1

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

3

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

5

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

7 2011-2024} published under the same MIT Licence**, see U{Vector-based geodesy

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

9'''

10

11 from pygeodesy.basics import _copysign, islistuple, isscalar, map1, map2, \

12 _signOf, _zip

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

14 _float0, isnear0, isnear1, isneg0, \

15 _pos_self, _1_0

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

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

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

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

20 from pygeodesy.named import _NamedBase, _NotImplemented, _xother3

21# from pygeodesy.namedTuples import Vector3Tuple # _MODS

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

23 property_doc_, property_RO, _update_all

24 from pygeodesy.streprs import Fmt, strs, unstr

25 from pygeodesy.units import Float, Scalar

26 from pygeodesy.utily import sincos2, atan2, fabs

27

28 from math import ceil as _ceil, floor as _floor, trunc as _trunc

29

30__all__ = _ALL_LAZY.vector3dBase

31__version__ = '24.10.12'

32

33

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

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

36 '''

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

38

39 _ll = None # original latlon, '_fromll'

40# _x = INT0 # X component

41# _y = INT0 # Y component

42# _z = INT0 # Z component

43

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

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

46

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

48 distance from earth centre or height relative to the surface

49 of the earth' sphere or ellipsoid.

50

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

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

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

54 C{list} of 3+ C{scalar} items).

55 @kwarg y: Y component of vector (C{scalar}), ignored if B{C{x_xyz}}

56 is not C{scalar}, otherwise same units as B{C{x_xyz}}.

57 @kwarg z: Z 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 ll: Optional latlon reference (C{LatLon}).

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

61

62 @raise VectorError: Invalid B{C{x_xyz}}, B{C{y}} or B{C{z}}.

63 '''

64 self._x, \

65 self._y, \

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

67 _xyz3(type(self), x_xyz)

68 if ll:

69 self._ll = ll

70 if name:

71 self.name = name

72

73 def __abs__(self):

74 '''Return the norm of this vector.

75

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

77 '''

78 return self.length

79

80 def __add__(self, other):

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

82

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

84

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

86 '''

87 return self.plus(other)

88

89 def __bool__(self): # PYCHOK PyChecker

90 '''Is this vector non-zero?

91

92 @see: Method C{bools}.

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, see method C{float}.'''

131 return _NotImplemented(self) # must return C{float}

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 '''Not implemented, see method C{ints}.'''

219 return _NotImplemented(self) # must return C{int}

220

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

222 '''Not implemented.'''

223 return _NotImplemented(self, other, *mod)

224

225 def __isub__(self, other):

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

227

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

229

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

231 '''

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

233

234# def __iter__(self):

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

236# '''

237# return iter(self.xyz3)

238

239 def __itruediv__(self, scalar):

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

241

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

243

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

245 '''

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

247

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

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

250

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

252

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

254

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

256 '''

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

258

259# def __len__(self):

260# '''Return C{3}, always.

261# '''

262# return len(self.xyz)

263

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

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

266

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

268

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

270

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

272 '''

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

274

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

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

277

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

279

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

281

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

283 '''

284 return self.cross(other)

285

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

287 '''Not implemented.'''

288 return _NotImplemented(self, other)

289

290 def __mul__(self, scalar):

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

292

293 @arg scalar: Factor (C{scalar}).

294

295 @return: Product (L{Vector3d}).

296 '''

297 return self.times(scalar)

298

299 def __ne__(self, other):

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

301

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

303

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

305

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

307 '''

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

309

310 def __neg__(self):

311 '''Return the opposite of this vector.

312

313 @return: A negated copy (L{Vector3d})

314 '''

315 return self.negate()

316

317 def __pos__(self): # PYCHOK no cover

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

319

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

321 '''

322 return self if _pos_self else self.copy()

323

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

325 '''Not implemented.'''

326 return _NotImplemented(self, other, *mod)

327

328 __radd__ = __add__ # PYCHOK no cover

329

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

331 '''Not implemented.'''

