Coverage for pygeodesy/ellipsoidalNvector.py: 99%

123 statements  

« prev     ^ index     » next       coverage.py v7.2.2, created at 2023-04-12 11:45 -0400

1 

2# -*- coding: utf-8 -*- 

3 

4u'''Ellipsoidal, C{N-vector}-based geodesy. 

5 

6Ellipsoidal classes geodetic (lat-/longitude) L{LatLon}, geocentric 

7(ECEF) L{Cartesian}, DEPRECATED L{Ned} and L{Nvector} and functions 

8L{meanOf}, L{sumOf} and DEPRECATED L{toNed}. 

9 

10Pure Python implementation of n-vector-based geodetic (lat-/longitude) 

11methods by I{(C) Chris Veness 2011-2016} published under the same MIT 

12Licence**, see U{Vector-based geodesy 

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

14 

15These classes and functions work with: (a) geodesic (polar) lat-/longitude 

16points on the earth's surface and (b) 3-D vectors used as n-vectors 

17representing points on the earth's surface or vectors normal to the plane 

18of a great circle. 

19 

20See also Kenneth Gade U{'A Non-singular Horizontal Position Representation' 

21<https://www.NavLab.net/Publications/A_Nonsingular_Horizontal_Position_Representation.pdf>}, 

22The Journal of Navigation (2010), vol 63, nr 3, pp 395-417. 

23''' 

24# make sure int/int division yields float quotient, see .basics 

25from __future__ import division as _; del _ # PYCHOK semicolon 

26 

27from pygeodesy.basics import issubclassof, map2, _xinstanceof 

28from pygeodesy.datums import _ellipsoidal_datum, _spherical_datum, _WGS84 

29# from pygeodesy.dms import toDMS # _MODS 

30from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, _TOL_M, \ 

31 LatLonEllipsoidalBase, _nearestOn 

32from pygeodesy.errors import _IsnotError, _xkwds 

33# from pygeodesy.fmath import fdot # from .nvectorBase 

34from pygeodesy.interns import NN, _Nv00_, _COMMASPACE_ 

35from pygeodesy.interns import _down_, _east_, _north_, _pole_ # PYCHOK used! 

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

37# from pygeodesy.ltp import Ltp # _MODS 

38from pygeodesy.ltpTuples import Aer as _Aer, Ned as _Ned, Ned4Tuple, \ 

39 sincos2d_, _xnamed 

40# from pygeodesy.named import _xnamed # from .ltpTuples 

41from pygeodesy.nvectorBase import fabs, fdot, NorthPole, LatLonNvectorBase, \ 

42 NvectorBase, sumOf as _sumOf 

43from pygeodesy.props import deprecated_class, deprecated_function, \ 

44 deprecated_method, Property_RO 

45from pygeodesy.streprs import Fmt, fstr, _xzipairs 

46from pygeodesy.units import Bearing, Distance, Height, Scalar 

47# from pygeodesy.utily import sincos2d_ # from .ltpTuples 

48 

49# from math import fabs # from .nvectorBase 

50 

51__all__ = _ALL_LAZY.ellipsoidalNvector 

52__version__ = '23.04.11' 

53 

54 

55class Ned(_Ned): 

56 '''DEPRECATED, use class L{pygeodesy.Ned}.''' 

57 

58 def __init__(self, north, east, down, name=NN): 

59 deprecated_class(self.__class__) 

60 _Ned.__init__(self, north, east, down, name=name) 

61 

62 @deprecated_method # PYCHOK expected 

63 def toRepr(self, prec=None, fmt=Fmt.SQUARE, sep=_COMMASPACE_, **unused): 

64 '''DEPRECATED, use class L{pygeodesy.Ned}. 

65 

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

67 @kwarg fmt: Enclosing backets format (C{str}). 

68 @kwarg sep: Separator between NEDs (C{str}). 

69 

70 @return: This Ned as "[L:f, B:degrees360, E:degrees90]" (C{str}) 

71 with length or slantrange C{L}, bearing or azimuth C{B} 

72 and elevation C{E}. 

73 ''' 

74 dms = _MODS.dms 

75 t = (fstr(self.slantrange, prec=3 if prec is None else prec), 

76 dms.toDMS(self.azimuth, form=dms.F_D, prec=prec, ddd=0), 

77 dms.toDMS(self.elevation, form=dms.F_D, prec=prec, ddd=0)) 

78 return _xzipairs('LBE', t, sep=sep, fmt=fmt) 

79 

80 

81class Cartesian(CartesianEllipsoidalBase): 

82 '''Extended to convert geocentric, L{Cartesian} points to 

83 L{Nvector} and n-vector-based, geodetic L{LatLon}. 

84 ''' 

85 @Property_RO 

86 def Ecef(self): 

87 '''Get the ECEF I{class} (L{EcefVeness}), I{lazily}. 

88 ''' 

89 return _MODS.ecef.EcefVeness 

90 

91 def toLatLon(self, **LatLon_and_kwds): # PYCHOK LatLon=LatLon, datum=None 

92 '''Convert this cartesian to an C{Nvector}-based geodetic point. 

93 

94 @kwarg LatLon_and_kwds: Optional L{LatLon}, B{C{datum}} and other 

95 keyword arguments. Use C{B{LatLon}=...} to 

96 override this L{LatLon} class or specify 

97 C{B{LatLon} is None}. 

98 

99 @return: The geodetic point (L{LatLon}) or if B{C{LatLon}} is set 

100 to C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, 

101 C, M, datum)} with C{C} and C{M} if available. 

102 

103 @raise TypeError: Invalid B{C{LatLon_and_kwds}}. 

104 ''' 

105 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon, datum=self.datum) 

106 return CartesianEllipsoidalBase.toLatLon(self, **kwds) 

107 

108 def toNvector(self, **Nvector_and_kwds): # PYCHOK Datums.WGS84 

109 '''Convert this cartesian to L{Nvector} components, I{including height}. 

110 

111 @kwarg Nvector_and_kwds: Optional L{Nvector}, B{C{datum}} and other 

112 keyword arguments. Use C{B{Nvector}=...} to 

113 override this L{Nvector} class or specify 

114 C{B{Nvector} is None}. 

115 

116 @return: The C{n-vector} components (L{Nvector}) or if B{C{Nvector}} 

117 is set to C{None}, a L{Vector4Tuple}C{(x, y, z, h)} 

118 

119 @raise TypeError: Invalid B{C{Nvector_and_kwds}}. 

120 

121 @example: 

122 

123 >>> from ellipsoidalNvector import LatLon 

124 >>> c = Cartesian(3980581, 97, 4966825) 

125 >>> n = c.toNvector() # (0.62282, 0.000002, 0.78237, +0.24) 

126 ''' 

127 kwds = _xkwds(Nvector_and_kwds, Nvector=Nvector, datum=self.datum) 

128 return CartesianEllipsoidalBase.toNvector(self, **kwds) 

129 

130 

131class LatLon(LatLonNvectorBase, LatLonEllipsoidalBase): 

132 '''An n-vector-based, ellipsoidal L{LatLon} point. 

133 

134 @example: 

135 

136 >>> from ellipsoidalNvector import LatLon 

137 >>> p = LatLon(52.205, 0.119) # height=0, datum=Datums.WGS84 

138 ''' 

139 _Nv = None # cached toNvector (L{Nvector}) 

140 

141 def _update(self, updated, *attrs, **setters): # PYCHOK args 

142 '''(INTERNAL) Zap cached attributes if updated. 

143 ''' 

144 if updated: 

145 LatLonNvectorBase._update(self, updated, _Nv=self._Nv) # special case 

146 LatLonEllipsoidalBase._update(self, updated, *attrs, **setters) 

147 

148# def crossTrackDistanceTo(self, start, end, radius=R_M): 

149# '''Return the (signed) distance from this point to the great 

150# circle defined by a start point and an end point or bearing. 

151# 

152# @arg start: Start point of great circle line (L{LatLon}). 

153# @arg end: End point of great circle line (L{LatLon}) or 

154# initial bearing (compass C{degrees360}) at the 

155# start point. 

156# @kwarg radius: Mean earth radius (C{meter}). 

157# 

158# @return: Distance to great circle, negative if to left or 

159# positive if to right of line (C{meter}, same units 

160# as B{C{radius}}). 

161# 

162# @raise TypeError: If B{C{start}} or B{C{end}} point is not L{LatLon}. 

