{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Measures of shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `esda.shape` module provides statistics that are used in the literature to measure the structure and regularity of polygons. These measures vary from very simple (such as the length-width difference) to very complex (such as the normalized moment of inertia). Regardless, we'll walk through computing a few of these measures for counties in Mississippi. \n", "\n", "\n", "Why Mississippi? Because counties on the west side of Mississippi touch the Mississippi river, with its many twists and turns. Generally speaking, we would think that counties on the left side of the state are more \"irregular\" than the more square counties on the right. You can see this in the map below:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/opt/anaconda3/envs/analysis/lib/python3.9/site-packages/geopandas/_compat.py:106: UserWarning: The Shapely GEOS version (3.9.1dev-CAPI-1.14.1) is incompatible with the GEOS version PyGEOS was compiled with (3.9.0-CAPI-1.16.2). Conversions between both will be slow.\n", " warnings.warn(\n" ] } ], "source": [ "import geopandas, libpysal\n", "from esda import shape as shapestats\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "counties = geopandas.read_file(libpysal.examples.get_path(\"south.shp\"))\n", "ms_counties = counties.query(\"STATE_NAME == 'Mississippi'\")" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Mississippi Counties')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ms_counties.plot()\n", "plt.title(\"Mississippi Counties\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first very simple measurement is the difference between the length and width of a shape. This measure is a measurement of *elongation*. You can see the effect below, where counties that are relatively square are colored very dark blue, whereas the elongated rectangular counties are colored in light yellow. Since this measure does not \"see\" the twists and turns taken by the river, the river counties are judged to be relatively square and not elongated. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'length-width difference')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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6c+pyIOLagohzx56O89zz5ON0jgzzhdfczrNnz3D/0dSRB1L5IWgZ2qPZsImPDRVzuN3a8qKlxc1U+bwICh9u9h3uT3uNOBh6qwsURJwzqosCvNJj+EWU+Xyc6utNf1GK53WmNnE2sGNOtI0M0GY2vJWeAEaYvdT4S73YHYquK87+apV48v+p55Gl5RUUe4wv7kf797LvYvqoA6mWpbsybImzgzOr2OpSeq3Ifgct1zbxq1LEbQP9fPB3v+bZc22MRIy1NE+2tVpyWUx1Ts+hMS6TOsf1ysbohNOOndVbO3Cwo6k0d2PE8Co1J350YC9PtrXyZFur5WvWFdVQrfxc6kg+hto7OIrrOY0N19dzWNkbhsoWTjPEWrbHHZTfWJq7KWd4lbTEx7q7+MXRwxOt6NmB1P4JiaiNFHFo3wU6+1P7J8Z0nUDM2ZRZNjp2TrF6ZycrPppKciviV0VLXOL18qk/PMq9B/extrqWHecc5P2z0wI51GI2fOqdOrNb/QHZbYiLPR7KfBnMg1vgVSHixpJSHn7neznW083xnm5WVlZxtHumO2NqrCtTd2I4Yiw43daweOrd4m57uLuT4Uh4xnXxOE44b9Ugt1l+Y0lpTuKvxfOqEPE/7niKk729fOb6m3jb2nW8c/1Gbvn37ESyTISmCeUu/0Q09/F2bmmgGpdLoVyJn8kel8bu3uRPic2eZQRVdHLOQoEhfSYiwauosxXTVu1Ku+ZEru1heBWIWCnFo6dO0DE8zBvv+3fesHI1F0eyt5QoESG3ondgZoSfroEOrlncyP4Ba8ueptNxbJSuwdQzapdtK3Zozlg1J+y1xLkemYBXgYhFhE9uu4H7Dxgdu67+UVxobKtZbD5CjRhPgqJ1pJ9Lo8kEbv3LS+XNlusYEE4f3caUuYXapQkaOJ3GHHfq4FUgYoC3rVvPmupa9l3o4HOPPZH0vFWN1SlEbF0cqaafc2weGjHRsnCPuqWllDcZ/tHjdVZAoNzLJm+96X6pzEWnRrKbcXdM3VwkoJSiuTx3y5LGSStiEfEDzwA+8/xfKqX+Z9zxTwJfBWqVUtYzoMwy6+vr6BhMt3QoeSujmjQW11UDUzUy2ZaP7xDawsmH8DJpia1oc7TVxRr/KkTAW6Shlg1OjFioKf+RKftFQfl7IIZODJ1Kj4+n2hOYPRHzzyJVZbkdmYAMkjEqpV4UkWbgtcDZnNYyC0RiMR4/eSr1SSlUMuaKcLDnYsb1yPVIcGtcjOLyUg+jVc4mXcq82TED6ormgDmRJhnjN4BPAb/NSe2ywOGLl/j0I9s51dNLJNliOStkyZjNJMCKXXs3k7ebrR/bouLcd+wsjayIiEtE9gOdwGNmMsa7gfNKqQO5rKBdHj1+gl8dOkJM19GV4hs7nudYV7clAbtiJO+4zAXfHpvEbHbCsk2px0eZ15/z+zhNxng5cA+QNlXkbGcULfX5+PiDj/C5x5/gu2+9m9tWLOfp02csXdvwnaOEdp5G0wSXx43b68LlceFyu6h8nwfW5Lbu6bEnSj3PTfGi4tx36sB5MsY3A8uAAyJyBlgM7BWRhgTXfE8ptUUptaW2tjbjCqfjuqVLuO/df0K5389Hfv1bPvf4k9YvHg8mrSsioQhjQ0GGe0cY6BxEBTNLZTCBw9k882JbZ2eS/zAbceVmw5QA58kY9yml6pRSLUqpFqAd2KyUyrznkwUub2zgfZs3EYrG7EWETHVqrsfGckC6lFy5ZrZaYsfJGHNbrcwYCYf5wa499i9MKeLsCGJNyRhryoy4e+N/UQW/v5Q+sYbd31FM1x1PBGTjNztnRKyUOghcmeaclmxVKBvcu2cfvaP2fQhSTqlmqSV+d9NB1vgfm3pf3DQXvYOwDhEFYV0I6xivdQiZrztsxlnLVqhZp8yWObEgZ+xae1MniElGKhGrLIk4pM/8yIUoH1/007TXfujERzjfZ2d5kBGMUHcWoDhjFpfMwY7dfOEvrrmaEq/X/oUpvjiVoTmxOKB41/IYFZ7R9Ccnwesg/ojm9Me3kMyJ+cjy6ip+9d538aUnnuaZ1jOWr0vVEpfr5dx6zIW4xHB71AREEM3c1gS8wqO15/j6liGuqzlHTGnoSiOmNKo8PZRJ+jCxqXC7rP+Qrr6umnPei3SHkw9RfGgVxOhC0DBcgIw/RGNobIBMoi37XW6qfYEMSrDOghHx4YuXOD84yNFLXVxWV8sda1bx0Wu22hJxKiMyHIZTp5KnxAXwed1U3uljfXkbDa7nrd/XIh47z02vTnc4na/IMAORxCu8i101ZNIcNxWX5dwZfpwFI+JHj5/kOy/unHi9rLKSdrtr6WxaDF6vi+XbGukpC1Mcc3PC108fIzkbjXPbiL6TqA6NRV6uqPLhFoVLEyIpRkSdGk9uNKJKnzVTwrjnAqE6MDWsamuf/c5d6nHVmceWra/n0apzXK7XMOqK4ldu1lBJePS84fOXZSrLNVqavIYJg+FLoZnRqUSUEVVeM3yjl1T2UeGe6kBf5/MRik1mghpKMX8jpB/ym4GCVSMNnO3pZ2WN89AFdpnXIlZK8T+2/4GXO7v47G2v4e9uvoElFeVU+It4//2/sp36yu4iy+hoFJcS6k67OXHE8BaLAa3VVWy41lZRlogt76S+wZpX2lnFDJfJKlueaTYErMCjaWxWS9nXaZgnVUWZxWq2w7wWcVTX+f2x4wyGQnzyof/kp+96Ow2lJZzq6cWtaYRjNvNX2HyGnnqlk5ZTGieiU4XVOVDKweGriYmLmHITUxoxXMR04199ymsNty7EYuASHZfEcEkMt+hoEsMtsYl/I9HMBpM0xHLica+nh/dd1mjEH2Yyq5Iy847s74Qz/THW+uop1n1c6hxhX9+kfV1flnsXzHHmtYg9LhffeNMb+MRDj9DW38+t3/shVzcv5vm2s84SEKY0JxK3TNEEOSr+/dcxnvHfyY6YNTfrK4uWsLcj/Yz9mzYHM/rG7HS0+iInEe/JiXcdP7oXUEsp77mGut5hjg0ljl/XUJbb+GvxzPtx4puXt/Db978Hv9tNOBZjx5k2RwIGsjrFpdsYDpstv4ye8ABl7mUZlzOqd3HkXBedQ8kXrTaUzp6I53VLPE5DaQlFHjfBqD1Ps80DHsoen2wtO872JD3Xrr3s7gYszrrOlmtRb7iPxf6azAtyjXLrxhK2H0ge0quhYE5Y48Wz56gqKuJs/wB9Y0Hb1xcHFW27rMVjszvmOdYehHXWzp2HDnKUlSYXcMDrocTnYMbUIfNaxHvPd/BPz6ZOHp4KLYcOMjKHDDW/VsFQaBkawsFeheH+PbUfq5TxejASxi0ay0o8xBRU+l4hRvuMMgcHy4DEQm4ozX3Un3jmtYjfcfkG2of7OT3RuTDXHk+EUBj/IONW9ZqrfAXwlKUOCRWPXXPZTkT1bAcS9MbK8EXqEN2D6B7cWjE7R+3Fn2s1zd23NFdDnIhlbDUHD62jqSb5dHZ9WW7jEU9nXou4ujjAF267nXc+eB8Huy4S1u0Nqa0qrrB8rt2GRctwds0OSkH56Ea622s4fWmU3pGpbqjLajzGOhwHRMfqkOiVRIPlnDlfyb62AaJ6P4fPJ7+mfhY7dTDPRQxw37GD/MmajXzl5ju485c/siVkD2InhII9HKaVdUJJ9/X85+4hIHHHNBPT5vCpYg6fGP+UrM2C1pUURGyZ3Rfb+cpLT/P5629nRUUVG2vrKfX6ONx9ie6x9C6PLmVdxHZikDVfW4O+2g1W+5oW9d7TvZhifxOaptCI4Y24ONUmPH+pP+V1jt0xgZiDhXp1pQVzwjIK+Kdb7mJNVQ3fO7CTw92d/OLud/GlF5+yLGKr2OmoqFUeXgw6CxqYiufPGgGWrqtoJhKOcfCctSWNmdjcThZM1xXMCetsbVjM9w7s5M8f+w26UjSXlhNTOnsupjDY4rAzH2GVxe9t5ESSx3oyTgU7WdlUhks0hgeNxa2DodBEPpHp7Dll7f2Nk4k5EUuSqzkVhZbYJnetWMv54UFiSnFlXSPvevDnRC0G0U0SJjghib5Klxti0+ZXzroGLD0F4umNjNIbMa8x53e3lLew6/yF5BfZIJOW2JGICzaxPRaVlPH5629nLBrh1p//K8HpqkqBZtM/aDpbPlqM7o8QOVnEiaeGGemPEdKzE5/C8dR5AjLpY0YciLi2ZHZWdIwz70U8znPn2+gYSbeSYSquVA4/mlC+vsEY/hJBeWcq4aVvjbD8M4P0rOrHt1pjlbaYKH52dUToDmY27uE4bUEiZrFjVxkowuueXVktGBGf7reQDXQaqVbAFzdXsO/9LROvbxQ/nDS2FdC0tpQlNwrHo8ZEQEzptJpea011wraiZsLhMnZfGKIvZF/QsTnSEkdttsR1JbNrD8MCEvF1i5YCsKS0nFWVNfzhbJowroArmvwL0nzTPpo4UbVsa6BnSZRjFXsTXqujaBszBL2kQeN6fzNjwRJ2dQwxGE5tbrx+aRE1AR2PPsDaRg8x3bh1TBmxDnVdkBEhpgu6boSq6h9RHGxN/EPxuISaehdFpY0p7zuOkftDJofllhbT3FRkPBkUKCUTT4nxoNogZtBtWFNdaek+2WTBiHh9dR3Lyyv5h+tuo7G4xJKI95eNsuEnb2ZoeKYAgigY7p94HS3XJhbsjDRpln3aYkrnzJgx5bu80UWzfwnDYwF2dgwyEpn6KGgsdtNYcYSRWD9hF+CZ9JWdslp/Wv7xVa4VHGytT3j/ijIv+7TDYMHSaimu5czItKxSbmyp5MrG2VtbN86CEbGI8NO73kFNIMDfP7Pd0jUD4RCdvghnRvrTdqReGLjAVW9dRCDkoi06jM9lf9wqqmK0jhlec6ub3CwuWsLgaBE7LwwQjMZ40+rz9EX6bZebavTBzkRHNnw4avyz54I5zoIRMRhJTj786AM83nbS8jUnhrrZsKie811DDIZCKc/d0zc5ubDSW+G0mgBEVJTW0dMArFvs5fKyJfRF7I3/TpJCxLYM4szt8BpfQcQZE7IxxDbO4f5LXNPQzK426+Oy2RwCC+thvO6TYN2pbgrTq3Ld1iraPe0oFFF9EKsL67LhPlkQcRao9DlbZWt3eDebk3031jbSFdrn+Prp4tO8Ov3h1PnukpTkuA7jVOdBxHPIddsZl0aG+cnR/QyEggyEghzqdhYieSRsrxks8jgIjJYEtziPzwbAdB8QcRZdW7Lw08yHiOd9S3yk5xKf3fEYX3zhSYo9HnqDztLClvjTL6cp8XoZCYe5YlENRY1t2IwvlJCtlfV0h17OqIwYGpvWVkxMzIy5nGVMzUrHriBi+9y8