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_pop 

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, _MODS 

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

28from pygeodesy.named import notImplemented, _xother3 

29from pygeodesy.namedTuples import Trilaterate5Tuple, Vector3Tuple, \ 

30 Vector4Tuple, map1 

31from pygeodesy.props import deprecated_method, 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__ = (_NorthPole_, _SouthPole_) # constants 

41__version__ = '23.08.05' 

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 @example: 

72 

73 >>> from pygeodesy.sphericalNvector import Nvector 

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

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

76 ''' 

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

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

79 if h: 

80 self.h = h 

81 if d is not None: 

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

83 

84 @Property_RO 

85 def datum(self): 

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

87 ''' 

88 return self._datum 

89 

90 @Property_RO 

91 def Ecef(self): 

92 '''Get the ECEF I{class} (L{EcefKarney}), I{lazily}. 

93 ''' 

94 return _MODS.ecef.EcefKarney # default 

95 

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

97 def h(self): 

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

99 ''' 

100 return self._h 

101 

102 @h.setter # PYCHOK setter! 

103 def h(self, h): 

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

105 

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

107 

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

109 ''' 

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

111 if self._h != h: 

112 _update_all(self) 

113 self._h = h 

114 

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

116 def H(self): 

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

118 ''' 

119 return self._H 

120 

121 @H.setter # PYCHOK setter! 

122 def H(self, H): 

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

124 ''' 

125 self._H = str(H) if H else NN 

126 

127 def hStr(self, prec=-2, m=NN): 

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

129 

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

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

132 

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

134 ''' 

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

136 

137 @Property_RO 

138 def isEllipsoidal(self): 

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

140 ''' 

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

142 

143 @Property_RO 

144 def isSpherical(self): 

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

146 ''' 

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

148 

149 @Property_RO 

150 def lam(self): 

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

152 ''' 

153 return self.philam.lam 

154 

155 @Property_RO 

156 def lat(self): 

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

158 ''' 

159 return self.latlon.lat 

160 

161 @Property_RO 

162 def latlon(self): 

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

164 ''' 

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

166 

167 @Property_RO 

168 def latlonheight(self): 

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

170 ''' 

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

172 

173 @Property_RO 

174 def latlonheightdatum(self): 

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

176 ''' 

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

178 

179 @Property_RO 

180 def lon(self): 

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

182 ''' 

183 return self.latlon.lon 

184 

185 @Property_RO 

186 def phi(self): 

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

188 ''' 

189 return self.philam.phi 

190 

191 @Property_RO 

192 def philam(self): 

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

194 ''' 

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

196 

197 @Property_RO 

198 def philamheight(self): 

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

200 ''' 

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

202 

203 @Property_RO 

204 def philamheightdatum(self): 

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

206 ''' 

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

208 

209 @deprecated_method 

210 def to2ab(self): # PYCHOK no cover 

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

212 

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

214 ''' 

215 return self.philam 

216 

217 @deprecated_method 

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

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

220 

221 @kwarg height: Optional height, overriding this 

222 n-vector's height (C{meter}). 

223 

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

225 

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

227 ''' 

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

229 self.philam.to3Tuple(height) 

230 

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

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

233 

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

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

236 (C{Cartesian}). 

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

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

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

240 

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

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

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

244 available. 

245 

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

247 argument. 

248 

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

250 

251 @example: 

252 

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

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

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

256 ''' 

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

258 E = d.ellipsoid 

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

260 

261 x, y, z = self.x, self.y, self.z 

262 # Kenneth Gade eqn 22 

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

264 r = h + n * E.a2_b2 

265 

266 x *= r 

267 y *= r 

268 z *= h + n 

269 

270 if Cartesian is None: 

271 r = self.Ecef(d).reverse(x, y, z, M=True) 

272 else: 

273 kwds = _xkwds(Cartesian_kwds, datum=d) # h=0 

274 r = Cartesian(x, y, z, **kwds) 

275 return self._xnamed(r) 

276 

277 @deprecated_method 

278 def to2ll(self): # PYCHOK no cover 

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

280 

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

282 ''' 

283 return self.latlon 

284 

285 @deprecated_method 

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

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

288 

289 @kwarg height: Optional height, overriding this 

290 n-vector's height (C{meter}). 

