Coverage for pygeodesy/latlonBase.py: 93%

448 statements  

« prev     ^ index     » next       coverage.py v7.2.2, created at 2023-10-11 16:04 -0400

1 

2# -*- coding: utf-8 -*- 

3 

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

5 

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

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

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

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

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

11''' 

12 

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

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

15 _0_0, _0_5, _1_0, _180_0 

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

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

18# from pygeodesy.ecef import EcefKarney # _MODS 

19from pygeodesy.errors import _AttributeError, _incompatible, \ 

20 _IsnotError, IntersectionError, \ 

21 _TypeError, _ValueError, _xattr, _xdatum, \ 

22 _xError, _xkwds, _xkwds_not 

23from pygeodesy.fmath import favg, sqrt_a 

24from pygeodesy.formy import antipode, compassAngle, cosineAndoyerLambert_, \ 

25 cosineForsytheAndoyerLambert_, cosineLaw, \ 

26 equirectangular, euclidean, flatLocal_, \ 

27 flatPolar, _hartzell, haversine, isantipode, \ 

28 _isequalTo, isnormal, normal, philam2n_xyz, \ 

29 thomas_, vincentys, _spherical_datum 

30from pygeodesy.interns import NN, _COMMASPACE_, _concentric_, _height_, \ 

31 _intersection_, _LatLon_, _m_, _negative_, \ 

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

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

34# from pygeodesy.karney import Caps # _MODS 

35from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

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

37from pygeodesy.named import _NamedBase, notOverloaded, Fmt 

38from pygeodesy.namedTuples import Bounds2Tuple, LatLon2Tuple, PhiLam2Tuple, \ 

39 Trilaterate5Tuple, Vector3Tuple 

40# from pygeodesy.nvectorBase import _N_vector_ # _MODS 

41from pygeodesy.props import deprecated_method, Property, Property_RO, \ 

42 property_RO, _update_all 

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

44from pygeodesy.units import Distance_, Lat, Lon, Height, Radius, Radius_, \ 

45 Scalar, Scalar_ 

46from pygeodesy.utily import sincos2d, _unrollon, _unrollon3, _Wrap 

47from pygeodesy.vector2d import _circin6, Circin6Tuple, _circum3, circum4_, \ 

48 Circum3Tuple, _radii11ABC 

49from pygeodesy.vector3d import nearestOn6, Vector3d, PointsIter 

50 

51from contextlib import contextmanager 

52from math import asin, cos, degrees, fabs, radians 

53 

54__all__ = _ALL_LAZY.latlonBase 

55__version__ = '23.10.08' 

56 

57 

58def _latlonheight3(latlonh, height, wrap): # in .points.LatLon_.__init__ 

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

60 ''' 

61 try: 

62 lat, lon = latlonh.lat, latlonh.lon 

63 height = _xattr(latlonh, height=height) 

64 except AttributeError: 

65 raise _IsnotError(_LatLon_, latlonh=latlonh) 

66 if wrap: 

67 lat, lon = _Wrap.latlon(lat, lon) 

68 return lat, lon, height 

69 

70 

71class LatLonBase(_NamedBase): 

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

73 ellipsoidal earth models. 

74 ''' 

75 _clipid = INT0 # polygonal clip, see .booleans 

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

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

78 _lat = 0 # latitude (C{degrees}) 

79 _lon = 0 # longitude (C{degrees}) 

80 

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

82 '''New C{LatLon}. 

83 

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

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

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

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

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

89 (C{meter}, conventionally). 

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

91 (C{bool}). 

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

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

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

95 

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

97 

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

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

100 

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

102 

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

104 

105 @example: 

106 

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

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

109 >>> r = LatLon(p) 

110 ''' 

111 if name: 

112 self.name = name 

113 

114 if lon is None: 

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

116 elif wrap: 

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

118 else: 

119 lat = latlonh 

120 

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

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

123 if height: # elevation 

124 self._height = Height(height) 

125 if datum: 

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

127 

128 def __eq__(self, other): 

129 return self.isequalTo(other) 

130 

131 def __ne__(self, other): 

132 return not self.isequalTo(other) 

133 

134 def __str__(self): 

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

136 

137 def antipode(self, height=None): 

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

139 to this point. 

140 

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

142 this point's height otherwise. 

143 

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

145 ''' 

146 h = self._heigHt(height) 

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

148 

149 @deprecated_method 

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

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

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

153 

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

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

156 bounding box centered at this location. 

157 

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

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

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

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

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

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

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

165 overriding the point's height. 

166 

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

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

169 

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

171 ''' 

172 w = Scalar_(wide=wide) * _0_5 

173 t = Scalar_(tall=tall) * _0_5 

174 if radius is not None: 

175 r = Radius_(radius) 

176 c = cos(self.phi) 

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

178 t = degrees(t / r) 

179 y, t = self.lat, fabs(t) 

180 x, w = self.lon, fabs(w) 

181 

182 h = self._heigHt(height) 

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

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

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

186 

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

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

189 this and an other point. 

190 

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

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

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

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

195 point (C{bool}). 

196 

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

198 

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

200 ''' 

201 def _v3d(ll): 

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

203 return Vector3d(t.x, t.y, t.z) 

204 

205 p = self.others(other) 

206 if wrap: 

207 p = _Wrap.point(p) 

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

209 

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

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

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

213 

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

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

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

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

218 B{C{point3}} (C{bool}). 

219 

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

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

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

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

224 

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

226 than version 1.10. 

