Coverage for pygeodesy/nvectorBase.py: 96%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''(INTERNAL) Private elliposiodal and spherical C{Nvector} base classes 

5L{LatLonNvectorBase} and L{NvectorBase} and function L{sumOf}. 

6 

7Pure Python implementation of C{n-vector}-based geodesy tools for ellipsoidal 

8earth models, transcoded from JavaScript originals by I{(C) Chris Veness 2005-2016} 

9and published under the same MIT Licence**, see U{Vector-based geodesy 

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

11''' 

12 

13# from pygeodesy.basics import map1 # from .namedTuples 

14from pygeodesy.constants import EPS, EPS1, EPS_2, R_M, _2_0, _N_2_0 

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

16from pygeodesy.errors import IntersectionError, _ValueError, VectorError, \ 

17 _xkwds, _xkwds_pop2 

18from pygeodesy.fmath import fdot, fidw, hypot_ # PYCHOK fdot shared 

19from pygeodesy.fsums import Fsum, fsumf_ 

20from pygeodesy.formy import _isequalTo, n_xyz2latlon, n_xyz2philam, \ 

21 _spherical_datum 

22# from pygeodesy.internals import _under # from .named 

23from pygeodesy.interns import NN, _1_, _2_, _3_, _bearing_, _coincident_, \ 

24 _COMMASPACE_, _distance_, _h_, _insufficient_, \ 

25 _intersection_, _no_, _NorthPole_, _point_, \ 

26 _pole_, _SPACE_, _SouthPole_ 

27from pygeodesy.latlonBase import LatLonBase, _ALL_DOCS, _ALL_LAZY, _MODS 

28# from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS # from .latlonBase 

29from pygeodesy.named import _xother3, _under 

30from pygeodesy.namedTuples import Trilaterate5Tuple, Vector3Tuple, \ 

31 Vector4Tuple, map1 

32from pygeodesy.props import deprecated_method, Property_RO, property_doc_, \ 

33 property_RO, _update_all 

34from pygeodesy.streprs import Fmt, hstr, unstr, _xattrs 

35from pygeodesy.units import Bearing, Height, Radius_, Scalar 

36from pygeodesy.utily import sincos2d, _unrollon, _unrollon3 

37from pygeodesy.vector3d import Vector3d, _xyzhdn3 

38 

39from math import fabs, sqrt 

40 

41__all__ = _ALL_LAZY.nvectorBase 

42__version__ = '24.05.13' 

43 

44 

45class NvectorBase(Vector3d): # XXX kept private 

46 '''Base class for ellipsoidal and spherical C{Nvector}s. 

47 ''' 

48 _datum = None # L{Datum}, overriden 

49 _h = Height(h=0) # height (C{meter}) 

50 _H = NN # height prefix (C{str}), '↑' in JS version 

51 

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

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

54 

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

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

57 L{Vector4Tuple}). 

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

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

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

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

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

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

64 @kwarg datum: Optional, I{pass-thru} datum (L{Datum}). 

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

66 

67 @raise TypeError: Non-scalar B{C{x}}, B{C{y}} or B{C{z}} 

68 coordinate or B{C{x}} not an C{Nvector}, 

69 L{Vector3Tuple} or L{Vector4Tuple} or 

70 invalid B{C{datum}}. 

71 ''' 

72 h, d, n = _xyzhdn3(x_xyz, h, datum, ll) 

73 Vector3d.__init__(self, x_xyz, y=y, z=z, ll=ll, name=name or n) 

74 if h: 

75 self.h = h 

76 if d is not None: 

77 self._datum = _spherical_datum(d, name=self.name) # pass-thru 

78 

79 @Property_RO 

80 def datum(self): 

81 '''Get the I{pass-thru} datum (C{Datum}) or C{None}. 

82 ''' 

83 return self._datum 

84 

85 @property_RO 

86 def Ecef(self): 

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

88 ''' 

89 NvectorBase.Ecef = E = _MODS.ecef.EcefKarney # overwrite property_RO 

90 return E 

91 

92 @property_RO 

93 def ellipsoidalNvector(self): 

94 '''Get the C{Nvector type} iff ellipsoidal, overloaded in L{pygeodesy.ellipsoidalNvector.Nvector}. 

