.. DO NOT EDIT.
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.. "auto_examples\RelatedFields\plot_deformfield.py"
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.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_RelatedFields_plot_deformfield.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_RelatedFields_plot_deformfield.py:


============================================
Anisotropic textures from field deformations
============================================

.. codeauthor:: Frédéric Richard <frederic.richard_at_univ-amu.fr>

In this example, we show how to simulate
:term:`anisotropic<isotropy>` textures from the deformation
of an :term:`isotropic<isotropy>` random field.

Given a fractional Brownian field :math:`X` and  an affine transformation
:math:`T`, the transformed field is defined by composition

.. math::
    Y = X \circ T.

The anisotropic texture is obtained by simulation of :math:`Y`.

.. note::
    This approach could also be applied to more generic afbf.

.. seealso::
   Deformed fields have been of interest in several studies;
   see for instance :cite:p:`Guyon2000`.

.. GENERATED FROM PYTHON SOURCE LINES 65-92



.. rst-class:: sphx-glr-horizontal


    *

      .. image:: /auto_examples/RelatedFields/images/sphx_glr_plot_deformfield_001.png
          :alt: Simulation of the deformed field.
          :class: sphx-glr-multi-img

    *

      .. image:: /auto_examples/RelatedFields/images/sphx_glr_plot_deformfield_002.png
          :alt: Simulation of the undeformed field.
          :class: sphx-glr-multi-img





.. code-block:: default

    import numpy as np
    from afbf import coordinates, tbfield

    # Define a fractional Brownian field.
    X = tbfield()
    # Define an affine transform.
    T = np.array([[1, 0], [2, 1]], dtype=int)

    # Define a uniform grid.
    coord = coordinates(256)
    # Simulate the field without transformation.
    n0 = int(np.random.randn())
    np.random.seed(n0)
    y0 = X.Simulate()

    # Apply the coordinate transform to the grid.
    coord.ApplyAffineTransform(T)
    # Simulate the field with transformation (with a same seed).
    np.random.seed(n0)
    y = X.Simulate(coord)

    # Display of simulations.
    y.name = 'Simulation of the deformed field.'
    y.Display(1)

    y0.name = 'Simulation of the undeformed field.'
    y0.Display(2)


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

   **Total running time of the script:** ( 0 minutes  16.995 seconds)


.. _sphx_glr_download_auto_examples_RelatedFields_plot_deformfield.py:


.. only :: html

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

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



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