Coverage for pygeodesy/vector3dBase.py: 93%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''(INTERNAL) Private, 3-D vector base class C{Vector3dBase}. 

5 

6A pure Python implementation of vector-based functions by I{(C) Chris Veness 

72011-2015} published under the same MIT Licence**, see U{Vector-based geodesy 

8<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. 

9''' 

10 

11from pygeodesy.basics import _copysign, islistuple, isscalar, map1, \ 

12 map2, _signOf, _zip 

13from pygeodesy.constants import EPS, EPS0, INT0, PI, PI2, _copysignINF, \ 

14 _float0, isnear0, isnear1, isneg0, \ 

15 _pos_self, _0_0, _1_0 

16from pygeodesy.errors import CrossError, VectorError, _xcallable, _xError 

17from pygeodesy.fmath import euclid_, fdot, hypot_, hypot2_ 

18from pygeodesy.interns import _coincident_, _colinear_, _COMMASPACE_, _xyz_ 

19from pygeodesy.lazily import _ALL_LAZY, _ALL_DOCS, _ALL_MODS as _MODS, \ 

20 _sys_version_info2 

21from pygeodesy.named import _NamedBase, _NotImplemented, _xother3 

22# from pygeodesy.namedTuples import Vector3Tuple # _MODS 

23from pygeodesy.props import deprecated_method, Property, Property_RO, \ 

24 property_doc_, property_RO, _update_all 

25from pygeodesy.streprs import Fmt, strs, unstr 

26from pygeodesy.units import Float, Scalar 

27# from pygeodesy.utily import sincos2 # _MODS 

28 

29# from builtints import hash, int, isinstance, map, max, round, type, zip 

30from math import atan2, ceil, fabs, floor, trunc 

31 

32__all__ = _ALL_LAZY.vector3dBase 

33__version__ = '24.06.11' 

34 

35 

36class Vector3dBase(_NamedBase): # sync __methods__ with .fsums.Fsum 

37 '''(INTERNAL) Generic 3-D vector base class. 

38 ''' 

39 _crosserrors = True # un/set by .errors.crosserrors 

40 

41 _ll = None # original latlon, '_fromll' 

42# _x = INT0 # X component 

43# _y = INT0 # Y component 

44# _z = INT0 # Z component 

45 

46 def __init__(self, x_xyz, y=INT0, z=INT0, ll=None, **name): 

47 '''New L{Vector3d} or C{Vector3dBase} instance. 

48 

49 The vector may be normalised or use x, y, z for position and 

50 distance from earth centre or height relative to the surface 

51 of the earth' sphere or ellipsoid. 

52 

53 @arg x_xyz: X component of vector (C{scalar}) or a (3-D) vector 

54 (C{Cartesian}, L{Ecef9Tuple}, C{Nvector}, L{Vector3d}, 

55 L{Vector3Tuple}, L{Vector4Tuple} or a C{tuple} or 

56 C{list} of 3+ C{scalar} items). 

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 ll: Optional latlon reference (C{LatLon}). 

62 @kwarg name: Optional C{B{name}=NN} (C{str}). 

63 

64 @raise VectorError: Invalid B{C{x_xyz}}. 

65 ''' 

66 self._x, \ 

67 self._y, \ 

68 self._z = _xyz3(type(self), x_xyz, y, z) if isscalar(x_xyz) else \ 

69 _xyz3(type(self), x_xyz) 

70 if ll: 

71 self._ll = ll 

72 if name: 

73 self.name = name 

74 

75 def __abs__(self): 

76 '''Return the norm of this vector. 

77 

78 @return: Norm, unit length (C{float}); 

79 ''' 

80 return self.length 

81 

82 def __add__(self, other): 

83 '''Add this to an other vector (L{Vector3d}). 

84 

85 @return: Vectorial sum (L{Vector3d}). 

86 

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

88 ''' 

89 return self.plus(other) 

90 

91 def __bool__(self): # PYCHOK PyChecker 

92 '''Is this vector non-zero? 

93 ''' 

94 return bool(self.x or self.y or self.z) 

95 

96 def __ceil__(self): # PYCHOK no cover 

97 '''Return a vector with the C{ceil} of these components. 

98 

99 @return: Ceil-ed (L{Vector3d}). 

100 ''' 

101 return self._mapped(ceil) 

102 

103 def __cmp__(self, other): # Python 2- 

104 '''Compare this and an other vector (L{Vector3d}). 

105 

106 @return: -1, 0 or +1 (C{int}). 

107 

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

109 ''' 

110 return _signOf(self.length, self._other_cmp(other)) 

111 

112 cmp = __cmp__ 

113 

114 def __divmod__(self, other): # PYCHOK no cover 

115 '''Not implemented.''' 

116 return _NotImplemented(self, other) 

117 

118 def __eq__(self, other): 

119 '''Is this vector equal to an other vector? 

120 

121 @arg other: The other vector (L{Vector3d}). 

