.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/orientations/orientation_from_aligning_directions.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_orientations_orientation_from_aligning_directions.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_orientations_orientation_from_aligning_directions.py:


====================================
Orientation from aligning directions
====================================

This example demonstrates how to use
:meth:`~orix.quaternion.Orientation.from_align_vectors` to estimate an orientation
:math:`O` from two sets of aligned vectors.
One set of vectors :math:`\mathbf{v}` is given in the sample reference reference frame,
:math:`(x, y, z)`, the other set :math:`\mathbf{t}` is given in the crystal reference
frame, :math:`(e_1, e_2, e_3)`.

.. GENERATED FROM PYTHON SOURCE LINES 14-66



.. image-sg:: /examples/orientations/images/sphx_glr_orientation_from_aligning_directions_001.png
   :alt: orientation from aligning directions
   :srcset: /examples/orientations/images/sphx_glr_orientation_from_aligning_directions_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Vector angle deviation [deg]:  2.0924516958786885
    Error distance:  0.029581035312684273






|

.. code-block:: Python


    from diffpy.structure import Lattice, Structure
    import matplotlib.pyplot as plt
    import numpy as np

    from orix.crystal_map import Phase
    from orix.quaternion import Orientation
    from orix.vector import Miller, Vector3d

    plt.rcParams.update({"figure.figsize": (5, 5), "lines.markersize": 8})

    # Specify an hexagonal crystal structure and symmetry
    phase = Phase(
        point_group="6/mmm",
        structure=Structure(lattice=Lattice(1, 1, 2, 90, 90, 120)),
    )

    # Define a reference orientation (goal)
    O_ref = Orientation.from_axes_angles([1, 1, 1], -45, phase.point_group, degrees=True)

    # Specify two crystal directions (any will do)
    t = Miller(uvw=[[2, 1, 1], [1, 3, 1]], phase=phase)

    # Find out where these directions in the reference orientation (crystal)
    # point in the sample reference frame
    v = Vector3d(~O_ref * t)

    # Plot the reference orientation sample directions as empty circles
    fig = v.scatter(
        c="none",
        ec=["r", "b"],
        grid=True,
        axes_labels=["X", "Y"],
        return_figure=True,
        figure_kwargs={"layout": "tight", "figsize": (5, 5)},
    )

    # Add some randomness to the sample directions (0 error magnitude gives
    # exact result)
    err_magnitude = 0.1
    v_err = v + Vector3d(np.random.normal(0, err_magnitude, 3))
    angle_err = v_err.angle_with(v, degrees=True).mean()
    print("Vector angle deviation [deg]: ", angle_err)

    # Obtain the orientation which aligns the crystal directions with the
    # sample directions
    O_new, err = Orientation.from_align_vectors(t, v_err, return_rmsd=True)
    print("Error distance: ", err)

    # Plot the crystal directions in the new orientation
    v2 = Vector3d(~O_new * t)
    v2.scatter(c=["r", "b"], figure=fig)


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.508 seconds)

**Estimated memory usage:**  9 MB


.. _sphx_glr_download_examples_orientations_orientation_from_aligning_directions.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: orientation_from_aligning_directions.ipynb <orientation_from_aligning_directions.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: orientation_from_aligning_directions.py <orientation_from_aligning_directions.py>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_