227 

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

229 a trilateration or C{numpy} issue. 

230 

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

232 

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

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

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

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

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

238 height)} representing the differences between both results from 

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

240 

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

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

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

244 ''' 

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

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

247 datum=self.datum) # PYCHOK unpack 

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

249 

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

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

252 this and two other points. 

253 

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

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

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

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

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

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

260 B{C{point3}} (C{bool}). 

261 

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

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

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

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

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

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

268 

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

270 version 1.10. 

271 

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

273 incompatible C{Ecef} classes or a trilateration 

274 or C{numpy} issue. 

275 

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

277 

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

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

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

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

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

283 height)} representing the difference between both results from 

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

285 

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

287 ''' 

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

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

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

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

292 

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

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

295 

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

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

298 (C{bool}), default C{False}. 

299 

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

301 an instance of this (sub-)class. 

302 

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

304 version 1.10. 

305 

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

307 

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

309 

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

311 

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

313 ''' 

314 def _cs(ps, C, wrap=False): 

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

316 for i, p in enumerate(ps): 

317 yield C(i=i, points=_wp(p)) 

318 

319 C = self._toCartesianEcef 

320 c = C(point=self) 

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

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

323 return t.dup(center=c) 

324 

325 @property 

326 def clipid(self): 

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

328 ''' 

329 return self._clipid 

330 

331 @clipid.setter # PYCHOK setter! 

332 def clipid(self, clipid): 

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

334 ''' 

335 self._clipid = int(clipid) 

336 

337 @deprecated_method 

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

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

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

341 

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

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

344 this and an other point. 

345 

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

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

348 larger distances. 

349 

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

351 @kwarg adjust_wrap: Optional keyword arguments for function 

352 L{pygeodesy.compassAngle}. 

353 

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

355 

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

357 

358 @note: Courtesy of Martin Schultz. 

359 

360 @see: U{Local, flat earth approximation 

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

362 ''' 

363 p = self.others(other) 

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

365 

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

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

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

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

370 

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

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

373 the B{C{other}} point (C{bool}). 

374 

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

376 point's datum ellipsoid). 

377 

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

379 

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

381 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, 

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

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

384 L{thomasTo} and L{vincentysTo}. 

385 ''' 

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

387 

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

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

390 the U{Forsythe-Andoyer-Lambert correction 

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

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

393 formula. 

394 

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

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

397 the B{C{other}} point (C{bool}). 

398 

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

400 this point's datum ellipsoid). 

401 

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

403 

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

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

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

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

408 ''' 

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

410 

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

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

413 U{spherical Law of Cosines 

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

415 formula. 

416 

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

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

419 for the mean radius of this point's datum 

420 ellipsoid. 

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

422 the B{C{other}} point (C{bool}). 

423 

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

425 

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

427 

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

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

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

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

432 ''' 

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

434 

435 @property_RO 

436 def datum(self): # PYCHOK no cover 

437 '''I{Must be overloaded}.''' 

438 notOverloaded(self) 

439 

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

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

442 

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

444 L{Ned} or L{Local9Tuple}). 

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

446 or C{None}. 

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

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

449 

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

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

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

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

454 is un-/specified. 

455 

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

457 ''' 

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

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

460 

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

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

463 ''' 

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

465 if r is None: 

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

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

468 

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

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

471 ''' 

472 p = self.others(other, up=2) 

473 D = self.datum 

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

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

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

477 

478 @Property_RO 

479 def Ecef(self): 

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

481 ''' 

482 return _MODS.ecef.EcefKarney # default 

483 

484 @Property_RO 

485 def _Ecef_forward(self): 

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

487 ''' 

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

489 

490 @Property_RO 

491 def _ecef9(self): 

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

493 ''' 

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

495 

496 @deprecated_method 

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

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

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

500 

501 @deprecated_method 

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

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

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

505 

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

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

508 using the U{Equirectangular Approximation / Projection 

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

510 

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

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

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

514 

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

516 @kwarg radius_adjust_limit_wrap: Optional keyword arguments 

517 for function L{pygeodesy.equirectangular}, 

518 overriding the default mean C{radius} of this 

519 point's datum ellipsoid. 

520 

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

522 

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

524 

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

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

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

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

529 ''' 

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

531 

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

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

534 an other point. 

535 

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

537 

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

539 @kwarg radius_adjust_wrap: Optional keyword arguments for function 

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

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

542 

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

544 

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

546 

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

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

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

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

551 ''' 

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

553 

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

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

556 U{ellipsoidal Earth to plane projection 

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

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

559 

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

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

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

563 datum ellipsoid. 

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

565 the B{C{other}} point (C{bool}). 

566 

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

568 

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

570 

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

572 

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

574 L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo}, 

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

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

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

578 ''' 

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

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

581 

582 hubenyTo = flatLocalTo # for Karl Hubeny 

583 

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

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

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

587 Geographical_distance#Polar_coordinate_flat-Earth_formula>} formula. 

588 

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

590 @kwarg radius_wrap: Optional keyword arguments for function 

591 L{pygeodesy.flatPolar}, overriding the 

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

593 datum ellipsoid. 

594 

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

596 

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

598 

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

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

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

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

603 ''' 

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

605 

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

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

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

609 

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

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

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

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

614 this point's C{datum} ellipsoid. 

