.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_meshdomain2.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_meshdomain2.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_plot_meshdomain2.py:


Mesh distance
=============

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In this example we will see how to use the mesh domain adapter to compute distance from a point to a Mesh
We will also how it can be combined with LevelSetMesher to compute the intersection of meshes

.. GENERATED FROM PYTHON SOURCE LINES 11-16

.. code-block:: Python

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








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Create a mesh from an interval

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.. code-block:: Python

    dim = 2
    mesh = ot.IntervalMesher([1] * dim).build(ot.Interval([-0.7] * dim, [0.7] * dim))








.. GENERATED FROM PYTHON SOURCE LINES 22-23

Create the domain adapter from the mesh

.. GENERATED FROM PYTHON SOURCE LINES 23-25

.. code-block:: Python

    domain = otm.MeshDomain2(mesh)








.. GENERATED FROM PYTHON SOURCE LINES 26-28

Sample points and compute distances from the mesh
a negative distance means the point is inside the mesh

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.. code-block:: Python

    n = 200
    points = ot.Normal(dim).getSample(n)
    distances = domain.computeDistance(points)
    print(f"min={distances.getMin()} max={distances.getMax()}")





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

 .. code-block:: none

    min=[-0.641941] max=[2.56369]




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Plot the points according to the distance to the mesh

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.. code-block:: Python

    dmax = distances.getMax()[0]
    cmap = matplotlib.colormaps["PiYG"]
    graph = mesh.draw()
    for i in range(n):
        di = distances[i, 0]
        if di < 0.0:
            rgba = cmap(-di)
        else:
            rgba = cmap(1.0 - 0.5 * (di) / dmax)
        cloud = ot.Cloud([points[i]])
        color = ot.Drawable.ConvertFromRGBA(*rgba)
        cloud.setColor(color)
        graph.add(cloud)








.. GENERATED FROM PYTHON SOURCE LINES 50-53

.. code-block:: Python

    graph.setTitle("Mesh domain")
    view = otv.View(graph)




.. image-sg:: /auto_examples/images/sphx_glr_plot_meshdomain2_001.png
   :alt: Mesh domain
   :srcset: /auto_examples/images/sphx_glr_plot_meshdomain2_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 54-55

We will see that we can use the mesh distance to compute an intersection of meshes

.. GENERATED FROM PYTHON SOURCE LINES 55-82

.. code-block:: Python



    def levelSetIntersectionMeshing(mesh1, mesh2, n=20):
        """Compute an intersection using mesh distance."""
        dim = mesh1.getDimension()
        min1 = mesh1.getVertices().getMin()
        min2 = mesh2.getVertices().getMin()
        max1 = mesh1.getVertices().getMax()
        max2 = mesh2.getVertices().getMax()
        minB = list(map(min, min1, min2))
        maxB = list(map(max, max1, max2))
        bbox = ot.Interval(minB, maxB)
        domain1 = otm.MeshDomain2(mesh1)
        domain2 = otm.MeshDomain2(mesh2)

        def _exec(X):
            d1 = domain1.computeDistance(X)
            d2 = domain2.computeDistance(X)
            return [max(d1, d2)]

        f = ot.PythonFunction(dim, 1, _exec)
        levelSet = ot.LevelSet(f, ot.LessOrEqual(), 0.0)
        mesher = ot.LevelSetMesher([n] * dim)
        mesh = mesher.build(levelSet, bbox, False)
        return mesh









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Define two intersecting square meshes

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.. code-block:: Python

    dim = 2
    mesh1 = ot.IntervalMesher([1] * dim).build(ot.Interval([0.0] * dim, [3.0] * dim))
    mesh2 = ot.IntervalMesher([1] * dim).build(ot.Interval([1.0] * dim, [4.0] * dim))








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Compute the intersection: it should be the interval [1,3]^2

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.. code-block:: Python

    inter = levelSetIntersectionMeshing(mesh1, mesh2)
    graph = inter.draw()
    view = otv.View(graph)




.. image-sg:: /auto_examples/images/sphx_glr_plot_meshdomain2_002.png
   :alt: Mesh Unnamed
   :srcset: /auto_examples/images/sphx_glr_plot_meshdomain2_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 95-96

.. code-block:: Python

    otv.View.ShowAll()








.. _sphx_glr_download_auto_examples_plot_meshdomain2.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_meshdomain2.ipynb <plot_meshdomain2.ipynb>`

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

      :download:`Download Python source code: plot_meshdomain2.py <plot_meshdomain2.py>`

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

      :download:`Download zipped: plot_meshdomain2.zip <plot_meshdomain2.zip>`