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

.. only:: html

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

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

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

.. _sphx_glr_api_gallery_chaos_billiards_plot_poincare_comparison.py:


Comparing All Five Billiards
=============================

Every billiard here is a point particle moving in a straight line at
constant speed inside a closed boundary, undergoing specular reflection

.. math::

    \mathbf{v}' = \mathbf{v} - 2(\mathbf{v}\cdot\mathbf{n})\,\mathbf{n}

whenever it strikes the boundary; the five shapes below differ only in that
boundary's geometry: a disk :math:`x^2+y^2=r^2` (Circle), a rectangle
:math:`|x|\le w/2,\ |y|\le h/2` (Rectangle), a disk with a flat chord cut
off (Truncated Circle), a square cell with a circular scatterer removed from
its center (Sinai), and two semicircular caps joined by straight edges
(Bunimovich Stadium). This is a side-by-side comparison of the Poincare
section for every billiard shape ``physicskit.chaos`` ships, from fully
integrable (Circle, Rectangle) through mixed (Truncated Circle) to fully
chaotic (Sinai, Bunimovich Stadium).

.. GENERATED FROM PYTHON SOURCE LINES 22-34

.. code-block:: Python


    import matplotlib.pyplot as plt

    from physicskit.chaos.systems.billiards import (
        BunimovichStadium,
        CircleBilliard,
        RectangleBilliard,
        SinaiBilliard,
        TruncatedCircleBilliard,
    )
    from physicskit.chaos.visualizers.phase_space import plot_poincare_section








.. GENERATED FROM PYTHON SOURCE LINES 35-39

Build one instance of each billiard and plot its Poincare section into its
own subplot, using the ``ax=`` parameter of
:func:`physicskit.chaos.visualizers.phase_space.plot_poincare_section` to draw into
a shared figure.

.. GENERATED FROM PYTHON SOURCE LINES 39-55

.. code-block:: Python

    billiards = {
        "Circle (integrable)": CircleBilliard(radius=1.0),
        "Rectangle (integrable)": RectangleBilliard(width=2.0, height=1.0),
        "Truncated Circle (mixed)": TruncatedCircleBilliard(radius=1.0, cut=0.3),
        "Sinai (chaotic)": SinaiBilliard(cell_size=2.0, scatterer_radius=0.5),
        "Bunimovich Stadium (chaotic)": BunimovichStadium(radius=1.0, straight_length=2.0),
    }

    fig, axes = plt.subplots(2, 3, figsize=(15, 9))
    for ax, (name, billiard) in zip(axes.flat, billiards.items()):
        plot_poincare_section(billiard, n_rays=25, n_bounces=150, ax=ax, s=1.0)
        ax.set_title(name)
    axes.flat[-1].axis("off")
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/chaos/billiards/images/sphx_glr_plot_poincare_comparison_001.png
   :alt: Circle (integrable), Rectangle (integrable), Truncated Circle (mixed), Sinai (chaotic), Bunimovich Stadium (chaotic)
   :srcset: /api/gallery/chaos/billiards/images/sphx_glr_plot_poincare_comparison_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.179 seconds)


.. _sphx_glr_download_api_gallery_chaos_billiards_plot_poincare_comparison.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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