{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Computational Geometry" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook introduces some key notions of computational geometry." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. the convex hull of 20 random points in the plane" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from scipy.spatial import ConvexHull, convex_hull_plot_2d" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from matplotlib import pyplot as plt" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "points = np.random.rand(20, 2)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "hull = ConvexHull(points)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The vertices :\n", "[18 4 5 19 12 16 10 8 9]\n" ] } ], "source": [ "print('The vertices :')\n", "print(hull.vertices)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The edges :\n", "[ 4 18]\n", "[12 19]\n", "[9 8]\n", "[ 9 18]\n", "[ 5 19]\n", "[5 4]\n", "[16 12]\n", "[10 8]\n", "[10 16]\n" ] } ], "source": [ "print('The edges :')\n", "for simplex in hull.simplices:\n", " print(simplex)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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KZBgGuru78dZbbzldypxYCfR2AEviHtcAOGdyzD5VvaaqPQB+A2CtPSXai0MuRJRo48aNvtgj3UqgHwRQKyLLRSQPwGMAWhKOeRXAPSKSIyKFAO4AcMLeUu3BQCeiRMXFxXjwwQc9v0d6ykBX1QiApwDsx3hIv6Sqx0Vkq4hsnTjmBIB9AI4CeBfjUxvfT1/Zs8dAJyIzhmHg9OnTeP99V0aXJZbm7qnqHgB7Ep7blfB4J4Cd9pVmP1XlRVEiMvWZz3wmtkf6Lbfc4nQ5sxKolaL/753TqPqv/xv/N7Ke+4kT0SRVVVW48847PT2OHphAbz7Sge/+eytyShYBEO4nTkRJDMPAH/7wB5w5c8bpUmYlMIG+c38rhiKTL3ZwP3Eiiuf1PdIDE+jcT5yIUqmtrUV9fb1nh10CE+jcT5yIrDAMA7/+9a9x6dIlp0uZscAE+vamMPISzjaT+4nzBs/uxd8NxfPyHumBCXRjXQiPLo8g0teV8f3EeYNn9+LvhhI1NDQgFAp5ctglMIEOALfMH0THrq/gtSeW4/c7NmRsb3He4Nm9+LuhRCICwzCwb98+DAx46xpboAJ9aGgIAJCfn5/R9+UFWffi74bMGIaB69ev45e//KXTpcxIoAJ9cHAQADBv3ryMvi8vyLoXfzdk5t577/XkHumBCnSnOnTe4Nm9+LshM7m5ufj0pz+NlpYWRCIRp8uxjIGeAbzBs3vxd0NTMQwDPT09ePPNN50uxbJA3VjTqUAHeINnN+Pvhsw0NTWhZM0D+G+vdWFwz2tYXFqA7U1hV/9dCVSgDw4OQkSQm5vrdClE5HK/aruCBU1PYUDG8yI6pRWAa0M9cEMu+fn5EDG7qx4R0Sd27m+FZk1u/tw+pTWQgU5ElIoXp7Qy0ImITHhxSmugAn1wcDDjc9CJyJu8OKU1UIHODp2IrIpOac0a6AVUPTGlNVCzXBjolAnNRzqwc38rzvUOeGKqG03NWBfCT//hFzh16hR+f+yY0+WkxA6dyEbcvdF/ampq0NHhjd9foAKdY+iUbty90X9CoRAuX76M69evO11KSoEKdHbolG5enOpG06upqQEAT3TpDHQiG3lxqhtNLxQav/7R3t7ucCWpBSrQBwcHGeiUVl6c6kbTiwa6Fzr0wM1y4Rg6pVN0NgtnufiHlzr0wAU6O3RKN+7e6C9FRUUoKSlhh+42DHTv4xxvckJNTQ07dLfhtEVvi87xjk4L9MJ2puQPoVDIEx16oC6KskP3Ns7xJqd4pUMPTKCrKgPd4zjHm5wSCoVw/vx5jIyMOF3KtCwFuohsFJFWEWkTkR3THHe7iIyKyOftK9EekUgEqspA9zDO8San1NTUQFVx/vx5p0uZVspAF5FsAD8CsAlAPYDHRaR+iuN+AGC/3UXaYXBwEAA4hu5hnONNTvHKXHQrHXojgDZVPa2qwwBeBLDF5Li/BfCvALpsrM82Tt4gmuwR3c40VFoAATyxnSn5Q3T5v9vH0a3McgkBOBv3uB3AHfEHiEgIwGcBbABwu23V2YiB7g+c401A5qeveqVDtxLoZndU1oTHzwD4hqqOTncDZhF5EsCTALB06VKrNdqCgU7kD05MXy0rK0N+fr7rO3QrQy7tAJbEPa4BcC7hmAYAL4rIxwA+D+A5ETESf5Cq7lbVBlVtqKiomGXJs8MxdCJ/cGL6qoh4Yi66lQ79IIBaEVkOoAPAYwC+GH+Aqi6Pfi0iPwXw76rabGOdc8YOncgfnJq+6oW56Ck7dFWNAHgK47NXTgB4SVWPi8hWEdma7gLtwkAn8genpq96oUO3NA9dVfeoap2qrlTV/znx3C5V3WVy7JdU9V/sLnSuGOhE/uDU9NXorehUEy8hukdgVopyDJ3IH5yavhoKhTA0NISLFy+m9X3mIjCbc7FDJ/IPJ6avxk9dLC8vz+h7WxWYDp2BTkRz4YXFRYEJ9OiQCwOdiGbDC4uLAhPo0Q6dY+hENBtVVVXIyspih+4GHHIhornIzc1FZWUlO3Q3YKAT0Vy5fXFRYAKd0xaJaK7cvrgoMIEe7dDz8vIcroSIvIoduksMDQ0hLy8P0+0GSUQ0nVAohL6+PvT39ztdiqlABTrHz4loLqJz0d067BKYQB8cHOT4ORHNidvnogcm0NmhE9FcuX21KAOdiMgiduguwUAnorkqLCzEggUL2KE7jWPoRGQHN89FD0ygs0MnIjtEb3ThRgx0IqIZCIVCHHJxGgOdiOwQCoVw4cIFjIyMOF1KksAEOsfQicgONTU1UFV0dnY6XUqSwAQ6O3QisoObpy4y0ImIZsDNi4sCE+iDg4MMdCKaM3boLjA0NMQxdCKas4ULF2LevHns0J3EIRcisoOIuHZxEQOdiGiG3Hqji0AEeiQSwejoKIdciMgW7NAdxBtEE5Gdosv/VdXpUiZhoBMRzVAoFMLw8DB6enqcLmUSBjoR0Qy5dS56IAJ9cHAQADiGTkS2cOtc9EAEOjt0IrKTpzt0EdkoIq0i0iYiO0xe/0sROTrx500RWWt/qbPHQCciO1VWViIrK8t7HbqIZAP4EYBNAOoBPC4i9QmHfQTgXlVdA+B7AHbbXehcMNCJyE45OTmorq72XqADaATQpqqnVXUYwIsAtsQfoKpvqurliYdvA6ixt8y54Rg6EdnNjTe6sBLoIQBn4x63Tzw3la8C2Gv2gog8KSKHRORQd3e39SrniB06EdnNjYuLrAS6mDxnOpteRO7HeKB/w+x1Vd2tqg2q2lBRUWG9yjlioBOR3dy4/N9KoLcDWBL3uAbAucSDRGQNgB8D2KKqF+0pzx4MdCKyWygUwpUrV3D16lWnS4mxEugHAdSKyHIRyQPwGICW+ANEZCmAlwH8tap+aH+Zc8MxdCKyW3TqopuGXVIGuqpGADwFYD+AEwBeUtXjIrJVRLZOHPYdAGUAnhORP4rIobRVPAvs0InIbm5cXJRj5SBV3QNgT8Jzu+K+/hsAf2NvafZhoPtD85EO7NzfinO9A1hcWoDtTWEY66a7Pk+UPm5cXGQp0L2Oge59zUc68M2Xj2FgZBQA0NE7gG++fAwAGOrkCDd26IFY+s8xdO/bub81FuZRAyOj2Lm/1aGKKOj2f3AJS77+U+zuW4O7nz6A5iPOBzs7dPKEc70DM3qeKJ2inxizissBuOcTYyA69KGhIeTk5CArKxCn60uLSwtm9DxROrn1E2MgEm5wcJDducdtbwqjIDd70nMFudnY3hR2qCIKMrd+YvR9oDcf6cDenDtRtu1F14xz0cwZ60L4/uduQai0AAIgVFqA73/uFl4QJUe49ROjr8fQYzMjsgohcM84F82OsS7E3xu5wqOr8vGPv72MrNxPJlq44ROjrzv0qca5vtfyHrq6ulx3g1cicj9Vxas//HsM//b/oHp+vqs+Mfq6Q59qPKvn+igqKytRWlqKcDiMuro6hMPh2Ne1tbUoKODFNiJK1tLSgtdffx3PPvsstm170OlyJhGnutSGhgY9dCi9OwTc/fQBdJiE+sJ84L8sbMOHH36I1tZWtLa2TlrtJSJYunRpUtCHw2EsWbKEs2WIAmp4eBg333wzcnNzcfToUeTkZL4nFpHDqtpg9pqvO/TtTeFJqwuB8XGu7xi3wFj38KRjr127hpMnT6K1tXVS0P/sZz+btJvavHnzUFtbGwv6+LAvLS3N2LkRUeZEt53o6L2OyIPfwl/dsciRME/F1x06MPf9P1QVFy5ciAV8fNifPn0ao6Of/GOxaNEi065+xYoVyMvLS8fpEVGaJW47AYw3hk6NmU/Xofs+0NNpZGQEp0+fNg37rq6u2HHZ2dlYsWKFadhXVVVBxOweIkTkpN7eXhw7dgzb9l3EldHcpNdDpQX4/Y4NGa8rsEMu6ZabmxsL6ES9vb2xgI8P+gMHDmBg4JNx/eLiYtOgr6urww033JDJ0yEKpNHRUZw6dQrvvfcejh49Gvvvn//8ZwDA0v/eArOey+lFRGbYoWfY2NgY2tvbTbv6M2fOTJpKGQqFTMfqly1bhuzs7GnehYjM9Pb2Tgrt9957D++//36sycrOzkY4HMaaNWuwdu1arFmzBv9wJAcXro4k/Sw3dugMdBcZGBhAW1tbUtC3trait7c3dlxeXh5uuummpKAPh8MoKytz8AyI3GF0dBRtbW1JXfeZM2dix5SVlcVCO/rf+vr6pF1ZOYZuAQPdOlVFT0+PaVd/6tQpjIx80j0sXLjQNOhvuukm7mdDvnT