.. _sphx_glr_auto_examples_a_coordinate_systems:

:orphan:

Core Modules: Coordinate Systems
================================

This gallery highlights examples built around the :mod:`coordinates` module, PyMetric's foundation
for defining and working with structured coordinate systems.

The :mod:`coordinates` module provides a flexible API for defining Cartesian,
polar, cylindrical, spherical, and general curvilinear systems,
as well as custom user-defined coordinates. These examples showcase how to:

- Instantiate and explore predefined coordinate systems,
- Evaluate coordinate transforms and Jacobians,
- Work with symbolic metrics and basis vectors,
- Integrate coordinate systems into grid construction and field definitions.

Whether you're visualizing a spherical metric or customizing an orthogonal system for a simulation,
these examples serve as practical guides to mastering the geometry backbone of PyMetric.

.. hint::

    For in-depth user documentation, see :ref:`coordinates_user`.



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="Visualize how the radial coordinate lines (R-contours) in the OblateSpheroidalCoordinateSystem change as a function of eccentricity.">

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  .. image:: /auto_examples/a_coordinate_systems/images/thumb/sphx_glr_plot_ellipsoidal_coordinates_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_a_coordinate_systems_plot_ellipsoidal_coordinates.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Oblate Spheroidal Coordinates: Effect of Eccentricity</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Visualize how the radial coordinate lines (R-contours) in the OblateHomoeoidalCoordinateSystem change as a function of eccentricity.">

.. only:: html

  .. image:: /auto_examples/a_coordinate_systems/images/thumb/sphx_glr_plot_homoeoidal_coordinates_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_a_coordinate_systems_plot_homoeoidal_coordinates.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Oblate Homoeoidal Coordinates: Effect of Eccentricity</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /auto_examples/a_coordinate_systems/plot_ellipsoidal_coordinates
   /auto_examples/a_coordinate_systems/plot_homoeoidal_coordinates