{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Region Simplification\n", "\n", "These methods can be used to simplify regions as a preprocessing step before they are fed to labeled region scanning methods. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import shapefile\n", "import pyscan\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "def plot_points(ax, pts, c):\n", " xs = []\n", " ys = []\n", " for pt in pts:\n", " xs.append(pt[0] )\n", " ys.append(pt[1])\n", " ax.scatter(xs, ys, color=c)\n", "\n", "def plot_points_traj(ax, pts, c):\n", " xs = []\n", " ys = []\n", " for pt in pts:\n", " xs.append(pt[0])\n", " ys.append(pt[1])\n", " ax.plot(xs, ys, color=c)\n", " \n", "def plot_approx(ax, traj_pts, core_set_pts):\n", "# ax.set_xlim([-.01, 1.01])\n", "# ax.set_ylim([-.01, 1.01])\n", " plot_points_traj(ax, traj_pts, \"g\")\n", " plot_points(ax, core_set_pts, \"b\")\n", " ax.set_axis_off()\n", "\n", "shape = shapefile.Reader(\"county_shapes/cb_2017_us_county_500k.shp\")\n", "#first feature of the shapefile\n", "\n", "#feature = shape.shapeRecords()[0]\n", "pts1 = shape.shapes()[0].points\n", "pts = [pyscan.Point(p[0], p[1], 1.0) for p in pts1]\n", "\n", "alpha = .02\n", "r_min = .05\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Halfplane Compression\n", "These methods provide guarantees on regions with respect to halfplanes.\n", "\n", "### Convex Hull\n", "This method takes the convex hull of the trajectory. Since points internal to the convex hull will not effect halfplane labeled scanning we can do this as a preprocessing step to speed up the scanning without effecting the spatial error." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f, ax = plt.subplots(figsize=(16, 12))\n", "core_set_pts = pyscan.hull(pts)\n", "plot_approx(ax, pts, core_set_pts)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Directional Hull\n", "\n", "This method uses an approximation of the convex hull to simplify the region even more. The spatial error is bounded by alpha. In practice this method can reduce the number of points needed significantly over just taking the convex hull, and therefore speed up halplane labeled scanning even more than the previous method.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f, ax = plt.subplots(figsize=(16, 12))\n", "core_set_pts = pyscan.halfplane_kernel(pts, alpha)\n", "plot_approx(ax, pts, core_set_pts)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### DP Simplification\n", "This is the popular Douglas Peucker simplification algorithm. It has the same error guarantees as the Directional Hull method, but usually produces a larger number of points per region." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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a2ArYDNiEZnfmKTTd5rnt+5cWyKgx5mRVktRFTlYlrZOscjlwBEDU8SHgprKJOmNqe702q5y7ujdFHSPvW9TzROo5J6uSpC5ysippLPwc2LV0iI4YWf67phI6Ulbv7GEWjRMnq5KkLnKyKmksnA+8K+p4EvAQ4M6s8oTCmYbVaCem00b5Pg0AJ6uSpC5ysippLJxP8/3094FjgC9GHY8tmmh4jbasDvUy4AgOimBuBMvb60GlM/WSk1VJUhc5WZU0Fn4EvAr4B/BH4IfA56OOk4Cf8d5FW7B8ygdozma9Cjg8k5OLpR1sQ19Wo44AJtL8AOTu1zk/fS7r/9vHiFyP27YAYhYwJwKG9f9XllVJUhdNB5YBnsEnaZ21my3NGXkedbwWOBL4IADPO2AZXztpIos3gOa4m3ErFm3xmbDCY+Xno32tl79ubb72A9vf2miXAb9/hX8GKxa/1ZfBsf3cunytuMff2SE7/+vjH74Tzn8/NH+fHQmWVUmShsUMYGFWmaWDSBoeWeUpwClRx3343vv+xB7v2YRDHgvX7gQTlsKEJdOZcvucqM85iOb78MkrXGfSHMeie3btGj7/B2ABcAjNDyWX0Zy9uuJ1Va/d0+dGPl48Bl9j3d9/1qc+wfS/B3u8B+7YZMXf88zR/IMbRJH+PS1J6pio43PAvlnlFqWzSBpOESzngecFT38DTF4IyyfD8kmwbDLc/9eX0JwDuqS9LqU5r/UqmmIyFpav8MiVnq/qtUF4z+1Z5fVj9M9n4EQwl0ecNIv9XwSf+yX8bceRT83LZHbBaD3jZFWS1EUz8H5VSb11FX958iw+89uVX5+XyaNLBNLAO5wHnncCd2w8ieseOfLaQuDwgpl6yt2AJUldNB13ApbUW4dz9x+KDXWxUG9lcjIP/N4fuG2rxeTEBOYBhwzr5kpgWZUkdZOTVUk91RaIQ2gKRSeKhcbBRlefwWa/nch7YqNMZg/7/59cBixJ6iInq5J6ri0SQ10mNO5+T7N78APaj4eak1VJUhc5WZUkDaKRc8JvLZpinFhWJUld5GRVkjSINmivtxVNMU4sq5KkLnKyKkkaRBu21wVFU4wTy6okqYucrEqSBtGWwPyscqzO4+1rllVJUhc5WZUkDZSoI4C9gQtKZxkvllVJUqdEHROBqVhWJUmD5VHAVsCZpYOMF8uqJKlrlgNLgWmlg0iStBaeTfN32Fmlg4wXy6okqVOyygRuADYvnUWSpLWwL/CTrPLG0kHGi2VVktRF12NZlSQNiKhjJrADHVoCDJZVSVI3XYdlVZI0OPZtr2cUTTHOLKuSpC66Hrh/6RCSJI3SvsAfs8orSgcZT5ZVSVIXXQ9s1h4DIElS34o61gN2B75dOMq4s6xKkrroemAysEnpIJIkrcESYAFw39JBxptlVZLURde3V+9blST1taxyKXAu8PSoo1P9rVO/WUmSWpZVSdIgOZtmr4VdSgcZT5ZVSVIXXddeLauSpEHwbZoftJ4cdWxROsx4saxKkrrIyaokaWBklTcBzwQ2Bc6KOjYoHGlcWFYlSV10E7AMj6+RJA2IrPKXwHOB7YHToo7JhSP1nGVVktQ5WeVy4AacrEqSBkhWeQ7wKuBpwGsLx+k5y6okqauux7IqSRowWeUXgMuBZ5fO0muWVUlSV1lWJUmD6hxgt6hjaukgvWRZlSR1lWVVkjSorgAmAUO9M7BlVZLUVdcBm0cdUTqIJElraeQIti2Lpugxy6okqauuB6YAG5UOIknSWnoskMC80kF6ybIqSeqqkbNWPb5GkjQw2hVBLwQuyCr/r3SeXrKsSpK6an57dbIqSRokjwO2AU4qHaTXLKuSpK5a0l4nFU0hSdLaeT1wC3Bq6SC9ZlmVJHXVSFmdXDSFJEmjFHU8ADgA+HxWuaB0nl6zrEqSusqyKkkaNI8HJgInlw4yHiyrkqSuWtpeXQYsSRoUt7XXTvzdZVmVJHWVk1VJ0qAZ2Rxw46IpxollVZLUVU5WJUmDZqSs3rdoinFiWZUkdZWTVUnSoJkH/B34YNQxu2yU3rOsSpK6yrIqSRooWeXtwNOADYFLo46Doo4oHKtnLKuSpK5yGbAkaeBklZcAOwG/B04Cvhp1bFo2VW9YViVJXeVkVZI0kLLKPwFPAN4B7AdcHnU8s2yqsWdZlSR1lZNVSdLAyiqXZZVH0UxZbwS+HXV8NuoYmh/CWlYlSV3lZFWSNPCyyl/RFNaPAK8Bzow6ZpRNNTb8abIkaa1FHf8GfB3YCJh4D48A3pFVfrZQ1HsyMlm1rEqSBlpWuQh4a9SxCHgn8Ezg1LKp7j3LqiRpXTwQeAzwA+AaYNlqHi8GHg/0Y1kdmaz6d6EkaSBFHesDWwMz28c+wN+As0rmGiv+BS1JWhc3t9dPZZWnr+5NUcfjgE3GJ9JacxmwJGlgtauc/gBMX+HlO4GXtkfcDDzLqiRpXcxvrxuv4X03079l1Q2WJEmD7AU0RfXlNMfYzAOuzyqXF001hvwLWpK0LkYmq2sqovOBB/Q4yzrJKjPqWIaTVUnSYDoIuDirPL50kF5xN2BJ0rpYQHNP6iBPVqGZrlpWJUkDJerYDngkcHLpLL1kWZUkrbWsMmmmpqMpq2t6TxERHMTiGVO46I1vjWBuBAeVziRJ0ig9vL3+tGiKHrOsSpLW1XzWPDW9GZgadaw3DnlGrS2mc1g2JZiwBGAWMMfCKkkaEBe3112Kpugx71mVpD4WdUwEpgFT2+vIYxLNMtzl9/baTknXxWimpiP3tm4bdfyDZsntpPax4sdrer42713zr33RU59OTlyPKbfBhJF9lpgOHMmQL6mSJA2+rHJe1PEXYA/gf0vn6RXLqiQVEHVsCRxLM5lcVRkded7zP6ejjmTdyu6WwCVr+PJ/b6+XjXnwu0ua42iWrvBYssqPZ9ywHssnw7U7wZ/2XvFrzByHnJIkjYULgP2jjolZ5bLSYXrBsipJZTwSeCbwS5rDu+9c4bFoFM+X0tzKMbHw9Zw1/D7PBl5JM91cVYFcfaFcy+drs1V/BHNplv6u7KrRfg1Jkgr7NfAKYGvgT4Wz9IRlVZLKuK29viOr/G7RJD2UVd4BfL50jlU4HJjDXQ9SX9i+LklSX4s6AngR8Gdgbtk0veMGS5JUxkhZ3aBoio7K5GTgEJoD1LO9HtK+LklSv9sD2Ak4OqtcuqY3Dyonq5JUxq3t1bJaSFtMLaeSpIESdWwLfAq4DjihcJyecrIqSWWMTFY3LJpCkiQNjKjjeTT7XWwGvCirvLNwpJ5ysipJZbgMWJIkjUrUMQ34GHAo8BPg+Vnl1WVT9Z6TVUkqIKtcRLOTrWVVkiStVtSxDU1BPRQ4Gti9C0UVnKxKUkm3YVmVJEmrEXUcQLOr/jJg36zyW4UjjSvLqiSVcxvesypJklYSdUwFPgK8Dvgp8Lyscl7ZVOPPZcCSVM6tOFmVJEkriDq2Bi6kKaofA57YxaIKTlYlqSSXAUuSpH+KOh4PnEVzBvh+WeUZhSMVZVmVpHLuANYrHUKSJJUXdWwMfAW4EXhqVvnXwpGKs6xKUjkbAPNLh5AkSX3hQ8CWwOMsqg3vWZWkcjYCbikdQpIklRV13Ac4GDguq/xZ6Tz9wrIqSeVsiGVVkiTBi4CpwDGlg/QTlwFL0ii0W8i/haZgzm1fnrLSY/IoXxt5fXMsq5IkdVrUEcCrgJ9nlZeVztNPLKuSViuCg4AjgZnAVcDhmZxcNtX4izo2B74GPB5YQlM0V2UJsHiFx8rPV3xtAXA2cHovs0uSpL63K7AdcEjpIP3GsippldqiOof1bprOhtfAog1nceeGc2LKlAm5eP0vr/XXq2MCTcmbyr+mi6v6eE2f79V7zwFenFXetlLuHYAzgU2B59GU1s2A5dy1hC7NKnNt/7lIkqTOexXND7FPKR2k30T6vZWkVYjJC+exyydm8oQjYeqClT99O3ArzRLWW2nOAltTOezFD8dGppSL+FdpXNXHa/r8NJq/KH4DPDOr/D+AqGN/4ETgJuDZWeUlPfg9SJKkjoo6NgGuBU7IKl9TOk+/cbIq6S7a+yYO4LWzZ7LJXPj9fvCbF8Dk22HqrTBtfrLHe46h2cl2w/YajL4Yru3Hq/v84rGcZEYdZwKnARdHHc8E/gN4D3AR8Jys8rqx+t+SJElqvZDmh+bHlg7Sj5ysSvqnqOPRwP8Au3HDQ5dwzqcm89c9V37bvExmj3u4cdAu+T0LuD/NbuknAK/OKhcVDSZJkoZOOyD4Fc0P4B9TOk8/8ugaSQBEHR8Efg48GHgVx/7yZfx1z4UrvW0hcPi4hxsn7Q58OwPnAm8EXmZRlSRJPbIz8Aicqq6Wk1VJRB37AmcAXwT+O6u8BdwNWJIkqVeijuOA5wNbrLzBoxqWVUlEHVcCdwCPySoXl84jSZI07KKOnwALs8onl87Sr1wGLAlgPjDfoipJkjRu1qc5VUGrYVmVBHA+sEvUMaN0EEmSpI7YgOZ8Va2GZVUSwPeAycBupYNIkiR1xPpYVu+RZVUSwI+BJcDdzqmRJElST1hW18CyKoms8nbgYmD3wlEkSZKGXtQxCZiGZfUeWVYljVgATCwdQpIkqQNG9gmxrN4Dy6qkEbOBeaVDSJIkdcCT2us1RVP0uUmlA0gqK+oI4N3AQ4GvFo4jSZI01KKOicAHgCuBbxSO09csq5LeBdTAl4CjCmeRJEkadgcBDweel1UuKR2mn1lWJT0Y+DtwcFaZpcNIkiQNq6hjKvBe4BLg9MJx+p73rEq6AtgU2Lx0EEmSpCH3app9Qt6eVS4vnKXvWValDos69qZZBjwXWFQ2jSRJ0vBqj6t5F3A+cF7hOAPBsip12wHArcCjs8qbS4eRJEkaYkFztupfvPVqdCyrUke1uwA/HPhzVnlT6TySJEnDrN1M6Wxg33ZHYK2BZVXqrv2Ax9LsAixJkqTe+wawGbBr6SCDwLIqdVDUMQ34KPAb4JjCcSRJkrriHJp9Qt7R3sOqe2BZlTom6tgE+DSwNfCGrHJp4UiSJEmdkFXeCrwZeAbw6fa2LK2GbV7qiKhjBvB64DBgY+B/ssrzy6aSJEnqlqzy01HHVsA7gGuBunCkvuVkVeqAqOMRwK+BDwI/BnbIKt9YNpUkSVJnvRM4AXhP1PGq0mH6VaS7JktDLep4LvBFYD7wwqzy+0UDSZIkiahjMnAG8DRgu6zyD4Uj9R0nq9KQijoi6vgAcCpwGfAYi6okSVJ/aI+yeSmwDHhN2TT9ybIqDa8DgcOBzwN7ZJV/K5xHkiRJK8gqbwC+BhwcdUwvnaffWFalIRR1bAB8DLgUeHVWubhwJEmSJK3aN2k2v/z30kH6jbsBS8PpCGBLYP+sclnpMJIkSVqtjdurxwmuxA2WpCHTHlEzHzgpq3xp4TiSJElajXaTpT8AtwE7ZpXLC0fqK05WpeGzlOa/7StLB5EkSdI9ehnwQOBZFtW7855VafgkTWHdsHQQSZIkrVrUMY3m1q2LgbMKx+lLTlal4bM7zX/bPy6cQ5IkSavQ3rb1aWAr4MVZeW/mqlhWpeGzH7AQ+G7pIJIkSbqrqGM34Is0y3+PyiovKJuof1lWpeGzL/CdrPKO0kEkSZIEUcdUmu/RXgE8FZgL7J5V/rBkrn5nWZWGzxY0u8pJkiSpkKhjc+ARwN7AS4BNgauB9wIfySoXFIw3ECyr0vBZBkwsHUKSJKkLoo71ge1oiukjgIe31/u1b1kCnAEcB5yXVS4rkXMQWVal4bMUy6okSVJPRB1bAq8GdqAppg9c4dMLgd8A3wIubx+XZpU3jXfOYWBZlYaPk1VJkqQxFnUE8HLgo8AGwBXAL2k2Sxoppn/1vNSxY1mVhkj7h2hiWZUkSRozUcdGwGnAU4AfAq/MKq8sm2r4TSgdQNKYegHNT/ouLx1EkiRpiHwE2Av4T2APi+r4cLIqDYmo48nAHOCnwPGF40iSJA2FqGNX4JXAh7PKz5bO0yVOVqUhEHXsA5wF/Bl4trvMSZIkjZmd2+vRRVN0kGVVGnBRx2zgKzRLf3fPKq8vGkiSJGm4TGuvUTRFB1lWpQEWdUygWfKbwAFuiy5JkjTmzm6vBxZN0UGWVWmwvR7YHXgfWuKvAAAgAElEQVRjVjm3bBRJkqThk1X+GrgMOLh0lq6xrEoDKOq4T9TxNuAomntVv1A4kiRJ0jA7Edgp6nho6SBdYlmVBkjUsV7U8SngauBDwIXAK7LKLJtMkiRpqJ0MLMPp6riyrEqD5fXAa4FTgUdmlU9xQyVJkqTear/fOgd4cdQxsXServCcVWlARB0bAP8NfC+rfFnpPJIkSR1zIrAPsCfw3cJZOsHJqjQA2vsjfgZsDryvcBxJkqQu+hYwH5cCjxvLqtTnoo7pwHeA+wBPzip/UDiSJElS52SVdwKnAM+JOjYsnacLLKtS/3sHMBPYP6u8oHQYSZKkDjsBWA84oHSQLrCsSn0s6tgDeBvw5azywtJ5JEmSOu6nwJXAS0oH6QLLqtSHoo7to46zgPOB64HDCkeSJEnqvPa4wBOAJ0UdW5fOM+wsq1IfiTq2jjq+BFwGPA54O/CQrPLasskkSZLU+lJ7fXHRFB0QmVk6gyQg6jgCeBfNgdOfAD6UVd5cNpUkSZJWFnWcT7OnyIOzymWl8wwrJ6tSH4g6dgFq4EzgQVnl2y2qkiRJfeszwDbAMVFHlA4zrJysSoW1f8D9EPh3mqK6oHAkSZIkrUHU8X7gncBHgbe297NqDE0qHUASzwZ2A15jUZUkSRoY7wY2Bt4M3Ax8oGyc4eMyYKmgqGMy8CHgD8DnC8eRJEnSKLWT1P/ihoddCLw/dv7k8gjmRnBQ6WzDwrIqlfVcYFvgsKxyaekwkiRJWgvvyedzzGU78sd9YO83BDNumAXMsbCODcuqVNYuwALg26WDSJIkaa0dyYSl05m/NUTClNsApgNHFs41FLxnVSok6pgO7A38KqtcXjqPJEmSRi/quA9PfO9Mdv4kzLgRrnoc3LblyKdnlsw2LCyrUgFRx32AjwEPAg4tHEeSJEmjFHXMBN4IHMKeRwRX7g0XHgbzngj88xSbq4oFHCKWVWkcRR1Tac7lOhiYCByVVZ5XNpUkSZLWJOrYmGbY8GKaVvoVzvj8b7j05UfQLP0dsRA4vEDEoWNZlcZJ1HFf4BvAE4BPAl8Gfl40lCRJktYo6ng4zfdxs4FPAx/PKudRQQRX09yjOpNmonp4JicXCztEIj27Vuq5qGMb4BxgFvCSrPKrhSNJkiRpFKKO7YCLgNuBA7LKHxeO1BmWVanHoo5dgTNpdt9+dlZ5YeFIkiRJGoV26e/PgA2BnbLKqwtH6hSPrpF6KOo4ADgfuAXYxaIqSZI0GKKOCcCXgK1pJqoW1XHmPatSD0QdAbwZOBr4CbBfVnlj2VSSJElaC0cA+wCvd+BQhpNVqTc+SlNUTwP2sqhKkiQNjqjjWUAFnEizoZIK8J5VaYxFHbsBPwI+C7wuq1xeOJIkSZJGKerYlubEhj8Bu2WVdxSO1FmWVWkMtfc2XARsBWybVS4sHEmSJEmjFHVsAFwMbA48OqucVzhSp3nPqjS2DgQeC7zUoipJkjQ4oo6JwBeAhwBPs6iWZ1mVxkjUMQ04CrgM+HLhOJIkSRqFqGMW8LL2MRN4W1Z5XtlUAsuqNJZeD8wCXpFVLisdRpIkSasWdUwB9gVeCTy1ffm7wJuAr5fKpbvynlVpDEQdm9LchH9hVrlP6TySJEm6u6hjNvA64GBgU+AamqW/x2eVc4sF0yo5WZXupfZM1Q8DGwBvKxxHkiRJqxB1vBA4BpgGnAF8HjjXFXH9y7Iq3Qvt7r+fornH4ais8neFI0mSJGklUce+NHuKXAi8MKu8qnAkjYJlVVoH7WZKDwf+C3gxcDRweNFQkiRJupt2uPAJ4LfAnlnlksKRNEqWVWktRB0PAE4DdgImti/XQJ2VN4BLkiT1oYcAs4GXW1QHi2VVGqV217jTaCaqHwIuBX6ZVf61aDBJkiTdk8e214uLptBas6xKo/cGYBfgwKzytNJhJEmSNCo7A7cCfywdRGtnQukA0gCZDiRwdukgkiRJGrXHAj/PKpeXDqK1Y1mVRu8yIIBHlA4iSZKkNYs61gO2B35WOovWnmVVGr3L2usORVNIkiRptJ5Mc+vjT0sH0dqzrEqjN7J0ZOOiKSRJkrRGUcduwInA74HvFY6jdeAGS9IoRB3/BnysffrVklkkSZK0au3pDc8FXk+zsdK1wN5Z5YKiwbROLKvSPYg6/h04DHgJzf2qH/SoGkmSpP4SddwfeDXwGuD+wBU0hfWErPK2ktm07iyr0ipEHROBOcDBwBLgWODorHJe0WCSJEn6p6hjJ+C/gOcBk4FzgP8FznX338FnWZVW7VDgZcAngSOzyusK55EkSVIr6pgJfBx4DrAAOAb4VFZ5RdFgGlOWVXVeBAcBRwIzgauY9YMP8zKOBM4F3pBVZtGAkiRJAiDqmAq8