.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/misorientations/misorientation_from_aligning_directions.py"
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.. only:: html

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

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

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

.. _sphx_glr_examples_misorientations_misorientation_from_aligning_directions.py:


=======================================
Misorientation from aligning directions
=======================================

This example demonstrates how to use
:meth:`~orix.quaternion.Misorientation.from_align_vectors` to estimate a misorientation
:math:`M` from two sets of aligned crystal directions :math:`t_{1,2}`, one set in each
crystal reference frame :math:`(e_1, e_2, e_3)`.

.. GENERATED FROM PYTHON SOURCE LINES 11-78



.. image-sg:: /examples/misorientations/images/sphx_glr_misorientation_from_aligning_directions_001.png
   :alt: misorientation from aligning directions
   :srcset: /examples/misorientations/images/sphx_glr_misorientation_from_aligning_directions_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Vector angular deviation [deg]:  7.1025833620124
    Error distance:  0.1710643081829647






|

.. 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 Misorientation, Orientation
    from orix.vector import Miller

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

    # Specify a cubic and an hexagonal crystal structures and symmetries
    phase1 = Phase(
        point_group="m-3m",
        structure=Structure(lattice=Lattice(1, 1, 1, 90, 90, 90)),
    )
    phase2 = Phase(
        point_group="6/mmm",
        structure=Structure(lattice=Lattice(1, 1, 2, 90, 90, 120)),
    )

    # Specify one orientation per crystal
    O_cubic = Orientation.from_axes_angles(
        [1, 1, 1], -60, symmetry=phase1.point_group, degrees=True
    )
    O_hex = Orientation.from_axes_angles(
        [1, 3, 2], -90, symmetry=phase2.point_group, degrees=True
    )

    # Get the reference misorientation (goal). Misorientations are obtained
    # from the right, so: crystal 1 -> sample -> crystal 2
    M_ref = Misorientation(O_hex * ~O_cubic, symmetry=(O_cubic.symmetry, O_hex.symmetry))

    # Specify two directions in the first crystal
    t_cubic = Miller(uvw=[[1, 1, 1], [0, 0, 1]], phase=phase1)

    # Express the same directions with respect to the second crystal [in the
    # Cartesian reference frame, (e1, e2, e3)]
    v_hex = Miller(xyz=(M_ref * t_cubic).data, phase=phase2)

    # Add some randomness to the second crystal directions (0 error
    # magnitude gives exact result)
    error_magnitude = 0.1
    v_err = Miller(xyz=np.random.normal(0, error_magnitude, 3), phase=phase2)
    v_hex_err = Miller(xyz=(v_hex + v_err).data, phase=phase2)
    angle_err = v_hex_err.angle_with(v_hex, degrees=True).mean()
    print("Vector angular deviation [deg]: ", angle_err)

    # Get the misorientation that aligns the directions in the first crystal
    # with those in the second crystal
    M_new, err = Misorientation.from_align_vectors(v_hex_err, t_cubic, return_rmsd=True)
    print("Error distance: ", err)

    # Plot the two directions in the (unrotated) first crystal's reference
    # frame as open circles
    fig = t_cubic.scatter(
        c="none",
        ec=["r", "b"],
        grid=True,
        axes_labels=["e1", "e2"],
        return_figure=True,
        figure_kwargs={"layout": "tight"},
    )

    # Plot the two directions in the second crystal with respect to the
    # first crystal's axes
    (~M_ref * v_hex_err).scatter(c=["r", "b"], figure=fig)


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

   **Total running time of the script:** (0 minutes 0.524 seconds)

**Estimated memory usage:**  10 MB


.. _sphx_glr_download_examples_misorientations_misorientation_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: misorientation_from_aligning_directions.ipynb <misorientation_from_aligning_directions.ipynb>`

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

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


.. only:: html

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

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