332 return _NotImplemented(self, other)

333

334# def __repr__(self):

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

336# '''

337# return self.toRepr()

338

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

340 '''Not implemented.'''

341 return _NotImplemented(self, other)

342

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

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

345

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

347

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

349

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

351 '''

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

353

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

355 '''Not implemented.'''

356 return _NotImplemented(self, other)

357

358 __rmul__ = __mul__

359

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

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

362

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

364

365 @return: Rounded (L{Vector3d}).

366 '''

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

368 return self.classof(*(round(_, *ndigits) for _ in self.xyz3))

369

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

371 '''Not implemented.'''

372 return _NotImplemented(self, other, *mod)

373

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

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

376

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

378

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

380

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

382 '''

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

384

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

386 '''Not implemented.'''

387 return _NotImplemented(self, scalar)

388

389# def __str__(self):

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

391# '''

392# return self.toStr()

393

394 def __sub__(self, other):

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

396

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

398

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

400

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

402 '''

403 return self.minus(other)

404

405 def __truediv__(self, scalar):

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

407

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

409

410 @return: Quotient (L{Vector3d}).

411

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

413 '''

414 return self.dividedBy(scalar)

415

416 def __trunc__(self): # PYCHOK no cover

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

418

419 @return: Trunc-ed (L{Vector3d}).

420 '''

421 return self._mapped(_trunc)

422

423 if _MODS.sys_version_info2 < (3, 0): # PYCHOK no cover

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

425 __div__ = __truediv__

426 __idiv__ = __itruediv__

427 __long__ = __int__

428 __nonzero__ = __bool__

429 __rdiv__ = __rtruediv__

430

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

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

433

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

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

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

437 positive if this->other is clockwise looking

438 along vSign or negative in opposite direction,

439 otherwise angle is unsigned.

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

441

442 @return: Angle (C{radians}).

443

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

445 '''

446 x = self.cross(other)

447 s = x.length

448 # use vSign as reference to set sign of s

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

450 s = -s

451

452 a = atan2(s, self.dot(other))

453 if wrap and fabs(a) > PI:

454 a -= _copysign(PI2, a)

455 return a

456

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

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

459 of this and an other vector.

460

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

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

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

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

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

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

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

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

469

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

471

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

473 '''

474 _xcallable(fun2=fun2)

475 if fun2_kwds:

476 def _f2(a, b):

477 return fun2(a, b, **fun2_kwds)

478 else:

479 _f2 = fun2

480

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

482 xyz = (_f2(a, b) for a, b in _zip(self.xyz3, xyz)) # strict=True

483 return self.classof(*xyz)

484

485 def bools(self):

486 '''Return the vector with C{bool} components.

487 '''

488 return self._mapped(bool)

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).xyz3

506 x, y, z = self.xyz3

507 xyz = ((y * Z - z * Y),

508 (z * X - x * Z),

509 (x * Y - y * X))

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) # name__=self.cross

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 fdot(

560 self.xyz3, *self.others(other).xyz3)

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.xyz3))

576

577 def equirectangular(self, other):

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

579

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

581

582 @return: The length 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.xyz3))

590

591 def fabs(self):

592 '''Return the vector with C{fabs} components.

593 '''

594 return self._mapped(fabs)

595

596 def floats(self):

597 '''Return the vector with C{float} components.

598 '''

599 return self._mapped(_float0)

600

601 @Property

602 def _fromll(self):

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

604 '''

605 return self._ll

606

607 @_fromll.setter # PYCHOK setter!

608 def _fromll(self, ll):

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

610 '''

611 self._ll = ll or None

612

613 @property_RO

614 def homogeneous(self):

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

616 '''

617 x, y, z = self.xyz3

618 if z:

619 x = x / z # /= chokes PyChecker

620 y = y / z

621# z = _1_0

622 else:

623 if isneg0(z):

624 x = -x

625 y = -y

626 x = _copysignINF(x)

627 y = _copysignINF(y)

628# z = NAN

629 return self.classof(x, y, _1_0)

630

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

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

633 and an other vector.

