.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "example_gallery/auto_examples/basic/face_area_vectors.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_face_area_vectors.py>`
        to download the full example code.

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

.. _sphx_glr_example_gallery_auto_examples_basic_face_area_vectors.py:


Inspect oriented face area vectors
==================================

This tutorial computes oriented area vectors on a surface mesh and compares
them with ``face_areas() * face_normals()``. It is a good first example when
you want to understand what ``face_area_vectors()`` represents geometrically.

.. 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 and extract its surface
---------------------------------------------------------

.. 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: Compute area vectors, normals, and areas
------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 37-77

.. 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()

        face_centroids = surface_mesh.geometry.face_centroids()
        face_area_vectors = surface_mesh.geometry.face_area_vectors()
        face_normals = surface_mesh.geometry.face_normals()
        face_areas = surface_mesh.geometry.face_areas()

        reconstructed = face_normals * face_areas

        print(f"Surface face count: {surface_mesh.n_cells}")
        print(f"face_area_vectors shape: {tuple(face_area_vectors.shape)}")
        print(
            "face_area_vectors == face_normals * face_areas: "
            f"{torch.allclose(face_area_vectors, reconstructed)}"
        )
        print(f"First area vector: {face_area_vectors[0].tolist()}")

        plotter = pv.Plotter(window_size=[900, 700])
        plotter.add_mesh(
            surface_mesh.pvmesh,
            show_edges=True,
            color="white",
            opacity=0.85,
        )
        plotter.add_arrows(
            face_centroids.detach().cpu().numpy(),
            face_area_vectors.detach().cpu().numpy(),
            mag=0.35,
            color="tomato",
        )
        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_face_area_vectors_001.png
   :alt: face area vectors
   :srcset: /example_gallery/auto_examples/basic/images/sphx_glr_face_area_vectors_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Surface face count: 32
    face_area_vectors shape: (32, 3)
    face_area_vectors == face_normals * face_areas: True
    First area vector: [0.03840000182390213, 0.04800000041723251, -0.800000011920929]





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

   **Total running time of the script:** (0 minutes 0.202 seconds)


.. _sphx_glr_download_example_gallery_auto_examples_basic_face_area_vectors.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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