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

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_a_coordinate_systems_plot_ellipsoidal_coordinates.py:


======================================================
Oblate Spheroidal Coordinates: Effect of Eccentricity
======================================================

Visualize how the radial coordinate lines (R-contours) in the OblateSpheroidalCoordinateSystem
change as a function of eccentricity.

.. GENERATED FROM PYTHON SOURCE LINES 10-12

.. code-block:: Python

    import matplotlib.pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 13-28

In this example, we'll showcase a more complex coordinate system:
:class:`~coordinates.coordinate_systems.OblateSpheroidalCoordinateSystem`.

The oblate spheroidal coordinate system is an orthogonal coordinate system
with coordinate variables :math:`(\mu,\nu,\theta)` for which the :math:`\mu`
coordinate contours form confocal ellipses.

.. hint::

      The big difference between :class:`~coordinates.coordinate_systems.OblateHomoeoidalCoordinateSystem`
      and :class:`~coordinates.coordinate_systems.OblateSpheroidalCoordinateSystem` is that spheroidal coordinates
      are **confocal** while homoeoidal coordinates are **concentric**.

In this example, we'll show off how to make these coordinate systems
and then display some of its properties.

.. GENERATED FROM PYTHON SOURCE LINES 28-32

.. code-block:: Python

    import numpy as np

    from pymetric import OblateSpheroidalCoordinateSystem








.. GENERATED FROM PYTHON SOURCE LINES 33-36

To visualize, we'll use an *x-z* grid and then convert it into the
relevant coordinate systems with different eccentricities. We can then
plot contours for the effective radius :math:`\xi`.

.. GENERATED FROM PYTHON SOURCE LINES 36-42

.. code-block:: Python


    # Create the cartesian grid.
    x = np.linspace(-1.5, 1.5, 200)
    z = np.linspace(-1.5, 1.5, 200)
    X, Z = np.meshgrid(x, z)








.. GENERATED FROM PYTHON SOURCE LINES 43-47

The class requires an eccentricity parameter when
initialized, so we'll iterate through each of them,
create a coordinate system class, and then perform
the conversions.

.. GENERATED FROM PYTHON SOURCE LINES 47-69

.. code-block:: Python

    _as = [0.1, 0.2, 0.3, 0.5, 1, 2]

    fig, axes = plt.subplots(int(np.ceil(len(_as) / 3)), 3, sharex=True, sharey=True)

    for i, a in enumerate(_as):
        ax = axes.ravel()[i]
        csys = OblateSpheroidalCoordinateSystem(a=a)

        # Convert Cartesian (x, z) to native coordinates (λ, μ, φ)
        Lambda, Mu, Phi = csys.from_cartesian(X, 0, Z)

        # Plot λ contours (these correspond to elliptical shells)
        contour = ax.contour(X, Z, Lambda, levels=15, cmap="viridis")
        ax.set_title(f"$a= {a}$")
        ax.set_aspect("equal")
        ax.set_xlabel("x")
        if i == 0:
            ax.set_ylabel("z")

    fig.suptitle(r"Oblate Spheroidal Coordinate Contours ($\lambda$-lines)", fontsize=14)
    plt.tight_layout()
    plt.show()



.. image-sg:: /auto_examples/a_coordinate_systems/images/sphx_glr_plot_ellipsoidal_coordinates_001.png
   :alt: Oblate Spheroidal Coordinate Contours ($\lambda$-lines), $a= 0.1$, $a= 0.2$, $a= 0.3$, $a= 0.5$, $a= 1$, $a= 2$
   :srcset: /auto_examples/a_coordinate_systems/images/sphx_glr_plot_ellipsoidal_coordinates_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 4.515 seconds)


.. _sphx_glr_download_auto_examples_a_coordinate_systems_plot_ellipsoidal_coordinates.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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