163# 

164# @example: 

165# 

166# >>> p = LatLon(53.2611, -0.7972) 

167# 

168# >>> s = LatLon(53.3206, -1.7297) 

169# >>> b = 96.0 

170# >>> d = p.crossTrackDistanceTo(s, b) # -305.7 

171# 

172# >>> e = LatLon(53.1887, 0.1334) 

173# >>> d = p.crossTrackDistanceTo(s, e) # -307.5 

174# ''' 

175# self.others(start=start) 

176# 

177# if isscalar(end): # gc from point and bearing 

178# gc = start.greatCircle(end) 

179# else: # gc by two points 

180# gc = start.toNvector().cross(end.toNvector()) 

181# 

182# # (signed) angle between point and gc normal vector 

183# v = self.toNvector() 

184# a = gc.angleTo(v, vSign=v.cross(gc)) 

185# a = (-PI_2 - a) if a < 0 else (PI_2 - a) 

186# return a * float(radius) 

187 

188 def deltaTo(self, other, Ned=Ned): 

189 '''Calculate the local delta from this to an other point. 

190 

191 @note: This is a linear delta, I{unrelated} to a geodesic 

192 on the ellipsoid. 

193 

194 @arg other: The other point (L{LatLon}). 

195 @kwarg Ned: Class to use (L{pygeodesy.Ned} or 

196 L{pygeodesy.Ned4Tuple}), overriding the 

197 default DEPRECATED L{Ned}. 

198 

199 @return: Delta from this to the other point (B{C{Ned}}). 

200 

201 @raise TypeError: The B{C{other}} point is not L{LatLon} or 

202 B{C{Ned}} is not L{pygeodesy.Ned} nor 

203 L{pygeodesy.Ned4Tuple} nor DEPRECATED L{Ned}. 

204 

205 @raise ValueError: If ellipsoids are incompatible. 

206 

207 @example: 

208 

209 >>> a = LatLon(49.66618, 3.45063) 

210 >>> b = LatLon(48.88667, 2.37472) 

211 >>> delta = a.deltaTo(b) # [N:-86126, E:-78900, D:1069] 

212 >>> d = delta.length # 116807.681 m 

213 >>> b = delta.bearing # 222.493° 

214 >>> e = delta.elevation # -0.5245° 

215 ''' 

216 self.ellipsoids(other) # throws TypeError and ValueError 

217 

218 # get delta in cartesian frame 

219 dc = other.toCartesian().minus(self.toCartesian()) 

220 # rotate dc to get delta in n-vector reference 

221 # frame using the rotation matrix row vectors 

222 ned_ = map2(dc.dot, self._rotation3) 

223 if issubclassof(Ned, Ned4Tuple): 

224 ned_ += (_MODS.ltp.Ltp(self, ecef=self.Ecef(self.datum)),) 

225 elif not issubclassof(Ned, _Ned): 

226 raise _IsnotError(Fmt.sub_class(_Ned, Ned4Tuple), Ned=Ned) 

227 return Ned(*ned_, name=self.name) 

228 

229# def destination(self, distance, bearing, radius=R_M, height=None): 

230# '''Return the destination point after traveling from this 

231# point the given distance on the given initial bearing. 

232# 

233# @arg distance: Distance traveled (C{meter}, same units as 

234# given earth B{C{radius}}). 

235# @arg bearing: Initial bearing (compass C{degrees360}). 

236# @kwarg radius: Mean earth radius (C{meter}). 

237# @kwarg height: Optional height at destination point, 

238# overriding default (C{meter}, same units 

239# as B{C{radius}}). 

240# 

241# @return: Destination point (L{LatLon}). 

242# 

243# @example: 

244# 

245# >>> p = LatLon(51.4778, -0.0015) 

246# >>> q = p.destination(7794, 300.7) 

247# >>> q.toStr() # '51.5135°N, 000.0983°W' ? 

248# ''' 

249# r = _angular(distance, radius) # angular distance in radians 

250# # great circle by starting from this point on given bearing 

251# gc = self.greatCircle(bearing) 

252# 

253# v1 = self.toNvector() 

254# x = v1.times(cos(r)) # component of v2 parallel to v1 

255# y = gc.cross(v1).times(sin(r)) # component of v2 perpendicular to v1 

256# 

257# v2 = x.plus(y).unit() 

258# return v2.toLatLon(height=self.height if height is C{None} else height) 

259 

260 def destinationNed(self, delta): 

261 '''Calculate the destination point using the supplied NED delta 

262 from this point. 

