Coverage for pygeodesy/nvectorBase.py: 95%

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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 _xattrs, _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, property_ROnce, _update_all 

33from pygeodesy.streprs import Fmt, hstr, unstr 

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__ = '24.10.12' 

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}), required if B{C{x_xyz}} is 

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

58 @kwarg z: Z component of vector (C{scalar}), like B{C{y}}. 

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

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

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

62 latlon C{B{ll}=None} (C{LatLon}). 

63 

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

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

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

67 ''' 

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

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

70 if h: 

71 self.h = h 

72 if d is not None: 

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

74 

75 @Property_RO 

76 def datum(self): 

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

78 ''' 

79 return self._datum 

80 

81 @property_ROnce 

82 def Ecef(self): 

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

84 ''' 

85 return _MODS.ecef.EcefKarney 

86 

87 @property_RO 

88 def ellipsoidalNvector(self): 

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

90 ''' 

91 return False 

92 

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

94 def h(self): 

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

96 ''' 

97 return self._h 

98 

99 @h.setter # PYCHOK setter! 

100 def h(self, h): 

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

102 

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

104 

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

106 ''' 

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

108 if self._h != h: 

109 _update_all(self) 

110 self._h = h 

111 

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

113 def H(self): 

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

115 ''' 

116 return self._H 

117 

118 @H.setter # PYCHOK setter! 

119 def H(self, H): 

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

121 ''' 

122 self._H = str(H) if H else NN 

123 

124 def hStr(self, prec=-2, m=NN): 

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

126 

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

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

129 

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

131 ''' 

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

133 

134 @Property_RO 

135 def isEllipsoidal(self): 

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

137 ''' 

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

139 

140 @Property_RO 

141 def isSpherical(self): 

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

143 ''' 

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

145 

146 @Property_RO 

147 def lam(self): 

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

149 ''' 

150 return self.philam.lam 

151 

152 @Property_RO 

153 def lat(self): 

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

155 ''' 

156 return self.latlon.lat 

157 

158 @Property_RO 

159 def latlon(self): 

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

161 ''' 

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

163 

164 @Property_RO 

165 def latlonheight(self): 

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

167 ''' 

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

169 

170 @Property_RO 

171 def latlonheightdatum(self): 

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

173 ''' 

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

175 

176 @Property_RO 

177 def lon(self): 

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

179 ''' 

180 return self.latlon.lon 

181 

182 @Property_RO 

183 def phi(self): 

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

185 ''' 

186 return self.philam.phi 

187 

188 @Property_RO 

189 def philam(self): 

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

191 ''' 

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

193 

194 @Property_RO 

195 def philamheight(self): 

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

197 ''' 

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

199 

200 @Property_RO 

201 def philamheightdatum(self): 

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

203 ''' 

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

205 

206 @property_RO 

207 def sphericalNvector(self): 

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

209 ''' 

210 return False 

211 

212 @deprecated_method 

213 def to2ab(self): # PYCHOK no cover 

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

215 

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

217 ''' 

218 return self.philam 

219 

220 @deprecated_method 

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

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

223 

224 @kwarg height: Optional height, overriding this 

225 n-vector's height (C{meter}). 

226 

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

228 

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

230 ''' 

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

232 self.philam.to3Tuple(height) 

233 

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

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

236 

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

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

239 (C{Cartesian}). 

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

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

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

243 

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

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

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

247 available. 

248 

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

250 argument. 

251 

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

253 ''' 

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

255 E = D.ellipsoid 

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

257 

258 x, y, z = self.x, self.y, self.z 

259 # Kenneth Gade eqn 22 

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

261 r = h + n * E.a2_b2 

262 

263 x *= r 

264 y *= r 

265 z *= h + n 

266 

267 if Cartesian is None: 

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

269 else: 

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

271 r = Cartesian(x, y, z, **kwds) 

272 return self._xnamed(r) 

273 

274 @deprecated_method 

275 def to2ll(self): # PYCHOK no cover 

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

277 

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

279 ''' 

280 return self.latlon 

281 

282 @deprecated_method 

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

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

285 

286 @kwarg height: Optional height, overriding this 

287 n-vector's height (C{meter}). 

288 

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

290 

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

292 ''' 

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

294 self.latlon.to3Tuple(height) 

295 

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

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

298 

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

300 height (C{meter}). 

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

302 (C{LatLon}) or C{None}. 

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

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

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

306 

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

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

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

310 

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

312 argument. 

313 

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

315 ''' 

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

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

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

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

320 if LatLon is None: 

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

322 else: 

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

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

325 return r 

326 

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

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

329 

330 Height component is only included if non-zero. 

331 

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

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

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

335 

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

337 B{C{fmt}} brackets (C{str}). 

338 ''' 

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

340 if self.h: 

341 t = sep.join((t, self.hStr())) 

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

343 

344 def toVector3d(self, norm=True): 

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

346 

347 @kwarg norm: If C{True}, normalize the 3-D vector (C{bool}). 