122 

123 @return: C{True} if equal, C{False} otherwise. 

124 

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

126 ''' 

127 return self.isequalTo(other, eps=EPS0) 

128 

129 def __float__(self): # PYCHOK no cover 

130 '''Not implemented.''' 

131 return _NotImplemented(self) 

132 

133 def __floor__(self): # PYCHOK no cover 

134 '''Return a vector with the C{floor} of these components. 

135 

136 @return: Floor-ed (L{Vector3d}). 

137 ''' 

138 return self._mapped(floor) 

139 

140 def __floordiv__(self, other): # PYCHOK no cover 

141 '''Not implemented.''' 

142 return _NotImplemented(self, other) 

143 

144 def __format__(self, *other): # PYCHOK no cover 

145 '''Not implemented.''' 

146 return _NotImplemented(self, *other) 

147 

148 def __ge__(self, other): 

149 '''Is this vector longer than or equal to an other vector? 

150 

151 @arg other: The other vector (L{Vector3d}). 

152 

153 @return: C{True} if so, C{False} otherwise. 

154 

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

156 ''' 

157 return self.length >= self._other_cmp(other) 

158 

159# def __getitem__(self, key): 

160# '''Return C{item} at index or slice C{[B{key}]}. 

161# ''' 

162# return self.xyz[key] 

163 

164 def __gt__(self, other): 

165 '''Is this vector longer than an other vector? 

166 

167 @arg other: The other vector (L{Vector3d}). 

168 

169 @return: C{True} if so, C{False} otherwise. 

170 

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

172 ''' 

173 return self.length > self._other_cmp(other) 

174 

175 def __hash__(self): # PYCHOK no cover 

176 '''Return this instance' C{hash}. 

177 ''' 

178 return hash(self.xyz) # XXX id(self)? 

179 

180 def __iadd__(self, other): 

181 '''Add this and an other vector I{in-place}, C{this += B{other}}. 

182 

183 @arg other: The other vector (L{Vector3d}). 

184 

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

186 ''' 

187 return self._xyz(self.plus(other)) 

188 

189 def __ifloordiv__(self, other): # PYCHOK no cover 

190 '''Not implemented.''' 

191 return _NotImplemented(self, other) 

192 

193 def __imatmul__(self, other): # PYCHOK Python 3.5+ 

194 '''Cross multiply this and an other vector I{in-place}, C{this @= B{other}}. 

195 

196 @arg other: The other vector (L{Vector3d}). 

197 

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

199 

200 @see: Luciano Ramalho, "Fluent Python", O'Reilly, 2016 p. 397+, 2022 p. 578+. 

201 ''' 

202 return self._xyz(self.cross(other)) 

203 

204 def __imod__(self, other): # PYCHOK no cover 

205 '''Not implemented.''' 

206 return _NotImplemented(self, other) 

207 

208 def __imul__(self, scalar): 

209 '''Multiply this vector by a scalar I{in-place}, C{this *= B{scalar}}. 

210 

211 @arg scalar: Factor (C{scalar}). 

212 

213 @raise TypeError: Non-scalar B{C{scalar}}. 

214 ''' 

215 return self._xyz(self.times(scalar)) 

216 

217 def __int__(self): # PYCHOK no cover 

218 '''Return a vector with the C{int} of these components. 

219 

220 @return: Int-ed (L{Vector3d}). 

221 ''' 

222 v = self.classof(_0_0) 

223 v._x, v._y, v._z = map2(int, self.xyz) 

224 return v 

225 

226 def __ipow__(self, other, *mod): # PYCHOK no cover 

227 '''Not implemented.''' 

228 return _NotImplemented(self, other, *mod) 

229 

230 def __isub__(self, other): 

231 '''Subtract an other vector from this one I{in-place}, C{this -= B{other}}. 

232 

233 @arg other: The other vector (L{Vector3d}). 

234 

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

236 ''' 

237 return self._xyz(self.minus(other)) 

238 

239# def __iter__(self): 

240# '''Return an C{iter}ator over this vector's components. 

241# ''' 

242# return iter(self.xyz) 

243 

244 def __itruediv__(self, scalar): 

245 '''Divide this vector by a scalar I{in-place}, C{this /= B{scalar}}. 

246 

247 @arg scalar: The divisor (C{scalar}). 

248 

249 @raise TypeError: Non-scalar B{C{scalar}}. 

250 ''' 

251 return self._xyz(self.dividedBy(scalar)) 

252 

253 def __le__(self, other): # Python 3+ 

254 '''Is this vector shorter than or equal to an other vector? 

255 

256 @arg other: The other vector (L{Vector3d}). 

257 

258 @return: C{True} if so, C{False} otherwise. 

259 

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

261 ''' 

262 return self.length <= self._other_cmp(other) 

263 

264# def __len__(self): 

265# '''Return C{3}, always. 