615 

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

617 to the distance to this C{pov}. 

618 

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

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

621 outside or away from the ellipsoid. 

622 

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

624 

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

626 ''' 

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

628 

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

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

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

632 formula. 

633 

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

635 @kwarg radius_wrap: Optional keyword arguments for function 

636 L{pygeodesy.haversine}, overriding the 

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

638 datum ellipsoid. 

639 

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

641 

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

643 

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

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

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

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

648 ''' 

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

650 

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

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

653 

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

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

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

657 

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

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

660 ''' 

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

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

663 

664 @Property 

665 def height(self): 

666 '''Get the height (C{meter}). 

667 ''' 

668 return self._height 

669 

670 @height.setter # PYCHOK setter! 

671 def height(self, height): 

672 '''Set the height (C{meter}). 

673 

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

675 

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

677 ''' 

678 h = Height(height) 

679 if self._height != h: 

680 _update_all(self) 

681 self._height = h 

682 

683 def _heigHt(self, height): 

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

685 ''' 

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

687 

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

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

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

691 

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

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

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

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

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

697 ellipsoid's surface, otherwise the intersection of the 

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

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

700 (C{LatLon}) or C{None}. 

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

702 ignored if C{B{LatLon} is None}. 

703 

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

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

706 

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

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

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

710 

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

712 

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

714 

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

716 ''' 

717 c = self.toCartesian() 

718 if LatLon is None: 

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

720 else: 

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

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

723 return r 

724 

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

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

727 

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

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

730 

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

732 ''' 

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

734 

735 @deprecated_method 

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

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

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

739 

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

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

742 on diametrically opposite sides of the earth. 

743 

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

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

746 

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

748 tolerance, C{False} otherwise. 

749 ''' 

750 p = self.others(other) 

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

752 

753 @Property_RO 

754 def isEllipsoidal(self): 

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

756 ''' 

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

758 

759 @Property_RO 

760 def isEllipsoidalLatLon(self): 

761 '''Get C{LatLon} base. 

762 ''' 

763 return False 

764 

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

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

767 

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

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

770 

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

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

773 

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

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

776 this C{class} or C{type}. 

777 

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

779 

780 @see: Method L{isequalTo3}. 

781 ''' 

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

783 

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

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

786 

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

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

789 

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

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

792 

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

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

795 this C{class} or C{type}. 

796 

797 @see: Method L{isequalTo}. 

798 ''' 

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

800 _isequalTo(self, other, eps=eps) 

801 

802 @Property_RO 

803 def isnormal(self): 

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

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

806 

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

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

809 ''' 

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

811 

812 @Property_RO 

813 def isSpherical(self): 

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

815 ''' 

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

817 

818 @Property_RO 

819 def lam(self): 

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

821 ''' 

822 return radians(self.lon) 

823 

824 @Property 

825 def lat(self): 

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

827 ''' 

828 return self._lat 

829 

830 @lat.setter # PYCHOK setter! 

831 def lat(self, lat): 

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

833 

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

835 ''' 

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

837 if self._lat != lat: 

838 _update_all(self) 

839 self._lat = lat 

840 

841 @Property 

842 def latlon(self): 

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

844 ''' 

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

846 

847 @latlon.setter # PYCHOK setter! 

848 def latlon(self, latlonh): 

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

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

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

852 

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

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

855 

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

857 

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

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

860 ''' 

861 if isstr(latlonh): 

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

863 else: 

864 _xinstanceof(list, tuple, latlonh=latlonh) 

865 if len(latlonh) == 3: 

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

867 elif len(latlonh) != 2: 

868 raise _ValueError(latlonh=latlonh) 

869 else: 

870 h = self.height 

871 

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

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

874 _update_all(self) 

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

876 

877 def latlon2(self, ndigits=0): 

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

879 

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

881 

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

883 and rounded away from zero. 

884 

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

886 if B{C{ndigits}} is omitted. 

887 ''' 

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

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

890 

891 @deprecated_method 

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

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

894 return self.latlon2(ndigits=ndigits) 

895 

896 latlon2round = latlon_ # PYCHOK no cover 

897 

898 @Property 

899 def latlonheight(self): 

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

901 ''' 

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

903 

904 @latlonheight.setter # PYCHOK setter! 

905 def latlonheight(self, latlonh): 

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

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

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

909 

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

911 ''' 

912 self.latlon = latlonh 

913 

914 @Property 

915 def lon(self): 

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

917 ''' 

918 return self._lon 

919 

920 @lon.setter # PYCHOK setter! 

921 def lon(self, lon): 

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

923 

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

925 ''' 

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

927 if self._lon != lon: 

928 _update_all(self) 

929 self._lon = lon 

930 

931 @Property_RO 

932 def _ltp(self): 

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

934 ''' 

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

936 

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

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

939 

940 Points are converted to and distances are computed in 

941 I{geocentric}, cartesian space. 

942 

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

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

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

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

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

948 account for distances. 

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

950 the B{C{points}} (C{bool}). 

951 

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

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

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

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

956 units as the cartesian axes. 

957 

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

959 

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

961 C{Ecef} invalid. 

962 

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

964 

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

966 ''' 

967 def _cs(Ps, h, w, C): 

968 p = None # not used 

969 for i, q in Ps.enumerate(): 

970 if w and i: 

971 q = _unrollon(p, q) 

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

973 p = q 

974 

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

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

977 

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

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

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

981 

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

983 height=height) 

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

985 p = _r(c).toLatLon(**kwds) 

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

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

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

989 

990 def normal(self): 

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

992 C{abs(lon) <= 180}. 

993 

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

995 wasn't (but is now). 

