amep.utils.unit_vector_3D

amep.utils.unit_vector_3D(theta: float | ndarray, phi: float | ndarray) → ndarray

Generates 3D unit vectors with components

\[ \begin{align}\begin{aligned}x = \sin(\theta)\cos(\phi)\\y = \sin(\theta)\sin(\phi)\\z = \cos(\theta).\end{aligned}\end{align} \]

Parameters:

• theta (float or np.ndarray) – Angle in degrees. A single value can be given as a float or multiple values as an array of shape (N,).

• phi (float or np.ndarray) – Angle in degrees. A single value can be given as a float or multiple values as an array of the same shape as theta.

Returns:

Unit vector(s).

Return type:

np.ndarray

Examples

>>> import amep
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> print(amep.utils.unit_vector_3D(60, 60))
>>> theta = np.array([0, 30, 60, 90, 120, 150, 180])
>>> phi = np.array([0, 60, 120, 180, 240, 300, 360])
>>> t, p = np.meshgrid(theta, phi)
>>> vectors = amep.utils.unit_vector_3D(
...     t.flatten(), p.flatten()
... )
>>> fig = plt.figure()
>>> axs = fig.add_subplot(111, projection='3d')
>>> axs.quiver(
...     0, 0, 0, vectors[:,0], vectors[:,1],
...     vectors[:,2], length=0.05
... )
>>> axs.set_xlabel(r'$x$')
>>> axs.set_ylabel(r'$y$')
>>> axs.set_zlabel(r'$z$')
>>> fig.savefig('./figures/utils/utils-unit_vector_3D.png')
>>>