95 ''' 

96 return False 

97 

98 @property_doc_(''' the height above surface (C{meter}).''') 

99 def h(self): 

100 '''Get the height above surface (C{meter}). 

101 ''' 

102 return self._h 

103 

104 @h.setter # PYCHOK setter! 

105 def h(self, h): 

106 '''Set the height above surface (C{meter}). 

107 

108 @raise TypeError: If B{C{h}} invalid. 

109 

110 @raise VectorError: If B{C{h}} invalid. 

111 ''' 

112 h = Height(h=h, Error=VectorError) 

113 if self._h != h: 

114 _update_all(self) 

115 self._h = h 

116 

117 @property_doc_(''' the height prefix (C{str}).''') 

118 def H(self): 

119 '''Get the height prefix (C{str}). 

120 ''' 

121 return self._H 

122 

123 @H.setter # PYCHOK setter! 

124 def H(self, H): 

125 '''Set the height prefix (C{str}). 

126 ''' 

127 self._H = str(H) if H else NN 

128 

129 def hStr(self, prec=-2, m=NN): 

130 '''Return a string for the height B{C{h}}. 

131 

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

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

134 

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

136 ''' 

137 return NN(self.H, hstr(self.h, prec=prec, m=m)) 

138 

139 @Property_RO 

140 def isEllipsoidal(self): 

141 '''Check whether this n-vector is ellipsoidal (C{bool} or C{None} if unknown). 

142 ''' 

143 return self.datum.isEllipsoidal if self.datum else None 

144 

145 @Property_RO 

146 def isSpherical(self): 

147 '''Check whether this n-vector is spherical (C{bool} or C{None} if unknown). 

148 ''' 

149 return self.datum.isSpherical if self.datum else None 

150 

151 @Property_RO 

152 def lam(self): 

153 '''Get the (geodetic) longitude in C{radians} (C{float}). 

154 ''' 

155 return self.philam.lam 

156 

157 @Property_RO 

158 def lat(self): 

159 '''Get the (geodetic) latitude in C{degrees} (C{float}). 

160 ''' 

161 return self.latlon.lat 

162 

163 @Property_RO 

164 def latlon(self): 

165 '''Get the (geodetic) lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}). 

166 ''' 

167 return n_xyz2latlon(self.x, self.y, self.z, name=self.name) 

168 

169 @Property_RO 

170 def latlonheight(self): 

171 '''Get the (geodetic) lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}). 

172 ''' 

173 return self.latlon.to3Tuple(self.h) 

174 

175 @Property_RO 

176 def latlonheightdatum(self): 

177 '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}). 

178 ''' 

179 return self.latlonheight.to4Tuple(self.datum) 

180 

181 @Property_RO 

182 def lon(self): 

183 '''Get the (geodetic) longitude in C{degrees} (C{float}). 

184 ''' 

185 return self.latlon.lon 

186 

187 @Property_RO 

188 def phi(self): 

189 '''Get the (geodetic) latitude in C{radians} (C{float}). 

190 ''' 

191 return self.philam.phi 

192 

193 @Property_RO 

194 def philam(self): 

195 '''Get the (geodetic) lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}). 

196 ''' 

197 return n_xyz2philam(self.x, self.y, self.z, name=self.name) 

198 

199 @Property_RO 

200 def philamheight(self): 

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

202 ''' 

203 return self.philam.to3Tuple(self.h) 

204 

205 @Property_RO 

206 def philamheightdatum(self): 

207 '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}). 

208 ''' 

209 return self.philamheight.to4Tuple(self.datum) 

210 

211 @property_RO 

212 def sphericalNvector(self): 

213 '''Get the C{Nvector type} iff spherical, overloaded in L{pygeodesy.sphericalNvector.Nvector}. 

214 ''' 

215 return False 

216 

217 @deprecated_method 

218 def to2ab(self): # PYCHOK no cover 

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

220 

221 @return: A L{PhiLam2Tuple}C{(phi, lam)}. 

