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_, _point_, _pole_, _SPACE_ 

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, _under 

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, _xyzhdlln4 

37 

38from math import fabs, sqrt 

39 

40__all__ = _ALL_LAZY.nvectorBase 

41__version__ = '24.06.06' 

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, datum=None, **ll_name): 

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 L{Vector4Tuple}). 

56 @kwarg y: Y component of vector (C{scalar}), ignored if B{C{x_xyz}} is not 

57 C{scalar}, otherwise same units as B{C{x_xyz}}. 

58 @kwarg z: Z component of vector (C{scalar}), ignored if B{C{x_xyz}} is not 

59 C{scalar}, otherwise same units as B{C{x_xyz}}. 

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

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

62 @kwarg ll_name: Optional C{B{name}=NN} (C{str}) and optional, original 

63 latlon C{B{ll}=None} (C{LatLon}). 

64 

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

66 B{C{x_xyz}} not an C{Nvector}, L{Vector3Tuple} or 

67 L{Vector4Tuple} or invalid B{C{datum}}. 

68 ''' 

69 h, d, ll, n = _xyzhdlln4(x_xyz, h, datum, **ll_name) 

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

71 if h: 

72 self.h = h 

73 if d is not None: 

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

75 

76 @Property_RO 

77 def datum(self): 

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

79 ''' 

80 return self._datum 

81 

82 @property_RO 

83 def Ecef(self): 

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

85 ''' 

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

87 return E 

88 

89 @property_RO 

90 def ellipsoidalNvector(self): 

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

92 ''' 

93 return False 

94 

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

96 def h(self): 

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

98 ''' 

99 return self._h 

100 

101 @h.setter # PYCHOK setter! 

102 def h(self, h): 

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

104 

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

106 

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

108 ''' 

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

110 if self._h != h: 

111 _update_all(self) 

112 self._h = h 

113 

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

115 def H(self): 

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

117 ''' 

118 return self._H 

119 

120 @H.setter # PYCHOK setter! 

121 def H(self, H): 

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

123 ''' 

124 self._H = str(H) if H else NN 

125 

126 def hStr(self, prec=-2, m=NN): 

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

128 

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

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

131 

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

133 ''' 

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

135 

136 @Property_RO 

137 def isEllipsoidal(self): 

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

139 ''' 

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

141 

142 @Property_RO 

143 def isSpherical(self): 

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

145 ''' 

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

147 

148 @Property_RO 

149 def lam(self): 

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

151 ''' 

152 return self.philam.lam 

153 

154 @Property_RO 

155 def lat(self): 

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

157 ''' 

158 return self.latlon.lat 

159 

160 @Property_RO 

161 def latlon(self): 

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

163 ''' 

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

165 

166 @Property_RO 

167 def latlonheight(self): 

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

169 ''' 

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

171 

172 @Property_RO 

173 def latlonheightdatum(self): 

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

175 ''' 

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

177 

178 @Property_RO 

179 def lon(self): 

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

181 ''' 

182 return self.latlon.lon 

183 

184 @Property_RO 

185 def phi(self): 

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

187 ''' 

188 return self.philam.phi 

189 

190 @Property_RO 

191 def philam(self): 

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

193 ''' 

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

195 

196 @Property_RO 

197 def philamheight(self): 

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

199 ''' 

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

201 

202 @Property_RO 

203 def philamheightdatum(self): 

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

205 ''' 

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

207 

208 @property_RO 

209 def sphericalNvector(self): 

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

211 ''' 

212 return False 

213 

214 @deprecated_method 

215 def to2ab(self): # PYCHOK no cover 

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

217 

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

219 ''' 

220 return self.philam 

221 

222 @deprecated_method 

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

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

225 

226 @kwarg height: Optional height, overriding this 

227 n-vector's height (C{meter}). 

228 

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

230 

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

232 ''' 

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

234 self.philam.to3Tuple(height) 

235 

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

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

238 

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

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

241 (C{Cartesian}). 

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

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

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

245 

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

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

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

249 available. 

250 

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

252 argument. 

253 

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

255 ''' 

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

257 E = D.ellipsoid 

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

259 

260 x, y, z = self.x, self.y, self.z 

261 # Kenneth Gade eqn 22 

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

263 r = h + n * E.a2_b2 

264 

265 x *= r 

266 y *= r 

267 z *= h + n 

268 

269 if Cartesian is None: 

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

271 else: 

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

273 r = Cartesian(x, y, z, **kwds) 

274 return self._xnamed(r) 

275 

276 @deprecated_method 

277 def to2ll(self): # PYCHOK no cover 

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

279 

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

281 ''' 

282 return self.latlon 

283 

284 @deprecated_method 

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

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

287 

288 @kwarg height: Optional height, overriding this 

289 n-vector's height (C{meter}). 

290 

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

292 

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

294 ''' 

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

296 self.latlon.to3Tuple(height) 

297 

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

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

300 

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

302 height (C{meter}). 

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

304 (C{LatLon}) or C{None}. 

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

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

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

308 

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

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

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

312 

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

314 argument. 

