.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/geometry/simplification/plot_01_douglas_peucker.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_simplification_plot_01_douglas_peucker.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_geometry_simplification_plot_01_douglas_peucker.py:


Douglas-Peucker line simplification
=========================================

Simplifies a wiggly coastline-like curve at several tolerances. Larger
tolerances keep fewer vertices, and every discarded vertex stays within
the tolerance of the simplified line.

.. GENERATED FROM PYTHON SOURCE LINES 11-16

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from mathematicskit.geometry import douglas_peucker








.. GENERATED FROM PYTHON SOURCE LINES 17-19

A rough curve and its simplifications
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 19-32

.. code-block:: Python


    rng = np.random.default_rng(2)
    x = np.linspace(0, 10, 2000)
    y = np.sin(x) + 0.3 * np.sin(5 * x) + 0.05 * np.cumsum(rng.normal(size=x.size)) / np.sqrt(x.size) * 10
    line = np.column_stack([x, y])

    fig, ax = plt.subplots(figsize=(9, 4))
    ax.plot(*line.T, color="0.7", lw=3, label=f"original ({len(line)} points)")
    for eps, color in ((0.05, "tab:blue"), (0.2, "tab:green"), (0.6, "tab:red")):
        simple = douglas_peucker(line, eps)
        ax.plot(*simple.T, "o-", color=color, ms=3, lw=1, label=f"epsilon = {eps}: {len(simple)} points")
    ax.legend()
    ax.set_title("Douglas-Peucker (1973)")



.. image-sg:: /api/gallery/geometry/simplification/images/sphx_glr_plot_01_douglas_peucker_001.png
   :alt: Douglas-Peucker (1973)
   :srcset: /api/gallery/geometry/simplification/images/sphx_glr_plot_01_douglas_peucker_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(0.5, 1.0, 'Douglas-Peucker (1973)')




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

   **Total running time of the script:** (0 minutes 0.035 seconds)


.. _sphx_glr_download_api_gallery_geometry_simplification_plot_01_douglas_peucker.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_douglas_peucker.ipynb <plot_01_douglas_peucker.ipynb>`

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

      :download:`Download Python source code: plot_01_douglas_peucker.py <plot_01_douglas_peucker.py>`

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

      :download:`Download zipped: plot_01_douglas_peucker.zip <plot_01_douglas_peucker.zip>`


.. only:: html

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

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