263 

264 @arg delta: Delta from this to the other point in the local 

265 tangent plane (LTP) of this point (L{Ned}). 

266 

267 @return: Destination point (L{LatLon}). 

268 

269 @raise TypeError: If B{C{delta}} is not L{pygeodesy.Ned} or 

270 DEPRECATED L{Ned}. 

271 

272 @example: 

273 

274 >>> a = LatLon(49.66618, 3.45063) 

275 >>> delta = Ned(-86126, -78900, 1069) # from Aer(222.493, -0.5245, 116807.681) 

276 >>> b = a.destinationNed(delta) # 48.886669°N, 002.374721°E or 48°53′12.01″N, 002°22′29.0″E +0.20m 

277 ''' 

278 _xinstanceof(_Ned, delta=delta) 

279 

280 nv, ev, dv = self._rotation3 

281 # convert NED delta to standard coordinate frame of n-vector 

282 dn = delta.ned 

283 # rotate dn to get delta in cartesian (ECEF) coordinate 

284 # reference frame using the rotation matrix column vectors 

285 dc = Cartesian(fdot(dn, nv.x, ev.x, dv.x), 

286 fdot(dn, nv.y, ev.y, dv.y), 

287 fdot(dn, nv.z, ev.z, dv.z)) 

288 

289 # apply (cartesian) delta to this Cartesian to obtain destination as cartesian 

290 v = self.toCartesian().plus(dc) 

291 return v.toLatLon(datum=self.datum, LatLon=self.classof) # Cartesian(v.x, v.y, v.z).toLatLon(...) 

292 

293 def distanceTo(self, other, radius=None, wrap=False): 

294 '''I{Approximate} the distance from this to an other point. 

295 

296 @arg other: The other point (L{LatLon}). 

297 @kwarg radius: Mean earth radius, ellipsoid or datum 

298 (C{meter}, L{Ellipsoid}, L{Ellipsoid2}, 

299 L{Datum} or L{a_f2Tuple}), overriding the 

300 mean radius C{R1} of this point's datum.. 

301 @kwarg wrap: Wrap/unroll the angular distance (C{bool}). 

302 

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

304 

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

306 

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

308 

309 @example: 

310 

311 >>> p = LatLon(52.205, 0.119) 

312 >>> q = LatLon(48.857, 2.351); 

313 >>> d = p.distanceTo(q) # 404300 

314 ''' 

315 self.others(other) 

316 

317 a = self._N_vector.angleTo(other._N_vector, wrap=wrap) 

318 d = self.datum if radius is None else _spherical_datum(radius) 

319 return fabs(a) * d.ellipsoid.R1 # see .utily.radians2m 

320 

321 @Property_RO 

322 def Ecef(self): 

323 '''Get the ECEF I{class} (L{EcefVeness}), I{lazily}. 

324 ''' 

325 return _MODS.ecef.EcefVeness 

326 

327 @deprecated_method 

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

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

330 ''' 

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

332 

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

334 '''Compare this point with an other point. 

335 

336 @arg other: The other point (L{LatLon}). 

337 @kwarg eps: Optional margin (C{float}). 

338 

339 @return: C{True} if points are identical, including 

340 datum, I{ignoring height}, C{False} otherwise. 

341 

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

343 

344 @raise ValueError: Invalid B{C{eps}}. 

345 

346 @see: Method C{isequalTo3} to include I{height}. 

347 

348 @example: 

349 

350 >>> p = LatLon(52.205, 0.119) 

351 >>> q = LatLon(52.205, 0.119) 

352 >>> e = p.isequalTo(q) # True 

353 ''' 

354 return LatLonEllipsoidalBase.isequalTo(self, other, eps=eps) \ 

355 if self.datum == other.datum else False 

356 

357# def greatCircle(self, bearing): 

358# '''Return the great circle heading on the given bearing 

359# from this point. 

360# 

361# Direction of vector is such that initial bearing vector 

362# b = c × p, where p is representing this point. 

