colorized_voronoi.ipynb

{
 "metadata": {
  "name": ""
 },
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 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from scipy.spatial import Voronoi"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def voronoi_finite_polygons_2d(vor, radius=None):\n",
      "    \"\"\"\n",
      "    Reconstruct infinite voronoi regions in a 2D diagram to finite\n",
      "    regions.\n",
      "\n",
      "    Parameters\n",
      "    ----------\n",
      "    vor : Voronoi\n",
      "        Input diagram\n",
      "    radius : float, optional\n",
      "        Distance to 'points at infinity'.\n",
      "\n",
      "    Returns\n",
      "    -------\n",
      "    regions : list of tuples\n",
      "        Indices of vertices in each revised Voronoi regions.\n",
      "    vertices : list of tuples\n",
      "        Coordinates for revised Voronoi vertices. Same as coordinates\n",
      "        of input vertices, with 'points at infinity' appended to the\n",
      "        end.\n",
      "\n",
      "    \"\"\"\n",
      "\n",
      "    if vor.points.shape[1] != 2:\n",
      "        raise ValueError(\"Requires 2D input\")\n",
      "\n",
      "    new_regions = []\n",
      "    new_vertices = vor.vertices.tolist()\n",
      "\n",
      "    center = vor.points.mean(axis=0)\n",
      "    if radius is None:\n",
      "        radius = vor.points.ptp().max()*2\n",
      "\n",
      "    # Construct a map containing all ridges for a given point\n",
      "    all_ridges = {}\n",
      "    for (p1, p2), (v1, v2) in zip(vor.ridge_points, vor.ridge_vertices):\n",
      "        all_ridges.setdefault(p1, []).append((p2, v1, v2))\n",
      "        all_ridges.setdefault(p2, []).append((p1, v1, v2))\n",
      "\n",
      "    # Reconstruct infinite regions\n",
      "    for p1, region in enumerate(vor.point_region):\n",
      "        vertices = vor.regions[region]\n",
      "\n",
      "        if all([v >= 0 for v in vertices]):\n",
      "            # finite region\n",
      "            new_regions.append(vertices)\n",
      "            continue\n",
      "\n",
      "        # reconstruct a non-finite region\n",
      "        ridges = all_ridges[p1]\n",
      "        new_region = [v for v in vertices if v >= 0]\n",
      "\n",
      "        for p2, v1, v2 in ridges:\n",
      "            if v2 < 0:\n",
      "                v1, v2 = v2, v1\n",
      "            if v1 >= 0:\n",
      "                # finite ridge: already in the region\n",
      "                continue\n",
      "\n",
      "            # Compute the missing endpoint of an infinite ridge\n",
      "\n",
      "            t = vor.points[p2] - vor.points[p1] # tangent\n",
      "            t /= np.linalg.norm(t)\n",
      "            n = np.array([-t[1], t[0]])  # normal\n",
      "\n",
      "            midpoint = vor.points[[p1, p2]].mean(axis=0)\n",
      "            direction = np.sign(np.dot(midpoint - center, n)) * n\n",
      "            far_point = vor.vertices[v2] + direction * radius\n",
      "\n",
      "            new_region.append(len(new_vertices))\n",
      "            new_vertices.append(far_point.tolist())\n",
      "\n",
      "        # sort region counterclockwise\n",
      "        vs = np.asarray([new_vertices[v] for v in new_region])\n",
      "        c = vs.mean(axis=0)\n",
      "        angles = np.arctan2(vs[:,1] - c[1], vs[:,0] - c[0])\n",
