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 _xattrs, _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.internals import _under # from .named

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

24 _COMMASPACE_, _distance_, _h_, _insufficient_, \

25 _intersection_, _no_, _point_, _pole_, _SPACE_

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 _xother3, _under

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

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

35 from pygeodesy.utily import sincos2d, _unrollon, _unrollon3

36 from pygeodesy.vector3d import Vector3d, _xyzhdlln4

37

38 from math import fabs, sqrt

39

40__all__ = _ALL_LAZY.nvectorBase

41__version__ = '24.06.12'

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, 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_RO

82 def Ecef(self):

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

84 '''

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

86 return E

87

88 @property_RO

89 def ellipsoidalNvector(self):

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

91 '''

92 return False

93

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

95 def h(self):

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

97 '''

98 return self._h

99

100 @h.setter # PYCHOK setter!

101 def h(self, h):

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

103

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

105

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

107 '''

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

109 if self._h != h:

110 _update_all(self)

111 self._h = h

112

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

114 def H(self):

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

116 '''

117 return self._H

118

119 @H.setter # PYCHOK setter!

120 def H(self, H):

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

122 '''

123 self._H = str(H) if H else NN

124

125 def hStr(self, prec=-2, m=NN):

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

127

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

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

130

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

132 '''

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

134

135 @Property_RO

136 def isEllipsoidal(self):

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

138 '''

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

140

141 @Property_RO

142 def isSpherical(self):

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

144 '''

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

146

147 @Property_RO

148 def lam(self):

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

150 '''

151 return self.philam.lam

152

153 @Property_RO

154 def lat(self):

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

156 '''

157 return self.latlon.lat

158

159 @Property_RO

160 def latlon(self):

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

162 '''

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

164

165 @Property_RO

166 def latlonheight(self):

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

168 '''

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

170

171 @Property_RO

172 def latlonheightdatum(self):

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

174 '''

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

176

177 @Property_RO

178 def lon(self):

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

180 '''

181 return self.latlon.lon

182

183 @Property_RO

184 def phi(self):

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

186 '''

187 return self.philam.phi

188

189 @Property_RO

190 def philam(self):

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

192 '''

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

194

195 @Property_RO

196 def philamheight(self):

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

198 '''

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

200

201 @Property_RO

202 def philamheightdatum(self):

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

204 '''

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

206

207 @property_RO

208 def sphericalNvector(self):

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

210 '''

211 return False

212

213 @deprecated_method

214 def to2ab(self): # PYCHOK no cover

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

216

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

218 '''

219 return self.philam

220

221 @deprecated_method

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

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

224

225 @kwarg height: Optional height, overriding this

226 n-vector's height (C{meter}).

227

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

229

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

231 '''

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

233 self.philam.to3Tuple(height)

234

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

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

237

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

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

240 (C{Cartesian}).

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

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

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

244

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

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

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

248 available.

249

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

251 argument.

252

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

254 '''

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

256 E = D.ellipsoid

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

258

259 x, y, z = self.x, self.y, self.z

260 # Kenneth Gade eqn 22

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

262 r = h + n * E.a2_b2

263

264 x *= r

265 y *= r

266 z *= h + n

267

268 if Cartesian is None:

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

270 else:

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

272 r = Cartesian(x, y, z, **kwds)

273 return self._xnamed(r)

274

275 @deprecated_method

276 def to2ll(self): # PYCHOK no cover

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

278

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

280 '''

281 return self.latlon

282

283 @deprecated_method

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

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

286

287 @kwarg height: Optional height, overriding this

288 n-vector's height (C{meter}).

289

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

291

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

293 '''

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

295 self.latlon.to3Tuple(height)

296

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

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

299

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

301 height (C{meter}).

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

303 (C{LatLon}) or C{None}.

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

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

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

307

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

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

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

311

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

313 argument.

314

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

316 '''

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

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

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

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

321 if LatLon is None:

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

323 else:

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

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

326 return r

327

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

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

330

331 Height component is only included if non-zero.

332

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

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

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

336

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

338 B{C{fmt}} brackets (C{str}).

339 '''

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

341 if self.h:

342 t = sep.join((t, self.hStr()))

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

344

345 def toVector3d(self, norm=True):

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

347

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

349

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

351 '''

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

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

354

355 @deprecated_method

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

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

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

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

360

361 def unit(self, ll=None):

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

363

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

365

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

367 '''

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

369

370 @Property_RO

371 def xyzh(self):

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

373 '''

374 return self.xyz.to4Tuple(self.h)

375

376

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

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

379

380

381 class _N_vector_(NvectorBase):

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

383 '''

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

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

386 if h:

387 self._h = h

388 if name:

389 self.name = name

390

391

392 class LatLonNvectorBase(LatLonBase):

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

394 spherical C{LatLon} classes.

