Add TriMesh element (#2143)

examples/reference/elements/bokeh/TriMesh.ipynb

@@ -0,0 +1,181 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "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'>Bokeh</a></dd> <dd><a href='../matplotlib/TriMesh.ipynb'>Matplotlib</a></dd>\n",
+    "</dl>\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "import holoviews as hv\n",
+    "from scipy.spatial import Delaunay\n",
+    "\n",
+    "hv.extension('bokeh')"
+   ]
+  },
+  {
+   "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",
+    "delauney = Delaunay(np.column_stack([x, y]))\n",
+    "\n",
+    "# Mask off unwanted triangles.\n",
+    "xmid = x[delauney.simplices].mean(axis=1)\n",
+    "ymid = y[delauney.simplices].mean(axis=1)\n",
+    "mask = np.where(xmid*xmid + ymid*ymid < min_radius*min_radius, 1, 0)\n",
+    "simplices = delauney.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": [
+    "nodes = hv.Points(nodes, vdims='z')\n",
+    "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_index`` plot option:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%%opts TriMesh [filled=True edge_color_index='z' width=400 height=400 tools=['hover'] inspection_policy='edges'] (cmap='viridis')\n",
+    "hv.TriMesh((simplices, nodes))"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

examples/reference/elements/matplotlib/TriMesh.ipynb

@@ -0,0 +1,180 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "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 pandas as pd\n",
+    "import holoviews as hv\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",
+    "delauney = Delaunay(np.column_stack([x, y]))\n",
+    "\n",
+    "# Mask off unwanted triangles.\n",
+    "xmid = x[delauney.simplices].mean(axis=1)\n",
+    "ymid = y[delauney.simplices].mean(axis=1)\n",
+    "mask = np.where(xmid*xmid + ymid*ymid < min_radius*min_radius, 1, 0)\n",
+    "simplices = delauney.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_index`` plot option:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%%opts TriMesh [filled=True edge_color_index='z' fig_size=200] (cmap='viridis')\n",
+    "hv.TriMesh((simplices, hv.Points(nodes, vdims='z')))"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

holoviews/core/data/__init__.py

@@ -275,7 +275,11 @@ def add_dimension(self, dimension, dim_pos, dim_val, vdim=False, **kwargs):
             dims.insert(dim_pos, dimension)
             dimensions = dict(kdims=dims)
 
-        data = self.interface.add_dimension(self, dimension, dim_pos, dim_val, vdim)
+        if issubclass(self.interface, ArrayInterface) and np.asarray(dim_val).dtype != self.data.dtype:
+            element = self.clone(datatype=['pandas', 'dictionary'])
+            data = element.interface.add_dimension(element, dimension, dim_pos, dim_val, vdim)
+        else:
+            data = self.interface.add_dimension(self, dimension, dim_pos, dim_val, vdim)
         return self.clone(data, **dimensions)