996 

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

998 ''' 

999 n = self.isnormal 

1000 if not n: 

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

1002 return n 

1003 

1004 @Property_RO 

1005 def _N_vector(self): 

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

1007 ''' 

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

1009 

1010 @Property_RO 

1011 def phi(self): 

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

1013 ''' 

1014 return radians(self.lat) 

1015 

1016 @Property_RO 

1017 def philam(self): 

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

1019 ''' 

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

1021 

1022 def philam2(self, ndigits=0): 

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

1024 

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

1026 

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

1028 and rounded away from zero. 

1029 

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

1031 if B{C{ndigits}} is omitted. 

1032 ''' 

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

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

1035 

1036 @Property_RO 

1037 def philamheight(self): 

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

1039 ''' 

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

1041 

1042 @deprecated_method 

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

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

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

1046 

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

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

1049 

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

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

1052 ignoring any duplicate or closing final 

1053 B{C{points}} (C{bool}). 

1054 

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

1056 and C{list} or C{tuple}. 

1057 

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

1059 

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

1061 ''' 

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

1063 

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

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

1066 

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

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

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

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

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

1072 

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

1074 

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

1076 ''' 

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

1078 

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

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

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

1082 

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

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

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

1086 B{C{point3}} (C{bool}). 

1087 

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

1089 

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

1091 

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

1093 

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

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

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

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

1098 ''' 

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

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

1101 

1102 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3 

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

1104 the B{C{radius}}' earth model iff non-C{None}. 

1105 ''' # in .ellipsoidalBase.LatLonEllipsoidalBase.intersecant2 

1106 try: 

1107 d = self._rhumb3dict 

1108 t = d[(exact, radius)] 

1109 except KeyError: 

1110 D = self.datum if radius is None else _spherical_datum(radius) # ellipsoidal OK 

1111 try: 

1112 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical) 

1113 except AttributeError as x: 

1114 raise _AttributeError(datum=D, radius=radius, cause=x) 

1115 t = r, D, _MODS.karney.Caps 

1116 while d: 

1117 d.popitem() 

1118 d[(exact, radius)] = t # cache 3-tuple 

1119 return t 

1120 

1121 @Property_RO 

1122 def _rhumb3dict(self): 

1123 return {} # single-item cache 

1124 

1125 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False): 

1126 '''Return the azimuth (bearing) of a rhumb line (loxodrome) 

1127 between this and an other (ellipsoidal) point. 

1128 

1129 @arg other: The other point (C{LatLon}). 

1130 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), 

1131 see method L{Ellipsoid.rhumb_}. 

1132 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1133 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

1134 L{a_f2Tuple}), overriding this point's datum. 

1135 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1136 B{C{other}} point (C{bool}). 

1137 

1138 @return: Rhumb azimuth (compass C{degrees360}). 

1139 

1140 @raise TypeError: The B{C{other}} point is incompatible or 

1141 B{C{radius}} is invalid. 

1142 ''' 

1143 r, _, Cs = self._rhumb3(exact, radius) 

1144 return r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12 

1145 

1146 def rhumbDestination(self, distance, azimuth, exact=False, radius=None, height=None): 

1147 '''Return the destination point having travelled the given distance 

1148 from this point along a rhumb line (loxodrome) at the given azimuth. 

1149 

1150 @arg distance: Distance travelled (C{meter}, same units as this 

1151 point's datum (ellipsoid) axes or B{C{radius}}, 

1152 may be negative. 

1153 @arg azimuth: Azimuth (bearing) at this point (compass C{degrees}). 

1154 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), 

1155 see method L{Ellipsoid.rhumb_}. 

1156 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1157 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

1158 L{a_f2Tuple}), overriding this point's datum. 

1159 @kwarg height: Optional height, overriding the default height 

1160 (C{meter}). 

1161 

1162 @return: The destination point (ellipsoidal C{LatLon}). 

1163 

1164 @raise TypeError: Invalid B{C{radius}}. 

1165 

1166 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, 

1167 B{C{radius}} or B{C{height}}. 

1168 ''' 

1169 r, D, _ = self._rhumb3(exact, radius) 

1170 d = r._Direct(self, azimuth, distance) 

1171 h = self._heigHt(height) 

1172 return self.classof(d.lat2, d.lon2, datum=D, height=h) 

1173 

1174 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False): 

1175 '''Return the distance from this to an other point along 

1176 a rhumb line (loxodrome). 

1177 

1178 @arg other: The other point (C{LatLon}). 

1179 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), 

1180 see method L{Ellipsoid.rhumb_}. 

1181 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1182 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

1183 L{a_f2Tuple}), overriding this point's datum. 

1184 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1185 B{C{other}} point (C{bool}). 

1186 

1187 @return: Distance (C{meter}, the same units as this point's 

1188 datum (ellipsoid) axes or B{C{radius}}. 

1189 

1190 @raise TypeError: The B{C{other}} point is incompatible or 

1191 B{C{radius}} is invalid. 

1192 

1193 @raise ValueError: Invalid B{C{radius}}. 

