{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Machine Learning\n",
"## Voronoi diagram (tessellation)\n",
"We have a finite number of points called **seeds** in a *metric space* (a vector space with a distance function). Then, we can **partition** the space into disjoint regions called **Voronoi cells**. Specifically, a point of the space belongs to a seed if the point is closer to the seed than to any other seeds. The closeness is measured by the distance function of the metric space.\n",
" **Contents:**\n",
"- Defining the distance functions **Euclidean** and **Manhattan**.\n",
"- Defining a function to generate random seeds, and then a function to create the Voronoi diagram.\n",
"- Examples with the same seeds but with different distance functions.\n",
"\n",
"The code is at : https://github.com/ostad-ai/Machine-Learning\n",
" Explanation: https://www.pinterest.com/HamedShahHosseini/machine-learning/background-knowledge/"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# importing the required modules\n",
"import numpy as np\n",
"from matplotlib import pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# the function to compute the Euclidean distance between two vectors\n",
"def Euclidean(x1,x2):\n",
" return np.sqrt(np.sum((x1-x2)**2,axis=1))\n",
"\n",
"# the function to compute the Manhattan distance between two vectors\n",
"def Manhattan(x1,x2):\n",
" return np.sum(np.abs(x1-x2),axis=1)\n",
"\n",
"# a function to generate random seeds\n",
"# given the number of seeds and the size of the space\n",
"def generate_seeds(no_seeds=15,size=(200,500)):\n",
" rows,cols=size\n",
" # random seeds in the space of the image\n",
" seeds=np.random.rand(noSeeds,2)\n",
" seeds[:,0]*=rows; seeds[:,1]*=cols\n",
" return seeds\n",
"\n",
"# a function to create the Voronoi diagram given the seeds,\n",
"# the size of the space, and the distance function in that space\n",
"def generate_voronoi(seeds,size=(200,500),distance=Euclidean):\n",
" rows,cols=size\n",
" image=np.zeros((rows,cols),dtype=np.int16)\n",
" for row in range(rows):\n",
" for col in range(cols):\n",
" point=np.array([row,col])\n",
" image[row,col]=np.argmin(distance(seeds,point))\n",
" return image"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# size of the 2D space as rows and columns of the image\n",
"rows,cols=200,500\n",
"# number of seeds\n",
"noSeeds=13\n",
"# random seeds in the space of the image\n",
"seeds=generate_seeds(noSeeds,(rows,cols))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
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xxiz0tmv1DezUOBcaY9a2Ecfngd8bY8qNMQ3eMQDw3nPXAd/zYtiAnS7pxqP8XU3ASBHpbYzZbYxpa1oipQJLEyul/LU17v5eoHU81gnAeK/7qMbr+rgBGJTwfLwvqGuxCckWr4toRNx+fhG3j13YlqPido5xLLYFoiLuUBvjjvkK8CtsK8Y2EblfRHon+wNF5EoRedPrcqsBrgIGxG2y3RizP+7xCcDTcTGtws4tODDJ7v8P20LyothuxjsT1rf1+g5O+Hvqsa1AxV5ytwSbRF2ATYgWAueRPLFq6xiJ5mFb6C7Azt/4mre/jwKvG2NibTwvmY4es1XieRycuIHYCZl/4nXB1mFb/MCeqwHAMdjWu7Z8F/i1MabyKNsMThJLqwHYVseNCeuLj7K/z2HfTxtFZJ6InHuUbZUKJE2slMqMCmCeMaZP3K2nMeb2ZBsbY+YYYy7Ftt68j+2eat3P5IT9dDfGLGznGNuxXXSlcYcZknDMXxpjzgZGAqdgv1gPIyLdsK1gPwUGGmP6YCdilvhdJfnbr0yI6xhjTFWSv3uPMebbxpgTgU8B3xKRi5O9Rgk2YxO41jijQH9sdyfYJOgibPfoW97jy7Hdb/M7sP9k5mFb6i707i+g7WStlV8VmRPP4+Yk2/wrtuv4EuwE40O95YLtNt1P3Di7JC4Dvi8inzvKNluSxNJqB7YF6oSE9a3n5IjXwhjzljHmauA44Bk6NxmzUoGgiZVSmfE8cIqI3OgNoC4QkY94g3gPIyIDReRqLzk4ANRju9fAjj/6XusgZK9b55r2jmGMaQH+CvxQRHqIyEhgUtwxPyIi40WkAGjAfukma3EpxI7D2Q40i52E+bJ2/vaZwI+97kpE5FgRuTrZhiLyCRE5WUQEqMW2bHWk5edx4CYRGeMlf9Ox46g2eOvnAV8EVhpjGvHGPQEfGmO2d2D/RzDGrMFO6/MFbEJbhx1v9DnaTqyqgRIRKezKMeP8wDuPp2HHQT2RZJte2PfPTqAH9jVpjT0G/A64W0QGe61b53qvXav3sGOofi0in2ojjieBL4nISLHTHU2NO0aLt/7HItLLO//fAlrrbB32WohIoYjcICJFxpgm7DjDzrT6KRUImlgplQHGmD3YBOQ6bOvCVg4N8E6Uh/0C2ozt6vsocLu3n6e95/3Z694pB67s4DG+hu1i2oodMP37uGP2xraK7cZ21+zEdssl+zv+HfuFuRvbKvJcO3/+L7xtXhSRPdiB7OPb2HY4MBebTL4B/MYY82o7+8cYMxf4AbY1bQu2Jea6uE0WYgekt7ZOrcQmj11trWo1D9hpjKmIeyxAW2ODXsEmLFtFZEeKx10LvAz81BjzYpJt/oA9l1XYv/fNhPXfAVZgW/B2Yd8rh30neOPMPgE84CXRJKz/B3ZQ/CtePK8kbHIHNlFfj23R+xM2oYPkr8WNwAbvvX0btitbqayicwUqpZRSSvlEW6yUUkoppXyiiZVSSimllE/SlliJyBViKz+vTXLJtFJKKaVU6KRljJVXGO4D4FKgEjs48npjzErfD6aUUkopFRDparEaB6w1xqz3Lm3+M7aeilJKKaVUaKVr5vliDq/GW0nC5dUicitwK0A0Gj17xIgRKJXcAfyrqxhCsV3s3Nr+Zrmor+sAVKDk5QGDjphnWoVFy76MVT5b+u6WHcaYY5OtS1di1S5jzP3A/QBjx441S5YscRWKCrwPsEXDVVJ7ZvHI3a6DCKZewMU4/KBTgREdBEzuhi2VpkKnttxWTMvQb3Ap+eHGttal6/OmisOnOSjh0DQGSnVCJVp8WXXVHrStU3m6gSZVYRSDvSszmlS1J11jrN7CziY/zJuu4Drar86sVBI6q4VKzUpsZ7JSKmyaway0c0AEJKmCNCVWxphm7PQZc7Az2T9pjHkvHcdSSqmjWQM0ug5CORXtDZzuOgrlr0ZgY/Lpxx1L29ADY8wL2Fnvleqi/a4DUEqFwWnA2aNcR6F80whUQ9U+14EkpZXXVYCtdx2ACokDQIvrIJRSPmgGqqCq1nUgbdLESikVeq8B210HoZwQ0G+6UFkDVQ2ugzgqvQpZKaVUaPX4HDBKuwFV5mhipQKoGVjrOgillFJB0lSeFU3P2kCqAkpLLCh/vQV86DoIpVTX7C2HnQSqrEJbNLFSSuWEA0CT6yBURkWvBkbpxEZZb1+5LWmYJVegaFegCphGYIfrIJRSYXAC2KlrVdZqKYdasiapAm2x6rKKCrjjDhg3zv5bUdH+c1RHNAM1roNQIbWDrBiioZQiBqyDarIqqQJtseqSigoYPRrq66GpCZYtg8ceg+XLobS03aerNjWjRUFVOm3GThmXdEp6FSrRYqCn6yhU18SA7YEtANoebbHqghkzDiVVYP+tr7fLVSrqga2ug1BKhcEt3aFAyyxknxiwG6qyt21ZW6y6YNGiQ0lVq6YmWLzYTTwqlzVqI18nxbA9CxHXgYRIZW1v7lkwgSVVJYwtruSbExdSUlTnOiyVdWLATqiqdh1ISjSx6oLx4233X3xyVVBgx1splVFvPssjc1wHkV02Ag3AhY7jCIvK2t6cc99tNDQW0hSL8O7WQTyx4gzevH2mJleqkyqgao/rIFKmXYFdMGUK9