sknano.core.math.Rx¶

sknano.core.math.Rx(angle, degrees=False)[source][source]¶

Generate the \(3\times3\) rotation matrix \(R_x(\theta)\) for a rotation about the \(x\) axis by an angle \(\theta\).

Parameters:

Parameters:	angle : float The rotation angle \(\theta\) in radians. If the angle is given in degrees, then you must set degrees=True to correctly calculate the rotation matrix. degrees : bool, optional if True, then `angle` is converted from degrees to radians.
Returns:	`ndarray` \(3\times3\) rotation matrix \(R_x(\theta)\) for a rotation about the \(x\) axis by an angle \(\theta\). \[\begin{split}R_x = \begin{pmatrix} 1 & 0 & 0\\ 0 & \cos\theta & -\sin\theta\\ 0 & \sin\theta & \cos\theta \end{pmatrix}\end{split}\]

angle : float

The rotation angle \(\theta\) in radians. If the angle is given in degrees, then you must set degrees=True to correctly calculate the rotation matrix.

degrees : bool, optional

if True, then angle is converted from degrees to radians.

Returns:

ndarray

\(3\times3\) rotation matrix \(R_x(\theta)\) for a rotation about the \(x\) axis by an angle \(\theta\).

\[\begin{split}R_x = \begin{pmatrix} 1 & 0 & 0\\ 0 & \cos\theta & -\sin\theta\\ 0 & \sin\theta & \cos\theta \end{pmatrix}\end{split}\]

Examples

>>> import numpy as np
>>> from sknano.core.math import Rx
>>> Rx(np.pi/4)
array([[ 1.        ,  0.        ,  0.        ],
       [ 0.        ,  0.70710678, -0.70710678],
       [ 0.        ,  0.70710678,  0.70710678]])
>>> np.alltrue(Rx(np.pi/4) == Rx(45, degrees=True))
True