1194 ''' 

1195 r, _, Cs = self._rhumb3(exact, radius) 

1196 return r._Inverse(self, other, wrap, outmask=Cs.DISTANCE).s12 

1197 

1198 def rhumbLine(self, azimuth_other, exact=False, radius=None, wrap=False, 

1199 **name_caps): 

1200 '''Get a rhumb line through this point at a given azimuth or 

1201 through this and an other point. 

1202 

1203 @arg azimuth_other: The azimuth of the rhumb line (compass 

1204 C{degrees}) or the other point (C{LatLon}). 

1205 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), 

1206 see method L{Ellipsoid.rhumb_}. 

1207 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1208 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

1209 L{a_f2Tuple}), overriding this point's datum. 

1210 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1211 C{azimuth_B{other}} point (C{bool}). 

1212 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see 

1213 L{RhumbLine} C{B{caps}}. 

1214 

1215 @return: A C{RhumbLine} instance. 

1216 

1217 @raise TypeError: Invalid B{C{radius}} or BC{C{azimuth_other}} 

1218 not a C{scalar} nor a C{LatLon}. 

1219 

1220 @see: Modules L{rhumbaux} and L{rhumbx}. 

1221 ''' 

1222 r, _, _ = self._rhumb3(exact, radius) 

1223 a, kwds = azimuth_other, _xkwds(name_caps, name=self.name) 

1224 if isscalar(a): 

1225 r = r._DirectLine(self, a, **kwds) 

1226 elif isinstance(a, LatLonBase): # isLatLon(a) 

1227 r = r._InverseLine(self, a, wrap, **kwds) 

1228 else: 

1229 raise _TypeError(azimuth_other=a) 

1230 return r 

1231 

1232 def rhumbMidpointTo(self, other, exact=False, radius=None, 

1233 height=None, fraction=_0_5, wrap=False): 

1234 '''Return the (loxodromic) midpoint on the rhumb line between 

1235 this and an other point. 

1236 

1237 @arg other: The other point (C{LatLon}). 

1238 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), 

1239 see method L{Ellipsoid.rhumb_}. 

1240 @kwarg radius: Optional earth radius (C{meter}) or earth model 

1241 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

1242 L{a_f2Tuple}), overriding this point's datum. 

1243 @kwarg height: Optional height, overriding the mean height 

1244 (C{meter}). 

1245 @kwarg fraction: Midpoint location from this point (C{scalar}), 0 

1246 for this, 1 for the B{C{other}}, 0.5 for halfway 

1247 between this and the B{C{other}} point, may be 

1248 negative or greater than 1. 

1249 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1250 B{C{other}} point (C{bool}). 

1251 

1252 @return: The midpoint at the given B{C{fraction}} along the 

1253 rhumb line (C{LatLon}). 

1254 

1255 @raise TypeError: The B{C{other}} point is incompatible or 

1256 B{C{radius}} is invalid. 

1257 

1258 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}. 

1259 ''' 

1260 r, D, _ = self._rhumb3(exact, radius) 

1261 f = Scalar(fraction=fraction) 

1262 d = r._Inverse(self, other, wrap) # C.AZIMUTH_DISTANCE 

1263 d = r._Direct( self, d.azi12, d.s12 * f) 

1264 h = self._havg(other, f=f, h=height) 

1265 return self.classof(d.lat2, d.lon2, datum=D, height=h) 

1266 

1267 def thomasTo(self, other, wrap=False): 

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

1269 U{Thomas'<https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>} 

1270 formula. 

1271 

1272 @arg other: The other point (C{LatLon}). 

1273 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll 

1274 the B{C{other}} point (C{bool}). 

1275 

1276 @return: Distance (C{meter}, same units as the axes of 

1277 this point's datum ellipsoid). 

1278 

1279 @raise TypeError: The B{C{other}} point is not C{LatLon}. 

1280 

1281 @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo}, 

1282 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

1283 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

1284 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}. 

1285 ''' 

1286 return self._distanceTo_(thomas_, other, wrap=wrap) 

1287 

1288 @deprecated_method 

1289 def to2ab(self): # PYCHOK no cover 

1290 '''DEPRECATED, use property L{philam}.''' 

1291 return self.philam 

1292 

1293 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds): 

1294 '''Convert this point to cartesian, I{geocentric} coordinates, 

1295 also known as I{Earth-Centered, Earth-Fixed} (ECEF). 

1296 

1297 @kwarg height: Optional height, overriding this point's height 

1298 (C{meter}, conventionally). 

1299 @kwarg Cartesian: Optional class to return the geocentric 

1300 coordinates (C{Cartesian}) or C{None}. 

1301 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} 

1302 keyword arguments, ignored if 

1303 C{B{Cartesian} is None}. 

1304 

1305 @return: A B{C{Cartesian}} or if B{C{Cartesian}} is C{None}, 

1306 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, 

1307 datum)} with C{C=0} and C{M} if available. 

1308 

1309 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}. 

1310 ''' 

1311 r = self._ecef9 if height is None else self.toEcef(height=height) 

1312 if Cartesian is not None: # class or .classof 

1313 r = self._xnamed(Cartesian(r, **Cartesian_kwds)) 

1314 _xdatum(r.datum, self.datum) 

1315 return r 

1316 

1317 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point): 

1318 '''(INTERNAL) Convert to cartesian and check Ecef's before and after. 

