{
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    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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      },
      "outputs": [],
      "source": [
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Create Triangulated Surface {#triangulated_surface}\n\nCreate a surface from a set of points through a Delaunay triangulation.\nThis example uses\n`pyvista.PolyDataFilters.delaunay_2d`{.interpreted-text role=\"func\"}.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np\n\nimport pyvista as pv"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Simple Triangulations\n\nFirst, create some points for the surface.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "# Define a simple Gaussian surface\nn = 20\nx = np.linspace(-200, 200, num=n) + np.random.default_rng().uniform(-5, 5, size=n)\ny = np.linspace(-200, 200, num=n) + np.random.default_rng().uniform(-5, 5, size=n)\nxx, yy = np.meshgrid(x, y)\nA, b = 100, 100\nzz = A * np.exp(-0.5 * ((xx / b) ** 2.0 + (yy / b) ** 2.0))\n\n# Get the points as a 2D NumPy array (N by 3)\npoints = np.c_[xx.reshape(-1), yy.reshape(-1), zz.reshape(-1)]\npoints[0:5, :]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Now use those points to create a point cloud PyVista data object. This\nwill be encompassed in a `pyvista.PolyData`{.interpreted-text\nrole=\"class\"} object.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "# simply pass the numpy points to the PolyData constructor\ncloud = pv.PolyData(points)\ncloud.plot(point_size=15)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Now that we have a PyVista data structure of the points, we can perform\na triangulation to turn those boring discrete points into a connected\nsurface.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "surf = cloud.delaunay_2d()\nsurf.plot(show_edges=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Masked Triangulations\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "x = np.arange(10, dtype=float)\nxx, yy, zz = np.meshgrid(x, x, [0])\npoints = np.column_stack((xx.ravel(order=\"F\"), yy.ravel(order=\"F\"), zz.ravel(order=\"F\")))\n# Perturb the points\npoints[:, 0] += np.random.default_rng().random(len(points)) * 0.3\npoints[:, 1] += np.random.default_rng().random(len(points)) * 0.3\n# Create the point cloud mesh to triangulate from the coordinates\ncloud = pv.PolyData(points)\ncloud"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Run the triangulation on these points\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "surf = cloud.delaunay_2d()\nsurf.plot(cpos=\"xy\", show_edges=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Note that some of the outer edges are unconstrained and the\ntriangulation added unwanted triangles. We can mitigate that with the\n`alpha` parameter.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "surf = cloud.delaunay_2d(alpha=1.0)\nsurf.plot(cpos=\"xy\", show_edges=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We could also add a polygon to ignore during the triangulation via the\n`edge_source` parameter.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "# Define a polygonal hole with a clockwise polygon\nids = [22, 23, 24, 25, 35, 45, 44, 43, 42, 32]\n\n# Create a polydata to store the boundary\npolygon = pv.PolyData()\n# Make sure it has the same points as the mesh being triangulated\npolygon.points = points\n# But only has faces in regions to ignore\npolygon.faces = np.insert(ids, 0, len(ids))\n\nsurf = cloud.delaunay_2d(alpha=1.0, edge_source=polygon)\n\np = pv.Plotter()\np.add_mesh(surf, show_edges=True)\np.add_mesh(polygon, color=\"red\", opacity=0.5)\np.show(cpos=\"xy\")"
      ]
    }
  ],
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