266# ''' 

267# return len(self.xyz) 

268 

269 def __lt__(self, other): # Python 3+ 

270 '''Is this vector shorter than an other vector? 

271 

272 @arg other: The other vector (L{Vector3d}). 

273 

274 @return: C{True} if so, C{False} otherwise. 

275 

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

277 ''' 

278 return self.length < self._other_cmp(other) 

279 

280 def __matmul__(self, other): # PYCHOK Python 3.5+ 

281 '''Compute the cross product of this and an other vector, C{this @ B{other}}. 

282 

283 @arg other: The other vector (L{Vector3d}). 

284 

285 @return: Cross product (L{Vector3d}). 

286 

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

288 ''' 

289 return self.cross(other) 

290 

291 def __mod__(self, other): # PYCHOK no cover 

292 '''Not implemented.''' 

293 return _NotImplemented(self, other) 

294 

295 def __mul__(self, scalar): 

296 '''Multiply this vector by a scalar, C{this * B{scalar}}. 

297 

298 @arg scalar: Factor (C{scalar}). 

299 

300 @return: Product (L{Vector3d}). 

301 ''' 

302 return self.times(scalar) 

303 

304 def __ne__(self, other): 

305 '''Is this vector not equal to an other vector? 

306 

307 @arg other: The other vector (L{Vector3d}). 

308 

309 @return: C{True} if so, C{False} otherwise. 

310 

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

312 ''' 

313 return not self.isequalTo(other, eps=EPS0) 

314 

315 def __neg__(self): 

316 '''Return the opposite of this vector. 

317 

318 @return: This instance negated (L{Vector3d}) 

319 ''' 

320 return self.classof(-self.x, -self.y, -self.z) 

321 

322 def __pos__(self): # PYCHOK no cover 

323 '''Return this vector I{as-is} or a copy. 

324 

325 @return: This instance (L{Vector3d}) 

326 ''' 

327 return self if _pos_self else self.copy() 

328 

329 def __pow__(self, other, *mod): # PYCHOK no cover 

330 '''Not implemented.''' 

331 return _NotImplemented(self, other, *mod) 

332 

333 __radd__ = __add__ # PYCHOK no cover 

334 

335 def __rdivmod__ (self, other): # PYCHOK no cover 

336 '''Not implemented.''' 

337 return _NotImplemented(self, other) 

338 

339# def __repr__(self): 

340# '''Return the default C{repr(this)}. 

341# ''' 

342# return self.toRepr() 

343 

344 def __rfloordiv__(self, other): # PYCHOK no cover 

345 '''Not implemented.''' 

346 return _NotImplemented(self, other) 

347 

348 def __rmatmul__(self, other): # PYCHOK Python 3.5+ 

349 '''Compute the cross product of an other and this vector, C{B{other} @ this}. 

350 

351 @arg other: The other vector (L{Vector3d}). 

352 

353 @return: Cross product (L{Vector3d}). 

354 

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

356 ''' 

357 return self.others(other).cross(self) 

358 

359 def __rmod__(self, other): # PYCHOK no cover 

360 '''Not implemented.''' 

361 return _NotImplemented(self, other) 

362 

363 __rmul__ = __mul__ 

364 

365 def __round__(self, *ndigits): # PYCHOK no cover 

366 '''Return a vector with these components C{rounded}. 

367 

368 @arg ndigits: Optional number of digits (C{int}). 

369 

370 @return: Rounded (L{Vector3d}). 

371 ''' 

372 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__> 

373 return self.classof(*(round(_, *ndigits) for _ in self.xyz)) 

374 

375 def __rpow__(self, other, *mod): # PYCHOK no cover 

376 '''Not implemented.''' 

377 return _NotImplemented(self, other, *mod) 

378 

379 def __rsub__(self, other): # PYCHOK no cover 

380 '''Subtract this vector from an other vector, C{B{other} - this}. 

381 

382 @arg other: The other vector (L{Vector3d}). 

383 

384 @return: Difference (L{Vector3d}). 

385 

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

387 ''' 

388 return self.others(other).minus(self) 

389 

390 def __rtruediv__(self, scalar): # PYCHOK no cover 

391 '''Not implemented.''' 

392 return _NotImplemented(self, scalar) 

393 

394# def __str__(self): 

395# '''Return the default C{str(self)}. 

396# ''' 

397# return self.toStr() 

398 

399 def __sub__(self, other): 

400 '''Subtract an other vector from this vector, C{this - B{other}}. 

401 

402 @arg other: The other vector (L{Vector3d}). 

403 

404 @return: Difference (L{Vector3d}). 

405 

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

407 ''' 

408 return self.minus(other) 

409 

410 def __truediv__(self, scalar): 

411 '''Divide this vector by a scalar, C{this / B{scalar}}. 

412 

413 @arg scalar: The divisor (C{scalar}). 

414 

415 @return: Quotient (L{Vector3d}). 

