Homochoric

class orix.vector.Homochoric(data=None)

Bases: NeoEuler

Equal-volume mapping of the unit quaternion hemisphere.

The homochoric vector representing a rotation with rotation angle \(\theta\) has magnitude \(\left[\frac{3}{4}(\theta - \sin\theta)\right]^{\frac{1}{3}}\).

Notes

The homochoric transformation has no analytical inverse.

Attributes

Homochoric.angle	Calling this attribute raises an error since it cannot be determined analytically.
Homochoric.axis	Return the axes of rotation.
Homochoric.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].
Homochoric.data	Return the data.
Homochoric.ndim	Return the number of navigation dimensions of the object.
Homochoric.norm	Return the norm of the data.
Homochoric.perpendicular	Return the perpendicular vectors.
Homochoric.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].
Homochoric.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].
Homochoric.shape	Return the shape of the object.
Homochoric.size	Return the total number of entries in this object.
Homochoric.unit	Return the unit object.
Homochoric.x	Return or set the x coordinates.
Homochoric.xyz	Return the coordinates as three arrays, useful for plotting.
Homochoric.y	Return or set the y coordinates.
Homochoric.z	Return or set the z coordinate.

Methods

Homochoric.angle_with(other[, degrees])	Return the angles between these vectors in other vectors.
Homochoric.cross(other)	Return the cross product of a vector with another vector.
Homochoric.dot(other)	Return the dot products \(D\) of the vectors.
Homochoric.dot_outer(other[, lazy, ...])	Return the outer dot products of all vectors and all the other vectors.
Homochoric.draw_circle([projection, figure, ...])	Draw great or small circles with a given opening_angle to to the vectors in the stereographic projection.
Homochoric.empty()	Return an empty object with the appropriate dimensions.
Homochoric.flatten()	Return a new object with the same data in a single column.
Homochoric.from_path_ends(vectors[, close, ...])	Return vectors along the shortest path on the sphere between two or more consectutive vectors.
Homochoric.from_polar(azimuth, polar[, ...])	Initialize from spherical coordinates according to the ISO 31-11 standard [Weisstein, 2005].
Homochoric.from_rotation(rotation)	Create an homochoric vector from a rotation.
Homochoric.get_circle([opening_angle, steps])	Get vectors delineating great or small circle(s) with a given opening_angle about each vector.
Homochoric.get_nearest(x[, inclusive, tiebreak])	Return the vector in x with the smallest angle to this vector.
Homochoric.get_random_sample([size, ...])	Return a new flattened object from a random sample of a given size.
Homochoric.in_fundamental_sector(symmetry)	Project vectors to a symmetry's fundamental sector (inverse pole figure).
Homochoric.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.
Homochoric.mean()	Return the mean vector.
Homochoric.pole_density_function([...])	Plot the Pole Density Function (PDF) on a given hemisphere in the stereographic projection.
Homochoric.random([shape])	Create object with random data.
Homochoric.reshape(*shape)	Return a new object with the same data in a new shape.
Homochoric.rotate([axis, angle])	Convenience function for rotating this vector.
Homochoric.scatter([projection, figure, ...])	Plot vectors in the stereographic projection.
Homochoric.squeeze()	Return a new object with the same data with length 1-dimensions removed.
Homochoric.stack(sequence)	Return a stacked object from the sequence.
Homochoric.to_polar([degrees])	Return the azimuth \(\phi\), polar \(\theta\), and radial \(r\) spherical coordinates defined as in the ISO 31-11 standard [Weisstein, 2005].
Homochoric.transpose(*axes)	Return a new object with the same data transposed.
Homochoric.unique([return_index, return_inverse])	Return a new object containing only this object's unique entries.
Homochoric.xvector()	Return a unit vector in the x-direction.
Homochoric.yvector()	Return a unit vector in the y-direction.
Homochoric.zero([shape])	Return zero vectors in the specified shape.
Homochoric.zvector()	Return a unit vector in the z-direction.