58uVJoX306NGkrnvVqlWTgnvt2rWorq62fP3KTTdXYaD7WCQSwccff2wa9p2dnbHjsrKysGzZMtOwD4VCvDBLrheJREy77rNnz8aOKS8vN+26/dTMMNAD6urVq5MCPv4i7bVr12LHFRYWTnlhdv78+Q6eAQXVpUuXksa6jx8/HrtZTU5OjmnXHYRZYwx0mkRVce7cOdOu/uOPP8bY2Fjs2KqqKtOufvny5a5cWEHuM91wRSQSwcmTJ5O67viV2xUVFUld9+rVq33Vdc8EA50sGxoawqlTp0zD/uLFi7HjcnJysHLlyqSgD4fDqKio8H2XRNaYXVDMwRjq+g6i6+CepK579erVSV13ZWUl/z7FYaCTLS5evGg6t/7kyZMYHh6OHVdSUjLlhdnCwkIHz4CsUlVcv34dV69eRX9/f+y/8V9bee3KvduBGxYm/fyx/h6s+vDnSV03V1SnxkCntBodHcWZM2dMu/r4j84AsHTpUtMdLpcuXcpNz+ZgaGgoZbjOJIyvXbtmeXvp3NxcFBcXo6ioCEVFRbGvi4uLcaTuqzBblSMAPnr64eQfRikx0Mkx8ZueJYb9VJueJYb9ggULHDwD+42OjsZC1Grwpgrj+Kmr0xER0+Cd6rnpXot+PV1XPdWOp04tyvEDBjq5zkw2PauoqDAN+pUrVyaFid3zhVUVAwMDtgXv1atXJ239kMq8efNsC96ioiIUFhZmdDzabYty/ICBTp4yPDyMjz76yNKmZ8uXL48FfWTxX2DfpTIMfzJJB3nZwBOrc/CpooFZhXF/f/+kWT/Tyc7ORnFxseVwTfXaDTfc4IuZRG5alOMHDHTyjfhNzxLn1pd96TnklCxK+p5IXxc6dn0l6floiM6m0zV7LT8/n7MxKO242yL5RmlpKRobG9HY2Djp+bGxMaz81l6YtSc5JYtw+PDhSSFcWFjIi7DkOwx08oWsrCwsLi2Y8gLcrbfe6kBVRJnFFoV8Y3tTGAW5k7cVLsjNxvam5P3qifyIHTr5RvRCGy/AUVBZCnQR2QjgnwBkA/ixqj6d8LpMvL4ZwHUAX1LVP9hcK1FKxroQA5wCK+WQi4hkA/gRgE0A6gE8LiL1CYdtAlA78edJAP9sc51ERJSClTH0RgBtqnpaVYcBvAhgS8IxWwA8r+PeBlAqItU210pERNOwEughAGfjHrdPPDfTY4iIKI2sBLrZSonE6b5WjoGIPCkih0TkUHd3t5X6iIjIIiuB3g5gSdzjGgDnZnEMVHW3qjaoakNFRcVMayUiomlYCfSDAGpFZLmI5AF4DEBLwjEtAJ6QcesB9KlqZ+IPIiKi9Ek5bVFVIyLyFID9GJ+2+BNVPS4iWyde3wVgD8anLLZhfNril9NXMhERmbE0D11V92A8tOOf2xX3tQLYZm9pREQ0E1z6T0TkEwx0IiKfYKATEfkEA52IyCcY6EREPuHYLehEpBvAnzP4luUAejL4fk7gOfpHEM6T5zg7y1TVdGWmY4GeaSJyaKr78PkFz9E/gnCePEf7cciFiMgnGOhERD4RpEDf7XQBGcBz9I8gnCfP0WaBGUMnIvK7IHXoRES+xkAnIvIJXwW6iGwUkVYRaRORHSavi4j8cOL1oyJyqxN1zpWF8/zLifM7KiJvishaJ+qci1TnGHfc7SIyKiKfz2R9drByjiJyn4j8UUSOi8ivM12jHSz8fS0RkX8TkfcmztNz22+LyE9EpEtE3p/i9cxkj6r64g/G92o/BWAFgDwA7wGoTzhmM4C9GL9l3noA7zhdd5rO8y4ACya+3uS187RyjnHHHcD41s6fd7ruNPweSwH8CcDSiceLnK47Tef5LQA/mPi6AsAlAHlO1z7D8/zPAG4F8P4Ur2cke7sCVVgAAAKISURBVPzUoTcCaFPV06o6DOBFAFsSjtkC4Hkd9zaAUhGpznShc5TyPFX1TVW9PPHwbYzfEtBLrPwuAeBvAfwrgK5MFmcTK+f4RQAvq+oZAFBVv56nAigWEQFQhPFAj2S2zLlR1d9gvO6pZCR7/BToIQBn4x63Tzw302Pcbqbn8FWMdwZekvIcRSQE4LMAdsGbrPwe6wAsEJE3ROSwiDyRsersY+U8nwWwGuP3IT4G4O9UdSwz5WVMRrLH0h2LPEJMnkuck2nlGLezfA4icj/GA/0/pbUi+1k5x2cAfENVR8cbO8+xco45AG4D8ACAAgBvicjbqvphuouzkZXzbALwRwAbAKwE8B8i8ltVvZLu4jIoI9njp0BvB7Ak7nENxv/Fn+kxbmfpHERkDYAfA9ikqhczVJtdrJxjA4AXJ8K8HMBmEYmoanNmSpwzq39fe1T1GoBrIvIbAGsBeCnQrZznlwE8reODzW0i8hGAVQDezUyJGZGR7PHTkMtBALUislxE8gA8BqAl4ZgWAE9MXHFeD6BPVTszXegcpTxPEVkK4GUAf+2xbi4q5Tmq6nJVvVFVbwTwLwC+7qEwB6z9fX0VwD0ikiMihQDuAHAiw3XOlZXzPIPxTyEQkUoAYQCnM1pl+mUke3zToatqRESeArAf41fWf6Kqx0Vk68TruzA+G2IzgDYA1zHeGXiKxfP8DoAyAM9NdLAR9dCudhbP0dOsnKOqnhCRfQCOAhgD8GNVNZ0W51YWf5ffA/BTETmG8aGJb6iqp7bVFZEXANwHoFxE2gF8F0AukNns4dJ/IiKf8NOQCxFRoDHQiYh8goFOROQTDHQiIp9goBMR+QQDnYjIJxjoREQ+8f8BGiz7Ol/Wu94AAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "convex_hull_plot_2d(hull)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Euler's formula" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of vertices : 47\n", "number of simplices : 90\n" ] } ], "source": [ "points = np.random.rand(320, 3)\n", "hull = ConvexHull(points)\n", "nv = hull.vertices.size\n", "ns = hull.simplices.shape[0]\n", "print('number of vertices :', nv)\n", "print('number of simplices :', ns)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of edges : 135\n", "nv - ne + ns : 2\n" ] } ], "source": [ "edges = []\n", "for simplex in hull.simplices:\n", " x, y, z = simplex\n", " edge = ((x, y) if x < y else (y, x))\n", " if edge not in edges: edges.append(edge)\n", " edge = ((y, z) if y < z else (z, y))\n", " if edge not in edges: edges.append(edge)\n", " edge = ((z, x) if z < x else (x, z))\n", " if edge not in edges: edges.append(edge)\n", "ne = len(edges)\n", "print('number of edges :', ne);\n", "print('nv - ne + ns :', nv - ne + ns)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. The Voronoi diagram of 10 random points" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Voronoi diagram of a collection of sites in the plane partitions the plane into regions of those points closest to each site in the collection." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "from scipy.spatial import Voronoi, voronoi_plot_2d" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "points = np.random.rand(10, 2)\n", "vor = Voronoi(points)\n", "voronoi_plot_2d(vor)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We examine the attributes." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "the input points :\n", "[[0.84631085 0.33320175]\n", " [0.64933072 0.57163221]\n", " [0.22988703 0.81085314]\n", " [0.40875177 0.90204868]\n", " [0.90863561 0.51495282]\n", " [0.5453243 0.12274075]\n", " [0.76918235 0.69627201]\n", " [0.08938106 0.44155196]\n", " [0.82477598 0.83088415]\n", " [0.17972343 0.54398563]]\n", "the vertices :\n", "[[ 0.3387185 0.31270238]\n", " [ 0.42457031 0.38721366]\n", " [ 0.61221662 0.83988339]\n", " [ 0.57070789 0.76717827]\n", " [ 0.95789182 0.69712257]\n", " [ 0.78324786 0.56280324]\n", " [ 0.76160938 0.46380848]\n", " [ 0.61538303 0.34300309]\n", " [ 0.4205712 0.65786252]\n", " [ 0.4097534 0.63889488]\n", " [-0.15054815 0.74421586]]\n", "the ridge vertices :\n", "[[2, 4], [2, 3], [3, 5], [4, 5], [-1, 4], [-1, 2], [6, 7], [-1, 6], [-1, 7], [5, 6], [-1, 0], [0, 1], [1, 7], [8, 9], [-1, 8], [9, 10], [-1, 10], [1, 9], [3, 8], [0, 10]]\n", "the ridge points :\n", "[[6 8]\n", " [6 3]\n", " [6 1]\n", " [6 4]\n", " [8 4]\n", " [8 3]\n", " [0 1]\n", " [0 