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Example gallery
===============

This gallery is split into two sections:

- ``Basic tutorials``: short examples that introduce one core operation at a time
- ``Advanced examples``: longer workflows for optimization and continuous metrics



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Basic tutorials
===============

These examples introduce one core ``graphlow`` operation at a time.

Read them in order if you are new to the project:

1. create a ``TensorMesh`` from PyVista
2. compute cell volumes on a volume mesh
3. extract a boundary surface
4. compute enclosed volume on a watertight surface
5. transfer data between points and cells
6. inspect oriented face area vectors


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    <div class="sphx-glr-thumbcontainer" tooltip="This tutorial shows the first step in most graphlow workflows: build a small PyVista volume mesh, convert it to TensorMesh, and inspect the basic mesh information exposed by the geometry/topology wrappers.">

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  .. image:: /example_gallery/auto_examples/basic/images/thumb/sphx_glr_create_tensor_mesh_thumb.png
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  :doc:`/example_gallery/auto_examples/basic/create_tensor_mesh`

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      <div class="sphx-glr-thumbnail-title">Create a TensorMesh from a PyVista mesh</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This tutorial computes per-cell volumes on a small volume mesh and compares their sum with PyVista&#x27;s total volume. Use this example when you want the simplest geometry calculation on a TensorMesh.">

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  .. image:: /example_gallery/auto_examples/basic/images/thumb/sphx_glr_cell_volumes_thumb.png
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  :doc:`/example_gallery/auto_examples/basic/cell_volumes`

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      <div class="sphx-glr-thumbnail-title">Compute cell volumes on a volume mesh</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This tutorial extracts the boundary surface of a volume mesh and shows that the surface points keep their connection to the parent volume points by default.">

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  .. image:: /example_gallery/auto_examples/basic/images/thumb/sphx_glr_extract_surface_thumb.png
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  :doc:`/example_gallery/auto_examples/basic/extract_surface`

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      <div class="sphx-glr-thumbnail-title">Extract a boundary surface from a volume mesh</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="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.">

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  .. image:: /example_gallery/auto_examples/basic/images/thumb/sphx_glr_surface_enclosed_volume_thumb.png
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  :doc:`/example_gallery/auto_examples/basic/surface_enclosed_volume`

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      <div class="sphx-glr-thumbnail-title">Compute enclosed volume on a surface mesh</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This tutorial starts with a point field, maps it to cells with a mean reduction, then maps it back to points. It is the shortest introduction to the point/cell mapping helpers in mesh.topology.">

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  .. image:: /example_gallery/auto_examples/basic/images/thumb/sphx_glr_point_cell_mapping_thumb.png
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  :doc:`/example_gallery/auto_examples/basic/point_cell_mapping`

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      <div class="sphx-glr-thumbnail-title">Transfer data between points and cells</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="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.">

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  .. image:: /example_gallery/auto_examples/basic/images/thumb/sphx_glr_face_area_vectors_thumb.png
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  :doc:`/example_gallery/auto_examples/basic/face_area_vectors`

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      <div class="sphx-glr-thumbnail-title">Inspect oriented face area vectors</div>
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Advanced examples
=================

These examples assume you already understand the basic ``TensorMesh``,
geometry, and topology workflows.

They focus on optimization loops, continuous metrics, and richer end-to-end
applications.


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    <div class="sphx-glr-thumbcontainer" tooltip="This tutorial: define φ(x,y), build the isoAM gradient operator, then compute ∇φ and visualize it.">

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  .. image:: /example_gallery/auto_examples/advanced/images/thumb/sphx_glr_gradient_thumb.png
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  :doc:`/example_gallery/auto_examples/advanced/gradient`

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      <div class="sphx-glr-thumbnail-title">Compute gradient of scalar field on a mesh</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Using an ellipsoid (different radii per axis) and many target points makes the optimization non-trivial and shows the mesh deforming toward the target. The same topology (sphere-like) allows the loss to converge to a low value. Soft-min Chamfer ensures gradients reach all vertices for stable convergence.">

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  .. image:: /example_gallery/auto_examples/advanced/images/thumb/sphx_glr_target_fitting_thumb.gif
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  :doc:`/example_gallery/auto_examples/advanced/target_fitting`

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      <div class="sphx-glr-thumbnail-title">Target fitting: minimize Chamfer distance to a point cloud</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example walks through: loading a mesh, building a deformation model, defining a differentiable cost, and running the optimization loop. Helper functions are defined at module level with clear roles.">

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  .. image:: /example_gallery/auto_examples/advanced/images/thumb/sphx_glr_shape_optimization_thumb.gif
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  :doc:`/example_gallery/auto_examples/advanced/shape_optimization`

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      <div class="sphx-glr-thumbnail-title">Shape optimization: minimize surface area under volume constraint</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="The deformation is parameterized as a continuous transform chain, where only vertex positions evolve while the underlying mesh connectivity remains fixed.">

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  .. image:: /example_gallery/auto_examples/advanced/images/thumb/sphx_glr_sphere_eversion_continuous_metrics_thumb.gif
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  :doc:`/example_gallery/auto_examples/advanced/sphere_eversion_continuous_metrics`

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      <div class="sphx-glr-thumbnail-title">Continuous sphere eversion with graphlow geometry APIs</div>
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.. toctree::
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   /example_gallery/auto_examples/basic/index.rst
   /example_gallery/auto_examples/advanced/index.rst


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      :download:`Download all examples in Python source code: auto_examples_python.zip </example_gallery/auto_examples/auto_examples_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip </example_gallery/auto_examples/auto_examples_jupyter.zip>`


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