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

.. only:: html

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

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

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

.. _sphx_glr_examples_symmetry_create_symmetry.py:


=======================
Create crystal symmetry
=======================

This example shows various ways to obtain a :class:`~orix.quaternion.symmetry.Symmetry`.

.. GENERATED FROM PYTHON SOURCE LINES 29-31

The simplest way is to import pre-defined point groups.
They are named after the Schoenflies notation and can be imported directly

.. GENERATED FROM PYTHON SOURCE LINES 31-37

.. code-block:: Python

    from orix.quaternion.symmetry import D6h, Oh

    print(Oh)  # m-3m in international/Hermann-Mauguin notation

    print(D6h)  # 6/mmm





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

 .. code-block:: none

    Symmetry (48,) m-3m
    [[ 1.      0.      0.      0.    ]
     [ 0.7071  0.      0.      0.7071]
     [ 0.      0.      0.      1.    ]
     [-0.7071  0.      0.      0.7071]
     [ 0.5     0.5     0.5     0.5   ]
     [ 0.      0.      0.7071  0.7071]
     [-0.5    -0.5     0.5     0.5   ]
     [-0.7071 -0.7071  0.      0.    ]
     [ 0.      1.      0.      0.    ]
     [ 0.      0.7071  0.7071  0.    ]
     [ 0.      0.      1.      0.    ]
     [ 0.     -0.7071  0.7071  0.    ]
     [-0.5     0.5     0.5    -0.5   ]
     [ 0.      0.      0.7071 -0.7071]
     [ 0.5    -0.5     0.5    -0.5   ]
     [ 0.7071 -0.7071  0.      0.    ]
     [ 0.      0.7071  0.      0.7071]
     [-0.5     0.5     0.5     0.5   ]
     [-0.7071  0.      0.7071  0.    ]
     [-0.5    -0.5     0.5    -0.5   ]
     [ 0.      0.7071  0.     -0.7071]
     [ 0.5     0.5     0.5    -0.5   ]
     [ 0.7071  0.      0.7071  0.    ]
     [ 0.5    -0.5     0.5     0.5   ]
     [ 1.      0.      0.      0.    ]
     [ 0.7071  0.      0.      0.7071]
     [ 0.      0.      0.      1.    ]
     [-0.7071  0.      0.      0.7071]
     [ 0.5     0.5     0.5     0.5   ]
     [ 0.      0.      0.7071  0.7071]
     [-0.5    -0.5     0.5     0.5   ]
     [-0.7071 -0.7071  0.      0.    ]
     [ 0.      1.      0.      0.    ]
     [ 0.      0.7071  0.7071  0.    ]
     [ 0.      0.      1.      0.    ]
     [ 0.     -0.7071  0.7071  0.    ]
     [-0.5     0.5     0.5    -0.5   ]
     [ 0.      0.      0.7071 -0.7071]
     [ 0.5    -0.5     0.5    -0.5   ]
     [ 0.7071 -0.7071  0.      0.    ]
     [ 0.      0.7071  0.      0.7071]
     [-0.5     0.5     0.5     0.5   ]
     [-0.7071  0.      0.7071  0.    ]
     [-0.5    -0.5     0.5    -0.5   ]
     [ 0.      0.7071  0.     -0.7071]
     [ 0.5     0.5     0.5    -0.5   ]
     [ 0.7071  0.      0.7071  0.    ]
     [ 0.5    -0.5     0.5     0.5   ]]
    Symmetry (24,) 6/mmm
    [[ 1.     0.     0.     0.   ]
     [ 0.5    0.     0.     0.866]
     [-0.5    0.     0.     0.866]
     [ 0.     0.     0.     1.   ]
     [-0.866  0.     0.     0.5  ]
     [-0.866  0.     0.    -0.5  ]
     [ 0.     1.     0.     0.   ]
     [ 0.     0.5    0.866  0.   ]
     [ 0.    -0.5    0.866  0.   ]
     [ 0.     0.     1.     0.   ]
     [ 0.    -0.866  0.5    0.   ]
     [ 0.    -0.866 -0.5    0.   ]
     [ 0.     0.     0.     1.   ]
     [-0.866  0.     0.     0.5  ]
     [-0.866  0.     0.    -0.5  ]
     [-1.     0.     0.     0.   ]
     [-0.5    0.     0.    -0.866]
     [ 0.5    0.     0.    -0.866]
     [ 0.     0.    -1.     0.   ]
     [ 0.     0.866 -0.5    0.   ]
     [ 0.     0.866  0.5    0.   ]
     [ 0.     1.     0.     0.   ]
     [ 0.     0.5    0.866  0.   ]
     [ 0.    -0.5    0.866  0.   ]]




.. GENERATED FROM PYTHON SOURCE LINES 38-42

If one wanted to, one can also combine two point groups to get a third.
Here're two versions of the orthorhombic point group *mm2* (*C2v*) with the 2-fold
axis about different axes (importing C2v directly gives the group with the axis about
z)

.. GENERATED FROM PYTHON SOURCE LINES 42-47

.. code-block:: Python

    from orix.quaternion.symmetry import C2x, C2z, Csx, Csz, Symmetry

    C2v_x = Symmetry.from_generators(C2x, Csz)
    C2v_z = Symmetry.from_generators(C2z, Csx)








.. GENERATED FROM PYTHON SOURCE LINES 48-49

Notice the different symmetrically equivalent directions

.. GENERATED FROM PYTHON SOURCE LINES 49-55

.. code-block:: Python

    from orix.vector import Vector3d

    v = Vector3d([1.0, 1, 1])

    print(C2v_x * v)
    print(C2v_z * v)




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

 .. code-block:: none

    Vector3d (4,)
    [[ 1.  1.  1.]
     [ 1. -1. -1.]
     [ 1.  1. -1.]
     [ 1. -1.  1.]]
    Vector3d (4,)
    [[ 1.  1.  1.]
     [-1. -1.  1.]
     [-1.  1.  1.]
     [ 1. -1.  1.]]





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

   **Total running time of the script:** (0 minutes 0.609 seconds)

**Estimated memory usage:**  548 MB


.. _sphx_glr_download_examples_symmetry_create_symmetry.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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