Vector3d#

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

Bases: Object3d

Three-dimensional vectors.

Vectors \(\mathbf{v} = (x, y, z)\) support the following mathematical operations:

Unary negation.
Addition to other vectors, numbers, and compatible array-like objects.
Subtraction to and from the above.
Multiplication to 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([[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]]

Vectors can be rotated by quaternion-like objects (which are interpreted as basis transformations)

>>> from orix.quaternion import Rotation
>>> R = Rotation.from_axes_angles([0, 0, 1], -45, degrees=True)
>>> v2 = Vector3d([1, 1, 1.])
>>> v3 = R * v2
>>> v3
Vector3d (1,)
[[ 1.4142 -0.      1.    ]]
>>> v3_np = np.dot(R.to_matrix().squeeze(), v2.data.squeeze())
>>> np.allclose(v3.data, v3_np)
True

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.data`	Return the data.
`Vector3d.ndim`	Return the number of navigation dimensions of the object.
`Vector3d.norm`	Return the norm of the data.
`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.shape`	Return the shape of the object.
`Vector3d.size`	Return the total number of entries in this object.
`Vector3d.unit`	Return the unit object.
`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.empty`()	Return an empty object with the appropriate dimensions.
`Vector3d.flatten`()	Return a new object with the same data in a single column.
`Vector3d.from_path_ends`(vectors[, close, steps])	Return vectors along the shortest path on the sphere between two or more consectutive vectors.
`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.get_random_sample`([size, replace, ...])	Return a new flattened object from a random sample of a given size.
`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.random`([shape])	Create object with random data.
`Vector3d.reshape`(*shape)	Return a new object with the same data in a new shape.
`Vector3d.rotate`([axis, angle])	Convenience function for rotating this vector.
`Vector3d.scatter`([projection, figure, ...])	Plot vectors in the stereographic projection.
`Vector3d.squeeze`()	Return a new object with the same data with length 1-dimensions removed.
`Vector3d.stack`(sequence)	Return a stacked object from the sequence.
`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.transpose`(*axes)	Return a new object with the same data transposed.
`Vector3d.unique`([return_index, return_inverse])	Return a new object containing only this object's unique entries.
`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.