) 

1312 _xdatum(r.datum, self.datum) 

1313 return r 

1314 

1315 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point): 

1316 '''(INTERNAL) Convert to cartesian and check Ecef's before and after. 

1317 ''' 

1318 p = self.others(up=up, **name_point) 

1319 c = p.toCartesian(height=height) 

1320 E = self.Ecef 

1321 if E: 

1322 for p in (p, c): 

1323 e = _xattr(p, Ecef=None) 

1324 if e not in (None, E): # PYCHOK no cover 

1325 n, _ = _xkwds_item2(name_point) 

1326 n = Fmt.INDEX(n, i) 

1327 raise _ValueError(n, e, txt=_incompatible(E.__name__)) # txt__ 

1328 return c 

1329 

1330 def toDatum(self, datum2, height=None, **name): 

1331 '''I{Must be overloaded}.''' 

1332 self._notOverloaded(datum2, height=height, **name) 

1333 

1334 def toEcef(self, height=None, M=False): 

1335 '''Convert this point to I{geocentric} coordinates, also known as 

1336 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}). 

1337 

1338 @kwarg height: Optional height, overriding this point's height (C{meter}, 

1339 conventionally). 

1340 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}). 

1341 

1342 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with 

1343 C{C=0} and C{M} if available. 

1344 

1345 @raise EcefError: A C{.datum} or an ECEF issue. 

1346 ''' 

1347 return self._ecef9 if height in (None, self.height) else \ 

1348 self._Ecef_forward(self.lat, self.lon, height=height, M=M) 

1349 

1350 @deprecated_method 

1351 def to3llh(self, height=None): # PYCHOK no cover 

1352 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.''' 

1353 return self.latlonheight if height in (None, self.height) else \ 

1354 self.latlon.to3Tuple(height) 

1355 

1356 def toNormal(self, deep=False, **name): 

1357 '''Get this point I{normalized} to C{abs(lat) <= 90} and C{abs(lon) <= 180}. 

1358 

1359 @kwarg deep: If C{True}, make a deep, otherwise a shallow copy (C{bool}). 

1360 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1361 

1362 @return: A copy of this point, I{normalized} (C{LatLon}), optionally renamed. 

1363 

1364 @see: Property L{isnormal}, method L{normal} and function L{pygeodesy.normal}. 

1365 ''' 

1366 ll = self.copy(deep=deep) 

1367 _ = ll.normal() 

1368 if name: 

1369 ll.rename(name) 

1370 return ll 

1371 

1372 def toNvector(self, h=None, Nvector=None, **name_Nvector_kwds): 

1373 '''Convert this point to C{n-vector} (normal to the earth's surface) components, 

1374 I{including height}. 

1375 

1376 @kwarg h: Optional height, overriding this point's height (C{meter}). 

1377 @kwarg Nvector: Optional class to return the C{n-vector} components (C{Nvector}) 

1378 or C{None}. 

1379 @kwarg name_Nvector_kwds: Optional C{B{name}=NN} (C{str}) and optionally, 

1380 additional B{C{Nvector}} keyword arguments, ignored if C{B{Nvector} 

1381 is None}. 

1382 

1383 @return: An B{C{Nvector}} instance or a L{Vector4Tuple}C{(x, y, z, h)} if 

1384 C{B{Nvector} is None}. 

1385 

1386 @raise TypeError: Invalid B{C{h}}, B{C{Nvector}} or B{C{name_Nvector_kwds}}. 

1387 

1388 @see: Methods C{toCartesian}, C{toVector} and C{toVector3d}. 

1389 ''' 

1390 h = self._heigHt(h) 

1391 if Nvector is None: 

1392 r = self._n_xyz3.to4Tuple(h) 

1393 n, _ = _name2__(name_Nvector_kwds, _or_nameof=self) 

1394 if n: 

1395 r.rename(n) 

1396 else: 

1397 x, y, z = self._n_xyz3 

1398 r = Nvector(x, y, z, h=h, ll=self, **self._name1__(name_Nvector_kwds)) 

1399 return r 

1400 

1401 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected 

1402 '''Convert this point to a "lat, lon[, +/-height]" string, formatted in the 

1403 given C{B{form}at}. 

1404 

1405 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see functions 

1406 L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}. 

1407 @kwarg joined: Separator to join the lat-, longitude and height strings (C{str} 

1408 or C{None} or C{NN} for non-joined). 

1409 @kwarg m: Optional unit of the height (C{str}), use C{None} to exclude height 

1410 from the returned string. 