348 

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

350 ''' 

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

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

353 

354 @deprecated_method 

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

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

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

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

359 

360 def unit(self, ll=None): 

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

362 

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

364 

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

366 ''' 

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

368 

369 @Property_RO 

370 def xyzh(self): 

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

372 ''' 

373 return self.xyz.to4Tuple(self.h) 

374 

375 

376NorthPole = NvectorBase(0, 0, +1, name='NorthPole') # North pole (C{Nvector}) 

377SouthPole = NvectorBase(0, 0, -1, name='SouthPole') # South pole (C{Nvector}) 

378 

379 

380class _N_vector_(NvectorBase): 

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

382 ''' 

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

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

385 if h: 

386 self._h = h 

387 if name: 

388 self.name = name 

389 

390 

391class LatLonNvectorBase(LatLonBase): 

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

393 spherical C{LatLon} classes. 

394 ''' 

395 

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

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

398 

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

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

401 ''' 

402 if updated: 

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

404 if _Nv is not None: 

405 if _Nv._fromll is not None: 

406 _Nv._fromll = None 

407 self._Nv = None 

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

409 

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

411# '''I{Must be overloaded}.''' 

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

413 

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

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

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

417 

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

419 '''Refined class comparison. 

420 

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

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

423 keyword arguments. 

424 

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

426 

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

428 ''' 

429 if other: 

430 other0 = other[0] 

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

432 return other0 

433 

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

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

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

437 return other 

438 

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

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

441 

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

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

444 or use C{B{Nvector}=None}. 

445 

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

447 

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

449 ''' 

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

451 

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

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

454 from this and the other point. 

455 

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

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

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

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

460 the mean height (C{meter}). 

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

462 I{normalized} (C{bool}). 

463 

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

465 

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

467 

468 @raise Valuerror: Points coincide. 

469 ''' 

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

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

472 

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

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

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

476 

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

478 as B{C{radius}}). 

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

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

481 B{C{radius}}). 

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

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

484 B{C{radius}}). 

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

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

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

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

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

490 I{normalized} (C{bool}). 

491 

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

493 

494 @raise IntersectionError: No intersection, trilateration failed. 

495 

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

497 

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

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

500 

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

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

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

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

505 ''' 

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

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

508 radius=radius, height=height, useZ=useZ, 

509 wrap=wrap, LatLon=self.classof) 

510 

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

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

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

514 C{trilaterate} otherwise. 

515 

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

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

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

519 margin and count C{n = 1}. 

520 

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

522 (yet) supported. 

523 

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

525 ''' 

526 if area: 

527 self._notImplemented(area=area) 

528 

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

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

531 radius=radius, useZ=True, wrap=wrap, 

532 LatLon=self.classof) 

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

534 # like function C{.latlonBase._trilaterate5} 

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

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

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

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

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

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

541 

542 

543def _nsumOf(nvs, h_None, Vector, Vector_kwds): # .sphericalNvector, .vector3d 

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

545 ''' 

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

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

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

549 X += v.x 

550 Y += v.y 

551 Z += v.z 

552 H += v.h 

553 if n < 1: 

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

555 

556 x, y, z = map1(float, X, Y, Z) 

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

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

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

560 

561 

562def sumOf(nvectors, Vector=None, h=None, **Vector_kwds): 

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

564 

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

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

567 or C{None}. 

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

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

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

571 

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

573 z, h)} if C{B{Vector} is None}. 

574 

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

576 ''' 

577 try: 

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

579 except (TypeError, ValueError) as x: 

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

581 

582 

583def _triangulate(point1, bearing1, point2, bearing2, height=None, 

584 wrap=False, **LatLon_and_kwds): 

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

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

587 

588 def _gc(p, b, _i_): 

589 n = p.toNvector() 

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

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

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

593 dest = de.times(s) 

594 dnct = dn.times(c) 

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

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

597 

598 if wrap: 

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

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

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

602 

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

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

605 

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

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

608 kwds = _xkwds(LatLon_and_kwds, height=h) 

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

610 

611 

612def _trilaterate(point1, distance1, point2, distance2, point3, distance3, 

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

614 wrap=False, **LatLon_and_kwds): 

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

616 # three other points, see LatLon.triangulate above 

617 

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

619 for q in qs: 

620 if _isequalTo(p, q, eps=EPS): 

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

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

623 

624 p1, r = point1, Radius_(radius) 

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

626 

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

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

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

630 

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

632 y = n3.minus(n1) 

633 x = n2.minus(n1) 

634 z = None 

635 

636 d = x.length # distance n1->n2 

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

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

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

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

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

642 if fabs(j) > EPS_2: 

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

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

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

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

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

648 if z > EPS: 

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

650 if useZ: # include Z component 

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

652 n = n.plus(Z.times(sqrt(z))) 

653 if height is None: 

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

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

656 else: 

657 h = Height(height) 

658 kwds = _xkwds(LatLon_and_kwds, height=h) 

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

660 

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

662 t = _SPACE_(_no_, _intersection_, NN) 

663 raise IntersectionError(point1=point1, distance1=distance1, 

664 point2=point2, distance2=distance2, 

665 point3=point3, distance3=distance3, 

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

667 

668 

669__all__ += _ALL_DOCS(LatLonNvectorBase, NvectorBase, sumOf) # classes 

670 

671# **) MIT License 

672# 

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

674# 

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

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

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

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

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

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

681# 

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

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

684# 

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

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

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

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

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

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

691# OTHER DEALINGS IN THE SOFTWARE.