416 

417 @raise TypeError: Non-scalar B{C{scalar}}. 

418 ''' 

419 return self.dividedBy(scalar) 

420 

421 def __trunc__(self): # PYCHOK no cover 

422 '''Return a vector with the C{trunc} of these components. 

423 

424 @return: Trunc-ed (L{Vector3d}). 

425 ''' 

426 return self._mapped(trunc) 

427 

428 if _sys_version_info2 < (3, 0): # PYCHOK no cover 

429 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions> 

430 __div__ = __truediv__ 

431 __idiv__ = __itruediv__ 

432 __long__ = __int__ 

433 __nonzero__ = __bool__ 

434 __rdiv__ = __rtruediv__ 

435 

436 def angleTo(self, other, vSign=None, wrap=False): 

437 '''Compute the angle between this and an other vector. 

438 

439 @arg other: The other vector (L{Vector3d}). 

440 @kwarg vSign: Optional vector, if supplied (and out of the 

441 plane of this and the other), angle is signed 

442 positive if this->other is clockwise looking 

443 along vSign or negative in opposite direction, 

444 otherwise angle is unsigned. 

445 @kwarg wrap: If C{True}, wrap/unroll the angle to +/-PI (C{bool}). 

446 

447 @return: Angle (C{radians}). 

448 

449 @raise TypeError: If B{C{other}} or B{C{vSign}} not a L{Vector3d}. 

450 ''' 

451 x = self.cross(other) 

452 s = x.length 

453 # use vSign as reference to set sign of s 

454 if s and vSign and x.dot(vSign) < 0: 

455 s = -s 

456 

457 a = atan2(s, self.dot(other)) 

458 if wrap and fabs(a) > PI: 

459 a -= _copysign(PI2, a) 

460 return a 

461 

462 def apply(self, fun2, other_x, *y_z, **fun2_kwds): 

463 '''Apply a 2-argument function pairwise to the components 

464 of this and an other vector. 

465 

466 @arg fun2: 2-Argument callable (C{any(scalar, scalar}), 

467 return a C{scalar} or L{INT0} result. 

468 @arg other_x: Other X component (C{scalar}) or a vector 

469 with X, Y and Z components (C{Cartesian}, 

470 L{Ecef9Tuple}, C{Nvector}, L{Vector3d}, 

471 L{Vector3Tuple} or L{Vector4Tuple}). 

472 @arg y_z: Other Y and Z components, positional (C{scalar}, C{scalar}). 

473 @kwarg fun2_kwds: Optional keyword arguments for B{C{fun2}}. 

474 

475 @return: New, applied vector (L{Vector3d}). 

476 

477 @raise ValueError: Invalid B{C{other_x}} or B{C{y_z}}. 

478 ''' 

479 _xcallable(fun2=fun2) 

480 if fun2_kwds: 

481 def _f2(a, b): 

482 return fun2(a, b, **fun2_kwds) 

483 else: 

484 _f2 = fun2 

485 

486 xyz = _xyz3(self.apply, other_x, *y_z) 

487 xyz = (_f2(a, b) for a, b in _zip(self.xyz, xyz)) # strict=True 

488 return self.classof(*xyz) 

489 

490 def cross(self, other, raiser=None, eps0=EPS): # raiser=NN 

491 '''Compute the cross product of this and an other vector. 

492 

493 @arg other: The other vector (L{Vector3d}). 

494 @kwarg raiser: Optional, L{CrossError} label if raised (C{str}, non-L{NN}). 

495 @kwarg eps0: Near-zero tolerance (C{scalar}), same units as C{x}, C{y} and 

496 C{z}. 

497 

498 @return: Cross product (L{Vector3d}). 

499 

500 @raise CrossError: Zero or near-zero cross product and if B{C{raiser}} and 

501 L{crosserrors<pygeodesy.crosserrors>} are both C{True}. 

502 

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

504 ''' 

505 X, Y, Z = self.others(other).xyz 

506 x, y, z = self.xyz 

507 xyz = ((y * Z - Y * z), 

508 (z * X - Z * x), 

509 (x * Y - X * y)) 

510 

511 if raiser and self.crosserrors and eps0 > 0 \ 

512 and max(map(fabs, xyz)) < eps0: 

513 r = other._fromll or other 

514 s = self._fromll or self 

515 t = self.isequalTo(other, eps=eps0) 

516 t = _coincident_ if t else _colinear_ 

517 raise CrossError(raiser, s, other=r, txt=t) 

518 

519 return self.classof(*xyz) 

520 

521 @property_doc_('''raise or ignore L{CrossError} exceptions (C{bool}).''') 

522 def crosserrors(self): 

523 '''Get L{CrossError} exceptions (C{bool}). 

524 ''' 

525 return self._crosserrors 

526 

527 @crosserrors.setter # PYCHOK setter! 

528 def crosserrors(self, raiser): 

529 '''Raise or ignore L{CrossError} exceptions (C{bool}). 

