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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_MeshGeneration_demo_heart.py>`
        to download the full example code.

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

.. _sphx_glr_examples_MeshGeneration_demo_heart.py:


Implicit Heart
==============

This example generates a surface mesh of an implicit function and then performs 
Laplacian smoothing on it.

Defining an implicit function
-----------------------------
Implicit functions are defined as functions of three arguments (x, y, z), which 
can handle vectorized inputs. 

.. GENERATED FROM PYTHON SOURCE LINES 15-21

.. code-block:: Python

    from mymesh import implicit, mesh, improvement

    def heart(x, y, z):
        # Taubin's Heart Surface
        return (x**2 + 9/4*y**2 + z**2 -1)**3 - x**2*z**3 - 9/80*y**2*z**3








.. GENERATED FROM PYTHON SOURCE LINES 22-24

Creating a Surface
------------------

.. GENERATED FROM PYTHON SOURCE LINES 24-29

.. code-block:: Python

    bounds = [-1.5, 1.5, -1.5, 1.5, -1.5, 1.5]
    h = 0.05 # element size
    Heart = implicit.SurfaceMesh(heart, bounds, h)
    Heart.plot(bgcolor='white', color='red')




.. image-sg:: /examples/MeshGeneration/images/sphx_glr_demo_heart_001.png
   :alt: demo heart
   :srcset: /examples/MeshGeneration/images/sphx_glr_demo_heart_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    RFBOutputContext()




.. GENERATED FROM PYTHON SOURCE LINES 30-35

Smoothing
---------
The heart surface has a bit of a ridge in the middle, this can be eliminated 
by smoothing the mesh. This will also improve the quality of the elements in 
the mesh and more evenly distribute the nodes.

.. GENERATED FROM PYTHON SOURCE LINES 35-39

.. code-block:: Python



    Heart = improvement.LocalLaplacianSmoothing(Heart)
    Heart.plot(bgcolor='white', color='red')



.. image-sg:: /examples/MeshGeneration/images/sphx_glr_demo_heart_002.png
   :alt: demo heart
   :srcset: /examples/MeshGeneration/images/sphx_glr_demo_heart_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Identifying volume node neighbors...Done

    Identifying volume node element connectivity...Done

    Identifying boundary nodes...
            Identifying boundary...Done
            Done
            RFBOutputContext()





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

   **Total running time of the script:** (0 minutes 0.608 seconds)


.. _sphx_glr_download_examples_MeshGeneration_demo_heart.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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