eBmfv+42vrrr2ZQCvklbQs+ZYYqKPBSXeafYA0qBNiqsC9RwdDR5Kr6t6xWjrkF0+hghw9bTpNQTYjjo0Bg2GVMeTpeemNzhuGqZibjE7cfv8mRUhhMcJ2MUkS9i5O7QMbIqfUAplR2PFRu4NI33b9jMVQ2LeNdDP2conHiEwRWBjp7kixsB1l3ZlPK4pvsYctvzUEuFX3MzFsu8vGzZ55n266p9s+v4M44Vm3g8GeMVwCbgDhG5BviqUupypdQm4CHgH3JWyzQopfC5XJT7kqeb0i3kr0gXgvj5I0ECl67Gr7LzZV1RUUN/pCv9ifOEfJgSkEEyRqVUfLNWTO5zbyelrb+fv/n9w5QpL2sCNUZuYXR0ZaR51ZVCLKyySNUQVRYJS6t0hF6urqjiUkzjleHULXsqijQ3SPYd5zMh0yG2OStiMJIxAnuAlcC3lVIvmfu/BLwPGABuyVUl03GhZ5DWl1M7AKn6irTlpGqJ79qoU1H96MTrRR5hfdkmnu3W6Qrbj3lxbU0FHcGZS+GdkaX1fBk2Q9W+2cnRMR1LQ2xKqZhpNiwGrhaRDeb+e5RSzcBPgY8lulZEPiIiu0Vkd1dX9h+duq74lydfpDJQxL0fejs3r0myrNfC95yqdz7THFH0h/dxRdlh/qjJy+aKSqyqwKe56Awds3TubJLp6ERtHqacwXkyxjumHfoP4I+SXJPTZIwP7DvC3rYLVAT8bF22mD/estFxWalaYj3JejydGH3hQ1S4X+TNDUO8vr6aUnfqHvqa0mpiKkvJHcleGKxMO3YN/oqs1MMuVkYnaoGIUqo/LhnjV0RklVJqfFznbiAvTcsjB18BoMRvRLX2umZOQnhcGu3n0vsbl5WEuLbBhUtAE4WmYWxrUFc+TLophKFoB9DBtZU+SjzrODro5lgCu7nGF6EjgQUi4S2MhCrM9lymTCcrDDdIMKeZZfJ1yO1npUuhUBORfJR5oq6Mjq8yrwt4NTRXjK5YJ0uLqqkrGzQDdivcEqWlrMa8h+leaU6B6HFhXY1/1eQ+pYgBjUX5MSccJ2MUkV+JyBqM99UGfDSH9UzK/3zzbTx57DSv37AagLEEiyuvaGzg8IHUo3/bNmus2vpLWlTisWY7c2BRFaI/vI8mP1xWuoz+aAPPd/ejEG6sreRC8HDC6zoGa3jmfPJx6mRsqmlkf2fi3BupKGsMEvFllgwnnqbAB7NWlh0cJ2NUSiU0H2ab5qoK3nfd5onXFwdmOs5qaZbmb9ussf7GJ4gkEXAmDERaEVq5paYEl3sLIX2UpqLpmc6NJnfUn9qLLhlObdlsxnfR0Cj3zL4vMSyAGbtxgpEo33z8OX78/NTVFs2V5ZxrS25K5FLA8fg9Kzg8dDDlOV53Ysf2dDjVYjZj/lV4K9DyFEVx3jsAjfO1/3yGe5/bO8MtsTZQTN9AYoG6NDUrAg64F3MumN6fwakDjtPx3WyKuMpblf6kHLFgRHyyM9n0bXJhxHThgX+7haET0wdbskuURgYi6eOYzXaY4mx++QURZ4HWbmf5nPsGFe0XsudWOQOlcT5oMdzULGewzWYM4UrP7C8QHWdBiFgpxZqGWqqL7QftCBSB1wNeLTfOKyXelYzFrDmoz3bE+Gx27PLZEi+Ijp2I8L33vxWARw69wmd/vZ2xiDGZkM7KXNmiseK6h0mRAtkxXq2K7oj1j9i5pvKfL6FgTmSRYp/XVpN28OUYHfvfQLm+IWt1ELyUea/iUqSMzpD1lSaOzQKH1y2UlnhBifiBvUf4y5/8lrHw5ITHeEvs0oQif6LpYCEahYd/u5QyWZHR/QUPJd5tjLGSw0OtDEXteblJOl/QpNc5umzBjE4sCHMC4Dd7j3DPr2fGmzje1U3dqgoisRgXB4dY2VKNpgmaGeVGE2HxquMs3fISg8pehEGloNx3BTo+Ijp0h/toGzqR/sIk5MMmzoYV5RIXZZ78TDnDAhLxhf6pM3V/ccs2nj1+hsPnL3G2t39i/4mumUNxod3N3PSanYjNQYpy32YOD51xUNsEKGFwtBRjDcL8osKTv4kOWEDmxAdv3MKS6goCXg/v3nYFH7v1WmotBnsuXxJgJGQ9o7hXq6TUu5Vjw06DnczEFd7CpSGnSb3zO+2cT1MCFlBL7Pe4ue/P30Wp30tYj/GDXbs4OdhDfU0Jl7onZ8uqKwIEiqbaxgeGuuhsr+eGJdsI+F9KWL5HK8fvXoxQxNGhNnTSx3pLh9Z7I6GQH83t56HzF7myDko9PtOrzFCYYPhGTCYzE0TUlH0e0agtCpjHJ5nqBaeYfoILF16tbGL35D1nqntqMrW4/SLU+qwFK8wVC0bEABUBP6ORMDf98nt0B0ehCKorAxDnGFa/soTdfdNa0DD09wbZVFdDIMEyPSMq5dUcGdqTlXoqXfCNXc5/HlCMhAdZ3+gjrMd46aKzlR7Ly3S6gvaXOPeMldGvZ/owVmwoLbTEWePMYB+/O/0yd7as4aev7EdXylaw6l8dj+LW7mRVRQkb6waoLtuOUhoXgncyFNEI+LJTz3DHa3no8ACYuZva+4aghFkf7s3W7arytCxpnAVjEwN84aU/8E/7drC6oobtb/kg2xqaZzz+Ukk6rMcYjUY40N3LxVANI9Hb+H3H9TzTeSkr9XNH6glfeB3bD08NuzIQDNLgn/3l7tkaDan25scFc5wF1RLfvGg5T7Sf5nMvPc4H1l2FV3NN2oIm018n4jUr6jg4epyDcU/o86PDLHPdgGmVTpQmCH5XjLC8kLxAJQyeuYNnjveiksQNavSVcTHkLHKPU7In4vy2xAtKxO9ft5mhSIiv7X2Wfz2yG4Byb/JYFMnQEmSk6QwN0RlKHKl6WXE1TUnWSCoFo2dfz9PHUy+PKlLOI+c4n+nLjorztcp5nAUlYoCPXXEty8oqOT3QyzWNS/jRkT2cCwxwdrSfSl8Rp0es5Paw+eWmOL3v9J08dzL9PUdGnSeqcbrSPms2caElzj53LVsLQDAaYTQW4WC/4b/QbyE+RG3Az3GbGekjegy/tgilwugqhE6YqArijTaws7XfUhnt/YOOO3f5XNlR5PIRcNt/2mWTBSnicd67/RfsumRv2OryRcUcGrYXHrZ9tJ/2UR9GuDrDrnCJxvLwSiIxa37Og8EQjTUldMymXZwFEee7FYYFNjoxnTWVNRPbZV4ff7Qylaea8VDui/Vn5d7rfMt56ag9R/0Gh738fJoT+e7UwQJviT+37XbetfoKjvV1UeUP8Mlnf5/wvPpiP+7yLqq8JfSE7SV0TERLUR17D9iffPDL7H4d2RBxvseIYYG3xG5NY311PX+0cgPtwwP0JJnVGo1EiagYl0IDjMUyixVc7S3l5b3C0FhmGUXt4FiMDl0/48n3GDEs8JY4puv81dMPUltUwoOtyaOxr6kt56xuP2jJdBp8lUTOVzKWhdbcDvk0J2p9BRHnFE2EzrERHj7zSsrzfIHgZPDaDKiJ1fLMeWcLVvNBNkRc58+v3wQsUHPiWG8Xz3cYw2SBNMH9ADxZ+i07iPCaX7Kg4gZ//lY5j7NgWuLO0WFe6DjL/ScOsa/rAqPRCJtrm2gfTp0eZl1NFUeHT2elDt7SzOzg4piH63xLwQwAyHhwwPG8yub2uE+TMh2cykb9bHQ3mcEEJ/Muj7+a2FaTpodSCi0cQCJrETHm7oyVLoZ7pWbO58nEa0CYcBMd90Wu9hZEnBUuDA9y+wP/ymh0qoj2dqUOIri6qoqIO7OO3DiCQCSzpCvBUJS9NhJCjrPFt4ijnfZjP1dX+zgxaGUGMzEuESq81hYe5JIFYU7s7+6YIuCr6xdz59LVFKcxJQJFwsUx5ykLxllSVIs6vYhn9uTHHnbasbOQxiQlVb6ArdzRuWJBiHhjdT01fmNlw5W1TRR7vHzn1rckTESztrqarc11XLOkgQtjA4Rj9haHJiIgRfQOZWFt3CzrQWWo4mp//lthWCDmRHNpBbve+Zd0jY1QFyhhJBLm8bMnuTAyOdS1takBt0uIobOvb2rCF1GCymDMNEr2or7PJrEMRTzecOSbBSFiMDobdYESgtEoP3p5L9/c/xyLSkporihlz4WLKFds5rIkE4/mJqycd8rOh7qpLqulZzBD+9qhppw+0a2kRUvFXGmJF4Q5AfD1Q0/wk5O7iegxvrbnGVZUVjCgDbKnvw0CIQ4kETCA2+5a/WmMxcK4srFk3aEY7SzBiifzlnhuiDiTjKJfBd4EhIFTwH8xE9PkhQ+s2sa9J3by/x3YzpWLazg11EVIt/aYf1OzD5fEaUjGs2YYf0bmCiaGmFBq4mRBIWh4F7cb28YJ5raZPUPGM19M7ps4BnGvT3PHVjejwVL+6UHrQ1dOndujemahU+aTOTGeUXRYRDzADhF5BHgM+IxSKioiXwE+A/z3HNY1JdX+Yv524y3s6jrLu5/6sa1rA64O+qPHHd+7zF2D5usnomeQsnxczwJakRuXdhcx3Zo4nban0VimIp4bLXHaZ6AySJRRdLtSE3msXsTIcZdXRqNh/vnI07avU3gzuu9gtJuApzmjMuLRibK0xoZ54tAMiUYzE3H1PGqJk2YUjeODwM+TXPsR4CMAS5YscV7TFDx49jD/fOQZuoMjDEftD3VJFkYX+iKjuPGjk525Z5cYhkwuicRiGXXt501LDMkzigKIyD1AFCOraKJrc5qMUSnFd15+jjPDvY4EDKDI3G2yP3KJMt/6jMtxhMOOXTjjlngeiXic6RlFReT9wBuB9yinXeQMeb6zlRODmabbzc44b+voccq9l2WlrNkgFM1someumBNpRSwitSJSYW6PZxQ9JiJ3YHTk7lZK2V/GkAUGw0H+98EnMi5Hz0JLDKDQQeZG62SFUMT5j7fU48PnmhvTDJlkFD2JMez2mBmI7kWl1KxlFY1Ge7j/xH/Q4O3DVS5cCgpdoYnBMFvoGUx0TKd19GWWBzbRH9qftTLT46xn52TKvVjzsLKkjhrP7EcsSkYmGUVX5qRGaRga/RUe1zKGx37DreXf59YpCwsEkRKUlKJTQn90CYcHm9h+qYRdvcbxmSii2c5jN8tr5axENUqEIHhdbkKx5C1yseahKVBBpVbMwGiIE7097O/rpKZodqMVpWJuPA8sMhp8hq7ejxHwv47qii8yOPz9aWcolBoCNYQGVGnHuakCbqoAkVoG9HXs6FnON09M2nJvWeYnpGf3C4llMl7sADvtsEJR4vMS8Hnwu9yUFruMyRpxoaEhStB1xWg4wqWREbpHRzne1w/0TyknGJ07/iLzSsTB0E4ARoPbGbu0w9a1SnVRJk9zXZXGN1k3sb8xEMp6bPZwNPP1eulQKMqLfVSVF+Ev19hcWo/LJYgGShS66ERUjLAeI6hHCMaijERDDEfDDKsQw0DRcDFnzjkzpYIpWu/ZZt6IWNdHGR779cRrp33JCvdJfn1tiPEJ414aeCFzl+IpDOoBajxVDEXSB+JWugtdryQWLScaqyASLSUYCVBbWU9pqYYSRVTXieg6oViUsWiE4UiExtISjmrn6GGAEzaDvWSDqK4T1XXcWv7db+aNiAeDI5wd+FPWNQwT8N9CV98niEQdJHnRz1FMnCum6/bsVdIkOlxF12AFkeBKQsEAoTEf4bCbi5UuRsIwHNYZDMUYCoUZNjM9bW1axK72eCel1Cs8aoqLMnbfytSfPRiNUuLNbLYzG8wbEX/7qcP85KUQX7n7JBvqv5HFkrMzvK10Qetbz9n9l7H7YD/6xLC5DoxRUuTl7Mrkrpp29ZTpqgxnd51KMBopiNgqwUiU+3YfRAG/O7KVDfUPZq1sXQlgcWxXRUFCxvkqjCKCUMpg2x089bsBIlEdSLxEKX0eZXuCytQXGDJvicfmSOduXog4FI0SMT2udrWNEYqW4HNnZ0Thud7l/LzN2vTrokA5V1YKD5/vn9J+X4WYAk5OehHbE6WuMs9Al2l84mB09qIcpSL/VrkF4l0GQ9EYf/2bv2Mo1JCVsnUbH8H50QEemiZgq2R7+ZyelVn+zMoYjRREnJTW7j7+9hcP0zdqTEJsPzq1A3e2b4R/fPwvebr1g5zouY32gasd24iGOTELpL2NvXrE8uOqMoWROdISz0lzwu9x89jLp/jDsVOU+n0MBmeO5B66MMShCzWAEb71qx9YjmgxMNdQJHJknFyvMXms2K/xxy2TuQp+3z7CaIbeXYlI9+geiYRZVllBa1+/pfKyYxNn9gOeKy3xnBRxY3kpBz7734jqMcIxnf9y7y85dD51BqMdQ53ElJOORseUV6WejYw6dOlMRTq9HOnqpNJfxOqaao53z0zdO51YVmzizCiIOA2aJng1Ny9f7ODYxfQzYCoLXyrk0L6yoJi+4Bh9wTFW1VRT4fNxtLOLkSRCyXSRJ2Q+OjEayU70pEyZkyKO6TrPnzrL9qMn+NW+I5Y6MU6dYKaTKwvZzkjAiV6jJV5SVk5ocJBoAsFmwybOdHRirrTEc7Jjd7Z3gD/7yQP8Yu9hi71wlT0R5ygs08BwkGv89nIgnx0cYGN94lGYbAyxZUpBxCmI2PRzdWUrXTzj3cLsE9N1vA7yKCfzTciGOZEpI3PEnJiTIrYbD8GVxXeRrQSFyUq3fUWSJ0Msw5gRqcq2ylhhiC0xSikWVZSxpKqcs73W/HKz6UiVK3MCEtvtLSXleDQ3Cp2ortBRxJSOhBVezUVJxMUqfwW6eb1SgK7QEGIxtxmmxYxJLGoyRrGAHj/YKJPrScfPL1E+I86wgC4K5Zp87/F1VcroBMbHNgZnK0NywZwScVtPP//1Z7/l4Y+9n+//6du4+19+bGkx43wwJ8zCZ+ALuTndPTNGcPUFjdFojP0JckGv9JRyviN9GNnqigB9A8lXrQTpZzxu6Mpbmnlu2F5s5JGaQks8g4qAnwv9gxw6f5HLGuqoDBRxcTC9j0RWW+IsmxOLFldQtqgYpcAd8HBlcUNc8CpFT7d9v+iYxcg9dmIHO3kAjc2Rjt2cEnF5kZ8vvvm1/OkP7+eqpYtmCHhRrZctW2IgChVzEYu4aG0VOrqylywj29ZESUUROzvsR39PhWUR2/h1O3n+jIULIk5IkcdDOBbj+VNnp+xf2+KneWMHZyKdTJh6XvCsga0b66nxbqQ7fAhRLqp9y1CU4BLoDA0TjIXMcH7mf9XElrlt2pQoqgId1BZriGh0v3QlF/tGpubIYGY+jNObgrjunBqVvtldTvBgCF+JC7K8cqRiURm1zRUIQnQ0wivHE6/ssGNlOfnxzpUhtjkn4tvWruBb77ybv/zZ71i/vIhlyxT9/lMMxYbpTPKZXQpfojMsNBetQ9N0Dg1eADozrstIMELfSPpWPhoW+sNTbc9OhnGv0NDKPOkWadjm4IXJKfitzU1Jz5Mcq3h0jrTEc3KIbX1jHaUBF+WXHeec5wBDsfR2sUJxdqyDYlf24iFY/V6TTbRElc6Ynr8v2s5Ii5NI+QWbOI4fPrcHXenUl5XSOzLKz3Yd5Kr1fvpi9js9RwZP0VLcRPtY5s2fZQmk+P5HcuBMNPXWyW+u2WiJnXikFsyJOJ48fppdZ9oBxbJFfs70hFi6zHk4KC3DyO8TWGzJUglpOBomtxllkpdtK7ORA3NirrTEc8Kc+Pwbb2N1YwV3v1GnfOMh3vwGDdVw0nF5WpZEY7WUVGMFQ5GQo06TVV+QVHEc7U3c2DcnQtFYVmYOM2VOiHh5bRX3vP0K2qInUSjO6C8zEHXepc/WWK91cyK1AEoD+VkRbMeccPqRjWUQlDBbzAkRA9T767JXWLYGey137FJTtcqXcVWcYKtj5/Aec8GkmDMifqLTXliqVMy2OZHu0X98KNP4yc7ubee3PJ9FPCc6drrSebFnbxZLnN3UnFbii1duMD7q6oFSTp7LZvrc5O/Vlk3s8CObCyMUc6Il1kTjk2s+SpFrZhpbJ2Rt6tjy6ER6Lo0Nc2lsGFWTbc+v7HTsnC4qCBZs4klWly7n7y/7q6yUNdsdOzsrhV4e7GTzlfVs3lTP5Wuz0Q9INcRmvZT5bE5YSXfgF5GdInJARI6IyOfN/W83X+sisiUblVlZ0kKtrzoLJc12x86eBF4cbOPFoTaGizJ3XEptE+e+YzcX4hRnkozxMPA24P9moyKDkWF+ee5BukLpl6vPFtnq2GVKWZmfsvIiujoHCYWmmSMpbj0rIp4D5oSVdAcKSJSM8WXIzkqIE0Ot/OzsbwjpYVaWtIzf1/h3siZT/HDjD04XUZW3kqWBZgRBRMz0tpq5bdR3usmR6G0EF9fSUFqB26Xh1sw/l4ZL0/C4XHjdxp9qSD7gn0rgAfESKtLN+wsd/YNcGhpGAa6GyffXHwtxrKub9RtqcQ/CyFCQvooYXpeLXp+Ov9hDcGTmY314NITH7SJiYWFBsQabVgbMlSHmh2F67aFkcinu+H/MeWql5X+dXbaSMaa6Nm0yxlWly/iH9R+3WuTssS79KdnkB8/t4qHDryQ9fqSzi9qSYrw1LnoGDL+SDoZYU+pPKOL2C32UlhYRGU4v4mhXH5HLDtuus1Y2yx9SojpYOSlVMkYL1+Y0GeNC4Xz/IN95Zmfa87qGRzg/MHU2U3Mn/xqtPifdXmdP1JCe/5Y4o2SMBbJHOBZjJOxMEFqK5d5WfYpdHodpxOaAiNOaEyJSC0SUUv1xyRi/kvOavcrYeeZc+pOSsOadQVq06DT7e3z5S7/RH1BGz0CU2S+Y+BdQbsY8PY4Sq86FljiTZIxvBf5/oBZ4WET2K6Ven8O6Lmh+/OI+x9f2u7voijic2hbwagFGo86G+8Kx/I8TZ5KM8QHggVxU6tXGrrZ2Lg05j3yf6RBfJiNMc6ElnjMzdq9mjl/qZjiUiRjyF9KqIOICvNh6ji9vfyajMvSUbvnpyWSkP5THNYTjFEScZ77w+ydsB1CcTsbmRAYyngujEwUR55mlVRUZl2HFFTQlGTTFofnQsSuQO4KRKOcs5uhIhZ5hS1wSvQyfboSTEQCZPlRnhiUUBUohMukA4IpWZHTvbFAQcR65f89BTnbNDCZoF5WhTbzj3CCDYWehBVZX+BKMXc0uBRHnkcxGJCaJNyc8UoRfSs0wr8qMy6pQSkehzE6gsWWE8dKJ6M5t8rkQo7gg4jzymtXL+d6OXRn75MaPTlTICh6zu/wpg2X3cyE1bkHEeWRdYx0fuHYz3302veNPox4gGInicblwuTQ8pkuo26XR3xtgWIWJKJ1TEftRkzIhWOjYFWjtsdZqjoWjjCQxP1zDUUbIJFyW847hWDSCUiqnEfbTURhiyzOvXbvS0nmphtEyHSfOZIQuphSRPEcBKog4z9y6ZgUBjyftebnM5ZzpjyAYy69dXBBxngl4Pfz4A2/H60odBFFP0dplOtmR6c8jmOcRioKI5wAbmup58xWXJTy2rX4RW6obU6ZFcxKWNR5rCS+TM5bnzl2hYzdH+B933kKRx8OPXzL8irfVL6L1Qi/7Tpy3YLPmNzFjvofZCiKeI3jdbj71upuoLPLzk5f2EQ7F6BtOnr4rHjW+iMMx8zspY8GcmEO4NY2P3rSNaj3A4bbEyWQSkeu4F+komBMFpiAiVBb7abVxjVOb+Mb65dyx+DLO9A/yry/vJuRwlCHfUYAKLfEcpL6i1N4FDjtmwViU6+qX8anNN/PUW/6MP16xwZFhMRrNr09xoSWeg9zztlt54tBJSymBb1jbwuuuXkHrUA8/PrmLkRSCWlZSxba6Fq6pW8q22qXU+CczTTUWl/G16+/iQ+u28uU9T/H0hclngd/l5q3L17O0tJJ/OfzCDI+3QseuwAzKi/185U/fwKd/+kjaWGfFfi9vWboREeE3bYemiLi5uIJr6lrYVruUa+paqC9K38JfVlnHvbf/CTsunOG7R17k+sYW3rnyCir9RQC8Y+Xl/J8DO/jJ8X3ElGJJSQUryqsye8MZUhDxHOX6tS1UlwY435s6d8mj+49z++UruWPTGqp8Aa4xW9pr6lpoCpQ7vv8NTS3c0NQyY3+lv4jPb3stf7rmSo72dnJXy1rc2Uyu7YCCiOcov9l1JK2AAe7YtJob1y4zrnnth3NdrQlWVdSwqqJm1u6XikLHbo7y9ms34koRgsrt0vj7t93C/37vGyj25yc701yhIOI5ikvTuGnd8qTHv/3ht/CuGzbl1QVyrlAQ8Rzmo6/blrA1XlpbwbWrE4fJfTVSsInnMOsW1/Nnt1/Nb3cdpdjnpcTvpdjn5XVXrC60wHFIxjELbLBlyxa1e/fuWbtfgfmDiOxRSjnK/VIwJwrMewoiLjDvKYi4wLynIOIC855MkjFWichjInLC/Lcy99UtUGAmVlri8WSMVwCbgDtE5Brg08AflFKrgD+YrwsUmHXSilgZzEjGCLwZuNfcfy/wllxUsECBdFiyiUXEJSL7gU7gMTMZY71SqgPA/Ddhtm0R+YiI7BaR3V1dDpOjFCiQgkIyxgLzHlvTzmYuu6cwkjFeEpFGpVSHiDRitNIp2bNnT7eItDmrqiNqgO5ZvF8qCnWZSXw9ljotJO20c4JkjNsxkjHeDPQopb4sIp8GqpRSn3JakVwgIrudTmVmm0JdclePTJIxvgDcLyIfAs4Cb8+0MgUKOCGTZIw9wG25qFSBAnZY6DN238t3BeIo1GUmWanHrLpiFiiQCxZ6S1zgVUBBxAXmPQtSxCJyhYi8ICKHRORBESkz91eLyJMiMiwi38pnXcxjnxGRkyLyioi8Psf12CQiL4rIfnMG9Wpzv1dE/s2s3wEReU0u65GmLh4Rudesy8si8hlLBSqlFtwfsAu42dz+IPBFc7sYuAH4KPCtPNdlHXAA8AHLgFOAK4f12A7caW6/AXjK3P5L4N/M7TpgD6Dl+DNJVpd3A/eZ2wHgDNCSrrwF2RIDa4Dx1PWPAX8EoJQaUUrtAIL5rguGA9V9SqmQUqoVOAlcncN6KGD8KVAOXDC312F4IaKU6gT6gVxPhCSriwKKRcQNFAFhIG0EmYUq4sPA3eb224HmOViXRcC5uPPazX254m+Ar4rIOeBrwPij+gDwZhFxi8gy4Cpy/3klq8svgRGgA2MC7WtKqbR5g+ftkn0ReRxoSHDoHozH9j+LyD8Av8P4Rc+1uiRac5/ReGeaetwGfFwp9SsR+RPgX4HbgR8ClwG7gTbgeSDjMJcO63I1EAOagErgWRF5XCl1OuXNZttene0/YDWwc9q+DzBLNnGyumC0Pp+JO/YocG0O7z3A5LyAAINJznseWJfjzyFhXYBvA++NO++HwJ+kK29BmhMiUmf+qwGfBb47B+vyO+CdIuIzH+OrgPT5cZ1zAcNpC+BW4IRZr4CIFJvbrwWiSqmjOaxH0rpgmBC3ikExcA1wLG1p+Wohc/xL/2vguPn3ZcxfvXnsDNALDGPYobludVLV5R6MUYlXMHvrOazHDRgjDweAl4CrzP0t5v1fBh4Hls7C95OsLiXAL4AjwFHg76yUV5h2LjDvWZDmRIFXFwURF5j3FERcYN5TEHGBeU9BxAXmPQURF5j3FERcYN7z/wChQYbty5lgMAAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ms_counties.plot(shapestats.length_width_diff(ms_counties.geometry))\n", "plt.title(\"length-width difference\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Ideal Shape Measures" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next class of shape measures are usually taken to be *ideal shape* measures of compactness. This means that they construct the relationship between one (or more) aspects of the polygon (such as its perimeter or area) and compares this to an analogous value for an \"ideal\" shape. \n", "\n", "Ideal shapes come in a few flavors. \n", "- \"relative ideal shapes\" are shapes whose properties are fixed relative to the original shape. For example, the `isoperimetric_quotient`, compares the area of a polygon to the area of the circle w/ the same perimeter as the original polygon. Mathematically, these measures generally are constructed so that they vary between zero and one, and are one when the shape is the same as its relative ideal shape. Measures in this family include the `isoperimetric_quotient` and `isoareal_quotient`, as well as our implementation of the `fractal_dimension`, as will be discussed later. \n", "- \"absolute ideal shapes\" are shapes that have some fixed, known relationship to the original shape and serve as a \"bound\" on that shape in some manner. For example, the `convex_hull_ratio` compares the area of a polygon to the area of its convex hull. Since a convex hull is guaranteeed to be at least as large as the original shape, this measure also is between zero and one, with one meaning that a polygon is its own convex hull. Measures in this family include the `boundary_amplitude`, the `convex_hull_ratio`, the `radii_ratio`, the `diameter_ratio`, and the `minimum_bounding_circle_ratio`. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Absolute Ideal Shape Measures" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `boundary_amplitude` and `convex_hull_ratio` are two simple and very-related measures of shape regularity. The boundary amplitude is the perimeter of the convex hull divided by the perimeter of the original shape. This varies between zero and one, where one indicates the case where the polygon is its own convex hull. This is because the convex hull will always have *at most* the perimeter of the original shape; it will be shorter than the original shape when the shape has many concave parts that cut back into the shape. \n", "\n", "In the map below, you can see that the counties on the Mississippi River have very poor `boundary_amplitude` scores, since their boundaries are very wiggly: " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'boundary amplitude')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ms_counties.plot(shapestats.boundary_amplitude(ms_counties.geometry))\n", "plt.title(\"boundary amplitude\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Related, the convex hull ratio is the *area* of the original shape divided by the area of the convex hull. This varies between zero and one again: since the convex hull always *contains* the original shape, its area is always larger. The measure, thus, is related to the `boundary_amplitude`, but will be different for different polygons, since it pertains to *area*, not *perimeter*. Generally speaking, perimeter-based measures will be more sensitive to non-convexities than areal-based measures. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'convex hull areal ratio')" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ms_counties.plot(shapestats.convex_hull_ratio(ms_counties.geometry))\n", "plt.title(\"convex hull areal ratio\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another useful measure is the `minimum_bounding_circle_ratio`, sometimes called the Reock measure after the author of the first journal article in which it was used to analyze congressional districts. The ratio compares the area of the original shape to the area of the smallest circle that can fully enclose the shape. This measure strongly penalizes elongation, as the minimum bounding circle has to get larger and larger to contain the shape. It also varies between zero and one, where one reflects the case where a polygon is its own bounding circle. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'minimum bounding circle ratio')" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ms_counties.plot(shapestats.minimum_bounding_circle_ratio(ms_counties))\n", "plt.title(\"minimum bounding circle ratio\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A related measure is the `radii_ratio`. Instead of comparing the areas of the two shapes, the `radii_ratio` actually mixes the reference and ideal shape concepts together. It relates the radius of the minimum bounding circle to the radius of the *isoareal* circle, or the circle that contains the same area as the original shape. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'radii ratio')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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6psV7CZwy+ugIDifpLT00SWxf5n7zvMVbd440ca4ndfASEGKAN11yCReVVnKwuZ17Hv5jwnYNG8psEWJJksss17ngref/nX7euoI8VuS5p8RfKAQo9hoE9Wtjr02I/YkyQczoMWVEj2Hgcq3M5p+TFimFWER8wE6iuT5dwINKqX+a8v7/AT4PVCqlLuRqoNmysa6KjgHrZkR5QYSXl0Sz/cXSAE7YoTO5EMnVx5BaQOv1AMsKNoOCPqOQu168emL9I1rVaPrdYPyYCeQbbozYTo6aoiCFrl/N6r83HP1Ll7rShWETxy3GqJTaJSL1wE1Ac05HaQNhw+CPx2bvzphKsjuqISFOjSTOo5Y2OVbFunF2IoJDD1fxdMfskNF02FJRgDVv93TyXRU29JKcbIsxfhH4KPDLnIzOBo6c7+STP/sdp7t7iSTLsQRzVGJy7lJK6ZKbBIWZUOTObfAPpOnhFhFdRA4AXcBjsWKMtwDnlVIHcznATHnsyEl+/sIRDNPENBVf/v2zNHZcSC3AgKYk57EHua+PNIlONkKc/Ug9Wj5ePXcbRMexWoxxC/AJ4FWpzp3riqIFPi93/eQ3fOZXf+Qrf3ELL79oNU+daErr3JqdQQKNITRN0HUNl1tH1zV0l0aeuGCdDQOcw3KUWhaa2I5hFrlzG702jtVijLcCq4CDItIELAdeEJGaOOd8Qyl1uVLq8srK3AZHA1y9ZgXf+8vbKc7z8YHv/ZLPPPx4+ifHvjnTVITDBmOjIYaHAgz0jaJCdkmf9X5UhtpRJ4vt+xai1WZSuFCEOEExxv1KqSqlVINSqgFoBS5TSiUv3zNHbF5ewx07thGMGGmFV46TtKXFON1Z3djSS3pko4nt0MVFrtzbw5BFMcbcDis7RoIh7nt6X+YnJvnebFBMAARb8xgc3YJoRNNXaSaiK/LWHktjvSFDTZykUlIqMtX68ZgrTZyOd+IQcGmKNg12DcgOvvfsfnpHMk+1mqoOmx2c/YHGIz8Yf6UBUdv7jm9fiWgmohuI20DTDMRtIpqBuAxEj2CsHk6YzDse2QQi2fFRzJVNvCRX7M71pJeZPSNsirwW72wNFwkb3P+2mbd+nenZG+CKpyIsy2ABTCRa1SgTk2ry5MxPmcmCsYkXI3defyUF3syzOibXxNmppvxRD2uaSzH7rN/iTTPzr0u3GAbpaOJ5ZlVlGT/6qz/jc488ydMnm9I/MckXZ1Z6qdZXo4kgItFHmJLLQXBpcGqskW3PVqL2jSG6TPyNnR/h7K4XOZ/Fv8sw0rclvtX2Tr7TlE/YTJws+3W7yxluGkJ0DU2LjnP8sfZ6A663PlaXePHrJdY7yORac3KVOeDI+U7a+gc51tbNRbWVvGrTOu68/oqMhDiZ8hlxRTg6kDzjpVdzUV2Qh3YmwtH/SV4iwQpmBkLcFcqjfTR5tvfQhSAdTb1x36u/JDt3aKG7KufB8OMsGSF+7MgpvvHknonXDRWltPZlmLk9w3uoV3NxaUUNYTWKWzxcCF2gLzKKqNxkxzSM9M0JM447pTLs46KBInQDdFMY60uSZ8OiPaEMF2gRCudguXmcJSPE5TOyLjZdyHxyl+n3dklJNSdHG6n31RE2R3Bpbmq9VZhe616BZHQFavAMGdHM8Upi2eMlKrAisWMaphKCHfnUd07/TFb4C+i690h6F7NYcOm5R27nTNsQt73sEqjPvA8rLGohVkpx9y//QGNHNx+/+Qb+7tXXUl9WTEmen/d8+6HMZ+XJ2se5MwaMCBoahpHH4b7JxCslK0oyu26a/GvjlZzc059m69lhp9WevAyulr4poBRgujm9+zYaW6J3vyLf3BWpXtRCHDFNHj18gsFAkL9/8Lfc/57bqC4u4Ex3Ly5dI5Qo43MCMlU+Rwc6cUk+3Wp65iCz0k3t6xvQ3DriEsSlxR5jEz2XhugauATRwQi5CRuAoVARc+JRRUyImKhI9HW/lp3LIJMkW92nwPfEjdEFGC2ag1j0yVokrrWnMUq7CXVfzlBvNQePeGjumjTfqktzl1R7JotaiN26zuf/18189Ce/obmnn1f/+7e5omE5z51utuQbtbLYEVGzTYdnq7u5+q5VHBpILznLCjawt2Pmir3GTA/oxogGWbjAtQyWHRtf6KYxQV7CunXluG68gab2IF39o0RDzoPT2lTnsLzBTBa9n/i69Q08+IE78LldhCIGz5w6Z825DzZHmKXfmfUtRZnRHh6l+srs97xdaBvihRMDMQGOTy5rdMxkUWvicWqKC/C5XQTCmS0kbPWVUXB2MkFeW1d8dxNkXh85ksHcbo48UbQPDbPKBls1NBJie3klu7sSuxxzWaNjJotaiPecaaE0309L7wD9o5lnW8hXOk0n0k2ikpmk9QbTH89cRrbZhTaYeKNdntdNgc9aHTwrLGoh3t/czn88Zi2HA2RmI2ZKJo7+XGviFeXw7tccA6WhRYD3q9gvZ8rdJRZqaroHEeUidH4Fmtvgue/kc2rP7HSuZrGbRFlaqksK52yhAxa5EL/l8k20h3toNSdva+O7kJWa1HATx6acK0D+EPBYbsamzaN+rSoWVtfo+DwKrwdqSwxG1dHomy5Sf+sCLI/mq6tZ92pOTa4hUbWxmuCmkqQmf1Xx3LnXYJELcXlBHp985at4/55vcbS/lXCcumvJWFWWwdJqhjKpZaCJMmkbH8WrL9NZv6aDoNbMmDl9pbLEU2d50ppXXcjyHVW4ir2MlLo42t1DpCt5Rv3KOZzUwRLwTvyydS+3LNvOD6/9EG7JrNyAK+vyBInJ7IPNzi3yjpsMqtY8Rj+HZwkwZOf9aPOY7PWNsivYx+GO7rQ23FblsARuPBa1Jj7Yd46vNP6Wj268hYaCSi4uXkaB28fxgfP0hkZSnq8lydQzm/QF7ZKSKgo9roQ240zSFTF/ZTRWAwWiFBuruimtOEm/0ZS8f9Es/04ydPgAUDnH5sSi1sRKKT615Xa2lK7ke2eeonGwjfetu5GGgvSCT/SMJnbpty30uDg80GR71/v6zvNcfzOXrjnLNRtfREofSynAGXQfl0gk87MrHU2cPtvKGvjemaf46Avfx0RR5y/FVIqDfekl0c5ME6fH1VV1tI5llsaqU53n0hX56Gi09+oopRgIBhmJxC/yEtafZSAj89+6GIciM6fEqZlrTbyohRjgptrNdAT6MJRic0k979/9LYw4S8Hx0DPaKTH7i9RldpbIrmA/vaHMkhIOGkMMGrGAnZgS21x8EbvaUldzSodsbOKIhTSxjibOkBp/CXdtvIWAEeLNO79I0Ez/U9cs1J+YymXl9RjKQCnhxEA3I0aIkJlFrocpJClcmjHZ+GxDFv45FYWZRMtlz6IX4nH2XDhNVyCzIHhJJsSaomxNQWwhQqKf1Iwv9PkLLdTl59MVGEQXjU2l1RR6PERMg8FI5rutp2I5/sNmQhlq4tICPx733IrVkhHicyOZp1MVI7EQF1b7af6zyciyiwr8MFH2WNGQX0pVXuGE/W0ok+OD0du/hrCheDl5LhdNIx0MRzJfEjdtVMXZmBOZauLKorm1h2EJCfEV5asBWOYvY1VBFU93H095jpZEiDXPjPemaMZtZTUoLcALvU1xzzVRHBuICrQuGhuK6vHpGmdG2hkzklfkvHiwAf+YD83087JIPSbRpUcThRJQopDma6L5KDQTNAM8wxhlJ+L2p3AzGFqOlsaWqRrfIF7dYHwLLMA1l4bZtkGiOYyVYJrEdpMQez75Wpmwojw3W7OSsWSEeENRHSvyK/jIxa+nyleUlhAfL2xjw2dqGIlTkcgQA6bcSqN3yOgCtttlEExTUxrK5OhAW7QP0dlQvAK3BmeG2wnMsN9LIvl0P2nQ25+80n0T0wVl4/oG1rwlvhBrqoR7T44CqTXk+9cN49ePTjtWufpYyvOmsq7o5oza28GSEWIR4WtXvIdybwGfffEXaZ0zFBmj1zdMa6grqvGScHjgLFdVr8CFm55wH27J/KMLK4MX+6Ob9r2ai/VFK9AFTg+3ETYMinfW0NLfn3G/SedtGa1iZu9y9LvsSM2dGUtGiAGq/cV8ZN/32NmVvvY4M9zNRUV1dAR7UtquxwYnE+KvyMtuS3vQjHA4JtA+3c1l5jr2n7dWWy9JnRvIwBduhxWep+c+M/xMlpQQA5ZcXMcH29levpKD/enXes40SD4ZwXCErp3B1A3TZCz0cnZ2RlAoIqbJzK1DiRAbNHGeo4mzp9jtT90oDmaaCyTj2Jl88Mru9RxqT56YJRnaDHMiYHjoCw1m3I+yIb7a7yrLuo9MWdSxEwDdgUEeat7NYHiMwfAYxwasJYpK5TWYiVd3p26UJpEsK/TOtIlDlhdxbBBi3dHEGdM42MbnjvySLx57BL/uoT+cPHVTIvJdvpRt8nQvY0aI9YV1dFnYDhWPbQOrOX0ieXxuKgy3oMztQDShSo9Vy8SG3Rh5c1AtaSaLXoivrlzPXRv/lK81/i6pAF+cv45zg8MUuD0UezwzarkpBkeEel8dLYG2hH3UeKvoDozQPDRiaQEjHq5WN0Era7tTCBYIPz4Lsap0TFmVyYhsLSSPVoBLW4B+4kTFGEXkHqK1O0yiVZXeqZRKLAE5QheN21dezZaSFfzVnnsTCpdSwvnR5MvSf1I3q+TINLy6TmfAvrrQPtNNT4e1O0duyE4T+/W5t4chPZt4vBjjVmAb8BoR2QF8Xim1RSm1Dfg18I85G2UKlFJ4NBdFSSZ16cUiJP8Sz46cZ3tFDcXu1KZHOmwcXEFHV/Y/Crv2ZGZb4mA+fMSQRTFGpdTU6W8+c1rcajqtF7q5+8HvUKjBOinC1BWmBoaYKB1MTUFpau9DstoyPrwUqWL6h8Os01fSafbRYlifkflNDz3P2+dWs4fs5vnz4V6DNG3iWNGZfcBa4KtKqd2x4/8PeDswALw8V4NMRdeBdto/sDdpm/JP5sOm5P0k00QrVANPH+5j3HoS4IpVF9Pma6HfzLyo+eYzqzl8YUEUm5ogWy00X5o4rZ+eUsqImQ3LgStFZFPs+CeUUvXAD4APxjtXRO4Ukb0isre729qEIxmmafL9ex6kuKKQLzx+N1e97rK47SSS+itKFu010y+sgD1nO+ho9LJ+9CLWuJanPTHymW6O78/Sr5YTsjMn5mO1DqwXY3zNjLd+CLw5wTk5Lcb4u+88wYtPH6eovJCt11/Cze+9MW47SUPCklbsSPD9RkyTF1o6OXhkhLKulWyWDeRJ8hn66rEawpnkuUqBXTZxtjnhCuaoRsdM0vFOVAJhpVT/lGKM/yIi65RSJ2PNbgFSh43lgMd/HM0AlF8c3U3g9s7+J7k8Lo5sSO3G0iIulkktgjbxhQoaokBCqdMytfQP0tI/iN9VxOb6Cob8PXHt5rxzecTLH/zeW4fYsLIPERWtAzL+iJpyLCr8Wuw4olCeQvT8PjRMNFEIJhoKTUw0TESirwWTC5EyWsaKeLA9n5dXCSdDZbF/qSIo+cCrYt7m6J8WuzYTx8zYdU2EaCxmdEwGPr025WeUCywXYxSRh0RkA1Ej8Rzw/hyOMyEf/q87ee5Xe3nZbTsACIzMniytfuMmHs1LvkVhra+avYf7GY0mCo7TIn2/8Fgkwp6zUXt3feUaSivghHkOMWHbmbUcPhjfFr526xnKC/+Q9nXGcbkvxQwfSKttkQtWF8L1hXDO2MEfz0+6xZqzdH2/cUVyF2WusFyMUSkV13yYa2pXV/OmD79u4nV3y+zVL1XuIVkQzFpfNeebAoyGLeyKTMGJ7l7ohmJvOTed8hFo6+EqFV2yVigEmbC3O04WUB7fpE+BxTJfNqba0tAocRfb1l8mLPoVu3GCY0Hu++SP+NmXHpl2vGZDDQe3J7Y/cynAU9nS7ePQQ4eTthl8vdV4DKtCbF/oTKmnGC1pTGjuWDJC/I27vsevvvborONFl1TRmR9fQAWhbQ4EeF04j8hvW1K2UxYDd6xOyOJVWLJKuWd+VutgCUSxjXPuaGv8N5J4JRQKqQtw2Tr7vSZTWXc8Qk9bf8p2ymIyF6v+XTs1cbm31La+MmXJCHFLo7WwjREzyKDKXfyCpqBjX3rhoVY1sXUfm32auMzjCHFWKKVYs3UlJVVxJhYp1JRHXOiiUeTNTfTV1mABw0lqW0zF6i79ZMvlybBVE8+jObEkbGIR4bP/8wkAnvzJs3zh3V8jMBrzRqT4gms8xTSetC8ybVrfpofiP14gdX7OKHOtiU1bNXGJbX1lypIQ4qn4C/3T7pKpthGdC/Swed0yGHFzuM2epWCfEq7tKWTw0SbautP/gVgWYovY6WIr9zqa2BYe/c7j/Ptf/jfm1ETQMRl2GeCLaAzPKFkrscQkPd5e1lWWcbI7cQWlVHiV8MqWfEYOd9OcQWH0cUyrQmzRy2B1IhmP8nm0iZeMEP/u/if4wru/Nut4y+OnuOZUKZFAhAtNF9i+fSXaRIVPDXFpDL48TKPPpMPMUICV4rqhYgoGTLSBMP2N3ZxqabL8b7C8UdOq7NukiXXRKHYX2dKXFZaMEHeemx4h9xf/8Bb2/GY/J/aepv3YZIrU5r1Ns85d3jUKdyzPeJr7iv5iWu8/jPV9ypOIDoUX56aweSKUTZFDpe7SeVvogCXinQC4/a5bqFtbg7/Axy1//WrefvftlNeld4sru+YSLtfTyy4PUGm6eVVnIZ0PZJbiKRmXfaAW1ma243oCy+aEPUI8nz5iWEKa2Ov38pVdnyW/OI9w2OQnX/89za29VG5YRnfjpJ+2dGUl/rKpSaCFU13DFJuKyzdUsNeMn12z3HSzfsxPwaii9cdHabIhlLL+QxsxynWqqhX9tc8SppQxVR5dn5FoUj81kdxPYub9zOPgVz68El2wSZzURc14BF1zUTKxpWuqcTH1WSyab5q8T2+5zJfbxaJULBkhBigqK2QsEOKOd3ydvv5RKC+jZLUfpghx1au2c6RphqAOBRgcCrBu9YoEpegVV5SUcObLe8luc30UcQk1tzbw/Lp+RowQ2/IqKVMRftvTzW/ZmnF/76rxUm/BqKlzd1Poyv5mXOvPfMx2smTMCYDz5/v46UPP87LrNqDNTIszTpI7aNPO86zfCS87W8INZjSsUBfYsa2cvmr7VvVq797E09cNMRJL2HJ2eCir7fLWjQJ7zIlC1/yaE0tKiP/zv//Afd99moaVFXz76+9m65b6jJJVh8MGgUCYsye7cFcYXLWxkvINYfYPNdnydRddVELdPVt4qmB6LY6BUACfNve3ZLu8E0Vuxya2jSsvX8WuPaf5ytd+z5vesB23e7ZtkI7GW/v2Wnbmn54WgtzmGmblF6fvNJVY6V13v6L500cSd6gJlZ/fzG69DUX8GA9d1WE16YlYDAFSs4oFW8MRYht5463bGRkJcu/9T/Hgz6K7nwsLZsREpKF8IoUqul9lCp2hITpd8VffVi1LvFqlgJrPbeZZPXmAUiBcGE2GYAGr+tQR4gXKX/z5NSxfXkZLay/btqzgZz/fS3t5AW09IxQXemm9kHp7vRYhI0MrWTxvxZc282wC7TuV7jFFuX05CtMiGgCUvZdlvm3iJSfEADe87CIAgsEwY6EwjeeiPoWh4dSbyArrfOx3tWb03YYxqLyiishwmPBQiPBgmNBQiOKLStmvdaXVV9PQEGWF1mJ5LJsTNviJPZoPn24tna5dLEkhHueuj/+Ew0cSBMsnoPwNxZwy+zI6pyXUT8vbx195AA8uKaSkaBnh3vTinAfCAXxaFUGVeRBSduZEdhTNsxaGJeadmMmqVZMz/oICL6++KXEKoPFFgg5v5smp47GltJ4X0hTgcVxqbre82yLE82wPwxLXxB/66xv505u3cvpMNyUlfj73+f+J26643s/ZWwaocBfQHc48JdVM1hRWcrQvc40aNvwJFltSkY13IjsKF4AQL2lNrOsaa9dU8+qbNtHRMUj/QPwFi9BghLBp0B4cYDTDjPEzqfAWcG5okOEExcWTYXXDp9Xz7MgA6WjiHGMYJp/53MOUleXzx8cTB+tUXVlCE9mbEXX+YtziocOwVhLXajGb7PzE2VHsnp8kglNZ0kKsaUJPzzBP7EyeYWvkknC6BYaSUusvZXd36q35ibBcSFyUJbVqh3ei1D2/wT+wRM2JM2e72X8gWnPZ70/tfPUa9vyWI2a89Fe5Zz69E6We+RfiJaOJe3qG2X+wmd88eoijx9sIBMJccnEdHZ3JzYSGdeXsjljXnlPJNi58hX+Muvyq2Pbl8fU0FTMXVCxEUwFmTPPGjmtuSvStTDdIxut3jGcEja2Rx54roMvI5/Iig6hVLTEn9XgyRZk8PvHezD8oc8/f3rpxloQQd3UN8o6//BaBwPRMPkeOJXdxNdSXYQzYk/1HAN2aa2GCfHc/faEXMj4v4l2LUkcTvp84wngVg+GmjK83jqDjd83ftqRxloQ5cayxbZoAb9lcz8uuXY/fnzwdq1fXuWBDzYxVBRUU6AVZ2cOQTSYfa+hZLjn79GJkHrcljTP/I7CB9etqKC2J5ifeeHEdfr+bT/3DG2cH/wCrVpSzaV0NWy+qo6tjgHA4ezs23+WlL2TNIzEdqy42a+hxU9imj1+ff/caLBFzoramhId+9EH6+kYoKytgbCzEs7tO0TUl58OmDXXommAaJkcOT1+K1kyJFqexSNimCV3U5rWlq7TIWojnoQRuPJaEEEPUPVVWVkAoFOFnv9zH/d9/hurKIqorCjlyog0VMTl8NH5ONA86AawXRGwZ6aXM46fXFm08d+hZ/JsBfHqJPQPJkiVhTgB865tP8Iuf7yUcNrj3Ozupry1loGuIFw80o0YjHEsgwABuM7uPYdQIoWl2fJTWnWVWyFaIF40mTlJR9PPAnwIh4DTwrlhhmnnhzW+5gp899Dxf++rvuaihiuZzFwilWW72mtoKIl6DqDBMBooLEnNxRZm8208RGgFRGl3nilmppqydqZgjS016wxSTabXGd5gopWLH4Yn9Bn73Ssryw6xb/SOLn0T6aGTnmVlMNvF4RdFhEXEDT4vIb4DHgI8rpSIi8i/Ax4G/z+FYk1Jams973nsDhw4187cf+n5G5wbUIGdGMgvZnEqFp5Qz3RF6huxx17k1jbUNOqLldvHEJdnFiSwUIU55D1RR4lUU/Z1SalzV7SJa425eGRsLcf99T2V8nivLFbsLoT421NsXGB42TYxI+kVcrAYAaSwNIc6qougU3g38OMG5dwJ3AqxYscL6SJPwxz8c4Tv3PUV/3wgjcaonpcLUzOx36ZS1k+ctZDRoTyoqsTHZXyJ0laU5sUBs4qwqigKIyCeACNGqovHOzWkxRqUUP/jeM5xv7bUkwACGZH/b7gz18Ceb87PuxxpWJ3bZ1fxalN6JmRVFReQdwOuBO1SqRMA54oV9TTTNzOiTIREbhBigSTvG5esLbelrLtCyDN1bKOZESiEWkUoRKYk9H68oelxEXkN0IneLUjksepGE4aEA3/j6H7PuJ5Klq2kcE5OK8rnNbJkNurKuiT1aAbqWusrqXJBNRdFTRN1uj8XiYHcppeasqmj/wCj/8ZVHGQ2FKassIDAaYmQkZGmKE7ZJiAFOGse4fssmnjxkz169XKJb0MRuzUeVp56ieSq8GI9sKoquzcmIUvC7J46yvLaEPzx1nD/sOTX5hg5S7CbP7yHP78HndVNS6EczFBfaB+hsH4gv4KIIKBsi4qfg8y8ObSwCungwVGIvhVvzUeKuotCVjzL7GQmfJhTpZkgtjEkdLLJl570HmvjMvz/CNVeu4UPvfQU//dW+ae8rBSOjIUZGo19KC5Nb70vqi1lWVYyETRoPTfqEN76lghOGtfRRiei0t7uUZHL3UUqhpAAl+YypPKq89WgIuqbjEi0WKWxgqlFCRhdBoxuMboZmTBsM094ffjYsKiE+FFs6fnbPafYfas7o3P6BUfoHRtm0fvq2eE+9/fPRtp7s/K/poSjQ8yhxFZKvC6PaZZhKRwmYSmFgYqowpgphqgCmGsMwhzHVMDAADNAUWUFEHbB0dcPmu1c2LBohDgTDPPbkZOD3WMCaj7O7b5i1l9ZPqC+t3wSbzbv6TZ1UtS7nxXOpi3+JQJHfS5HfRWGBRp5Xx+sV+tU2jOAWQqZGwISAAWOGwUgkwkgkxMq8PD5Y+yUAjJDVVITWUUQwVQRN5l+E5n8EaTLQP8o121aR9zIfV162in/9z0c515J5yuvO7iE6p4RoXro6/TIH6VLscqMXhlmz3U2e18DrMdBdBs+31RAyI4yZEUYjIYbDQYYjIXoJcnFdLWeNYxNJvE+lSFtRY/qyHme2UZ+GCjpCnAkPPrCbhx96npVb6rj/x8/Z17FN1oQA6wtLWZVv0BF4EVUX7TgY+/NpeezvS+aPzkykrFYfnXXJLPoxVRCYrwWeSRaFEAeDYX79i30oBe6wvTasMgWvpFcS11AmEcJ4xIuhIkSUgU/zcVnRCoLaUxjqPO0JXa/JhTTT3fqGDWtLVmMuJsZgjlnMWGQvi0KIQ8EIkVihl3OnuvGWuAlG7FllGyzTOdKWnlG8PL+ItaU+nmztmqbA6l06+fnJfc2pc0pkJpR2CHG2BkUki8USO1kUQhyZUiE0FIpQpeXTn2cwNGqDFyCD77F1ZJDWEauLGKkulJlA2SPE2WGYC2Mny4Lc2dHa3MP/+6efMxjLnfb0E9Mz+HR1DFDr8bF1dQ2r68qorypOr45BPOZoT5vdl1kYmnhhCPGC1MQer5tndjby7FMnyC/wMhwnOfa5MxfgzOTr9X+1EnO8iAaTc5aJR4lzwxbQSmGHZ9nEoQPdnQQM+5ahp10sCYOBCDX+ajrC6ZXyMmyYkWbtnTDnJWRmFgtSiKuqi/j1H/6eSMQgEjH46N/8gMZj7UnP2ZV/ztqu4xmZXItchTkS4uQc6umizOtnbdVyWkOpd5k4mniSBWlOQDQZoMfj4tzZC5xJ5TQFTGVPvIKWI/siHU9Ab3CMPS3DFAbXsNazPqnXxK5/bzY4mjgJhmHywvNneerJ4zz6yMG0atGZdk10LMiw3VOsxv4eGvthRWENel4rRpz8ELa42LIsUO5o4iS0n+/j//6fH/Gbhw+kJcDKcmbf2VjxnaZzxpgxzBvXZrbK1jw0wErPqrjvLQTvRGSBaOIFKcThDH3Amj6HaXMsYmJQ4MncBNASrCYYtpgTWS52OJo4MUaGFeztFOIs77BJsZYPOP45dghxtv/UyALxEy84m1gpRXVNMXXLSmk7n2YpLhuFOFcTO4hfzmBTRR5eHQwlREwTQ0HEVLjEwKsJNXlhvP5ClAIThakUI70+MDQuXNiCSDR/sYo9CgpEIZigGbiLIkz+fKa6IBURVY5JdPLolgg+bTyBzGSSl8mxj/9fJv8dCyQcc0EJ8fnWXv7xYz/l3u+/j8/+21u58+3fTCuLj67beEPJpSaOU15gS10n3aHZKbbq/SMYsS31MzNaND7wOlpaB/m/vDLp9Srr3ZTccSDFqKJL7u+s9rJO/1WKttPx6YlTg80lC0qIi4r8dHUM0HisjbXraigu8dOdTv5gzUZzwmYpLnUvw6OXg4KApnNTQ8FkSisgZGZeKsyIpDepy8TMsvIRKsecmE1hkZ+//fvX8Xcf+B6bttbPEuDyNX7q7/CgNIUW0lGjQs+uMF0n7AtEsVsRe/VCjg9N2Qvom7yOAAMW1lUiac4Z9AwizDQL2WPmaZP7LBaUEAP4fC7C4QgvPH922vHlVxSi3zbA0UhT9IAHKABugTpXFXVaJU+2deMW4crqQuoLIoRNHbROQjGNocZrXIzXvxh/PmEHmsB5touOILyv+gya2crU+heTzyf/Pv7tjzI8duO08a5c7qNq24uYhv15KC57/QBmwIcK63Sdzufggd647bQM1KuVH68jxAm45roN3P3Zt/BPH3+QFVcXUXa1i9bqZrqMThLtrG+LdCF08/IVNVT5hukInKLdhgA3nUFMlXr3SN9QiP7h6ZOc7v5R9KPL2bi2BO91R7IfzBQiqyY3BVRxExyI307LRBNL5n5npVJvv5oLFpwQA6zbUIu/1MXwG87TYYySTkJzhaJltJ3l/uWA9QyX0/tMTz8lWncwTJPR0fH5f45IMsTcC7GjiSf46QO7ME1FZWUh/f2jPPzzfax+bTEnjcxnv8/1tHJ52XLaA3YIcrpCnFgARkbD5DbZU2JbVs9kYmdhzdMR4inseuYkhw40A4rqTQV0toxQZFovt5polWs+GB6zJ2dxIpLFP2iuTIQ4c0zHOzHJ39z1Wj59z4MUvm2Mk3KWraG1tOe1JLSBU5FtYMuUntJqlSy8Y3gsBKZAxoVt0m2fWBOLln4vYim3bQClDKIZzuaPBbHsvGJlBe/65x2ckLMoFMc8J+mPWK8vJ7b9s7I3JwDcOfBQjJOsjFyubWIAtQDiJxaEEAPU+ue/RnCuuPDEZbnrPInwZeZisyrE828XLxghfrTDvlwSc21OpIqKPNncn/1QLCB6+oJpZWIHC0OIF4RNbCiTp7v329jj3P420wnIb/7ZnwCw6ZXdDBafsO/iSTVxBt2ISt+AnsJCEOIFoYl10fiHS95Lnp59aiZ7sUcTA3T1jdDVN0LbvmWpG9tEJuaEZjG007GJp3BR0So+vfmvbOnL7iCe1KSvwo6f7SPv+A0UnLye4vYrsr6yJPF6ZOI0kKU8sRMRn4jsEZGDInJERD4VO35b7LUpIpfbMZj1hSup9tqRvHlh2cQz2flMP0/sHOD8sQILY5p19YTvZGROWCwfpRZAFqBsijG+CLwJ+LodAxkID/PDc7+hMxg/mCUT7AzMTAerm1TTPa1Y91Pq8dERGCKgZjjPk2jQjDSxZSGef02cTrkDxWR2hqnFGI+BPZ6A44NN3H/2YYJmiPWFK8evHLv++KvZ20EnSszO6K/EXUy9fwWIMJ77XKY+jw582jnxTBC3uwy3uxbBBeJCcBH9HeuIeCb+3nHTZZhxAt6njjEehUUaxTV5E6996jR+zqKJwqMVMv4j8tNFOLKLrf6tnAlW0hsJsd1/FBEv5mXPsPvX19DXP/v6/e0mnktdRGYKfhwuRMro42pATfldqCmuNxXbRTL9PXdEZgXtzzV2FWNMdm7KYowXFTXwz1v/d7pdLjg+cKs9/bQP/jet/V+P/iqnKMbxhetI5CCr3VWs9niIGLGyZ3Keqoqr4wrx6YMBtr3eSySNZDC/7q/g3GjmyWfe5SngxnmuepZ1McY0zs1pMcalQjDSStvAf6ZsFzG7iBjTg5s87mR2SXp3Ss3iHD9kzkVph+RkVYzRwT6UCsXqaWSO2534vXQ9NZJs/ToJwQUgxCnNCRGpBMJKqf4pxRj/Jecje4kxGNxl+dyxqyso2Tapjafq5abOQjQRRKL76KJzg9ijxDLcV/UQsJgIZSFo4myKMb4R+ApQCTwiIgeUUq/O4ViXNJ2D37Z87tngKGdGEgRMpbH5wlvQRTidhnEImbkNNU2HbIox/hz4eS4G9VJjKLCbsJFeStd42FK/wyILQRMvmBW7lzKj4UYMZT301MwyE102K5xBwxHilzyDgWdp6ftMVn1kr4mtC7GjiR041/sPKLIThPnMkOkIsQM+d/zUrZmQamdJKrIxJxaCEC+IeOKXKqYZIBA5l3U/2WriV1R40aSY8f0d0b9okZPxhcOJ4wrMWCUUBRS5518POkI8j3QN/5BA+GTW/WSbJd8vu4iY1iaWRbI6q2vbgSPE84jVFbpZ/Ux5XumDFfnRyV5EKQwzGp8WUWCYUa0dMTUiSmGa0bw0Sln39Rrm4gjFdMgRxf5X0D74NcwsY3KnauI/Xz3GZSUPZHR+h2G9