530 ''' 

531 self._crosserrors = bool(raiser) 

532 

533 def dividedBy(self, divisor): 

534 '''Divide this vector by a scalar. 

535 

536 @arg divisor: The divisor (C{scalar}). 

537 

538 @return: New, scaled vector (L{Vector3d}). 

539 

540 @raise TypeError: Non-scalar B{C{divisor}}. 

541 

542 @raise VectorError: Invalid or zero B{C{divisor}}. 

543 ''' 

544 d = Scalar(divisor=divisor) 

545 try: 

546 return self._times(_1_0 / d) 

547 except (ValueError, ZeroDivisionError) as x: 

548 raise VectorError(divisor=divisor, cause=x) 

549 

550 def dot(self, other): 

551 '''Compute the dot (scalar) product of this and an other vector. 

552 

553 @arg other: The other vector (L{Vector3d}). 

554 

555 @return: Dot product (C{float}). 

556 

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

558 ''' 

559 return self.length2 if other is self else \ 

560 fdot(self.xyz, *self.others(other).xyz) 

561 

562 @deprecated_method 

563 def equals(self, other, units=False): # PYCHOK no cover 

564 '''DEPRECATED, use method C{isequalTo}. 

565 ''' 

566 return self.isequalTo(other, units=units) 

567 

568 @Property_RO 

569 def euclid(self): 

570 '''I{Approximate} the length (norm, magnitude) of this vector (C{Float}). 

571 

572 @see: Properties C{length} and C{length2} and function 

573 L{pygeodesy.euclid_}. 

574 ''' 

575 return Float(euclid=euclid_(self.x, self.y, self.z)) 

576 

577 def equirectangular(self, other): 

578 '''I{Approximate} the different between this and an other vector. 

579 

580 @arg other: Vector to subtract (C{Vector3dBase}). 

581 

582 @return: The lenght I{squared} of the difference (C{Float}). 

583 

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

585 

586 @see: Property C{length2}. 

587 ''' 

588 d = self.minus(other) 

589 return Float(equirectangular=hypot2_(d.x, d.y, d.z)) 

590 

591 @Property 

592 def _fromll(self): 

593 '''(INTERNAL) Get the latlon reference (C{LatLon}) or C{None}. 

594 ''' 

595 return self._ll 

596 

597 @_fromll.setter # PYCHOK setter! 

598 def _fromll(self, ll): 

599 '''(INTERNAL) Set the latlon reference (C{LatLon}) or C{None}. 

600 ''' 

601 self._ll = ll or None 

602 

603 @property_RO 

604 def homogeneous(self): 

605 '''Get this vector's homogeneous representation (L{Vector3d}). 

606 ''' 

607 x, y, z = self.xyz 

608 if z: 

609 x = x / z # /= chokes PyChecker 

610 y = y / z 

611# z = _1_0 

612 else: 

613 if isneg0(z): 

614 x = -x 

615 y = -y 

616 x = _copysignINF(x) 

617 y = _copysignINF(y) 

618# z = NAN 

619 return self.classof(x, y, _1_0) 

620 

621 def intermediateTo(self, other, fraction, **unused): # height=None, wrap=False 

622 '''Locate the vector at a given fraction between (or along) this 

623 and an other vector. 

624 

625 @arg other: The other vector (L{Vector3d}). 

626 @arg fraction: Fraction between both vectors (C{scalar}, 

627 0.0 for this and 1.0 for the other vector). 

628 

629 @return: Intermediate vector (L{Vector3d}). 

630 

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

632 ''' 

633 f = Scalar(fraction=fraction) 

634 if isnear0(f): # PYCHOK no cover 

635 r = self 

636 else: 

637 r = self.others(other) 

638 if not isnear1(f): # self * (1 - f) + r * f 

639 r = self.plus(r.minus(self)._times(f)) 

640 return r 

641 

642 def isconjugateTo(self, other, minum=1, eps=EPS): 

643 '''Determine whether this and an other vector are conjugates. 

644 

645 @arg other: The other vector (C{Cartesian}, L{Ecef9Tuple}, 

646 L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). 

647 @kwarg minum: Minimal number of conjugates required (C{int}, 0..3). 

648 @kwarg eps: Tolerance for equality and conjugation (C{scalar}), 

649 same units as C{x}, C{y}, and C{z}. 

650 

651 @return: C{True} if both vector's components either match 

652 or at least C{B{minum}} have opposite signs. 

653 

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

655 

656 @see: Method C{isequalTo}. 

657 ''' 

658 self.others(other) 

659 n = 0 

660 for a, b in zip(self.xyz, other.xyz): 

661 if fabs(a + b) < eps and ((a < 0 and b > 0) or 

662 (a > 0 and b < 0)): 

663 n += 1 # conjugate 

664 elif fabs(a - b) > eps: 

665 return False # unequal 

666 return bool(n >= minum) 

667 

668 def isequalTo(self, other, units=False, eps=EPS): 

669 '''Check if this and an other vector are equal or equivalent. 

