Vector3d#

class orix.vector.Vector3d(data=None)[source]#

Bases: Object3d

Vector base class.

Vectors support the following mathematical operations:

Unary negation.
Addition to other vectors, scalars, numbers, and compatible array-like objects.
Subtraction to and from the above.
Multiplication to scalars, numbers, and compatible array-like objects.
Division by the same as multiplication. Division by a vector is not defined in general.

Examples

>>> from orix.vector import Vector3d
>>> v = Vector3d((1, 2, 3))
>>> w = Vector3d(np.array([[1, 0, 0], [0, 1, 1]]))
>>> w.x
array([1, 0])
>>> v.unit
Vector3d (1,)
[[0.2673 0.5345 0.8018]]
>>> -v
Vector3d (1,)
[[-1 -2 -3]]
>>> v + w
Vector3d (2,)
[[2 2 3]
 [1 3 4]]
>>> w - (2, -3)
Vector3d (2,)
[[-1 -2 -2]
 [ 3  4  4]]
>>> 3 * v
Vector3d (1,)
[[3 6 9]]
>>> v / 2
Vector3d (1,)
[[0.5 1.  1.5]]
>>> v / (2, -2)
Vector3d (2,)
[[ 0.5  1.   1.5]
 [-0.5 -1.  -1.5]]

Attributes

`Vector3d.azimuth`	Azimuth spherical coordinate, i.e. the angle \(\phi \in [0, 2\pi]\) from the positive z-axis to a point on the sphere, according to the ISO 31-11 standard [Weisstein, 2005].
`Vector3d.dim`	Return the number of dimensions for this object.
`Vector3d.perpendicular`	Return the perpendicular vectors.
`Vector3d.polar`	Polar spherical coordinate, i.e. the angle \(\theta \in [0, \pi]\) from the positive z-axis to a point on the sphere, according to the ISO 31-11 standard [Weisstein, 2005].
`Vector3d.radial`	Return the radial spherical coordinate, i.e. the distance from a point on the sphere to the origin, according to the ISO 31-11 standard [Weisstein, 2005].
`Vector3d.x`	Return or set the x coordinates.
`Vector3d.xyz`	Return the coordinates as three arrays, useful for plotting.
`Vector3d.y`	Return or set the y coordinates.
`Vector3d.z`	Return or set the z coordinate.

Methods

`Vector3d.angle_with`(other[, degrees])	Return the angles between these vectors in other vectors.
`Vector3d.cross`(other)	Return the cross product of a vector with another vector.
`Vector3d.dot`(other)	Return the dot products of the vectors and the other vectors.
`Vector3d.dot_outer`(other[, lazy, ...])	Return the outer dot products of all vectors and all the other vectors.
`Vector3d.draw_circle`([projection, figure, ...])	Draw great or small circles with a given `opening_angle` to to the vectors in the stereographic projection.
`Vector3d.from_polar`(azimuth, polar[, ...])	Initialize from spherical coordinates according to the ISO 31-11 standard [Weisstein, 2005].
`Vector3d.get_circle`([opening_angle, steps])	Get vectors delineating great or small circle(s) with a given `opening_angle` about each vector.
`Vector3d.get_nearest`(x[, inclusive, tiebreak])	Return the vector in `x` with the smallest angle to this vector.
`Vector3d.in_fundamental_sector`(symmetry)	Project vectors to a symmetry's fundamental sector (inverse pole figure).
`Vector3d.inverse_pole_density_function`([...])	Plot the Inverse Pole Density Function (IPDF) within the fundamental sector of a given point group symmetry in the stereographic projection.
`Vector3d.mean`()	Return the mean vector.
`Vector3d.pole_density_function`([resolution, ...])	Plot the Pole Density Function (PDF) on a given hemisphere in the stereographic projection.
`Vector3d.rotate`([axis, angle])	Convenience function for rotating this vector.
`Vector3d.scatter`([projection, figure, ...])	Plot vectors in the stereographic projection.
`Vector3d.to_polar`([degrees])	Return the azimuth \(\phi\), polar \(\theta\), and radial \(r\) spherical coordinates defined as in the ISO 31-11 standard [Weisstein, 2005].
`Vector3d.xvector`()	Return a unit vector in the x-direction.
`Vector3d.yvector`()	Return a unit vector in the y-direction.
`Vector3d.zero`([shape])	Return zero vectors in the specified shape.
`Vector3d.zvector`()	Return a unit vector in the z-direction.

Examples using `Vector3d`#

Vector3d#

Examples using Vector3d#

Examples using `Vector3d`#