Coverage for pygeodesy/vector3dBase.py: 93%
274 statements
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2# -*- coding: utf-8 -*-
4u'''(INTERNAL) Private, 3-D vector base class C{Vector3dBase}.
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'''
11from pygeodesy.basics import _copysign, islistuple, isscalar, map1, \
12 map2, _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
29# from builtints import hash, int, isinstance, map, max, round, type, zip
30from math import atan2, ceil, fabs, floor, trunc
32__all__ = _ALL_LAZY.vector3dBase
33__version__ = '24.05.19'
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
41 _ll = None # original latlon, '_fromll'
42# _x = INT0 # X component
43# _y = INT0 # Y component
44# _z = INT0 # Z component
46 def __init__(self, x_xyz, y=INT0, z=INT0, ll=None, **name):
47 '''New L{Vector3d} or C{Vector3dBase} instance.
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.
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}).
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
75 def __abs__(self):
76 '''Return the norm of this vector.
78 @return: Norm, unit length (C{float});
79 '''
80 return self.length
82 def __add__(self, other):
83 '''Add this to an other vector (L{Vector3d}).
85 @return: Vectorial sum (L{Vector3d}).
87 @raise TypeError: Incompatible B{C{other}} C{type}.
88 '''
89 return self.plus(other)
91 def __bool__(self): # PYCHOK PyChecker
92 '''Is this vector non-zero?
93 '''
94 return bool(self.x or self.y or self.z)
96 def __ceil__(self): # PYCHOK no cover
97 '''Return a vector with the C{ceil} of these components.
99 @return: Ceil-ed (L{Vector3d}).
100 '''
101 return self._mapped(ceil)
103 def __cmp__(self, other): # Python 2-
104 '''Compare this and an other vector (L{Vector3d}).
106 @return: -1, 0 or +1 (C{int}).
108 @raise TypeError: Incompatible B{C{other}} C{type}.
109 '''
110 n = self.others(other).length
111 return -1 if self.length < n else (
112 +1 if self.length > n else 0)
114 cmp = __cmp__
116 def __divmod__(self, other): # PYCHOK no cover
117 '''Not implemented.'''
118 return _NotImplemented(self, other)
120 def __eq__(self, other):
121 '''Is this vector equal to an other vector?
123 @arg other: The other vector (L{Vector3d}).
125 @return: C{True} if equal, C{False} otherwise.
127 @raise TypeError: Incompatible B{C{other}} C{type}.
128 '''
129 return self.isequalTo(other, eps=EPS0)
131 def __float__(self): # PYCHOK no cover
132 '''Not implemented.'''
133 return _NotImplemented(self)
135 def __floor__(self): # PYCHOK no cover
136 '''Return a vector with the C{floor} of these components.
138 @return: Floor-ed (L{Vector3d}).
139 '''
140 return self._mapped(floor)
142 def __floordiv__(self, other): # PYCHOK no cover
143 '''Not implemented.'''
144 return _NotImplemented(self, other)
146 def __format__(self, *other): # PYCHOK no cover
147 '''Not implemented.'''
148 return _NotImplemented(self, *other)
150 def __ge__(self, other):
151 '''Is this vector longer than or equal to an other vector?
153 @arg other: The other vector (L{Vector3d}).
155 @return: C{True} if so, C{False} otherwise.
157 @raise TypeError: Incompatible B{C{other}} C{type}.
158 '''
159 return self.length >= self.others(other).length
161# def __getitem__(self, key):
162# '''Return C{item} at index or slice C{[B{key}]}.
163# '''
164# return self.xyz[key]
166 def __gt__(self, other):
167 '''Is this vector longer than an other vector?
169 @arg other: The other vector (L{Vector3d}).
171 @return: C{True} if so, C{False} otherwise.
173 @raise TypeError: Incompatible B{C{other}} C{type}.
174 '''
175 return self.length > self.others(other).length
177 def __hash__(self): # PYCHOK no cover
178 '''Return this instance' C{hash}.
179 '''
180 return hash(self.xyz) # XXX id(self)?
182 def __iadd__(self, other):
183 '''Add this and an other vector I{in-place}, C{this += B{other}}.
185 @arg other: The other vector (L{Vector3d}).
187 @raise TypeError: Incompatible B{C{other}} C{type}.