670 

671 @arg other: The other vector (L{Vector3d}). 

672 @kwarg units: Optionally, compare the normalized, unit 

673 version of both vectors. 

674 @kwarg eps: Tolerance for equality (C{scalar}), same units as 

675 C{x}, C{y}, and C{z}. 

676 

677 @return: C{True} if vectors are identical, C{False} otherwise. 

678 

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

680 

681 @see: Method C{isconjugateTo}. 

682 ''' 

683 if units: 

684 self.others(other) 

685 d = self.unit().minus(other.unit()) 

686 else: 

687 d = self.minus(other) 

688 return max(map(fabs, d.xyz)) < eps 

689 

690 @Property_RO 

691 def length(self): # __dict__ value overwritten by Property_RO C{_united} 

692 '''Get the length (norm, magnitude) of this vector (C{Float}). 

693 

694 @see: Properties L{length2} and L{euclid}. 

695 ''' 

696 return Float(length=hypot_(self.x, self.y, self.z)) 

697 

698 @Property_RO 

699 def length2(self): # __dict__ value overwritten by Property_RO C{_united} 

700 '''Get the length I{squared} of this vector (C{Float}). 

701 

702 @see: Property L{length} and method C{equirectangular}. 

703 ''' 

704 return Float(length2=hypot2_(self.x, self.y, self.z)) 

705 

706 def _mapped(self, func): 

707 '''(INTERNAL) Map these components. 

708 ''' 

709 return self.classof(*map2(func, self.xyz)) 

710 

711 def minus(self, other): 

712 '''Subtract an other vector from this vector. 

713 

714 @arg other: The other vector (L{Vector3d}). 

715 

716 @return: New vector difference (L{Vector3d}). 

717 

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

719 ''' 

720 xyz = self.others(other).xyz 

721 return self._minus(*xyz) 

722 

723 def _minus(self, x, y, z): 

724 '''(INTERNAL) Helper for methods C{.minus} and C{.minus_}. 

725 ''' 

726 return self.classof(self.x - x, self.y - y, self.z - z) 

727 

728 def minus_(self, other_x, *y_z): 

729 '''Subtract separate X, Y and Z components from this vector. 

730 

731 @arg other_x: X component (C{scalar}) or a vector's 

732 X, Y, and Z components (C{Cartesian}, 

733 L{Ecef9Tuple}, C{Nvector}, L{Vector3d}, 

734 L{Vector3Tuple}, L{Vector4Tuple}). 

735 @arg y_z: Y and Z components (C{scalar}, C{scalar}), 

736 ignored if B{C{other_x}} is not C{scalar}. 

737 

738 @return: New, vectiorial vector (L{Vector3d}). 

739 

740 @raise ValueError: Invalid B{C{other_x}} or B{C{y_z}}. 

741 ''' 

742 return self._minus(*_xyz3(self.minus_, other_x, *y_z)) 

743 

744 def negate(self): 

745 '''Return this vector in opposite direction. 

746 

747 @return: New, opposite vector (L{Vector3d}). 

748 ''' 

749 return self.classof(-self.x, -self.y, -self.z) 

750 

751 __neg__ = negate # PYCHOK no cover 

752 

753 @Property_RO 

754 def _N_vector(self): 

755 '''(INTERNAL) Get the (C{nvectorBase._N_vector_}) 

756 ''' 

757 return _MODS.nvectorBase._N_vector_(*self.xyz, name=self.name) 

758 

759 def _other_cmp(self, other): 

760 '''(INTERNAL) Return the value for comparison. 

761 ''' 

762 return other if isscalar(other) else self.others(other).length 

763 

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

765 '''Refined class comparison. 

766 

767 @arg other: The other vector (L{Vector3d}). 

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

769 keyword arguments. 

770 

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

772 

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

774 ''' 

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

776 if not isinstance(other, Vector3dBase): 

777 _NamedBase.others(self, other, name=name, up=up + 1) 

778 return other 

779 

780 def plus(self, other): 

781 '''Add this vector and an other vector. 

782 

783 @arg other: The other vector (L{Vector3d}). 

784 

785 @return: Vectorial sum (L{Vector3d}). 

786 

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

788 ''' 

789 xyz = self.others(other).xyz 

790 return self._plus(*xyz) 

791 

792 sum = plus # alternate name 

793 

794 def _plus(self, x, y, z): 

795 '''(INTERNAL) Helper for methods C{.plus} and C{.plus_}. 

796 ''' 

797 return self.classof(self.x + x, self.y + y, self.z + z) 

798 

799 def plus_(self, other_x, *y_z): 

800 '''Sum of this vector and separate X, Y and Z components. 