363# 

364# @arg bearing: Bearing from this point (compass C{degrees360}). 

365# 

366# @return: N-vector representing great circle (L{Nvector}). 

367# 

368# @example: 

369# 

370# >>> p = LatLon(53.3206, -1.7297) 

371# >>> g = p.greatCircle(96.0) 

372# >>> g.toStr() # '(-0.794, 0.129, 0.594)' 

373# ''' 

374# a, b, _ = self.philamheight 

375# t = radians(bearing) 

376# 

377# sa, ca, sb, cb, st, ct = sincos2_(a, b, t) 

378# return self._xnamed(Nvector(sb * ct - sa * cb * st, 

379# -cb * ct - sa * sb * st, 

380# ca * st) 

381 

382# def initialBearingTo(self, other): 

383# '''Return the initial bearing (forward azimuth) from this 

384# to an other point. 

385# 

386# @arg other: The other point (L{LatLon}). 

387# 

388# @return: Initial bearing (compass C{degrees360}). 

389# 

390# @raise TypeError: The B{C{other}} point is not L{LatLon}. 

391# 

392# @example: 

393# 

394# >>> p1 = LatLon(52.205, 0.119) 

395# >>> p2 = LatLon(48.857, 2.351) 

396# >>> b = p1.bearingTo(p2) # 156.2 

397# ''' 

398# self.others(other) 

399# 

400# v1 = self.toNvector() 

401# v2 = other.toNvector() 

402# 

403# gc1 = v1.cross(v2) # gc through v1 & v2 

404# gc2 = v1.cross(_NP3) # gc through v1 & North pole 

405# 

406# # bearing is (signed) angle between gc1 & gc2 

407# return degrees360(gc1.angleTo(gc2, vSign=v1)) 

408 

409 def intermediateTo(self, other, fraction, height=None, **unused): # PYCHOK wrap=False 

410 '''Return the point at given fraction between this and 

411 an other point. 

412 

413 @arg other: The other point (L{LatLon}). 

414 @arg fraction: Fraction between both points (C{scalar}, 

415 0.0 at this to 1.0 at the other point. 

416 @kwarg height: Optional height, overriding the fractional 

417 height (C{meter}). 

418 

419 @return: Intermediate point (L{LatLon}). 

420 

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

422 

423 @example: 

424 

425 >>> p = LatLon(52.205, 0.119) 

426 >>> q = LatLon(48.857, 2.351) 

427 >>> p = p.intermediateTo(q, 0.25) # 51.3721°N, 000.7073°E 

428 ''' 

429 self.others(other) 

430 

431 f = Scalar(fraction=fraction) 

432 i = self.toNvector().intermediateTo(other.toNvector(), f) 

433 

434 h = self._havg(other, f=f) if height is None else Height(height) 

435 return i.toLatLon(height=h, LatLon=self.classof) # Nvector(i.x, i.y, i.z).toLatLon(...) 

436 

437 @Property_RO 

438 def _rotation3(self): 

439 '''(INTERNAL) Get the rotation matrix from n-vector coordinate frame axes. 

440 ''' 

441 nv = self.toNvector() # local (n-vector) coordinate frame 

442 

443 dv = nv.negate() # down, opposite to n-vector 

444 ev = NorthPole.cross(nv, raiser=_pole_).unit() # east, pointing perpendicular to the plane 

445 nv = ev.cross(dv) # north, by right hand rule 

446 return nv, ev, dv # matrix rows 

447 

448 def toCartesian(self, **Cartesian_and_kwds): # PYCHOK Cartesian=Cartesian, datum=None 

449 '''Convert this point to an C{Nvector}-based geodetic point. 

450 

451 @kwarg Cartesian_and_kwds: Optional L{Cartesian}, B{C{datum}} and other 

452 keyword arguments. Use C{B{Cartesian}=...} 

453 to override this L{Cartesian} class or specify 

454 C{B{Cartesian} is None}. 

455 

456 @return: The geodetic point (L{Cartesian}) or if B{C{Cartesian}} is set 

457 to C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, 

458 datum)} with C{C} and C{M} if available. 

459 

460 @raise TypeError: Invalid B{C{Cartesian}} or other B{C{Cartesian_and_kwds}}. 