1319 ''' 

1320 p = self.others(up=up, **name_point) 

1321 c = p.toCartesian(height=height) 

1322 E = self.Ecef 

1323 if E: 

1324 for p in (p, c): 

1325 e = getattr(p, LatLonBase.Ecef.name, None) 

1326 if e not in (None, E): # PYCHOK no cover 

1327 n, _ = name_point.popitem() 

1328 if i is not None: 

1329 Fmt.SQUARE(n, i) 

1330 raise _ValueError(n, e, txt=_incompatible(E.__name__)) 

1331 return c 

1332 

1333 def toDatum(self, datum2, height=None, name=NN): 

1334 '''I{Must be overloaded}.''' 

1335 notOverloaded(self, datum2, height=height, name=name) 

1336 

1337 def toEcef(self, height=None, M=False): 

1338 '''Convert this point to I{geocentric} coordinates, also known as 

1339 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}). 

1340 

1341 @kwarg height: Optional height, overriding this point's height 

1342 (C{meter}, conventionally). 

1343 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}). 

1344 

1345 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} 

1346 with C{C=0} and C{M} if available. 

1347 

1348 @raise EcefError: A C{.datum} or an ECEF issue. 

1349 ''' 

1350 return self._ecef9 if height in (None, self.height) else \ 

1351 self._Ecef_forward(self.lat, self.lon, height=height, M=M) 

1352 

1353 @deprecated_method 

1354 def to3llh(self, height=None): # PYCHOK no cover 

1355 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.''' 

1356 return self.latlonheight if height in (None, self.height) else \ 

1357 self.latlon.to3Tuple(height) 

1358 

1359 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds): 

1360 '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}. 

1361 

1362 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z} 

1363 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}. 

1364 @kwarg ltp: The I{local tangent plane} (LTP) to use, 

1365 overriding this point's LTP (L{Ltp}). 

1366 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword 

1367 arguments, ignored if C{B{Xyz} is None}. 

1368 

1369 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None}, 

1370 a L{Local9Tuple}C{(x, y, z, lat, lon, height, 

1371 ltp, ecef, M)} with C{M=None}, always. 

1372 

1373 @raise TypeError: Invalid B{C{ltp}}. 

1374 ''' 

1375 p = _MODS.ltp._xLtp(ltp, self._ltp) 

1376 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds) 

1377 

1378 def toLtp(self, Ecef=None): 

1379 '''Return the I{local tangent plane} (LTP) for this point. 

1380 

1381 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ... 

1382 L{EcefYou}), overriding this point's C{Ecef}. 

1383 ''' 

1384 return self._ltp if Ecef in (None, self.Ecef) else _MODS.ltp.Ltp( 

1385 self, ecef=Ecef(self.datum), name=self.name) 

1386 

1387 def toNormal(self, deep=False, name=NN): 

1388 '''Get this point I{normalized} to C{abs(lat) <= 90} 

1389 and C{abs(lon) <= 180}. 

1390 

1391 @kwarg deep: If C{True} make a deep, otherwise a 

1392 shallow copy (C{bool}). 

1393 @kwarg name: Optional name of the copy (C{str}). 

1394 

1395 @return: A copy of this point, I{normalized} and 

1396 optionally renamed (C{LatLon}). 

1397 

1398 @see: Property L{isnormal}, method L{normal} and function 

1399 L{pygeodesy.normal}. 

1400 ''' 

1401 ll = self.copy(deep=deep) 

1402 _ = ll.normal() 

1403 if name: 

1404 ll.rename(name) 

1405 return ll 

1406 

1407 def toNvector(self, h=None, Nvector=None, **Nvector_kwds): 

1408 '''Convert this point to C{n-vector} (normal to the earth's surface) 

1409 components, I{including height}. 

1410 

1411 @kwarg h: Optional height, overriding this point's 

1412 height (C{meter}). 

1413 @kwarg Nvector: Optional class to return the C{n-vector} 

1414 components (C{Nvector}) or C{None}. 

1415 @kwarg Nvector_kwds_wrap: Optional, additional B{C{Nvector}} 

1416 keyword arguments, ignored if C{B{Nvector} 

1417 is None}. 

1418 

1419 @return: A B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} 

1420 if B{C{Nvector}} is C{None}. 

1421 

1422 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}. 

1423 ''' 

1424 return self.toVector(Vector=Nvector, h=self.height if h is None else h, 

1425 ll=self, **Nvector_kwds) 

1426 

1427 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected 

1428 '''Convert this point to a "lat, lon[, +/-height]" string, formatted 

1429 in the given C{B{form}at}. 

1430 

1431 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see 

1432 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}. 

1433 @kwarg joined: Separator to join the lat-, longitude and heigth 

1434 strings (C{str} or C{None} or C{NN} for non-joined). 

1435 @kwarg m: Optional unit of the height (C{str}), use C{None} to 

1436 exclude height from the returned string. 

1437 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator}, 

1438 B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword 

1439 arguments, see function L{pygeodesy.latDMS} or 

1440 L{pygeodesy.lonDMS}. 

1441 

1442 @return: This point in the specified C{B{form}at}, etc. (C{str} or 

1443 a 2- or 3-tuple C{(lat_str, lon_str[, height_str])} if 

1444 C{B{joined}=NN} or C{B{joined}=None}). 

1445 

1446 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more 

1447 details about keyword arguments C{B{form}at}, C{B{prec}ision}, 

1448 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}. 

