.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/geometry/triangulation/plot_01_voronoi_diagram.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_triangulation_plot_01_voronoi_diagram.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_geometry_triangulation_plot_01_voronoi_diagram.py:


Voronoi diagrams: every location goes to its nearest site
===============================================================

Partitions the plane around a set of sites so that each region holds
every location closer to its site than to any other. Colouring a fine
grid by nearest site reproduces exactly the cells that
:func:`~mathematicskit.geometry.voronoi_diagram` computes, and each
Voronoi vertex is equidistant from the three sites whose cells meet
there.

.. GENERATED FROM PYTHON SOURCE LINES 14-20

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from mathematicskit.geometry import voronoi_diagram
    from mathematicskit.geometry.visualizers.plots import plot_voronoi








.. GENERATED FROM PYTHON SOURCE LINES 21-23

Sites and their Voronoi diagram
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 23-29

.. code-block:: Python


    rng = np.random.default_rng(0)
    sites = rng.uniform(0, 10, size=(15, 2))
    result = voronoi_diagram(sites)
    print(f"{sites.shape[0]} sites, {result.vertices.shape[0]} Voronoi vertices, {result.ridge_points.shape[0]} ridges")





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

 .. code-block:: none

    15 sites, 22 Voronoi vertices, 36 ridges




.. GENERATED FROM PYTHON SOURCE LINES 30-34

Each vertex is equidistant from three sites
-----------------------------------------------------
A Voronoi vertex is where three cells meet, so it is the same distance
from the three nearest sites.

.. GENERATED FROM PYTHON SOURCE LINES 34-39

.. code-block:: Python


    dists = np.sort(np.linalg.norm(result.vertices[:, None, :] - sites[None, :, :], axis=2), axis=1)
    spread = np.max(dists[:, 2] - dists[:, 0])
    print(f"largest gap between a vertex's three nearest-site distances: {spread:.2e}")





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

 .. code-block:: none

    largest gap between a vertex's three nearest-site distances: 3.55e-15




.. GENERATED FROM PYTHON SOURCE LINES 40-42

Nearest-site colouring matches the cells
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 42-56

.. code-block:: Python


    xs = np.linspace(0, 10, 400)
    X, Y = np.meshgrid(xs, xs)
    grid = np.column_stack([X.ravel(), Y.ravel()])
    nearest = np.argmin(np.linalg.norm(grid[:, None, :] - sites[None, :, :], axis=2), axis=1)

    fig, ax = plt.subplots(figsize=(6, 6))
    ax.imshow(nearest.reshape(X.shape), origin="lower", extent=(0, 10, 0, 10), cmap="tab20", alpha=0.5)
    plot_voronoi(sites, ax=ax)
    ax.set_xlim(0, 10)
    ax.set_ylim(0, 10)
    ax.set_aspect("equal")
    ax.set_title("Voronoi cells = regions of nearest site")
    plt.show()



.. image-sg:: /api/gallery/geometry/triangulation/images/sphx_glr_plot_01_voronoi_diagram_001.png
   :alt: Voronoi cells = regions of nearest site
   :srcset: /api/gallery/geometry/triangulation/images/sphx_glr_plot_01_voronoi_diagram_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.063 seconds)


.. _sphx_glr_download_api_gallery_geometry_triangulation_plot_01_voronoi_diagram.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_voronoi_diagram.ipynb <plot_01_voronoi_diagram.ipynb>`

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

      :download:`Download Python source code: plot_01_voronoi_diagram.py <plot_01_voronoi_diagram.py>`

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

      :download:`Download zipped: plot_01_voronoi_diagram.zip <plot_01_voronoi_diagram.zip>`


.. only:: html

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

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