634

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

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

637 0.0 for this and 1.0 for the other vector).

638

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

640

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

642 '''

643 f = Scalar(fraction=fraction)

644 if isnear0(f): # PYCHOK no cover

645 r = self

646 else:

647 r = self.others(other)

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

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

650 return r

651

652 def ints(self):

653 '''Return the vector with C{int} components.

654 '''

655 return self._mapped(int)

656

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

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

659

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

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

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

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

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

665

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

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

668

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

670

671 @see: Method C{isequalTo}.

672 '''

673 self.others(other)

674 n = 0

675 for a, b in zip(self.xyz3, other.xyz3):

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

677 (a > 0 and b < 0)):

678 n += 1 # conjugate

679 elif fabs(a - b) > eps:

680 return False # unequal

681 return bool(n >= minum)

682

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

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

685

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

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

688 version of both vectors.

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

690 C{x}, C{y}, and C{z}.

691

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

693

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

695

696 @see: Method C{isconjugateTo}.

697 '''

698 if units:

699 self.others(other)

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

701 else:

702 d = self.minus(other)

703 return max(map(fabs, d.xyz3)) < eps

704

705 @Property_RO

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

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

708

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

710 '''

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

712

713 @Property_RO

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

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

716

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

718 '''

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

720

721 def _mapped(self, func):

722 '''(INTERNAL) Apply C{func} to all components.

723 '''

724 return self.classof(*map2(func, self.xyz3))

725

726 def minus(self, other):

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

728

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

730

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

732

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

734 '''

735 return self._minus(*self.others(other).xyz3)

736

737 def _minus(self, x, y, z):

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

739 '''

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

741

742 def minus_(self, other_x, *y_z):

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

744

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

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

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

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

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

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

751

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

753

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

755 '''

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

757

758 def negate(self):

759 '''Return the opposite of this vector.

760

761 @return: A negated copy (L{Vector3d})

762 '''

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

764

765 @Property_RO

766 def _N_vector(self):

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

768 '''

769 return _MODS.nvectorBase._N_vector_(*self.xyz3, name=self.name)

770

771 def _other_cmp(self, other):

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

773 '''

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

775

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

777 '''Refined class comparison.

778

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

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

781 keyword arguments.

782

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

784

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

786 '''

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

788 if not isinstance(other, Vector3dBase):

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

790 return other

791

792 def plus(self, other):

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

794

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

796

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

798

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

800 '''

801 return self._plus(*self.others(other).xyz3)

802

803 sum = plus # alternate name

804

805 def _plus(self, x, y, z):

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

807 '''

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

809

810 def plus_(self, other_x, *y_z):

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

812

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

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

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

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

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

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

819

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

821

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

823 '''

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

825

826 def rotate(self, axis, theta):

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

828

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

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

831

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

833

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

835 Rotation_matrix#Rotation_matrix_from_axis_and_angle>} and

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

837 Quaternions_and_spatial_rotation#Quaternion-derived_rotation_matrix>}.

838 '''

839 s, c = sincos2(theta) # rotation angle

840 d = _1_0 - c

841 if d or s:

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

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

844

845 ax, ay, az = r.xyz3 # quaternion-derived rotation matrix

846 bx, by, bz = r.times(d).xyz3

847 sx, sy, sz = r.times(s).xyz3

848

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

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

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

852 else: # unrotated

853 x, y, z = self.xyz3

854 return self.classof(x, y, z)

855

856 @deprecated_method

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

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

859 return self.rotate(axis, theta)

860

861 def times(self, factor):

862 '''Multiply this vector by a scalar.