1449 

1450 @example: 

1451 

1452 >>> LatLon(51.4778, -0.0016).toStr() # 51°28′40″N, 000°00′06″W 

1453 >>> LatLon(51.4778, -0.0016).toStr(F_D) # 51.4778°N, 000.0016°W 

1454 >>> LatLon(51.4778, -0.0016, 42).toStr() # 51°28′40″N, 000°00′06″W, +42.00m 

1455 ''' 

1456 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S), 

1457 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S)) 

1458 if self.height and m is not None: 

1459 t += (self.heightStr(m=m),) 

1460 return joined.join(t) if joined else t 

1461 

1462 def toVector(self, Vector=None, **Vector_kwds): 

1463 '''Convert this point to C{n-vector} (normal to the earth's 

1464 surface) components, I{ignoring height}. 

1465 

1466 @kwarg Vector: Optional class to return the C{n-vector} 

1467 components (L{Vector3d}) or C{None}. 

1468 @kwarg Vector_kwds: Optional, additional B{C{Vector}} 

1469 keyword arguments, ignored if 

1470 C{B{Vector} is None}. 

1471 

1472 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)} 

1473 if B{C{Vector}} is C{None}. 

1474 

1475 @raise TypeError: Invalid B{C{Vector}} or B{C{kwds}}. 

1476 

1477 @note: These are C{n-vector} x, y and z components, 

1478 I{NOT} geocentric (ECEF) x, y and z coordinates! 

1479 ''' 

1480 r = self._vector3tuple 

1481 if Vector is not None: 

1482 r = Vector(*r, **_xkwds(Vector_kwds, name=self.name)) 

1483 return r 

1484 

1485 def toVector3d(self): 

1486 '''Convert this point to C{n-vector} (normal to the earth's 

1487 surface) components, I{ignoring height}. 

1488 

1489 @return: Unit vector (L{Vector3d}). 

1490 

1491 @note: These are C{n-vector} x, y and z components, 

1492 I{NOT} geocentric (ECEF) x, y and z coordinates! 

1493 ''' 

1494 return self._vector3d # XXX .unit() 

1495 

1496 def toWm(self, **toWm_kwds): 

1497 '''Convert this point to a WM coordinate. 

1498 

1499 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments. 

1500 

1501 @return: The WM coordinate (L{Wm}). 

1502 

1503 @see: Function L{pygeodesy.toWm}. 

1504 ''' 

1505 return self._wm if not toWm_kwds else _MODS.webmercator.toWm( 

1506 self, **_xkwds(toWm_kwds, name=self.name)) 

1507 

1508 @deprecated_method 

1509 def to3xyz(self): # PYCHOK no cover 

1510 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector}, 

1511 L{toVector3d} or perhaps (geocentric) L{toEcef}.''' 

1512 return self.xyz # self.toVector() 

1513 

1514 @Property_RO 

1515 def _vector3d(self): 

1516 '''(INTERNAL) Cache for L{toVector3d}. 

1517 ''' 

1518 return self.toVector(Vector=Vector3d) # XXX .unit() 

1519 

1520 @Property_RO 

1521 def _vector3tuple(self): 

1522 '''(INTERNAL) Cache for L{toVector}. 

1523 ''' 

1524 return philam2n_xyz(self.phi, self.lam, name=self.name) 

1525 

1526 def vincentysTo(self, other, **radius_wrap): 

1527 '''Compute the distance between this and an other point using 

1528 U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>} 

1529 spherical formula. 

1530 

1531 @arg other: The other point (C{LatLon}). 

1532 @kwarg radius_wrap: Optional keyword arguments for function 

1533 L{pygeodesy.vincentys}, overriding the 

1534 default mean C{radius} of this point's 

1535 datum ellipsoid. 

1536 

1537 @return: Distance (C{meter}, same units as B{C{radius}}). 

1538 

1539 @raise TypeError: The B{C{other}} point is not C{LatLon}. 

1540 

1541 @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo}, 

1542 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

1543 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

1544 L{flatPolarTo}, L{haversineTo} and L{thomasTo}. 

1545 ''' 

1546 return self._distanceTo(vincentys, other, **_xkwds(radius_wrap, radius=None)) 

1547 

1548 @Property_RO 

1549 def _wm(self): 

1550 '''(INTERNAL) Get this point as webmercator (L{Wm}). 

1551 ''' 

1552 return _MODS.webmercator.toWm(self) 

1553 

1554 @Property_RO 

1555 def xyz(self): 

1556 '''Get the C{n-vector} X, Y and Z components (L{Vector3Tuple}C{(x, y, z)}) 

1557 

1558 @note: These are C{n-vector} x, y and z components, I{NOT} 

1559 geocentric (ECEF) x, y and z coordinates! 

1560 ''' 

1561 return self.toVector(Vector=Vector3Tuple) 

1562 

1563 @Property_RO 

1564 def xyzh(self): 

1565 '''Get the C{n-vector} X, Y, Z and H components (L{Vector4Tuple}C{(x, y, z, h)}) 

1566 

1567 @note: These are C{n-vector} x, y and z components, I{NOT} 

1568 geocentric (ECEF) x, y and z coordinates! 

1569 ''' 

1570 return self.xyz.to4Tuple(self.height) 

1571 

1572 

1573class _toCartesian3(object): # see also .geodesicw._wargs, .vector2d._numpy 

1574 '''(INTERNAL) Wrapper to convert 2 other points. 