395 '''

396

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

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

399

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

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

402 '''

403 if updated:

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

405 if _Nv is not None:

406 if _Nv._fromll is not None:

407 _Nv._fromll = None

408 self._Nv = None

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

410

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

412# '''I{Must be overloaded}.'''

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

414

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

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

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

418

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

420 '''Refined class comparison.

421

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

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

424 keyword arguments.

425

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

427

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

429 '''

430 if other:

431 other0 = other[0]

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

433 return other0

434

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

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

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

438 return other

439

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

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

442

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

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

445 or use C{B{Nvector}=None}.

446

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

448

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

450 '''

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

452

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

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

455 from this and the other point.

456

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

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

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

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

461 the mean height (C{meter}).

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

463 I{normalized} (C{bool}).

464

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

466

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

468

469 @raise Valuerror: Points coincide.

470 '''

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

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

473

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

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

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

477

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

479 as B{C{radius}}).

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

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

482 B{C{radius}}).

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

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

485 B{C{radius}}).

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

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

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

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

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

491 I{normalized} (C{bool}).

492

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

494

495 @raise IntersectionError: No intersection, trilateration failed.

496

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

498

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

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

501

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

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

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

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

506 '''

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

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

509 radius=radius, height=height, useZ=useZ,

510 wrap=wrap, LatLon=self.classof)

511

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

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

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

515 C{trilaterate} otherwise.

516

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

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

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

520 margin and count C{n = 1}.

521

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

523 (yet) supported.

524

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

526 '''

527 if area:

528 self._notImplemented(area=area)

529

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

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

532 radius=radius, useZ=True, wrap=wrap,

533 LatLon=self.classof)

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

535 # like function C{.latlonBase._trilaterate5}

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

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

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

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

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

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

542

543

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

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

546 '''

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

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

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

550 X += v.x

551 Y += v.y

552 Z += v.z

553 H += v.h

554 if n < 1:

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

556

557 x, y, z = map1(float, X, Y, Z)

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

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

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

561

562

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

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

565

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

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

568 or C{None}.

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

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

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

572

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

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

575

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

577 '''

578 try:

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

580 except (TypeError, ValueError) as x:

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

582

583

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

585 wrap=False, **LatLon_and_kwds):

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

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

588

589 def _gc(p, b, _i_):

590 n = p.toNvector()

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

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

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

594 dest = de.times(s)

595 dnct = dn.times(c)

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

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

598

599 if wrap:

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

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

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

603

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

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

606

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

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

609 kwds = _xkwds(LatLon_and_kwds, height=h)

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

611

612

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

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

615 wrap=False, **LatLon_and_kwds):

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

617 # three other points, see LatLon.triangulate above

618

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

620 for q in qs:

621 if _isequalTo(p, q, eps=EPS):

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

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

624

625 p1, r = point1, Radius_(radius)

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

627

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

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

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

631

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

633 y = n3.minus(n1)

634 x = n2.minus(n1)

635 z = None

636

637 d = x.length # distance n1->n2

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

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

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

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

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

643 if fabs(j) > EPS_2:

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

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

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

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

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

649 if z > EPS:

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

651 if useZ: # include Z component

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

653 n = n.plus(Z.times(sqrt(z)))

654 if height is None:

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

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

657 else:

658 h = Height(height)

659 kwds = _xkwds(LatLon_and_kwds, height=h)

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

661

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

663 t = _SPACE_(_no_, _intersection_, NN)

664 raise IntersectionError(point1=point1, distance1=distance1,

665 point2=point2, distance2=distance2,

666 point3=point3, distance3=distance3,

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

668

669

670__all__ += _ALL_DOCS(LatLonNvectorBase, NvectorBase, sumOf) # classes

671

672# **) MIT License

673#

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

675#

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

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

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

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

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

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

682#

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

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

685#

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

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

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

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

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

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

692# OTHER DEALINGS IN THE SOFTWARE.