315 

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

317 ''' 

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

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

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

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

322 if LatLon is None: 

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

324 else: 

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

326 r = LatLon(self.lat, self.lon, **self._name1__(kwds)) 

327 return r 

328 

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

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

331 

332 Height component is only included if non-zero. 

333 

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

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

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

337 

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

339 B{C{fmt}} brackets (C{str}). 

340 ''' 

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

342 if self.h: 

343 t = sep.join((t, self.hStr())) 

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

345 

346 def toVector3d(self, norm=True): 

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

348 

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

350 

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

352 ''' 

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

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

355 

356 @deprecated_method 

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

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

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

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

361 

362 def unit(self, ll=None): 

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

364 

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

366 

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

368 ''' 

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

370 

371 @Property_RO 

372 def xyzh(self): 

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

374 ''' 

375 return self.xyz.to4Tuple(self.h) 

376 

377 

378NorthPole = NvectorBase(0, 0, +1, name='NorthPole') # North pole (C{Nvector}) 

379SouthPole = NvectorBase(0, 0, -1, name='SouthPole') # South pole (C{Nvector}) 

380 

381 

382class _N_vector_(NvectorBase): 

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

384 ''' 

385 def __init__(self, x, y, z, h=0, **name): 

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

387 if h: 

388 self._h = h 

389 if name: 

390 self.name = name 

391 

392 

393class LatLonNvectorBase(LatLonBase): 

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

395 spherical C{LatLon} classes. 

396 ''' 

397 

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

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

400 

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

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

403 ''' 

404 if updated: 

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

406 if _Nv is not None: 

407 if _Nv._fromll is not None: 

408 _Nv._fromll = None 

409 self._Nv = None 

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

411 

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

413# '''I{Must be overloaded}.''' 

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

415 

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

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

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

419 

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

421 '''Refined class comparison. 

422 

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

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

425 keyword arguments. 

426 

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

428 

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

430 ''' 

431 if other: 

432 other0 = other[0] 

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

434 return other0 

435 

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

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

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

439 return other 

440 

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

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

443 

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

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

446 or use C{B{Nvector}=None}. 

447 

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

449 

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

451 ''' 

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

453 

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

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

456 from this and the other point. 

457 

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

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

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

461 @kwarg height: Optional height at the triangulated point, overriding 

462 the mean height (C{meter}). 

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

464 I{normalized} (C{bool}). 

465 

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

467 

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

469 

470 @raise Valuerror: Points coincide. 

471 ''' 

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

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

474 

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

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

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

478 

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

480 as B{C{radius}}). 

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

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

483 B{C{radius}}). 

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

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

486 B{C{radius}}). 

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

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

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

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

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

492 I{normalized} (C{bool}). 

493 

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

495 

496 @raise IntersectionError: No intersection, trilateration failed. 

497 

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

499 

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

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

502 

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

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

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

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

507 ''' 

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

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

510 radius=radius, height=height, useZ=useZ, 

511 wrap=wrap, LatLon=self.classof) 

512 

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

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

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

516 C{trilaterate} otherwise. 

517 

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

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

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

521 margin and count C{n = 1}. 

522 

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

524 (yet) supported. 

525 

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

527 ''' 

528 if area: 

529 self._notImplemented(area=area) 

530 

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

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

533 radius=radius, useZ=True, wrap=wrap, 

534 LatLon=self.classof) 

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

536 # like function C{.latlonBase._trilaterate5} 

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

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

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

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

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

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

543 

544 

545def _nsumOf(nvs, h_None, Vector, Vector_kwds): # .sphericalNvector, .vector3d 

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

547 ''' 

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

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

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

551 X += v.x 

552 Y += v.y 

553 Z += v.z 

554 H += v.h 

555 if n < 1: 

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

557 

558 x, y, z = map1(float, X, Y, Z) 

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

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

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

562 

563 

564def sumOf(nvectors, Vector=None, h=None, **Vector_kwds): 

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

566 

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

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

569 or C{None}. 

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

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

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

573 

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

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

576 

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

578 ''' 

579 try: 

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

581 except (TypeError, ValueError) as x: 

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

583 

584 

585def _triangulate(point1, bearing1, point2, bearing2, height=None, 

586 wrap=False, **LatLon_and_kwds): 

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

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

589 

590 def _gc(p, b, _i_): 

591 n = p.toNvector() 

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

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

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

595 dest = de.times(s) 

596 dnct = dn.times(c) 

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

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

599 

600 if wrap: 

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

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

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

604 

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

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

607 

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

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

610 kwds = _xkwds(LatLon_and_kwds, height=h) 

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

612 

613 

614def _trilaterate(point1, distance1, point2, distance2, point3, distance3, 

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

616 wrap=False, **LatLon_and_kwds): 

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

618 # three other points, see LatLon.triangulate above 

619 

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

621 for q in qs: 

622 if _isequalTo(p, q, eps=EPS): 

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

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

625 

626 p1, r = point1, Radius_(radius) 

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

628 

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

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

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

632 

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

634 y = n3.minus(n1) 

635 x = n2.minus(n1) 

636 z = None 

637 

638 d = x.length # distance n1->n2 

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

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

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

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

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

644 if fabs(j) > EPS_2: 

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

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

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

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

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

650 if z > EPS: 

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

652 if useZ: # include Z component 

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

654 n = n.plus(Z.times(sqrt(z))) 

655 if height is None: 

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

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

658 else: 

659 h = Height(height) 

660 kwds = _xkwds(LatLon_and_kwds, height=h) 

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

662 

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

664 t = _SPACE_(_no_, _intersection_, NN) 

665 raise IntersectionError(point1=point1, distance1=distance1, 

666 point2=point2, distance2=distance2, 

667 point3=point3, distance3=distance3, 

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

669 

670 

671__all__ += _ALL_DOCS(LatLonNvectorBase, NvectorBase, sumOf) # classes 

672 

673# **) MIT License 

674# 

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

676# 

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

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

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

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

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

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

683# 

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

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

686# 

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

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

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

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

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

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

693# OTHER DEALINGS IN THE SOFTWARE.