461 ''' 

462 kwds = _xkwds(Cartesian_and_kwds, Cartesian=Cartesian, datum=self.datum) 

463 return LatLonEllipsoidalBase.toCartesian(self, **kwds) 

464 

465 def toNvector(self, **Nvector_and_kwds): # PYCHOK signature 

466 '''Convert this point to L{Nvector} components, I{including height}. 

467 

468 @kwarg Nvector_and_kwds: Optional L{Nvector}, B{C{datum}} and other 

469 keyword arguments. Use C{B{Nvector}=...} 

470 to override this L{Nvector} class or specify 

471 C{B{Nvector} is None}. 

472 

473 @return: The C{n-vector} components (L{Nvector}) or if B{C{Nvector}} 

474 is set to C{None}, a L{Vector4Tuple}C{(x, y, z, h)}. 

475 

476 @raise TypeError: Invalid B{C{Nvector}} or other B{C{Nvector_and_kwds}}. 

477 

478 @example: 

479 

480 >>> p = LatLon(45, 45) 

481 >>> n = p.toNvector() 

482 >>> n.toStr() # [0.50, 0.50, 0.70710] 

483 ''' 

484 kwds = _xkwds(Nvector_and_kwds, Nvector=Nvector, datum=self.datum) 

485 return LatLonNvectorBase.toNvector(self, **kwds) 

486 

487 

488_Nvll = LatLon(0, 0, name=_Nv00_) # reference instance (L{LatLon}) 

489 

490 

491class Nvector(NvectorBase): 

492 '''An n-vector is a position representation using a (unit) vector 

493 normal to the earth ellipsoid. Unlike lat-/longitude points, 

494 n-vectors have no singularities or discontinuities. 

495 

496 For many applications, n-vectors are more convenient to work 

497 with than other position representations like lat-/longitude, 

498 earth-centred earth-fixed (ECEF) vectors, UTM coordinates, etc. 

499 

500 Note commonality with L{sphericalNvector.Nvector}. 

501 ''' 

502 _datum = _WGS84 # default datum (L{Datum}) 

503 

504 def __init__(self, x_xyz, y=None, z=None, h=0, datum=None, ll=None, name=NN): 

505 '''New n-vector normal to the earth's surface. 

506 

507 @arg x_xyz: X component of vector (C{scalar}) or (3-D) vector 

508 (C{Nvector}, L{Vector3d}, L{Vector3Tuple} or 

509 L{Vector4Tuple}). 

510 @kwarg y: Y component of vector (C{scalar}), ignored if B{C{x_xyz}} 

511 is not C{scalar}, otherwise same units as B{C{x_xyz}}. 

512 @kwarg z: Z component of vector (C{scalar}), ignored if B{C{x_xyz}} 

513 is not C{scalar}, otherwise same units as B{C{x_xyz}}. 

514 @kwarg h: Optional height above model surface (C{meter}). 

515 @kwarg datum: Optional datum this n-vector is defined in 

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

517 L{a_f2Tuple}). 

518 @kwarg ll: Optional, original latlon (C{LatLon}). 

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

520 

521 @raise TypeError: If B{C{datum}} is not a L{Datum}. 

522 

523 @example: 

524 

525 >>> from ellipsoidalNvector import Nvector 

526 >>> v = Nvector(0.5, 0.5, 0.7071, 1) 

527 >>> v.toLatLon() # 45.0°N, 045.0°E, +1.00m 

528 ''' 

529 NvectorBase.__init__(self, x_xyz, y=y, z=z, h=h, ll=ll, name=name) 

530 if datum not in (None, self._datum): 

531 self._datum = _ellipsoidal_datum(datum, name=name) 

532 

533 @Property_RO 

534 def datum(self): 

535 '''Get this n-vector's datum (L{Datum}). 

536 ''' 

537 return self._datum 

538 

539 def toCartesian(self, **Cartesian_and_kwds): # PYCHOK Cartesian=Cartesian 

540 '''Convert this n-vector to C{Nvector}-based cartesian (ECEF) coordinates. 

541 

542 @kwarg Cartesian_and_kwds: Optional L{Cartesian}, B{C{h}}, B{C{datum}} and 

543 other keyword arguments. Use C{B{Cartesian}=...} 

544 to override this L{Cartesian} class or specify 

545 C{B{Cartesian} is None}. 

546 

547 @return: The cartesian point (L{Cartesian}) or if B{C{Cartesian}} is set 

548 to C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, 

549 datum)} with C{C} and C{M} if available. 

