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, property_ROnce, _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__ = '24.07.12'

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_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

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

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

378

379

380 class _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

391 class 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

543 def _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

562 def 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

583 def _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

612 def _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.