.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/geometry/enclosing/plot_01_smallest_enclosing_circle.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_geometry_enclosing_plot_01_smallest_enclosing_circle.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_geometry_enclosing_plot_01_smallest_enclosing_circle.py:


Sylvester's problem: the smallest enclosing circle
========================================================

Finds the smallest circle containing a random point cloud with Welzl's
algorithm. The optimal circle always passes through two or three of the
points.

.. GENERATED FROM PYTHON SOURCE LINES 11-16

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from mathematicskit.geometry import min_enclosing_circle








.. GENERATED FROM PYTHON SOURCE LINES 17-19

Random points and their enclosing circle
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 19-34

.. code-block:: Python


    rng = np.random.default_rng(4)
    points = rng.normal(size=(200, 2)) * [1.5, 0.8]
    result = min_enclosing_circle(points)
    on_circle = np.isclose(np.linalg.norm(points - result.center, axis=1), result.radius, atol=1e-9)
    print(f"center {result.center.round(4)}, radius {result.radius:.4f}")
    print(f"points on the circle: {int(on_circle.sum())}")

    fig, ax = plt.subplots()
    ax.plot(*points.T, ".", color="0.5")
    ax.plot(*points[on_circle].T, "o", color="tab:red", label="points on the circle")
    ax.add_patch(plt.Circle(result.center, result.radius, fill=False, color="tab:red"))
    ax.set_aspect("equal")
    ax.legend()
    ax.set_title("Smallest enclosing circle (Welzl, 1991)")



.. image-sg:: /api/gallery/geometry/enclosing/images/sphx_glr_plot_01_smallest_enclosing_circle_001.png
   :alt: Smallest enclosing circle (Welzl, 1991)
   :srcset: /api/gallery/geometry/enclosing/images/sphx_glr_plot_01_smallest_enclosing_circle_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    center [-0.26    0.0599], radius 4.4673
    points on the circle: 2

    Text(0.5, 1.0, 'Smallest enclosing circle (Welzl, 1991)')




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

   **Total running time of the script:** (0 minutes 0.023 seconds)


.. _sphx_glr_download_api_gallery_geometry_enclosing_plot_01_smallest_enclosing_circle.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_smallest_enclosing_circle.ipynb <plot_01_smallest_enclosing_circle.ipynb>`

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

      :download:`Download Python source code: plot_01_smallest_enclosing_circle.py <plot_01_smallest_enclosing_circle.py>`

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

      :download:`Download zipped: plot_01_smallest_enclosing_circle.zip <plot_01_smallest_enclosing_circle.zip>`


.. only:: html

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

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