188 '''
189 return self._xyz(self.plus(other))
191 def __ifloordiv__(self, other): # PYCHOK no cover
192 '''Not implemented.'''
193 return _NotImplemented(self, other)
195 def __imatmul__(self, other): # PYCHOK Python 3.5+
196 '''Cross multiply this and an other vector I{in-place}, C{this @= B{other}}.
198 @arg other: The other vector (L{Vector3d}).
200 @raise TypeError: Incompatible B{C{other}} C{type}.
202 @see: Luciano Ramalho, "Fluent Python", O'Reilly, 2016 p. 397+, 2022 p. 578+.
203 '''
204 return self._xyz(self.cross(other))
206 def __imod__(self, other): # PYCHOK no cover
207 '''Not implemented.'''
208 return _NotImplemented(self, other)
210 def __imul__(self, scalar):
211 '''Multiply this vector by a scalar I{in-place}, C{this *= B{scalar}}.
213 @arg scalar: Factor (C{scalar}).
215 @raise TypeError: Non-scalar B{C{scalar}}.
216 '''
217 return self._xyz(self.times(scalar))
219 def __int__(self): # PYCHOK no cover
220 '''Return a vector with the C{int} of these components.
222 @return: Int-ed (L{Vector3d}).
223 '''
224 v = self.classof(_0_0)
225 v._x, v._y, v._z = map2(int, self.xyz)
226 return v
228 def __ipow__(self, other, *mod): # PYCHOK no cover
229 '''Not implemented.'''
230 return _NotImplemented(self, other, *mod)
232 def __isub__(self, other):
233 '''Subtract an other vector from this one I{in-place}, C{this -= B{other}}.
235 @arg other: The other vector (L{Vector3d}).
237 @raise TypeError: Incompatible B{C{other}} C{type}.
238 '''
239 return self._xyz(self.minus(other))
241# def __iter__(self):
242# '''Return an C{iter}ator over this vector's components.
243# '''
244# return iter(self.xyz)
246 def __itruediv__(self, scalar):
247 '''Divide this vector by a scalar I{in-place}, C{this /= B{scalar}}.
249 @arg scalar: The divisor (C{scalar}).
251 @raise TypeError: Non-scalar B{C{scalar}}.
252 '''
253 return self._xyz(self.dividedBy(scalar))
255 def __le__(self, other): # Python 3+
256 '''Is this vector shorter than or equal to an other vector?
258 @arg other: The other vector (L{Vector3d}).
260 @return: C{True} if so, C{False} otherwise.
262 @raise TypeError: Incompatible B{C{other}} C{type}.
263 '''
264 return self.length <= self.others(other).length
266# def __len__(self):
267# '''Return C{3}, always.
268# '''
269# return len(self.xyz)
271 def __lt__(self, other): # Python 3+
272 '''Is this vector shorter than an other vector?
274 @arg other: The other vector (L{Vector3d}).
276 @return: C{True} if so, C{False} otherwise.
278 @raise TypeError: Incompatible B{C{other}} C{type}.
279 '''
280 return self.length < self.others(other).length
282 def __matmul__(self, other): # PYCHOK Python 3.5+
283 '''Compute the cross product of this and an other vector, C{this @ B{other}}.
285 @arg other: The other vector (L{Vector3d}).
287 @return: Cross product (L{Vector3d}).
289 @raise TypeError: Incompatible B{C{other}} C{type}.
290 '''
291 return self.cross(other)
293 def __mod__(self, other): # PYCHOK no cover
294 '''Not implemented.'''
295 return _NotImplemented(self, other)
297 def __mul__(self, scalar):
298 '''Multiply this vector by a scalar, C{this * B{scalar}}.
300 @arg scalar: Factor (C{scalar}).
302 @return: Product (L{Vector3d}).
303 '''
304 return self.times(scalar)
306 def __ne__(self, other):
307 '''Is this vector not equal to an other vector?
309 @arg other: The other vector (L{Vector3d}).
311 @return: C{True} if so, C{False} otherwise.
313 @raise TypeError: Incompatible B{C{other}} C{type}.
314 '''
315 return not self.isequalTo(other, eps=EPS0)
317 def __neg__(self):
318 '''Return the opposite of this vector.
320 @return: This instance negated (L{Vector3d})
321 '''
322 return self.classof(-self.x, -self.y, -self.z)
324 def __pos__(self): # PYCHOK no cover
325 '''Return this vector I{as-is} or a copy.
