.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/stereographic_projection/restrict_to_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_stereographic_projection_restrict_to_fundamental_sector.py>`
        to download the full example code

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

.. _sphx_glr_examples_stereographic_projection_restrict_to_fundamental_sector.py:


==============================
Restrict to fundamental sector
==============================

This example shows how to restrict the stereographic plot to the fundamental sector of
one of the eleven Laue group symmetries :math:`S` using
:meth:`~orix.plot.StereographicPlot.restrict_to_sector`.
The sector is typically obtained from
:attr:`orix.quaternion.Symmetry.fundamental_sector`.
It is often called the 'fundamental triangle' or
'standard stereographic triangle (SST)'.

We demonstrate this functionality by drawing (near) great circles about some typically
strongly reflecting low-index reciprocal lattice vectors :math:`\mathbf{g} = \{hkl\}` in
crystals of point group :math:`S = m\bar{3}m`.
The deviations from the great circles are related to the kinematically calculated width
of a Kikuchi band scattered from these vectors, assuming a lattice parameter of
$a$ = 0.404 nm (aluminium) and an accelerating voltage of 20 kV.
The band width is assumed to be two times the Bragg angle :math:`\theta`.

.. GENERATED FROM PYTHON SOURCE LINES 22-68



.. image-sg:: /examples/stereographic_projection/images/sphx_glr_restrict_to_fundamental_sector_001.png
   :alt: Low-index $[uvw]$ in fundamental sector of $m\bar{3}m$
   :srcset: /examples/stereographic_projection/images/sphx_glr_restrict_to_fundamental_sector_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Miller (4,), point group m-3m, hkl
    [[1. 1. 1.]
     [2. 0. 0.]
     [2. 2. 0.]
     [3. 1. 1.]]






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from orix import plot
    from orix.crystal_map import Phase
    from orix.quaternion import symmetry
    from orix.vector import Miller

    plt.rcParams["font.size"] = 15

    # Symmetrically equivalent set of hkl
    g0 = Miller(
        hkl=[[1, 1, 1], [2, 0, 0], [2, 2, 0], [3, 1, 1]],
        phase=Phase(point_group=symmetry.Oh),
    )
    print(g0)
    g, idx = g0.symmetrise(unique=True, return_index=True)

    # Width of Kikuchi bands (deviation from great circles)
    theta = np.deg2rad([1.054, 1.218, 1.722, 2.019])
    theta = theta[idx]

    # Plot pair of near great circles
    fig = g.draw_circle(opening_angle=np.pi / 2 + theta, return_figure=True)
    g.draw_circle(opening_angle=np.pi / 2 - theta, figure=fig)

    # Restrict to fundamental sector of m-3m (with some padding outside sector)
    ax = fig.axes[0]
    ax.restrict_to_sector(
        g.phase.point_group.fundamental_sector, edgecolor="r", lw=2, pad=5
    )

    # Get symmetrically equivalent set of zone axes t = <uvw>
    t = g.reshape(g.size, 1).cross(g.reshape(1, g.size)).flatten()
    t = t.in_fundamental_sector()
    t = t.unique(use_symmetry=True)
    t = t.round().unique()
    t.scatter(
        figure=fig,
        c="none",
        vector_labels=plot.format_labels(t.coordinates),
        text_kwargs={"va": "center", "bbox": {"fc": "w", "pad": 1, "alpha": 0.75}},
    )

    _ = ax.set_title(r"Low-index $[uvw]$ in fundamental sector of $m\bar{3}m$", pad=10)


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

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

**Estimated memory usage:**  9 MB


.. _sphx_glr_download_examples_stereographic_projection_restrict_to_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: restrict_to_fundamental_sector.ipynb <restrict_to_fundamental_sector.ipynb>`

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

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


.. only:: html

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

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