BXhn+9K7gE9mlbeWS6VeifT7cHVYW1TnMOnO6Wz9PXjIGfDgM5Lpf1/KhOUPyyr/VDqjJEmSIOrYE/gc8CDga8CbssqryqZSLzlZVdcdCUznRU+D2T+ERevDn/YOLn3ZTXnl3hZVSZKk/nECzdGbT8sqzy0dRr1nWVXXzQTg/pfB5S+Abx4Py6YCbFY0lSRJklb2R2Bji2p3TCgdQCrsKqYsgGm3wvXbjxTV5nVJkiT1k4uBR0Ud74s6ppcOo96zrKrrDmeDa+4A4NatRl5bCBxeKpAkSZJW6aPAV2g2Vfp91PGcqCMKZ1IPWVbVaZmczHanfRSA27ZIYB5wSCYnFw0mSZKku8gqb84qXwQ8CbiFZpOlJ5dNpV6yrEp7HtHc93DwU56ayWyLqiRJUv/KKn8I7NM+nVUyi3rLsirB39vrpkVTSJIkabSWtFc3jB1illXJsipJkjRolrbXiUVTqKcsqxLcDCSWVUmSpEExsrHS5KIp1FOWVXVeVrmUprBaViVJkgbDW9vrT4umUE9ZVtV5Ucf9gfVK55AkSdKaRR2PAd4EHJtVXlQ6j3rHsirB+2huzv9E6SCSJElavahjAnAccD1wWOE46jF3z1InRR2TgO2AnYBXAP+TVV5ZNpUkSZLWYH3gkcD7s8r5pcOot5ysqquOAy4D5gBX00xXJUmS1MeyyluBK4GHl86i3rOsqnOijonAvsBZwCOAf88qby6bSpIkSaN0MbBr1BFrfKcGmsuA1UU7ApsAJ2WVvykdRpIkSWvlIuDFwCxgbtko6iUnq+qindrrxUVTSJIkaV2MHFezS9EU6jnLqjol6tgZeG37dHbBKJIkSVo3B7TX64qmUM9ZVtU1/wE8hGZzJf+AkyRJGiBRxxNpjqz5fFb5/cJx1GPes6rOiDoeCLwc+EVWuXPpPJIkSRqddoPMN9Oc4PBX4I1lE2k8WFbVCVHHfYFzgInASwrHkSRJGhoRHAQcCctnst2pf2fHz/+Abc77HTCZpm+s/FjV6xOAf9CsfBt5LAIeDDwM2Jlmddw3gEOzytvG73eoUiIzS2eQeirqmAacBzwGeHJWeWHhSJIkSUOhLapzmLh4OvsdDI84ZcVPL20fS1b4eHWvAdwX2Jy7D9T+BvwBmAOckpUFpiucrGqoRR0TgBOAxwPPs6hKkiSNqSOB6Tz4jKaofv8I+NE7YdmkeZkTZq/tF2u/d7sPcH9gPeDKrHL+2EbWoLCsatg9CjgQ+N+s8tTSYSRJkobMTAAmLm6eXflMWDblX6+vpaxyOfD39qGOczdgDbvfAwuA7UsHkSRJGkJXAXDlM2DZZNju1Lu+Lt0LllUNrahjCvA1YH3gpMJxJEmShtHhwELu3AR+/xzY+X/hARfd2b4u3StusKShFXU8DPgtcG5W+bTSeSRJkobRP3cDXu8fM3nNo5ax3j9uZcrCh2aVN5TOpsHmZFVDK6v8HXA08NSo45DSeSRJkoZRJidnMjsX3ncCG139WKYsnA6c0p6NKq0zy6qG3TuA7wGfjjpml40iSZI03LLKS4HXAXsALy2bRoPOsqphNx3YBrgWd5WTJEkaD18ALgLeH3WsXzqMBpdlVcPuocBs4MisckHhLJIkSUMvq0zgzTRnpb61cBwNMMuqht2lwM3AE0oHkSRJ6oqs8iLgVOCtUcdWpfNoMFlWNdSyyiXAN4F9o46ppfNIkiR1yNuBicB7SwfRYLKsqgtuATYEdigdRJIkqSuyyr/S3L/6Au9d1bqwrGpoRR0RdVTAfwMnA78oHEmSJKlrvgKsBzyzdBANHsuqhlLU8SjgR8B7gBOAl2SVy4qGkiRJ6p4fA38DDiwdRIPHsqqhE3XsQjNF3RY4BHi5RVWSJGn8td+D/QR4WOksGjyTSgeQeuAWmh/EvD+rPK50GEmSpI6bCCwuHUKDx8mqhtEWwFI8rkaSJKkfbAzcWTqEBo+TVQ2NqGMyzdbohwFX4DbpkiRJRUUd2wK7AR8rnUWDx7KqoRB1PIhmx9+dgGOBN2WVt5dNJUmS1F1Rx0bAGcB84JOF42gAWVY10KKOvYDDgZ1p7oU4IKv8WtlUkiRJ3RZ1TAROAh4EPDmrvKZwJA0g71nVoHsD8Gjgq8AjLaqSJEl94b00Z6v+V1b5g9JhNJicrGpgRR0B7Ap8Pat8Rek8kiRJgqjjQJqVb3OAYwrH0QBzsqpBtwSYVTqEJEmSIOrYATge+DHwuqwyC0fSALOsamC1f/gdC+wZdexaOo8kSVKXRR33A74J3ATsn1V6tqruFZcBa+BEHV8CHkuzs9yONOd2TSkaSpIkSccAmwNPyCqvLx1Ggy/SybwGSNSxFXAN8Euasno58OGs8m9Fg0mSJHVY1LE+zUT1f7PKt5TOo+HgZFWDZp/2enBW+duiSSRJkjRiL2AycFbpIBoellUNhHbn3+OBpwN/AX5XNpEkSZJW8AzgNpqNlaQx4QZLGhSTgBfS3J96uDvLSZIk9Yd2qPAM4LtuqqSxZFnVoEjgOuBXWeVXS4eRJEnSP20HPAA4p3QQDRfLqvpe1LEe8DWaPwS/UziOJEmS7uoZ7dWyqjHlPavqa1HHhsCZwBOB12aVny0cSZIkSXf1DJrVb/9XOoiGi5NV9bv3A7sBL8wqP1M6jCRJkv4l6tiE5nu1s0tn0fBxsqq+FHVsC7wReCXwhazyK4UjSZIkaQVRx1TgFCCA0wvH0RCyrKqvRB2PBw4DngUsBk5on0uSJKlPRB3TgROBpwIvzyovKRxJQyjSE0DUJ6KO7YBfAzcBnwE+k1VeXzaVJEmSVhR1PA74IvDvwJuyyo+XTaRh5WRV/eQ5NMtIts8q/1Y6jCRJkv4l6pgIHAm8Bbga2CurPL9sKg0zN1hSMREcFMHcCJZHMJd/POhZNGX14aWzSZIk6W5eALyNZqq6vUVVvWZZVRERHATMAWbRFNRZ/Pkpj2o//ajV/kJJkiSV8jrgd8AhWeWtpcNo+LkMWKUcCUxn81/Dw06HB1wE25w3id//x+089BsfKR1OkiRJd7MAmJpVLi8dRN3gBksqIoLlQPDqR8Hmv4brt4c/PxUueG/m0qlO/CVJkvpM1PEe4Ahgk6zylsJx1AGWApVyFQCRcNuWcOZxcN6HYNnUqwrnkiRJ0qp9h+b2rf8sHUTdYFlVKYcDCznrM82zV+4Km11+R/u6JEmS+kxWeTFwBvDOqGOL0nk0/CyrKiKTk4FDuGbneczfGpZMX87ERW9sX5ckSVJ/egswhWb/EamnvGdVRUUdOwMXA5/KKl9fOo8kSZLuWdTxYeCtwE5Z5S9K59HwcrKq0n5Jc//DoVHH00qHkSRJ0hq9H7gRb99Sj1lWVVRWuRQ4EPgNcHrUsU3hSJIkSboH7RmrlwAPKJ1Fw82yquKyytuAi4D1gfsVjiNJkqQ1uwXYqHQIDTfLqvrFju31x1HHaVHHlKJpJEmSdE8sq+o5y6r6xe7AnsAngAOAz0QdUTSRJEmSVseyqp6bVDqABJBV3gFcAFwQddwOvAv4I3B00WCSJElalVuAaVHHlKxycekwGk5OVtWPKuA04ENRx5alw0iSJOlulrXX6UVTaKhZVtV3ssrlwOlAABsXjiNJkqS7ezZweVY5v3QQDS/LqvrdeqUDSJIk6V+ijlcDOwMnlM6i4WZZVb+6FFgInBh1eJyNJElSH4g6/hM4BjgL+FThOBpyllX1pazySmAf4IHAeVHH1MKRJEmSOi3qeB3waeBbwP5Z5aLCkTTkLKvqZ78A5gGzcDmwJElSMVHHC4FPAmcAB1hUNR4sq+pnbwMeTHOG17VRxw6F80iSJHXVocBvgQM9qkbjxXNW1c+OB24CHgs8H5hWNo4kSVL3RB0bAbsCH7Soajw5WVXfyir/klV+HPh1+9LvS+aRJEnqqMXAzcBOpYOoWyyrGgT/114fXzSFJElSB2WVdwBHAk+NOvYsnUfdYVnVIDgFuAp4d9QRpcNIkiR10GeAa4AP+v2YxotlVX2vvTfiKGAXwJ/mSZIkjbOs8k6gotlLZL/CcdQRllUNiuOBvwHvLh1EkiSpo04E/gB8IOpwo1b1nGVVg2IR8Geao2wkSZI0zrLKpcA7gYfSTFmlnrKsalC8HNgNeG/pIJIkSR32DeDzwLuijv8uHUbDzbKqvhd17AUcA3wPOLZwHEmSpM7KKhN4NfA14ONRx0vLJtIwi8wsnUFarajj/sAfgauB3bLK+YUjSZIkdV7UMRX4FrAXsH9W+c3CkTSEnKyq370Y2BA40KIqSZLUH7LKRcBzgJ8BX406qqhjWuFYGjJOVtW32jO8Lgduyyp3LZ1HkiRJdxV1bEJzu9aBNJthvj6rPKdsKg0LJ6vqZw8GtgO+VDqIJEmS7i6rvDmrfB7wFGApcHbU8eLCsTQkLKvqZ5u01z8XTSFJkqT/396dx9lR1Xkf//zSnZCEfRVGhKgoywiCIjiA4oLC4MLighMUUGEAxQUVR9GxpkThGVB0XJARURAFVIZRHPERZB3BURjZBQbnIQFU9j0hIaTP80dVYxuTdHfS1adu3c/79bqvc2/dpb+dpW9/76k6tVypSD8HtgFuB96SOY46wrIqSZIkaaWlIj0JXA+8NHcWdYNlVZIkSdJKizL2AvYCzsudRd1gWZUkSZK0UqKM51CtM3I1cETmOOoIy6paKcp4NvCN+ua9ObNIkiRpVLsAqwMfSkVakDuMusGyqrY6BtgU2DcV6ZrcYSRJkrRcl9ajx6tqwnieVbVOlPE84Bbg86lIH82dR5IkSaOLMq4BFgE7psKSoZXnzKra6GPAk8CJuYNIkiRpzE4BXgLsljuIusGyqlaJMmYBBwCnpCLdnTeNJEmSxuFU4E7g01FG5A6j3mdZVdscDgwC38sdRJIkSWOXirQQ+AzVcat/mzmOOsCyqrb5MfAwcF6UMTfK+D+5A0mSJGnMvgXcjrOrmgCWVbVKKtIvgB2pztG1HrBN3kSSJEkaq1SkRVRndXgx8LrMcdTjLKtqnVSk/0lF2h24KXcWSZIkjdv363HrrCnU8yyrajN3HZEkSeo9M+rx8awp1PMsq2qlKOMoqt1H7sydRZIkSeOyWj1aVrVSLKtqq2OAnwNH5g4iSZKkcbGsakJYVtVWi4EbUpHm5w4iSZKkcbGsakJYVtU6UcYXgJnA1NxZJEmSNG7b1ePtWVOo51lW1UYb1uNJWVNIkiRpRexJVVRvzR1Evc2yqjY6ox63zJpCkiRJ4xJlzABeDfwkFSnlzqPeZllVG10A3A0ckDuIJEmSxuUVVKeu+UnmHOoAy6ra6E1Ux6vukjuIJEmSxmVP4AngstxB1Pssq2qVKGML4GzgDqofdpIkSeodrwAuS0V6IncQ9T7LqtrmsXr8RirSVVmTSJIkabxWAR7OHULdYFlV29wNzAWKepZVkiRJvWMxMJA7hLrBsqpWSUVaDOwBJODiKGODzJEkSZI0dpZVTRjLqlonFekW4EBgI2DHzHEkSZI0dpZVTRjLqtrqvnpcL2sKSZIkjccQllVNEMuq2upa4BbgyCgjcoeRJEnSmDizqgljWVUrpSINAccBWwOvzxxHkiRJY2NZ1YSxrKrNzgLmAJ9wdlWSJKknWFY1YSyraq1UpEXAVVSLLO2SOY4kSZJGtxg7hiaI/5DUdq+qR08uLUmS1H5PAVNzh1A3WFbVdo8DZ6Qi3ZA7iCRJkkZ1FzArdwh1g2VVbTcPmJE7hCRJksbkJmDjKGOt3EHU+yyrarv5wGq5Q0iSJGlMbqrHrbKmUCcM5g4gjeI64IAoY29gI+C+VKRzMmeSJEnS0v22HrcCrswZRL3Psqq2+yiwB/Dv9e1bAMuqJElSO21Ujw9mTaFOcDdgtVoq0oPA7sC7gCeB30cZp9QzrZIkSWqXVwEJuDRzDnWAZVWtl4p0E3AjMA14NXAwnndVkiSpVaKMacBewG/qCQdppVhW1SsGqJZCf6S+vWuUsUbGPJIkSapFGasBPwZeBJyUOY46IlJKuTNIYxZlDAKnAfsDG6Yi3ZM3kSRJUn+LMtYDfgJsDxySivTNzJHUEc6sqqekIj0FbAhcb1GVJEnKK8rYBPgFsA2wj0VVE8myql70TGDVKGPd3EEkSZL6VZQxfHqaDYHdU5HOyxxJHWNZVS86HNgY+HbuIJIkSf0oylgf+BnVuiK7piJdnjmSOsiyqp6TinQpcCrwsigjMseRJEnqK/UaImcD6wF7piJdlzmSOmowdwBpBd0GrA5cEmX8BrgG+PdUpMfzxpIkSeq8Y6jOp/rOVKRrcodRdzmzql51NvA1YAbVbsHfBj6ZNZEkSVLHRRn7AB8DTk5FOi1zHHWcp65Rz6t3RbkBuDsV6ZW580iSJHVRlLE5cBVwM/DyVKSFmSOp45xZVRfsCmwB/DR3EEmSpC6KMlYDzgUWAm+2qGoyeMyqelqU8ULgS8DcepQkSdIEqhe0/AbV5MBrUpHuzBxJfcKyqp4UZWwAfAd4DTAP2C8VaUHeVJIkSZ20LbAf8K+pSBfnDqP+4W7A6lWbUBXV64BnpSL9JHMeSZKkrroe+C/grVHGX+UOo/5hWVWvSlSnr3khsF3mLJIkSZ2VirQYOBCYDpxeH78qNc6yqp4TZbweuBJ4DvDfwEN5E0mSJHVbKtL/AO8DXg1cXa8bIjXKU9eop0QZzwJ+R3Wqmt1TkR7IHEmSJKlvRBmvBL4LrAN8GDgpFRYKNcOZVfWatYFpwD9bVCVJkiZXKtIlVIdhXQR8BTg3ylgnbyp1lWVVvWZ4l9/1s6aQJEnqU6lI9wFvoJpZfR1wbZSxc95U6iLLqnpGlLEq8M365q05s0iSJPWzVKShVKQTgZ2BRcBlUcYnooyBzNHUIZZV9ZL9gN24b4sr+ad0agRDEcyJYHbuYJIkSW0XZUyPMtarr78oyjgzynjRyrxmKtJVVGdm+AHwGeACT2+jieICS+oZUcaqPPTs/2Tt27fjFx+Fi46DNAVgPnBISpyZOaIkSVIrRRlrAJdSnU3hR8AB9V131Reozqf6xVSkm1fg9QN4J9VxrI8DB6Yi/XQlY6vPWVbVU2JwwRwOe9GmrH8znH0u3LLP8F1zU2JWxmiSJEmtEWU8m2r33D8Ag8D5wK7Ag1Qr+X4JmApsXj9lgGqX3unAT4HPAxePd6XfKGNL4HvA1sDngE+kIj25st+P+pNlVT0jygjm7DrErMvgpjfDj74JT64+fHdKyd3aJUmSooyDgG/VNxdSLVC5IXAgcAEwPRVpzlKetz5wGHAEsAFwLXAi8L3xFM4oYwZV2T0cuAp4WyrS/1vBb0d9zLKqnhIf2GwRUxYN8qX/haHBkXc5sypJkvpelLE98AvgSuD7VLv9Phs4PxXpW8t77ojXmA7MBj4E/HW9+a9TkX47zixvAk6lWifn71ORzh7P8yXLqnpK7P3Ok9jutMM5/SK4/VXDmz1mVZIkCYgyzqM6rcx2qUjXruRrrQvcX9/cJxXph/X2lwAbAT9PRZo/ymvMAs4E/oaquH4gFWneyuRS/3C3SfWW7U57lBRD3L/5XUAC5mJRlSRJfS7KGIwyjqUqqlAde7qyHgf+rb5+TpQxqz41zY+pFmm6P8r4YZRx0PAqw0uqdzfeFTgOeBdwlasFa6ycWVXPiDIGgTuBX6ci7ZU7jyRJUltEGdsC1wCXUO1y+7sJfO1fUe0OvCmwD3AKcAywNrA3sDHwFHBYKtKpy3md11CV3AuoZmotIlouZ1bVS3anWhxgTMdbSJIk9ZEbgHuB+yayqI547VWB26mK6i+BY1OR3gdsAryYqiSfEmW8fVkvkop0IVAAe/GnGWBpmSyr6iXvAu4DfpI7iCRJUpukIi0GzgVeX6/GO5GvfTCwA/Bz4Fhg11SkBfV9KRXpN1QF9FLg9CjjzUt7nQhmc9zDRwBw+cdPj2D2ROZU9wyO/hApv3op9TcAX05FWpQ7jyRJUgstAKZRnTN1QqUiXQXsu5z7n4gy3gj8X+CsKGMH4LOpSI9AXVThFNa+fSYA92y7FnBKBLj2iJbFmVX1isOoTlztLsCSJEkjRBmrRxlfBz4InJeK9HiOHPXXfR3wXeAo4LYo47B63ZFjgZk847rqwfdtCTCz3i4tlWVVrRdlHACUwL+nIt2YO48kSVJbRBm7AtcDBwMnAPvnzJOK9Egq0kHA9sAtwNeAa3juzzZh6nzY9dPwwGZw/xbDT9kkU1T1AFcDVqtFGW8AfghcDLxh+PgISZKkfhdlHAN8Evhf4MBUpCsyR/ozUUZQrR58AvAcHpoFa8+Bb10Kc3cdftjclJiVJaBaz5lVtd3fA3cAe1tUJUmSKlHGmlRF9Vxg27YVVXh68aVzga249XVnMuMh+K/3jyyq84Gj8yVU27nAklqrPmH0dsDVqUjzcueRJEnKIcrYGDgdWAe4HLgMeKK++4xcx6iOVSrSQmD/mPb4T1k08zNUu/7eARzt4kpaHncDVmtEGR8B3g28FNgW+B6wOtWs6oU5s0mSJOUQZWwPnAesBlxN9XvSyFPTbJWKdHOObFLTnFlVVlHGHsDeVP8W3/IWjBoAABhGSURBVF1v/hTwAeB3wKtTkW7KFE+SJCmbKGMfqpV17wV2SkW6McqYBrwEeDmwJnBrxohSo5xZVTZRxuHAScA8qqXLY8TdPwDenYr0WI5skiRJOUUZ6wC/p1rp942pSPdkjiRNOmdWNWmijKnAK4CLU5EWA+vXd21MVVhXA3YE/gDckAo/SZEkSX3rXcB04BCLqvqVM6uaNPUxqScAv6A6Fc3ewDbAC9zVV5Ik9bsoY3fg7cAuwCzgylSknbOGkjJyZlWNqndhKalWfXsZ1XnAXgjsBFwLfK7eJkmS1O9OBtYCfg58ETgrbxwpL2dWNeFGHPg/B3glcAbwW+Au4NPAdUB4PKokSep3UUYAA/XlUeDEVKSP500ltYMzq2rCG4Bz6uuL6nH7VKQnlvF4SZKkTosypgD7Am8DpgIXAesB7wHWHfHQ309+OqmdLKuaMFHGgcD+VJ8MAny9vv6ARVWSJPW5N1OdQ/6PVAtLvhFIVOdQvQoYAhZSnapGEpZVTazXAq8BHgYeAL6ainR93kiSJEl51bv6Ds+efiAV6QdRxqYAqUhz8yWT2s2yqpUWZQwCR1F9YngvsGUq0oN5U0mSJOUXZewIHEe1jsccqnU8LKnSGFhWtVKijBcApwEvBr4PHGFRlSRJ/S7K2Ar4LNWp+u4F3geckoq0MGswqYdYVrXCooy3Ad+m2u33LalI54zyFEmSpM6rz5d6PtWxqZ8CvpCK9HjeVFLv8dQ1Gpco4+XAtsCzgI/UmzdJRbozXypJkqR2iDJWAW4EFgO7pCLdnzmS1LOcWdWYRRnPAy6rby4A5gJXU61qJ0mS1DeijA2Bg6lORTMPOJlqtd/3A5sBu1tUpZVjWdV4vItqWfUtgdtS4bS8JEnqP1HGbsCZwPrA5VTnS/0mcCKwCvDDVKQL8iWUusGyqjGJMp4PHAScn4r0P5njSJIkTbooYwpwNPBp4GbglalIN9Wnpnk58B5ge+BD+VJK3eExq1quKGMH4GNUK9k9SbVLy2XLf5YkSVJviGA2cCywCXAHcHRKnPkXjyvjucBXgD2A7wKHpiLNm8ysUr+xrGqZoow9gf8AHgG+Cnw5FemevKkkSZImRl1UTwFmVlsSTFk0nzXueh8ffO6PgenAGsDhwKFUH9x/BDjZw6Gk5llWtVRRxkbA9cAfqFayeyxzJEmSpAkVwRxIm/Lyz8DOJ8DUeTBlaGkPXUxVaj+diuTCktIksazqL9THY1wA/A3w4lSkWzJHkiRJmnAxuHCINxwabHs63PJGuGcbWLwKPLVK4rUffT/V2Q8WAr9MRfpd5rhS37Gs6i9EGUcBxwMHpyKdmjuPJElSE+Lv9p7HFj+aySUlXPaPQAzfNTclZuVLJglgSu4AapcoYxZQAj+kWoJdkiSpm553Plx7wFNc9ilGFNX5VCv+SsrMsqolfY7qXKrvd+EASZLUVVHGAAOLZrLmnecBc4FUj4csbTVgSZPP86xqSc+i+kF9V+4gkiRJDVoTgGdf8p8p8abMWSQthTOrelqU8QzgfmArYMfMcSRJkpq0dj0+lDWFpGWyrAqAKOMw4G5gT+D7gCsAS5KkLtu6Hu/LmkLSMllWNWzaiOuHpSI9nC2JJElSg6KMmcCJwK3AxZnjSFoGj1nVsC8DhwMPpiK5O4wkSeqyTwLPBl6RirQgdxhJS+fMqobtCGwBPBxl+CGGJEnqpChjOvBe4OxUpMty55G0bJZVDTuqHvcENs8ZRJIkqUG7A2sAp2XOIWkUllURZXwI2Le++fFUpJty5pEkSWrQ3wKP4LGqUuu5u2efizICOAa4DdglFenezJEkSZKatAZwXyrSotxBJC2fM6t9LhUpAd8GZgGP500jSZLUuKmARVXqAZZVQfVD+3HA1fAkSVLXWValHmFZFcDOwBWpSEO5g0iSJDVsFSyrUk+wrAqqWdU1coeQJElqUpSxM/Aa4JrcWSSNzrLa56KM7al2/31plDEjdx5JkqQmRBnrA98D5gAfyZtG0li4GnAfizL+CriqvjkfSBnjSJIkNel0YH3gpalIj+QOI2l0zqz2sVSkPwAfrG9OBf4xypiaMZIkSdKEizJWpzq/6hdSkdwFWOoRltU+l4r0L8CbgQHgaOBleRNJkiRNuCeWGCX1AMtqn4syNgZ+ANwH/D1wadZAkiRJEywV6SmqQ55Wz51F0thZVvtYlDEAbAHMo/oBfqqnr5EkSR31BJZVqadYVvvbh4ELgVWBO4HIG0eSJGniRRnPB9YFbsydRdLYuRpwf5tTj7unIl2YM4gkSVKDdqrHi7KmkDQuzqz2qSjjnVTnGgN4fs4skiRJDftjPa6bNYWkcbGs9q9ixPWvRBkvyZZEkiSpWb+rx+dlTSFpXCyrfSjKCGDTJTbPyJFFkiRpEjyzHudnTSFpXCyrfSgVKQFvqW8uBJ6finR5xkiSJElN2hdYDPxH7iCSxs6y2r+2rsfXpyLdljWJJElSs64GBoDX5w4iaewsq/1reDU8FxqQJElddyZwHfDZKGNa7jCSxsay2r+GS+pGWVNIkiQ1LBVpCPgY8Bzg0MxxJI2RZbUPRRlbAd8GrgJOzhxHkiRpMvwMuBj4VJSxRu4wkkZnWe0zUcZawI+AecC+qUgLMkeSJElqXL3A5GeB9YDdM8eRNAaW1f4zG9gM+E4q0l25w0iSJE2i6fX4h6wpJI2JZbX/nAGcD3w4yjg