.. 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

        :ref:`Go to the end <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 8-16

.. code-block:: Python


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

    # License: MIT
    # sphinx_gallery_thumbnail_number = 2








.. GENERATED FROM PYTHON SOURCE LINES 17-21

NOTE: there is no visualization tool in slam, but we provide at the
 end of this script exemplare code to do the visualization with
 an external solution
##############################################################################

.. GENERATED FROM PYTHON SOURCE LINES 23-24

Importation of slam modules

.. GENERATED FROM PYTHON SOURCE LINES 24-27

.. code-block:: Python

    import slam.generate_parametric_surfaces as sgps
    import numpy as np








.. GENERATED FROM PYTHON SOURCE LINES 28-29

Generating a quadrix surface

.. GENERATED FROM PYTHON SOURCE LINES 29-43

.. code-block:: Python

    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])
    )








.. GENERATED FROM PYTHON SOURCE LINES 44-45

Generating an ellipsiods

.. GENERATED FROM PYTHON SOURCE LINES 45-51

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 52-53

Generating a sphere

.. GENERATED FROM PYTHON SOURCE LINES 53-55

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 56-58

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

.. GENERATED FROM PYTHON SOURCE LINES 58-62

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 63-64

Computation of the volume and volume error of the spheres

.. GENERATED FROM PYTHON SOURCE LINES 64-76

.. code-block:: Python

    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

 .. code-block:: none

    volume error for regular sampling: -2.307
    volume error for random sampling: -4.951




.. GENERATED FROM PYTHON SOURCE LINES 77-96

VISUALIZATION USING EXTERNAL TOOLS
############################################################################
 # import visbrain # visu using visbrain
 # show the quadric with its mean curvature
 visb_sc = splt.visbrain_plot(
     mesh=quadric,
     tex=quadric_mean_curv,
     caption="quadric",
     cblabel="mean curvature"
 )
 # show the ellipsoid
 visb_sc = splt.visbrain_plot(mesh=ellips, caption="ellipsoid")
 # show the sphere with regular sampling
 visb_sc = splt.visbrain_plot(mesh=sphere_regular, caption="sphere_regular")
 # show the sphere with random sampling
 visb_sc = splt.visbrain_plot(
     mesh=sphere_random, caption="sphere_random", visb_sc=visb_sc
 )
 visb_sc.preview()


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

   **Total running time of the script:** (0 minutes 0.074 seconds)


.. _sphx_glr_download_auto_examples_example_generate_parametric_surfaces.py:

.. only:: html

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

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

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

    .. 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-zip

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


.. only:: html

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

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