801 

802 @arg other_x: X component (C{scalar}) or a vector's 

803 X, Y, and Z components (C{Cartesian}, 

804 L{Ecef9Tuple}, C{Nvector}, L{Vector3d}, 

805 L{Vector3Tuple}, L{Vector4Tuple}). 

806 @arg y_z: Y and Z components (C{scalar}, C{scalar}), 

807 ignored if B{C{other_x}} is not C{scalar}. 

808 

809 @return: New, vectiorial vector (L{Vector3d}). 

810 

811 @raise ValueError: Invalid B{C{other_x}} or B{C{y_z}}. 

812 ''' 

813 return self._plus(*_xyz3(self.plus_, other_x, *y_z)) 

814 

815 def rotate(self, axis, theta): 

816 '''Rotate this vector around an axis by a specified angle. 

817 

818 @arg axis: The axis being rotated around (L{Vector3d}). 

819 @arg theta: The angle of rotation (C{radians}). 

820 

821 @return: New, rotated vector (L{Vector3d}). 

822 

823 @see: U{Rotation matrix from axis and angle<https://WikiPedia.org/wiki/ 

824 Rotation_matrix#Rotation_matrix_from_axis_and_angle>} and 

825 U{Quaternion-derived rotation matrix<https://WikiPedia.org/wiki/ 

826 Quaternions_and_spatial_rotation#Quaternion-derived_rotation_matrix>}. 

827 ''' 

828 s, c = _MODS.utily.sincos2(theta) # rotation angle 

829 d = _1_0 - c 

830 if d or s: 

831 p = self.unit().xyz # point being rotated 

832 r = self.others(axis=axis).unit() # axis being rotated around 

833 

834 ax, ay, az = r.xyz # quaternion-derived rotation matrix 

835 bx, by, bz = r.times(d).xyz 

836 sx, sy, sz = r.times(s).xyz 

837 

838 x = fdot(p, ax * bx + c, ax * by - sz, ax * bz + sy) 

839 y = fdot(p, ay * bx + sz, ay * by + c, ay * bz - sx) 

840 z = fdot(p, az * bx - sy, az * by + sx, az * bz + c) 

841 else: # unrotated 

842 x, y, z = self.xyz 

843 return self.classof(x, y, z) 

844 

845 @deprecated_method 

846 def rotateAround(self, axis, theta): # PYCHOK no cover 

847 '''DEPRECATED, use method C{rotate}.''' 

848 return self.rotate(axis, theta) 

849 

850 def times(self, factor): 

851 '''Multiply this vector by a scalar. 

852 

853 @arg factor: Scale factor (C{scalar}). 

854 

855 @return: New, scaled vector (L{Vector3d}). 

856 

857 @raise TypeError: Non-scalar B{C{factor}}. 

858 ''' 

859 return self._times(Scalar(factor=factor)) 

860 

861 def _times(self, s): 

862 '''(INTERNAL) Helper for C{.dividedBy} and C{.times}. 

863 ''' 

864 return self.classof(self.x * s, self.y * s, self.z * s) 

865 

866 def times_(self, other_x, *y_z): 

867 '''Multiply this vector's components by separate X, Y and Z factors. 

868 

869 @arg other_x: X scale factor (C{scalar}) or a vector's 

870 X, Y, and Z components as scale factors 

871 (C{Cartesian}, L{Ecef9Tuple}, C{Nvector}, 

872 L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple}). 

873 @arg y_z: Y and Z scale factors (C{scalar}, C{scalar}), 

874 ignored if B{C{other_x}} is not C{scalar}. 

875 

876 @return: New, scaled vector (L{Vector3d}). 

877 

878 @raise ValueError: Invalid B{C{other_x}} or B{C{y_z}}. 

879 ''' 

880 x, y, z = _xyz3(self.times_, other_x, *y_z) 

881 return self.classof(self.x * x, self.y * y, self.z * z) 

882 

883# @deprecated_method 

884# def to2ab(self): # PYCHOK no cover 

885# '''DEPRECATED, use property C{Nvector.philam}. 

886# 

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

888# ''' 

889# return _MODS.formy.n_xyz2philam(self.x, self.y, self.z) 

890 

891# @deprecated_method 

892# def to2ll(self): # PYCHOK no cover 

893# '''DEPRECATED, use property C{Nvector.latlon}. 

894# 

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

896# ''' 

897# return _MODS.formy.n_xyz2latlon(self.x, self.y, self.z) 

898 

899 @deprecated_method 

900 def to3xyz(self): # PYCHOK no cover 

901 '''DEPRECATED, use property L{xyz}. 

902 ''' 

903 return self.xyz 

904 

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

906 '''Return a string representation of this vector. 

907 

908 @kwarg prec: Number of decimal places (C{int}). 

909 @kwarg fmt: Enclosing format to use (C{str}). 

910 @kwarg sep: Separator between components (C{str}). 

911 

912 @return: Vector as "(x, y, z)" (C{str}). 