327 @return: This instance (L{Vector3d})
328 '''
329 return self if _pos_self else self.copy()
331 def __pow__(self, other, *mod): # PYCHOK no cover
332 '''Not implemented.'''
333 return _NotImplemented(self, other, *mod)
335 __radd__ = __add__ # PYCHOK no cover
337 def __rdivmod__ (self, other): # PYCHOK no cover
338 '''Not implemented.'''
339 return _NotImplemented(self, other)
341# def __repr__(self):
342# '''Return the default C{repr(this)}.
343# '''
344# return self.toRepr()
346 def __rfloordiv__(self, other): # PYCHOK no cover
347 '''Not implemented.'''
348 return _NotImplemented(self, other)
350 def __rmatmul__(self, other): # PYCHOK Python 3.5+
351 '''Compute the cross product of an other and this vector, C{B{other} @ this}.
353 @arg other: The other vector (L{Vector3d}).
355 @return: Cross product (L{Vector3d}).
357 @raise TypeError: Incompatible B{C{other}} C{type}.
358 '''
359 return self.others(other).cross(self)
361 def __rmod__(self, other): # PYCHOK no cover
362 '''Not implemented.'''
363 return _NotImplemented(self, other)
365 __rmul__ = __mul__
367 def __round__(self, *ndigits): # PYCHOK no cover
368 '''Return a vector with these components C{rounded}.
370 @arg ndigits: Optional number of digits (C{int}).
372 @return: Rounded (L{Vector3d}).
373 '''
374 # <https://docs.Python.org/3.12/reference/datamodel.html?#object.__round__>
375 return self.classof(*(round(_, *ndigits) for _ in self.xyz))
377 def __rpow__(self, other, *mod): # PYCHOK no cover
378 '''Not implemented.'''
379 return _NotImplemented(self, other, *mod)
381 def __rsub__(self, other): # PYCHOK no cover
382 '''Subtract this vector from an other vector, C{B{other} - this}.
384 @arg other: The other vector (L{Vector3d}).
386 @return: Difference (L{Vector3d}).
388 @raise TypeError: Incompatible B{C{other}} C{type}.
389 '''
390 return self.others(other).minus(self)
392 def __rtruediv__(self, scalar): # PYCHOK no cover
393 '''Not implemented.'''
394 return _NotImplemented(self, scalar)
396# def __str__(self):
397# '''Return the default C{str(self)}.
398# '''
399# return self.toStr()
401 def __sub__(self, other):
402 '''Subtract an other vector from this vector, C{this - B{other}}.
404 @arg other: The other vector (L{Vector3d}).
406 @return: Difference (L{Vector3d}).
408 @raise TypeError: Incompatible B{C{other}} C{type}.
409 '''
410 return self.minus(other)
412 def __truediv__(self, scalar):
413 '''Divide this vector by a scalar, C{this / B{scalar}}.
415 @arg scalar: The divisor (C{scalar}).
417 @return: Quotient (L{Vector3d}).
419 @raise TypeError: Non-scalar B{C{scalar}}.
420 '''
421 return self.dividedBy(scalar)
423 def __trunc__(self): # PYCHOK no cover
424 '''Return a vector with the C{trunc} of these components.
426 @return: Trunc-ed (L{Vector3d}).
427 '''
428 return self._mapped(trunc)
430 if _sys_version_info2 < (3, 0): # PYCHOK no cover
431 # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions>
432 __div__ = __truediv__
433 __idiv__ = __itruediv__
434 __long__ = __int__
435 __nonzero__ = __bool__
436 __rdiv__ = __rtruediv__
438 def angleTo(self, other, vSign=None, wrap=False):
439 '''Compute the angle between this and an other vector.
441 @arg other: The other vector (L{Vector3d}).
442 @kwarg vSign: Optional vector, if supplied (and out of the
443 plane of this and the other), angle is signed
444 positive if this->other is clockwise looking
445 along vSign or negative in opposite direction,
446 otherwise angle is unsigned.
447 @kwarg wrap: If C{True}, wrap/unroll the angle to +/-PI (C{bool}).
449 @return: Angle (C{radians}).
451 @raise TypeError: If B{C{other}} or B{C{vSign}} not a L{Vector3d}.
