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 

22from pygeodesy.interns import NN, _1_, _2_, _3_, _bearing_, _coincident_, \ 

23 _COMMASPACE_, _distance_, _h_, _insufficient_, \ 

24 _intersection_, _no_, _NorthPole_, _point_, \ 

25 _pole_, _SPACE_, _SouthPole_, _under 

26from pygeodesy.latlonBase import LatLonBase, _ALL_DOCS, _ALL_LAZY, _MODS 

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

28from pygeodesy.named import _xother3 

29from pygeodesy.namedTuples import Trilaterate5Tuple, Vector3Tuple, \ 

30 Vector4Tuple, map1 

31from pygeodesy.props import deprecated_method, Property_RO, property_doc_, \ 

32 property_RO, _update_all 

33from pygeodesy.streprs import Fmt, hstr, unstr, _xattrs 

34from pygeodesy.units import Bearing, Height, Radius_, Scalar 

35from pygeodesy.utily import sincos2d, _unrollon, _unrollon3 

36from pygeodesy.vector3d import Vector3d, _xyzhdn3 

37 

38from math import fabs, sqrt 

39 

40__all__ = _ALL_LAZY.nvectorBase 

41__version__ = '24.04.07' 

42 

43 

44class NvectorBase(Vector3d): # XXX kept private 

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

46 ''' 

47 _datum = None # L{Datum}, overriden 

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

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

50 

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

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

53 

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

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

56 L{Vector4Tuple}). 

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

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

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

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

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

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

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

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

65 

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

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

68 L{Vector3Tuple} or L{Vector4Tuple} or 

69 invalid B{C{datum}}. 

70 ''' 

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

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

73 if h: 

74 self.h = h 

75 if d is not None: 

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

77 

78 @Property_RO 

79 def datum(self): 

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

81 ''' 

82 return self._datum 

83 

84 @property_RO 

85 def Ecef(self): 

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

87 ''' 

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

89 return E 

90 

91 @property_RO 

92 def ellipsoidalNvector(self): 

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

94 ''' 

95 return False 

96 

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

98 def h(self): 

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

100 ''' 

101 return self._h 

102 

103 @h.setter # PYCHOK setter! 

104 def h(self, h): 

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

106 

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

108 

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

110 ''' 

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

112 if self._h != h: 

113 _update_all(self) 

114 self._h = h 

115 

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

117 def H(self): 

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

119 ''' 

120 return self._H 

121 

122 @H.setter # PYCHOK setter! 

123 def H(self, H): 

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

125 ''' 

126 self._H = str(H) if H else NN 

127 

128 def hStr(self, prec=-2, m=NN): 

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

130 

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

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

133 

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

135 ''' 

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

137 

138 @Property_RO 

139 def isEllipsoidal(self): 

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

141 ''' 

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

143 

144 @Property_RO 

145 def isSpherical(self): 

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

147 ''' 

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

149 

150 @Property_RO 

151 def lam(self): 

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

153 ''' 

154 return self.philam.lam 

155 

156 @Property_RO 

157 def lat(self): 

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

159 ''' 

160 return self.latlon.lat 

161 

162 @Property_RO 

163 def latlon(self): 

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

165 ''' 

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

167 

168 @Property_RO 

169 def latlonheight(self): 

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

171 ''' 

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

173 

174 @Property_RO 

175 def latlonheightdatum(self): 

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

177 ''' 

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

179 

180 @Property_RO 

181 def lon(self): 

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

183 ''' 

184 return self.latlon.lon 

185 

186 @Property_RO 

187 def phi(self): 

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

189 ''' 

190 return self.philam.phi 

191 

192 @Property_RO 

193 def philam(self): 

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

195 ''' 

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

197 

198 @Property_RO 

199 def philamheight(self): 

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

201 ''' 

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

203 

204 @Property_RO 

205 def philamheightdatum(self): 

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

207 ''' 

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

209 

210 @property_RO 

211 def sphericalNvector(self): 

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

213 ''' 

214 return False 

215 

216 @deprecated_method 

217 def to2ab(self): # PYCHOK no cover 

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

219 

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

221 ''' 

222 return self.philam 

223 

224 @deprecated_method 

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

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

227 

228 @kwarg height: Optional height, overriding this 

229 n-vector's height (C{meter}). 

230 

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

232 

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

234 ''' 

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

236 self.philam.to3Tuple(height) 

237 

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

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

240 

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

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

243 (C{Cartesian}). 

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

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

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

247 

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

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

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

251 available. 

252 

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

254 argument. 

255 

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

257 ''' 

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

259 E = D.ellipsoid 

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

261 

262 x, y, z = self.x, self.y, self.z 

263 # Kenneth Gade eqn 22 

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

265 r = h + n * E.a2_b2 

266 

267 x *= r 

268 y *= r 

269 z *= h + n 

270 

271 if Cartesian is None: 

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

273 else: 

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

275 r = Cartesian(x, y, z, **kwds) 

276 return self._xnamed(r) 

277 

278 @deprecated_method 

279 def to2ll(self): # PYCHOK no cover 

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

281 

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

283 ''' 

284 return self.latlon 

285 

286 @deprecated_method 

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

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

289 

290 @kwarg height: Optional height, overriding this 

291 n-vector's height (C{meter}). 

292 

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

294 

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

296 ''' 

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

298 self.latlon.to3Tuple(height) 

299 

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

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

302 

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

304 height (C{meter}). 

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

306 (C{LatLon}) or C{None}. 

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

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

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

310 

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

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

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

314 

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

316 argument. 

