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

.. only:: html

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

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

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

.. _sphx_glr_examples_rotations_rotations_mapping_fundamental_sector.py:


================================================
Rotations mapping the fundamental sector on *S2*
================================================

This example shows how to sample rotations :math:`\mathbf{R}` that when rotating the
vector :math:`\mathbf{v_z} = (0, 0, 1)`, the resulting vectors cover the fundamental
sector of a given Laue class.

We show this by comparing the vectors we get by: 

1. Sampling rotations for *4/mmm* and then rotating :math:`\mathbf{v_z}`
2. Sampling all of *S2* but only keeping those within the corresponding fundamental
   sector.

Apart from the first rotation, all rotations have a Euler angle
:math:`\phi = 0^{\circ}`.
These "reduced" rotations can be useful in template matching of spot patterns from the
transmission electron microscope.

.. GENERATED FROM PYTHON SOURCE LINES 21-36

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from orix import plot, sampling
    from orix.quaternion import symmetry
    from orix.vector import Vector3d

    # Sample rotations with an average misorientation
    res = 2
    pg = symmetry.D4h  # 4/mmm

    R = sampling.get_sample_reduced_fundamental(res, point_group=pg)
    print(np.allclose(R.to_euler()[1:, 0], 0))





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

 .. code-block:: none

    True




.. GENERATED FROM PYTHON SOURCE LINES 37-38

Get vectors within the fundamental sector following the two routes

.. GENERATED FROM PYTHON SOURCE LINES 38-48

.. code-block:: Python

    v1 = R * Vector3d.zvector()

    v2 = sampling.sample_S2(res)
    v2 = v2[v2 <= pg.fundamental_sector]

    # Only equivalent for the same S2 sampling method
    print(np.allclose(v1.data, v2.data))
    print(v1)
    print(v2)





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

 .. code-block:: none

    True
    Vector3d (852,)
    [[0.     0.     1.    ]
     [0.0341 0.     0.9994]
     [0.0682 0.     0.9977]
     ...
     [0.7063 0.7063 0.0483]
     [0.7069 0.7069 0.0241]
     [0.7071 0.7071 0.    ]]
    Vector3d (852,)
    [[ 0.      0.      1.    ]
     [ 0.0341  0.      0.9994]
     [ 0.0682  0.      0.9977]
     ...
     [ 0.7063  0.7063  0.0483]
     [ 0.7069  0.7069  0.0241]
     [ 0.7071  0.7071 -0.    ]]




.. GENERATED FROM PYTHON SOURCE LINES 49-50

Plot the vectors in the fundamental sector of Laue group 4/mmm

.. GENERATED FROM PYTHON SOURCE LINES 50-58

.. code-block:: Python

    fig, (ax0, ax1) = plt.subplots(
        ncols=2, subplot_kw={"projection": "ipf", "symmetry": pg}, layout="tight"
    )
    ax0.scatter(v1, s=5)
    ax1.scatter(v2, c="C1", s=5)
    ax0.set_title("Rotated Z vectors", loc="left")
    ax1.set_title("Directly sampled", loc="left")
    _ = fig.suptitle("Vectors in the fundamental sector of 4/mmm", y=0.8)



.. image-sg:: /examples/rotations/images/sphx_glr_rotations_mapping_fundamental_sector_001.png
   :alt: Vectors in the fundamental sector of 4/mmm, Rotated Z vectors, Directly sampled
   :srcset: /examples/rotations/images/sphx_glr_rotations_mapping_fundamental_sector_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.733 seconds)

**Estimated memory usage:**  353 MB


.. _sphx_glr_download_examples_rotations_rotations_mapping_fundamental_sector.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: rotations_mapping_fundamental_sector.zip <rotations_mapping_fundamental_sector.zip>`


.. only:: html

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

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