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

.. only:: html

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

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

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

.. _sphx_glr_matplotlib_plot_rect_billiard.py:


rectangular billard
=======================

.. GENERATED FROM PYTHON SOURCE LINES 5-88



.. image-sg:: /matplotlib/images/sphx_glr_plot_rect_billiard_001.png
   :alt: plot rect billiard
   :srcset: /matplotlib/images/sphx_glr_plot_rect_billiard_001.png
   :class: sphx-glr-single-img





.. code-block:: default


    import numpy as np
    import matplotlib.pyplot as plt

    fig, ax = plt.subplots(1,1, figsize=(6,6))

    x = np.array([-3/2, 3/2, 3/2, -3/2, -3/2])
    y = np.array([1, 1, -1, -1, 1])

    ax.plot(x, y, '-k', lw=3)
    ax.set_ylim(-2,2)
    ax.set_xlim(-2,2)

    def intersection(vec0, coord):
        a = vec0[1]/vec0[0]
        x0 = coord[0]
        y0 = coord[1]
        sg = np.sign(vec0[1])
        x1 = - ( - sg - a*x0 + y0 ) / a
        y1 = sg

        if np.abs(x1) >  3/2:
            sg = np.sign(vec0[0])
            x1 = sg*3/2
            y1 = (sg*3*a - 2*a*x0 + 2*y0)/2

        return np.array([x1, y1])

    def df(x0):
        x = x0[0]
        y = x0[1]

        if np.abs(np.abs(y) - 1) < 1e-10:
            z = np.array([0, -1])
        elif np.abs(np.abs(x) - 3/2) < 1e-10:
            z = np.array([-1, 0])

        return z
    

    traj = [np.array([]), np.array([])]

    x0 = np.array([0.1, 0.1])
    vec0 = np.array([-np.pi/10, 0.1])

    init_x = x0.copy()
    init_vec = vec0.copy()

    traj[0] = np.append(traj[0], x0[0])
    traj[1] = np.append(traj[1], x0[1])

    x1 = intersection(vec0, x0)

    traj[0] = np.append(traj[0], x1[0])
    traj[1] = np.append(traj[1], x1[1])

    n = df(x1)
    pn = - np.dot(vec0, n)/np.dot(n, n) * n
    vec1 = vec0 + 2*pn

    #ax.quiver(x1[0], x1[1], n[0], n[1], angles='xy', scale_units='xy', scale=1)
    #ax.quiver(x1[0], x1[1], vec1[0], vec1[1], angles='xy', scale_units='xy', scale=1)

    for i in range(10):
        x0 = x1.copy()
        vec0 = vec1.copy()
        x1 = intersection(vec0, x0)

        traj[0] = np.append(traj[0], x1[0])
        traj[1] = np.append(traj[1], x1[1])

        n = df(x1)
        pn = - np.dot(vec0, n)/np.dot(n, n) * n
        vec1 = vec0 + 2*pn

    
        #ax.quiver(x1[0], x1[1], vec1[0], vec1[1], angles='xy', scale_units='xy', scale=1)

    ax.plot(traj[0], traj[1], '-')
    ax.plot(init_x[0], init_x[1], 'ok')
    ax.quiver(init_x[0], init_x[1], init_vec[0], init_vec[1], angles='xy', scale_units='xy', scale=1)

    plt.show()


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

   **Total running time of the script:** ( 0 minutes  0.078 seconds)


.. _sphx_glr_download_matplotlib_plot_rect_billiard.py:

.. only:: html

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


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

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

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

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


.. only:: html

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

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