317 

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

319 ''' 

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

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

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

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

324 if LatLon is None: 

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

326 else: 

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

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

329 return r 

330 

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

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

333 

334 Height component is only included if non-zero. 

335 

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

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

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

339 

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

341 B{C{fmt}} brackets (C{str}). 

342 ''' 

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

344 if self.h: 

345 t = sep.join((t, self.hStr())) 

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

347 

348 def toVector3d(self, norm=True): 

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

350 

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

352 

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

354 ''' 

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

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

357 

358 @deprecated_method 

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

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

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

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

363 

364 def unit(self, ll=None): 

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

366 

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

368 

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

370 ''' 

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

372 

373 @Property_RO 

374 def xyzh(self): 

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

376 ''' 

377 return self.xyz.to4Tuple(self.h) 

378 

379 

380NorthPole = NvectorBase(0, 0, +1, name=_NorthPole_) # North pole (C{Nvector}) 

381SouthPole = NvectorBase(0, 0, -1, name=_SouthPole_) # South pole (C{Nvector}) 

382 

383 

384class _N_vector_(NvectorBase): 

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

386 ''' 

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

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

389 if h: 

390 self._h = h 

391 if name: 

392 self.name = name 

393 

394 

395class LatLonNvectorBase(LatLonBase): 

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

397 spherical C{LatLon} classes. 

398 ''' 

399 

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

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

402 

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

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

405 ''' 

406 if updated: 

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

408 if _Nv is not None: 

409 if _Nv._fromll is not None: 

410 _Nv._fromll = None 

411 self._Nv = None 

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

413 

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

415# '''I{Must be overloaded}.''' 

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

417 

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

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

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

421 

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

423 '''Refined class comparison. 

424 

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

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

427 keyword arguments. 

428 

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

430 

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

432 ''' 

433 if other: 

434 other0 = other[0] 

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

436 return other0 

437 

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

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

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

441 return other 

442 

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

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

445 

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

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

448 or use C{B{Nvector}=None}. 

449 

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

451 

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

453 ''' 

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

455 

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

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

458 from this and the other point. 

459 

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

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

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

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

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

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

466 I{normalized} (C{bool}). 

467 

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

469 

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

471 

472 @raise Valuerror: Points coincide. 

473 ''' 

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

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

476 

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

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

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

480 

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

482 as B{C{radius}}). 

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

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

485 B{C{radius}}). 

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

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

488 B{C{radius}}). 

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

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

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

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

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

494 I{normalized} (C{bool}). 

495 

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

497 

498 @raise IntersectionError: No intersection, trilateration failed. 

499 

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

501 

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

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

504 

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

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

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

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

509 ''' 

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

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

512 radius=radius, height=height, useZ=useZ, 

513 wrap=wrap, LatLon=self.classof) 

514 

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

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

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

518 C{trilaterate} otherwise. 

519 

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

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

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

523 margin and count C{n = 1}. 

524 

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

526 (yet) supported. 

527 

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

529 ''' 

530 if area: 

531 self._notImplemented(area=area) 

532 

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

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

535 radius=radius, useZ=True, wrap=wrap, 

536 LatLon=self.classof) 

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

538 # like function C{.latlonBase._trilaterate5} 

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

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

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

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

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

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

545 

546 

547def _nsumOf(nvs, h_None, Vector, Vector_kwds): # .sphericalNvector, .vector3d 

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

549 ''' 

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

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

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

553 X += v.x 

554 Y += v.y 

555 Z += v.z 

556 H += v.h 

557 if n < 1: 

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

559 

560 x, y, z = map1(float, X, Y, Z) 

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

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

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

564 

565 

566def sumOf(nvectors, Vector=None, h=None, **Vector_kwds): 

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

568 

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

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

571 or C{None}. 

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

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

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

575 

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

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

578 

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

580 ''' 

581 try: 

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

583 except (TypeError, ValueError) as x: 

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

585 

586 

587def _triangulate(point1, bearing1, point2, bearing2, height=None, 

588 wrap=False, **LatLon_and_kwds): 

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

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

591 

592 def _gc(p, b, _i_): 

593 n = p.toNvector() 

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

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

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

597 dest = de.times(s) 

598 dnct = dn.times(c) 

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

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

601 

602 if wrap: 

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

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

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

606 

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

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

609 

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

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

612 kwds = _xkwds(LatLon_and_kwds, height=h) 

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

614 

615 

616def _trilaterate(point1, distance1, point2, distance2, point3, distance3, 

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

618 wrap=False, **LatLon_and_kwds): 

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

620 # three other points, see LatLon.triangulate above 

621 

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

623 for q in qs: 

624 if _isequalTo(p, q, eps=EPS): 

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

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

627 

628 p1, r = point1, Radius_(radius) 

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

630 

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

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

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

634 

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

636 y = n3.minus(n1) 

637 x = n2.minus(n1) 

638 z = None 

639 

640 d = x.length # distance n1->n2 

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

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

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

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

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

646 if fabs(j) > EPS_2: 

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

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

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

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

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

652 if z > EPS: 

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

654 if useZ: # include Z component 

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

656 n = n.plus(Z.times(sqrt(z))) 

657 if height is None: 

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

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

660 else: 

661 h = Height(height) 

662 kwds = _xkwds(LatLon_and_kwds, height=h) 

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

664 

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

666 t = _SPACE_(_no_, _intersection_, NN) 

667 raise IntersectionError(point1=point1, distance1=distance1, 

668 point2=point2, distance2=distance2, 

669 point3=point3, distance3=distance3, 

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

671 

672 

673__all__ += _ALL_DOCS(LatLonNvectorBase, NvectorBase, sumOf) # classes 

674 

675# **) MIT License 

676# 

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

678# 

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

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

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

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

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

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

685# 

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

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

688# 

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

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

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

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

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

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

695# OTHER DEALINGS IN THE SOFTWARE.