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# -*- coding: utf-8 -*- 

 

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

 

A 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, isscalar, istuplist, map1, _zip 

from pygeodesy.constants import EPS, EPS0, INT0, PI, PI2, _float0, \ 

isnear0, isnear1, _1_0 

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 NN, _coincident_, _colinear_, _COMMASPACE_, \ 

_y_, _z_ 

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__ = '22.09.14' 

 

 

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}). 

''' 

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.