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@keflavich
Created January 21, 2021 17:01
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pylab as pl\n",
"import pylab as plt\n",
"from scipy.spatial import voronoi_plot_2d\n",
"from scipy.spatial import Voronoi\n",
"from sklearn.cluster import KMeans"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"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)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(-4.61929694474156, 3.437904863251044, -4.379570187748189, 4.203982516382792)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = np.zeros([2000,2])\n",
"third=2000//3\n",
"x[:third,0]=np.random.randn(third)+0.5\n",
"x[:third,1]=np.random.randn(third)+0.5\n",
"x[third:third*2,0]=np.random.randn(third)-0.5\n",
"x[third:third*2,1]=np.random.randn(third)+0.5\n",
"x[third*2:,0]=np.random.randn(third+2)\n",
"x[third*2:,1]=np.random.randn(third+2)-0.5\n",
"kmeans=KMeans(n_clusters=3)\n",
"y_pred=kmeans.fit_predict(x)\n",
"pl.scatter(x[:, 0], x[:, 1], c=y_pred, alpha=0.25, s=3, cmap=pl.cm.jet)\n",
"z = [x[y_pred==ii].mean(axis=0)\n",
" for ii in range(3)]\n",
"\n",
"vor = Voronoi(z)\n",
"\n",
"regions, vertices = voronoi_finite_polygons_2d(vor)\n",
"\n",
"segments = [[[vertices[0][0], vertices[ii][0]],\n",
" [vertices[0][1], vertices[ii][1]]] for ii in range(1, len(vertices))]\n",
"for seg in segments:\n",
" plt.plot(seg[0], seg[1], color='k', alpha=0.5)\n",
"\n",
"plt.axis('equal')"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"for jj in range(50):\n",
" x = np.zeros([2000,2])\n",
" x[:,0]=np.random.randn(2000)\n",
" x[:,1]=np.random.randn(2000)\n",
" kmeans=KMeans(n_clusters=3)\n",
" y_pred=kmeans.fit_predict(x)\n",
" #pl.scatter(x[:, 0], x[:, 1], c=y_pred)\n",
" z = [x[y_pred==ii].mean(axis=0)\n",
" for ii in range(3)]\n",
" \n",
" # compute Voronoi tesselation\n",
" vor = Voronoi(z)\n",
"\n",
" # plot\n",
" regions, vertices = voronoi_finite_polygons_2d(vor)\n",
"\n",
" segments = [[[vertices[0][0], vertices[ii][0]],\n",
" [vertices[0][1], vertices[ii][1]]] for ii in range(1, len(vertices)//2)]\n",
" for seg in segments:\n",
" plt.plot(seg[0], seg[1], alpha=0.3, color='k')\n",
" plt.axis('equal')"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"for jj in range(50):\n",
" x = np.zeros([2000,2])\n",
" third=2000//3\n",
" x[:third,0]=np.random.randn(third)+0.5\n",
" x[:third,1]=np.random.randn(third)+0.5\n",
" x[third:third*2,0]=np.random.randn(third)-0.5\n",
" x[third:third*2,1]=np.random.randn(third)+0.5\n",
" x[third*2:,0]=np.random.randn(third+2)\n",
" x[third*2:,1]=np.random.randn(third+2)-0.5\n",
"\n",
" kmeans=KMeans(n_clusters=3)\n",
" y_pred=kmeans.fit_predict(x)\n",
" #pl.scatter(x[:, 0], x[:, 1], c=y_pred)\n",
" z = [x[y_pred==ii].mean(axis=0)\n",
" for ii in range(3)]\n",
" \n",
" # compute Voronoi tesselation\n",
" vor = Voronoi(z)\n",
"\n",
" # plot\n",
" regions, vertices = voronoi_finite_polygons_2d(vor)\n",
"\n",
" segments = [[[vertices[0][0], vertices[ii][0]],\n",
" [vertices[0][1], vertices[ii][1]]] for ii in range(1, len(vertices)//2)]\n",
" for seg in (segments):\n",
" plt.plot(seg[0], seg[1], alpha=0.3, color='k')\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)"
]
}
],
"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": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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