1411 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator}, B{C{s_D}}, 

1412 B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword arguments, see function 

1413 L{pygeodesy.toDMS} for details. 

1414 

1415 @return: This point in the specified C{B{form}at}, etc. (C{str} or a 2- or 3-tuple 

1416 C{(lat_str, lon_str[, height_str])} if B{C{joined}} is C{NN} or C{None}). 

1417 

1418 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more details about 

1419 keyword arguments C{B{form}at}, C{B{prec}ision}, C{B{sep}arator}, B{C{s_D}}, 

1420 B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}. 

1421 ''' 

1422 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S), 

1423 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S)) 

1424 if self.height and m is not None: 

1425 t += (self.heightStr(m=m),) 

1426 return joined.join(t) if joined else t 

1427 

1428 def toVector(self, Vector=None, **Vector_kwds): 

1429 '''Convert this point to a C{Vector} with the I{geocentric} C{(x, y, z)} (ECEF) 

1430 coordinates, I{ignoring height}. 

1431 

1432 @kwarg Vector: Optional class to return the I{geocentric} components (L{Vector3d}) 

1433 or C{None}. 

1434 @kwarg Vector_kwds: Optionally, additional B{C{Vector}} keyword arguments, 

1435 ignored if C{B{Vector} is None}. 

1436 

1437 @return: A B{C{Vector}} instance or a L{Vector3Tuple}C{(x, y, z)} if C{B{Vector} 

1438 is None}. 

1439 

1440 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}. 

1441 

1442 @see: Methods C{toCartesian}, C{toNvector} and C{toVector3d}. 

1443 ''' 

1444 return self._ecef9.toVector(Vector=Vector, **self._name1__(Vector_kwds)) 

1445 

1446 def toVector3d(self, norm=True, **Vector3d_kwds): 

1447 '''Convert this point to a L{Vector3d} with the I{geocentric} C{(x, y, z)} 

1448 (ECEF) coordinates, I{ignoring height}. 

1449 

1450 @kwarg norm: If C{False}, don't normalize the coordinates (C{bool}). 

1451 @kwarg Vector3d_kwds: Optional L{Vector3d} keyword arguments. 

1452 

1453 @return: Named, unit vector or vector (L{Vector3d}). 

1454 

1455 @raise TypeError: Invalid B{C{Vector3d_kwds}}. 

1456 

1457 @see: Methods C{toCartesian}, C{toNvector} and C{toVector}. 

1458 ''' 

1459 r = self.toVector(Vector=_MODS.vector3d.Vector3d, **Vector3d_kwds) 

1460 if norm: 

1461 r = r.unit(ll=self) 

1462 return r 

1463 

1464 def toWm(self, **toWm_kwds): 

1465 '''Convert this point to a WM coordinate. 

1466 

1467 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments. 

1468 

1469 @return: The WM coordinate (L{Wm}). 

1470 

1471 @see: Function L{pygeodesy.toWm}. 

1472 ''' 

1473 return _MODS.webmercator.toWm(self, **self._name1__(toWm_kwds)) 

1474 

1475 @deprecated_method 

1476 def to3xyz(self): # PYCHOK no cover 

1477 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector}, 

1478 L{toVector3d} or perhaps (geocentric) L{toEcef}.''' 

1479 return self.xyz # self.toVector() 

1480 

1481# def _update(self, updated, *attrs, **setters): 

1482# '''(INTERNAL) See C{_NamedBase._update}. 

1483# ''' 

1484# if updated: 

1485# self._rhumb3dict.clear() 

1486# return _NamedBase._update(self, updated, *attrs, **setters) 

1487 

1488 def vincentysTo(self, other, **radius_wrap): 

1489 '''Compute the distance between this and an other point using U{Vincenty's 

1490 <https://WikiPedia.org/wiki/Great-circle_distance>} spherical formula. 

1491 

1492 @arg other: The other point (C{LatLon}). 

1493 @kwarg radius_wrap: Optional C{B{radius}=R_M} and C{B{wrap}=False} for 

1494 function L{pygeodesy.vincentys}, overriding the default 

1495 C{mean radius} of this point's datum ellipsoid. 

1496 

1497 @return: Distance (C{meter}, same units as B{C{radius}}). 

1498 

1499 @raise TypeError: The B{C{other}} point is not C{LatLon}. 

