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

.. only:: html

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

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

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

.. _sphx_glr_example_gallery_auto_examples_basic_surface_enclosed_volume.py:


Compute enclosed volume on a surface mesh
=========================================

This tutorial extracts a closed surface and computes its enclosed volume with
``surface_volume()``. The result can be compared with the sum of cell volumes
from the parent volume mesh.

.. GENERATED FROM PYTHON SOURCE LINES 11-13

Imports
-------

.. GENERATED FROM PYTHON SOURCE LINES 13-20

.. code-block:: Python

    import numpy as np
    import pyvista as pv
    import torch

    import graphlow









.. GENERATED FROM PYTHON SOURCE LINES 21-23

Step 1: Build a small volume mesh
---------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 23-34

.. code-block:: Python

    def make_volume_grid() -> pv.UnstructuredGrid:
        """Create a small warped hexahedral grid."""
        x = np.array([0.0, 1.0, 2.2, 3.5], dtype=np.float32)
        y = np.array([0.0, 0.8, 1.7], dtype=np.float32)
        z = np.array([0.0, 0.6, 1.4], dtype=np.float32)
        X, Y, Z = np.meshgrid(x, y, z, indexing="ij")
        Z = Z + 0.12 * X * Y
        grid = pv.StructuredGrid(X, Y, Z)
        return grid.cast_to_unstructured_grid()









.. GENERATED FROM PYTHON SOURCE LINES 35-37

Step 2: Compare volume from cells and from the closed surface
-------------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 37-61

.. code-block:: Python

    def main() -> None:
        """Run the tutorial."""
        volume_mesh = graphlow.from_pyvista(make_volume_grid(), backend="torch")
        surface_mesh = volume_mesh.extract_surface()

        total_cell_volume = torch.sum(volume_mesh.geometry.cell_volumes()).item()
        enclosed_volume = surface_mesh.geometry.surface_volume().item()

        print("surface_volume() is defined for watertight surface meshes.")
        print(f"Volume from cell_volumes().sum(): {total_cell_volume:.6f}")
        print(f"Enclosed volume from surface_volume(): {enclosed_volume:.6f}")
        print(
            f"Absolute difference: {abs(total_cell_volume - enclosed_volume):.6e}"
        )

        plotter = pv.Plotter(window_size=[800, 600])
        plotter.add_mesh(surface_mesh.pvmesh, show_edges=True, color="royalblue")
        plotter.show_bounds(mesh=surface_mesh.pvmesh, location="outer")
        plotter.camera_position = "iso"
        plotter.show()


    if __name__ == "__main__":
        main()



.. image-sg:: /example_gallery/auto_examples/basic/images/sphx_glr_surface_enclosed_volume_001.png
   :alt: surface enclosed volume
   :srcset: /example_gallery/auto_examples/basic/images/sphx_glr_surface_enclosed_volume_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    surface_volume() is defined for watertight surface meshes.
    Volume from cell_volumes().sum(): 8.330000
    Enclosed volume from surface_volume(): 8.330001
    Absolute difference: 9.536743e-07





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

   **Total running time of the script:** (0 minutes 0.129 seconds)


.. _sphx_glr_download_example_gallery_auto_examples_basic_surface_enclosed_volume.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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