452 '''
453 x = self.cross(other)
454 s = x.length
455 # use vSign as reference to set sign of s
456 if s and vSign and x.dot(vSign) < 0:
457 s = -s
459 a = atan2(s, self.dot(other))
460 if wrap and fabs(a) > PI:
461 a -= _copysign(PI2, a)
462 return a
464 def apply(self, fun2, other_x, *y_z, **fun2_kwds):
465 '''Apply a 2-argument function pairwise to the components
466 of this and an other vector.
468 @arg fun2: 2-Argument callable (C{any(scalar, scalar}),
469 return a C{scalar} or L{INT0} result.
470 @arg other_x: Other X component (C{scalar}) or a vector
471 with X, Y and Z components (C{Cartesian},
472 L{Ecef9Tuple}, C{Nvector}, L{Vector3d},
473 L{Vector3Tuple} or L{Vector4Tuple}).
474 @arg y_z: Other Y and Z components, positional (C{scalar}, C{scalar}).
475 @kwarg fun2_kwds: Optional keyword arguments for B{C{fun2}}.
477 @return: New, applied vector (L{Vector3d}).
479 @raise ValueError: Invalid B{C{other_x}} or B{C{y_z}}.
480 '''
481 _xcallable(fun2=fun2)
482 if fun2_kwds:
483 def _f2(a, b):
484 return fun2(a, b, **fun2_kwds)
485 else:
486 _f2 = fun2
488 xyz = _xyz3(self.apply, other_x, *y_z)
489 xyz = (_f2(a, b) for a, b in _zip(self.xyz, xyz)) # strict=True
490 return self.classof(*xyz)
492 def cross(self, other, raiser=None, eps0=EPS): # raiser=NN
493 '''Compute the cross product of this and an other vector.
495 @arg other: The other vector (L{Vector3d}).
496 @kwarg raiser: Optional, L{CrossError} label if raised (C{str},
497 non-L{NN}).
498 @kwarg eps0: Near-zero tolerance (C{scalar}), same units as
499 C{x}, C{y}, and C{z}.
501 @return: Cross product (L{Vector3d}).
503 @raise CrossError: Zero or near-zero cross product and both
504 B{C{raiser}} and L{pygeodesy.crosserrors} set.
506 @raise TypeError: Incompatible B{C{other}} C{type}.
507 '''
508 X, Y, Z = self.others(other).xyz
509 x, y, z = self.xyz
510 xyz = ((y * Z - Y * z),
511 (z * X - Z * x),
512 (x * Y - X * y))
514 if raiser and self.crosserrors and eps0 > 0 \
515 and max(map(fabs, xyz)) < eps0:
516 r = other._fromll or other
517 s = self._fromll or self
518 t = self.isequalTo(other, eps=eps0)
519 t = _coincident_ if t else _colinear_
520 raise CrossError(raiser, s, other=r, txt=t)
522 return self.classof(*xyz)
524 @property_doc_('''raise or ignore L{CrossError} exceptions (C{bool}).''')
525 def crosserrors(self):
526 '''Get L{CrossError} exceptions (C{bool}).
527 '''
528 return self._crosserrors
530 @crosserrors.setter # PYCHOK setter!
531 def crosserrors(self, raiser):
532 '''Raise or ignore L{CrossError} exceptions (C{bool}).
533 '''
534 self._crosserrors = bool(raiser)
536 def dividedBy(self, divisor):
537 '''Divide this vector by a scalar.
539 @arg divisor: The divisor (C{scalar}).
541 @return: New, scaled vector (L{Vector3d}).
543 @raise TypeError: Non-scalar B{C{divisor}}.
545 @raise VectorError: Invalid or zero B{C{divisor}}.
546 '''
547 d = Scalar(divisor=divisor)
548 try:
549 return self._times(_1_0 / d)
550 except (ValueError, ZeroDivisionError) as x:
551 raise VectorError(divisor=divisor, cause=x)
553 def dot(self, other):
554 '''Compute the dot (scalar) product of this and an other vector.
556 @arg other: The other vector (L{Vector3d}).
558 @return: Dot product (C{float}).
560 @raise TypeError: Incompatible B{C{other}} C{type}.
561 '''
562 return self.length2 if other is self else \
563 fdot(self.xyz, *self.others(other).xyz)
565 @deprecated_method
566 def equals(self, other, units=False): # PYCHOK no cover
567 '''DEPRECATED, use method C{isequalTo}.
