.. _sphx_glr_example_gallery_auto_examples_advanced:

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 id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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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
    :alt:

  :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>
    </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
    :alt:

  :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>
    </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
    :alt:

  :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>
    </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
    :alt:

  :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>
    </div>


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    </div>


.. toctree::
   :hidden:

   /example_gallery/auto_examples/advanced/gradient
   /example_gallery/auto_examples/advanced/target_fitting
   /example_gallery/auto_examples/advanced/shape_optimization
   /example_gallery/auto_examples/advanced/sphere_eversion_continuous_metrics