1575 ''' 

1576 @contextmanager # <https://www.python.org/dev/peps/pep-0343/> Examples 

1577 def __call__(self, p, p2, p3, wrap, **kwds): 

1578 try: 

1579 if wrap: 

1580 p2, p3 = map1(_Wrap.point, p2, p3) 

1581 kwds = _xkwds(kwds, wrap=wrap) 

1582 yield (p. toCartesian().copy(name=_point_), # copy to rename 

1583 p._toCartesianEcef(up=4, point2=p2), 

1584 p._toCartesianEcef(up=4, point3=p3)) 

1585 except (AssertionError, TypeError, ValueError) as x: 

1586 raise _xError(x, point=p, point2=p2, point3=p3, **kwds) 

1587 

1588_toCartesian3 = _toCartesian3() # PYCHOK singleton 

1589 

1590 

1591def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, # MCCABE 13 

1592 radius=R_M, wrap=False): 

1593 '''(INTERNAL) Trilaterate three points by I{area overlap} or by 

1594 I{perimeter intersection} of three circles. 

1595 

1596 @note: The B{C{radius}} is only needed for both the n-vectorial 

1597 and C{sphericalTrigonometry.LatLon.distanceTo} methods and 

1598 silently ignored by the C{ellipsoidalExact}, C{-GeodSolve}, 

1599 C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods. 

1600 ''' 

1601 p2, p3, w = _unrollon3(p1, p2, p3, wrap) 

1602 

1603 r1 = Distance_(distance1=d1) 

1604 r2 = Distance_(distance2=d2) 

1605 r3 = Distance_(distance3=d3) 

1606 m = 0 if area else (r1 + r2 + r3) 

1607 pc = 0 

1608 t = [] 

1609 for _ in range(3): 

1610 try: # intersection of circle (p1, r1) and (p2, r2) 

1611 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w) 

1612 

1613 if area: # check overlap 

1614 if c1 is c2: # abutting 

1615 c = c1 

1616 else: # nearest point on radical 

1617 c = p3.nearestOn(c1, c2, within=True, wrap=w) 

1618 d = r3 - p3.distanceTo(c, radius=radius, wrap=w) 

1619 if d > eps: # sufficient overlap 

1620 t.append((d, c)) 

1621 m = max(m, d) 

1622 

1623 else: # check intersection 

1624 for c in ((c1,) if c1 is c2 else (c1, c2)): 

1625 d = fabs(r3 - p3.distanceTo(c, radius=radius, wrap=w)) 

1626 if d < eps: # below margin 

1627 t.append((d, c)) 

1628 m = min(m, d) 

1629 

1630 except IntersectionError as x: 

1631 if _concentric_ in str(x): # XXX ConcentricError? 

1632 pc += 1 

1633 

1634 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate 

1635 

1636 if t: # get min, max, points and count ... 

1637 t = tuple(sorted(t)) 

1638 n = len(t), # as 1-tuple 

1639 # ... or for a single trilaterated result, 

1640 # min *is* max, min- *is* maxPoint and n=1, 2 or 3 

1641 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...) 

1642 

1643 elif area and pc == 3: # all pairwise concentric ... 

1644 r, p = min((r1, p1), (r2, p2), (r3, p3)) 

1645 m = max(r1, r2, r3) 

1646 # ... return "smallest" point twice, the smallest 

1647 # and largest distance and n=0 for concentric 

1648 return Trilaterate5Tuple(float(r), p, float(m), p, 0) 

1649 

1650 n, f = (_overlap_, max) if area else (_intersection_, min) 

1651 t = _COMMASPACE_(_no_(n), '%s %.3g' % (f.__name__, m)) 

1652 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t) 

1653 

1654 

1655def _intersecend2(p, d, a, b, r, radius, height, exact): # in .ellipsoidalBas, .sphericalBase 

1656 '''(INTERNAL) Compute the intersecant2 end-result. 

1657 ''' 

1658 if d > EPS: 

1659 s, c = sincos2d(b - a) 

1660 s = sqrt_a(r, fabs(s * d)) 

1661 if s > r: 

1662 raise IntersectionError(_too_(Fmt.distant(s))) 

1663 elif (r - s) < EPS: 

1664 return p, p # tangent 

1665 c *= d 

1666 else: # p and c coincide 

1667 s, c = r, 0 

1668 t = () 

1669 for d, b in ((s + c, b), (s - c, b + _180_0)): # bearing direction first 

1670 t += (p.destination(d, b, radius=radius, height=height) if exact is None else 

1671 p.rhumbDestination(d, b, radius=radius, height=height, exact=exact)), 

1672 return t 

1673 

1674 

1675__all__ += _ALL_DOCS(LatLonBase) 

1676 

1677# **) MIT License 

1678# 

1679# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved. 

1680# 

1681# Permission is hereby granted, free of charge, to any person obtaining a 

1682# copy of this software and associated documentation files (the "Software"), 

1683# to deal in the Software without restriction, including without limitation 

1684# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1685# and/or sell copies of the Software, and to permit persons to whom the 

1686# Software is furnished to do so, subject to the following conditions: 

1687# 

1688# The above copyright notice and this permission notice shall be included 

1689# in all copies or substantial portions of the Software. 

1690# 

1691# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1692# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1693# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1694# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1695# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1696# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1697# OTHER DEALINGS IN THE SOFTWARE.