.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/geometry/bezier/plot_01_de_casteljau.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_bezier_plot_01_de_casteljau.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_geometry_bezier_plot_01_de_casteljau.py:


De Casteljau's algorithm and Bézier curves
================================================

Draws a cubic Bézier curve and the construction lines of de Casteljau's
algorithm at t = 0.4: interpolate between neighbouring control points,
then between the new points, until one point, the curve point, is left.

.. GENERATED FROM PYTHON SOURCE LINES 11-16

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from mathematicskit.geometry import bezier_curve, de_casteljau








.. GENERATED FROM PYTHON SOURCE LINES 17-19

The construction at t = 0.4
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 19-33

.. code-block:: Python


    control = np.array([[0.0, 0.0], [1.0, 3.0], [3.5, 3.5], [4.5, 0.5]])
    curve = bezier_curve(control, np.linspace(0, 1, 200))
    levels = de_casteljau(control, 0.4)

    fig, ax = plt.subplots()
    ax.plot(*curve.T, "k", lw=2, label="Bézier curve")
    for level, color in zip(levels, ("tab:gray", "tab:blue", "tab:green", "tab:red")):
        ax.plot(*level.T, "o-", color=color, ms=6)
    ax.plot(*levels[-1][0], "o", color="tab:red", ms=10, label="B(0.4)")
    ax.set_aspect("equal")
    ax.legend()
    ax.set_title("de Casteljau's algorithm")




.. image-sg:: /api/gallery/geometry/bezier/images/sphx_glr_plot_01_de_casteljau_001.png
   :alt: de Casteljau's algorithm
   :srcset: /api/gallery/geometry/bezier/images/sphx_glr_plot_01_de_casteljau_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(0.5, 1.0, "de Casteljau's algorithm")



.. GENERATED FROM PYTHON SOURCE LINES 34-36

The curve stays inside the convex hull of its control points
----------------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 36-39

.. code-block:: Python


    print(f"curve x range [{curve[:, 0].min():.3f}, {curve[:, 0].max():.3f}], control x range [0, 4.5]")
    print(f"curve starts at {curve[0]} and ends at {curve[-1]}: the first and last control points")




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

 .. code-block:: none

    curve x range [0.000, 4.500], control x range [0, 4.5]
    curve starts at [0. 0.] and ends at [4.5 0.5]: the first and last control points





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

   **Total running time of the script:** (0 minutes 0.025 seconds)


.. _sphx_glr_download_api_gallery_geometry_bezier_plot_01_de_casteljau.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_de_casteljau.ipynb <plot_01_de_casteljau.ipynb>`

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

      :download:`Download Python source code: plot_01_de_casteljau.py <plot_01_de_casteljau.py>`

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

      :download:`Download zipped: plot_01_de_casteljau.zip <plot_01_de_casteljau.zip>`


.. only:: html

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

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