# Coverage for pygeodesy/vector3dBase.py : 97%

## 255 statements 248 run 7 missing 79 excluded

Hot-keys on this page

r m x p toggle line displays

j k next/prev highlighted chunk

0 (zero) top of page

1 (one) first highlighted chunk

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 | # -*- coding: utf-8 -*- u'''I{Veness}' 3-D vector base class C{Vector3dBase}. Pure Python implementation of vector-based functions by I{(C) Chris Veness 2011-2015} published under the same MIT Licence**, see U{Vector-based geodesy <https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. ''' from pygeodesy.basics import copysign0, isnear0, isnear1, isscalar, istuplist, \ map1, _zip from pygeodesy.errors import CrossError, _InvalidError, _IsnotError, VectorError from pygeodesy.fmath import euclid_, fdot, fsum1_, hypot_, hypot2_ # from pygeodesy.fsums import fsum1_ # from .fmath from pygeodesy.interns import EPS, EPS0, INT0, NN, PI, PI2, _coincident_, \ _colinear_, _COMMASPACE_, _float0, _y_, _z_, _1_0 from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS, _sys_version_info2 from pygeodesy.named import _NamedBase, _NotImplemented, _xother3 from pygeodesy.namedTuples import Vector3Tuple from pygeodesy.props import deprecated_method, Property, Property_RO, \ property_doc_, _update_all from pygeodesy.streprs import Fmt, strs from pygeodesy.units import Float, Scalar # from pygeodesy.utily import sincos2 # in Vector3dBase.rotate below from math import atan2 __all__ = _ALL_LAZY.vector3dBase __version__ = '22.06.16' class Vector3dBase(_NamedBase): '''(INTERNAL) Generic 3-D vector base class. In a geodesy context, these may be used to represent: - n-vector representing a normal to point on earth's surface - earth-centered, earth-fixed cartesian (= spherical n-vector) - great circle normal to vector - motion vector on earth's surface - etc. ''' _crosserrors = True # un/set by .errors.crosserrors _ll = None # original latlon, '_fromll' _x = INT0 # X component _y = INT0 # Y component _z = INT0 # Z component def __init__(self, x_xyz, y=INT0, z=INT0, ll=None, name=NN): '''New L{Vector3d} or C{Vector3dBase} instance. The vector may be normalised or use x, y, z for position and distance from earth centre or height relative to the surface of the earth' sphere or ellipsoid. @arg x_xyz: X component of vector (C{scalar}) or a (3-D) vector (C{Cartesian}, L{Ecef9Tuple}, C{Nvector}, L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple} or a C{tuple} or C{list} of 3+ C{scalar} values). @kwarg y: Y component of vector (C{scalar}), ignored if B{C{x_xyz}} is not C{scalar}, otherwise same units as B{C{x_xyz}}. @kwarg z: Z component of vector (C{scalar}), ignored if B{C{x_xyz}} is not C{scalar}, otherwise same units as B{C{x_xyz}}. @kwarg ll: Optional latlon reference (C{LatLon}). @kwarg name: Optional name (C{str}). @raise VectorError: Invalid B{C{x_xyz}}. ''' if isscalar(x_xyz): self._xyz(x_xyz, y, z) else: self.xyz = x_xyz if ll: self._ll = ll if name: self.name = name def __abs__(self): '''Return the norm of this vector. @return: Norm, unit length (C{float}); ''' return self.length def __add__(self, other): '''Add this to an other vector (L{Vector3d}). @return: Vectorial sum (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.plus(other) def __bool__(self): # PYCHOK PyChecker '''Is this vector non-zero? ''' return bool(self.x or self.y or self.z) def __cmp__(self, other): # Python 2- '''Compare this and an other vector @arg other: The other vector (L{Vector3d}). @return: -1, 0 or +1 (C{int}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' n = self.others(other).length return -1 if self.length < n else ( +1 if self.length > n else 0) cmp = __cmp__ def __divmod__(self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) def __eq__(self, other): '''Is this vector equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if