def fundamental_sector(self):
from orix.vector.neo_euler import AxAngle
from orix.vector.spherical_region import SphericalRegion
symmetry = self.antipodal
symmetry = symmetry[symmetry.angle > 0]
axes, order = symmetry.get_highest_order_axis()
if order > 6:
return Vector3d.empty()
axis = Vector3d.zvector().get_nearest(axes, inclusive=True)
r = Rotation.from_neo_euler(
AxAngle.from_axes_angles(axis, 2 * np.pi / order))
diads = symmetry.diads
nearest_diad = axis.get_nearest(diads)
if nearest_diad.size == 0:
nearest_diad = axis.perpendicular
n1 = axis.cross(nearest_diad).unit
n2 = -(r * n1)
next_diad = r * nearest_diad
n = Vector3d.stack((n1, n2)).flatten()
sr = SphericalRegion(n.unique())
inside = symmetry[symmetry.axis < sr]
if inside.size == 0:
return sr
axes, order = inside.get_highest_order_axis()
axis = axis.get_nearest(axes)
r = Rotation.from_neo_euler(
AxAngle.from_axes_angles(axis, 2 * np.pi / order))
nearest_diad = next_diad
n1 = axis.cross(nearest_diad).unit
n2 = -(r * n1)
n = Vector3d(np.concatenate((n.data, n1.data, n2.data)))
sr = SphericalRegion(n.unique())
return sr
class SphericalProjection:
"""Spherical projection of a cartesian vector according to the ISO
31-11 standard [SphericalWolfram]_.
References
----------
.. [SphericalWolfram] Weisstein, Eric W. "Spherical Coordinates,"
*From MathWorld--A Wolfram Web Resource*,
url: https://mathworld.wolfram.com/SphericalCoordinates.html
"""
spherical_region = SphericalRegion([0, 0, 1])
@classmethod
def project(cls, v: Union[Vector3d, np.ndarray]) -> np.ndarray:
"""Convert from cartesian to spherical coordinates according to
the ISO 31-11 standard [SphericalWolfram]_.
Parameters
----------
v
3D vector(s) on the form [[x0, y0, z0], [x1, y1, z1], ...].
Returns
-------
spherical_coordinates
Spherical coordinates theta, phi and r on the form
[[theta1, phi1, r1], [theta2, phi2, r2], ...].
Examples
--------
>>> import numpy as np
>>> from kikuchipy.projections.spherical_projection import (
... SphericalProjection
... )
>>> v = np.random.random_sample(30).reshape((10, 3))
>>> theta, phi, r = SphericalProjection.project(v)
>>> np.allclose(np.arccos(v[: 2] / r), theta)
True
>>> np.allclose(np.arctan2(v[:, 1], v[:, 2]), phi)
True
"""
return _get_polar(v)
def spherical_region(request):
return SphericalRegion(request.param)