568 '''
569 return self.isequalTo(other, units=units)
571 @Property_RO
572 def euclid(self):
573 '''I{Approximate} the length (norm, magnitude) of this vector (C{Float}).
575 @see: Properties C{length} and C{length2} and function
576 L{pygeodesy.euclid_}.
577 '''
578 return Float(euclid=euclid_(self.x, self.y, self.z))
580 def equirectangular(self, other):
581 '''I{Approximate} the different between this and an other vector.
583 @arg other: Vector to subtract (C{Vector3dBase}).
585 @return: The lenght I{squared} of the difference (C{Float}).
587 @raise TypeError: Incompatible B{C{other}} C{type}.
589 @see: Property C{length2}.
590 '''
591 d = self.minus(other)
592 return Float(equirectangular=hypot2_(d.x, d.y, d.z))
594 @Property
595 def _fromll(self):
596 '''(INTERNAL) Get the latlon reference (C{LatLon}) or C{None}.
597 '''
598 return self._ll
600 @_fromll.setter # PYCHOK setter!
601 def _fromll(self, ll):
602 '''(INTERNAL) Set the latlon reference (C{LatLon}) or C{None}.
603 '''
604 self._ll = ll or None
606 @property_RO
607 def homogeneous(self):
608 '''Get this vector's homogeneous representation (L{Vector3d}).
609 '''
610 x, y, z = self.xyz
611 if z:
612 x = x / z # /= chokes PyChecker
613 y = y / z
614# z = _1_0
615 else:
616 if isneg0(z):
617 x = -x
618 y = -y
619 x = _copysignINF(x)
620 y = _copysignINF(y)
621# z = NAN
622 return self.classof(x, y, _1_0)
624 def intermediateTo(self, other, fraction, **unused): # height=None, wrap=False
625 '''Locate the vector at a given fraction between (or along) this
626 and an other vector.
628 @arg other: The other vector (L{Vector3d}).
629 @arg fraction: Fraction between both vectors (C{scalar},
630 0.0 for this and 1.0 for the other vector).
632 @return: Intermediate vector (L{Vector3d}).
634 @raise TypeError: Incompatible B{C{other}} C{type}.
635 '''
636 f = Scalar(fraction=fraction)
637 if isnear0(f): # PYCHOK no cover
638 r = self
639 else:
640 r = self.others(other)
641 if not isnear1(f): # self * (1 - f) + r * f
642 r = self.plus(r.minus(self)._times(f))
643 return r
645 def isconjugateTo(self, other, minum=1, eps=EPS):
646 '''Determine whether this and an other vector are conjugates.
648 @arg other: The other vector (C{Cartesian}, L{Ecef9Tuple},
649 L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}).
650 @kwarg minum: Minimal number of conjugates required (C{int}, 0..3).
651 @kwarg eps: Tolerance for equality and conjugation (C{scalar}),
652 same units as C{x}, C{y}, and C{z}.
654 @return: C{True} if both vector's components either match
655 or at least C{B{minum}} have opposite signs.
657 @raise TypeError: Incompatible B{C{other}} C{type}.
659 @see: Method C{isequalTo}.
660 '''
661 self.others(other)
662 n = 0
663 for a, b in zip(self.xyz, other.xyz):
664 if fabs(a + b) < eps and ((a < 0 and b > 0) or
665 (a > 0 and b < 0)):
666 n += 1 # conjugate
667 elif fabs(a - b) > eps:
668 return False # unequal
669 return bool(n >= minum)
671 def isequalTo(self, other, units=False, eps=EPS):
672 '''Check if this and an other vector are equal or equivalent.
674 @arg other: The other vector (L{Vector3d}).
675 @kwarg units: Optionally, compare the normalized, unit
676 version of both vectors.
677 @kwarg eps: Tolerance for equality (C{scalar}), same units as
678 C{x}, C{y}, and C{z}.
680 @return: C{True} if vectors are identical, C{False} otherwise.
682 @raise TypeError: Incompatible B{C{other}} C{type}.
684 @see: Method C{isconjugateTo}.
685 '''
686 if units:
687 self.others(other)
688 d = self.unit().minus(other.unit())
689 else:
690 d = self.minus(other)
691 return max(map(fabs, d.xyz)) < eps
693 @Property_RO
694 def length(self): # __dict__ value overwritten by Property_RO C{_united}
695 '''Get the length (norm, magnitude) of this vector (C{Float}).
