.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/geometry/distances/plot_01_hausdorff_distance.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_distances_plot_01_hausdorff_distance.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_geometry_distances_plot_01_hausdorff_distance.py:


The Hausdorff distance between shapes
===========================================

Compares a circle with approximating polygons. The Hausdorff distance
measures the worst-case gap between the two shapes and shrinks like
1/n^2 as the polygon gains sides; a single stray point makes it large
even though every other point matches.

.. GENERATED FROM PYTHON SOURCE LINES 12-17

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from mathematicskit.geometry import hausdorff_distance








.. GENERATED FROM PYTHON SOURCE LINES 18-20

A circle against inscribed polygons
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 20-37

.. code-block:: Python


    t = np.linspace(0, 2 * np.pi, 4000, endpoint=False)
    circle = np.column_stack([np.cos(t), np.sin(t)])
    sides = [4, 8, 16, 32, 64]
    gaps = []
    for n in sides:
        corners = np.column_stack([np.cos(2 * np.pi * np.arange(n + 1) / n), np.sin(2 * np.pi * np.arange(n + 1) / n)])
        polygon = np.vstack([np.linspace(corners[k], corners[k + 1], 200) for k in range(n)])
        gaps.append(hausdorff_distance(circle, polygon))
        print(f"{n:2d}-gon: Hausdorff distance {gaps[-1]:.5f}, exact 1 - cos(pi/n) = {1 - np.cos(np.pi / n):.5f}")

    fig, ax = plt.subplots()
    ax.loglog(sides, gaps, "o-", label="Hausdorff distance")
    ax.loglog(sides, [np.pi**2 / (2 * n**2) for n in sides], "--", label=r"$\pi^2 / 2n^2$")
    ax.set_xlabel("polygon sides n")
    ax.legend()




.. image-sg:: /api/gallery/geometry/distances/images/sphx_glr_plot_01_hausdorff_distance_001.png
   :alt: plot 01 hausdorff distance
   :srcset: /api/gallery/geometry/distances/images/sphx_glr_plot_01_hausdorff_distance_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

     4-gon: Hausdorff distance 0.29291, exact 1 - cos(pi/n) = 0.29289
     8-gon: Hausdorff distance 0.07614, exact 1 - cos(pi/n) = 0.07612
    16-gon: Hausdorff distance 0.01924, exact 1 - cos(pi/n) = 0.01921
    32-gon: Hausdorff distance 0.00486, exact 1 - cos(pi/n) = 0.00482
    64-gon: Hausdorff distance 0.00142, exact 1 - cos(pi/n) = 0.00120

    <matplotlib.legend.Legend object at 0x1192f8440>



.. GENERATED FROM PYTHON SOURCE LINES 38-40

One outlier dominates
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 40-43

.. code-block:: Python


    outlier = np.vstack([circle, [[3.0, 0.0]]])
    print(f"\ncircle vs. circle plus one far point: {hausdorff_distance(circle, outlier):.3f}")




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

 .. code-block:: none


    circle vs. circle plus one far point: 2.000





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

   **Total running time of the script:** (0 minutes 0.113 seconds)


.. _sphx_glr_download_api_gallery_geometry_distances_plot_01_hausdorff_distance.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_hausdorff_distance.ipynb <plot_01_hausdorff_distance.ipynb>`

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

      :download:`Download Python source code: plot_01_hausdorff_distance.py <plot_01_hausdorff_distance.py>`

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

      :download:`Download zipped: plot_01_hausdorff_distance.zip <plot_01_hausdorff_distance.zip>`


.. only:: html

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

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