4]\n", " [0 5]\n", " [4 1]\n", " [5 7]\n", " [5 9]\n", " [5 1]\n", " [2 1]\n", " [2 3]\n", " [2 9]\n", " [2 7]\n", " [1 9]\n", " [1 3]\n", " [9 7]]\n", "the cells :\n", "[5, 3, 2, 4]\n", "[4, -1, 2]\n", "[-1, 7, 6]\n", "[-1, 4, 5, 6]\n", "[-1, 0, 1, 7]\n", "[-1, 8, 9, 10]\n", "[9, 1, 7, 6, 5, 3, 8]\n", "[-1, 2, 3, 8]\n", "[10, 0, 1, 9]\n", "[-1, 0, 10]\n", "[]\n", "the point_region :\n", "[2 6 5 7 3 4 0 9 1 8]\n" ] } ], "source": [ "print('the input points :')\n", "print(vor.points)\n", "print('the vertices :')\n", "print(vor.vertices)\n", "print('the ridge vertices :')\n", "print(vor.ridge_vertices)\n", "print('the ridge points :')\n", "print(vor.ridge_points)\n", "print('the cells :')\n", "for region in vor.regions:\n", " print(region)\n", "print('the point_region :')\n", "print(vor.point_region)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. The Delaunay triangulation of 10 random points" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Delaunay triangulation of a collection of sites is that triangulation with the largest minimal angle." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "from scipy.spatial import Delaunay, delaunay_plot_2d" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "points = np.random.rand(10, 2)\n", "tri = Delaunay(points)\n", "delaunay_plot_2d(tri)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us examine the attributes of the output." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "the input points :\n", "[[0.87698739 0.84805488]\n", " [0.53915857 0.27569069]\n", " [0.17685099 0.30413549]\n", " [0.00997181 0.89511302]\n", " [0.63137869 0.2958332 ]\n", " [0.41374227 0.53718402]\n", " [0.34018901 0.63019428]\n", " [0.67870867 0.16566682]\n", " [0.13207262 0.23055754]\n", " [0.31157981 0.76133136]]\n" ] } ], "source": [ "print('the input points :')\n", "print(tri.points)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "indices of the simplices :\n", "[9 0 3]\n", "[9 5 0]\n", "[4 7 0]\n", "[5 4 0]\n", "[9 6 5]\n", "[6 9 3]\n", "[1 4 5]\n", "[1 8 7]\n", "[4 1 7]\n", "[2 1 5]\n", "[1 2 8]\n", "[6 2 5]\n", "[8 2 3]\n", "[2 6 3]\n" ] } ], "source": [ "print('indices of the simplices :')\n", "for simplex in tri.simplices:\n", " print(simplex)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "indices to neighbor simplices :\n", "[-1 5 1]\n", "[3 0 4]\n", "[-1 3 8]\n", "[2 1 6]\n", "[11 1 5]\n", "[ 0 13 4]\n", "[3 9 8]\n", "[-1 8 10]\n", "[7 2 6]\n", "[ 6 11 10]\n", "[12 7 9]\n", "[ 9 4 13]\n", "[13 -1 10]\n", "[ 5 12 11]\n" ] } ], "source": [ "print('indices to neighbor simplices :')\n", "for neighbor in tri.neighbors:\n", " print(neighbor)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "the equations :\n", "[ 0.25875396 0.83431934 -0.48678294 -0.55252134]\n", "[ 0.45430834 0.57264054 -0.68241244 -0.34860262]\n", "[ 0.75276044 0.26876911 -0.60092835 -0.41657768]\n", "[ 0.55219289 0.45565691 -0.6981832 -0.32286317]\n", "[ 0.44953761 0.57230487 -0.68584479 -0.34570919]\n", "[ 0.07025055 0.57765543 -0.81325216 -0.18886488]\n", "[ 0.48049853 0.38558731 -0.78768242 -0.23628366]\n", "[ 0.37991771 -0.08083421 -0.92148161 -0.03153979]\n", "[ 0.54401703 0.19109002 -0.81702514 -0.21210048]\n", "[ 0.35052734 0.33998766 -0.872662 -0.13971087]\n", "[ 0.3543507 0.15331789 -0.92245824 -0.08214862]\n", "[ 0.22954091 0.45372234 -0.86107317 -0.15324611]\n", "[-0.22384722 0.47633474 -0.85029268 -0.08025848]\n", "[ 0.02781816 0.54115997 -0.84045942 -0.1447708 ]\n" ] } ], "source": [ "print('the equations :')\n", "for equation in tri.equations:\n", " print(equation)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5. duality" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dual of a Voronoi diagram is a Delaunay triangulation." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "points = np.random.rand(10, 2)\n", "vor = Voronoi(points)\n", "tri = Delaunay(points)\n", "fig, axs = plt.subplots()\n", "voronoi_plot_2d(vor, ax=axs)\n", "delaunay_plot_2d(tri, ax=axs)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 6. Lake Superior" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The code below is copied from pages 188-189 of the Mastering SciPy book of\n", "Francisco J. Blanco-Silva, Packt Publishing 2015." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "def read_poly(file_name):\n", " \"\"\"\n", " Simple poly-file reader, that creates a python dictionary\n", " with information about vertices, edges and holes.\n", " It assumes that vertices have no attributes or boundary markers.\n", " It assumes that edges have no boundary markers.\n", " No regional attributes or area constraints are parsed.\n", " \"\"\"\n", " from numpy import array\n", " output = {'vertices': None, 'holes': None, 'segments': None}\n", " # open file and store lines in a list\n", " file = open(file_name, 'r')\n", " lines = file.readlines()\n", " file.close()\n", " lines = [x.strip('\\n').split() for x in lines]\n", " # Store vertices\n", " vertices= []\n", " N_vertices,dimension,attr,bdry_markers = [int(x) for x in lines[0]]\n", " # We assume attr = bdrt_markers = 0\n", " for k in range(N_vertices):\n", " label,x,y = [items for items in lines[k+1]]\n", " vertices.append([float(x), float(y)])\n", " output['vertices'] = array(vertices)\n", " # Store segments\n", " segments = []\n", " N_segments,bdry_markers = [int(x) for x in lines[N_vertices+1]]\n", " for k in range(N_segments):\n", " label,pointer_1,pointer_2 = [items for items