291 

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

293 

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

295 ''' 

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

297 self.latlon.to3Tuple(height) 

298 

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

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

301 

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

303 height (C{meter}). 

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

305 (C{LatLon}) or C{None}. 

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

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

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

309 

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

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

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

313 

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

315 argument. 

316 

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

318 

319 @example: 

320 

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

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

323 ''' 

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

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

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

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

328 if LatLon is None: 

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

330 else: 

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

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

333 return r 

334 

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

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

337 

338 Height component is only included if non-zero. 

339 

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

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

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

343 

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

345 B{C{fmt}} brackets (C{str}). 

346 

347 @example: 

348 

349 >>> Nvector(0.5, 0.5, 0.7071).toStr() # (0.5, 0.5, 0.7071) 

350 >>> Nvector(0.5, 0.5, 0.7071, 1).toStr(-3) # (0.500, 0.500, 0.707, +1.00) 

351 ''' 

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

353 if self.h: 

354 t = sep.join((t, self.hStr())) 

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

356 

357 def toVector3d(self, norm=True): 

358 '''Convert this n-vector to a 3-D vector, I{ignoring 

359 the height}. 

360 

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

362 

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

364 ''' 

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

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

367 

368 @deprecated_method 

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

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

371 ''' 

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

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

374 

375 def unit(self, ll=None): 

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

377 

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

379 

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

381 ''' 

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

383 

384 @Property_RO 

385 def xyzh(self): 

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

387 ''' 

388 return self.xyz.to4Tuple(self.h) 

389 

390 

391NorthPole = NvectorBase(0, 0, +1, name=_NorthPole_) # North pole (C{Nvector}) 

392SouthPole = NvectorBase(0, 0, -1, name=_SouthPole_) # South pole (C{Nvector}) 

393 

394 

395class _N_vector_(NvectorBase): 

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

397 ''' 

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

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

400 if h: 

401 self._h = h 

402 if name: 

403 self.name = name 

404 

405 

406class LatLonNvectorBase(LatLonBase): 

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

408 and spherical C{LatLon} classes. 

409 ''' 

410 

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

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

413 

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

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

416 ''' 

417 if updated: 

418 _Nv = _xkwds_pop(setters, _Nv=None) 

419 if _Nv is not None: 

420 if _Nv._fromll is not None: 

421 _Nv._fromll = None 

422 self._Nv = None 

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

424 

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

426# '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. 

427# ''' 

428# _MODS.named.notOverloaded(self, other, **kwds) 

429 

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

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

432 ''' 

433 notImplemented(self, radius1, other, radius2, **kwds) 

434 

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

436 '''Refined class comparison. 

437 

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

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

440 keyword arguments. 

441 

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

443 

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

445 ''' 

446 if other: 

447 other0 = other[0] 

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

449 return other0 

450 

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

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

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

454 return other 

455 

456 def toNvector(self, Nvector=NvectorBase, **Nvector_kwds): # PYCHOK signature 

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

458 

459 @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword 

460 arguments, ignored if C{B{Nvector} is None}. 

461 

462 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if 

463 B{C{Nvector}} is C{None}. 

464 

465 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}} 

466 argument. 

467 ''' 

468 return LatLonBase.toNvector(self, Nvector=Nvector, **Nvector_kwds) 

469 

470 def triangulate(self, bearing1, other, bearing2, height=None, wrap=False): 

471 '''Locate a point given this and an other point and a bearing 

472 at this and the other point. 

473 

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

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

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

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

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

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

480 I{normalized} (C{bool}). 

481 

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

483 

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

485 

486 @raise Valuerror: Points coincide. 