equal, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.isequalTo(other, eps=EPS0) def __floordiv__(self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) def __format__(self, *other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, *other) def __ge__(self, other): '''Is this vector longer than or equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.length >= self.others(other).length # def __getitem__(self, key): # '''Return C{item} at index or slice C{[B{key}]}. # ''' # return self.xyz[key] def __gt__(self, other): '''Is this vector longer than an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.length > self.others(other).length def __iadd__(self, other): '''Add this and an other vector I{in-place}, C{this += B{other}}. @arg other: The other vector (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self._xyz(self.plus(other)) def __imatmul__(self, other): # PYCHOK Python 3.5+ '''Cross multiply this and an other vector I{in-place}, C{this @= B{other}}. @arg other: The other vector (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. @see: Luciano Ramalho, "Fluent Python", page 397-398, O'Reilly 2016. ''' return self._xyz(self.cross(other)) def __imul__(self, scalar): '''Multiply this vector by a scalar I{in-place}, C{this *= B{scalar}}. @arg scalar: Factor (C{scalar}). @raise TypeError: Non-scalar B{C{scalar}}. ''' return self._xyz(self.times(scalar)) def __int__(self): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self) def __isub__(self, other): '''Subtract an other vector from this one I{in-place}, C{this -= B{other}}. @arg other: The other vector (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self._xyz(self.minus(other)) def __itruediv__(self, scalar): '''Divide this vector by a scalar I{in-place}, C{this /= B{scalar}}. @arg scalar: The divisor (C{scalar}). @raise TypeError: Non-scalar B{C{scalar}}. ''' return self._xyz(self.dividedBy(scalar)) def __le__(self, other): # Python 3+ '''Is this vector shorter than or equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.length <= self.others(other).length # def __len__(self): # '''Return C{3}, always. # ''' # return len(self.xyz) def __lt__(self, other): # Python 3+ '''Is this vector shorter than an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.length < self.others(other).length def __matmul__(self, other): # PYCHOK Python 3.5+ '''Compute the cross product of this and an other vector, C{this @ B{other}}. @arg other: The other vector (L{Vector3d}). @return: Cross product (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.cross(other) def __mod__(self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) def __mul__(self, scalar): '''Multiply this vector by a scalar, C{this * B{scalar}}. @arg scalar: Factor (C{scalar}). @return: Product (L{Vector3d}). ''' return self.times(scalar) def __ne__(self, other): '''Is this vector not equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' return not self.__eq__(other) def __pos__(self): # PYCHOK no cover '''Return this vector I{as-is}. @return: This instance (L{Vector3d}) ''' return self # XXX self.copy() def __pow__(self, other, *mod): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other, *mod) __radd__ = __add__ # PYCHOK no cover def __rdivmod__ (self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) def __rfloordiv__(self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) def __rmatmul__(self, other): # PYCHOK Python 3.5+ '''Compute the cross product of an other and this vector, C{B{other} @ this}. @arg other: The other vector (L{Vector3d}). @return: Cross product (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.others(other).cross(self) def __rmod__(self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) __rmul__ = __mul__ def __round__(self, ndigits=None): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, ndigits=ndigits) def __rpow__(self, other, *mod): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other, *mod) def __rsub__(self, other): # PYCHOK no cover '''Subtract this vector from an other vector, C{B{other} - this}. @arg other: The other vector (L{Vector3d}). @return: Difference (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.others(other).minus(self) def __rtruediv__(self, scalar): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, scalar) def __sub__(self, other): '''Subtract an other vector from this vector, C{this - B{other}}. @arg other: The other vector (L{Vector3d}). @return: Difference (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.minus(other) def __truediv__(self, scalar): '''Divide this vector by a scalar, C{this / B{scalar}}. @arg scalar: The divisor (C{scalar}). @return: Quotient (L{Vector3d}). @raise TypeError: Non-scalar B{C{scalar}}. ''' return self.dividedBy(scalar) __trunc__ = __int__ if _sys_version_info2 < (3, 0): # PYCHOK no cover # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions> __div__ = __truediv__ __idiv__ = __itruediv__ __long__ = __int__ __nonzero__ = __bool__ __rdiv__ = __rtruediv__ def angleTo(self, other, vSign=None, wrap=False): '''Compute the angle between this and an other vector. @arg other: The other vector (L{Vector3d}). @kwarg vSign: Optional vector, if supplied (and out of the plane of this and the other), angle is signed positive if this->other is clockwise looking along vSign or negative in opposite direction, otherwise angle is unsigned. @kwarg wrap: Wrap/unroll the angle to +/-PI (C{bool}). @return: Angle (C{radians}). @raise TypeError: If B{C{other}} or B{C{vSign}} not a L{Vector3d}. ''' x = self.cross(other) s = x.length # use vSign as reference to set sign of s if s and vSign and x.dot(vSign) < 0: s = -s a = atan2(s, self.dot(other)) if wrap and abs(a) > PI: a -= copysign0(PI2, a) return a def apply(self, fun2, other_x, *y_z, **fun2_kwds): '''Apply a 2-argument function component-pairwise to this and an other vector. @arg fun2: 2-Argument callable (C{any(scalar, scalar}), return a C{scalar} or L{INT0} result. @arg other_x: Other X component (C{scalar}) or a vector with X, Y and Z components (C{Cartesian}, L{Ecef9Tuple}, C{Nvector}, L{Vector3d}, L{Vector3Tuple} or L{Vector4Tuple}). @arg y_z: Other Y and Z components, positional (C{scalar}, C{scalar}). @kwarg fun2_kwds: Optional keyword arguments for B{C{fun2}}. @return: New, applied vector (L{Vector3d}). @raise ValueError: Invalid B{C{other_x}} or B{C{y_z}}. ''' if not callable(fun2): raise _IsnotError(callable.__name__, fun2=fun2) if fun2_kwds: def _f2(a, b): return fun2(a, b, **fun2_kwds) else: _f2 = fun2 x_y_z = _other_x_y_z3(other_x, y_z) x_y_z = (_f2(a, b) for a, b in _zip(self.xyz, x_y_z)) # strict=True return self.classof(*x_y_z) def cross(self, other, raiser=None, eps0=EPS): # raiser=NN '''Compute the cross product of this and an other vector. @arg other: The other vector (L{Vector3d}). @kwarg raiser: Optional, L{CrossError} label if raised (C{str}, non-L{NN}). @kwarg eps0: Near-zero tolerance (C{scalar}), same units as C{x}, C{y}, and C{z}. @return: Cross product (L{Vector3d}). @raise CrossError: Zero or near-zero cross product and both B{C{raiser}} and L{pygeodesy.crosserrors} set. @raise TypeError: Incompatible B{C{other}} C{type}. ''' other = self.others(other) x = fsum1_(self.y * other.z, -self.z * other.y) y = fsum1_(self.z * other.x, -self.x * other.z) z = fsum1_(self.x * other.y, -self.y * other.x) if raiser and self.crosserrors and eps0 > 0 \ and max(map1(abs, x, y, z)) < eps0: t = self.isequalTo(other, eps=eps0) t = _coincident_ if t else _colinear_ r = other._fromll or other raise CrossError(raiser, r, txt=t) return self.classof(x, y, z) @property_doc_('''raise or ignore L{CrossError} exceptions (C{bool}).''') def crosserrors(self): '''Get L{CrossError} exceptions (C{bool}). ''' return self._crosserrors @crosserrors.setter # PYCHOK setter! def crosserrors(self, raiser): '''Raise L{CrossError} exceptions (C{bool}). ''' self._crosserrors = bool(raiser) def dividedBy(self, divisor): '''Divide this vector by a scalar. @arg divisor: The divisor (C{scalar}). @return: New, scaled vector (L{Vector3d}). @raise TypeError: Non-scalar B{C{divisor}}. @raise VectorError: Invalid or zero B{C{divisor}}. ''' d = Scalar(divisor=divisor) try: return self._times(_1_0 / d) except (ValueError, ZeroDivisionError) as x: raise VectorError(divisor=divisor, txt=str(x)) def dot(self, other): '''Compute the dot (scalar) product of this and an other vector. @arg other: The other vector (L{Vector3d}). @return: Dot product (C{float}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.length2 if other is self else \ fdot(self.xyz, *self.others(other).xyz) @deprecated_method def equals(self, other, units=False): # PYCHOK no cover '''DEPRECATED, use method C{isequalTo}. ''' return self.isequalTo(other, units=units) @Property_RO def euclid(self): '''I{Approximate} the length (norm, magnitude) of this vector (C{Float}). @see: Properties C{length} and C{length2} and function L{pygeodesy.euclid_}. ''' return Float(euclid=euclid_(self.x, self.y, self.z)) def equirectangular(self, other): '''I{Approximate} the different between this and an other vector. @arg other: Vector to subtract (C{Vector3dBase}). @return: The lenght I{squared} of the difference (C{Float}). @raise TypeError: Incompatible B{C{other}} C{type}. @see: Property C{length2}. ''' d = self.minus(other) return Float(equirectangular=hypot2_(d.x, d.y, d.z)) @Property def _fromll(self): '''(INTERNAL) Get the latlon reference (C{LatLon}) or C{None}. ''' return self._ll @_fromll.setter # PYCHOK setter! def _fromll(self, ll): '''(INTERNAL) Set the latlon reference (C{LatLon}) or C{None}. ''' self._ll = ll or None def intermediateTo(self, other, fraction, **unused): # height=None, wrap=False '''Locate the vector at a given fraction between (or along) this and an other vector. @arg other: The other vector (L{Vector3d}). @arg fraction: Fraction between both vectors (C{scalar}, 0.0 for this and 1.0 for the other vector). @return: Intermediate vector (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' f = Scalar(fraction=fraction) if isnear0(f): # PYCHOK no cover r = self else: r = self.others(other) if not isnear1(f): # self * (1 - f) + r * f r = self.plus(r.minus(self)._times(f)) return r def isconjugateTo(self, other, minum=1, eps=EPS): '''Determine whether this and an other vector are conjugates. @arg other: The other vector (C{Cartesian}, L{Ecef9Tuple}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @kwarg minum: Minimal number of conjugates required (C{int}, 0..3). @kwarg eps: Tolerance for equality and conjugation (C{scalar}), same units as C{x}, C{y}, and C{z}. @return: C{True} if both vector's components either match or at least C{B{minum}} have opposite signs. @raise TypeError: Incompatible B{C{other}} C{type}. @see: Method C{isequalTo}. ''' self.others(other) n = 0 for a, b in zip(self.xyz, other.xyz): if abs(a + b) < eps and ((a < 0 and b > 0) or (a > 0 and b < 0)): n += 1 # conjugate elif abs(a - b) > eps: return False # unequal return bool(n >= minum) def isequalTo(self, other, units=False, eps=EPS): '''Check if this and an other vector are equal or equivalent. @arg other: The other vector (L{Vector3d}). @kwarg units: Optionally, compare the normalized, unit version of both vectors. @kwarg eps: Tolerance for equality (C{scalar}), same units as C{x}, C{y}, and C{z}. @return: C{True} if vectors are identical, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. @see: Method C{isconjugateTo}. ''' if units: self.others(other) d = self.unit().minus(other.unit()) else: d = self.minus(other) return max(map(abs, d.xyz)) < eps @Property_RO def length(self): # __dict__ value overwritten by