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   "source": [
    "<div class=\"contentcontainer med left\" style=\"margin-left: -50px;\">\n",
    "<dl class=\"dl-horizontal\">\n",
    "  <dt>Title</dt> <dd> TriMesh Element</dd>\n",
    "  <dt>Dependencies</dt> <dd>Bokeh</dd>\n",
    "  <dt>Backends</dt> <dd><a href='./TriMesh.ipynb'>Matplotlib</a></dd> <dd><a href='../bokeh/TriMesh.ipynb'>Bokeh</a></dd>\n",
    "</dl>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import holoviews as hv\n",
    "\n",
    "from holoviews import opts\n",
    "from scipy.spatial import Delaunay\n",
    "\n",
    "hv.extension('matplotlib')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A ``TriMesh`` represents a mesh of triangles represented as the simplexes and vertexes. The simplexes represent the indices into the vertex data, made up of three indices per triangle. The mesh therefore follows a datastructure very similar to a graph, with the abstract connectivity between nodes stored on the ``TriMesh`` element itself, the node or vertex positions stored on a ``Nodes`` element and the concrete ``EdgePaths`` making up each triangle generated when required by accessing the edgepaths attribute.\n",
    "\n",
    "Unlike a Graph each simplex is represented as the node indices of the three corners of each triangle rather than the usual source and target node.\n",
    "\n",
    "We will begin with a simple random mesh, generated by sampling some random integers and then applying Delaunay triangulation, which is available in SciPy. We can then construct the ``TriMesh`` by passing it the **simplexes** and the **vertices** (or **nodes**)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_verts = 100\n",
    "pts = np.random.randint(1, n_verts, (n_verts, 2))\n",
    "tris = Delaunay(pts)\n",
    "\n",
    "trimesh = hv.TriMesh((tris.simplices, pts))\n",
    "trimesh"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make this easier TriMesh also provides a convenient ``from_vertices`` method, which will apply the Delaunay triangulation and construct the ``TriMesh`` for us:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "hv.TriMesh.from_vertices(np.random.randn(100, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just like the ``Graph`` element we can access the ``Nodes`` and ``EdgePaths`` via the ``.nodes`` and ``.edgepaths`` attributes respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "trimesh.nodes + trimesh.edgepaths"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's make a slightly more interesting example by generating a more complex geometry. Here we will compute a geometry, then apply Delaunay triangulation again and finally apply a mask to drop nodes in the center."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# First create the x and y coordinates of the points.\n",
    "n_angles = 36\n",
    "n_radii = 8\n",
    "min_radius = 0.25\n",
    "radii = np.linspace(min_radius, 0.95, n_radii)\n",
    "\n",
    "angles = np.linspace(0, 2*np.pi, n_angles, endpoint=False)\n",
    "angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)\n",
    "angles[:, 1::2] += np.pi/n_angles\n",
    "\n",
    "x = (radii*np.cos(angles)).flatten()\n",
    "y = (radii*np.sin(angles)).flatten()\n",
    "z = (np.cos(radii)*np.cos(angles*3.0)).flatten()\n",
    "nodes = np.column_stack([x, y, z])\n",
    "\n",
    "# Apply Delaunay triangulation\n",
    "delaunay = Delaunay(np.column_stack([x, y]))\n",
    "\n",
    "# Mask off unwanted triangles.\n",
    "xmid = x[delaunay.simplices].mean(axis=1)\n",
    "ymid = y[delaunay.simplices].mean(axis=1)\n",
    "mask = np.where(xmid*xmid + ymid*ymid < min_radius*min_radius, 1, 0)\n",
    "simplices = delaunay.simplices[np.logical_not(mask)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again we can simply supply the simplices and nodes to the ``TriMesh``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "hv.TriMesh((simplices, nodes))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also do something more interesting, e.g. by adding a value dimension to the vertices and coloring the edges by the vertex averaged value using the ``edge_color`` plot option:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "hv.TriMesh((simplices, hv.Points(nodes, vdims='z'))).opts(\n",
    "    opts.TriMesh(cmap='viridis', edge_color='z', filled=True, fig_size=200))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For full documentation and the available style and plot options, use ``hv.help(hv.TriMesh).``"
   ]
  }
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