.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/relativity/interactive/plot_interactive_orbit_and_shadow.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_relativity_interactive_plot_interactive_orbit_and_shadow.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_relativity_interactive_plot_interactive_orbit_and_shadow.py:


Interactive Plotly visualizations
======================================

Every other visualizer in physicskit is Matplotlib-based: static, ideal for
publication figures and this documentation's gallery.
:mod:`physicskit.relativity.visualizers.interactive` offers the same
information as pan/zoom/rotate-enabled Plotly figures instead, convenient
for interactively exploring a 3D orbit or a ray-traced shadow image in a
Jupyter notebook. This example builds two such figures: a precessing,
eccentric timelike geodesic around a Schwarzschild black hole of mass
:math:`M`, obtained by integrating the geodesic equation

.. math::

    \frac{d^2 x^\mu}{d\tau^2} + \Gamma^\mu_{\alpha\beta}
        \frac{dx^\alpha}{d\tau}\frac{dx^\beta}{d\tau} = 0

and a backward ray-traced silhouette (shadow) of a rotating Kerr black hole
with spin parameter :math:`a = 0.9M`, then saves each as a standalone
HTML file.

.. GENERATED FROM PYTHON SOURCE LINES 23-28

.. code-block:: Python


    from physicskit.relativity.chapters.schwarzschild import SchwarzschildBlackHole
    from physicskit.relativity.visualizers.interactive import interactive_orbit_3d, interactive_shadow_image
    from physicskit.relativity.visualizers.shadow_render import render_black_hole_image








.. GENERATED FROM PYTHON SOURCE LINES 29-35

An interactive 3D precessing orbit
------------------------------------
A bound, eccentric equatorial orbit starting at apoapsis :math:`r_0=15M`
with tangential velocity reduced 20% below circular, integrated exactly
(no post-Newtonian approximation) so its relativistic apsidal precession
is directly visible in the resulting rosette.

.. GENERATED FROM PYTHON SOURCE LINES 35-41

.. code-block:: Python

    bh = SchwarzschildBlackHole(M=1.0)
    y0 = bh.eccentric_orbit_initial_state(r0=15.0, eccentricity_boost=0.2)
    trajectory = bh.integrate_geodesic(y0, dtau=0.02, n_steps=8000)
    fig = interactive_orbit_3d(trajectory, M=1.0)
    fig.write_html("orbit_interactive.html")








.. GENERATED FROM PYTHON SOURCE LINES 42-48

An interactive ray-traced shadow image
------------------------------------------
Backward ray-tracing a camera image around a near-extremal Kerr black
hole (:math:`a=0.9M`) using the Carter-separated null geodesic equations
produces the shadow and lensed accretion disk seen below, now pannable
and zoomable.

.. GENERATED FROM PYTHON SOURCE LINES 48-53

.. code-block:: Python

    result = render_black_hole_image(M=1.0, a=0.9, ny=120, nx=120)
    fig = interactive_shadow_image(result)
    fig.write_html("shadow_interactive.html")

    print("Wrote 2 standalone interactive HTML files.")




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Wrote 2 standalone interactive HTML files.





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

   **Total running time of the script:** (0 minutes 1.234 seconds)


.. _sphx_glr_download_api_gallery_relativity_interactive_plot_interactive_orbit_and_shadow.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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