863

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

865

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

867

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

869 '''

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

871

872 def _times(self, s):

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

874 '''

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

876

877 def times_(self, other_x, *y_z):

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

879

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

881 X, Y, and Z components as scale factors

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

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

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

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

886

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

888

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

890 '''

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

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

893

894# @deprecated_method

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

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

897#

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

899# '''

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

901

902# @deprecated_method

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

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

905#

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

907# '''

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

909

910 @deprecated_method

911 def to3xyz(self): # PYCHOK no cover

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

913 '''

914 return self.xyz

915

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

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

918

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

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

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

922

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

924 '''

925 t = sep.join(strs(self.xyz3, prec=prec))

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

927

928 def unit(self, ll=None):

929 '''Normalize this vector to unit length.

930

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

932

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

934 '''

935 u = self._united

936 if ll:

937 u._fromll = ll

938 return u

939

940 @Property_RO

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

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

943 '''

944 n = self.length

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

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

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

948 else:

949 u = self.copy()

950 u._update(False, _united=u)

951 if self._fromll:

952 u._fromll = self._fromll

953 return u

954

955 @Property

956 def x(self):

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

958 '''

959 return self._x

960

961 @x.setter # PYCHOK setter!

962 def x(self, x):

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

964 '''

965 x = Float(x=x)

966 if self._x != x:

967 _update_all(self, needed=3)

968 self._x = x

969

970 @Property

971 def xyz(self):

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

973 '''

974 return _MODS.namedTuples.Vector3Tuple(*self.xyz3, name=self.name)

975

976 @xyz.setter # PYCHOK setter!

977 def xyz(self, xyz):

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

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

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

981 '''

982 self._xyz(xyz)

983

984 def _xyz(self, x_xyz, *y_z):

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

986 '''

987 _update_all(self, needed=3)

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

989 return self

990

991 @property_RO

992 def xyz3(self):

993 '''Get the X, Y and Z components as C{3-tuple}.

994 '''

995 return self.x, self.y, self.z

996

997 @property_RO

998 def x2y2z2(self):

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

1000 '''

1001 return self.x**2, self.y**2, self.z**2

1002

1003 @Property

1004 def y(self):

1005 '''Get the Y component (C{float}).

1006 '''

1007 return self._y

1008

1009 @y.setter # PYCHOK setter!

1010 def y(self, y):

1011 '''Set the Y component, if different (C{float}).

1012 '''

1013 y = Float(y=y)

1014 if self._y != y:

1015 _update_all(self, needed=3)

1016 self._y = y

1017

1018 @Property

1019 def z(self):

1020 '''Get the Z component (C{float}).

1021 '''

1022 return self._z

1023

1024 @z.setter # PYCHOK setter!

1025 def z(self, z):

1026 '''Set the Z component, if different (C{float}).

1027 '''

1028 z = Float(z=z)

1029 if self._z != z:

1030 _update_all(self, needed=3)

1031 self._z = z

1032

1033

1034 def _xyz3(where, x_xyz, *y_z): # in .cartesianBase._rtp3

1035 '''(INTERNAL) Get , Y and Z as 3-tuple C{(x, y, z)}.

1036 '''

1037 try:

1038 xyz3 = map1(_float0, x_xyz, *y_z) if y_z else ( # islistuple for Vector*Tuple

1039 map2(_float0, x_xyz[:3]) if islistuple(x_xyz, minum=3) else

1040 x_xyz.xyz) # .xyz3

1041 except (AttributeError, TypeError, ValueError) as x:

1042 raise _xError(x, unstr(where, x_xyz, *y_z))

1043 return xyz3

1044

1045

1046__all__ += _ALL_DOCS(Vector3dBase)

1047

1048# **) MIT License

1049#

1050# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1051#

1052# Permission is hereby granted, free of charge, to any person obtaining a

1053# copy of this software and associated documentation files (the "Software"),

1054# to deal in the Software without restriction, including without limitation

1055# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1056# and/or sell copies of the Software, and to permit persons to whom the

1057# Software is furnished to do so, subject to the following conditions:

1058#

1059# The above copyright notice and this permission notice shall be included

1060# in all copies or substantial portions of the Software.

1061#

1062# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1063# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1064# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1065# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1066# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1067# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1068# OTHER DEALINGS IN THE SOFTWARE.