in lines[N_vertices+k+2]]\n", " segments.append([int(pointer_1)-1, int(pointer_2)-1])\n", " output['segments'] = array(segments)\n", " # Store holes\n", " N_holes = int(lines[N_segments+N_vertices+2][0])\n", " holes = []\n", " for k in range(N_holes):\n", " label,x,y = [items for items in lines[N_segments + N_vertices + 3 + k]]\n", " holes.append([float(x), float(y)])\n", " output['holes'] = array(holes)\n", " return output" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Following the Mastering Scipy book of Francisco J. Blanco-Silva, \n", "Packt Publishing 2015, this script plots the convex hull of the\n", "Lake Superior polygon, available for download at\n", "``https://github.com/blancosilva/Mastering-Scipy/blob/master/chapter6/superior.poly``" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This polygon has 7 holes (for the islands),\n", "518 vertices, and 518 edges.\n", "The .poly format comes from the Triangle software, available at\n", "``http://www.cs.cmu.edu/~quake/triangle.html``" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "the number of vertices : 1036\n" ] } ], "source": [ "lake_superior = read_poly('superior.poly')\n", "points = lake_superior['vertices']\n", "print('the number of vertices : ', end='')\n", "print(points.size)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "hull = ConvexHull(points)\n", "# convex_hull_plot_2d(hull)\n", "plt.plot(points[:,0], points[:,1], 'b.')\n", "for simplex in hull.simplices:\n", " plt.plot(points[simplex, 0], points[simplex, 1], 'r-')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us compute the Delaunay triangulation." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "tri = Delaunay(points)\n", "# convex_hull_plot_2d(hull)\n", "plt.triplot(points[:,0], points[:,1], tri.simplices, 'k-')\n", "plt.plot(points[:,0], points[:,1], 'r.')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the triangle software, a constrained triangulation is computed." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "from triangle import triangulate\n", "from triangle import plot as tplot" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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u3bvrHKtevbresrt376bevXtTXl4e1a5dW3Du0qVLBtuIi4uj9PR0atCggcEy9gSv/61Tpw799ddfFBcXVyrtWovMzExq164drVu3jmbOnEktW7Y0Wn716tWl1LP/NkQGLMIkUlNTDZ7r3Lmzyet564SgoCB27OLFi4IyHMcRx3EkkUho27Zt1LdvX4NMujhmzJhBW7duJU9PT7PK24rc3Fw6cOAAEREVFRVRQUFBudb/nj17lpo0aULHjh2jDz/8kHbv3k1r166liIgIg9cUFRWVYg//uxAZsAijMLUhs3//fvrrr7+MluEZsFQqpREjRugtA4A6duxIarWaevToQT/++CP179/fZP9++uknevvtt41K4PbG4cOHGYPKyckhuVxOsbGxpda+JdizZw/FxMRQTk4OLViwgBYuXEinTp2i1atXU3BwcFl37z8PkQGLMApjS1GO48jNzY26dOlCN2/eNFiOZ8BZWVk0cuRIg+UCAwOpRo0atGfPHiIiunXrlsGyEomELly4QC+99JKpIdgdvPqBSCMNN23alJydnUu9H6awcuVK6tSpE1WuXJmGDRtGkyZNImdnZ1q6dCnNmzePdu7cWdZd/M9DZMAijMLYUhQAOTg4UGZmJnXu3JmePHmit5w2A46IiKDo6GjB+R49ehAR0SeffEIXLlygp0+fmuwXx3FmqyjsDd4BQ6FQ0P3798ud+qGoqIjeeOMNSk5OptatW1N4eDjNnz+f4uLiaODAgczhZc+ePUadU0RztFKAvp05Q1QRdnpF2A+WBmCPi4tDXl6eTj3e3t6sTHZ2Nouba07qdGNUFsjOzmYZNni33v3795dJX/QhKyuLxb7o3bs3oqOjmVVDQkICiDRJO/fu3YvatWuL5milBBLN0ESYC1uSbg4ZMkQQc+H58+cgIgQHB4NIE6Ph6dOnUKlUqFSpktXMt6wCx2jnl6P/t0/W99EpC9y4cQMNGjSAVCrFwIED4e/vD2dnZ7z11luoWrUqZDIZFi9ejIULF0IulyMwMBA7d+4UzdFKASIDFmEWLHGcMESzZs1i9V25cgVEGmcFIsLZs2cBAHXq1LGpjbJiDJMmTRL0Iz4+vkz6URxHjx6Fv78/VCoVevToAblcjtDQUIwcORJyuRyVKlXChg0bWJzmXr164dChQyydUnmc638TRAYswijsnWr+s88+A/DCY+z1118HEaFnz552qf/JkydlMk9RUVGCfrz77rtl0g9tbNq0CUqlEgEBASy7c0xMDOLi4kBE6NKlCz7++GO4ubnBxcUFa9aswbvvvguFQgEPDw9WTmTCJQeRAYswCHsm26xSpQr7vXv3bqxfvx5EhJYtW9qtDSKCp6dnqc/To0ePWOZlno4ePVrq/eChVquxYMECNu/VqlUDEaFjx44ICQmBVCrF1KlTWfjOZs2a4ccff2R64e7du+PixYt48803Tc63qA+2DSIDFqEXJZHpmE9NxL+49qxbO7vDn3/+WapzxQd/58nd3d2oC3ZJIi8vj8XGqFKlCtzd3eHs7Iy4uDg4ODggKCgICxYsQOXKlSGVSjF9+nTMmjULcrkc3t7eWL9+Pb7//numm69Vq5YoBZcgRAYsQgB7qxxKmvgd/ClTpgiO2zvIujGMGzdO0Hb37t1LrW1t3L9/H61atQIRISAgADKZDL6+vqhbty6INNYow4cPB8dxCA0NRWpqKho2bAgiQr9+/XD48GF07NgRRIT69evjt99+A2Dex1hkwtZBZMAiAFQ8xkuksXhQq9WIjo7WCcizatWqUpu7+vXrC9peunRpqbXN4/z586hevTqINBHoeCbs7e0NiUSCwYMHM2Y7aNAgvP7665BKpfD398f69esxe/ZsODo6wtXVFR988AEKCgoE9ZvDhMPDw0t93BUdIgMWYVd1g0KhKDUGzEtdGzduBNGLlEQ8ZWdnl/jcZWZm6vTrzJkzJd6uNvbt2wcPDw9BH7y9vSGXyxEQEIB+/fpBqVTCy8sLU6ZMYRYtQ4YMwbfffstS0/fr1w+3b9822I6l98UaJCcnsxCnUqkU4eHhgv983cXLFW/T1PnyApEB/8dhKfM1R0o2Fh7SnsRbPBQWFqJGjRo6kmi/fv1KfP6+//57QZt+fn6lqv745JNPmANI8Y9g/fr12cZay5YtkZiYCIlEguDgYKxevRq9e/cGkcbxZc+ePSbbioyMtPgDaYgR6mO05q7Awl1c9B4fMWIE8vPzMWLECLt/GEoKIgP+D8Metr1lSS1btmRj4b3oGjduLChz7ty5Ep3DlJQUQXv9+/cv0fZ4FBUV6dge8ySRSNC4cWN4eXnB0dERffr0YR/FoUOHYubMmXBxcYFCocDcuXPx/Plzs9r84osv7HLfwv/fKqO0qTxmdxYZ8H8Q9tb38sG8S4NcXFywaNEi9v/w4cMANJ51gYGBTA/Kk6enZ4lKpMWtBNauXVtibfF4+vQpevTooXd+XF1dmSt3WFgY2rZtC47jEBISgtmzZ6NevXog0tgAX7lyxaJ2Dx06VCaM055U3iAy4P8QKuJGmzb16tULRIT58+cLjufn5wMA3nvvPRBpzMC0z2/cuLFE5vOff/4BEcHBwYG1ZSlTsxS3b99Go0aN9M6Pm5sb3NzcwHEcIiMjERgYCCKNKubll18GEaFy5crYvHmzVR+l+/fvl/kzYAuJErCIMkFFZ7y8TSqRxmnA3d0dkydPZsfmzp0LQBNwxt3dHY6Ojjp1PH361O7zum7dOsb4iAhVq1a1exvaOH78uCDfnTbJ5XJwHAeVSsVWAaGhoUhMTISHhwdkMhneeustm+ehrJ8FW0jUAYsoNWhvclQk0t6o0WayvKNFcHAwJBIJRo4cKbjuwoULAIBp06bprXfSpEl2n+Phw4fD1dWVMfxhw4bZvQ0eP/74IzMvM0S8S7FEIkHbtm2ZuqF169Z2s8ywh5WLPfYeIiIiLL6mPEJkwP8yVFRpV59La3Z2NjuvbWZVu3ZtODg4IDExkR2LjY2FWq3G3bt3DTIJnknbC9WqVUNISAirf926dXatH9C4FfOqFWPEW0IEBQWhcePGkEgk8PX1xVdffWVXHbi2N6MpKp50lf+4nj9/XqdsrVq1BFYRrq6ugvOenp44ePAg+5+QkIBr164xSw5TVB6lX0BkwP8aVFTGq0368Morr7DzvL0qz3D4SGo8ffrppwCA0aNH662fZ9L2wLVr19jHgK8/IyPDLnXzMGZSVZykUimqVq0KDw8PcByH0aNH49GjR3btDwBMnz7drP74+PhgwIABgmPXr18HAKaPlsvlCAoKws2bN3XaycrKgqenp+D6kJAQzJs3j/2fM2cOAGDXrl1WPVvlASIDruCwB+ONjIzEqFGj0LdvX8THxzPX1dIkQxsk169f11uel/iaNWvGjsnlcty9exdXrlwxqH753//+Z5d5/+yzz9jcEdnfC+zhw4dmRSMjIjg6OrKNx+joaKSnp9u1L9rYsGGD1ff4p59+wtGjR9l/V1dXnDhxwmBbN27cgFwuF9QRERGBBg0asP9btmwBYFw3XZ499EQGXIFgb72uOcuyoqIiPHr0CFeuXEF6ejr27NmDb775Rif2gq3Upk0bg33o0KEDK6dUKgXXVa1aVfB/wIABAGDQNM7BwQHPnj2z+V4MHjwY3t7eLMrbmDFjbK6Tx6VLl8wKgqNN7u7uSE1NLfEgQH/++afV97hx48YsVgURYdeuXSbbS09P16lHe1NWpVLh3LlzRt+L8mj9wENkwBUA9lYvDBo0yG79sicTPn/+vN52fvvtN6PXFXfD3bFjB06ePGmw/IwZM2wat1qtRnBwsEAfai/JOi0tTUf/aYqGDBmCu3fv2qV9U9DWy9tCvLrIHBSPNlecatWqZfKDVV4hMuByDHsyXldXV/z999+Qy+V49dVX7dpHS/ohkUjQoUMH1KpVC9WqVcOqVasE57OysnTaUKvVbEffHAoJCcHTp0/RuXNng2UuXbpk9ZgvXrwIImI51ogIDx8+tGUaAQBffvmlRXNZp06dUs87Z6+PrqWbYh988IHR+oy9J6IELMIi2Fvi5R/eefPmYezYsZBKpXZ30TX3xeRDN/Iqgjlz5gjOR0VF6d0o++abbywa84QJE5CWlmbwfJcuXaweK//R4DeTateubcvUoaioyKD5nD5ydnbG4sWLmQNKacGeKx5LmaJarWabq8WtXEzlECyvFhCAyIDLDeyt3y2+g9yjRw8olUqkp6fDxcUFvXv3tvsYateuzbIvaNMvv/wi+N+0aVOoVCo0adIECoUC77//vuD8/PnzderOz88XBF03RRKJBMeOHWOpeHjivcOINJtC1qBfv34ICAhA06ZNQWSbjXFOTg769Olj9rh69eqFGzduWN2eLSgJu/LZs2cjPT0dRUVFJtsvKChAp06dIJVK0aRJE7PbKM8QGXAZw57SLp8W57vvvtMxARo0aBAUCgVefvllzJo1C0SEI0eO2HUsjRo1QpcuXXS8tQYMGCDQlzZr1gzOzs6oWbMmlEolunfvrjOW3bt369TPp9kxlyIiIvDDDz8Ijnl7e8Pb2xtEmowROTk5Fo1RrVbDz88P/fr1Y3Xu3LnTqvnKyMhgMXpNUbVq1bB9+3ar2rEVN2/eZMGOSpISExPx9ddf4969ewb7kpWVhfr168PV1VXnGddH5Vn6BUQGXGawJ+OVy+Xo06cP8vLyoFAo8MYbb+hlVqNGjQIRYfPmzfD29kZcXJxdx9SiRQu0adNGIGXyxOeA44nPBccvH/m+adPVq1cF9d+/f1+vm7ExWrRokY7nlbZ51+zZsy0a45kzZ0D0IpkokXVuzidPntQJI2no3s6aNcviD4UtePbsGXbs2IFx48aVWMS80NBQ9OvXT++KiYjQqFEjTJs2DQcOHNAJDn/jxg0EBASgcuXKApM0fVTeITLgUoS91Ay+vr5wd3eHp6cns//kl9OxsbFo0qQJtm7dCiLCmjVr2HW8sX54eDjzrtInaVqLDh06oEmTJggICNDpc/Xq1XU8o4KDgyGTySCRSFC9enWd68LDw3UYT3EXZGMkkUjg5OQk0DM7OjqiRo0aAldWSwLoLFu2DESEt956C0QalYal2LZtm1n9j4+Pt7v3nj6o1WqcPHkSixcvRvv27dlHztHREa1bt0bv3r2RmJhoUtdqLVWqVEnH3leb3Nzc0KtXL6xevZo5c6Snp8PJycloveV5842HyIBLAfaSdmvXrg03NzcEBgYyfahMJoOXlxfy8vIAAJMmTYJcLse5c+dAREhNTRXYzvLLtoULF6JKlSpo1KiRWfo3c9CjRw/Uq1cPfn5+en31586dq5dJ8r+L62uJNKoT7U25s2fPmj1fKpUKSqUScXFxbA78/f1BpLHb5cslJCSYPcaePXuiSpUqTG0ya9Ysi+Zo6dKlJvsdGBiI77//vkTDaGZmZuLbb7/FK6+8IlixhIaGIjo6GrGxsWjevLmAyYWHh5dJDGm5XC7Y0wgPD8cbb7xh0mGovKsfAJEBlyjswXilUimqVKmCOnXqIDIykkkh2i9GSkoKa/N///sfiAgHDhyASqVCSkqKjk0svwnGx9XdsGGDXcY7cOBAhIaGwtfXl2XmLU580kd95OTkxPSz2lQ8x5qxOooTr2PlN8x4BhcdHS0wI9u2bZvJ8RUVFcHT01MwtrS0NLPmpqCgAK+++qrJ/k6YMEGvKZ6tyM/PR1paGqZNm4aoqCj2XCqVSvj4+KBSpUoICwsTWBjUr18fY8aMwcaNGwV2xrZYQwwZMgQzZ8606tpWrVph0KBBaN++vSAEqCGqCBAZcAnAXhLvyZMnAQA1a9ZE586dIZPJdGLdEhEOHTrE2r5z5w6ICIsXL0ZMTAxatGgBAMxji0gjScvlcgwaNAh169ZF9erV7WLS9Oqrr8Lf3x8+Pj56dbpEhL59+xods6GIX9qMbufOnWbNH8dxCAgIQP369QUfLF7S5tUJRBrJLzc31+j4eC+wjz76iF3HrzyM4fHjxzrpkopT8+bN2f22Fy5fvowVK1agW7duep07HBwcmEpMIpEgMjISb7zxBjZv3owHDx4Yrdsc/bU2dejQQaeOmzdvYvHixVa9G7Nnz41DoycAACAASURBVDZ6viJIv4DIgO0Oe9hK8g/X5cuXkZ+fD5lMhtatW7MXRbtstWrVdJaq1apVQ48ePTBy5Ei4u7tDrVbj+PHjguv4XGFTp04FEWHlypU2j/3111+HSqWCt7c3kpOTDQbFadKkCZRKpUU6RT8/P9y6dQuARmdZu3ZtNhfFTe544o8PHDhQwDAcHR3h7++Pdu3aCYLdvPPOO0bHt2TJEhC90Ks7ODiYnJOrV6+aHNtnn31mFzVQVlYWfvrpJ4wePdpkXj6pVIrGjRtj4sSJ2Lp1Kx4/fmxRW3w9+ixYeEpKSkJ+fj68vLwwcOBAo/VdvnwZ8+fPNxjv2FKqKBAZsB1hLfPlpWV+Y4zfYc/IyGC6XEPxT2fOnKnTj8TERPj7++Pjjz8GEbFoU8X1dx4eHoiMjESzZs0QEBBgc4yEKVOmMJ10SkoKvvvuO719rlOnDogIL730kkXz1LRpU5a/jHeGCAoKgkKhYLrd4lS9enW4ubnpRBXjQ1lu2bKFSd1KpRLXrl0zOL6uXbuievXqrC5TLs2mUviMGDHCpKRpDEVFRTh27Bjmz5+PVq1aGd3IksvliImJwZQpU7Bz506b1Bz5+fms3sOHD7Pf2uEiiTTqBgBISkqCSqUyO/fcmTNnMHPmTJuSu4oS8H8M1jDfTp06gYhYYkfeG2rw4MEg0rjl8n7whsx19MVPWL58OYiIJVHk7UePHDkiuJbffOHbW7BggU1z8M4774BI4/Y8evRo3Lhxw+DYfX194erqKtgMM4dGjhwJQGMq5enpibp160IqlaJFixasjHawlsjISHAch+TkZMEL3apVK7i5uaF3796C5WyPHj30jq2goACurq4CKwxjUcc+//xzg2OoXLkyy2VnKTIyMvDFF19gwIAB8PHxMdiGo6MjWrZsiRkzZuDnn3+2SwAiHtrxfLWjm+3du1enH2q1mll9bN261aJ2+JXbpEmTULlyZYueE33xpcsjRAZsB1jKfHnG+9VXX4GImFE/Xw8vGRYWFrKNMi8vL516GjdurLc/vLqBl4Dfffdddq54anEnJyd4enoiJiYGbm5uNklk/BJdIpFgzJgxUKvVBueAVx+8+eabZjkjaKsQ+MSXU6dOBcdxaNeuHeRyucHlcIcOHeDg4IBPP/1UcPz1118Hx3E4duyYQILesWOHztj++OMPEJHAJVpf5DG1Wm3UVG7p0qU6dq3G8Pz5c/z888+YOHGiUZtXpVKJtm3bYs6cOfj1119N6rNtwZYtW1i72lL+jh07dPqVlpaG58+fw83NDUOHDrW6TbVajUOHDmHs2LEGVzvFqSJIwSIDthGWmOXwS+8NGzZAIpFg+vTp8PDwYOEWeZfU2NhYODo6AgCGDRtm0HZ42bJlevtUUFAAZ2dnvPbaawgKChJEPzMUWaxFixbgOM4mt9rU1FRW39ixYwFozLaMzYmLiwt++eUXk5s62isABwcH/PHHH7h16xZkMhlefvllODo6sqSdREJni06dOkGhUGDQoEGCAO/jx4+HQqHAsGHDsHr1anY8LCxMZ7m8cOFCEAndqosjNzfXoF67c+fO+Oeff0zOoVqtxt9//42PPvrIaDAhJycnxMfHY968eTh48KBZm4H2Av+hJdLYkfO/tb0O+RUAbyedmJgIT09Pu2z2FhYWYu/evYJg+BWVCYsM2AaYK/mOGDECvr6+6NChA1QqFZKSkhAVFYVWrVohJiaGbYi1a9eOMWpPT08AGscKfXVKpVKjLptt2rRBZGQkOnbsiIYNGwrONW7cWKc+iUSCevXqQaFQ6M1QYA54lQeRRroEYNYu9+TJk3WC8hQnZ2dngaQcHByMu3fvYsCAAXB1dcWrr74KjuMEHoC+vr7s98iRI8FxnE5cipSUFMjlcly/fp19IIk0gYu0ER8fjzp16rBNy+Lxf+/du2ew77/88ovReXv06BE2btxo1ExNIpGgc+fOePfdd/H777+XeiAebWhL+LzZI5FwdZCbm8t+P3r0iJWzp+MPALOYcHlmxCIDthLmMl/tBJMSiQStWrWCp6cnxowZA0dHRwwaNAg+Pj5QqVQs3XhQUBCCg4MBwKCez1Q0r2nTprEcXI6OjoJl76+//qq3zqCgIMjlcgwfPtyqOfn+++9ZXePGjQMAHDhwwOQcOTk54fbt2yYTLbZr1w5eXl6QSCSQSqVo3bo12wSaPn06XF1d0aNHD6YD5j9oRIT+/fuz1QafzZiI8OWXX0IqlWLChAkCDzWlUsm8rvLy8uDk5CTQV58+fZqN21CQ8ilTpuiVTAsLC3H48GHMnj3baIChhIQELFmyBOnp6SUeaN0StGnThvWRV6MRET755BP2Oycnh93PRYsWIScnB87OzkyHb0+Y8x6WV0YsMmALYYmNL8dxLOzjpUuXQPTCMYA30eKX6J6eniy7g5OTE2rWrImHDx8arPvbb7812k/eFTkpKQlEhLNnzwrOazsmaBPP4P7++2+L50abgb3xxhsANJtl5szVm2++iRMnTkAul+uN98AHXZ8wYQKIiCXDfOONN9C8eXNUrVqVGfhv2rSJXTdkyBD2m/fE+/nnn/X2YejQoYKgQb