Oxpkymw//bsaZerrtpGIKcpV0od1T0LJhxMqgCaYhEaGgu4Z8EEZzFFpxYDJzk7vsptmlh1QWmpHag+ebJtpZo8WQeup04LgqrMmAh8/DyIjncdSTgsqSo5mFS1aorls6TKZZkD7YzJPqtga/a3VoG++7qstBTuvdd1FEqpzuoG0AuIQfQj0PCW44Cy3NjiSt7dOuiw5Kogr5mxxVUOo1JZJVZua6FkWVmFtmiLlQqAXdgrApVKr4lAycnegzygH0RHgjiMKdt9c+JCooWNFOTZb8WCvGaihU18c+JCx5GprGC8qWpCNC2CtlipAKjHVlxXKr2GAZwct0CAIdCjHg5sspXUVOeUFNXx5u0zvasCixlbXOX0qsDoxQAFTo6tOmuNrdgboqQKNLFSzu1Fv85UJpwC5B3XxsqR0G0vyI7QfcZnRElRHT/7+GzXYdiWx4kj0c6YbLAFth4ITfdfPH33Kcc2o4WYVCacOwg46ygbjIXCPtrWoVR6xYBaqNoZyqQKUkisRKRURF4VkZUi8p6IfN1b/kMRqRKRZd7tKv/CVUqpzusBHWufPwcKj9NfnNmqhw6WC7gYsB+qwj25bipdgc3At40xb4tIL2CpiLzkrbvHGPPT1MNTSqnUXTMaOL6DG58F3VdBw8Z0RqT8FhXgP3UKm2BrgKrw/8fqcmJljNkCbPHu7xGRVYDLwiUq67yP1q9SgXQqRHtBQ7nrQJQKi+qsnv+vM3xp8RaRocCZwCJv0ddE5F0R+Z2I9G3jObeKyBIRWbJ9e2682EqpzJs0DhjUhScWQ/Rsv6NRSoVdyomViPQEngK+YYypA+7DziUwBtui9bNkzzPG3G+MGWuMGXvsscemGoZSSiXXna4VqhKgvy0iqoIt2gv4T73sILg2Qg41oKSUWIlIATapeswY81cAY0y1MabFGBMDHgB0amKVRCXaDajSbdJxeKXWuygP6AvRM3wKSKVHAUCZ6yhUUutg156cKlWYylWBAjwErDLG3B23PH6I6GcAHaWgktBZ71V65YEdoJBqu3wecDxET9QK7Up1zoewex/scx1HZqVyVeB5wI3AChFZ5i27C7heRMYABtgATE7hGCqUNKlS6ZUPTPBzhwKc4lVo36YlbYMk2o2j1ydTjlTBroacS6ogtasCF5D8B9wLXQ9HhV8M2w2oVPoUAsOuSMOOz4JubwC1mlwFxjDgPC2zECy7YdvunJ3GQOvgKaVCJQIUpfMA50K3PvrhqVRy+2FrVc4mVaCfDUqpkBkEXJaO1qp450D3gTrmyjUB/RYLlGaoWhvaqWo6St+SKoMasUVBlQqBM6HHya6DyG09LgaucdsNWFHRnTvuGM24cR/jjjtGU1HR3Wk87uyHKv18h9QGryulVKCMAUZfnMEDngTRHtDwbgaPqQKjoqI7o0dfQn19Pk1NeSxb1ofHHhvC8uVzKS3NpVHbtbA13PP/dYa2WCmlQiMPvJpGGSLAIK3QnqtmzDjlYFIF0NSUR319hBkzTnEcWabFcr77L54mVipD9gObXQehQmwCcPpIBwduLSI62sGxc1j0YmBi1GkMixb1O5hUtWpqirB4cT9HEbmwHWqrXAcRKJpYqQxpBva6DkKFWD+AIY4Ong/ozFyZNRhsrQV3xo/fRUHB4TNIFBS0MG7cLkcRZdoWaKiGetdxBIsmVkqprHca0H+A4yDyINqVyZ5V1poy5QN69mw+mFwVFLTQs2cLU6Z84DiyTKiGvTuhxnUcwaOJlcqAZmxXoFLpMbY7MNZxEHnAGIhGtQxDukUHAn1dRwGlpftYvnwukyevZ9y4XUye/GGODFzfDXu2w27XcQSTXhWoMqAG2OY6CBVSfQGCdIX7+dDjZdjbZOf1UmkwCegejGrrpaX7uPfe5a7DyKC9sKsqJ6eq6ShtsVJKZbVPnQiMcx1FgouhR6G2XKmwaYZt6zWpaocmVirNNqOtVSonXQQ90jq3jlIZtvn9nJ6qpqM0sVJKZa1JZwPDXUdxFOdAtNh1EOESnVoE3V3U1chlzbC5XPu2O0gTK6VU9ooQ7P42AU6FqE5946N89Ksrk/bCtvc1qeoEfXeqNNqMFjhR6TLpRKC36yg6IB8YAtERrgNRqiti2v3XSZpYqTRqxJZaUCoNhpE91zUXAoMhGuRuyywQvRFAB65lzh7Yu8F1EFlHEyulVFbJAz4NthswmxRiW650zFXXnXgy0MN1FDmiFpo2aq2qLtDESqVJPdpapdIhDyi6guz89CoARkFUG11UoNVCS4Ve0N1F2fjRpLLCZmxXoFL+iQClroNIlQDnQrQg2OPugybaD/QrKxP2QmMFbHUdR/ZK+V0qIhtEZIWILBORJd6yfiLykois8f4NwOQDKnNi7W+iVBf0Ai64wnUUPrkYeuRpctUR+QB3jML2p6r0aYQ962G76ziym1/p/8eMMWOMMa2zdd0JvGyMGQ687D1WOeMDtBtQpUPokpDLoEc310EoBRCDnR9Anes4sl+62lWvBh7x7j+CN9ZUKaW66iTgU5e7jiINPgbR/q6DUDmveiXsdx1EOPiRWBngRRFZKiK3essGGmO2ePe3AgMTnyQit4rIEhFZsn27tjsqpTogdE1WnjMhOsR1ECo3xaC6XDsZfORHFZiJxpgqETkOeElE3o9faYwxInJEzVZjzP3A/QBjx47Vmq6hsR4dY6X8dhZw+lmuo0ijfOBkiHaDhjWugwmWaAT4frbV1sgWzbDrfU2qfJZyi5Uxpsr7dxvwNHae+WoROR7A+1cv2swZ2pas/Ncd4DjXUaRZIVCiRUSPEAE41XUUIbQXGt6Hfa7jCJ+UEisRiYpIr9b7wGVAOfAcMMnbbBLwbCrHUUrlrjOAk48YTBBS3YBSiJ7gOhAVfi1Q4zqGcEq1K3Ag8LSItO7rT8aY2SLyFvCkiNwMbAQ+n+JxVFaocR2ACqERAGe6jiKDCoHhEK2Hhp2ug3ErmgeMdx1FGO3F1hpU6ZBSYmWMWQ+MTrJ8J3BxKvtW2aYZ/Y+q/HY80D0XZzDJB8ZC9DXYe8BeIZSTBgEXjXIdRcjsByqgSmdWThctY6t8ogPWlf8u6w9c4DoKRwT4GPSQ8F4MqTKtEVinSVWaaWKlfLAfWOs6CBUyEdCMAuByW6E91wjoN5SvYtD4AVTlbPtnxujbVikVSF84FRjb7ma54TKIRl0HkVk9zgJu1m5A39St1KlqMkQTK6WUygbnQTRXro5U/tpZDvWug8gdmlipFNUDm1wHoUJm0qlAsesoAiYPOA2iQ10HorLKznI4QA5fAZF5mlipFMXQsr2OLJjFW3NcB5Em/fBnXoiwKQROgOhJrgNJr+h44JNabT01MdhTbofAalKVUZpYKRUAFRX53HHHIMaNG8YddwyioqIDWcX7sDL9oWXcpAhwjOsoAqw7tkL7UNeBpNFA0GrrqWiEppVQ5zqO3KS/CVUK9qMd96mrqMhn9OiTqK/Po6lJWLbsGB57rIjly9dRWupPa+DO2t68sGAC66tKOLG4kqsmLqR/UUA/dS9Gf/K1pztwIkT3QUO162BU8MR0IjmH9ONLpaAOrbaeuhkzBhxMqgCamoT6emHGjAG+7H9nbW9+cN9tvLZ0LB9uLua1pWP5wX23sbO2ty/790seMAq0xEJHFQKjw3e1YLQ/cKzrKLJZI3r5n1uaWKkuiqFFQf2xaFH3g0lVq6amPBYv7u7L/l9YMIEDjYW0xOyYlZZYhAONBbywYIIv+/dLIXD2FWhi1Rl5wPkQDdNrdg1QomUWuqYZ2A5Vta4DyWmaWKku2gzsch1EKIwfv4+CgsNHlxYUxBg3zp9p59dXlRxMqlq1xPJZXxWcy+7ysImV6qLL9fVTMexUNbtdB5LzNLFSyrEpU3bQs2fsYHJVUBCjZ0/DlCk7fNn/icWVRPJaDlsWyWvmxOIqX/bvhwHAZ65wHYVSWcyshKoG11EoNLFSyrnS0maWL1/H5Mm7GTduH5Mn1/g6cP2qiQvpVth4MLmK5DXTrbCJqyYu9GX/KhgKLodogesoUhP9ATBwpOswss++ctjiOgjVSq8KVF2wAXtFoPJLaWkz9967NS377l9Ux3/dPtO7KrCYE4urAnVV4KnAuPNcRxECgh1vtQQagnFqOy9P0N/7nbSnHPagtaoCRBMr1QU6cD3b9C+q48aPz3YdRlIRgF6uowiJ1isFV0ODXm4ffnvKoQFNqgJGfxoopZw5Azi7xHUUIRMFTsq+eQWj1wPom6HDGr2WqpZ2t1QZpomV6qRd6BQ2yi/Hg1e8SvmqCFtA1J9SaJlxSjE2cHV0MWCVLVWlLVWBpImV6qQdaGIVEP3hJGCw6zi6aAgwSGsEpE8RcCpEtZs1ZGJQpc1UQdblMVYiUgY8EbfoROA/gT7Av3Go9OtdxpgXunoc5UolsCbJ8o3YJoYemQ1HxVkDNMJQmLgJGmvgpbi1/hRpSL+P5QEXuY4i5KLARyA6DxoC/F0c7Qc65LcjYtj+PxVkXX4nG2NWA2MARCQCVAFPAzcB9xhjfupHgCpTtnHYgPQND7H6keRblk2NAedkIih1hBp4YhnEXUBY2Ac+HrfFrJpDwy6aCeYQjGNAv0czpRC4BArmQJPrWNpyxwj0DdEeL6mqCk79OZWcX+/ki4F1xpiNImGaWyGsjryib9O0++h4nW/tCnQjBg+8BHuPvtU1fQ7df6MG1h6+h0C4tgQdW5VJAoVXQMvs4LwHVGdthyqdAzAb+JVYXQc8Hvf4ayLyRWAJ8G1jjNbYD4oPprHm8SMXd+bDdvW0LZR9axb0usa3sFR7YvCrpzrd/HRuHzg3fsFeeKTRx7BUVul+OcTm0IkfUSoY1kGVnrVsIcakdlmBiBRiJ447zRhTLSIDscM8DPBfwPHGmC8ned6twK0AQ4YMOXvjxo0pxaES1bN12s+OWLofOODD3o8BTrgGGKnJVfrVwIMv2Xo1fohLrP66N/MjNiadCpSil8640gQsgAY/PghSdAwQmVqKXg14FLFyO1IjiH36OUxKfrjUGDM22To/WqyuBN42xlQDtP4LICIPAM8ne5Ix5n7gfoCxY8fqRaOpeG0avJ6wzEA65zffD+yYBQMumgXna3KVHvPhqWrbnOjnFGBxV+J9dh/EvP99q7BNzGl3DJpUuVQAjIfocmhI54dEh2lS1abGctiNJlVZxo/E6nriugFF5HhjTOusRZ8Byn04hgJgJfxp1hFLd605dAlmJu0ECl6BopZZcKEmV/56Bp5vshdnplPRoRzntDo4PqFP+G8+H25SH+x1w8qtHsBIiK6Bhmy5jDTXNJVDDTqkNQullFiJSBS4FJgct3iGiIzBdgVuSFinOmPXNPgw/jGsTlYBwaGtQNFbwIWOAwmVv8BLBtZl+LC9oV/Cook1h+6vxJaHTcmZQLdUd6J80VpEFDfJVTQP+9NbJfGe1mLOYiklVsaYBqB/wrIbU4ooJ1XCgYeOWBq7N3klqaA5sBe67Z4FfbXVKjV/haYWeBXbLxcAJ/U5dD+v5vCW0WY69/68ALQLMGj6ARGINjnoFowCo/TS0CNthM1Gq6pnMS0cknF/57DRwwB732X1/zkJxhcbgL6/hOOmvghc5jiabPUWPNyS3oFxKRrWB4bFL9gHdXEDoHfQ9lCQPGDYFemKTKWkCDtx85vQoFeMOhaDKi0Amu00sUqbOuylHIfbNm0JYaw9sRvYM62Wk6ZuBE5wHU6WqYb7NhyRb3dFxe7ezHh5Aos2lTB+SCVTLl5Iad+61HecTHe4ovuhhy/UHBpj38yhPycPHZ4ceD2A8+GYl+2FKcoVffXDQBMrXyT5z1B9D6tnZj4Sl5qB1dMWUzZ1IF5tbdWuevjFfF/2VLG7N6Nn3Eb9gUKaYhGWVQ7isaVnsHzKzPQlV3Gu6nPo/toaeNO7HwU+pa1VwVcAkcshb076i4gKaLfwEfZD1XrXQSgfaGKVsmZWT/tf10GorFTtW1IFMOPlCQeTKoCmWIT6xgJmvDyBe/9ltm/H6YiT+8DJrQ/0UyZ7CHS/Ahpnp3f6mx4nAV/Q8VWH1EJVhesglE/0I6+zNk5j48Ougwi2DdP+xtCpY0kYkaNamVnwW3wfnLpoU8nBpKpVU0s+izcV+3sgFXqFl0HhS9CgA6gzoAo2h3GASO7SxKpN+9mXpCWqDu0Fb88BoHbaEoqmbkTrMCTYPsuWzE1D1evxQypZVjnosOSqINLMuCEOJ23tAYxwd3jVRXnABRB9CxramZtSpWIdbNunVwCGjCZWACumwcKEZQY2OQkmHLYCRdO3w3dnQYGWYQCgchbMx2bnaTDl4oU8tvSMg92BBZFmehY2MeXixDd3BgmHVXpXWaQ79mrBVdBQ499uoyOBz/m3v+y1Cna2pLfPVTmRY4nVBnjtkSOWHphnSwYof61ugrKZwJd0wma2zoIFpLVEfmnfOpZPmcmMlyeweFMx44ZUpfeqQBV+RcBwiK6Hhp0+7bMvkJfr46tW26RKuz9CKeSJ1QzYHjcj+DZYPc9dNLlo9S4oWwac7zoSR/bMss38L+FD2fL2lfaty/hAdRVyXgnoaHNQ5hbMdhthe5Mv5VVUMIUksdoFPHPk4p/sY3UAZnDPeRVgm2smOg4kk2LAa/Aw6b92Xal06w+cBtF3oGFfu1u3KVoEDPYrqGy0Har36FQ1IZeFiVU5R74rX2P1NP0pFVSr10DZr7fAV9cBJ7kOJwOagdXwC7/6TpQKgN7AOOgxD7o8nv1KoCyHuwE3V+fUQPWKzb2Z8ZsJLFpWwvgxlUz5ykJKB4d/aEKAE6tGknVA75r2VDqHqag0Wb0Dhk97m7ypA4GersNJk9Z64x/CL1a6Dsa9PLxKkCo0uoNcBnkvakNs5+VWM1XF5t6MvvQ26hsKaWqOsKx8EI89fQbLX5oZ+uQquIlV7f+w+ueug1B+WgMUTfsHg6aGdCB73dPwe9dBBEhfYLjrIKyK6t7M+OMEFq0sYfzISqbcuJDSgeH+cE+bPFtEdO/snGp8SVEzVL3vOoiMmvGbCQeTKoCm5gj1ewuY8ZsJ3Pvf4R4HGojE6sDmzaybNu2wZfofNpxqgX3TZjEsbMnV6ll2gLoKnIrq3oz+wm3U7/N+OX8wiMfmnMHyR2dqcpWCHpdDy5yOX9gW/QZQNDKNEQXVXtice1PVLFpWcjCpatXUlM/iZeEvWByI2ZoMtpE0/tbiNCKVTqFrEH9zFryKvmkDasYfJxxMqsD75byvgBl/nOA4siwnELkIogUd3z4gXzkZtBuq1+dkS8H4MZUU5B/+oVhQ0My4MQ4LFmdIrr3LVQDEAH4yi7RVysykf86CFaSlkrryx6KVSX45N+ezeGX4fzmnXSHwEYj2ch1IEG2BXVUh/CXZMVO+spCe0caDyVVBQTM9ezQx5SsOCxZniCZWyonVB4DH5uDVYsgyMVg6y97KSeESKZUJ40cm+eWc38y4keH/5ZwRvYF2Wq2inwN6H5uJaAKiAmp3QgqlKbJd6eA6lr80k8lfWMK4MZVMvmFpTgxch4CMsVK5afVaKHvlTbioDjjNdTgdtBe2/t2W5VJtqq2B/BqIBmDw+pQbF/LYnDMOdgcW5DfTs3sTU24M/y/njBkM0X1HqXE1KgoMzGREDlVBXS3Uu47DvdLBdaEfqJ6Mtlgpp1a/DjRlS2mCOmj6OzzhOo7g2lUDVTXwT+BFgLedhgNA6cA6lj86k8mfXsK4kZVM/vRSHbjutxLgJIjm/LyQ26F2N+xxHYdyqUMtViLyO+ATwDZjzChvWT/sV8xQ7FR7nzfG7BYRAX4BXIXtJPmSMSYAH68qsKqAoVuA411HchR1wCvwG9dxBNOBGvvv00B1/PJtcJ2DeBKVDqzj3u/k3i/njCoBCiC6DBriBmtH+0BuzMS9B3ZW6/x/qsMtVg8DVyQsuxN42RgzHHjZewy2tu5w73YrcF/qYaowW/0IsGwBwWw73wvUQNMc+IVOQ38Ygx1Dsg/uAX7G4UkVeBdKNmQ4LuXOQODchCFXXz8RCPuFAo1QvVGTKgV0MLEyxsznyClkrwYe8e4/Anw6bvkfjPUm0EdEgtwUoQJg9bPA8/8gWPWcY7Dk7/CLl7SlKpEB6mD6AXtr66xtBH71Ojl5uXnO6g2FF7kOIsOqPsjZq//UkVIZYzXQGLPFu7+VQyMTizn8Uq9Kwv9zRflg9VLgV0+5DuOQ55+yg4XUYdbWwPRamN7BZKkO+MkcNLnKJYUQvcx1EEq54cvgdWOMoZMfmyJyq4gsEZElu/fq9erKWrsT+NEs12HAk7PsyEF10N9r4O4a+GsXnhsDfj6HnL78POfkQfRiCPfF581QXe46CBUwqbzjq0XkeGPMFq+rb5u3vAoojduuxFt2GGPM/cD9AKMGD9bfsgqwY3IaDESdHL0RnnrW3t2GVlL3PFpjh47UYKeY7qq9wKPz4AtnAcf5EJgKvo5WZc9K9bBrg3YBqiOk0mL1HDDJuz8JeDZu+RfFOgeojesyVKpdOwAezXSr1Q54/VnbcV2JJlVN8HSNvVVi88xUkqpWm4DZbwNrfdiZyg4bPyCYF6akYjfs2aAtsCqpjpZbeBy4EBggIpXAVOAnwJMicjN2jOrnvc1fwJZaWIv9kXqTzzGrkNsPbFgHQ1nhLTmV9HYnbISViwNRc8m1php4C/sjfFWajvE2cEVNmnaugmcrcEKYfqnshH1bQjEjl0qPDn1bGWOub2PVxUm2NcBXUwlK5bZuwNBigDXekh7YOjj9vft+Wgeb3oaXfN5tlqmrge3AFmB+Bo63YQcM3QQMycDBlHv7KqB7BOjpOpIU7YQDW468Rl6pOGEeVaiyVG+AW+InzV3u/XsacCw2yUr1A3oNsBs2bbRVLXNQfc2hMgmvAu9l8Nh/Aq5dCScVEOy6sMof7wLjd5LdidUe2LsFdruOQwWdJlYqUPKBXm2ubf3qHwycRderOe+AV5fZD/tcYzg43OU3uB13+wRw5XI4M4qXTSsVVPuhbqNOVaM6RBMrFSgnRYDvR9rZajN2+N6F3uPOXIPRDLNetbvIJa0FUepheoBqsP4D2LoQrrwE/TQKvZh3y7YpamOwfa0/V2+onJBt73ClPDXAM96tEx58OveSKmBjLUyvC1ZS1eod4OG5rqNQabeoIYsmXI+zdaUmVapT9DeiCoyyYrp4Dekz3r+X0fbg9hj89qmcm8vrHzWwgmBNFJSMFrJTSoWFJlYqOCJApL1uwGRa04bXsI2wp3NoFqUP4U9L7N0cSqoerrGdpQ1kR/3CauCx2XBD4lTvKlzKgZPLodco15F0QAy2r9SadqrTNLFSgVA2FLg81b20Zk7vAetgX7W93G17qvvNEi3whDe4divBb6WKF8MWD/3HbLjyMnSQQlg1kiXdao2w54MsiVUFjSZWKhgGAoO60lqVTL29xbClr9a0s3mWa6mBedgf1uscx5IKgx1vVfoijPoo0N1xQCo9tgM9y6FbUFutVsF9LcH6QXYqMMF1EKqjNLFSzpX1Ij2FIqMROKPF9oetaHfrrFNTYyfh3Am86TgWPz0HDJ4H/c4FilxHo3xXi61EO9RxHIl2lduSeZth7rZ2t86oU1dCcdhmBcqUHsDEzB5SEyvl3qXASL9aqxJ0j8BHW+yH+ab0HCLTamugCViIHbISRjOBu3agiZVKv53l9sfXUzA3oNPUrAJWheTzK9P6Amdn+HNEEyvlVH/oep3PjopE4DMxeMTY+b2yafBRnFiN/fdP5Ejx5+1ACXaOIxUuLWCrbbZdDjgzVrPpV/CB4yhU+uwG5i7K7DF1iKhyasBtQFmaWqsOkweTIrZZOJve9QbbPNVoZz3/CTmSVAHTa4AFZMdljapzdgDvbXQYwB5gD0unNWlSpXynLVYqt9wcgUdb7MCkLHCgFn7mOgiHpjfBLXPhOC3DoHyzh7nTXCZ1Kuw0sVLOlH0X6CGZP/AN3r8LgLczf/iOWF4DL7gOIiAeAi6dDWM1uQqXeuCdcjgzk1cHruK1aVqYSqWXJlbKnQg46ZcTr+vxnBY7xGNe5kNI5vc1h+Z4bUSrkbcy2HJku2fDpZpchUumxjsuKmfZbDu0S3uWVbppYqWcKLsRnwetd2Fy14IInNoCBYCruepi8EfvSqRqsnZcfdo1cSjpVCESAz4oh1NGkrYfWbPLeX+RHdalVCZoYqUyLg/gRMHfD9Iu7qtbBE5sgQuxM+JkSEsNzMG2xlRk7rBZbTOwajacqq1W4REjfVdjPFIOO+HDPVCZpkMolYwmViqjCoFhp7qOIkF3r+VqD7A0vYfaVQMfYstqLUvvoUKnDpgNHDcb+mtypZKKwd9WArB0Q+5cQauCRRMrlVEFAJ/PRHmFTiqMwHktUIPNfHzuk9tZY2cyXEp4i3pmwj7gAeDO14HzyK7SGeooVgPDSe0raT+8t5ZX3tYudeVWux9LIvI7EdkmIuVxy/5PRN4XkXdF5GkR6eMtHyoi+0RkmXebmcbYVZbJB4pdB3E0EoFPiK1aOgBffnYcqLG3vwCPoEmVH2LA9AZgLToSOSwWtdD1GY93w95y2LaWuX/RpEq515GvjoeBXwF/iFv2EvA9Y0yziPwv8D3gP7x164wxY/wMUoXD8YBM7UprVRcGpndZHvyrd/evLXZgT2evzjbY5ingbvTqvnSZvh7u6gMc5zoS5Y8mOv9/fS8srWLu82kKSakuaPcdbIyZD+xKWPaiMab1t+Kb2IknlDqqrlesctTf89kInNLJwxtoqYXpB+xNk6o00xc4PBZV0PHKvTGgGf62XpMqFTh+jLH6MvBE3ONhIvIOdqzp940xr/twDJXlynoB33JQDDRVlwn0NXbG43asqoGn0x6QOzW1vXl9wQQqq0ooKa7k/IkL6VPkdtba6e/AXcXA6U7DUBlWM21lUGv7KpVaYiUi/w87yuExb9EWYIgxZqeInA08IyKnGWOO+PQVkVuBWwEGF+kU9rkhG0ca58HZXiHROcm3eLrGjncP83Cfmtre3HvfbTQ2FhKLRdi8dRDLVpzBHbfPdJ5c3V0F39oKXOo0DOWHpdVwdg12IHtyG6aVp+P6EqV80+VvOhH5EvAJ4AZjjAEwxhwwxuz07i8F1mE7U45gjLnfGDPWGDO2b48eXQ1DZYGyYuBLiUuz6GMxLwInYd/tcR6pgQdr7Bjq/YQ7sXp9wYSDSRVALBahsbGA1xdMcByZfe1/2wI1s11HolLWDMk/G/azcVo5G6eVs4HOD3tUKpO61GIlIlcAU4CPGmP2xi0/FthljGkRkROxPzvW+xKpyl69gH6Jg9azrPWqIAJDbCHRp5+xizaTO0N8KqtKDiZVrWKxfCqrgnGd507gGeDK2TBQa1xltw+a4JRVwKnQWA4/AWNgjeu4lOqgjpRbeBx4AygTkUoRuRl7lWAv4KWEsgoXAO+KyDLsFea3GWN2Jduvyg1l/YDRrqPwSUEERsBnesAqciepAigpriQv7/B2gry8ZkqKqxxFdKTNwErXQajU7Qb2tkBtOfwa5hp42XVMSnVCuy1Wxpjrkyx+qI1tnwKeSjUoFSJjgBEBLAjaVd0i8O0W+C/XgWTW+RMXsmzFGQe7A/PymiksbOL8iR0Y1Z9BOwD+iS0eqrLXe8BSmOt2+J5SXaKV11XalIBt18yITNa6yj19iuq44/aZ3lWBxZQUVwXiqsBEa4Df74Gb3gdGuI5GdVXsBXjFdRBKdZEmViptojcAJ2eqtSqzSdVAoDqjR3SvT1Edn/x48EeIbwF+vgG+cRzQz3EwSuWobbW9eWLBBFZXlVBWXMm1ExdyXMB+iKWL/sRXaRGBVCqCBltehJunRtBrWYNrL/A/i7HFvFV2ieXW+MUw2lbbm8n33cbfl45l9eZi/r50LJPvu41ttb1dh5YRmliptDj534GTwppZqWxggOkvAw2uI1GdUf0ivOo6CJWSJxZMYF9jIS3elcQtsQj7Gwt4IgDlWTJBEyuVRtn89mq/ztY37oQTMhCJSs1PXwcqXUehVO5YXVVyMKlq1RzLZ3VAyrOkWzZ/86mAKrsN6OM6ilR14L9Gt4j+B8oCjZBV9WiVynZlxZVEEsqz5Oc1Uxag8izppN8Lyn8DAAlRiYWjuP4KW1FCBdvTK7HFx5RSaXftxIV0L2w8mFzl5zVzTGET1wasPEu66FWByjd5wPDzyK10fXyEPrN1go2gWwUUbYSL9gFnuY5GqXA7rqiO394+07sqsJiy4qqcuipQEyvlmzyAS4TcyqxgwgDYvsPWNFTB9SZQuA0mvgOc6ToaldQy0Kk6wuG4ojruyILyLOmQW9+AKm3ygZO6u47Cka9GmOg6BtUh84FXqoEPXEeiknlvK+TGKBwVZppYKV/0ApgSIbhvqfSOXu4vWosyW7wJ/F2nhldKpUlQvwVVFskDCl0H0a40v9X/M8JtA9N7COWfFvAuF1RKKX9pYqVSdhLQZ2pXrwLU6+BV5pUDD+lkdEqpNNDESjmmb0HlRjVwT26OrVVKpZF+q6mUlPWBvO+6jiIgJsFdo1wHoTpjH3DfbKDZdSRq+WzY5joIpXygiZVKTSHQIwjFQAPQpdg9An1dB6E6azfw1FwgN0rsBFYD3tg3pbKc1rHKMltqe/Pgggm8W1XCGcWV3DJxIcc7KrpW1g+41MmhkwjIb4TT4K4VML3GdSCqM1aDfqsrpXyhiVUW2VLbm6vvu429jYU0xyKs2jqIv604g2dvn5nx5KqsCJtUnRyE1qoAGRiBT7bAH10Hojpr0yIYMg6tm6GUSklAfuarjnhwwYSDSRVAcyzC3sYCHlwwIfPBTARGaFKVVBSuch2D6rRHgdrFwHbXkSilslm7iZWI/E5EtolIedyyH4pIlYgs825Xxa37noisFZHVInJ5ugLPRe9WlRxMqlo1x/J5t6o4o3EMAsjVKusdMTDCmO+4DkJ1xa+BmqXYgVcqc6oDMUpSKV90pMXqYeCKJMvvMcaM8W4vAIjISOA64DTvOb8REW3W8MkZxZXk5x0+ECQ/r5kzijM7CUTRzcBpmTytWfiRK9DHdQyqS34DfLgIe8mgSj8Dr7wD+13HoZRP2k2sjDHz6fi8mFcDfzbGHDDGfAisBcalEJ+Kc8vEhfQobDyYXOXnNdOjsIlbJi7MWAxu+o6zsMe6R4SvTJVsjFwBjwNvzHMdhVIqG6UyeP1rIvJFYAnwbWPMbqAYOxVXq0pvmfLB8UV1PHv7TO+qwGLOKK7K+FWBw78DRCVjx1NKKaWySVcTq/uA/wKM9+/PgC93ZgcicitwK8DgoqIuhpF7ji+q4wcfd1guWiArW5CU6qR5wI7Z8MlkAyGUUqoNXfqGNMZUG2NajDEx4AEOdfdVAaVxm5Z4y5Lt435jzFhjzNi+PXp0JQyVYWU34+Og9SwcN9UFd14LvV0HobokBrwP/E2nvUmfRiifkyufBipXdCmxEpHj4x5+BjunKcBzwHUi0k1EhgHDgcWphagCoxjw7VqEXGj1yoMREfTqjezVBKwC5mtylR4GtrqOQSmfdaTcwuPAG0CZiFSKyM3ADBFZISLvAh8DvglgjHkPeBJYCcwGvmqM0XrGWS4fKDsLEB1b1RW3D4CBroNQXdYM/BPYoHMKKqU6oN0xVsaY65Msfugo2/8Y+HEqQalgyQf4pLa7dNlXIxw7rYVq13GoLjPAn4C7WtD5KpRSR5UL/TEqBfnACVmRUwV7lMbp6PzMobAK2z+olFJt0MRKHdUAgO9nQ2YV7LfysKkRzncdhErZ9K3AOjS58kMMqHcdhFL+C/a3kXIuG1KqbJGPV61CZbXpG4Dl2P5B1XW7Ye5broNQyn+aWKk2lXWDnlM1FfDLiKnCFNdBKF9M3wGNc1xHoZQKIk2sVDty9S2SjjFbufpahtPPgXVahkEplUCvb1FJlQ0E/tV1FC5pEqSOrhmtvqCUOpJ+e6jkugO9dYSV3yKT4D9cB6F8Mx+vvpVSSnk0sVJHKOsPnOs6ipAaGiEy3HUQyi/bgblAlSZXnVMNu3TgugopTazUkUYAp2hrVdqcAp91HYPyzTbgWaBRk6uOq4W3XcegVJpoYqUOMwygv+soQm5shBFXuQ5C+akG+CXYbEHLMCiV0zSxUocpvAY4M4ytVQGrzF4Ipa5jUL5qBKZvAzajyZVSOUwTK3VQIYT4HRGwP2x0hBtvcx2ESofpK9CK4krlMC23oA4a9hXg2MTWqhjpTUrSvX8Xwvg3KaWU6gj99FftSPdbJIxvwQ7+TQOFu76b3kiUGz/5J7DBdRQBtRBeXe86CKXSJ4zfaqoLyr6GN+NyZlVU9OaOOy5n3LibuOOOy6mo6J35IJzJgwLXMah0iAH3vg8sdh1JABlocR2DUmmkXYHK6gVIZgetV1T0ZvTof6O+vpCmpgjLlg3iscdGsXz5A5SW1nVyb9r9poJlD/DILpg0B7jcdTRKqUzRb6IclweUXYKTlpMZM849mFQBNDVFqK8vYMaMrlQnzdK3cj7cVaa/cMKqCphl4IDWuFIqZ2Tpt5Hy1XmS8dYqgEWLBh9Mqlo1NeWzePHgjMfijETguoj+RwyxNUC56yCUUhmjn+c5LB8YXuTu+OPHb6ag4PDRFgUFzYwbt9lRRBmyrwU2H347Gx1uFWbbAN51HUUAbIb6Pa6DUCq92k2sROR3IrJNRMrjlj0hIsu82wYRWeYtHyoi++LWzUxj7CpF3QG+EcFVfj1lyhv07Nl4MLkqKGimZ88mpkx5w0k8/ovBnhaoS7htAt48/Pax0+EUvFpiKnTeAWZtxp77HLb3XfuWVyrMOjK042HgV8AfWhcYY65tvS8iPwNq47ZfZ4wZ41N8Kk3ygB6OYygtrWP58geYMeNcFi8ezLhxm5ky5Y0kA9cDPjC9paXtwu4vdXw3V58Os1bYriMVPmuAmSvhtr7Yi0WUUqHUbmJljJkvIkOTrRMRAT4PXORzXCrNhgDdprqfuqa0tI57753TzlZBSKqOMiXOQmB7xgJRWWwX8H//hO9eDojraJRS6ZDqxUjnA9XGmPgf2cNE5B2gDvi+Meb1ZE8UkVuBWwEGFzkc6KPiBLxlyKXNJiN9GNeMggXlMD/9h1KONAHT58BdF6MD65QKoVQTq+uBx+MebwGGGGN2isjZwDMicpox5oiiRMaY+4H7AUYNHqxTlmZQWS/gq8nWaFIFMXjeHNlAlak5nAUmlsGxq+GpDB1SKaWUf7qcWIlIPvBZ4OzWZcaYA8AB7/5SEVmHHZO7JMU4lZ8iQLfOdgP63ZrluHVsWUvb3XeNGY3kSIVQNhS+tMEOcFTh9OjL8IVzgRxpsK+dDe+5DkKpDEilxeoS4H1jTGXrAhE5FthljGkRkROB4YDOChUgZf2AT3blmX4nQRlIqmpbYGUb63biPoE6ml5OZhhSGbQJePENuGwkdtBjyO0G9roOQqkMaDexEpHHgQuBASJSCUw1xjwEXMfh3YAAFwA/EpEmbJPEbcaYXf6GrFIyCBjqftC6795rgcQO5QZs53SWKjwOrtoGL7gORKXNEqDfShi7H9u2r5TKeh25KvD6NpZ/Kcmyp9ChIYFVJsBQ11GkYGeLTZaS+YAjE6tsNxDGFMCuKq39E2YvAt3Ww