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

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_plot_decomposition.py:


Convex decomposition
====================

.. GENERATED FROM PYTHON SOURCE LINES 7-11

.. code-block:: Python

    import openturns as ot
    import openturns.viewer as otv
    import otmeshing








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Define a non-convex polyhedra surface mesh: a cube with folded corner

.. GENERATED FROM PYTHON SOURCE LINES 13-30

.. code-block:: Python

    vertices = [
        [0, 0, 0], [2, 0, 0], [2, 2, 0], [0, 2, 0],  # 0–3 bottom
        [0, 0, 2], [2, 0, 2], [0, 2, 2],  # 4–7 top
        [1, 1, 1], [2, 1, 1], [2, 2, 1], [1, 2, 1],  # notch bottom
        [1, 1, 2], [2, 1, 2], [1, 2, 2]]  # notch top
    simplices = [
        [0, 1, 5, 5], [0, 5, 4, 4],  # y=0
        [0, 4, 6, 6], [0, 6, 3, 3],  # x=0
        [0, 2, 1, 1], [0, 3, 2, 2],  # z=0
        [10, 9, 2, 2], [10, 2, 3, 3], [10, 3, 6, 6], [10, 6, 13, 13],  # y=2 wall
        [8, 2, 9, 9], [8, 1, 2, 2], [8, 5, 1, 1], [8, 12, 5, 5],  # x=2 wall
        [11, 13, 6, 6], [11, 6, 4, 4], [11, 4, 5, 5], [11, 5, 12, 12],  # z=2 wall
        [8, 7, 12, 12], [7, 11, 12, 12],  # y=1 notch
        [7, 10, 13, 13], [7, 13, 11, 11],  # x=1 notch
        [7, 8, 9, 9], [7, 9, 10, 10]]  # z=1 notch
    polyhedra = ot.Mesh(vertices, simplices)








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We can check the mesh is not convex

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.. code-block:: Python

    otmeshing.ConvexDecompositionMesher.IsConvex(polyhedra)





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

 .. code-block:: none


    False



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Draw the polyhedra

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.. code-block:: Python

    shading = True
    thetaX, thetaY, thetaZ = 6.1, 3.7, 4.3
    drawEdge = True
    graph = polyhedra.draw3D(drawEdge, thetaX, thetaY, thetaZ, shading)
    V = polyhedra.getVerticesNumber()
    T = polyhedra.getSimplicesNumber()
    volume = round(polyhedra.getVolume())
    graph.setTitle(f"non-convex polyhedra V={V} T={T} volume={volume}")
    view = otv.View(graph)




.. image-sg:: /auto_examples/images/sphx_glr_plot_decomposition_001.png
   :alt: non-convex polyhedra V=14 T=24 volume=24
   :srcset: /auto_examples/images/sphx_glr_plot_decomposition_001.png
   :class: sphx-glr-single-img





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Build the decomposition

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.. code-block:: Python

    mesher = otmeshing.ConvexDecompositionMesher()
    decomposition = mesher.build(polyhedra)
    for i, convex in enumerate(decomposition):
        V = convex.getVerticesNumber()
        T = convex.getSimplicesNumber()
        volume = round(convex.getVolume())
        graph = convex.draw3D(drawEdge, thetaX, thetaY, thetaZ, shading)
        graph.setTitle(f"convex #{i} V={V} T={T} volume={volume}")
        view = otv.View(graph)




.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/images/sphx_glr_plot_decomposition_002.png
         :alt: convex #0 V=12 T=14 volume=4
         :srcset: /auto_examples/images/sphx_glr_plot_decomposition_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/images/sphx_glr_plot_decomposition_003.png
         :alt: convex #1 V=10 T=10 volume=2
         :srcset: /auto_examples/images/sphx_glr_plot_decomposition_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/images/sphx_glr_plot_decomposition_004.png
         :alt: convex #2 V=8 T=6 volume=1
         :srcset: /auto_examples/images/sphx_glr_plot_decomposition_004.png
         :class: sphx-glr-multi-img





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.. code-block:: Python

    otv.View.ShowAll()








.. _sphx_glr_download_auto_examples_plot_decomposition.py:

.. only:: html

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

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

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

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

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

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

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