+yvDfgCRJ6hcvqcdbs6aQNCaRUsqdQZMsyhgE/gV4D3Au8I5UJE+SLUmSOqtes+Nq4PJUpD1y55E0OmfV+lAq0lPAEcCRwD7AV/MmkqTeEcHsCOZEMFSPs3NnkrR8UcamwL8BjwMH5U0jaawsq32qXmTgNGAh8HDeNJLUG+piegqwKRD1eIqFVWqvKONVwH9Tna7vralId2eOJGmM3A24z0QZqwL7A3sBuwHTgFelIl2SNZgk9YAI5gCb8ozrYefjgQRpCgw8OY8XfP8HwBCwuB7HcmnisW35+gtTkeatxB+3tNKijNlUp+u7Fdg7Fem2zJEkjcNg7gCadB8HPgHcDpwEnJOKdEXeSJLUMzYBYMtzYZvvwoPPhRiCGFoVeDXVHkvLugws575OijLuAx4AFgBPUO3J82C97SEgUX1oukp9Gev1KcBTIy6Ll7g9lm2P1VmGLw8scfuxei8k9agoY0uqPSGuAF6fivRY5kiSxsmy2n9eBNwAvNA3YUkatzuATUlR3frSbVR7AzM3JWat6ItGGcHYi+14SvDKPHZlX3sm8BxgLarThcwA1ge2ANYB1qy//aeAJ6kOS1m4nOuPjLie6q83OOIyfHv6MrYveVkdWHU5fy2Lo4wHqUr2ohGXJ5e4vbRtY3nMRD5vUf3nuAgY8v0doozpwFnAfODvLKpSb7Ks9oEoYw/g08AzqY7X+I5vZJK0Qo4GTiFNmQlUs6ppYH69fYXVP5MX15e+UK9Mn1KRsn3PUcYqVMV5WZd1qcrv1PoybcT1qVQzvasvsW1pjxveFpP0fQ0X16WNy7tvLI8Zvr4ImFdfHh/DOH8y/q7r48eP5W/ftyk7fhmuOOqEdMHxnlNV6lGW1f6wL7A11SeMv6c6dkOSNE4pcWYEMLDwq8BaxOK5pIGjU+LM3Nl6Tb0yfe4MC4E/1pfGRRkDLL/ULqvkjrZtcMQ4uBLbVgFWG+Nzp1HNno/n+3+CsZfbsYzzgMdTkRbBiAXQNj9vJjt+GX75Qbjw+PdGcK3/R6Xe5AJLHRdlbAb8J3BnKtIOufNIUhdEGR8HjgWm14VH6jtRxhSq3btXo9qlennjWB4zchzPsdzV8ciLZkxjaDAYfALu3Rq+8UtYvAqs5G76kvJxZrXD6t2bLqLahemgvGkkqVOG6rGziyNJo0lFGuJPM5wTpj6GezpjL7czgQGues9HicUwNBV+fcRwUYXhhdEk9RzLarctBu4BnkW1y4wkaWJYVqWG1MdwP1Ff7h/r8yLYj+rcx0u6Y4KiSZpkvsl2WH080Byq5fg9AbYkTRzLqtQ+R1Ot/jvSSi+AJikfZ1Y7IsqYBjwP2Ax4bn2ZC+wFnJyK9GTGeJLUNZZVqWWeXgCtOp58E6oZVRdAk3qYZbUD6uX//wvYbsTmx6iW0wc4fdJDSVK3WValFqqLqeVU6gjfZLvhbVRF9ZPADsC6qUhrAC8G9ktF+k3OcJLUQZZVSZIa5sxqj4syXgiUwA3AcfXKfADUJdWiKkkTb3E9WlYlSWqIZbWHRRkzgV9RLRn/7pFFVZLUKGdWJUlqmGW1tz0B/BYYAC7LnEWS+ollVZKkhllWe9s/AJtT/bI0kwk+KbckaZksq5IkNcw32R4VZQQwm6qk/pg//eIkSWqeZVWSpIb5JtujUpES8DLgG8BbgGuijJ3yppKkvmFZlSSpYb7J9rBUpEdSkQ4BXgvMAC6PMmZlDSVJ/cGyKklSw3yT7YBUpAuBD1AttLRO5jiS1A8sq5IkNcw32e5YvR6PrE9pI0lqjmVVkqSG+SbbHVcCNwJvBzbMnEWSum64rA5kTSFJUodZVjsiFel/gauA+4HbM8eRpK5zZlWSpIb5JtstOwFX1isFS5KaY1mVJKlhvsl2RJSxHrA51e7AkqRmWVYlSWqYb7Ld8dJ6tKxKUvMsq5IkNcw32e7YqR7fEWU8P2sSSeo+y6okSQ3zTbY77gWeBA4Bds6cRZK6zrIqSVLDfJPtji8DNwNzgbMyZ5GkrhteyM73UUmSGjKYO4AmzG7AC4H9U5EW5A4jSR23ej0+ljWFJEkd5ifC3bFFPV6QNYUk9YcN6vHerCkkSeowy2p3rFWPn4gypmdNIknd9wxgMfBQ7iCSJHWVZbU7PgecDXwQODBzFknqug2A+1KRhkZ9pCRJWiGW1e6YD2wEPAz8MHMWSeq6dYEHcoeQJKnLXGCpO94K7Aocmop0T+4wktRxg8Ci3CEkSeoyZ1a7Yxuq8/59I3cQSeoDU6iOWZUkSQ2xrHbHAqq/z91zB5GkPjBA9QGhJElqiGW1O04DbgDOjzJ2zJxFkrpuAGdWJUlqlGW1I1KR7gReV9/cNmcWSeoDllVJkhpmWe2Wu+vxGVlTSFL3TcHdgCVJapRltUNSkRYBD2JZlaSmObMqSVLDLKvdczewYe4QktRxllVJkhpmWe2ee3BmVZKa5m7AkiQ1bDB3AE2MKGMQ2A5YHVgrcxxJ6jpnViVJaphltQOijB2AX43Y9KNcWSSpT1hWJUlqmGW1G34/4vpfpSL9MVsSSeoPU7CsSpLUKMtqN6xLdezU1yyqkjQpBvCYVUmSGuUCS91wAhDA13MHkaQ+4W7AkiQ1zLLaDbfV42+ijH/ImkSS+oO7AUuS1DDLagekIh0BfIHqk35JUvPcDViSpIZZVrvjIOAC4PjMOSSpH7gbsCRJDbOsdsd9wAbAkVHG83KHkaSOczdgSZIaZlntjsuBbYHPA0dmziJJXeduwJIkNcyy2h2HArvV1y/LGUSS+sBiXCdAkqRGWVY7IhUpAXsAi4CfZo4jSV33KLB67hCSJHWZZbUjoowA9gEuSkV6NHceSeq4R4E1coeQJKnLLKvdsT7wXOCS3EEkqQ88CqyZO4QkSV1mWe2O+4FHqAqrJKlZzqxKktQwy2p37ED1Kf89uYNIUh+wrEqS1DDLagdEGYPAScDvgRMyx5GkfmBZlSSpYZbVbjgc2A74YCrSY7nDSFIfeBSYEWVMzR1EkqSusqz2uChjI+AzwAXAv2WOI0n9YviDwdWyppAkqcMsq73vc8B04Ij6XKuSpMnjz11JkhpiWe1hUcbBwGzgn1ORbsudR5L6yGA9PpU1hSRJHWZZ7VFRxtuBrwM/pdoNWJI0eYbL6uKsKSRJ6rDB0R+iNoky1qM6Tc3pwCXAm1KRnsybSpL6zkA9OrMqSVJDLKs9JMrYAvglsBbwCPDGVKQn8qaSpL7kzKokSQ2zrPaAKGMzqkU8/gOIevOFqUjz8qWSpL42CAylIg3lDiJJUldZVlsuytgRuJLq+OKFwCuBGcCNOXNJUp8bxF2AJUlqlGW1xaKMAeBrwN31eFUq0i/zppIkYVmVJKlxltV22w/YDtgvFen7ucNIkp5mWZUkqWGeuqbd3gHMBc7JHUSS9GcGcHElSZIaZVltqShjA+A1wFku4CFJrePMqiRJDbOsttdbqT65/27uIJKkv2BZlSSpYZbV9tofuD4VyVV/Jal9LKuSJDXMstpCUcbGwEuBs3JnkSQtlWVVkqSGWVbbaet6vCJrCknSslhWJUlqmGW1nbasx5uzppAkLYurAUuS1DDLastEGa8F3gvcnYp0f+48kqSlcmZVkqSGWVZbJMo4FfgZkIDZmeNIkpbNsipJUsMGcwfQn9kZ+C3w4lSkBbnDSJKWybIqSVLDnFltlxuBLfDvRZLazrIqSVLDLEUtEWWsA7yJ6u9k48xxJEnLZ1mVJKlhltWWSEV6ENi/vvm1nFkkSaNyNWBJkhpmWW2X4V98zs6aQpI0GmdWJUlqmGW1JaKMVYHjgeuAb2aOI0laPsuqJEkNczXgFogyZgA/ojpW9R2pSO5aJkntZlmVJKlhltXMooxpwDnAq4ADU5EuzxxJkjQ6y6okSQ2zrGYUZQwCZwF7AoemIp2ROZIkaWwsq5IkNcxjVjOJMgaA04F9gSNTkb6eOZIkaexcDViSpIZZVjOIMqYA/wrMBo5ORfpi5kiSpPFxZlWSpIZZVidZlBHAvwDvBj6TinRc5kiSpPGzrEqS1DCPWZ0EUcYLgM2ATYCdgP2AE4FP5cwlSVphllVJkhpmWW1YlLEbcOGITQuAzwNHpSKlPKkkSSvJsipJUsMsq80b/jN+N/Bj4H5LqiT1PMuqJEkNs6yuoAi+AhzGn1aEPDkljqgXT/oYsAvVSr8H1k/5VSrSfVnCSpImTASz+dia63DdAe+J4HXA0SlxZu5ckiR1jWV1BdRF9b0jNg0A741V75/KR1mPqqQCXArsCHw8FemmyU0pqS2ijKnADGDmcsbx3jeV6oOyofoy2vXxPHaiX2Oyn7fCrzHani8RzAZOIYamMDQIsClwSgRYWCVJmliR3CN13CJ4ChjgiM1h7dvhghNg3gbwsmPhGTcOAR+mKqwvA84ADnTXXymveiXuaVRlb/qIcfoo20a7fyzbVvSDwSfqy/wR4/D1RVQruk+h+sBsrNcn4rGxgt9PL0gsr9jOX2dNhgansNq9cMVRcOHxw8+bmxKzcgSWJKmrLKsrIILqD+2flvr72neAi4G/Bt4JHAM8ydh+QZwCPAbcybJPNr+8XxJX9D6ofkFbzJ/PRiztMjTi8cu7jPaYyXiNxr7Gsj58qAvR0i4sY/tkPTb31x9v1qlMXFEcOa6MxVQlccGIccEYt40sm8sqn0tuW5iKNPz/rVXqf+dNF+I2PO8vt/36PUcwpf7x/Ov3wr1bD/+xpJQ8HZwkSRPJsroCnp5ZPfJZsOZdueMor+H/QF2eaWqbJQvhaIVxrIVyudtSkVxMR0Qwh2rX3yU5sypJ0gSzrK6Ap49ZnXk/rHY3pCkwNAAzHvgOB+9csILHT6UipShjbeCZo0RY3l/ait635GzCsi4TMYM22v0T8RqT8TVGPma0GdyxzvSO97FNvGYbsg7PYi5ZHhe6S71yevqY1eq44WHzgUM8ZlWSpIllWV1By1oNOG8qSVLT6sJ6LLAJcAeuBixJUiMsq5IkSZKk1nExCEmSJElS61hWJUmSJEmtY1mVJEmSJLWOZVWSJEmS1DqWVUmSJElS61hWJUmSJEmtY1mVJEmSJLWOZVWSJEmS1DqWVUmSJElS61hWJUmSJEmtY1mVJEmSJLWOZVWSJEmS1DqWVUmSJElS61hWJUmSJEmtY1mVJEmSJLWOZVWSJEmS1DqWVUmSJElS61hWJUmSJEmtY1mVJEmSJLWOZVWSJEmS1DqWVUmSJElS61hWJUmSJEmtY1mVJEmSJLWOZVWSJEmS1DqWVUmSJElS61hWJUmSJEmtY1mVJEmSJLWOZVWSJEmS1DqWVUmSJElS61hWJUmSJEmtY1mVJEmSJLWOZVWSJEmS1DqWVUmSJElS61hWJUmSJEmtY1mVJEmSJLWOZVWSJEmS1DqWVUmSJElS61hWJUmSJEmtY1mVJEmSJLWOZVWSJEmS1DqWVUmSJElS61hWJUmSJEmtY1mVJEmSJLWOZVWSJEmS1DqWVUmSJElS61hWJUmSJEmtY1mVJEmSJLWOZVWSJEmS1DqWVUmSJElS61hWJUmSJEmtY1mVJEmSJLWOZVWSJEmS1Dr/H9jVR0heU0kfAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f, ax = plt.subplots(figsize=(16, 12))\n", "core_set_pts = pyscan.dp_compress(pts, alpha)\n", "plot_approx(ax, pts, core_set_pts)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Disk(or Rectangle) Compression\n", "For disk or rectangle regions we have to handle the inside of the region. We need a guarantee that any disk or rectangle of a certain minimum size contained completely inside the region will be hit. We then handle the boundaries of the region differently then the insides to get the correct guarantees for certain regions. \n", "\n", "### Gridding\n", "\n", "We can apply a grid inside of the region." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "core_set_pts = pyscan.polygon_grid(pts, r_min * 2)\n", "f, ax = plt.subplots(figsize=(16, 12))\n", "plot_approx(ax, pts, core_set_pts)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Boundary Conditions\n", "\n", "Below we show a couple of different boundary methods. We recommend using the grid even for rectangles and grid_hull version for disks. Even chooses points at even spaced intervals along the region boundary. Grid hull grids the boundary of the region using a different resolutions based on the $\\alpha$ parameter and then applies a directional hull aproximation internally. The r_min parameter is the minimum radius of the disk that we get $\\alpha$ error on. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "core_set_pts = pyscan.polygon_grid_even(pts, r_min * 2, alpha)\n", "f, ax = plt.subplots(figsize=(16, 12))\n", "plot_approx(ax, pts, core_set_pts)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "core_set_pts = pyscan.polygon_grid_hull(pts, r_min, alpha)\n", "f, ax = plt.subplots(figsize=(16, 12))\n", "plot_approx(ax, pts, core_set_pts)\n", "plt.show()" ] } ], "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": "3.6.7" } }, "nbformat": 4, "nbformat_minor": 2 }