222 ''' 

223 return self.philam 

224 

225 @deprecated_method 

226 def to3abh(self, height=None): # PYCHOK no cover 

227 '''DEPRECATED, use property L{philamheight} or C{philam.to3Tuple(B{height})}. 

228 

229 @kwarg height: Optional height, overriding this 

230 n-vector's height (C{meter}). 

231 

232 @return: A L{PhiLam3Tuple}C{(phi, lam, height)}. 

233 

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

235 ''' 

236 return self.philamheight if height in (None, self.h) else \ 

237 self.philam.to3Tuple(height) 

238 

239 def toCartesian(self, h=None, Cartesian=None, datum=None, **Cartesian_kwds): 

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

241 

242 @kwarg h: Optional height, overriding this n-vector's height (C{meter}). 

243 @kwarg Cartesian: Optional class to return the (ECEF) coordinates 

244 (C{Cartesian}). 

245 @kwarg datum: Optional datum (C{Datum}), overriding this datum. 

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

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

248 

249 @return: The cartesian (ECEF) coordinates (B{C{Cartesian}}) or 

250 if C{B{Cartesian} is None}, an L{Ecef9Tuple}C{(x, y, z, 

251 lat, lon, height, C, M, datum)} with C{C} and C{M} if 

252 available. 

253 

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

255 argument. 

256 

257 @raise ValueError: Invalid B{C{h}}. 

258 ''' 

259 D = _spherical_datum(datum or self.datum, name=self.name) 

260 E = D.ellipsoid 

261 h = self.h if h is None else Height(h) 

262 

263 x, y, z = self.x, self.y, self.z 

264 # Kenneth Gade eqn 22 

265 n = E.b / hypot_(x * E.a_b, y * E.a_b, z) 

266 r = h + n * E.a2_b2 

267 

268 x *= r 

269 y *= r 

270 z *= h + n 

271 

272 if Cartesian is None: 

273 r = self.Ecef(D).reverse(x, y, z, M=True) 

274 else: 

275 kwds = _xkwds(Cartesian_kwds, datum=D) # h=0 

276 r = Cartesian(x, y, z, **kwds) 

277 return self._xnamed(r) 

278 

279 @deprecated_method 

280 def to2ll(self): # PYCHOK no cover 

281 '''DEPRECATED, use property L{latlon}. 

282 

283 @return: A L{LatLon2Tuple}C{(lat, lon)}. 

284 ''' 

285 return self.latlon 

286 

287 @deprecated_method 

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

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

290 

291 @kwarg height: Optional height, overriding this 

292 n-vector's height (C{meter}). 

293 

294 @return: A L{LatLon3Tuple}C{(lat, lon, height)}. 

295 

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

297 ''' 

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

299 self.latlon.to3Tuple(height) 

300 

301 def toLatLon(self, height=None, LatLon=None, datum=None, **LatLon_kwds): 

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

303 

304 @kwarg height: Optional height, overriding this n-vector's 

305 height (C{meter}). 

306 @kwarg LatLon: Optional class to return the geodetic point 

307 (C{LatLon}) or C{None}. 

308 @kwarg datum: Optional, spherical datum (C{Datum}). 

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

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

311 

312 @return: The geodetic point (C{LatLon}) or if C{B{LatLon} is None}, 

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

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

315 

316 @raise TypeError: Invalid B{C{LatLon}} or B{C{LatLon_kwds}} 

317 argument. 

318 

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

320 ''' 

321 d = _spherical_datum(datum or self.datum, name=self.name) 

322 h = self.h if height is None else Height(height) 

323 # use self.Cartesian(Cartesian=None) for better accuracy of the height 

324 # than self.Ecef(d).forward(self.lat, self.lon, height=h, M=True) 

325 if LatLon is None: 

326 r = self.toCartesian(h=h, Cartesian=None, datum=d) 

327 else: 

328 kwds = _xkwds(LatLon_kwds, height=h, datum=d) 

329 r = self._xnamed(LatLon(self.lat, self.lon, **kwds)) 

330 return r 

331 

332 def toStr(self, prec=5, fmt=Fmt.PAREN, sep=_COMMASPACE_): # PYCHOK expected 

333 '''Return a string representation of this n-vector. 

