1

2# -*- coding: utf-8 -*-

3

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

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

6

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

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

9 and 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

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

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

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

17 _xkwds, _xkwds_pop2

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

19 from pygeodesy.fsums import Fsum, fsumf_

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

21 _spherical_datum

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

23 _COMMASPACE_, _distance_, _h_, _insufficient_, \

24 _intersection_, _no_, _NorthPole_, _point_, \

25 _pole_, _SPACE_, _SouthPole_, _under

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

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

28 from pygeodesy.named import notImplemented, _xother3

29 from pygeodesy.namedTuples import Trilaterate5Tuple, Vector3Tuple, \

30 Vector4Tuple, map1

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

32 property_RO, _update_all

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

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

35 from pygeodesy.utily import sincos2d, _unrollon, _unrollon3

36 from pygeodesy.vector3d import Vector3d, _xyzhdn3

37

38 from math import fabs, sqrt

39

40__all__ = _ALL_LAZY.nvectorBase

41__version__ = '24.02.18'

42

43

44 class 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

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

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

382

383

384 class _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

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

417

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

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

420 notImplemented(self, 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 notImplemented(self, 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

547 def _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

566 def 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

587 def _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

616 def _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.