697 @see: Properties L{length2} and L{euclid}.
698 '''
699 return Float(length=hypot_(self.x, self.y, self.z))
701 @Property_RO
702 def length2(self): # __dict__ value overwritten by Property_RO C{_united}
703 '''Get the length I{squared} of this vector (C{Float}).
705 @see: Property L{length} and method C{equirectangular}.
706 '''
707 return Float(length2=hypot2_(self.x, self.y, self.z))
709 def _mapped(self, func):
710 '''(INTERNAL) Map these components.
711 '''
712 return self.classof(*map2(func, self.xyz))
714 def minus(self, other):
715 '''Subtract an other vector from this vector.
717 @arg other: The other vector (L{Vector3d}).
719 @return: New vector difference (L{Vector3d}).
721 @raise TypeError: Incompatible B{C{other}} C{type}.
722 '''
723 xyz = self.others(other).xyz
724 return self._minus(*xyz)
726 def _minus(self, x, y, z):
727 '''(INTERNAL) Helper for methods C{.minus} and C{.minus_}.
728 '''
729 return self.classof(self.x - x, self.y - y, self.z - z)
731 def minus_(self, other_x, *y_z):
732 '''Subtract separate X, Y and Z components from this vector.
734 @arg other_x: X component (C{scalar}) or a vector's
735 X, Y, and Z components (C{Cartesian},
736 L{Ecef9Tuple}, C{Nvector}, L{Vector3d},
737 L{Vector3Tuple}, L{Vector4Tuple}).
738 @arg y_z: Y and Z components (C{scalar}, C{scalar}),
739 ignored if B{C{other_x}} is not C{scalar}.
741 @return: New, vectiorial vector (L{Vector3d}).
743 @raise ValueError: Invalid B{C{other_x}} or B{C{y_z}}.
744 '''
745 return self._minus(*_xyz3(self.minus_, other_x, *y_z))
747 def negate(self):
748 '''Return this vector in opposite direction.
750 @return: New, opposite vector (L{Vector3d}).
751 '''
752 return self.classof(-self.x, -self.y, -self.z)
754 __neg__ = negate # PYCHOK no cover
756 @Property_RO
757 def _N_vector(self):
758 '''(INTERNAL) Get the (C{nvectorBase._N_vector_})
759 '''
760 return _MODS.nvectorBase._N_vector_(*self.xyz, name=self.name)
762 def others(self, *other, **name_other_up):
763 '''Refined class comparison.
765 @arg other: The other vector (L{Vector3d}).
766 @kwarg name_other_up: Overriding C{name=other} and C{up=1}
767 keyword arguments.
769 @return: The B{C{other}} if compatible.
771 @raise TypeError: Incompatible B{C{other}} C{type}.
772 '''
773 other, name, up = _xother3(self, other, **name_other_up)
774 if not isinstance(other, Vector3dBase):
775 _NamedBase.others(self, other, name=name, up=up + 1)
776 return other
778 def plus(self, other):
779 '''Add this vector and an other vector.
781 @arg other: The other vector (L{Vector3d}).
783 @return: Vectorial sum (L{Vector3d}).
785 @raise TypeError: Incompatible B{C{other}} C{type}.
786 '''
787 xyz = self.others(other).xyz
788 return self._plus(*xyz)
790 sum = plus # alternate name
792 def _plus(self, x, y, z):
793 '''(INTERNAL) Helper for methods C{.plus} and C{.plus_}.
794 '''
795 return self.classof(self.x + x, self.y + y, self.z + z)
797 def plus_(self, other_x, *y_z):
798 '''Sum of this vector and separate X, Y and Z components.
800 @arg other_x: X component (C{scalar}) or a vector's
801 X, Y, and Z components (C{Cartesian},
802 L{Ecef9Tuple}, C{Nvector}, L{Vector3d},
803 L{Vector3Tuple}, L{Vector4Tuple}).
804 @arg y_z: Y and Z components (C{scalar}, C{scalar}),
805 ignored if B{C{other_x}} is not C{scalar}.
807 @return: New, vectiorial vector (L{Vector3d}).
809 @raise ValueError: Invalid B{C{other_x}} or B{C{y_z}}.