913 ''' 

914 t = sep.join(strs(self.xyz, prec=prec)) 

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

916 

917 def unit(self, ll=None): 

918 '''Normalize this vector to unit length. 

919 

920 @kwarg ll: Optional, original location (C{LatLon}). 

921 

922 @return: Normalized vector (L{Vector3d}). 

923 ''' 

924 u = self._united 

925 if ll: 

926 u._fromll = ll 

927 return u 

928 

929 @Property_RO 

930 def _united(self): # __dict__ value overwritten below 

931 '''(INTERNAL) Get normalized vector (L{Vector3d}). 

932 ''' 

933 n = self.length 

934 if n > EPS0 and fabs(n - _1_0) > EPS0: 

935 u = self._xnamed(self.dividedBy(n)) 

936 u._update(False, length=_1_0, length2=_1_0, _united=u) 

937 else: 

938 u = self.copy() 

939 u._update(False, _united=u) 

940 if self._fromll: 

941 u._fromll = self._fromll 

942 return u 

943 

944 @Property 

945 def x(self): 

946 '''Get the X component (C{float}). 

947 ''' 

948 return self._x 

949 

950 @x.setter # PYCHOK setter! 

951 def x(self, x): 

952 '''Set the X component, if different (C{float}). 

953 ''' 

954 x = Float(x=x) 

955 if self._x != x: 

956 _update_all(self, needed=3) 

957 self._x = x 

958 

959 @Property 

960 def xyz(self): 

961 '''Get the X, Y and Z components (L{Vector3Tuple}C{(x, y, z)}). 

962 ''' 

963 return _MODS.namedTuples.Vector3Tuple(self.x, self.y, self.z, name=self.name) 

964 

965 @xyz.setter # PYCHOK setter! 

966 def xyz(self, xyz): 

967 '''Set the X, Y and Z components (C{Cartesian}, L{Ecef9Tuple}, 

968 C{Nvector}, L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple} 

969 or a C{tuple} or C{list} of 3+ C{scalar} items). 

970 ''' 

971 self._xyz(xyz) 

972 

973 def _xyz(self, x_xyz, *y_z): 

974 '''(INTERNAL) Set the C{_x}, C{_y} and C{_z} attributes. 

975 ''' 

976 _update_all(self, needed=3) 

977 self._x, self._y, self._z = _xyz3(_xyz_, x_xyz, *y_z) 

978 return self 

979 

980 @property_RO 

981 def x2y2z2(self): 

982 '''Get the X, Y and Z components I{squared} (3-tuple C{(x**2, y**2, z**2)}). 

983 ''' 

984 return self.x**2, self.y**2, self.z**2 

985 

986 @Property 

987 def y(self): 

988 '''Get the Y component (C{float}). 

989 ''' 

990 return self._y 

991 

992 @y.setter # PYCHOK setter! 

993 def y(self, y): 

994 '''Set the Y component, if different (C{float}). 

995 ''' 

996 y = Float(y=y) 

997 if self._y != y: 

998 _update_all(self, needed=3) 

999 self._y = y 

1000 

1001 @Property 

1002 def z(self): 

1003 '''Get the Z component (C{float}). 

1004 ''' 

1005 return self._z 

1006 

1007 @z.setter # PYCHOK setter! 

1008 def z(self, z): 

1009 '''Set the Z component, if different (C{float}). 

1010 ''' 

1011 z = Float(z=z) 

1012 if self._z != z: 

1013 _update_all(self, needed=3) 

1014 self._z = z 

1015 

1016 

1017def _xyz3(where, x_xyz, *y_z): # in .cartesianBase._rtp3 

1018 '''(INTERNAL) Helper for C{Vector3dBase.__init__}, C{-.apply}, C{-.times_} and C{-._xyz}. 

1019 ''' 

1020 try: 

1021 x_y_z = map1(_float0, x_xyz, *y_z) if y_z else ( # islistuple for VectorXTuple 

1022 map2(_float0, x_xyz[:3]) if islistuple(x_xyz, minum=3) else 

1023 x_xyz.xyz) 

1024 except (AttributeError, TypeError, ValueError) as x: 

1025 raise _xError(x, unstr(where, x_xyz, *y_z)) 

1026 return x_y_z 

1027 

1028 

1029__all__ += _ALL_DOCS(Vector3dBase) 

1030 

1031# **) MIT License 

1032# 

1033# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1034# 

1035# Permission is hereby granted, free of charge, to any person obtaining a 

1036# copy of this software and associated documentation files (the "Software"), 

1037# to deal in the Software without restriction, including without limitation 

1038# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1039# and/or sell copies of the Software, and to permit persons to whom the 

1040# Software is furnished to do so, subject to the following conditions: 

1041# 

1042# The above copyright notice and this permission notice shall be included 

1043# in all copies or substantial portions of the Software. 

1044# 

1045# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1046# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1047# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1048# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1049# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1050# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1051# OTHER DEALINGS IN THE SOFTWARE.