550 

551 @raise TypeError: Invalid B{C{Cartesian_and_kwds}}. 

552 

553 @example: 

554 

555 >>> v = Nvector(0.5, 0.5, 0.7071) 

556 >>> c = v.toCartesian() # [3194434, 3194434, 4487327] 

557 >>> p = c.toLatLon() # 45.0°N, 45.0°E 

558 ''' 

559 kwds = _xkwds(Cartesian_and_kwds, h=self.h, Cartesian=Cartesian, 

560 datum=self.datum) 

561 return NvectorBase.toCartesian(self, **kwds) # class or .classof 

562 

563 def toLatLon(self, **LatLon_and_kwds): # PYCHOK height=None, LatLon=LatLon 

564 '''Convert this n-vector to an C{Nvector}-based geodetic point. 

565 

566 @kwarg LatLon_and_kwds: Optional L{LatLon}, B{C{height}}, B{C{datum}} 

567 and other keyword arguments. Use C{B{LatLon}=...} 

568 to override this L{LatLon} class or specify 

569 C{B{LatLon} is None}. 

570 

571 @return: The geodetic point (L{LatLon}) or if B{C{LatLon}} is set 

572 to C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, 

573 C, M, datum)} with C{C} and C{M} if available. 

574 

575 @raise TypeError: Invalid B{C{LatLon_and_kwds}}. 

576 

577 @example: 

578 

579 >>> v = Nvector(0.5, 0.5, 0.7071) 

580 >>> p = v.toLatLon() # 45.0°N, 45.0°E 

581 ''' 

582 kwds = _xkwds(LatLon_and_kwds, height=self.h, datum=self.datum, LatLon=LatLon) 

583 return NvectorBase.toLatLon(self, **kwds) # class or .classof 

584 

585 def unit(self, ll=None): 

586 '''Normalize this vector to unit length. 

587 

588 @kwarg ll: Optional, original latlon (C{LatLon}). 

589 

590 @return: Normalised vector (L{Nvector}). 

591 ''' 

592 u = NvectorBase.unit(self, ll=ll) 

593 if u.datum != self.datum: 

594 u._update(False, datum=self.datum) 

595 return u 

596 

597 

598def meanOf(points, datum=_WGS84, height=None, LatLon=LatLon, 

599 **LatLon_kwds): 

600 '''Compute the geographic mean of several points. 

601 

602 @arg points: Points to be averaged (L{LatLon}[]). 

603 @kwarg datum: Optional datum to use (L{Datum}). 

604 @kwarg height: Optional height at mean point, overriding 

605 the mean height (C{meter}). 

606 @kwarg LatLon: Optional class to return the mean point 

607 (L{LatLon}) or C{None}. 

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

609 keyword arguments, ignored if 

610 C{B{LatLon} is None}. 

611 

612 @return: Geographic mean point and mean height (B{C{LatLon}}) 

613 or if B{C{LatLon}} is C{None}, an L{Ecef9Tuple}C{(x, 

614 y, z, lat, lon, height, C, M, datum)} with C{C} and 

615 C{M} if available. 

616 

617 @raise ValueError: Insufficient number of B{C{points}}. 

618 ''' 

619 Ps = _Nvll.PointsIter(points) 

620 # geographic mean 

621 m = sumOf(p._N_vector for p in Ps.iterate(closed=False)) 

622 kwds = _xkwds(LatLon_kwds, height=height, datum=datum, 

623 LatLon=LatLon, name=meanOf.__name__) 

624 return m.toLatLon(**kwds) 

625 

626 

627def nearestOn(point, point1, point2, within=True, height=None, wrap=False, 

628 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds): 

629 '''Iteratively locate the closest point on the geodesic between 

630 two other (ellipsoidal) points. 

631 

632 @arg point: Reference point (C{LatLon}). 

633 @arg point1: Start point of the geodesic (C{LatLon}). 

634 @arg point2: End point of the geodesic (C{LatLon}). 

635 @kwarg within: If C{True} return the closest point I{between} 

636 B{C{point1}} and B{C{point2}}, otherwise the 

637 closest point elsewhere on the geodesic (C{bool}). 