      "        new_region = np.array(new_region)[np.argsort(angles)]\n",
      "\n",
      "        # finish\n",
      "        new_regions.append(new_region.tolist())\n",
      "\n",
      "    return new_regions, np.asarray(new_vertices)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# make up data points\n",
      "np.random.seed(1234)\n",
      "points = np.random.rand(15, 2)\n",
      "\n",
      "# compute Voronoi tesselation\n",
      "vor = Voronoi(points)\n",
      "\n",
      "# plot\n",
      "regions, vertices = voronoi_finite_polygons_2d(vor)\n",
      "print \"--\"\n",
      "print regions\n",
      "print \"--\"\n",
      "print vertices\n",
      "\n",
      "# colorize\n",
      "for region in regions:\n",
      "    polygon = vertices[region]\n",
      "    plt.fill(*zip(*polygon), alpha=0.4)\n",
      "\n",
      "plt.plot(points[:,0], points[:,1], 'ko')\n",
      "plt.axis('equal')\n",
      "plt.xlim(vor.min_bound[0] - 0.1, vor.max_bound[0] + 0.1)\n",
      "plt.ylim(vor.min_bound[1] - 0.1, vor.max_bound[1] + 0.1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "--\n",
        "[[10, 15, 14, 21, 20], [19, 7, 12, 17], [22, 23, 4, 3, 0], [24, 14, 16, 18, 25], [5, 26, 27], [9, 1, 0, 3, 2, 8], [12, 7, 6, 4, 3, 2, 11], [13, 8, 2, 11], [28, 29, 0, 1], [18, 19, 7, 6, 5, 30, 31], [17, 12, 11, 13, 15, 14, 16], [32, 1, 9, 10, 33], [34, 35, 5, 6, 4], [19, 17, 16, 18], [15, 10, 9, 8, 13]]\n",
        "--\n",
        "[[ 0.51204146  0.28170809]\n",
        " [ 0.31568864  0.2231658 ]\n",
        " [ 0.60181497  0.48198612]\n",
        " [ 0.61195783  0.46638446]\n",
        " [ 0.76349576  0.49961565]\n",
        " [ 0.86163554  0.77300743]\n",
        " [ 0.82428491  0.74711566]\n",
        " [ 0.5955872   0.86737793]\n",
        " [ 0.3398531   0.5360898 ]\n",
        " [ 0.20717026  0.45505837]\n",
        " [ 0.19839983  0.46568522]\n",
        " [ 0.54203769  0.60556533]\n",
        " [ 0.52991347  0.64525971]\n",
        " [ 0.34632775  0.58619376]\n",
        " [ 0.28095359  0.68979933]\n",
        " [ 0.27956806  0.65401536]\n",
        " [ 0.32776593  0.71199644]\n",
        " [ 0.40994669  0.69667456]\n",
        " [ 0.41517255  1.51501742]\n",
        " [ 0.46233568  1.32637502]\n",
        " [-1.51846216  1.25291487]\n",
        " [-1.42673123  1.49674306]\n",
        " [ 1.80180548 -1.09809421]\n",
        " [ 2.5145059  -0.20841621]\n",
        " [-1.42673123  1.49674306]\n",
        " [ 0.11182282  3.37923966]\n",
        " [ 2.73878052  0.56402822]\n",
        " [ 0.92996562  2.66051282]\n",
        " [-0.89071967 -1.23008044]\n",
        " [ 1.80180548 -1.09809421]\n",
        " [ 0.92996562  2.66051282]\n",
        " [ 0.11182282  3.37923966]\n",
        " [-0.89071967 -1.23008044]\n",
        " [-1.51846216  1.25291487]\n",
        " [ 2.5145059  -0.20841621]\n",
        " [ 2.73878052  0.56402822]]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "(-0.086231550409317764, 0.98264119063611655)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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56b6VeY88JHVJk3bXtMWh4WkLTw8Tvp6+M+rYoNv19vbi6jpIYODY7Ring9E4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\nE2FTdPzY/R7JOYdkL+M2yOYgNplMJCYmkpGRQVJ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       "text": [
        "<matplotlib.figure.Figure at 0x9e0a96c>"
       ]
      }
     ],
     "prompt_number": 3
    }
   ],
   "metadata": {}
  }
 ]
}