.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/example_generate_parametric_surfaces.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_auto_examples_example_generate_parametric_surfaces.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_example_generate_parametric_surfaces.py:


.. _example_generation_parametric_surfaces:

===================================
Generating parametric surfaces in slam
===================================

.. GENERATED FROM PYTHON SOURCE LINES 8-17

.. code-block:: default


    # Authors:
    # Guillaume Auzias <guillaume.auzias@univ-amu.fr>
    # Julien Barrès <julien.barres@etu.univ-amu.fr>

    # License: BSD (3-clause)
    # sphinx_gallery_thumbnail_number = 2









.. GENERATED FROM PYTHON SOURCE LINES 18-19

Importation of slam modules

.. GENERATED FROM PYTHON SOURCE LINES 19-23

.. code-block:: default

    import slam.generate_parametric_surfaces as sgps
    import slam.plot as splt
    import numpy as np








.. GENERATED FROM PYTHON SOURCE LINES 24-25

Generating a quadrix surface

.. GENERATED FROM PYTHON SOURCE LINES 25-47

.. code-block:: default


    K = [1, 1]
    quadric = sgps.generate_quadric(
        K,
        nstep=[20, 20],
        ax=3,
        ay=1,
        random_sampling=True,
        ratio=0.3,
        random_distribution_type="gamma",
    )
    quadric_mean_curv = sgps.quadric_curv_mean(K)(
        np.array(quadric.vertices[:, 0]), np.array(quadric.vertices[:, 1])
    )

    visb_sc = splt.visbrain_plot(
        mesh=quadric, tex=quadric_mean_curv, caption="quadric", cblabel="mean curvature"
    )

    visb_sc.preview()





.. image:: /auto_examples/images/sphx_glr_example_generate_parametric_surfaces_001.png
    :alt: example generate parametric surfaces
    :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 48-49

Generating an ellipsiods

.. GENERATED FROM PYTHON SOURCE LINES 49-61

.. code-block:: default


    nstep = 50
    randomSampling = True
    a = 2
    b = 1
    ellips = sgps.generate_ellipsiod(a, b, nstep, randomSampling)

    visb_sc = splt.visbrain_plot(mesh=ellips, caption="ellipsoid")

    visb_sc.preview()





.. image:: /auto_examples/images/sphx_glr_example_generate_parametric_surfaces_002.png
    :alt: example generate parametric surfaces
    :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 62-63

Generating a sphere

.. GENERATED FROM PYTHON SOURCE LINES 63-71

.. code-block:: default

    sphere_regular = sgps.generate_sphere_icosahedron(subdivisions=3, radius=4)


    visb_sc = splt.visbrain_plot(mesh=sphere_regular, caption="sphere_regular")

    visb_sc.preview()





.. image:: /auto_examples/images/sphx_glr_example_generate_parametric_surfaces_003.png
    :alt: example generate parametric surfaces
    :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 72-74

Generating a more randomized sphere (random sampling with the same
number of vertices)

.. GENERATED FROM PYTHON SOURCE LINES 74-86

.. code-block:: default


    sphere_random = sgps.generate_sphere_random_sampling(
        vertex_number=sphere_regular.vertices.shape[0], radius=4
    )

    visb_sc = splt.visbrain_plot(
        mesh=sphere_random, caption="sphere_random", visb_sc=visb_sc
    )

    visb_sc.preview()





.. image:: /auto_examples/images/sphx_glr_example_generate_parametric_surfaces_004.png
    :alt: example generate parametric surfaces
    :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 87-88

Computation of the volume and volume error of the spheres

.. GENERATED FROM PYTHON SOURCE LINES 88-100

.. code-block:: default


    analytical_vol = (4 / 3) * np.pi * np.power(4, 3)
    print(
        "volume error for regular sampling: {:.3f}".format(
            sphere_regular.volume - analytical_vol
        )
    )
    print(
        "volume error for random sampling: {:.3f}".format(
            sphere_random.volume - analytical_vol
        )
    )




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

 Out:

 .. code-block:: none

    volume error for regular sampling: -2.307
    volume error for random sampling: -5.000





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

   **Total running time of the script:** ( 0 minutes  1.998 seconds)


.. _sphx_glr_download_auto_examples_example_generate_parametric_surfaces.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



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

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



  .. container:: sphx-glr-download sphx-glr-download-jupyter

     :download:`Download Jupyter notebook: example_generate_parametric_surfaces.ipynb <example_generate_parametric_surfaces.ipynb>`


.. only:: html

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

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