638 @kwarg height: Optional height for the closest point (C{meter}, 

639 conventionally) or C{None} or C{False} for the 

640 interpolated height. If C{False}, the closest 

641 takes the heights of the points into account. 

642 @kwarg wrap: Wrap and unroll longitudes (C{bool}). 

643 @kwarg equidistant: An azimuthal equidistant projection (I{class} 

644 or function L{pygeodesy.equidistant}) or C{None} 

645 for the preferred C{B{point}.Equidistant}. 

646 @kwarg tol: Convergence tolerance (C{meter}). 

647 @kwarg LatLon: Optional class to return the closest point 

648 (L{LatLon}) or C{None}. 

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

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

651 

652 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon} 

653 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}. 

654 

655 @raise ImportError: Package U{geographiclib 

656 <https://PyPI.org/project/geographiclib>} 

657 not installed or not found. 

658 

659 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}} 

660 or B{C{point2}} or invalid B{C{equidistant}}. 

661 

662 @raise ValueError: No convergence for the B{C{tol}}. 

663 

664 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ 

665 calculating-intersection-of-two-circles>} and U{Karney's paper 

666 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME 

667 BOUNDARIES} for more details about the iteration algorithm. 

668 ''' 

669 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap, 

670 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds) 

671 

672 

673def sumOf(nvectors, Vector=Nvector, h=None, **Vector_kwds): 

674 '''Return the vectorial sum of two or more n-vectors. 

675 

676 @arg nvectors: Vectors to be added (L{Nvector}[]). 

677 @kwarg Vector: Optional class for the vectorial sum (L{Nvector}). 

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

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

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

681 

682 @return: Vectorial sum (B{C{Vector}}). 

683 

684 @raise VectorError: No B{C{nvectors}}. 

685 ''' 

686 return _sumOf(nvectors, Vector=Vector, h=h, **Vector_kwds) 

687 

688 

689@deprecated_function 

690def toNed(distance, bearing, elevation, Ned=Ned, name=NN): 

691 '''DEPRECATED, use L{pygeodesy.Aer}C{(bearing, elevation, 

692 distance).xyzLocal.toNed(B{Ned}, name=B{name})} or 

693 L{XyzLocal}C{(pygeodesy.Aer(bearing, elevation, 

694 distance)).toNed(B{Ned}, name=B{name})}. 

695 

696 Create an NED vector from distance, bearing and elevation 

697 (in local coordinate system). 

698 

699 @arg distance: NED vector length (C{meter}). 

700 @arg bearing: NED vector bearing (compass C{degrees360}). 

701 @arg elevation: NED vector elevation from local coordinate 

702 frame horizontal (C{degrees}). 

703 @kwarg Ned: Optional class to return the NED (C{Ned}) or 

704 C{None}. 

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

706 

707 @return: An NED vector equivalent to this B{C{distance}}, 

708 B{C{bearing}} and B{C{elevation}} (DEPRECATED L{Ned}) 

709 or a DEPRECATED L{Ned3Tuple}C{(north, east, down)} 

710 if C{B{Ned} is None}. 

711 

712 @raise ValueError: Invalid B{C{distance}}, B{C{bearing}} 

713 or B{C{elevation}}. 

714 ''' 

715 if True: # use new Aer class 

716 n, e, d, _ = _Aer(bearing, elevation, distance).xyz4 

717 else: # DEPRECATED 

718 d = Distance(distance) 

719 

720 sb, cb, se, ce = sincos2d_(Bearing(bearing), 

721 Height(elevation=elevation)) 

722 n = cb * d * ce 

723 e = sb * d * ce 

724 d *= se 

725 

726 r = _MODS.deprecated.Ned3Tuple(n, e, -d) if Ned is None else \ 

727 Ned(n, e, -d) 

728 return _xnamed(r, name) 

729 

730 

731__all__ += _ALL_OTHER(Cartesian, LatLon, Ned, Nvector, # classes 

732 meanOf, sumOf, toNed) 

733 

734# **) MIT License 

735# 

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

737# 

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

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

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

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

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

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

744# 

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

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

747# 

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

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

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

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

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

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

754# OTHER DEALINGS IN THE SOFTWARE.