334 

335 Height component is only included if non-zero. 

336 

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

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

339 @kwarg sep: Optional separator between components (C{str}). 

340 

341 @return: Comma-separated C{"(x, y, z [, h])"} enclosed in 

342 B{C{fmt}} brackets (C{str}). 

343 ''' 

344 t = Vector3d.toStr(self, prec=prec, fmt=NN, sep=sep) 

345 if self.h: 

346 t = sep.join((t, self.hStr())) 

347 return (fmt % (t,)) if fmt else t 

348 

349 def toVector3d(self, norm=True): 

350 '''Convert this n-vector to a 3-D vector, I{ignoring height}. 

351 

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

353 

354 @return: The (normalized) vector (L{Vector3d}). 

355 ''' 

356 v = Vector3d.unit(self) if norm else self 

357 return Vector3d(v.x, v.y, v.z, name=self.name) 

358 

359 @deprecated_method 

360 def to4xyzh(self, h=None): # PYCHOK no cover 

361 '''DEPRECATED, use property L{xyzh} or C{xyz.to4Tuple(B{h})}.''' 

362 return self.xyzh if h in (None, self.h) else Vector4Tuple( 

363 self.x, self.y, self.z, h, name=self.name) 

364 

365 def unit(self, ll=None): 

366 '''Normalize this n-vector to unit length. 

367 

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

369 

370 @return: Normalized vector (C{Nvector}). 

371 ''' 

372 return _xattrs(Vector3d.unit(self, ll=ll), _under(_h_)) 

373 

374 @Property_RO 

375 def xyzh(self): 

376 '''Get this n-vector's components (L{Vector4Tuple}C{(x, y, z, h)}) 

377 ''' 

378 return self.xyz.to4Tuple(self.h) 

379 

380 

381NorthPole = NvectorBase(0, 0, +1, name=_NorthPole_) # North pole (C{Nvector}) 

382SouthPole = NvectorBase(0, 0, -1, name=_SouthPole_) # South pole (C{Nvector}) 

383 

384 

385class _N_vector_(NvectorBase): 

386 '''(INTERNAL) Minimal, low-overhead C{n-vector}. 

387 ''' 

388 def __init__(self, x, y, z, h=0, name=NN): 

389 self._x, self._y, self._z = x, y, z 

390 if h: 

391 self._h = h 

392 if name: 

393 self.name = name 

394 

395 

396class LatLonNvectorBase(LatLonBase): 

397 '''(INTERNAL) Base class for n-vector-based ellipsoidal and 

398 spherical C{LatLon} classes. 

399 ''' 

400 

401 def _update(self, updated, *attrs, **setters): # PYCHOK _Nv=None 

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

403 

404 @see: C{ellipsoidalNvector.LatLon} and C{sphericalNvector.LatLon} 

405 for the special case of B{C{_Nv}}. 

406 ''' 

407 if updated: 

408 _Nv, setters = _xkwds_pop2(setters, _Nv=None) 

409 if _Nv is not None: 

410 if _Nv._fromll is not None: 

411 _Nv._fromll = None 

412 self._Nv = None 

413 LatLonBase._update(self, updated, *attrs, **setters) 

414 

415# def distanceTo(self, other, **kwds): # PYCHOK no cover 

416# '''I{Must be overloaded}.''' 

417# self._notOverloaded(other, **kwds) 

418 

419 def intersections2(self, radius1, other, radius2, **kwds): # PYCHOK expected 

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

421 self._notImplemented(radius1, other, radius2, **kwds) 

422 

423 def others(self, *other, **name_other_up): 

424 '''Refined class comparison. 

425 

426 @arg other: The other instance (C{LatLonNvectorBase}). 

427 @kwarg name_other_up: Overriding C{name=other} and C{up=1} 

428 keyword arguments. 

429 

430 @return: The B{C{other}} if compatible. 

431 

432 @raise TypeError: Incompatible B{C{other}} C{type}. 

433 ''' 

434 if other: 

435 other0 = other[0] 

436 if isinstance(other0, (self.__class__, LatLonNvectorBase)): # XXX NvectorBase? 