Property_RO C{_united} '''Get the length (norm, magnitude) of this vector (C{Float}). @see: Properties L{length2} and L{euclid}. ''' return Float(length=hypot_(self.x, self.y, self.z)) @Property_RO def length2(self): # __dict__ value overwritten by Property_RO C{_united} '''Get the length I{squared} of this vector (C{Float}). @see: Property L{length} and method C{equirectangular}. ''' return Float(length2=hypot2_(self.x, self.y, self.z)) def minus(self, other): '''Subtract an other vector from this vector. @arg other: The other vector (L{Vector3d}). @return: New vector difference (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.classof(self.x - other.x, self.y - other.y, self.z - other.z) def negate(self): '''Return this vector in opposite direction. @return: New, opposite vector (L{Vector3d}). ''' return self.classof(-self.x, -self.y, -self.z) __neg__ = negate # PYCHOK no cover @Property_RO def _N_vector(self): '''(INTERNAL) Get the (C{nvectorBase._N_vector_}) ''' return _MODS.nvectorBase._N_vector_(*self.xyz, name=self.name) def others(self, *other, **name_other_up): '''Refined class comparison. @arg other: The other vector (L{Vector3d}). @kwarg name_other_up: Overriding C{name=other} and C{up=1} keyword arguments. @return: The B{C{other}} if compatible. @raise TypeError: Incompatible B{C{other}} C{type}. ''' other, name, up = _xother3(self, other, **name_other_up) if not isinstance(other, Vector3dBase): _NamedBase.others(self, other, name=name, up=up + 1) return other def plus(self, other): '''Add this vector and an other vector. @arg other: The other vector (L{Vector3d}). @return: Vectorial sum (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.classof(self.x + other.x, self.y + other.y, self.z + other.z) sum = plus # alternate name def rotate(self, axis, theta): '''Rotate this vector around an axis by a specified angle. See U{Rotation matrix from axis and angle<https://WikiPedia.org/wiki/ Rotation_matrix#Rotation_matrix_from_axis_and_angle>} and U{Quaternion-derived rotation matrix<https://WikiPedia.org/wiki/ Quaternions_and_spatial_rotation#Quaternion-derived_rotation_matrix>}. @arg axis: The axis being rotated around (L{Vector3d}). @arg theta: The angle of rotation (C{radians}). @return: New, rotated vector (L{Vector3d}). @JSname: I{rotateAround}. ''' p = self.unit().xyz # point being rotated r = self.others(axis=axis).unit() # axis being rotated around s, c = _MODS.utily.sincos2(theta) # rotation angle ax, ay, az = r.xyz # quaternion-derived rotation matrix bx, by, bz = r.times(_1_0 - c).xyz sx, sy, sz = r.times(s).xyz x = fdot(p, ax * bx + c, ax * by - sz, ax * bz + sy) y = fdot(p, ay * bx + sz, ay * by + c, ay * bz - sx) z = fdot(p, az * bx - sy, az * by + sx, az * bz + c) return self.classof(x, y, z) @deprecated_method def rotateAround(self, axis, theta): # PYCHOK no cover '''DEPRECATED, use method C{rotate}.''' return self.rotate(axis, theta) def times(self, factor): '''Multiply this vector by a scalar. @arg factor: Scale factor (C{scalar}). @return: New, scaled vector (L{Vector3d}). @raise TypeError: Non-scalar B{C{factor}}. ''' return self._times(Scalar(factor=factor)) def _times(self, s): '''(INTERNAL) Helper for C{.dividedBy} and C{.times}. ''' return self.classof(self.x * s, self.y * s, self.z * s) def times_(self, other_x, *y_z): '''Multiply this vector's components by separate X, Y and Z factors. @arg other_x: X scale factor (C{scalar}) or a vector's X, Y, and Z components as scale factors (C{Cartesian}, L{Ecef9Tuple}, C{Nvector}, L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple}). @arg y_z: Y and Z scale factors (C{scalar}, C{scalar}), ignored if B{C{other_x}} is not C{scalar}. @return: New, scaled vector (L{Vector3d}). @raise ValueError: Invalid B{C{other_x}} or B{C{y_z}}. ''' x, y, z = _other_x_y_z3(other_x, y_z) return self.classof(self.x * x, self.y * y, self.z * z) # @deprecated_method # def to2ab(self): # PYCHOK no cover # '''DEPRECATED, use property C{Nvector.philam}. # # @return: A L{PhiLam2Tuple}C{(phi, lam)}. # ''' # return _MODS.formy.n_xyz2philam(self.x, self.y, self.z) # @deprecated_method # def to2ll(self): # PYCHOK no cover # '''DEPRECATED, use property C{Nvector.latlon}. # # @return: A L{LatLon2Tuple}C{(lat, lon)}. # ''' # return _MODS.formy.n_xyz2latlon(self.x, self.y, self.z) @deprecated_method def to3xyz(self): # PYCHOK no cover '''DEPRECATED, use property L{xyz}. ''' return self.xyz def toStr(self, prec=5, fmt=Fmt.PAREN, sep=_COMMASPACE_): # PYCHOK expected '''Return a string representation of this vector. @kwarg prec: Number of decimal places (C{int}). @kwarg fmt: Enclosing format to use (C{str}). @kwarg sep: Separator between components (C{str}). @return: Vector as "(x, y, z)" (C{str}). ''' t = sep.join(strs(self.xyz, prec=prec)) return (fmt % (t,)) if fmt else t def unit(self, ll=None): '''Normalize this vector to unit length. @kwarg ll: Optional, original location (C{LatLon}). @return: Normalized vector (L{Vector3d}). ''' u = self._united if ll: u._fromll = ll return u @Property_RO def _united(self): # __dict__ value overwritten below '''(INTERNAL) Get normalized vector (L{Vector3d}). ''' n = self.length if n > EPS0 and abs(n - _1_0) > EPS0: u = self._xnamed(self.dividedBy(n)) u._update(False, length=_1_0, length2=_1_0, _united=u) else: u = self.copy() u._update(False, _united=u) if self._fromll: u._fromll = self._fromll return u @Property def x(self): '''Get the X component (C{float}). ''' return self._x @x.setter # PYCHOK setter! def x(self, x): '''Set the X component, if different (C{float}). ''' x = Float(x=x) if self._x != x: _update_all(self) self._x = x @Property def xyz(self): '''Get the X, Y and Z components (L{Vector3Tuple}C{(x, y, z)}). ''' return Vector3Tuple(self.x, self.y, self.z, name=self.name) @xyz.setter # PYCHOK setter! def xyz(self, xyz): '''Set the X, Y and Z components (C{Cartesian}, L{Ecef9Tuple}, C{Nvector}, L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple} or a C{tuple} or C{list} of 3+ C{scalar} values). ''' if istuplist(xyz, 3): self._xyz(*xyz[:3]) else: self._xyz(xyz) def _xyz(self, x_xyz, *y_z): '''(INTERNAL) Set the C{_x}, C{_y} and C{_z} attributes. ''' if len(self.__dict__) > 3: # any other than initial ._x, ._y and ._z attrs _update_all(self) try: self._x, \ self._y, \ self._z = map1(_float0, x_xyz, *y_z) if y_z else x_xyz.xyz except (AttributeError, TypeError, ValueError) as x: raise VectorError(txt=str(x), **_xyzkwds(y_z, x_xyz=x_xyz)) return self @Property_RO def x2y2z2(self): '''Get the X, Y and Z components I{squared} (3-tuple C{(x**2, y**2, z**2)}). ''' return self.x**2, self.y**2, self.z**2 @Property def y(self): '''Get the Y component (C{float}). ''' return self._y @y.setter # PYCHOK setter! def y(self, y): '''Set the Y component, if different (C{float}). ''' y = Float(y=y) if self._y != y: _update_all(self) self._y = y @Property def z(self): '''Get the Z component (C{float}). ''' return self._z @z.setter # PYCHOK setter! def z(self, z): '''Set the Z component, if different (C{float}). ''' z = Float(z=z) if self._z != z: _update_all(self) self._z = z def _other_x_y_z3(other_x, y_z): '''(INTERNAL) Helper for C{Vector3dBase.apply} and C{Vector3dBase.times_}. ''' try: return map1(_float0, other_x, *y_z) if y_z else \ (other_x.x, other_x.y, other_x.z) # not .xyz! except (AttributeError, TypeError, ValueError) as x: raise _InvalidError(txt=str(x), **_xyzkwds(y_z, other_x=other_x)) def _xyzkwds(y_z, **xyz): # PYCHOK no cover '''(INTERANL) Helper for C{_other_x_y_z3} and C{Vector3dBase._xyz}. ''' if y_z: d = dict(_zip((_y_, _z_), y_z)) # if y_z else {}, strict=True for x in xyz.values(): d.update(x=x) return d return xyz # **) MIT License # # Copyright (C) 2016-2022 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.