+mCbeNXSmU1naIsl1wKfCTgrVUtLfZ60mRWkntlDfrBRd3gTe1QD7W/AUXrYIgmVkplPU2sckRPCN6l3Y1Juu92os0ziQT6ADWOw1DptQ9gD+EsHtoALe1vpVQoaGKVI4on4WhsVQxMG310s4HmjAaTnXrAV0bCjJX6coXZU8CEf8KFlxC6T+Z3Xre/mZTKBSH776sCZ4nJ+fnRfBGBKaPg7nLY7zoWlTYLgS1z4forXEeilOoqTaxyQNnXgP5pnj/jQAv8I8nyTBXWzAUC3yqDh1ZDtetYVNp8CPx2NkzW5EqprKSJVS4oAN/qRs1tsXNyJDJoEpUJha4DUJmwC/j9bLhJ5xRUKutoYhVyZZ/DG7neCWtb2q7/tIfwlTXIMjd3hz/v08q7YWaAra6DUEp1iSZWYTcSyGtj0HpLC6xIsnw7NoFSwXQyfG6FLRyqU4SElwHK58CoLJ+s+cDstsvPKRVGmliFVB4w/ARsN8LGluTXOjejzR5ZquB0GLJCE6uwew4ofRmKzgeirqPpmkUEe/YopfymiVVI5QF8HNgBvEvycVEqqx0PDAY2uw5EpdWvgbsWAOcCvR0Ho5RqVwZmwlUudAd43btpUhVKg06Hz2KLh6pwm26AN9BZjJXKAppYhVBPYPDprqPouoodvbnjwSsY9x+3cMeDV1CxQ3+mt6X36fCVgqwegqM6aLqBhvmuo+gk/VGncpB2BYbMAKB/lidVo791G/X7C2lqibDsw0E8Nv8Mlt89k9IBbU0imONGwHe3wXQtbqWCJAZzX3YdhFKZpy1WITIU6D/KdRSpmfHMhINJFUBTS4T6/QXMeGaC48iUcu+XwPuzXUehlDoaTaxCoiwC3UaQ9cUEF60pOZhUtWpqyWfxmmJHEWWJ/nDXINdBqHQzwPPAAk2ulAosTaxCoKwbcCKhGGgzfnglBZHDa0MURJoZN7zKUURZIgL0g7t6ZH1urdrRCCwB5mtypVQgaWKV5coKgVLgGNeR+GPKpxfS85jGg8lVQaSZnsc0MeXTCx1HlgUiwImaWOWCvdjkapkmV0oFjiZWWWw4wAl4tRXCoXRAHcvvnsnky5Yw7uRKJl+2VAeud9In0SkFc8F+4BXXQbSlCXjVdRBKuaFXBWap44G8UwnlGSwdUMe9t+hP8S4ROO102LXCtmjscx2PSqsWsLXqJhKspspGmKulFlSO0harLFQE9B5FKJMq5Y/zTwcdyx5+TcD0BmAdEHMcjFIK0MQq6+RjK24H6tepCqRu6H/wXDF9LbAFTa6UCgD93FUqpD57OoxzHYTKmOkr0EnVlQoAMca4jgER2Q40YKcMVtlnAHruspmev+ym5y976bnLXicYY45NtiIQiRWAiCwxxox1HYfqPD132U3PX3bT85e99NyFk3YFKqWUUkr5RBMrpZRSSimfBCmxut91AKrL9NxlNz1/2U3PX/bScxdCgRljpZRSSimV7YLUYqWUUkopldWcJ1YicoWIrBaRtSJyp+t41JFE5Hcisk1EyuOW9RORl0RkjfdvX2+5iMgvvfP5roic5S5yJSKlIvKqiKwUkfdE5Ovecj1/WUBEjhGRxSKy3Dt/07zlw0RkkXeenhCRQm95N+/xWm/9UKd/gEJEIiLyjog87z3WcxdyThMrEYkAvwauBEYC14vISJcxqaQeBq5IWHYn8LIxZjjwsvcY7Lkc7t1uBe7LUIwquWbg28aYkcA5wFe9/2N6/rLDAeAiY8xoYAxwhYicA/wvcI8x5mRgN3Czt/3NwG5v+T3edsqtrwOr4h7ruQs51y1W44C1xpj1xphG4M/A1Y5jUgmMMfOBXQmLrwYe8e4/Anw6bvkfjPUm0EdEjs9IoOoIxpgtxpi3vft7sB/wxej5ywreeaj3HhZ4NwNcBPzFW554/lrP61+Ai0VEJ8ByRERKgI8DD3qPBT13oec6sSoGKuIeV3rLVPANNMZs8e5vBQZ69/WcBpTXtXAmsAg9f1nD60paBmwDXsJOuVxjjGn2Nok/RwfPn7e+Fuif0YBVvJ8DUzg0i2N/9NyFnuvESoWAsZeW6uWlASYiPYGngG8YY+ri1+n5CzZjTIsxZgxQgm3lH+E2ItURIvIJYJsxZqnrWFRmuU6sqoDSuMcl3jIVfNWtXUTev9u85XpOA0ZECrBJ1WPGmL96i/X8ZRljTA3wKnAutos231sVf44Onj9vfRGwM7ORKs95wKdEZAN2mMtFwC/Qcxd6rhOrt4Dh3lUShcB1wHOOY1Id8xwwybs/CXg2bvkXvavLzgFq47qcVIZ5YzQeAlYZY+6OW6XnLwuIyLEi0se73x24FDtO7lXgX7zNEs9f63n9F+AVo8UKnTDGfM8YU2KMGYr9bnvFGHMDeu5Cz3mBUBG5CtsPHQF+Z4z5sdOA1BFE5HHgQuxM7NXAVOAZ4ElgCLAR+LwxZpf3Rf4r7FWEe4GbjDFLHIStABGZCLwOrODQOI+7sOOs9PwFnIicgR3QHMH+EH7SGPMjETkR2wrSD3gH+IIx5oCIHAP8ETuWbhdwnTFmvZvoVSsRuRD4jjHmE3ruws95YqWUUkopFRauuwKVUkoppUJDEyullFJKKZ9oYqWUUkop5RNNrJRSSimlfKKJlVJKKaWUTzSxUkoppZTyiSZWSimllFI+0cRKKaWUUson/x+Aprjwawq2aAAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#assigning points of the 2D space (pixesl) to the seeds\n",
"# with Euclidean distance\n",
"image=generate_voronoi(seeds,(rows,cols))\n",
"# diaplying the Voronoi diagram (tessellation) along the seeds\n",
"plt.figure(figsize=(10,5))\n",
"plt.imshow(image,cmap=plt.cm.hot,alpha=.5)\n",
"plt.scatter(seeds[:,1],seeds[:,0],marker='o',s=30,c='b')\n",
"plt.title('The Voronoi diagram with Euclidean distance.\\n The seeds are shown with black dots')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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7LndfBiwjJFiZzAfebGYjkse/Sh4fSZjbblkXz8ukq/dNV2Yn5/FJ4MfAxZk2cveb3H1b2us+PmlFKiMkXZ909wZ3b3X3hcl27T4FfBY4w91XdhHH+4Afu/tyD3Mofql9RfKeuwi4NolhFWG6nw/u4+dqJkzLM8TdX3H3rqYoEslbSqxEcmtt2v2dQPt4rDHA5KT7qDHp+riEMIfaHpIPqPcTEpI1SRfRsWn7+W7aPjYTWo6quznGYYQWiPQ5115KO+b9wPcIrRjrzewGM8s48a2ZnWdmjyRdbo3A+cChaZtscPdX0x6PAe5Ii+kZwjyDwzPs/r8JLSR/ttDNeE2n9V29viM7/TzbCa1A1Ulyt4SQRJ1OSIgWAm8ic2LV1TE6m09ooTudMJfjA8n+3gw85O5tXTwvk54es13n8ziy8wYWJhr/etIFu5XQ4gfhXB0KHEBovevKZ4Hvu3tX8/+RHDfjeyo5RkWnZS8R3qtdeTfh/fSSmc03s1P3sa1IXlJiJdI/6oD57j4s7TbY3a/OtLG73+3u5xBab/5O6J5q38/0TvsZ6O4LuznGBkIXXU3aYUZ3Oub/uPspwHHA6wgfrHswswGEVrBvAMPdfRhhUmZL31WGn/28TnEd4O4NGX7ube7+r+5+FPB24F/M7KxMr1EnqwkJXHucVcAhhO5OCEnQmYTu0UeTx+cSut8e7MH+M5lPaKk7I7m/gK6TtXa5qsjc+TyuzrDNPxG6js8mTDY+NlluhG7TV0kbZ5fBWwkTOL97H9usyRBLu42EFqgxnda3n5O9Xgt3f9TdLwQOB35D6LoWKShKrET6xx+A15nZB5MB1BVm9g/JIN49mNlwM7swSQ52A9sJ3WsQxh9d2z4IOenWeW93x3D3VuDXwJfMbJCZHQdcmnbMfzCzyWZWAewgfOhmanGpJIzD2QC0WJiQ+a3d/Oxzga8k3ZWY2WFmdmGmDc3sAjM7xswM2EJo2epJy8/NwIfNbEKS/H2VMI5qVbJ+PvAh4Gl3byIZ9wS86O4berD/vbj7c4Qpfj5ASGi3EsYbvZuuE6t1wCgzq+zNMdN8ITmPxxPGQd2SYZsDCe+fTcAgwmvSHnsbcBPwLTMbmbRunZq8du2eIoyh+r6Zvb2LOG4FLjOz4yxMfTQr7RityfqvmNmByfn/F6C9ztYer4WZVZrZJWY21N2bCeMM96fVTyQvKLES6Qfuvo2QgFxEaF1Yy2sDvDsrI3wArSZ09b0ZuDrZzx3J836ZdO8sB87r4TE+QehiWksYMP3jtGMOIbSKvULortlE6JbL9HP8M+ED8xVCq8jvuvnxv5ts82cz20YYyD65i23HAfcSksmHgR+4+1+62T/ufi/wBUJr2hpCS8xFaZssJAxIb2+depqQPPa2tardfGCTu9elPTagq7FB9xMSlrVmtjHL464E7gO+4e5/zrDNzwjnsoHw8z7Saf1ngCcJLXibCe+VPT4TknFmFwA3Jkk0ndbfSRgUf38Sz/2dNplBSNRfILTo/R8hoYPMr8UHgVXJe/sqQle2SEHRXIEiIiIiOaIWKxEREZEcUWIlIiIikiN9lliZ2TQLlZ9XZrhkWkRERKTo9MkYq6Qw3LPAOUA9YXDkxe7+dM4PJiIiIpIn+qrFahKw0t1fSC5t/iWhnoqIiIhI0eqrmeer2bMabz2dLq82syuBKwGqqqpOOfbYYxHJjWZC+aMSsGMzm7bEDqJ/DAAGD83BjnZD26vdbybFyQAbuddc05JLzbtiR9DnHntizUZ3PyzTur5KrLrl7jcANwBMnDjRlyxZEisUKTqrgcbYQfSPR27jp3fHDqJ/HA1MnZaDHb0IO1bkYD9SkCqBilknxA6juK1dXvTfbW3Ul17qal1fdQU2sOc0B6N4bRoDERERkaLUV4nVo4TZ5I