437 return other0 

438 

439 other, name, up = _xother3(self, other, **name_other_up) 

440 if not isinstance(other, (self.__class__, LatLonNvectorBase)): # XXX NvectorBase? 

441 LatLonBase.others(self, other, name=name, up=up + 1) 

442 return other 

443 

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

445 '''Convert this point to C{Nvector} components, I{including height}. 

446 

447 @kwarg Nvector_and_kwds: Optional C{Nvector} class and C{Nvector} keyword arguments, 

448 Specify C{B{Nvector}=...} to override this C{Nvector} class 

449 or use C{B{Nvector}=None}. 

450 

451 @return: An C{Nvector} or if C{Nvector is None}, a L{Vector4Tuple}C{(x, y, z, h)}. 

452 

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

454 ''' 

455 return LatLonBase.toNvector(self, **_xkwds(Nvector_and_kwds, Nvector=NvectorBase)) 

456 

457 def triangulate(self, bearing1, other, bearing2, height=None, wrap=False): # PYCHOK signature 

458 '''Locate a point given this, an other point and the (initial) bearing 

459 from this and the other point. 

460 

461 @arg bearing1: Bearing at this point (compass C{degrees360}). 

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

463 @arg bearing2: Bearing at the other point (compass C{degrees360}). 

464 @kwarg height: Optional height at the triangulated point, 

465 overriding the mean height (C{meter}). 

466 @kwarg wrap: If C{True}, use this and the B{C{other}} point 

467 I{normalized} (C{bool}). 

468 

469 @return: Triangulated point (C{LatLon}). 

470 

471 @raise TypeError: Invalid B{C{other}} point. 

472 

473 @raise Valuerror: Points coincide. 

474 ''' 

475 return _triangulate(self, bearing1, self.others(other), bearing2, 

476 height=height, wrap=wrap, LatLon=self.classof) 

477 

478 def trilaterate(self, distance1, point2, distance2, point3, distance3, 

479 radius=R_M, height=None, useZ=False, wrap=False): 

480 '''Locate a point at given distances from this and two other points. 

481 

482 @arg distance1: Distance to this point (C{meter}, same units 

483 as B{C{radius}}). 

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

485 @arg distance2: Distance to point2 (C{meter}, same units as 

486 B{C{radius}}). 

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

488 @arg distance3: Distance to point3 (C{meter}, same units as 

489 B{C{radius}}). 

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

491 @kwarg height: Optional height at trilaterated point, overriding 

492 the mean height (C{meter}, same units as B{C{radius}}). 

493 @kwarg useZ: Include Z component iff non-NaN, non-zero (C{bool}). 

494 @kwarg wrap: If C{True}, use this, B{C{point2}} and B{C{point3}} 

495 I{normalized} (C{bool}). 

496 

497 @return: Trilaterated point (C{LatLon}). 

498 

499 @raise IntersectionError: No intersection, trilateration failed. 

500 

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

502 

503 @raise ValueError: Some B{C{points}} coincide or invalid B{C{distance1}}, 

504 B{C{distance2}}, B{C{distance3}} or B{C{radius}}. 

505 

506 @see: U{Trilateration<https://WikiPedia.org/wiki/Trilateration>}, 

507 Veness' JavaScript U{Trilateration<https://www.Movable-Type.co.UK/ 

508 scripts/latlong-vectors.html>} and method C{LatLon.trilaterate5} 

509 of other, non-C{Nvector LatLon} classes. 

510 ''' 

511 return _trilaterate(self, distance1, self.others(point2=point2), distance2, 

512 self.others(point3=point3), distance3, 

513 radius=radius, height=height, useZ=useZ, 

514 wrap=wrap, LatLon=self.classof) 

515 

516 def trilaterate5(self, distance1, point2, distance2, point3, distance3, # PYCHOK signature 

517 area=False, eps=EPS1, radius=R_M, wrap=False): 

518 '''B{Not implemented} for C{B{area}=True} and falls back to method 

519 C{trilaterate} otherwise. 

520 

521 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)} 

522 with a single trilaterated intersection C{minPoint I{is} 

523 maxPoint}, C{min I{is} max} the nearest intersection 

524 margin and count C{n = 1}. 