1500 

1501 @see: Function L{pygeodesy.vincentys} and methods L{cosineLawTo}, C{distanceTo*}, 

1502 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo} / L{hubenyTo}, 

1503 L{flatPolarTo}, L{haversineTo} and L{thomasTo}. 

1504 ''' 

1505 return self._distanceTo(_formy.vincentys, other, **_xkwds(radius_wrap, radius=None)) 

1506 

1507 def _wrap_name2(self, wrap=False, **name): 

1508 '''(INTERNAL) Return the C{wrap} and C{name} value. 

1509 ''' 

1510 return wrap, (self._name__(name) if name else NN) 

1511 

1512 @property_RO 

1513 def xyz(self): 

1514 '''Get the I{geocentric} C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)}) 

1515 ''' 

1516 return self._ecef9.xyz 

1517 

1518 @property_RO 

1519 def xyz3(self): 

1520 '''Get the I{geocentric} C{(x, y, z)} coordinates as C{3-tuple}. 

1521 ''' 

1522 return tuple(self.xyz) 

1523 

1524 @Property_RO 

1525 def xyzh(self): 

1526 '''Get the I{geocentric} C{(x, y, z)} coordinates and height (L{Vector4Tuple}C{(x, y, z, h)}) 

1527 ''' 

1528 return self.xyz.to4Tuple(self.height) 

1529 

1530 

1531class _toCartesian3(object): # see also .formy._idllmn6, .geodesicw._wargs, .vector2d._numpy 

1532 '''(INTERNAL) Wrapper to convert 2 other points. 

1533 ''' 

1534 @contextmanager # <https://www.Python.org/dev/peps/pep-0343/> Examples 

1535 def __call__(self, p, p2, p3, wrap, **kwds): 

1536 try: 

1537 if wrap: 

1538 p2, p3 = map1(_Wrap.point, p2, p3) 

1539 kwds = _xkwds(kwds, wrap=wrap) 

1540 yield (p. toCartesian().copy(name=_point_), # copy to rename 

1541 p._toCartesianEcef(up=4, point2=p2), 

1542 p._toCartesianEcef(up=4, point3=p3)) 

1543 except (AssertionError, TypeError, ValueError) as x: # Exception? 

1544 raise _xError(x, point=p, point2=p2, point3=p3, **kwds) 

1545 

1546_toCartesian3 = _toCartesian3() # PYCHOK singleton 

1547 

1548 

1549def _latlonheight3(latlonh, height, wrap): # in .points.LatLon_.__init__ 

1550 '''(INTERNAL) Get 3-tuple C{(lat, lon, height)}. 

1551 ''' 

1552 try: 

1553 lat, lon = latlonh.lat, latlonh.lon 

1554 height = _xattr(latlonh, height=height) 

1555 except AttributeError: 

1556 raise _IsnotError(_LatLon_, latlonh=latlonh) 

1557 if wrap: 

1558 lat, lon = _Wrap.latlon(lat, lon) 

1559 return lat, lon, height 

1560 

1561 

1562def latlon2n_xyz(lat_ll, lon=None, **name): 

1563 '''Convert lat-, longitude to C{n-vector} (I{normal} to the earth's surface) X, Y and Z components. 

1564 

1565 @arg lat_ll: Latitude (C{degrees}) or a C{LatLon} instance, L{LatLon2Tuple} or other C{LatLon*Tuple}. 

1566 @kwarg lon: Longitude (C{degrees}), required if C{B{lon_ll} is degrees}, ignored otherwise. 

1567 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1568 

1569 @return: A L{Vector3Tuple}C{(x, y, z)}. 

1570 

1571 @see: Function L{philam2n_xyz}. 

1572 

1573 @note: These are C{n-vector} x, y and z components, I{NOT geocentric} x, y and z (ECEF) coordinates! 

1574 ''' 

1575 lat = lat_ll 

1576 if lon is None: 

1577 try: 

1578 lat, lon = lat_ll.latlon 

1579 except AttributeError: 

1580 lat = lat_ll.lat 

1581 lon = lat_ll.lon 

1582 # Kenneth Gade eqn 3, but using right-handed 

1583 # vector x -> 0°E,0°N, y -> 90°E,0°N, z -> 90°N 

1584 sa, ca, sb, cb = sincos2d_(lat, lon) 

1585 return Vector3Tuple(ca * cb, ca * sb, sa, **name) 

1586 

1587 

1588def philam2n_xyz(phi_ll, lam=None, **name): 

1589 '''Convert lat-, longitude to C{n-vector} (I{normal} to the earth's surface) X, Y and Z components. 

1590 

1591 @arg phi_ll: Latitude (C{radians}) or a C{LatLon} instance with C{phi}, C{lam} or C{philam} attributes. 

