.. _sphx_glr_api_gallery_geometry_triangulation:

Voronoi diagrams and Delaunay triangulation
--------------------------------------------------

Nearest-site partitions and empty-circumcircle triangulations, both via
scipy's Qhull wrapper.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="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 voronoi_diagram computes, and each Voronoi vertex is equidistant from the three sites whose cells meet there.">

.. only:: html

  .. image:: /api/gallery/geometry/triangulation/images/thumb/sphx_glr_plot_01_voronoi_diagram_thumb.png
    :alt:

  :doc:`/api/gallery/geometry/triangulation/plot_01_voronoi_diagram`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Voronoi diagrams: every location goes to its nearest site</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Triangulates a random point set with delaunay_triangulation, checks Delaunay&#x27;s defining property (no point lies inside any triangle&#x27;s circumcircle), and shows on four points that choosing the Delaunay diagonal maximizes the smallest angle and avoids needle-like triangles.">

.. only:: html

  .. image:: /api/gallery/geometry/triangulation/images/thumb/sphx_glr_plot_02_delaunay_triangulation_thumb.png
    :alt:

  :doc:`/api/gallery/geometry/triangulation/plot_02_delaunay_triangulation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Delaunay triangulation: empty circumcircles and fat triangles</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/geometry/triangulation/plot_01_voronoi_diagram
   /api/gallery/geometry/triangulation/plot_02_delaunay_triangulation