525 

526 @raise NotImplementedError: Keyword argument C{B{area}=True} not 

527 (yet) supported. 

528 

529 @see: Method L{trilaterate} for other and more details. 

530 ''' 

531 if area: 

532 self._notImplemented(area=area) 

533 

534 t = _trilaterate(self, distance1, self.others(point2=point2), distance2, 

535 self.others(point3=point3), distance3, 

536 radius=radius, useZ=True, wrap=wrap, 

537 LatLon=self.classof) 

538 # ... and handle B{C{eps}} and C{IntersectionError} 

539 # like function C{.latlonBase._trilaterate5} 

540 d = self.distanceTo(t, radius=radius, wrap=wrap) # PYCHOK distanceTo 

541 d = min(fabs(distance1 - d), fabs(distance2 - d), fabs(distance3 - d)) 

542 if d < eps: # min is max, minPoint is maxPoint 

543 return Trilaterate5Tuple(d, t, d, t, 1) # n = 1 

544 t = _SPACE_(_no_(_intersection_), Fmt.PAREN(min.__name__, Fmt.f(d, prec=3))) 

545 raise IntersectionError(area=area, eps=eps, radius=radius, wrap=wrap, txt=t) 

546 

547 

548def _nsumOf(nvs, h_None, Vector, Vector_kwds): # .sphericalNvector, .vector3d 

549 '''(INTERNAL) Separated to allow callers to embellish exceptions. 

550 ''' 

551 X, Y, Z, n = Fsum(), Fsum(), Fsum(), 0 

552 H = Fsum() if h_None is None else n 

553 for n, v in enumerate(nvs or ()): # one pass 

554 X += v.x 

555 Y += v.y 

556 Z += v.z 

557 H += v.h 

558 if n < 1: 

559 raise ValueError(_SPACE_(Fmt.PARENSPACED(len=n), _insufficient_)) 

560 

561 x, y, z = map1(float, X, Y, Z) 

562 h = H.fover(n) if h_None is None else h_None 

563 return Vector3Tuple(x, y, z).to4Tuple(h) if Vector is None else \ 

564 Vector(x, y, z, **_xkwds(Vector_kwds, h=h)) 

565 

566 

567def sumOf(nvectors, Vector=None, h=None, **Vector_kwds): 

568 '''Return the I{vectorial} sum of two or more n-vectors. 

569 

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

571 @kwarg Vector: Optional class for the vectorial sum (C{Nvector}) 

572 or C{None}. 

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

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

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

576 

577 @return: Vectorial sum (B{C{Vector}}) or a L{Vector4Tuple}C{(x, y, 

578 z, h)} if B{C{Vector}} is C{None}. 

579 

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

581 ''' 

582 try: 

583 return _nsumOf(nvectors, h, Vector, Vector_kwds) 

584 except (TypeError, ValueError) as x: 

585 raise VectorError(nvectors=nvectors, Vector=Vector, cause=x) 

586 

587 

588def _triangulate(point1, bearing1, point2, bearing2, height=None, 

589 wrap=False, **LatLon_and_kwds): 

590 # (INTERNAL) Locate a point given two known points and initial 

591 # bearings from those points, see C{LatLon.triangulate} above 

592 

593 def _gc(p, b, _i_): 

594 n = p.toNvector() 

595 de = NorthPole.cross(n, raiser=_pole_).unit() # east vector @ n 

596 dn = n.cross(de) # north vector @ n 

597 s, c = sincos2d(Bearing(b, name=_bearing_ + _i_)) 

598 dest = de.times(s) 

599 dnct = dn.times(c) 

600 d = dnct.plus(dest) # direction vector @ n 

601 return n.cross(d) # great circle point + bearing 

602 

603 if wrap: 

604 point2 = _unrollon(point1, point2, wrap=wrap) 

605 if _isequalTo(point1, point2, eps=EPS): 

606 raise _ValueError(points=point2, wrap=wrap, txt=_coincident_) 

607 

608 gc1 = _gc(point1, bearing1, _1_) # great circle p1 + b1 

609 gc2 = _gc(point2, bearing2, _2_) # great circle p2 + b2 

610 

611 n = gc1.cross(gc2, raiser=_point_) # n-vector of intersection point 

612 h = point1._havg(point2, h=height) 

613 kwds = _xkwds(LatLon_and_kwds, height=h) 

614 return n.toLatLon(**kwds) # Nvector(n.x, n.y, n.z).toLatLon(...) 