1592 @kwarg lam: Longitude (C{radians}), required if C{B{phi_ll} is radians}, ignored otherwise. 

1593 @kwarg name: Optional name (C{str}). 

1594 

1595 @return: A L{Vector3Tuple}C{(x, y, z)}. 

1596 

1597 @see: Function L{latlon2n_xyz}. 

1598 

1599 @note: These are C{n-vector} x, y and z components, I{NOT geocentric} x, y and z (ECEF) coordinates! 

1600 ''' 

1601 phi = phi_ll 

1602 if lam is None: 

1603 try: 

1604 phi, lam = phi_ll.philam 

1605 except AttributeError: 

1606 phi = phi_ll.phi 

1607 lam = phi_ll.lam 

1608 return latlon2n_xyz(degrees(phi), degrees(lam), **name) 

1609 

1610 

1611def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, radius=R_M, wrap=False): # MCCABE 13 

1612 '''(INTERNAL) Trilaterate three points by I{area overlap} or by I{perimeter intersection} of three circles. 

1613 

1614 @note: The B{C{radius}} is needed only for C{n-vectorial} and C{sphericalTrigonometry.LatLon.distanceTo} 

1615 methods and silently ignored by the C{ellipsoidalExact}, C{-GeodSolve}, C{-Karney} and 

1616 C{-Vincenty.LatLon.distanceTo} methods. 

1617 ''' 

1618 p2, p3, w = _unrollon3(p1, p2, p3, wrap) 

1619 rw = dict(radius=radius, wrap=w) 

1620 

1621 r1 = Distance_(distance1=d1) 

1622 r2 = Distance_(distance2=d2) 

1623 r3 = Distance_(distance3=d3) 

1624 m = 0 if area else (r1 + r2 + r3) 

1625 pc = 0 

1626 t = [] 

1627 for _ in range(3): 

1628 try: # intersection of circle (p1, r1) and (p2, r2) 

1629 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w) 

1630 

1631 if area: # check overlap 

1632 if c1 is c2: # abutting 

1633 c = c1 

1634 else: # nearest point on radical 

1635 c = p3.nearestOn(c1, c2, within=True, wrap=w) 

1636 d = r3 - p3.distanceTo(c, **rw) 

1637 if d > eps: # sufficient overlap 

1638 t.append((d, c)) 

1639 m = max(m, d) 

1640 

1641 else: # check intersection 

1642 for c in ((c1,) if c1 is c2 else (c1, c2)): 

1643 d = fabs(r3 - p3.distanceTo(c, **rw)) 

1644 if d < eps: # below margin 

1645 t.append((d, c)) 

1646 m = min(m, d) 

1647 

1648 except IntersectionError as x: 

1649 if _concentric_ in str(x): # XXX ConcentricError? 

1650 pc += 1 

1651 

1652 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate 

1653 

1654 if t: # get min, max, points and count ... 

1655 t = tuple(sorted(t)) 

1656 n = len(t), # as 1-tuple 

1657 # ... or for a single trilaterated result, 

1658 # min *is* max, min- *is* maxPoint and n=1, 2 or 3 

1659 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...) 

1660 

1661 elif area and pc == 3: # all pairwise concentric ... 

1662 r, p = min((r1, p1), (r2, p2), (r3, p3)) 

1663 m = max(r1, r2, r3) 

1664 # ... return "smallest" point twice, the smallest 

1665 # and largest distance and n=0 for concentric 

1666 return Trilaterate5Tuple(float(r), p, float(m), p, 0) 

1667 

1668 n, f = (_overlap_, max) if area else (_intersection_, min) 

1669 t = _COMMASPACE_(_no_(n), '%s %.3g' % (f.__name__, m)) 

1670 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t) 

1671 

1672 

1673__all__ += _ALL_DOCS(LatLonBase) 

1674 

1675# **) MIT License 

1676# 

1677# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

1678# 

1679# Permission is hereby granted, free of charge, to any person obtaining a 

1680# copy of this software and associated documentation files (the "Software"), 

1681# to deal in the Software without restriction, including without limitation 

1682# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1683# and/or sell copies of the Software, and to permit persons to whom the 

1684# Software is furnished to do so, subject to the following conditions: 

1685# 

1686# The above copyright notice and this permission notice shall be included 

1687# in all copies or substantial portions of the Software. 

1688# 

1689# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1690# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1691# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1692# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1693# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1694# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1695# OTHER DEALINGS IN THE SOFTWARE.