SLuxSOKJHXJEvmcT1YXvpX0wdeDPLwduJmiEcGk6uui4REcXDV10/uOKZ3DJAEIYUw1l7nLLwhyJmPOfaNsR4nkmED6TuhEQNIIEzEDcXCmmvwlDrJbrhWzqPxkqgFLKxh3mmTP/U8uXOKV56YWbJK8Pld3ELpvaUwoD02qqJptwhHieKfHfhCZ5Kdsl80DMd+0oY55NCkeI5xldy+Oi6h8jeJK2M5PsgVMWdypP6SGrs+d7cucI8QIg37OZivw3x33vlHEbB4JvxVTJtg5la05kV05svoXYmdgtEFaU3Y2m+egcug+AU5HbODw8xHCkPaXNajWPml1E5tlX7AjxAkETL/Uln0CXMpoGfkBfRGco7cyg2RZmzLayqCPEDjFEXNQVf5D7zjfTGWxJ+zyl1LzO7hxN7DANESHfVRhNWZPuORbNiVLfdZTnvZbicDcn+h/AsFghdL41sTOxW4CUeOxI5ZUaQwUo9V/DlvIPcPPKh2gofD1WVPp813h2NPEC5Pb6d3K4fy/hNAJzNhZt5aKKtzAWOUPb4HcxkpTl8rtWUezbQYl/B8W+q/DoFRPv5bmquar6n9hQ8ucc7PkKHaOT+aJ18bKy8GYK3Ms51vcdwjMi3uZbEztCvADJdxXwjlUf4P6zXyOskgedezUfVQVvQEToGv4FhjEpxD5XfVRofTso9u3A66pOee0S7zqur/syHaO7Od73XarzrmR10a149RIAVhfdwou93+T0wEMoDPJdyyj0NGTzz80aR4gXKBcXbaXQXUxvqDtpu/39u9nWfyWXle7ArZdR7Ls6pml34HPVWb5+Td5V1ORdNeu4Vy9he+VdrC1+M/3BE9QX3Igm8ytGjhAvUHb1PJlSgAEuK93BxqKtAFxa98tcD2uCYs9qij3zHxAPzsRuwXJtxSuT5kfTRee2+nfwzoYP4tPnOy/l/OII8QJFE41LimflrJng/Wvu4mWVr5rXEMiFgiPEC5jX1r4xrjau9NawoTDtxKRLHscmXsDU563iVTW3srt3Jz7Nj0+P/l1acpWjgafgCPEC53V1b+F1dW+Z72EsaBxzwmHR4wixw6LHEWKHRY8jxA6LnmyKMZaJyGMicjL2WJr74To4zCYdTTxejHErsA14jYjsAD4G/EEptQ74Q+y1g8Ock1KIVZRZxRiBW4H7Y8fvB96QiwE6OKQiLZtYRHQROQB0AY/FijFWK6XaAWKPcRN6icidIrJXRPZ2d6cOaHFwyBSnGKPDoiejFbtYLbsniBZj7BSRWqVUu4jUEtXSSdm3b98FEck+q3T6VAAX5vB6yXDGMpup41iZrGEyJFWq/DjFGH9HtBjj9UCPUupzIvIxoEwp9VGrA8kFIrJXKXX5fI8DnLHkchzZFGN8DviJiLwHaAZuy3YwDg5WyKYYYw/wylwMysEhE5b6it035nsAU3DGMhtbxpHSJnZwWOgsdU3s8BLAEWKHRc+SFGIR2Soiz4nIYRF5WESKYsfLReRxERkWkdTVXnI4lth7HxeRUyLSKCLp1T2wPo5tIrJLRA7EVlCvjB33iMh9sfEdFJEbcjmOFGNxi8j9sbEcE5GPp9WhUmrJ/QHPA9fHnr8buCf2PB+4Fng/8J/zPJaNwEHAC6wCTgN6DsfxO+C1sec3A0/Enn8AuC/2vArYB2g5/kwSjeXPgR/FnucBTUBDqv6WpCYGNgA7Y88fA94MoJQaUUo9Dcxl8rC4YyEaQPUjpVRQKXUWOAVcmcNxKGD8LlAMtMWebyQahYhSqgvoB3K9EJJoLArIFxEX4AdCQMqyUEtViF8Ebok9vw2oX4BjWQZMTULcGjuWKz4MfF5EWoAvAOO36oPArSLiEpFVwHZy/3klGsuDwAjQTnQB7QtKqd5UnS3a3c4i8nugJs5bnyB62/6yiPwj8Cuiv+iFNpZ4e+6z8nemGMcrgb9VSj0kIrcD9wI3At8GLgb2AueAZyH7ml4Wx3Il0Uq9dUAp8JSI/F4plbzY31zbq3P9B6wH9sw49k7myCZONBai2ufjU957FLg6h9ceYHJdQIDBBO2eBTbm+HOIOxbgq8DbprT7NnB7qv6WpDkhIlWxRw34JPDfC3AsvwLeKiLe2G18HbAnh0NpIxq0BfAK4GRsXHkikh97fhMQUUodzeE4Eo6FqAnxComSD+wAjqfsbb40ZI5/6X8DnIj9fY7Yrz72XhPQCwwTtUNzrXWSjeUTRL0SjcRm6zkcx7VEPQ8Hgd3A9tjxhtj1jwG/B1bOwfeTaCwFwE+BI8BR4K50+nOWnR0WPUvSnHB4aeEIscOixxFih0WPI8QOix5HiB0WPY4QOyx6HCF2WPT8f901WP1Qhjk4AAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ms_counties.plot(shapestats.radii_ratio(ms_counties.geometry))\n", "plt.title(\"radii ratio\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This measure generally performs about the same as the `minimum_bounding_circle_ratio`, with a bit more sensitivity to concavities in the shape. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Minimum Bounding Circle Ratio')" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(shapestats.radii_ratio(ms_counties.geometry), \n", " shapestats.minimum_bounding_circle_ratio(ms_counties.geometry))\n", "plt.plot((0,1),(0,1), color='k', linestyle=':')\n", "plt.xlim(.2, .9)\n", "plt.ylim(.2, .9)\n", "plt.xlabel(\"Radii Ratio\")\n", "plt.ylabel(\"Minimum Bounding Circle Ratio\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A similar measure to the minimum bounding circle ratio is the diameter ratio. This measures the ratio between a shape's \"longest\" and \"shortest\" diameters. This can be measured as the longest and shortest axis of a shape's minimum rotated rectangle. Alternatively, one can use the raw bounding box for shapes, but this is biased towards shapes that are east-west and north-south oriented. This again is quite a strong measure of elongation, and shapes with very large differences between their longest and shortest axes will have low scores. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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mq8mVq6/lntNYCFUCrBdjPCylbJRSrpRSrgQuA9dJKR3Mqmcd2+tb+ODG64lqiZxlqWYhW1OHXKUW1PhmSxLbn2mNe2EkseVijPmdlj1MxGN8/fh+R8d0aosi0K+zeSiATKWz0kUyqulsQ9D6TkUG2JHETmCh1Akj1oljwLU52qx0akJO4FunDjAYze4okw7Zspw7JUK9v+hh5HuzSx643CrXfv5V6Apoqo5UIKGAroIuJAlFoqkS5hSDzAU7lhAnUDQkXoy4MGYsULIg8MzXSxJxjb5P5a59rP28DdK5ZGSAEMmqRqZUqhRsbcqkUJQLu8WCT2zZQ4Xba76j44mqp1EVU9g+4EOOWq/LoUjztwM1z5sr2VBMOvGiw5qqOh58/Qf43IEn+K1R8xrZHcpdAR874q0IIZKZW4VIOg/NeFZUeC7eye0nPHheGklWCFUFQlWIdo/Tue+CraAlkTBOSG98Nwd7YsT1iYxt7jzbzlh3CEUVyfkrIvlaEdTrOpFt1ufqFh4CrnxvOCexZEj80mAvVyZGOT7Ux+aaRl6/YiP/actukyTOfC4kdU5292ft73O5qFrhxdcV4swjxrLMm4IJSRxLuOgLZ0+EEhuJ03NlJO25ZWtqzMxsHqo99XnfYp/EkiHxI5dOc//L07XmVlfW0hUcMTeISUXQ61LZsqqJcTVCGW46E8P0xUN587ZUTLhByjSEr9f9rI/UoOrJsSbGMscLWtaJpYpEWzBVApYQiet8s4MzrSzuzH5xG1sbeC7WwaayBoZlAq/iYrW3Ftz5WVi6IlUEQmoyg3wqhEkgpiW0TKoFSIF2ysM1p2Y73yyrq+T0foM5lK3UvpHQMbqbixMj1K/Ybn4Ai1jUJJZS8pf7fs3J4avcu/N2/vza21hRUU21t4zfffx75lflJtvH4hqqW+APenn58nRY0era/PgLdBxu4cIjIwZbz1d96ivMzMu4KiAlCOEiGL2ZM+PJ/a4qd/59JiaxqEmckDoPd55kLBblvz77EN973ftp9ldwbnQQl1CI2XGAmYN0NteT3f34FC8v67Pj4mStl6Y3rkF1K+BSUFwKwiXAJRAuBaEmn3EJUAUkVDQJaDoyIVMPDRI6MjF5TCfhsqenGCkiPonBLmg5emuq0pIkWWMkVX9ESBLLLhKt7MfLRiJ6NSdG4nSFpjdsG335jXCeiUVNYrei8uWb38If7/05HePD3PLgP3ND03Ke7e2wZhvNlvEyAwHSZVPfS5A9n9zEoej5maOnHvPbbyhbzaGB7jlH1dRjGtdeVMBGpTEzESenTwxxOsPatG1NFb73rudS/zKuRoKkk/pNvoWxTMASsBPf1rqah/7Dh/GpLmK6xjM9Fy0RGJxdj+mK8S3fhTLlXh0JsmK1faec/r4JjgxfTRE4PZrKFo7Ei1oST6LFX0GZy01EMxfFsHO8ntoXYlPve3oyx9eZ/V1oE6phEeFE5h8juDoUpL6xzvY40WCC6+Ir2e/KbL5sKqkTxvB8bye1Xj+XgiMMR81na6yIuug8bnC1bpJnw0NxMCj0CripZh0DZNwC96seyl0WdkwtYlGT+FD/Fe478rTl/hYT9Rgbu4iIWVlbhndnAEUIhhHU7GiZkV0oGYgkUwGk41oMl6KwTPOjK5LQwVEGL6ZxPMpiBm4qq1ywjQ5Y5CR+z9rtKFyg2nV0xpcC07G8sz9IOSc9lNKb4NvfMXo1c4w3Ywlw+uuubxCsWCUoKwOvV+KpEDzQlX23cS4ukNztu6mxYRaJW7ZVor1Wg8y72TQu4KIOFjmJ68sC/P6W93Kk9yHGoy8hMedc41qxHrjeYGuTmW9MLJntSy3Ja+5UWHddN1FPJxF9ZNbZCnU5dG2yNHKgzctKTy3uWpXwyhin4t0konpW5pRIbBI94z+kufydbKj/Bw5ceZM5Ikt33uZlLoGKPb3mvR+KI1t/wyhkyCho3QjV3zrKucbUuiGWve0kGrz5K7yYDouaxKORg1wYvo91dffid6+mwrsVl1LOePQ4cT13Jh+p5effv2ZdNYFGCeb98rNC3ayybl0TQgehS7bVXaW6/TRjMleZBuuSXrMQ9t9QksRmINnYcB8B9zq6Rr9BMHacHc3/zvmhLzAaNUBiPT//fnkjHAl1GG5vlGIHwsl0tP95a4KAe5ygdpQxQ0LcOomt5K5o9JUksWFU+XbSNfoNjl/9BKDjc7Uh0RmLHjLUX88DiW+4qZpLidyltGaiK9rLpvpKXEJhaEJHRzIWizKRSH//lspegiZ21O3U10tXlDIXGkokNoeGwOuJJK4AOhXe7RztvQeJsU0PM+pEOt8JhfkqaJ8+zFAsy9I9DUbiE4zEU31SQvOa2jXsv2pjj3kWrEtiHfP+Jw3ekjphCj7XMtbV3Yumh3nxyl3oMmK4r54w/u+n21W7vq2VhKaDkJwZGGQiFieqWw8/mjU3R23YNiSxBXWi3ltu+XpWsOhJPInhyPNENXNpLzQtc905VZVs3KwmQ48UCPnm39pfvHyFFn85fWNBXIrCNU2NVIRAc3UxanNVZ9X/Ix3sjJQwqU7UePx41IWl1ZIhcTieu5DiXOiJzCRe1qbyxc9P74T85ML7eaIn6Q8gkFzf6kERjRzuTHqfJXSdkz1XoQcU4WNjWyv+BjivXiaI+S1xJ0mMtC6JdZOSeKHNa7CESFzt2w2Az9WO372WofCTOftoWUjs884mUWJGmv9P7o7wwS2/Zdc/35a2ry4lJ7oGoAtcip8Nbe346nXOqV2EyF5W9pr4CrwxH+6wh936SqSQKSdOSTKgQxLpfTWK0BGKDkJD8YyjVp5MPxfdTX9kBdcsM5BiVQqEkooXSRU09/sSNMgaJuW5nPM8/WOTSCRry03kFHAIS4bE5Z7NlLlWsbb2M3hdzYZIXLn8ee77/lZWuuf7BqjKbN12R1M/kCwm855NJxAGHS8Sus7xS/1wCdxqORvbV+Cu0zirdBGZs3tQLQP0Hk0wOJbdunGK2Trn1lVr2HlnehJLavn6yQgw1195PlaX13F+bliXSa1onX+FuQ4OYMmQWAjB9uYHcKt1nB2811AfTY7i8fdQrlwkV/Gs9RWP8uSHbuTCSBMV7qto0ryXVlzTeamjHzrA66pkU3sdam2cs6KLKAmqTjTSOTZietxsu9ZCGq837YTTTkPZwi7qYAmRGMDraublvj9gMDw/TX8m9MXO4/ZtZqW4jJDZ00Q1e56jOVUwPsI6O1MlmtA4dvEqXASfu5pdK5rZ32eutt4ksu5wZy2C4zwayxYutm4SS4rEALrMrnOmw+XICaoCr6JWe9HMlUxfJxOi8QQ9XdnriZhBf/BuHr2UrG+XDJ8y5vTgBN0bCyCJF3140ly41WpL/cqEOaO+UZ3YCHYta6VrIHOxmtxzmf0+FPcyFA0zHI0wHjfotZMcyfIcJtHgK5HYNKKJPrrHvktcGyWujTIefdnSOG5pbpctpjl324xF7UVlz/VdjpmsNTcJJ/zYS+qEBQRjJzg79FnOD/8DqvAT17OnbsqECBXkkiGScmCC4cT1/OkjRv2Qs2NHczNnO+xVTtNUQTi6OxUEIOgLWWWjfRYXQp1Y9CSuLbuFtbX/jYvD/zMrgZ/r/zCPdFVS7VFpL9enwnEkyZRPP0DhnrYydlU+k3GMfzr0Ll7s8hBJQIYUZqahxJM6sR2E3Qr/cmJmyUNrGYjsSuIKtxefK38+2plguRijEOJzJGt36CSrKn1ISpnbGOkwhFBprbyHSu91HO39AJpMv0AajgboHA/SCRzN4KV5S30ru7L4rrSUxzh0xbn6mD6XyuCYw07HNiAspI6diYYCqBJgTCeeLMa4HdgB3C2E2A3cJ6XcJqXcATwEGDPO5gFSShThxa1mDhOPabn/1bie3ab6zvU/4cmPHmFljTOWic31jXQPmcv+ng6OxWTaXKwWQpUAG8UYpZxlVA2Q78rbWTAc6uGRE19EEatRxAqEoqGIBEIkUBUNIRKE47lvc/EsGwPBaDVXx5aTkHF21tehaJILFjYmJlHmdnG13xmzmlMfvJng1nQoWhJDshgjcBBYC9wvpdyXOv73wAeAUeA1+ZpkLpzqjvP3P96Qtc2W7RXASNY22STxk6ffwN99b1LXGEIIuHFjK6djQwxGjbt/Ts2nppEj553RvpyLlrarThSGxIZsMVJKLaU2tAG7hBBbUsc/I6VsB74DfDJdXyHEx4UQB4QQB/r7zYWNG4GuS77yxAvUBMr414+/i1s3rkrbzkipgGySWJlTTktKOHbyComOKDeUNXNNdb3hNEFel8rxjqKoljYbNj3nmoqZxJOYUYzx7jmn/h14R4Y+eS3G+NODxznU0U2138erVrfxzldttTxWNkk8l8ST0DSd42d76Hy5n/WxKvbULaM8xwp9bU0tcc3J8lzOyGK7vhPLAgsb0TEJI9aJBiAupRyZUYzxC0KIdVLKyRIUbwZO5XGeGfGrY6cBKPclHXLcrvlEdKsKZ/TcttjgRBknenajo6DrCpquoEsVXap09DdCjrCn7v5RuvtH8XlcbFuzjD5CnB8fmdfOJ9N/7K+52UNdYyyZPhWmFlpTu4MCpkqHT74W4HMPs8urI4SeOj+zX/IYSBCSeCLAWNTLCz2S7dUB+q7UgkwKYfe4yo2qn5S5OZXHO+V6OdMlFNCRyWMy+axJybKyhcu/NhOWizEKIX4shNhA8lPqBH4/j/PMiHvfejtPnrzAXVvXAxCOzQ8PumZNE89qnVnH2SwaePQHE/wsuiNDC+O23EgswbGTyfi4rW11+Oq8HB3uQwrYUd/MkXPpdeHmlaP0Ki8Zvs4kVvrXMBo7bri98MCeFaAGt/DwSfO+Jpmw7K4ilcSZijFKKdOqDwuN9rpqPnDzdVPve0fnr/iFW2T119ksGgg+P0E46kx83ExcvDwIl6GuzMNOfxXhrjFuleXMtClMqqJ6ZyJZMdskrGoBc9N82YEqBPXl/twN84BFv2M3iUg8wZd//Sz/9uzscP22uipOicwLynwSeCbWe8s59uvTWds03lRticSWdWKbmxsz0VhRjmomd5eDWPQOQJP44i+f5oG9h+YtsOtq/Qxo6Z17FCmYeCH/BF5RUc74S7lzUaSreGQE1qnoHImbqwpjmYAlROJzfbkz/syFLiRDN8RZ9+qmPMxoGq0hhcE+AztzC01iByVxS+XCB4hOYsmQuKM/g/NPDtvnOHGGVPPRyEahAFdO9hlrbNlMa1WdcO7rbyqR2B6klGxoaaAu7cIi+xfsxYULhQp/fjKbb6iqIjhm8Edi0XRs3bzroCQuoDqxJBZ2Qgi++pG3AfDIsdP81Q8fJWzQvbFNVND31Ehe5lXv8+K+aMI/wvLt3Vo/J60TJUnsIAJezyzRlK3oOMB5fZjlt9azcZ1zerFXUdhdVUfVyXGuXDDh8F7SiS1hSUjiSTx44Dif/cljaGkSmblQ8CouJvQ5MWcCNKFzvnWcVdE6Ll4yv0CchFtR2OWvYaxjmLP7z+buMBeWd6ILF8kxiUJaJ5YMiX968Dh/9aNH5x0/1zXIpsoG4ppO78g425tbUJRkhhtFSbof+sYFvWdHuKiZJLCUXF9Thy8BRDQGLw1zqtsCeaeGs0oqiytChySxS1GoCxRmowOWEIm7h2frnn9w+w08fbqD45f7uDQjkvhcmlp1q+tr06ZuzYUbauo597h10s6EUMC9xhoZrdbBc0onLuRGBywhnfgjt+5keV01fo+b9+3Zzifu2EOjwYLc1eu8rN5p3MOu1uvlxqo6Op/OXIzQLDZ8sJn48vxuusyDQ5K4kJYJWEKS2Od28d1PvI8Kn4eYrvEv+1/k3NgATY0B+q5O79jV1ZTh9892lXw52ktDo5/V19Zz4XD6hVi1x8MKfzl+KTj/2/OcTvTYnnPrB9egVatU1cOF2qNcSwseEWBStia9yMQsSSsmXcyYdp0UuPCrNakW6aW5TPMqpqrUBKZjBqfXwzPILWZed2675PEV9TUUEkuGxADVfh+hRIxbfvoVBiMhqIE6rz8ZxppC4+YAB0fnpIuKwUgszM11mZLhSbbtqOb4/3XG21SogqY7W3mhZZiJRIztngbiMsH+oS6SkV7mUO1W6bVQUbWpMkSvA3GvgVqP/UFsYMmoEwAd40P8y4n9vH75xql4sblyKdsNdD+XmbhTp+HNVWy4NZmiVFXhuvdXMrraeoaeuWj8w3U8tWVkqiZH5+i43aAKi3BIJ/YXVp1YUiT+3IHH+cdjz7C+qp5fv/Gj3NC4fJ6dOBtXYrpGWItzMtiHd1WM695YQ9X7xjmmn3fk665YU0nzH6/nt+psf+KRWIQqdeFvyU4t7JrKCxOqP4klpU7csmw1v7lynr858Bgf2rATj6rOI60RK8RrVjZxInQKypnyhe9zj7Lqv7dNDjL99UtQRxXO/o9LmQdUBLV/to7nE93IDHmCAzQyhrXsRZbh0MKu0JJ4SZH4gxt2Mh6L8qWjT/ONU8kMl1Vu80qfoszPjdYfH6M/TTJugOWt9RnHkkDDn6xjbyJ7ZLOeKLN8Xyy0K2ZjoCSJHcUnt97EqspaLowNsbtpOQ+cOkBX2SidkWFqPX4uhI2keDL35Waz01b/5Tr2xnKH5g+HdHImg3MY1jdXZqMxUJLEjuM/rEgW444k4oQScY6NJc1ho7Hc+SEaynycDWWPx5uLOBoN11WTCCaITySIjSWIBuNUranikMHCjB1jY7QEHMzmYwj2LxZwuyn3FNY6sSRJPIl7nvgeB/rNZV/f1lLO8aBB/98UuuND8P7Zx1ShUKfUEb9iLNfGaCzKRrWWMd1aMsBCoaHAUhiWmHViLjbWTO/CVXp8vGN1tpwUyQXfiDbizLUDq3jOIIEnUY7zeTmywQl1oqnA+jAscUn82Z2v431rr+XkyFXqvH7+5LmH0rZrDpThLu+nxlPBUMx+frQV/ib2XTKfKFDq+XHMzwwH8hH7C0/iJS2JXYrC5tom3rF6K5cnRhmMpk+jOhFLEJcaV6MjhDUz5QHmo9ZTwdFLGuNp8l/kglVHHssh+w5I4kIv6mCJS2JN1/mjZ39Ogy/ALzpOZGy3oa6KywYyBOVCs6+G8Hgl4YS13T0rnnTJjtb6ObFJ2FJeOGf4SSxpEitC0Bca5+HO9IUKJ1FWFgFzJTvSolap54lB60kTF9QwAY5sdrRWFCbrz0wsSXXi1PBVnu9NmskC7tzmH5dwJkV/ZIE9KadQwAxAbZWFJ/GSkcRXQ0Ge7+vkh+ePcXjgCqFEnOvqW7k8kf3WvqmygZPBc47Mwee1V3vjmqoR3lAFQiaT/4lUCr/p5+nkgEKksgCis9yrsLY2NqMts16Lqbin2eefCg2j3ZqY4d4ppl6LKfmmJN9PSe0ZxyW0VRV+YbckSNw9Mcadv/gaocRsUXho4ErWfusCDYTHBDjgjigQoNv7OOu8/SQSz5nu5/Vuxa+bT0Soik30x41txqSDgkKlp3BhSdPzWAI4MtA9i8C7Gtu5e/kGAq7sqoQ34aU3GMzaxgjayxqIjTbyxAV7ScStL7Ss9XSZLEA5F+WuCpQFLrubDoWfgQPYWtdMnS8pEa6tX0bA5eErt7ydKs98EbuhvJHr/Mt5VflKukfHiWn2vkgAv1rGQNiBFKlWWWzRxubB3v9e4S68PgxLRJ1oL6/mxXf8IQORCRrKypmIx3j88lm6Q9MbDtdVtuNCRdMkB7tnhxYJKZA2KgclpD1deBLWF1rW5u4W9laila7CJNWeiyVBYkjGmzWUlRPVEjxw+gD/+9heWn1VLPNUc3i8CxkX7O9J703mEi7iWP9CuyMD1JfVMhA2X4DGGVgjv1vY+/GVJLHDuO/5Z2gKlPO2jZv54pHfsr68kY6eca5oPYCLw2Qu9OISKnFpncRhLYZLsW+uWnBJbOOHC4tIEmepKHof8CYgBpwHPpwqTFMQfHj79Xzr6CH+7pmn2Opt51zfEFGD+u76oQ1oCT25YzZzA2AmN1JldAUzNshSz4oQ0AdbEUzV251sN117d/o9069l6hwS9p1vwu9bTU1djA2v/Zbh/90q9d0ihh05tpgk8WRF0aAQwg3sFUL8CngM+LSUMiGE+ALwaeDP8zjXrKj3+/nTPTezv/sy7/nJ9031HbyscabLumWhuboC0RVhfNQZdcKlKqy/VUWo9hed2ZCUxDZI7CoOEue0Tsgk0lUUfVTKqRXNCyRr3BUUoXic/7XPvJ3V7bJnpOkdGad5uXOBnglNJxFaZqKHReuEsGdRWUySOGNF0Rn4CJBW/AkhPg58HGD58uXWZ5oFPz9zkn/c9zyD4QnGY+a90NIlIDSLfhHB61WJRp2RnjJLYUin4MYeiYtFJ7ZVURRACPEZkjHB38nQN6/FGKWU3H9gHx2jw5YIDJBI2C+MeHlojDXbzUhPJ2F1Ybc0JLGtiqJCiA8CbwR+R+ZKBJwnPHv5EmeGrKdjhWRVUCdwsLeHNZvyW//DSbiFvTIPi0YnFkI0CCGqU68nK4qeEkLcTXIh92YpZXpv8zxjLBrh8889bXucWMIZFUDTJZ7qwgZNmoEb6yQuU/24FWe8/+zCTkXRcyTNbo+lEtu9IKVcsKqio0NB/u7Hj6CNh2hVfYyLBGMibmkLNuEQiQFe7Opm57WtnDqc3fnISVg2sVlQJ8oUD2vKG2gsAsefSdipKLo2LzPKgd/89CDLVtTz24cO8/I3k5aIitSjVQjKyr2UVXjxBrwEllcSbvNyvjrKRTWUnuASx+vYKd7F4ZIiBLiFO+tGT5niocVXTYPXgyKHGY51EE90MSyrF26iObCoduwO7z3Dff/lO9xw+zX8/mffyk+/OVuVkFISGo8QGk/Za88m3Qy9wA315TRc08jYWh9PV0/7GL+qvIXTYXMh+rkQGizU9nNu6BIispKgrEYobtYGGlBEss6ISxG40BFo6ISIJAYIaX1AFyNzhHZC2otFdBKLisTHDySTWu974jhHnzeXoX10IMjob4OsVdbAdCloyhLOfwTDAw7EOuVAcpOvloRo5my4nU75RkLSx4TmZkJ3MaEpBHWYSEgmNI0JLcGEFiOUiKCnrBl3NnQhOYwOmNWoErpzhc3tYtGQOBKO8eTPpus2R0LWJMHouSHeEKlKahZC4Frl/JcRaVZpr6mny0DlJJdL0lIPTXU6y+p1Gmo16qtibGuspsyzCbfQcJFAJYZKFEWGETJIiHbef3pyf2kk9WzfN9oodDR0qaGI/Nuzc2HRkHh4IsSWe7Zx64jKzls38r/+4gd0nTOvBvR3DdPfNZ19cn3lJnDYoFAWcOMKuFizrBXFq6B7wOXW+es9D+P1hPC4griUcQRjiBTxVM8NuOKzi6tnq6akKoU35SX0KB618Au8RUPir144wAOu49zW6ee773zMsXFtuBHPG2h5ey3eJi9HBnrRJ83m0eSj0uuhrvwZhy42M27OzhjCRjQJJGQUDyUSG0IkEec7Zw4jgZEby+Hnzo0thaSszJi9U9M1YlEdX5mLRFwnntAoD3jYtKuJvZ1XOK4PQQY/olxmMLOJU4TNqAywH+0cLxK9eFGQOKppxPWk5DkRH2R9hZvEuDNmsYktKv11xpKdtJZVsSFWzwtax5QEmyDMCm/N1PwyQcllvzYpEp2QxHYzXSRkcZB4URg04/q01InqGsN/tQJfszOh4mYKzV8Jj/L8DAKbgdOJUZyQxHZnFdeLw5RYlCS+MDbEJ5/+GcOR5Lbory6dmXX+cmSc0H9dzrKPbaLxjnZqb2i2nszGgYgMQ8itT5iEfRLbzYUc1+35XjiFolQnfKqLRy+d5bGuc1S4vYylSY59OjzE6TamvJjftHIHUpNzvpnJWIw5mHko5OVWViNF8vD+ii7CNgMo0yGXzqvrQYS6EkXrMDaetK9O2NWJYyUSZ8ayQCWnfudTxHWNuK7xO49+n6OD2YsfHhwcIm7FpXJO7hD/3W7CNmPP0iGX1NMTL6OLWtzqOhQt90aOE+qEkDatE0WiThQliSG5EPKqLk4MXeXkcO4sNboDju0AyqRIdhiGhpRDxBNDKK71KKIGJXEKQSYHwfyGLhlBrETizNB0nWd6Onik8zQ/OP/StM01C4y0MQIreqKRlKzCxMB64gw6INTluLUYIk1ofVEs7GRxkLgoF3adwRE+9MQP+d65Y8bIORk17ACEhRWiEYIOhaM8fOX9OdvNhNQuId3XZDhbeElcLAu7oiRx3GRqKWXhM/uaRkLXGYhUm+4nM/omFIEkLpE4M3JtHMyF6mDdLDO3fbNQhBWLQob5yGIgcXGoE0WnE0spaS+vYkVFNZ3jI4b6WFEBso6VJx6LNI4aI6xDw4uCBmgoQkORGkMTAWLSi1TaUXQFBR1F6Aih44pLQKEm3sTkVp8kmdM4mZslWbdXpur3Sjmnjm8KelSioyIAlyuO15OYPd7s2c84lnzWbWRNchJFReKOsWE++uSPefwtH+WB29/NXb/4JlEtd74wVXHuhpJPxURNQ+IXIs0MxLrmHf/Sk6+bkbGzZda5TcEaugZyb5XXVZTRH818yz/GdK6Mj74+jL/xVznHnAW5wLWoM6CoSFzjLePKxBhHB3q4praJWm8ZPaHcJbkUB+OsrVYwyoRd7YI7Ng4gkLT7E1zmRqa3GSQRC3ql0TwZwkTuYNWCHEjI4tCJi4rEVV4fn99zN+/+9b+zq7FtHoGb3OWsVOuQUqKqydt+nz7OVQNENwqnJfGqOg3NtReAi7Hkwy4SBlMMmFkrCAv6emmzIwPKVDcxLcEzPR2zjq8qq0EZdXFweH561pU11bRc7+fUwW4UVbBqXQPuWg+KDj3aBKF4PBXOk0zkJ6VM5fib+SzRJYx1QY1SgyIEO26aYDA+AkzriJNjzDzSXH6Su+tne3RVikaOngkQ8Dnv6VXT7qepvQJFChJBjeOd6YMDzCRxVyw4VpdInAGvW76Or972dj7+1E9YU1ZHo1LOuZ5huvoyh950DI/QyQjrbq5DJODQQP+87WQrCOtRxhK54+VCeoTgnHajjNCwWkHzO58V6GBwOk3tTRWZU+CZKUWgWNDJ4oVJNzIPRUdigK11TQRUN8O9UTojxsrLSuDM0CC7WtrAfl1FwLh+nGmjRZM6Yb1wK3gz1sJ0lpNcKEniGfj68f1oUtLir2AgMsF3zhxhY1kTRyPmY+j291xmQ0M9Z/vtpbYyh8wECGn5dRzPlj3MlCS2QOKSnXgGHr98jn19Xcm6aL4qLkdHua68zPJ4LodMbkYFWbavP6Tl+YvOIm7NfAxW9niKxTpRFDt2f7/7LtZV1HOdu42+SyF2eZfT3Ws9/Ny5XTeD6kQWGoe1iLnwkckxDTqDZLu2mc/Bym6iJmPojuwc2kNRkHhtVR2f2vxqjl3pQwKHLvUwMGF90eBUsIZhSZyDcIpiPnukCeNY5uuaGcWisb0Y4uyKgsQAK2qcy7RuO+7GNLIT4GJ0W0GuLUz8mq0GniaKwAmoaEj8g2Pmy7pmglP/lGHrRI7znaHMlZvyCTN3JMuSuAgWd0WxsNN0nV+dPpO7oUE4pRMb/VqNOMW/HHoVANvLg2j6SRuzmnvtzDCzhW7FxAYQL4LFXVFIYlVR+Mrb3ky5x5l8Uk6R2PgouQkwFBtlKDZKZ3Th0k8thDqhFUEClaIgMcC1y5bxzXe+3ZGxHHTMNNTKTFTJhYluItxOTLwWlD0W5zXj2lnOmfkcrEriRBGEKBkpd+ATQuwXQhwVQhwXQvxN6vi7Uu91IcROJyazvaWZtir7dSDy6dieDkbUiZnYP9LFC8OX6Yo4cefJstlhRhJbJXERSGI7xRhfBt4OfNWJiQyFwnz5uee4PGpsm3khYHyzI781d+oCHuoCHrqGQ4Tjs2/7TkliLEWdFIeJzUi5A8l04tuZxRhPgjNS70h3D198Zi/heJztLc2T100+T81jht/YZNnZqfqzs8drrihnU1MDApFcoQuBknqk3jL3K073b6wJaDQHanAJFVUoyWdFQRUqbqHiVly4FRdV7kQWMmU+E1BdNHpaJ2fAuWCIixMxNAmv2Vo+NceIMs7F8CV2t7YxNlTBUDBO5bKruIWLcuUqgQsuJkLzgwfGwzHcqkLcgOvm6FgtUu5MfRbTHnsiFR2SzEMz7QctkQgBE1UiWWuigHCqGGO2vjmLMe5Y1sL/e8+7jA65ZHE+9CSP9v0y9W5+es3z4cvUVlVSX63SF03KlauMUFG5Oi2JL/WPUFHlYzScW2999Lk2Oi+ZT9Pa8K4athY4VbLtYowG+ua1GONSQW94mH+7+ETOdkOxMfqis8OCXKr9u6HVEK9ILHf4WL5hqxhjCc4hLhOWPd7ULCTOmVJ2cgyLamEkXngS51QnhBANQFxKOTKjGOMX8j6zVxgOD5+33LdFqaK81j/L1DeZSlECreUBRGpNgEj5VIjkekYIUDyCcYs1UCKxwkc82ynG+Dbgn4AG4GEhxBEp5V15nOuSxg8vWS+F0DcwweWr1q06/goPwYg1EkcXgyTOUozxQeDBfEzqlYYjwxcYiFonod1kinY06vBi04lLyA8uBHuYsOE8b99KbZ3GkXjh1YkSiQuMQ0PnuP/sL2yNYVsS2xDFi846UYLz+J+nHyRuMzrCvjphncXFoBOXSFxgtPnrbY9hNJQpIxa5JC4Kf+JXKqJanO6w/ahsuwnGX39nDF1IpBRTuZ6TD5E020nQU69nndOhLlD4QuUlEhcQP7/yAh0T5tMSzIVddUJvfJGIbqyoumC24PZ624HfsXV9uyiRuIBwKpx/piD2+92UV/lAl+hSInWQU6+TqbqklOh66r0uSejWVYK4XpLEr2jsqd/M/+t4kqjNLEEz1YkVG+t4LjI/X102JHRpeXUUXwyumCXkD+srWnn38lv4dkdux59KtZqIHsMtXEm3UEXFJRRUoTB+vR9iHuK6zktx8zq2FNYr2hVDfecSiQuMrlCGiuZzENZiKQeh+aQJBt2MR62rBHZ27OJ6FCnlgkfTzETJxFZg3NJgzKs1W/SIXQubHROdjo4mC2tmK5G4wLip4RrK1NyxdtnMaHbDo+zVFYWELOzirkTiAqNM9fDl6/4Aj5Jds9Oz1HK2LYktBolOotB6cYnERYANlW3c1Xx92nNbK9ewqWIViWwktu0CZK/YeaFJXFrYFQn+aMNb8apuftSVrO+xpXINF4P9HB7uzEnS/MZa50aswOpEicRFAo/i4j+tfSNVrgA/uryXmJ5gJG5sF03arONn17BQaElcUieKCC5F5QOrbiegVnB89LLhfvnOe5ELhSZxSRIXGYQQVLsDdKYJ2c8Iixy+ZflK3rB6HXV1TTw38AvLVoYSiUuYh0Zflan2Vu28kUSCm9pX0F65jV11d/NE33c5MvykackeK5G4hLn41Ka38Nurx4kZcMzZU7+Bm5fv4vzIMA8cO0wwnlmarq6uYXdrO3ta29nd2k6DPzB1rspdz9vb/jM31r2JR3v/jbPBw1Pn3MLD9prbqPU08/TVH8/zeCu0/0SJxEWIKrefv9n6Xv76pe/ndA7yq17etmEzQggePH1iFomXV1axp7WdPa3L2dPWTlOgPOe1m8tW8oFV93I+eJRn+h9kdfk2dtbcgd+VTPR4fc3t/Obq93lx8BF0dGo8TTR4W3OMml+USFyk2F2/gVpPOT2R7EXAn+g7xm19W7ijeRu1ZWXsaVueIm47rRXWM4yuKd/OmvLt8477XZW8cdnH2FV7Nz2Ri2ypuglVqJav4wRKJC5SPHzlQE4CA9zRvI099RsAeOjd9+R7WlNo9LXT6GtfsOtlQ8nEVqR4a/sNqFmKKbqEyqc2voW/3fo+Ai7vAs6s+FAicZFCFQo31W/MeP5L132Idy7fU1AXyGJBicRFjI+suT2tNG731/Oq2rUFmFFxoqQTFzE2VLbywVWv4ZfdB/G7vARcPvyql9c2bS1J4BkokbjI8bG1d/KxtXcWehpFjZI6UcKiR4nEJSx6lEhcwqJHicQlLHrYKcZYK4R4TAhxNvVck//pllDCfBiRxJPFGLcDO4C7hRC7gb8AnpBSrgOeSL0voYQFR04SyyTmFWME3gI8kDr+APDWfEywhBJywZBOLIRQhRBHgKvAY6lijE1Syh6A1HNjhr4fF0IcEEIc6O83Ea1QQgkGUSrGWMKih6kdu1Qtu6dIFmPsE0K0SCl7hBAtJKV0Vhw8eHBACNFpbaqWUA8MLOD1sqE0l/mYOY8VVgcRueKz0hRjfJRkMcZbgUEp5eeFEH8B1Eop/8zqRPIBIcQBOVl1u8AozSV/87BTjPF54AdCiN8DLgGlCuMlFAR2ijEOArfnY1IllGAGS33H7muFnsAMlOYyH47MI6dOXEIJxY6lLolLeAWgROISFj2WJImFENuFEM8LIV4SQvxCCFGZOl4nhHhSCBEUQvyfQs4lde7TQohzQojTQoi78jyPHUKIF4QQR1I7qLtSxz1CiG+l5ndUCHFbPueRYy5uIcQDqbmcFEJ82tCAUsol9wBeBG5Nvf4I8LnU6wBwM/D7wP8p8Fw2A0cBL7AKOA+oeZzHo8DrU6/fADyVev0J4Fup143AQUDJ82eSaS7vB76Xeu0HOoCVucZbkpIY2AA8nXr9GPAOACnlhJRyL+BMFUQbcyHpQPU9KWVUSnkROAfsyuM8JDB5F6gCJovdbSbphYiU8iowAuR7IyTTXCQQEEK4gDIgBozlGmypkvhl4M2p1+8CCpmqJtNcWoGuGe0up47lC38M3CeE6AK+CEzeqo8CbxFCuIQQq4Dryf/nlWkuPwImgB6SG2hflFIO5Rps0UY7CyEeB5rTnPoMydv2l4UQ9wI/J/mLLra5pIu5t2XvzDGP24H/IqX8sRDi3cA3gDuAbwKbgANAJ/AcYLuml8W57AI0YBlQAzwjhHhcSnkh68UWWl9d6AewHtg/59iHWCCdONNcSEqfT88492tgTx6vPcr0voAAxjK0ew7YnOfPIe1cgPuBe2a0+ybw7lzjLUl1QgjRmHpWgL8C/rkI5/Jz4L1CCG/qNr4O2J/HqXSTdNoCeC1wNjUvvxAikHp9J5CQUp7I4zwyzoWkCvFakUQA2A2cyjlaoSRknn/pfwScST0+T+pXnzrXAQwBQZJ6aL6lTra5fIakVeI0qdV6HudxM0nLw1FgH3B96vjK1PVPAo8DKxbg+8k0l3Lgh8Bx4ATwp0bGK207l7DosSTViRJeWSiRuIRFjxKJS1j0KJG4hEWPEolLWPQokbiERY8SiUtY9Pj/09drf5JLoh8AAAAASUVORK5CYII=", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ms_counties.plot(shapestats.diameter_ratio(ms_counties.geometry))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Relative ideal shape measures\n", "\n", "These classes of shape measures construct a relationship between the observed shape and a different shape with some known relation. As we discussed before with the `radii_ratio` measure, this often looks like a circle with the same perimeter or area as the source shape. \n", "\n", "In the case of the `isoareal_quotient`, this relates the shape's perimeter to the perimeter of a circle with the same area as the source shape:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ms_counties.plot(shapestats.isoareal_quotient(ms_counties))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The related measure, the `isoperimetric_quotient`, relates the shape's area to the area of a circle with the same perimeter of the original shape. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ms_counties.plot(shapestats.isoperimetric_quotient(ms_counties))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The two measures are directly related to one another, albeit non-linearly so" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Isoperimetric Quotient')" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(shapestats.isoareal_quotient(ms_counties), \n", " shapestats.isoperimetric_quotient(ms_counties))\n", "plt.plot((0,1),(0,1), color='k', linestyle=':')\n", "plt.xlim(.2, .9)\n", "plt.ylim(.2, .9)\n", "plt.xlabel(\"Isoareal Quotient\")\n", "plt.ylabel(\"Isoperimetric Quotient\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A final related measure is the fractal dimension of a shape. This measures the effective dimension of a shape's boundary, and generally varies between zero and two, where two implies a very convoluted boundary, and zero implies a very simple boundary. Hoever, our particular implementation approximates the true fractal dimension by assuming that shapes' boundaries move along either in a grid or a hexagonal lattice. Thus, the measure is effectively the relationship between a square (or hexagon) and the existing shape. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ms_counties.plot(shapestats.fractal_dimension(ms_counties, support='hex'))" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ms_counties.plot(shapestats.fractal_dimension(ms_counties, support='square'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The two are also extremely related:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Fractal Dimension (square)')" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(shapestats.fractal_dimension(ms_counties, support='hex'), \n", " shapestats.fractal_dimension(ms_counties, support='square'))\n", "plt.plot((0,2),(0,2), color='k', linestyle=':')\n", "plt.xlim(.4, 1.1)\n", "plt.ylim(.4, 1.1)\n", "plt.xlabel(\"Fractal Dimension (hex)\")\n", "plt.ylabel(\"Fractal Dimension (square)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Conclusion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are many more shape measures in the `esda.shape` module that are useful in a large variety of applications. The ones detailed here are the most common ones encountered in literatures on redistricting, which is noly one special area where shape measurements are useful. For more information on shape measures, a good introductory conceptual paper is [by Shlomo Angel et al. (2010)](https://doi.org/10.1111/j.1541-0064.2009.00304.x) on how shape is measured in geography. " ] } ], "metadata": { "kernelspec": { "display_name": "Analysis", "language": "python", "name": "analysis" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.4" } }, "nbformat": 4, "nbformat_minor": 4 }