487 

488 @example: 

489 

490 >>> p = LatLon("47°18.228'N","002°34.326'W") # Basse Castouillet 

491 >>> q = LatLon("47°18.664'N","002°31.717'W") # Basse Hergo 

492 >>> t = p.triangulate(7, q, 295) # 47.323667°N, 002.568501°W' 

493 ''' 

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

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

496 

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

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

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

500 

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

502 as B{C{radius}}). 

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

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

505 B{C{radius}}). 

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

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

508 B{C{radius}}). 

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

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

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

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

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

514 I{normalized} (C{bool}). 

515 

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

517 

518 @raise IntersectionError: No intersection, trilateration failed. 

519 

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

521 

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

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

524 

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

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

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

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

529 ''' 

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

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

532 radius=radius, height=height, useZ=useZ, 

533 wrap=wrap, LatLon=self.classof) 

534 

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

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

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

538 C{trilaterate} otherwise. 

539 

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

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

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

543 margin and count C{n = 1}. 

544 

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

546 (yet) supported. 

547 

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

549 ''' 

550 if area: 

551 notImplemented(self, area=area) 

552 

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

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

555 radius=radius, useZ=True, wrap=wrap, 

556 LatLon=self.classof) 

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

558 # like function C{.latlonBase._trilaterate5} 

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

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

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

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

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

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

565 

566 

567def _nsumOf(nvs, h_None, Vector, Vector_kwds): # .sphericalNvector, .vector3d 

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

569 ''' 

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

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

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

573 X += v.x 

574 Y += v.y 

575 Z += v.z 

576 H += v.h 

577 if n < 1: 

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

579 

580 x, y, z = map1(float, X, Y, Z) 

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

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

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

584 

585 

586def sumOf(nvectors, Vector=None, h=None, **Vector_kwds): 

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

588 

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

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

591 or C{None}. 

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

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

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

595 

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

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

598 

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

600 ''' 

601 try: 

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

603 except (TypeError, ValueError) as x: 

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

605 

606 

607def _triangulate(point1, bearing1, point2, bearing2, height=None, 

608 wrap=False, **LatLon_and_kwds): 

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

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

611 

612 def _gc(p, b, _i_): 

613 n = p.toNvector() 

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

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

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

617 dest = de.times(s) 

618 dnct = dn.times(c) 

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

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

621 

622 if wrap: 

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

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

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

626 

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

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

629 

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

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

632 kwds = _xkwds(LatLon_and_kwds, height=h) 

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

634 

635 

636def _trilaterate(point1, distance1, point2, distance2, point3, distance3, 

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

638 wrap=False, **LatLon_and_kwds): 

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

640 # three other points, see LatLon.triangulate above 

641 

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

643 for q in qs: 

644 if _isequalTo(p, q, eps=EPS): 

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

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

647 

648 p1, r = point1, Radius_(radius) 

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

650 

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

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

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

654 

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

656 y = n3.minus(n1) 

657 x = n2.minus(n1) 

658 z = None 

659 

660 d = x.length # distance n1->n2 

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

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

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

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

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

666 if fabs(j) > EPS_2: 

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

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

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

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

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

672 if z > EPS: 

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

674 if useZ: # include Z component 

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

676 n = n.plus(Z.times(sqrt(z))) 

677 if height is None: 

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

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

680 else: 

681 h = Height(height) 

682 kwds = _xkwds(LatLon_and_kwds, height=h) 

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

684 

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

686 t = _SPACE_(_no_, _intersection_, NN) 

687 raise IntersectionError(point1=point1, distance1=distance1, 

688 point2=point2, distance2=distance2, 

689 point3=point3, distance3=distance3, 

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

691 

692 

693__all__ += _ALL_DOCS(LatLonNvectorBase, NvectorBase, sumOf) # classes 

694 

695# **) MIT License 

696# 

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

698# 

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

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

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

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

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

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

705# 

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

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

708# 

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

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

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

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

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

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

715# OTHER DEALINGS IN THE SOFTWARE.