169QLw4iOivcTmTf+0mY428y4ex+LGjRtYs2aNUXvghIQEfPTRR/jrr7/s5p1YEtA2FVu5ciX7rW1XnZGRIdiUU6vV6NOnD3x9fe3+MbFmA7y8MGKRAVsAS250XFwc3NzcEB8fz17W+Ph4eHl5QaFQsGyu/O49x3Fwc3Nj10dGRgpMfLTJ2dnZ5K72/fv3QfRCr1zc223Pnj166+b1zTzzsQT79u1j9YwfP54d5yV7Y+To6IiMjAxmSVE81RCRJpJZREQEBg0aBIlEgqioKMFH7Msvv4SPjw/i4uLYB07bRtga5xiJRILo6GhwHMc+okQa/S9vm61N/Ifx2bNn2L59O+Lj440+I8uXL8fp06dL1O3YnuAzYvCrDG19sLb659y5cygqKmL/Dx8+zPLJlUQQ+f79+1dIJiwyYDNhCfOVy+UICAjAjBkzQPQiXQ0vmSmVSvj6+qJWrVoGdVixsbEGTZl4+0pTqFmzJtq3bw+pVIrp06cLzqnVapMxVS0NV8lbChBpJFUehhwyitO4ceOQn5+PyMhIeHh46Jge8R+rRYsWoUqVKqhcuTIiIiKYW2rLli1Z8HlzveUsId6DTp83X6NGjXDo0CEMGjTI4PUNGjTAqlWrcO7cuQrDcIuDV7fw90Jbd6+dMfn3338H8EJfnJCQgOzsbCgUCrvmz+PBh1itaExYZMAmYI1b8Ztvvgm5XI6EhATUrVsXISEhyMnJQX5+vsCEpk6dOnBxcdGJ8E+kMZ0ylPhyz549ZvX9lVdegbe3N2rWrIlu3brpnN++fbvRcbRt29YiRnHq1Cl27cSJE9nxr7/+2uy5u337Nk6ePAm5XC6w7eWpSZMm8PLywubNm8FxHBISEgTBZA4dOmTQnbm0iXeGuXTpUoVluMXBS7G87fikSZPYePlsJ0QvEm5q68cfP36M7t27IygoyO4qFn6vJCEhoUIxYUMMWEIiKCUlhVJTUzVfJDMQFxdHLVu2pI8//pi6d+9OP/30EzVq1IiuXbtGixYtIrlcTsOGDWPl7927R0+fPqW8vDydupydnen8+fM6x729valNmzZm9ScmJobu379PSqWSTp06pXO+Y8eOFBUVZfD6vXv30p49e8xqi4jIycmJ/eY4jv1u2rSp2XUsXLiQ6tWrR7NmzaIDBw7Qa6+9Jjhfp04devToEe3Zs4cmTpxIP/30E73yyivsfExMDD179szs9uwJjuNo/vz5dO3aNQJAGRkZNHr0aAoNDRXMR0XGhQsXiIgoJCSEiIiePn3KzmnP+5MnT4iIqEGDBuzYunXrqFevXnT79m06cuSIXfuVmZlJRERff/01de/e3aJrV69ebde+2AX6uLIh+jdKwNa6FX/yySeoUqUK/P39UbNmTbi4uCA6OhoKhQJXr17FtWvXzJKoExMTBWZRPGkv7U2Bl0h5D7Ds7GydMps3bzbaj8jISLOllYyMDHbd5MmT2XG1Wq03ypk2aUe3unnzJgoKCtCoUSN4e3vjtddeE5QdNmwYJBIJjhw5ggYNGsDX11evaV1p0Lhx45i1xH8BgwYNQqVKlZiuXlv3qv17zZo17Jp58+aBiODu7o5Hjx5BLpdb9Bybwt27d1m7AAQ23eYSbzFU2iBRAtYFL/maA7lcTjVr1qSEhAQiIho2bBilpKRQdnY2ZWdnU2FhId29e5cA0Pjx46lKlSrUsWNHk/UqFAo6d+6czvHExESzxxEeHk4qlYpJKWfOnNEpk5CQIJBSiuP48eP0/fffm9WeIQmY4ziTUrCDgwP7PX/+fJLJZPTFF19QVlYWZWRkUGBgIDuvVCrJw8ODJkyYQF999RVlZmbaXaIyFx988AFVrly5TNouC1y4cIFq1KhBBQUFRET04MEDdk5bAn78+DH7PWDAAHbs/Pnz1L59e9q0aZPZK0tTOHjwIBER+fr6EhFR586dLa6jqKiIUlNTKSUlxS59shn6uLIh+rdJwGTmV9PX1xdpaWlQKBRo2LChwFuL33jiJTs+HOKuXbtYfAdjpM+ttnLlyhbrEuPj45lOlHfhLQ5t+119FBYWZpbhv3aQlilTpgjO6QvGXpy0TbR4qXL+/PkgIh2p5sMPP7RZepVKpTaHDS1Lh4jShlqthru7O5KTkzF16lTIZDKBc4y292HxTV/+3g4dOpSZ7h07dswu/eJXq9penKZSFRmi0o4hQaIE/AIpKSkkkZg3dB8fH3rw4AFFRETQ999/T6dOnSInJyd2/fLly6ldu3aUn59PREQ5OTlERDR27Fhq3749BQUFGa3/1q1bevtnqS6xWbNmTDLRpwcmIurZsyeFh4cbrOPSpUv0ySefmGxLLpeTXC4nItLppyEJ2MXFhYiIpFIp3blzh1xdXYmIaOrUqURENHHiRIqOjqYpU6bQli1b2HXvvfeeyf4Uh1QqpeTkZPaQFxYW2iyFOTg40N9//21THRUFDx48oMePHzMJWCaT0d27d9l5bX0wrwPmMWrUKCIi+uyzz6h169YklUpp48aNdukXr8Nt1KgRO9a5c2er9O4AyocUrI8rG6J/gwRsrs63Vq1agv+8RQK/068dC8DR0VEQmYunxYsXmzSb0echZU068l27drHr27Zta7CcthupPvL39zcr+SRvyzxt2jTB8SdPnuiVNl1dXVkMYSISxHPgnRnOnDkDBwcH9OzZ02CmDUPER0LTB0v0/NrBkKRSKUaOHCkIcm8qlvC/AXwckW3btmHcuHFwdXUVxKfWThE0ePBgwbWZmZns3IoVKxAXF4caNWrYbB3C2yUTCZ2N+NCY2lK5uVSaueRINEMz/0WUSCTMgYJ/ubVjwvKZErSD5+gLMuPi4iKwmTWHatasadXYHj9+zBifj4+PwXKFhYWoUaOG0T7Mnz/fZHt8Yk19sXLr1aun86ATEerVqweO41CtWjV4eXmhWbNmICKWzQN4EQzHEjK2qWLuPecZuPaHgTexAoQ53lQqFZ48eWJyjioqPvvsMxARLl68iNdee415J/LEeycSkV6zRz4FVP369bFixQoQEU6dOmVTn7QdirTd7QsKCuDh4aFjsx0cHKyT1EAflRYMMeD/jArCkg23hIQEOnToEPsPgA4cOMD+jx07lmbOnElFRUXsWGFhoU49T58+paVLl9JLL71kdj8nTpxodlltuLm5UZ06dYhIY6qjvWTUhlQqpWnTphmt6+2336aHDx8aLcNvxOlb/hVXQ3AcRy4uLqRUKkkul5OXlxc9ePCAmcYdOHCArly5QkREV69eNdpucSQnJ9OKFSv0njPnnvP9f/fdd2nFihXM/IqIKC0tjf0eM2YMO5eVlUVubm6CZ+LfhAsXLpBMJqOQkBAqKChg6iYe2ioI7U04HgMHDiQiopMnT1JwcDBxHEebNm2yqU/8XIeFhZFMJmPHZTIZdejQgX799Vd6++232fFbt26VT7Oz4tDHlQ1RRZaAyQKJio9WpW1SpVAoBKEL1Wq1jtmUIeJTm5tDjx49snqM2lG2jDlxFBQUGAz8zpO2g4U+8MtQfdmC+c0XbZfrkJAQSKVSdOrUCUqlErGxsXBzc2MeVHxUOEvibxhTOZhbD79ptGTJEgAQxKeIiYnRqTs3N1ewiZicnFyuAujYA7169WIrsaSkJMF9JCJB9u3iEfgAYVyQYcOGoUWLFqhbt65NfeIDA+nzDv3yyy9BJAyZSUQs/KsxKi3Qf1UCtmTDTSqVkq+vL50/f54UCgU9f/6cnXv+/DkdO3aM/ec4jj766CPq37+/oA5tMyseW7du1ZEi9KFu3brk7u5uVl/1ISYmhv02tBFHpJEa+M0vbWj3cfHixXo3CHkolUoiMi4Bq1QqIiJydHQklUpFRUVF5OPjQ7m5uRQYGEhPnjwhDw8PIiJ6+PAhcRxn1mZZcnIyqdVqvZJvnTp1zHaqSU5OptatWxMRsWdE21lGexXEQ6FQ0IkTJ2j58uVERJSamkoymYxu3Lhhsr2KAt4EjUizstOWeImIcnNz2e/im3BEmtXRoEGDiIjo888/p/j4eDp9+rRgdWEJCgoKaN++fUREVK9ePZ3zHTt2JI7j6PDhwzRu3Dh2fNeuXUbrlUqlVvXHnvhXM2BzPdzc3NyISGMjGBYWRmlpaVStWjWdB097SUqkeWm/+OIL6tSpEzvm5+dHnp6egnKnT58mb29vk/2dO3euyTLG0KxZM/bbGAMmIho0aJCOXWvxB3L27NkGrzfGgGvVqkUqlYoxYDc3N7p8+TJFRETQH3/8QR06dKC0tDTq1q0bffzxx9SiRQujfdWGKZXD2bNnLapHrVYTEQnUSeYgJSVFYG9dpUoV2rBhg0V1lEeo1Wq6ePEiY8AFBQVG50YfAyZ6oYYoKipigoy1aojjx4+z3/oYsI+PDzVu3Ji2b98uYMCmMGLECKv6Y1foE4sNUUVSQZi7+dK8eXMddYNMJtNZdhFpsh3ow7Nnz1g9fDmVSmWR2oPIvNTnxqBWq1lUsKioKJPltTNb8BQaGir4byhcJb+8e/vtt/Web9++PcLDw+Hi4sLq5FMw8YFdtOMLmCJjKgfAMksH7Xr4PH3z5s3DkydPdMqaSvmTnZ0tCHbUrVs3vZ6IFQXXr18HEWHVqlUAINiM1kdSqVSvhUNBQQELlN+wYUM0adIEkZGRVvWJT2JLpAl/qQ9z5swBx3G4d+8eBg4caNZzUJqg/4oKglc5mLvh5uPjQ5GRkQJPn8LCQr1f9oMHD+qVBpycnGjr1q1Uv359IiLavn27xTaGDRs21Ku+sAQcxzEp+MyZMyaluqFDh+rYKd+8eZOqVq3K/k+ePFnvtcYkYCKNNH7u3Dlq3Lgx5eXlkZeXF0kkEnJ2dqbr16+Tp6cnLVq0yOyxGVI5WHq/pVIpLVu2jP3nN0+fP39Ot2/f1il/6dIlo/W5uLjQ4cOH6aOPPiIioh9//JFcXV0pPT3drP6UN/BqAm0VhDEUFRXpjckhk8moX79+RET0119/UUhICB0/ftziTVaiFxtw3t7e5Ofnp7dMly5dCADt3LmT2eQbQ3JyssX9KAn8qxiwpUF1KlWqRJs3b6bw8HCzrsnKyjK4tHd3d6edO3dScHAwEWmCzaxdu9bsvmszBVvAM+Dc3FyTD7ujoyNjsM7OzkRElJ+fz/SyREQ//fSTXvdfngEb0q83bdqU1Go1eXp60q1bt6hOnTq0b98+6t69O3355ZcmrSy0YehlsfR+BwcHU1FRkUB1wOsz8/Ly9Oq89QVKKg6O42js2LF09OhRdiw6OpoWLlzIVBwVBcUZMO+KbAyG1BDa7vT3798nIqIffvjBov6o1Wrmgly/fn2DH/yIiAjy8/Oj7du3m9WGITVWaeNfw4AtMTPjcfPmTfLz86MffviBateubdY1xfXA2ggICKD9+/ez/6NGjRJ4dRlD8+bNzSpnCuZuxPEYPnw4+fn5kZOTE3u4jx8/Tt26dWNlkpKSdJicKQm4cePGRPRiI06lUlFWVhb9/fffJqUqHhzHGdX5mnu/FQoFEb34yPz+++/sHO+5+Pz5c6sZMI+oqCh68OABu5dTpkyhpk2b6pWsyysuXLhAzs7OFBAQQES2MeCoqCiqXr06EWnmPCwszGKvuPPnz7PVqT79Lw+JREKdOnWiXbt2mVz5lRfpl+hfwoAtZb7t2rVjG053796lnJwcozv+2jBl+1mtWjU6efIkEWmWb7NnzzYZ6jEsLMxuYQyjo6PZb3MYsFKppIkTJ1JmZiYLp6hQKOjs2bPMIuPMmTO0e/duneuIDDNgLy8vqlGjBt2/f59CQkKoqKiIOI4TbKgYgzFLByKySMXj7+9PRJqXWalU6mXAtkjA2vD09KS0tDRasGABEREdPXqUgoOD6X//+59F9ZQVeAsI/r4a+1jyHzRDDJjjOLYZ9+zZM8rLy6Pff//d7HeNSPi+GWPARBq35EePHhktY+yDXibQpxg2ROVxE86SzRepVMoCOdsS1tAct0rttPBjxozBjh07DNZ38uRJu84JnySxd+/eZpV/+vQpvL29ER4eDkdHR+YePXz4cEE/tcNVvvnmmyDSpKcxhMGDB8PPz8/sjLY8mRMu0Ny6fHx8IJfLBcdq167N6uHTDQ0ZMgQjRozQud7ajSNANynqyJEjTaaYKmuEhoaib9++7L++YPk88UkHtm/fbrC+ixcvsvJ8sKilS5ea3R/tzCOmMrc8fvxY4J2qj8oK9G/bhLN086Vdu3ZUt25d2rlzJ1WqVImOHDnCvuCW4uLFiybLxMTE0I4dO4hIo999+PChQTMlS1UnpsDrgf/66y+zyjs7O9OECRPo7Nmz1LhxY8rMzKSQkBBav369IAj6+vXr2W9eAtYXZJ5H06ZN6e7du2YHsTGlcuBhjvQbGRlJUqmUMjMzdZbRf//9N/PgMiUBHz9+3OpAPq1ataKMjAymFlq1ahXVqVPH7PtS2sjPz6erV68y/S+RcRUEr14yJAETaVZ3vDqK36yzxByNl4A5jmOenobg5uZGsbGxZtddHlAhGbAlmy/Vq1cnFxcXqlq1Ku3bt48aNWpEN2/eJCKyOqOCuS6oHTt2pM8//5yINHaRtffto67/vxzWxlo7xyflGfClS5cERvPGMHr0aPL09CS1Wk2urq6kVCopPz9fwGAHDhzIXkieARurnzeeNwemVA48zFU3jRgxgrp27WrwPL9hxvffkA6Y6EUWBmvg7+9P+/fvZ44v165do4iICPrggw/K3QbdlStXSK1WCxiwMRUEH9HOGAMmemETzCMtLc2gq7w2bt26RdeuXSMiDSPXjkNtCMYEgnIJfWKxISovKggyc/lZu3ZtyOVyxMbGwsvLC/n5+cjOzrYqcpI2de3a1aL+Tp069YUaxIh6xF64fPkyq9eSWKxvv/02iF5kWOZtm7UD0cybNw8AWFLMsWPH6q0rPDzcrioHwDJ109q1a7F161aD53n7Zd5GuVOnToLMytpkr+y+xfsTHx9v0K61LMDHr/7jjz/YMWPxdnn1zbvvvmu03jt37uioBlauXGmyP99++y0r37NnT7PGYMwFvTSjnxUH/RtUEJa4FRNpduIB0LVr1+jBgwe0b98+cnFxoa1bt7LMFtrQp5Iw5FpsCebNm8fM0wztz1rqiWUM2na85mzE8RgzZgypVCrKzs6mwMBAysrKosDAQPriiy8oLi6OiIimTZtGz549YxKwtrs2D0s80sLDw83eFLFEVSOVSqlDhw4G4zHzG3G8CuLhw4cGTeMs3YgzhC5dutDVq1dZEKLdu3dT7dq1adu2bXap31YUN0EjMq6CUCgUJJVKTUrAfn5+1K5dO8Exc9QQBw4cYJvlpjbgiDTPHYysisuF51sxVBgGbInaoVatWkRE9MUXX1C9evXY0pLXwSoUCtq4cSNLocKjoKBAxxyNN6MpDkt2comIMjIyTJZZuHChXRgxx3Fs+W0JA3Z3d6fXX3+dduzYQS+//DKdOnWKmjdvTseOHROYpfXv35+ZdulTQZgThYrX9+pLn6QPlqpoZDIZyWQySkpKEhzn3a8PHTpEAFj/L1++bLAuezFgIk2Sy4MHD9Lo0aOJSBNNrGvXrjRmzBiz1UUlhQsXLpCvr68gHokxFQQAcnNz0xsRrTiKqyH27t0rcH7Sh4MHDzI9M+/kZAymnrtyZf3AQ59YbIjKSgVhydKT4zgWOYlIGLnJw8ND4O5bWFios/Pdtm1buLi4CI7VrFlTp53Vq1eb7LdarUZ6ejqzGDCXDhw4YPOcvfvuuyAiREREWHTdgwcP4OLigt69e6NWrVqoWbMmmjZtCm9vb6xdu5b1kY/zyltaJCcnm9yB5smapIiWzB8R4ZtvvgEAXL16Vef+8r8vXLggSBJqiCxVOZmLb7/9VhBHum7dujbHzbUFrVq1QmxsrOBY1apVDS7n27dvj2rVqmHgwIEm687KyhK8i0SETz/91GD5R48egeM4Fnv4woULJtsoiefOXqCKGJDdkrCCRJq8bC1btgSRxvxIX5niJjNqtVqHQRYPCt6zZ0+dery9vQ32+/Tp05g+fTrLUmwNJSQk4ObNm1bPXVpaGqvLUrz11lvgOA4LFixgDy7HcXj99dd1+lm5cmWLxmXNS2BN5urvvvuOXR8fH8+ODx48mP3+/PPP9TIWd3d3wbHq1atb3GdzcfbsWYG+3MHBAcuWLbM5g4Q18Pf3R1JSkuCYvkwvRJoMJ3FxcYiIiDD7A9WvXz9IpVL2oe7SpYvBsry+vEGDBnBycjIr5Kelef+0y5d0tuQKxYAtZbxEGim1Vq1aLCmmIdIXT1StVrMNKJ62bNliVrv8jbt48SLmzp3L4uRKJBLExcUJArUYIycnJ51A/IpXZAAAFE1JREFUOESaFDg5OTkWz2FOTg6r4/79+xZde+/ePTg5OSExMRExMTEICAjAoEGDIJVKsX//fqs/KuHh4RaPA7Bc+iUibNq0iV2vnYy0YcOGjCEPGTJE5zpvb28WK5lfCUmlUpsDJRnD06dPkZiYKOhH165dce/evRJrszj4QEQLFy4UHC++GuTJz88Pbdq0QevWrQUZTYyBf6e0A189fvxYb9m33noLcrkczZo1Q3R0tMm6tRPF2kolwYgrBAO2hvESaYJ5h4aG4sqVKywCE08qlUon75p2YHVtLFmyxOabFxsbi4RKleBh4TgCAwMhkUj0PvBBQUHYtGmTxVIRf/2vv/5q8b2YMGECJBIJkxLHjx8PDw8PtG3bVu+HwhyyBtZIvzzxH8e8vDzB8eKZl7WfIy8vL0RFRYFImPfPUFQ4e0GtVmPVqlUClYi/v78gLVJJIj09HUSEH374QXDc0NxWrVoVrVu3Rrdu3VC/fn2z2sjPz4eXl5cgx97XX3+tt2zz5s2Z6qu4VF4ceXl5elep5YkRl3sGbMuLxuuWzpw5g99//x0KhUJw/pVXXhH837Jli8F+2JIGfcaMGejQoQM4K6/Xlgz0Udu2bS3SEfKhBN9//32L70dGRgYUCgWSkpKQkJAAlUrFwkhaywytgb1epHHjxrH/f/31l+A8nwWjfv36UCqVLNSmtgnW5s2breq/pTh27JiO3nX8+PEGhQZ7gU/Wevr0acHx4veQ/123bl20bNkSQ4YMQeXKlc1uJzk5GQqFgqmuevTooVMmNzcXDg4OzAvuww8/NFjf8+fPWZjTkiJ7MGIqzwzYFuarTbxb7KZNmwTHIyIiBG61CQkJJd6XkiKO4zBmzBg8fPjQ5LyuX78eRARr79uYMWMgk8mwbdu2MnmI7XUvpFIpzp07x/7v3LlTcJ53qe3YsSOICP379wfRCztXItO2rvbEw4cPmcs8Tw0bNhRkA7Y3Zs+eDY7jdOIf8+07OjrC1dWV/W/SpAliY2MxduxYuLm5md0On8U4Ojqa1VU8fjK/f8Gn/Prll1/01pWTk2NW2iF7kK1MmMojA7ZW5aCdt6tFixasjmbNmrG6i6sTijMRfYG2S4v58kGsW7VqBT8/P8ycOdPiOry8vJCammp0c+LGjRusvDW4efOmVfeH6MUGhy2bG/aec339IyIWq4LXw44ePRpEws1XU8tge0OtVmPRokWCfiuVSqxatapENugGDBiAkJAQneN82+7u7gJVXps2bRATE4MZM2aA4zhBnBBjUKvVCAkJEcRi0d4wBYB58+aBiJgDkz5d+NOnTwUWLdpkTjZka54fW0DliQFby3j1UUREhCAl9Z07dwBobjSf7YBIs5zUTm2tzRwKCwuNBsuxN/EM6dChQyDSeJd99913Zl1b3GyqQYMGRj21+HLWvLSWfpBMZa0oybbtQbzExX8Qhw0bxs41b97cLuOyFGlpaQgICBD0s0ePHhZvrJpCVFQU4uPjdY7zbQYEBAjS0cfHx6Np06YsW8WTJ0/Mbmvq1KmQSCRo3749iHStITp16oTw8HAMGTIE/v7+OtdnZWUhNjZW7z2sVq2awLKJDwBkD7IFVF4YsDUvFr9ENERHjx5lv9euXcvaKigoMOpKaQ3Z+uHgOE4wHy+99BLc3Nzw8OFDgemYIQoICBBEF+P133369MH169f13XgQEa5evVqi98neO8f2vGeW0kcffQQiTWZo/pgxs8OSxp07d3SkvaCgIINLc0uhVquhUqnw2muvCY4XFhay9kJDQwXPXceOHdG4cWOsWbMGRKT32TOEM2fOgIgEghNv6VNYWAiVSoWRI0ciIiIC7du3F1z76NEjNGzY0OC927VrF2bNmiU41rlzZyQlJbHVBP8OW/ou2wIqDwzYWqlG21hdH6WnpzOdWZs2bQRtFg+paC1pMxhrxyHVw6hOnDgBjuPw1ltvAdDYhRqyvdSmpKQkODg4wNXVFVFRUVAoFFAqlZgzZ47AbK1Xr14gepHjyxRGjRpl09zYA+VFDz9nzhxIpVIWzvLBgwd2HaclKCwsxPTp01nfJBIJOI7D5MmTbTaRu3PnDoh0w0Tm5uay9urWrYtGjRoJmFpUVBQz8bM0pGrDhg0FemB+k5PfIP3888/h6OiICRMmsGsePHiAoKAgwT3i9fVEGhVkcRv+mTNn6qhHrOUJtoDKmgHb+6XSvhGrVq3CkSNH2H/tmKv2UHXoYzDW1qUPAwYMgFKpxD///AMA+Oeff1hMX2P0/vvvo169eiAidOjQAZ06dQIRoUqVKvj++++hVquxa9cuEBnfiLtz547Ae9BcsqfKQRvmetSVFvF7DocOHbL7WC3F9u3b4enpCalUKkjAao6nmCHwK6+dO3cKjmdnZ7M5qF27tmDZ37VrV0RGRmL37t0gstx7c/HixSAi9sGvV68eAGDZsmWsL0QaRgxobNOL35dFixahfv36gj7xv52dnQ1arljzfFV4HbC9XiovLy8QCXeo+QkqqRdQG7bqr/Xh0qVLkMlkGD16NDuWlZUl8OAiIr02wu+88w4mT54MjuNQrVo1zJ0712BUL17nPXLkSJs2KkqK8fIoqftoKxVfXZUVrl+/zjaxKleuDBcXFzg7O+PTTz+1StfPu5hfuXJFcPzhw4ds7KGhoYLnMSEhAQ0bNsQff/wBIsLWrVstavPWrVs63pV5eXno06cPKlWqhA0bNoBIE80vIyND516kpqZi2rRpeu9TWFgYzp07J2gvKysLO3fuNHiNKarwVhDmDJJnrsVJm/EMGDCgVF86e6getOn48eN652fUqFGQy+WClyA/P19gwyyRSODr66tj9xgeHo5u3bqV+nyUFOzZX21rjPDwcJs/1CX98TEXeXl5GDNmDIg0DiO8c0yfPn3w6NEji+qaNGkSHBwcdCxq7t69y8YdHByM7t27s//du3dH/fr1mXnfunXrLB5D27ZtERYWxgSGjRs3IjAwEP3798f06dMhkUhw6dIlnXtgTHjo0qULsrKycO/ePfzwww8YN24cGjVqxK6x9P7by0WZypoBmxp4cnIyJk2axP4HBAQIdn+1U5OUBhV/0eypQvnwww91JJVbt25BoVBg0KBBguNqtZrtyvv7+yMwMBAcx2HEiBECj6LSoNJiPCWlNtKGrfezPDBhAPjuu+/g4uICDw8PtG7dGjKZDJUrV0ZaWprZdXTv3l2vm/jt27fZeH19fQX61p49e6Ju3bpMOl2+fLnFff/kk09ApBt7Rdu01BJydXXFsGHD4OHhYbCMOfsrJXGPqawZsDkPvLbxefXq1UucmWh/FIzZrZbEplCXLl107BsnTpwIjuP0erutWbMGUqkUNWrUYMbnLVq0QKtWrUp0nvi5KU2GY497ay6svbccx+HgwYMWS5slgXPnzqFu3brgOA6dOnVC1apVIZFIMGPGDBQUFJi8Pjw8HN27d9c5fu3aNTZeNzc3gVler169EB4ezjbq5s+fb3G/Hz9+DEdHR4wdO7bEn2EHBwfUrVsXPXr0MPsae4LKmgED9pFs7EGWMhNbl61Dhw5FjRo1dI4HBATg559/Zu3cv38fKpVK78sAANu2bYOTkxNCQkIQGRlZ4vNUVsvt0ry3PCwJp2noBR8xYgRWrVqFgwcPmuWpaE88e/aMBRdq2rQpOnfuDCKNZUBx3a42CgsL4eDggEmTJumc006oqVAomMqDiPDyyy+jVq1aAAAHBwdMnjzZqn4bCndZHuhfJQEDZW9eZC1DsaVNb29vtGjRwmAUMY7jMGXKFOTn5wN4kRbo999/19uXo0eP6sS6sDeVdGg+UyjrF8bc59RQyFOe+Ih4Y8aMQWpqKvbv3293BwptqNVqrF27Fo6OjggKCsKYMWPg5uYGV1dXg0Fvrly5AiKh/TyPv//+mz3DEolEoCLs27cvatasCQDw8fHBqFGjLOprSfACjuPw+++/448//sC+ffuwbds2fPfdd/j888+xYsUKLF682KJ4JvZMYUTlgQEDJceEOY7T2WSxhzssYJsE3K9fP2bEXzzkoDY1adIEV65cQVZWFnx8fNC2bVuD/SmJlURZM11tmNNf7XtdUn039awGBgYiIyMDDx48wJYtWzBp0iSzdIy+vr5o3bo1Ro8ejeXLl2Pfvn12DT35559/IjQ0FDKZDGPHjmW5/RITE3U81nhzL3064xMnToDohTpQ28Ghf//+LE5yWFgY+vfvb1bfSloIq1SpEn744Qej1iCWvM/2ApUXBgzY9yaUxjLZkgSTxYl31czMzMQ///wjCGjCU+3ateHm5gaVSoVvv/2WRWTTVk9YOnf69NglzbDsBXOYb2nB1MsaEBCgw7yeP3+O3377DYsWLUJCQoJBs8Di5O3tjZYtW2LUqFFYtmwZfvnlF2RkZFhlWvb48WOm70xISMD48eMhkUhQtWpVHD58mJXjE67yLvza+PXXX1m/zOm/vudKrVbj0qVLNifCNed5P3jwILOL79KlCy5fvqx3bsx9h4p7rdqCcsWAAduluNJiIrbGo+WDAB08eBDAi2zC2sFIiDS7ys2aNQORxtTO09MTjRs3hlqttlg/WZ6ZqzkwNtbSHpup+69SqSCVSvHee+8ZZJRqtRrnzp3D2rVrMXToUL0bzI6OjvD390etWrXg5uYmOOfp6YnY2FiMGDECH330Efbs2YPbt2+bZMxqtRpLliyBTCZDaGgoli9fjipVqkAqleKdd97BqFGjdFaJturCiQhtatdG4/8Pal8apP1MFBQU4P3334eLiwsUCgXeeecdvaE8zX2v7YVyx4CtYWylLbnZKqkrFAqWIn7NmjUANA9IvXr1UKlSJRZti1+2JiUlYerUqTZFIKvozBcwPO9lNTZTqc75+9ijRw+DGR6K4+7du/jhhx8wYcIENG3alLk7E2lWRF27dsWgQYMwduxYjBgxArGxsTrmVe7u7oiJicHw4cPx/vvvY9euXbh586YOYz548CCCgoLg6OiIJUuW2JQqqzRI33NsrLy+D9HNmzfx8ssvg0iTLaf4alKtVv+3GTCguywuDb2eJbDXwySRSAQ+7bzrJ//yOTk5CbIvWEv/JpQnlYmpDzEvaUqlUoSFheHEiRMWt5GTk4P9+/dj3rx56Ny5s0AK9vPzQ69evfD+++9jy5Yt2LVrF5YtW4bk5GS0bNlSx4FJpVKhadOmSEpKwnvvvYcdO3YgPT0d7dq1K3Pmainj5WHsOj8/P3Tu3BkzZ87Ejz/+iFu3bjGmvGPHDuak0r9/f+bun5SUZLI//8pNuIoCe28WODs7C+pPTEyEg4MD0tLS7BIyr6w/Vv92GJOCo6OjkZ+fjwMHDiAgIABKpZLFMLAWRUVFOHXqFFJTU5GYmCgw13JyckLr1q0xffp07NixA48fP8a9e/fw66+/Yvny5Rg9ejTatGmjk57r/9q7e5fWuTgO4L9zI3aTIlwnQbxjBQdf/gA3wdH5Dl5oaQK6u7jqLkRwEEQctB3Ef0FFBHWrm2B9qWDXbKb5PcOlz9P2SdKT5uUk7fcDWWptTvPybXrOL6dJzbGhCcH8+zfznz/M5TJrfb7RyXxz8/v/mZmZ/+2fzlA+OzvjYrHI4+PjPDEx4TmVZZznFAI4oDgO1s4D7fPzs+trJ8I33WQ+kI+Pj7nRaPw7sVGxWHSd+H9QHx8ffH5+zltbW7y4uNg1veL8/DwbhsGnp6ddU0M2m82uW4iTWGRvZArSZZZk++PoyvMKYPH3b3KWlpb4/v5e+vlZJoRQ3QQpuq6TaZqqmzESZI+JSqVCDw8PtLe3RwsLC1StVml2djby9liWRXd3d3Rzc0PX19d0e3tLlmUREdH09DTlcjl6fn6OfL29hBDEzKRpGpVKJdfj0TAMOjw8pFar5fs8v3V4qVQq5DgOfX19UbPZ7Frq9Tq9vLwEej9BMlGWEOKBmZdcVya74Ao4PYvqftFRFOSYKBQKvLm5yfl8nvP5vO8PwUbl+/ubHx8feX9/f+Bfru5doqqlD8uvjVNTU1ytVn3/37Zt1ykte5e43iOhCyKYILWC7Z0WZ5G56hMABtu/nRMmbW9vS83NEJTjOPz6+spHR0e+vxbh92GRlgFPL37tb9+Wv76+7lrPLPs6MU+xigAOqt8J57XDwty4gdBNt7D16ysrK31Dwo/jOPz+/s4XFxe8sbER+hjLyvHl9x4sy+Ld3V3O5XI8OTnJJycnrqVp9Xq97wdRjO1HAA9i0JrUQa+Gs3JCjCrZ/dqvrPDq6kqq1K7RaPDl5SXv7OzwrwhvbshazXi/99Lehu1fbl5bW+O3t7fU3MSEAA4hTE2q7AGQtRNilMmG8KBTqi4vL/Pq6mpkYTsMx1mSMynGsX0QwCngFsboZsgm1TP7pSVYkpL1beUVwChDAxjQ3NwcPT09qW6GlKyXK46NjVGr1UpsfZqmkW3bkb2eVxnaj8jWADBiarVa6uvFhRCZD18iolKplOj6kgp7BDBACOVy2fXxNASzruvkOE7mw5eIyDRN0nWdNE0jor9XqIVCIbb1tdcTNwQwQAhuwaDrumcwJ2UYrnp7maZJtm0TM5Nt21Sr1bq2fZQSu+J26xj2WjAIByDPrXrG7bGo6sbbS5IT1qeJzA/tygyexrH9CINwAOllGAYdHBxE8lpBzulR1DkvBZHcXBZheQ3CjUW+JgAIrH3Shw1hXdejaM5QM00zNd0z6AMGSIne/mSi/wbz+g06DUu1w6hBAAOkSOdAEzOT4zhdg07M7DroNyzVDqMGfcAAADHDjRgAACmDAAYAUAQBDACgCAIYAEARBDAAgCIIYAAARRDAAACKIIABABQJdCOGEKJJRPX4mgMAMJRmmPln74OBAhgAAKKDLggAAEUQwAAAiiCAAQAUQQADACiCAAYAUAQBDACgCAIYAEARBDAAgCIIYAAARf4BOQqSVmOvsacAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cndt = triangulate(lake_superior, 'p')\n", "ax = plt.subplot(111)\n", "tplot(ax, **cndt)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the next triangulation we require that all angles are at least 20 degrees." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cncfq20dt = triangulate(lake_superior, 'pq20D')\n", "ax = plt.subplot(111)\n", "tplot(ax, **cncfq20dt)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A constrained conforming Delaunay triangulation (cfdt) is computed\n", "with the flag p to indicate that the source is a planar straight\n", "line graph and the flag D to enforce Steiner points.\n", "We furthermore require that all triangles have a minimum angle\n", "of at least 20 degrees and impose a maximum area on triangles." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cncfq20adt = triangulate(lake_superior, 'pq20a.001D')\n", "ax = plt.subplot(111)\n", "tplot(ax, **cncfq20adt)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false } }, "nbformat": 4, "nbformat_minor": 2 }