9Mpiu4iO6rM4uIiIgUtD7pCnT3FjP7BHA3kAJucven+uJYIiIiIvmiz8ZYufufCLPei4iIiJQEVV4XERERyRElViIiIiI5osRKREREJEeUWImIiIjkiBIrERERkRxRYiUiIiKSI0qsRERERHJEiVUv1dXBjBkwaVL4v66u++eIiIhIcYs2CXMhq6uD8eNh+3ZoboalS2HePFi2DGpqun26iIiIFCm1WPXCnDmvJVUQ/t++PSyX2FqAtthBiIhIiVKLVS8sWvRaUtWuuRkWL44Tj6SrB3bGDkKkpNRvGcK3F0xhScMoJlbX8+mpCxk1dGvssESiUGLVC5Mnh+6/9OSqoiKMt5KYVgJNsYMQKSn1W4bwxuuvYkdTJc1tKZ5YO4JbnjyJR66eq+RKSpK6Anth5kwYPDgkUxD+Hzw4LJdY/o6SKpH+9+0FUzqSKoDmthQ7mir49oIpkSMTiUOJVS/U1ISB6tOnh1aq6dM1cD2uZ9G4KumxMVB1UuwgiseShlEdSVW75rZyljRUR4qoa1UDoGLW8NhhSJFTV2Av1dTAddfFjqLUtQGrCAPWRXqoDDg8JFc7nogdTOGbWF3PE2tH7JFcVZS1MLG6IWJUe6saDkwHOCxyJFLs1GIlBaoFWA28GjsQKUTlhOTq9bEDKXyfnrqQqsomKspagZBUVVU28+mpCyNH9pqqo4CLATshdihSAtRiJQWoCdgMaGCsZKEcGA1V22BHfexgCteooVt55Oq5yVWB1UysbsirqwKrjgLeCgxVUiX9Q4mVFJgmoJGQWIlkyYAToGo77GrUSL3eGjV0K998212xw9hLVTUwDThMSZX0H3UFSgFpISRUG2MHIsXmjTBwkP4gFpOqIcAlKKmSftfrvyNmVmNmfzGzp83sKTP7ZLL8S2bWYGZLk9v5uQtXSlcbsBa1VEmfOT0kVxY7DsnaIIBPV8FAJVXS/7LpCmwB/tXdHzezA4HHzOyeZN233f0b2Ycn0m4VGqgufe50GLQYdih/L1gG2KwxwIGxQ5ES1esWK3df4+6PJ/e3Ac8A+Ve4RIrAsyipkn4zCarGxA5CesOAQbOOQ0mVxJSTIQVmNhY4GViULPqEmT1hZjeZ2UFdPOdKM1tiZks2bNiQizCkKD2L6lRJv6tVKYZCMwgYNKsGjZST2LJ+B5rZYOB24FPuvhW4HjgamACsAb6Z6XnufoO7T3T3iYcdpoJtkskLKKmSKMqAkVB1YuxApCeqDgSbVQEMjR2KSHaJlZlVEJKqee7+awB3X+fure7eBtwIaGpi2U9twMuo+0+iqiAUET0udiCyL1UjgI8C1EaORCTI5qpAA34EPOPu30pbfkTaZu8Elvc+PCk9LcB6YHvsQERCcjUyKTIpeadqDHAhcKCu/pP8kc1VgW8CPgg8aWZLk2WfAy42swmAEy7lmp7FMaSkqPin5KFyYBxUbYGdm8IfNomvqho4BxihpEryS68TK3dfQOaSL3/qfThSuloISZWKf0oeMuAfYNCDsGunKrTHVjWM0B9yiJIqyT+6fELyQBshoVJSJXnudBhYqSKiMVWlgI+hpErylhIryQP1qPtPCsaZMKgqdhClqRzg84dAhZIqyV9KrCSylWiguhSc06BqeOwgSs+AWccAR3S7XX+qqxvIjBnjmTTpLcyYMZ66uoGxQ5LIshm8LpIlFf+UAjYeqp6HHc/HDqT4lQMDZh0FHBA7lD3U1Q1k/Piz2b69nObmMpYuHca8eaNZtuxeamp2xQ5PIlGLlUSyEiVVUtDKgLGq0N7XqlIwYNZQkqmV88qcOa/rSKoAmpvL2L49xZw5r4scmcSkxEr6WXvxz6bYgYhkrwI4QkVE+1QKoCZ2FBktWnRwR1LVrrk5xeLFB0eKKLY22La85C+bVWIl/agFWIvGVElRqSQkV8fEDkT62+TJm6mo2DOLqKhoZdKkUrwYpwWan4atlHyxNyVW0k9aCFf+NUaOQ6QPVABHJdOrSMmYOfNZBg9u6UiuKipaGTy4lZkzn40cWX97FXg+TJohSqykP6j4p5SAMmACVFWpzlWpqKnZxbJl9zJ9+gtMmrSZ6dNfLMGB668CDdDQHDuQvKGrAqWPtRFaqpRUSYk4DQbdBzubS75HpCTU1OziuuuWxQ4jkiZCUlVKiWT31GIlfWwtSqqk5JwFg1ShXYpaG/CckqoMlFhJH1qFxlRJyToTBg2NHYRIH9n9NDSoTTYTJVbSR1YCO2MHIRLXG6GqOnYQIjm2Zbk6IvZBiZX0gZWoTpUIoS/w9SrFIEVk83LYETuI/KbESnJsFUqqRNKUA6Oh6tjYgYhkaevycBGgegD3SYmV5EgbsBp1/4lkUAmMhKpxsQMR6Y022L0ctqGkqgeUWEkOtBA63BsjxyGSxyoJLVcacyUFpQlYoTFV+0GJlWSphTCHgX7rRLpVAZwAVbpaUApCe52q1tiBFBQlVpKFNkIr1drIcYgUEANOhaoK1bmSfNYErIEGjVTfX1knVma2ysyeNLOlZrYkWXawmd1jZs8l/x+UfaiSfzaiyaFEeuksGFSm5EryUQvwEjRsix1IQcpVi9Vb3H2Cu09MHl8D3Ofu44D7ksdSVOpR959Ilt4KgwbEDkKkk7a/Q8Pu2FEUrL7qCrwQ+Gly/6fAO/roOBLFC4RxVSKStbdA1SGxgxBJ7FgOa2IHUdhykVg58Gcze8zMrkyWDXf39lOzFhje+UlmdqWZLTGzJRs2bMhBGNI/VhIKmYhIzpwMVaNjByElb8ty2BI7iMJXnoN9THX3BjM7HLjHzP6evtLd3cz2qnzh7jcANwBMnDhRlTEKwguo+KdIHygHjoGqAbDjudjBSEnaklRU16dx1rJusXL3huT/9cAdwCRgnZkdAZD8rxHOBa8etVSJ9KFKYJSKiEoEO5VU5VJWiZWZVZnZge33gbcCy4HfAZcmm10K/Dab40hMbYS8WGOqRPrcAKAGqsbEDkRKQwv4cngFJVU5lG1X4HDgDjNr39f/uftdZvYocKuZXQ68BLwvy+NIFCr+KdLvKoFxULUddmyKHYwUryagLsxEJjmVVWLl7i8A4zMs3wSclc2+JbY2QlKl4p8i/a4cmAhVD8DO3WpMkFxrAtZBw67YgRQlVV6XDNqAzSipEonIgLfAIFMRUcmlFkJFdV3+11eUWEkG69H1BiJ54txQoV0ke23A86qo3sf06yqdvExorRKRvPFWqKqKHYQUvKanoaE5dhRFT4mVpHkB2B47CBHJ5E1QtVepZZEe2rZc1yH1EyVWklDxT5G8VgYcD1VjYwciBWfLctiGroLoJ0qshND99yqh/11E8lYlMAaqjo4diBSMHSr+2d+UWJW0NsKVf+r+i62urpwZM0YwadKRzJgxgrq6XMw2JUVpIKFC+9jYgUh+a4PWZO4/JVX9Sn+9S1Yb0IgGqsdXV1fO+PFHs317Gc3NxtKlBzBv3lCWLXuempqWnBxj05Yh/GnBFF5oGMVR1fWcP3UhhwxVNf2CNRA4Cqp2wY51sYOR/NMCvKiKOZGoxaokqfhnPpkz59COpAqgudnYvt2YM+fQbp65AJ7qfv+btgzhC9dfxQOPTeTF1dU88NhEvnD9VWzaMiT74CWeSmC8rhaUzpoIdap2xw6kZCmxKknb0TwG+WPRooEdSVW75uYyFi8euO8n/nANP63vfv9/WjCF3U2VtLalAGhtS7G7qYI/LZjS25D73QHAQbGDyEdlwGlQpQqiAoSWqg0q/hmZEiuRyCZP3kVFxZ6DICoq2pg0KTfTTbzQMKojqWrX2lbOCw3VOdl/XysH3ggcPy12JHns3NA7KKWsDaiDhldiB1LylFiJRDZz5kYGD27rSK4qKtoYPNiZOTM3RWeOqq4nVda6x7JUWQtHVTfkZP997V3AGCVV3SqbBlUVsaOQaPxpaNgROwpBg9cLVBsvzv7PrIojHF0JXPveXAUkWaipaWHZsueZM+dQFi8eyKRJu5g5c2POBq6fP3UhDz95Ukd3YKqshQGVzZw/dWFO9t+XLh0GTI4dRQE5E6oegR3qCSotu5aDGqryhhKrgrORzbO/n3Upz5VNcOTs20jNUnKVD2pqWrjuur65mOCQoVv5z6vnJlcFVnNUdUNBXBV46WhgHJqBeH8YMBGqnoEdGkZZGrap+Ge+UWJVUJbCf/+WDTnYUyvwInDMf98Gn1VyVewOGbqVD77trthh9Nilo4BjAHVt7b8KYBxUVcKOVbGDkT61TcU/85HGWBWMu2Heb1mxM3d7bIWwv1tuI1ReF4nv0iqgllBOQHpnIDBaRUSLWlPSUtXa7ZbSz5RYFYQ74M5HWLGyb/a+4u/Aot+jGTolpnLgHQBTUUtVLgwiTH8zInYgklttwDOwAbVU5Sl1Bea9O+GuJ1ixuG+PsuIuqD3sL3DUVOCIvj2Y5MAj0ApdTRm3isL6IjsAOAUYqqv/cmsgYeLmXRrQXhxaCMU/C+m3u/T0OrEys1rglrRFRwFfBIYBH4WOoUCfc/c/9fY4pe1xuHUxK57pn6Ot+DnUXr4ARp0ODO+fg0ovPAd31cGrMHVY5i1ebYR1hD/D+e4AQs/fOCVVfaMCeCNU3Qs79HlcwFqATSr+WQB63RXo7ivcfYK7TyB82dwJ3JGs/nb7OiVVvbUevvv7fkuq2q34EfDUg2hi5nzVCLcshRX73ursYSE1Tu17s+jKgROACUqq+pYB54QkVgpRG7AOGnJx6ZL0tVyNsToLeN7dX8rR/kpcGztmX8+KxjhHX/Er4K47IatKWZJ7bXDjPT2e4vHsYV13FeaLs1BF9f6UmhaGXkmheVEV1QtIrhKri4Cb0x5/wsyeMLObzExTfO2nl2f/Jz2YAq5PrVgEzL09chTymjb43u2hXXg/nDosf+trXloGI86NHUXpsXOhSvPfFI7W5dCQm+mtpH9knViZWSXwduC2ZNH1hC/KE4A1wDe7eN6VZrbEzJZs2KDmzaCJtbNnky+/QivXAV++rdvtpK81wg9v7/Vo9GOHwDk5jSd7lx4KnImKf8ZgwJug6pDYgUi3di4PgyWloOTiqsDzgMfdfR1A+/8AZnYj8IdMT3L3G4AbACZOnKiLRqmH//gR+TQssRV4vhWO/vptcI2KiMbxPNz2eCgC2FtlMHIQfDCHNdCydiS6JjmmZHBb1UrYURhTRpaeHaqoXqhy8aftYtK6Ac3sCHdfkzx8J7A8B8cocovhx3eyIg9/gVqAlbvhmB/fBh9+Nyp91p8ehXtWQS6mJqmEsnwquKk6VfENBI6CqhTseDl2MLKHXSr+Wciy+pQ0sypCL8Ov0xbPMbMnzewJ4C3Ap7M5RvG7G/50Jyvy+A9bK4T4HrgdXS3YXx6Eh1fB07HjkKJWRSgiWh07EOngyYTKSqoKVlYtVu6+Azik07IPZhVRSbkbHniEFY/GjqNnVsyH2po74eg3A4fHDqeIPQKProM+LgorAoTk6pikiOjm2MGUsjagLjct1BKV+nWieQT+/Agr5seOY/+s+AWwfj6wPnYoReoZeKgOFsaOQ0rKQOANUDUgdiClqgXYAA3bYgciOaDho1HUwy/uZsXzsePonRXXQ+30+TDi9NihFJ8/LIcs3hd1rwxhzn1TWPTyKCaPrmfmWQupOWhr7uKT4lUOnAEH3K0p2ftXG/CKin8WESVW/a4Jvv4jVuyOHUd2/H/Bhj0YOwxJU/fKEMbPuYrtuytpbkuxtH4E8x47iWUz5yq5kp6xUES08i5oih1LSWgDGjRNTZFRV2A/2zT7awWfVEl+mnPflI6kCqC5LcX2pgrm3DclcmRSaCqmQZU+HfrBCiVVRUi/Ov2oYfZsNsYOIkdWArsaY0ch6Ra9PKojqWrX3FrO4pfz7JKv8cCBsYOQbp0NVTpPfadpOazWpX/FSIlVv9jKrtmzi6pQQdKAzZbGyIFIh8mj66ko2/MPdUWqhUmj86gC5HjCTMCquJ7/yoCJUKULgHNv53LYjIp/FiklVn1uJVz/bfK4TFWvtQIbgcbGyIEIADPPWsjgAU0dyVVFqoXBlc3MPCsPLjEsA45DSVWhGQDUqs5VTu1aDltRnaoipsHrfWoh/P4eVhRxZYIWYBNQ3giDh8WNpdTVHLSVZTPnMue+KSx+uZpJoxvy46rAFDAGGBI3DOmlKmBs+E/T32SpdTlsQUlVkVNi1Wf+An99kBWPx46j77UAa4HRjVA5LG4spa7moK1c9567YofxmnJCLVl1JxW2AwnT3+yGHcUyULRftQEvhgmV1f1X9NQV2CcWhqTq3thx9J9W4EUITdwiAJWEeRlGxw5EcqIKOBGqBsUOpNC0EYp/7lJSVSLUYpVzK+HOe1hRotORrGiD2iHs/ziaVwGVoSge5cDBwNjIcUhuDQCmwqA/w87YsRSE0i7+Wbd6CHN+MIVFS0cxeUI9Mz+2kJqRxf/tW4lVTm2HG+exotTnevoQkEp1u9keFrTCUjT2oBiUAUcAGvBcnMrApkHFXdAcO5a81gZsgoZ1sQOJom71EMafcxXbd1TS3JJi6fIRzLvjJJbdM7fokyt1BeZQ6+xvKqnab23hv6kpOCNqIJIrR5J3SVXduiHM+MY0Jn3kCmZ8Yxp16zSSPluV08JFntKVl0o2qQKY84MpHUkVQHNLiu07K5jzg+IvWKwWqxxZN3s2jbGDKEhpuf0JBsMcbo8XjWTpePKu+GfduiGM/8BVbN+VfHN+dgTz7j6JZb+YS83w4v7m3NdS50LVX2CH5r/Zky+HNbGDiGvR0lEdSVW75uZyFi/Ns29dfUAtVllro1FJVY6UhZaOi2PHIb1yEjA4dhB7m/PzKR1JFSTfnHdVMOfnxf/Nuc8ZMBWqhsYOJM84JT9QffKEeirKOxUsrmhh0oTir9mhxCorG+Fb/0npNvb2AUvBocB7Ywci+62CvCz+uejpDN+cW8pZ/HTxf3PuF5WEWmUiaWZ+bCGDq5o6kquKihYGD2pm5sfyoGBxH8uPrsAtq+H3s2NHsf+aYMW22EEUobIUHNEK04A/0zEMS+Jb1QhPd7Hu/F2E5CrPTD6unqXPjtgjuaoob2HSccX/zVkklpqRW1l2z1zm/GAKi5dWM2lCg64K7E+v7qAkCmnKfrAU1LbBZofHCVVIJaqXG+FhknplGRy/EMb8A6F2VR6Z+cGFzLv7pI7uwIryFgYPbGbmB4v/m7NITDUjt3Ldl/OoYHE/UVeg5LEyODUFryPUz5FoNjbCfLpOqgDmAZsfBfJsCqea4VtZ9ou5TH/HEiYdV8/0dzymgesi0md61GJlZjcBFwDr3f2EZNnBwC2EEoCrgPe5+ytmZsB3gfMJNeQuc3e1R0nvnZOCllZ4CRURjaCpEX4FbO7BtnOBKx+HQycRCoTmiZrhW7nuM6X3zVlE+l9PW6x+Qhjxku4a4D53HwfclzwGOA8Yl9yuBK7PPkwpbW1wXgqOJk86r0vILvgePUuq2t0APL84PFdEpNT0KLFy9wfZ+2/rhcBPk/s/Bd6RtvxnHjwCDDOzI3IQq5Ss5G16Tgomog7s/uLw1d1htqH9dQvw0HxK/pJzESk92XxEDXf39hJoa4Hhyf1qoC5tu3ryrg6zFKzJBm+NHUQJaIKvbsluFw8Bt9ydk2hERApGTr77u/t+l0MzsyvNbImZLXllp6bzlJ4qC4PZ3xM7juLV2gjfyNGv5AvAjzW0SURKSDaJ1br2Lr7k//ZrgRqAmrTtRiXL9uDuN7j7RHefeNCgQVmEIYUpi+JUlgqT/KqIaM41NsKNQK5mKHFCc/YvlVyJSInIJrH6HXBpcv9S4Ldpyz9kwRuBLWldhiKJLBtLy1IwgnCtquTE6kb4A/s3UL0nnNBy9cBd5C5jExHJUz36dDOzmwm1AWvNrN7MLge+DpxjZs8BZyePAf5E+Du6kvDl92M5j1oEQnJ1tMFUNKVGluobw5iol/vwGAuBlfcDKh8lIkWsRxevu3tX0+KelWFbBz6eTVAiPVcGpwCvtMJzqEWkF9Y3wgLCt6G+divwsYUwLA8rtIuI5IIuXJficLaFkX2q0L5fdja+1sTcX34A7HyU3Pc5iojkASVWUiTK4IJUuFRCRUR7ZhvcBKyOcOjvABsXE+ZmEBEpIkqspLhckILj0Du7O20wpzXucKcbgKceRBNsi0hR0cePFJ+3GJwWO4g81gZf3Zof+cxvgbvujR2FiEjuKLGSIlQG44F/jB1HHtoBc/Lsqry/AfNU50pEioQSKylOloKxqEJ7mt2N8L3m/GipSueEObCUXIlIMVBiJcWrvYjohbEDiW9TI/yS/C0h1UaooXXnXWRVlF9EJDYlVlLcUikYA5xJyb7b1zbC/WSYVyrPOKFbcPmfgV2RgxER6SVdmC7Fz1JwYhtsclgOtMYOqP+sa4S/EmqnForfASPnw8GnAkNjRyOyn55dDk+Sv83D0ueUWEmJKIMzgO2tYUBPCVRo394If6F/i3/mylzgMw9D5WTgoNjRiPTQhuVsvhkejx2HRFWinSNSepKBOxck466K/SvFFriFwkyq2n0D2L0I2BE7EpGeeIaVP1BSJcX/8SKSSPsO8c4U/KkVniX/LpHLke94cRQ1/yZw2UMw8iygInY00t8ckq77bXED6YHFs1vV+yeAEiuJro0oDafnp9j5aCvf6f8jy376CXD2fTBpWuxIpL9tBx5pBWa/FDsUkR5TV6BEpregdO9e4Leqc1VSNgBPxw5CpBf0qSYiBeEZ4JdKrkpCPbAKlTSTwqTESoqE/gQXuzbCh61arorby8A6inb4o5QAJVZSJPRWLgVthO6hxXehT94i9DKwkZKohiJFTJ9GIlJQnDDmau29FMeljwLAGsK4qt2xAxHJkhIrESlINwGtD6IK10XgFUqmbq+UgG4TKzO7yczWm9nytGX/bWZ/N7MnzOwOMxuWLB9rZrvMbGlym9uHsYtIifsvgIcphDJHkoET6r8+S0nNNCVFrictVj8BOleQuQc4wd1PIvxOXJu27nl3n5DcrspNmFLaNDBduvZVh51/Rc0dBcYJp+wJ9BsuxaXbxMrdHwQ2d1r2Z3dvHzr6CDCqD2ITSajHWvbtO8Dz95OU6pZC8Cqa/kWKUy4qr3+EMC1ZuyPN7G+EkQ+fd/eHcnAMEYmsccsQHlowhfqGUYyqrue0qQsZNjR/BjjdAky5G85Qhfa810ioSyZSjLJKrMzs3wkXPc9LFq0BRrv7JjM7BfiNmR3v7nv99TWzK4ErAUYOHZpNGCLSxxq3DOG666+iqamStrYUq9eOYOmTJzHj6rl5lVw9Amy+C96l5CpvrSfUIxMpVr3uYzGzy4ALgEvc3QHcfbe7b0ruPwY8D7wu0/Pd/QZ3n+juEw8aNKi3YUjB0qiKQvLQgikdSRVAW1uKpqYKHlowJXJke2oj/NG5Q0VE81I94eo/DVSXYtarxMrMpgEzgbe7+8605YeZWSq5fxQwDnghF4FKsYk/bmrQ++HjsYMoEPUNozqSqnZtbeXUN1RHiqhrzYQPb8kvdYTWKl1jIMWuJ+UWbiZc0FxrZvVmdjnwPeBA4J5OZRVOB54ws6XAr4Cr3H1zpv2KRHdsiqHvhumx4ygAo6rrKSvbs52hrKyFUdUNkSKSQrIaFf+U0tHtGCt3vzjD4h91se3twO3ZBiXSb05IccgBrbxzHtwRO5Y8dtrUhSx98qSO7sCyshYqK5s5berC2KFJnttIGHyrliopFbm4KlAkD7TR6+7FY1K8/upW6q6HJTmNqXgMG7qVGVfPTa4KrGZUdUPeXRUo+Wc7YSyIxlRJKVFiJUUiyzFbh6d467Wt1H0N1uUmoKIzbOhW/vFtGhUuPbMbeDJ2EBLN+i1DuGXBFFY0jKK2up73T13I4SXyRSz+CGKRfFGZ4vJZhq5RFclOMyr+WcrWbxnC9Ouv4o+PTWTF6mr++NhEpl9/Feu3DIkdWr9QYiWyhzI+NcsYHjsMkQK1A3Wpl7pbFkxhV1MlrcmVxK1tKV5tquCWPCvP0leUWInspYzLr4GTY4chUmA2ActjByHRrWgY1ZFUtWtpK2dFHpZn6QtKrEQyGZDivKvgH2PHIVJgVPpXaqvrSXUqz1Je1kJtiZRnUWIl0pXhKU58P1waOw4RkQLy/qkLGVjZ1JFclZe1cEBlM+8vkfIsSqxE9uXYFNVvh8tjxyEiUiAOH7qV/716Lm87ZQm1I+s5/5TH+N+r55bMVYEqtyDSnZNTDC9r5b2/gdtixyIiUgAOH7qVGSVankUtViI9MT7FuEthauw4REQkrymxkhKRgyG1Y1Oc/ikYk/2eRESkSCmxkhKRo7f60BSXfAEVERURkYyUWElkBXhxdlmKT81KKbkSEZG9KLGSyAr3Lfipz8ORsYMQEZG8UrifaiKxpVJcPANKY5IGERHpCSVWUiQidSkenOKMi+FdcY4uIiJ5RnWsCsyaLUP44YIpPNEwipOq67li6kKOKJGia/sW8TvC61Ice0ErH/gD/CJeFCIikgeUWBWQNVuGcOH1V7GzqZKWthTPrB3B7588id9ePVfJVWynpBjd0sr77oJbY8ciIiLRqCuwgPxwwZSOpAqgpS3FzqYKfrhAo3zywuQUx7wLzo4dh4iIRNNtYmVmN5nZejNbnrbsS2bWYGZLk9v5aeuuNbOVZrbCzM7tq8BL0RMNozqSqnYtbeU80VAdKaK91QBY7CgiOjHFpCvg2NhxiIhIFD1psfoJMC3D8m+7+4Tk9icAMzsOuAg4PnnOD8wsleG50gsnVddTnswW3q68rIWTqhsiRbSnocCgWQZluT7lBVbrqjrFuz4Lw2LHISIi/a7bxMrdHwQ293B/FwK/dPfd7v4isBKYlEV8kuaKqQsZVNnUkVyVl7UwqLKZK6YujBwZHAKMmJWib3qXC7DHelCKj80yDWIUESkx2XxifcLMnki6Cg9KllUDdWnb1CfLJAeOGLqV3149l/efsoQTR9bz/lMey4uB6+OAQ2eVcv9fV8qY+UU4qPsNRUSkSPT2C/X1wH8Cnvz/TeAj+7MDM7sSuBJg5NChvQyj9BwxdCtfeNtdscPoUHsIyVkswFal/mAprv6XVu74FjwTOxYREelzvfo0dPd17t7q7m3AjbzW3ddAMn45MSpZlmkfN7j7RHefeNAgzbpWiGqPBi4BKnszpqrAxk1l48AU77wU3hI7DhER6XO9SqzM7Ii0h+8E2q8Y/B1wkZkNMLMjCb1Ei7MLUfJR7euBc4CDejtQvcRauMamOPUCVWgXESl23XYFmtnNwBnAoWZWD8wCzjCzCYSuwFXAdAB3f8rMbgWeBlqAj7t7a4bdSgGrPRp4MzBcF3zul1NSHLurlffeB7fFjkVERPpEt4mVu1+cYfGP9rH9V4CvZBOU5K/ag4HzgYOVVPXK1BTjyls59264O3YsIiKScyXWHyPZOAbCQPW8TKoKaMzWG1Oc8l6YEDsOERHJOSVW0iPDgNQXgQH5mFRBwb2Vj0tx/tVweOw4REQkpwrs00hiGAwMn5UCFdHPrcNTXPE5qIgdh4iI5IwSK9mnEUC1in/2nYoUn51lVMaOQ0REckKJlXSptgKGfh5K823Sn2O2yvjMNXBE9xuKiEieK8VPTOmB2uHAJ4BUqXb/9fOvxoAUH/4onNy/RxURkRxTYiV7qT2aUPZ1SKkmVZGMTHHehfDW2HGIiEivKbGSPdQeTZh7RcU/45iQYuJb4O2x4xARkV5RYiUdag8nTFNTraQqqtNTnHAanBc7DhER2W9KrASA2hTwT6ilKl+cmeLkaa/Nbi4iIoVBiZVwGMC/AUOLOakqoMrs7SanOPsSGB07DhER6TElViVuIHDwLIOKYk6qoGDf6sek+MCnw3kSEZH8V6CfNpILBwKjZ6XY99ugr1t6CrAlqVu5/JnaYEiKT38RVKZVRCT/KbEqUaOBkV/oyZZ9/RYpxrdgLn+mZF9mXPv5kAyLiEj+KsZPNelGbRUM/AxQFr/7r65uCDNmnMukSR9mxoxzqasbEjukPFUGqRQzPgFHxg5FRES6VB47AOlftSOBC4Gq/Eiqxo//KNu3V9LcnGLp0hHMm3cCy5bdSE3N1v3cWxuF/T2hh/EfkuLi97Ry769gcZ/HJCIi+6uQP4lkP9WOAc4FDo+fVAHMmXNqR1IF0NycYvv2CubMObUXeyv0t/J+xH98irPfrArtIiL5qNA/jWR/1AKj8yOpAli0aGRHUtWuubmcxYtHRoqogJyR4tjYMYiIyF6UWEk0kyevpqKidY9lFRUtTJq0OlJEIiIi2ek2sTKzm8xsvZktT1t2i5ktTW6rzGxpsnysme1KWze3D2OXAjdz5sMMHtzUkVxVVLQweHAzM2c+HDkyERGR3unJ4PWfAN8Dfta+wN3f337fzL4JbEnb/nl3n5Cj+KRPxR3wXVOzlWXLbmTOnFNZvHgkkyatZubMhzMMXC+RgekiIlLwuk2s3P1BMxubaZ2ZGfA+4MwcxyX9Iv6HfU3NVq677u5utoofZ3YKPX4REempbP/inwasc/fn0pYdaWZ/M7P5ZnZaV080syvNbImZLXll584sw5DcKMYq6CIiIv0n2zpWFwM3pz1eA4x2901mdgrwGzM73t33Kkrk7jcANwCcMHKkZxmH5IRaVkRERLLR609SMysH3gXc0r7M3Xe7+6bk/mPA88Drsg1S8kGuW7PUOiYiIsUnmyaKs4G/u3t9+wIzO8zMUsn9o4BxwAvZhSj5IdetWWodExGR4tOTcgs3Aw8DtWZWb2aXJ6suYs9uQIDTgSeS8gu/Aq5y9805jFdEREQkb/XkqsCLu1h+WYZltwO3Zx+WlLS2VqjvfrNSN3ggjNsFz3W/qYiI9BNNwiz5pbUV1gFLYgdSAI6BC54MgxxVq15EJD9ooIvkj7YkqXokdiCFY+CJcNkAODB2ICIiAiixkrzRBqtQUtUbr4MZI/TLLCKSD/S3WPLDMoelsYMoYIfCNbWxgxAREY2xKhG1IwnlW3/TGjuUzFTWKjsGVMDnauHrK/RyiojEoharElA7ChiWPGjL05tkL0murhkBg2PHIiJSopRYFbnaw4EhQCp2JNIvDDgM/rkShseORUSkBCmxKlJlQO0g4HCUVJWi2jCR55Gx4xARKTFKrIpQOXA0yT8WNxaJZ9CJcA5wVOxARERKiBKrIlMJHAGUnRg7EskHh54IbwVqYgciIlIilFgVkXJCz98gJVWS5uAT4f3AQbEDEREpAUqsikQZMBqoKoKkqm7jEGb8cBqT/u0KZvxwGnUbh8QOqeBVnghXHwgVsQMRESlyqmNVJMYNAF4XO4rs1W0cwvh/uYrtr1bS3Jpi6YsjmPfgSSz71lxqDt0aO7zCNhY+uxW++lLsQEREipdarIpA7SHAuNhR5Mac30zpSKoAmltTbH+1gjm/mRI5siJxYCgiKiIifUMtVgWudiSh+GeRXP236LlRHUlVu+bWchY/Vx0poiJj6OuUiEgf0p/YQldJUdWpmjyunorUntPuVKRamDSuIVJEIiIiPafESvLKzHcsZPABTR3JVUWqhcEHNDPzHQsjRyYiItI9dQVKXqk5dCvLvjWXOb+ZwuLnqpk0roGZ71iogesiIlIQlFhJ3qk5dCvXXXFX7DBERET2m7oCRURERHJEiZWIiIhIjiixEhEREckRc/fYMWBmG4AdwMbYsUivHIrOXSHT+StsOn+FS+eucI1x98MyrciLxArAzJa4+8TYccj+07krbDp/hU3nr3Dp3BUndQWKiIiI5IgSKxEREZEcyafE6obYAUiv6dwVNp2/wqbzV7h07opQ3oyxEhERESl0+dRiJSIiIlLQoidWZjbNzFaY2UozuyZ2PLI3M7vJzNab2fK0ZQeb2T1m9lzy/0HJcjOz/0nO5xNm9oZ4kYuZ1ZjZX8zsaTN7ysw+mSzX+SsAZnaAmS02s2XJ+ZudLD/SzBYl5+kWM6tMlg9IHq9M1o+N+gMIZpYys7+Z2R+Sxzp3RS5qYmVmKeD7wHnAccDFZnZczJgko58A0zotuwa4z93HAfcljyGcy3HJ7Urg+n6KUTJrAf7V3Y8D3gh8PPkd0/krDLuBM919PDABmGZmbwT+C/i2ux8DvAJcnmx/OfBKsvzbyXYS1yeBZ9Ie69wVudgtVpOAle7+grs3Ab8ELowck3Ti7g8CmzstvhD4aXL/p8A70pb/zINHgGFmdkS/BCp7cfc17v54cn8b4Q98NTp/BSE5D9uThxXJzYEzgV8lyzufv/bz+ivgLDOz/olWOjOzUcDbgB8mjw2du6IXO7GqBurSHtcnyyT/DXf3Ncn9tcDw5L7OaZ5KuhZOBhah81cwkq6kpcB64B7geaDR3VuSTdLPUcf5S9ZvAQ7p14Al3XeAmUBb8vgQdO6KXuzESoqAh0tLdXlpHjOzwcDtwKfcfWv6Op2//Obure4+ARhFaOU/Nm5E0hNmdgGw3t0fix2L9K/YiVUDUJP2eFSyTPLfuvYuouT/9clyndM8Y2YVhKRqnrv/Olms81dg3L0R+AtwKqGLtjxZlX6OOs5fsn4osKl/I5XEm4C3m9kqwjCXM4HvonNX9GInVo8C45KrJCqBi4DfRY5JeuZ3wKXJ/UuB36Yt/1ByddkbgS1pXU7Sz5IxGj8CnnH3b6Wt0vkrAGZ2mJkNS+4PBM4hjJP7C/CeZLPO56/9vL4HuN9VrDAKd7/W3Ue5+1jCZ9v97n4JOndFL3qBUDM7n9APnQJucvevRA1I9mJmNwNnEGZiXwfMAn4D3AqMBl4C3ufum5MP8u8RriLcCXzY3ZdECFsAM5sKPAQ8yWvjPD5HGGel85fnzOwkwoDmFOGL8K3u/h9mdhShFeRg4G/AB9x9t5kdAPycMJZuM3CRu78QJ3ppZ2ZnAJ9x9wt07opf9MRKREREpFjE7goUERERKRpKrERERERyRImViIiISI4osRIRERHJESVWIiIiIjmixEpEREQkR5RYiYiIiOSIEisRERGRHPl/H2w78J7JEwgAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#assigning points of the 2D space (pixesl) to the seeds\n",
"# with Manhattan distance\n",
"image=generate_voronoi(seeds,(rows,cols),Manhattan)\n",
"# diaplying the Voronoi diagram (tessellation) along the seeds\n",
"plt.figure(figsize=(10,5))\n",
"plt.imshow(image,cmap=plt.cm.hot,alpha=.5)\n",
"plt.scatter(seeds[:,1],seeds[:,0],marker='o',s=30,c='b')\n",
"plt.title('The Voronoi diagram with Manhattan distance.\\n The seeds are shown with black dots')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.11.1"
}
},
"nbformat": 4,
"nbformat_minor": 4
}