random

classmethod SphericalRegion.random(shape: int | tuple[int, ...] = 1) → Object3d

Return uniformly distributed random data.

For objects that map to the surfaces of n-dimensional unit spheres (unit vectors, quaternions, octonions, etc), randomly sampling values for each axis gives a non-uniform sampling that coalesces near the poles. One proper method is to instead sample an n-dimensional gaussian distribution for each axis, then normalize the result.

For vectors, this would produce a uniform sampling of the 2D surface of the 3D unit sphere.

For rotations, this would be a uniform sampling of the 3D surface of the 4D quaternion unit sphere.

Note that this is not the only definition of a “random” sample, but is the one most commonly appropriate when discussing vectors and rotations in crystallography.

Parameters:

shape

Data shape.

Returns:

obj

Random data.