810 '''
811 return self._plus(*_xyz3(self.plus_, other_x, *y_z))
813 def rotate(self, axis, theta):
814 '''Rotate this vector around an axis by a specified angle.
816 @arg axis: The axis being rotated around (L{Vector3d}).
817 @arg theta: The angle of rotation (C{radians}).
819 @return: New, rotated vector (L{Vector3d}).
821 @see: U{Rotation matrix from axis and angle<https://WikiPedia.org/wiki/
822 Rotation_matrix#Rotation_matrix_from_axis_and_angle>} and
823 U{Quaternion-derived rotation matrix<https://WikiPedia.org/wiki/
824 Quaternions_and_spatial_rotation#Quaternion-derived_rotation_matrix>}.
825 '''
826 s, c = _MODS.utily.sincos2(theta) # rotation angle
827 d = _1_0 - c
828 if d or s:
829 p = self.unit().xyz # point being rotated
830 r = self.others(axis=axis).unit() # axis being rotated around
832 ax, ay, az = r.xyz # quaternion-derived rotation matrix
833 bx, by, bz = r.times(d).xyz
834 sx, sy, sz = r.times(s).xyz
836 x = fdot(p, ax * bx + c, ax * by - sz, ax * bz + sy)
837 y = fdot(p, ay * bx + sz, ay * by + c, ay * bz - sx)
838 z = fdot(p, az * bx - sy, az * by + sx, az * bz + c)
839 else: # unrotated
840 x, y, z = self.xyz
841 return self.classof(x, y, z)
843 @deprecated_method
844 def rotateAround(self, axis, theta): # PYCHOK no cover
845 '''DEPRECATED, use method C{rotate}.'''
846 return self.rotate(axis, theta)
848 def times(self, factor):
849 '''Multiply this vector by a scalar.
851 @arg factor: Scale factor (C{scalar}).
853 @return: New, scaled vector (L{Vector3d}).
855 @raise TypeError: Non-scalar B{C{factor}}.
856 '''
857 return self._times(Scalar(factor=factor))
859 def _times(self, s):
860 '''(INTERNAL) Helper for C{.dividedBy} and C{.times}.
861 '''
862 return self.classof(self.x * s, self.y * s, self.z * s)
864 def times_(self, other_x, *y_z):
865 '''Multiply this vector's components by separate X, Y and Z factors.
867 @arg other_x: X scale factor (C{scalar}) or a vector's
868 X, Y, and Z components as scale factors
869 (C{Cartesian}, L{Ecef9Tuple}, C{Nvector},
870 L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple}).
871 @arg y_z: Y and Z scale factors (C{scalar}, C{scalar}),
872 ignored if B{C{other_x}} is not C{scalar}.
874 @return: New, scaled vector (L{Vector3d}).
876 @raise ValueError: Invalid B{C{other_x}} or B{C{y_z}}.
877 '''
878 x, y, z = _xyz3(self.times_, other_x, *y_z)
879 return self.classof(self.x * x, self.y * y, self.z * z)
881# @deprecated_method
882# def to2ab(self): # PYCHOK no cover
883# '''DEPRECATED, use property C{Nvector.philam}.
884#
885# @return: A L{PhiLam2Tuple}C{(phi, lam)}.
886# '''
887# return _MODS.formy.n_xyz2philam(self.x, self.y, self.z)
889# @deprecated_method
890# def to2ll(self): # PYCHOK no cover
891# '''DEPRECATED, use property C{Nvector.latlon}.
892#
893# @return: A L{LatLon2Tuple}C{(lat, lon)}.
894# '''
895# return _MODS.formy.n_xyz2latlon(self.x, self.y, self.z)
897 @deprecated_method
898 def to3xyz(self): # PYCHOK no cover
899 '''DEPRECATED, use property L{xyz}.
900 '''
901 return self.xyz
903 def toStr(self, prec=5, fmt=Fmt.PAREN, sep=_COMMASPACE_): # PYCHOK expected
904 '''Return a string representation of this vector.
906 @kwarg prec: Number of decimal places (C{int}).
907 @kwarg fmt: Enclosing format to use (C{str}).
908 @kwarg sep: Separator between components (C{str}).
910 @return: Vector as "(x, y, z)" (C{str}).
911 '''
912 t = sep.join(strs(self.xyz, prec=prec))
913 return (fmt % (t,)) if fmt else t
915 def unit(self, ll=None):
916 '''Normalize this vector to unit length.
