Skip to content

Commit

Permalink
Added TriMesh reference entries
Browse files Browse the repository at this point in the history
  • Loading branch information
@philippjfr
philippjfr committed Nov 24, 2017
1 parent 3326430 commit b6a8f6c
Show file tree
Hide file tree
Showing 2 changed files with 330 additions and 0 deletions.
165 changes: 165 additions & 0 deletions examples/reference/elements/bokeh/TriMesh.ipynb
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,165 @@
{
"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 simplices and nodes. The simplices represent the indices into the node 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 positions stored on a ``Nodes`` element and the concrete ``EdgePaths`` making up each triangle generated when required by accessing the edgepaths.\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 **simplices** and the points (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": [
"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",
"nodes = np.column_stack([x, y])\n",
"z = (np.cos(radii)*np.cos(angles*3.0)).flatten()\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)]\n",
"z = z[simplices].mean(axis=1)"
]
},
{
"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. adding a value dimension to the simplices, which we can color each triangle by."
]
},
{
"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((np.column_stack([simplices, z]), 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
}
165 changes: 165 additions & 0 deletions examples/reference/elements/matplotlib/TriMesh.ipynb
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,165 @@
{
"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 simplices and nodes. The simplices represent the indices into the node 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 positions stored on a ``Nodes`` element and the concrete ``EdgePaths`` making up each triangle generated when required by accessing the edgepaths.\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 **simplices** and the points (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": [
"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",
"nodes = np.column_stack([x, y])\n",
"z = (np.cos(radii)*np.cos(angles*3.0)).flatten()\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)]\n",
"z = z[simplices].mean(axis=1)"
]
},
{
"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. adding a value dimension to the simplices, which we can color each triangle by."
]
},
{
"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((np.column_stack([simplices, z]), 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
}

0 comments on commit b6a8f6c

Please sign in to comment.