Rodrigues#

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

Bases: NeoEuler

In Rodrigues space, straight lines map to rotations about a fixed axis.

The Rodrigues vector representing a rotation with rotation angle $$\theta$$ has magnitude $$\tan\frac{\theta}{2}$$.

Attributes

 Rodrigues.angle Return the angle of the Rodrigues vector. Rodrigues.axis Return the axes of rotation. Rodrigues.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 . Rodrigues.data Return the data. Rodrigues.ndim Return the number of navigation dimensions of the object. Rodrigues.norm Return the norm of the data. Rodrigues.perpendicular Return the perpendicular vectors. Rodrigues.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 . Rodrigues.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 . Rodrigues.shape Return the shape of the object. Rodrigues.size Return the total number of entries in this object. Rodrigues.unit Return the unit object. Rodrigues.x Return or set the x coordinates. Rodrigues.xyz Return the coordinates as three arrays, useful for plotting. Rodrigues.y Return or set the y coordinates. Rodrigues.z Return or set the z coordinate.

Methods

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