918 @kwarg ll: Optional, original location (C{LatLon}).
920 @return: Normalized vector (L{Vector3d}).
921 '''
922 u = self._united
923 if ll:
924 u._fromll = ll
925 return u
927 @Property_RO
928 def _united(self): # __dict__ value overwritten below
929 '''(INTERNAL) Get normalized vector (L{Vector3d}).
930 '''
931 n = self.length
932 if n > EPS0 and fabs(n - _1_0) > EPS0:
933 u = self._xnamed(self.dividedBy(n))
934 u._update(False, length=_1_0, length2=_1_0, _united=u)
935 else:
936 u = self.copy()
937 u._update(False, _united=u)
938 if self._fromll:
939 u._fromll = self._fromll
940 return u
942 @Property
943 def x(self):
944 '''Get the X component (C{float}).
945 '''
946 return self._x
948 @x.setter # PYCHOK setter!
949 def x(self, x):
950 '''Set the X component, if different (C{float}).
951 '''
952 x = Float(x=x)
953 if self._x != x:
954 _update_all(self, needed=3)
955 self._x = x
957 @Property
958 def xyz(self):
959 '''Get the X, Y and Z components (L{Vector3Tuple}C{(x, y, z)}).
960 '''
961 return _MODS.namedTuples.Vector3Tuple(self.x, self.y, self.z, name=self.name)
963 @xyz.setter # PYCHOK setter!
964 def xyz(self, xyz):
965 '''Set the X, Y and Z components (C{Cartesian}, L{Ecef9Tuple},
966 C{Nvector}, L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple}
967 or a C{tuple} or C{list} of 3+ C{scalar} items).
968 '''
969 self._xyz(xyz)
971 def _xyz(self, x_xyz, *y_z):
972 '''(INTERNAL) Set the C{_x}, C{_y} and C{_z} attributes.
973 '''
974 _update_all(self, needed=3)
975 self._x, self._y, self._z = _xyz3(_xyz_, x_xyz, *y_z)
976 return self
978 @property_RO
979 def x2y2z2(self):
980 '''Get the X, Y and Z components I{squared} (3-tuple C{(x**2, y**2, z**2)}).
981 '''
982 return self.x**2, self.y**2, self.z**2
984 @Property
985 def y(self):
986 '''Get the Y component (C{float}).
987 '''
988 return self._y
990 @y.setter # PYCHOK setter!
991 def y(self, y):
992 '''Set the Y component, if different (C{float}).
993 '''
994 y = Float(y=y)
995 if self._y != y:
996 _update_all(self, needed=3)
997 self._y = y
999 @Property
1000 def z(self):
1001 '''Get the Z component (C{float}).
1002 '''
1003 return self._z
1005 @z.setter # PYCHOK setter!
1006 def z(self, z):
1007 '''Set the Z component, if different (C{float}).
1008 '''
1009 z = Float(z=z)
1010 if self._z != z:
1011 _update_all(self, needed=3)
1012 self._z = z
1015def _xyz3(where, x_xyz, *y_z): # in .cartesianBase._rtp3
1016 '''(INTERNAL) Helper for C{Vector3dBase.__init__}, C{-.apply}, C{-.times_} and C{-._xyz}.
1017 '''
1018 try:
1019 x_y_z = map1(_float0, x_xyz, *y_z) if y_z else ( # islistuple for VectorXTuple
1020 map2(_float0, x_xyz[:3]) if islistuple(x_xyz, minum=3) else
1021 x_xyz.xyz)
1022 except (AttributeError, TypeError, ValueError) as x:
1023 raise _xError(x, unstr(where, x_xyz, *y_z))
1024 return x_y_z
1027__all__ += _ALL_DOCS(Vector3dBase)
1029# **) MIT License
1030#
1031# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1032#
1033# Permission is hereby granted, free of charge, to any person obtaining a
1034# copy of this software and associated documentation files (the "Software"),
1035# to deal in the Software without restriction, including without limitation
1036# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1037# and/or sell copies of the Software, and to permit persons to whom the
1038# Software is furnished to do so, subject to the following conditions:
1039#
1040# The above copyright notice and this permission notice shall be included
1041# in all copies or substantial portions of the Software.
1042#
1043# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1044# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1045# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1046# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1047# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1048# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1049# OTHER DEALINGS IN THE SOFTWARE.