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

.. only:: html

    .. meta::
        :keywords: codex

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

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

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

.. _sphx_glr_gallery_images_contours_and_fields_trigradient_demo.py:


================
Trigradient Demo
================

Demonstrates computation of gradient with
`matplotlib.tri.CubicTriInterpolator`.

.. GENERATED FROM PYTHON SOURCE LINES 9-89

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from matplotlib.tri import (CubicTriInterpolator, Triangulation,
                                UniformTriRefiner)


    # ----------------------------------------------------------------------------
    # Electrical potential of a dipole
    # ----------------------------------------------------------------------------
    def dipole_potential(x, y):
        """The electric dipole potential V, at position *x*, *y*."""
        r_sq = x**2 + y**2
        theta = np.arctan2(y, x)
        z = np.cos(theta)/r_sq
        return (np.max(z) - z) / (np.max(z) - np.min(z))


    # ----------------------------------------------------------------------------
    # Creating a Triangulation
    # ----------------------------------------------------------------------------
    # First create the x and y coordinates of the points.
    n_angles = 30
    n_radii = 10
    min_radius = 0.2
    radii = np.linspace(min_radius, 0.95, n_radii)

    angles = np.linspace(0, 2 * np.pi, n_angles, endpoint=False)
    angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)
    angles[:, 1::2] += np.pi / n_angles

    x = (radii*np.cos(angles)).flatten()
    y = (radii*np.sin(angles)).flatten()
    V = dipole_potential(x, y)

    # Create the Triangulation; no triangles specified so Delaunay triangulation
    # created.
    triang = Triangulation(x, y)

    # Mask off unwanted triangles.
    triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
                             y[triang.triangles].mean(axis=1))
                    < min_radius)

    # ----------------------------------------------------------------------------
    # Refine data - interpolates the electrical potential V
    # ----------------------------------------------------------------------------
    refiner = UniformTriRefiner(triang)
    tri_refi, z_test_refi = refiner.refine_field(V, subdiv=3)

    # ----------------------------------------------------------------------------
    # Computes the electrical field (Ex, Ey) as gradient of electrical potential
    # ----------------------------------------------------------------------------
    tci = CubicTriInterpolator(triang, -V)
    # Gradient requested here at the mesh nodes but could be anywhere else:
    (Ex, Ey) = tci.gradient(triang.x, triang.y)
    E_norm = np.sqrt(Ex**2 + Ey**2)

    # ----------------------------------------------------------------------------
    # Plot the triangulation, the potential iso-contours and the vector field
    # ----------------------------------------------------------------------------
    fig, ax = plt.subplots()
    ax.set_aspect('equal')
    # Enforce the margins, and enlarge them to give room for the vectors.
    ax.use_sticky_edges = False
    ax.margins(0.07)

    ax.triplot(triang, color='0.8')

    levels = np.arange(0., 1., 0.01)
    ax.tricontour(tri_refi, z_test_refi, levels=levels, cmap='hot',
                  linewidths=[2.0, 1.0, 1.0, 1.0])
    # Plots direction of the electrical vector field
    ax.quiver(triang.x, triang.y, Ex/E_norm, Ey/E_norm,
              units='xy', scale=10., zorder=3, color='blue',
              width=0.007, headwidth=3., headlength=4.)

    ax.set_title('Gradient plot: an electrical dipole')
    plt.show()




.. image-sg:: /gallery/images_contours_and_fields/images/sphx_glr_trigradient_demo_001.png
   :alt: Gradient plot: an electrical dipole
   :srcset: /gallery/images_contours_and_fields/images/sphx_glr_trigradient_demo_001.png, /gallery/images_contours_and_fields/images/sphx_glr_trigradient_demo_001_2_00x.png 2.00x
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 90-103

.. admonition:: References

   The use of the following functions, methods, classes and modules is shown
   in this example:

   - `matplotlib.axes.Axes.tricontour` / `matplotlib.pyplot.tricontour`
   - `matplotlib.axes.Axes.triplot` / `matplotlib.pyplot.triplot`
   - `matplotlib.tri`
   - `matplotlib.tri.Triangulation`
   - `matplotlib.tri.CubicTriInterpolator`
   - `matplotlib.tri.CubicTriInterpolator.gradient`
   - `matplotlib.tri.UniformTriRefiner`
   - `matplotlib.axes.Axes.quiver` / `matplotlib.pyplot.quiver`


.. _sphx_glr_download_gallery_images_contours_and_fields_trigradient_demo.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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