.. _rotation:

.. automodule:: spintoolkit_py
    :no-index:

====================
Class
====================

.. autoclass:: spintoolkit_py.Mat3_rotation
    :members:
    :undoc-members:
    :show-inheritance:
    :exclude-members: __init__

    .. method:: __init__(self)

        Default constructor.

    .. method:: __init__(self, *, omega: spintoolkit_py.Vec3, theta: float)
        :no-index:

        Construct from axis and angle, :math:`R(\theta \hat{\omega})`.

        :param omega: Rotation axis.
        :param theta: Rotation angle.

    .. method:: __init__(self, *, alpha: float, beta: float, gamma: float)
        :no-index:

        Construct from Euler angles (ZYZ convention), :math:`R(\alpha,\beta,\gamma)=R(\alpha \hat{e}_z) R(\beta \hat{e}_y) R(\gamma \hat{e}_z)`.

        :param alpha: The first rotation angle :math:`\alpha` around the Z-axis, :math:`0\le \alpha \lt 2\pi`.
        :param beta: The second rotation angle :math:`\beta` around the Y-axis. :math:`0\le \beta \le \pi`.
        :param gamma: The third rotation angle :math:`\gamma` around the Z-axis. :math:`0 \le \gamma \lt 2\pi`.

    .. method:: __init__(self, *, vi: spintoolkit_py.Vec3, vf: spintoolkit_py.Vec3)
        :no-index:

        Construct from two vectors, :math:`R \, \vec{v}_i = \vec{v}_f`.

        :param vi: The starting vector.
        :param vf: The target vector.