615 

616 

617def _trilaterate(point1, distance1, point2, distance2, point3, distance3, 

618 radius=R_M, height=None, useZ=False, 

619 wrap=False, **LatLon_and_kwds): 

620 # (INTERNAL) Locate a point at given distances from 

621 # three other points, see LatLon.triangulate above 

622 

623 def _nr2(p, d, r, _i_, *qs): # .toNvector and angular distance squared 

624 for q in qs: 

625 if _isequalTo(p, q, eps=EPS): 

626 raise _ValueError(points=p, txt=_coincident_) 

627 return p.toNvector(), (Scalar(d, name=_distance_ + _i_) / r)**2 

628 

629 p1, r = point1, Radius_(radius) 

630 p2, p3, _ = _unrollon3(p1, point2, point3, wrap) 

631 

632 n1, r12 = _nr2(p1, distance1, r, _1_) 

633 n2, r22 = _nr2(p2, distance2, r, _2_, p1) 

634 n3, r32 = _nr2(p3, distance3, r, _3_, p1, p2) 

635 

636 # the following uses x,y coordinate system with origin at n1, x axis n1->n2 

637 y = n3.minus(n1) 

638 x = n2.minus(n1) 

639 z = None 

640 

641 d = x.length # distance n1->n2 

642 if d > EPS_2: # and y.length > EPS_2: 

643 X = x.unit() # unit vector in x direction n1->n2 

644 i = X.dot(y) # signed magnitude of x component of n1->n3 

645 Y = y.minus(X.times(i)).unit() # unit vector in y direction 

646 j = Y.dot(y) # signed magnitude of y component of n1->n3 

647 if fabs(j) > EPS_2: 

648 # courtesy of U{Carlos Freitas<https://GitHub.com/mrJean1/PyGeodesy/issues/33>} 

649 x = fsumf_(r12, -r22, d**2) / (d * _2_0) # n1->intersection x- and ... 

650 y = fsumf_(r12, -r32, i**2, j**2, x * i * _N_2_0) / (j * _2_0) # ... y-component 

651 # courtesy of U{AleixDev<https://GitHub.com/mrJean1/PyGeodesy/issues/43>} 

652 z = fsumf_(max(r12, r22, r32), -(x**2), -(y**2)) # XXX not just r12! 

653 if z > EPS: 

654 n = n1.plus(X.times(x)).plus(Y.times(y)) 

655 if useZ: # include Z component 

656 Z = X.cross(Y) # unit vector perpendicular to plane 

657 n = n.plus(Z.times(sqrt(z))) 

658 if height is None: 

659 h = fidw((point1.height, point2.height, point3.height), 

660 map1(fabs, distance1, distance2, distance3)) 

661 else: 

662 h = Height(height) 

663 kwds = _xkwds(LatLon_and_kwds, height=h) 

664 return n.toLatLon(**kwds) # Nvector(n.x, n.y, n.z).toLatLon(...) 

665 

666 # no intersection, d < EPS_2 or fabs(j) < EPS_2 or z < EPS 

667 t = _SPACE_(_no_, _intersection_, NN) 

668 raise IntersectionError(point1=point1, distance1=distance1, 

669 point2=point2, distance2=distance2, 

670 point3=point3, distance3=distance3, 

671 txt=unstr(t, z=z, useZ=useZ, wrap=wrap)) 

672 

673 

674__all__ += _ALL_DOCS(LatLonNvectorBase, NvectorBase, sumOf) # classes 

675 

676# **) MIT License 

677# 

678# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

679# 

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

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

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

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

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

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

686# 

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

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

689# 

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

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

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

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

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

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

696# OTHER DEALINGS IN THE SOFTWARE.