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

.. only:: html

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

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

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

.. _sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_export_field_vtk.py:


Export a field to VTK
=====================

.. GENERATED FROM PYTHON SOURCE LINES 6-12

The objective here is to create a field and export it as a VTK file. A field is the agregation of a mesh :math:`\mathcal{M}` of a domain :math:`\mathcal{D} \in \mathbb{R}^n` and a sample of values in :math:`\mathbb{R}^d` associated to each vertex of the mesh.

We note :math:`(\underline{t}_0, \dots, \underline{t}_{N-1})` the vertices of :math:`\mathcal{M}` and :math:`(\underline{x}_0, \dots, \underline{x}_{N-1})` the associated values in :math:`\mathbb{R}^d`.

A field is stored in the *Field* object that stores the mesh and the values at each vertex of the mesh.
It can be built from a mesh and values or as a realization of a stochastic process.

.. GENERATED FROM PYTHON SOURCE LINES 14-20

.. code-block:: default

    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    import math as m
    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 21-22

First, we define a regular 2-d mesh

.. GENERATED FROM PYTHON SOURCE LINES 22-32

.. code-block:: default

    discretization = [10, 5]
    mesher = ot.IntervalMesher(discretization)
    lowerBound = [0.0, 0.0]
    upperBound = [2.0, 1.0]
    interval = ot.Interval(lowerBound, upperBound)
    mesh = mesher.build(interval)
    graph = mesh.draw()
    graph.setTitle('Regular 2-d mesh')
    view = viewer.View(graph)




.. image-sg:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_export_field_vtk_001.png
   :alt: Regular 2-d mesh
   :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_export_field_vtk_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 33-34

We now create a field from a mesh and some values

.. GENERATED FROM PYTHON SOURCE LINES 34-41

.. code-block:: default

    values = ot.Normal([0.0]*2, [1.0]*2, ot.CorrelationMatrix(2)
                       ).getSample(len(mesh.getVertices()))
    for i in range(len(values)):
        x = values[i]
        values[i] = 0.05 * x / x.norm()
    field = ot.Field(mesh, values)








.. GENERATED FROM PYTHON SOURCE LINES 42-44

We can export the `field` to a VTK files. It can be
read later with an external program such as Paraview.

.. GENERATED FROM PYTHON SOURCE LINES 44-46

.. code-block:: default

    field.exportToVTKFile('field.vtk')








.. GENERATED FROM PYTHON SOURCE LINES 47-48

Display figures

.. GENERATED FROM PYTHON SOURCE LINES 48-49

.. code-block:: default

    plt.show()








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

   **Total running time of the script:** ( 0 minutes  0.139 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_export_field_vtk.py:


.. only :: html

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



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

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



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

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


.. only:: html

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

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