2-midpointCircle.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5325dbe7",
   "metadata": {},
   "source": [
    "There are three codes below for Mid Point Circle Drawing Algorithm->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "680e9285",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def mid_point_circle(radius):\n",
    "    x = 0\n",
    "    y = radius\n",
    "    p = 1 - radius\n",
    "\n",
    "    x_points = []\n",
    "    y_points = []\n",
    "\n",
    "    while x <= y:\n",
    "        x_points.extend([x, -x, x, -x, y, -y, y, -y])\n",
    "        y_points.extend([y, y, -y, -y, x, x, -x, -x])\n",
    "        x += 1\n",
    "        if p < 0:\n",
    "            p += 2 * x + 1\n",
    "        else:\n",
    "            y -= 1\n",
    "            p += 2 * (x - y) + 1\n",
    "    \n",
    "    return x_points, y_points\n",
    "\n",
    "# Set the radius of the circle\n",
    "radius = 5\n",
    "\n",
    "# Generate the points on the circle using the Mid-Point Circle algorithm\n",
    "x_points, y_points = mid_point_circle(radius)\n",
    "\n",
    "# Plot the circle\n",
    "plt.plot(x_points, y_points, 'b.')\n",
    "plt.axis('scaled')\n",
    "plt.title('Mid-Point Circle Algorithm')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d5457081",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def mid_point_circle_algo(radius):\n",
    "    x = 0\n",
    "    y = radius\n",
    "    d = 1 - radius\n",
    "    \n",
    "    # Define empty arrays to store the coordinates of points on the circle\n",
    "    x_coords = []\n",
    "    y_coords = []\n",
    "    \n",
    "    # Calculate points on the circle and plot them\n",
    "    while x <= y:\n",
    "        x_coords.extend([x, -x, x, -x, y, -y, y, -y])\n",
    "        y_coords.extend([y, y, -y, -y, x, x, -x, -x])\n",
    "        \n",
    "        if d < 0:\n",
    "            d += 2 * x + 3\n",
    "        else:\n",
    "            d += 2 * (x - y) + 5\n",
    "            y -= 1\n",
    "        x += 1\n",
    "        \n",
    "    # Plot the circle\n",
    "    plt.plot(x_coords, y_coords, 'bo')\n",
    "    plt.axis('scaled')\n",
    "    plt.show()\n",
    "\n",
    "# Test the function with radius = 5\n",
    "mid_point_circle_algo(5)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "197544b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HqdVhXRdN/h2k+oKTF9ev5IXdL9At4ghjhi/nrnGjrA5LKdVBliTHM3/6NJac2wqbfoJjxb9SV15+5Rd2Utrtc510xq5SgSHaFszyxL4QnYHDXQjuZeu6hWBN/tepctcxHBuL6D+tjxZ2lQoEHoXgw8Gw428rcTqdTL77Pqsjaxevd/uISL6IfCEi2SKS5T4WJSKbRORL979drplc5nDy8kdHKYrZRvHg13EO/Iwxc5J0mzilAkBDIdgZn0hN3wQ+kx6UOuusDqtdfNXnf4sxJs1jF/mngC3GmMHAFvfzLuXPO4/ws/cPsal4FNGzbiAuZaHVISmlfGzcxEnYZt3Oi73iWH3ipNXhtItV3T4LgOnux38CtgE/sCiWdtNZu0opcM0G/mb0CXoeWsc93YZQ+lHvLrMstC9a/gbYKCK7RaQhS/YzxhS6H58B+jV/kYgsFZEsEckqKSnxQZhXVu+o5fxHpziwrcA1azc5VWftKhXgokdnsHz4CILygil+7pfkPPsfVFVWWB3WFfmi5X+zMaZARPoCm0TkkOdJY4wREdP8RcaYFcAKgPT09MvOW0GLu0qpy3gsC31sfy7bjx/GsXF9py8Ae73lb4wpcP9bDKwBxgNFIhIH4P632NtxXK8yh5Otte9qcVcp1aLgyEjO/9N8zvdPorJXFC+eKO7URWCvJn8RsYtIr4bHwBwgB3gP+Ib7074BvOvNODrCn3ce4X9/msiB5L5a3FVKtWjcxElMz3iA3PhEnj16ulMXgb3d7dMPWCMiDddaZYzZICKZwBsi8ghwHLjHy3Fcs+oLTg5+Vghhu6iN3ENFxDhsNt1gXSl1ua60HLRXk78xJg+4sYXjpcBMb167oxzYVsDOdcdIm5fOU3O6cecgLfAqpdoWPTqDB3Z8zJm/7KUkaBVxy5dbHdJldG2fNjidZYRX7WFEaDdGhvbm4VEP67INSqkrs0dzOOF2cqJjOBYWyvbt23E4HFZH1YQu79CGo8dfpyj8JQZM+RFRkydbHY5SqgsZefsCsNs52z2MXZs2UVV/qVMtBa3JvwXlNeWszV3LhaIbycmfSfqwVAbp0sxKqXboGR7BuPl38dsjx9lRVEm08zSzHaWuoaGdgHb7tODN/W/zwu4XqO9xUJdmVkpdlyXJ8fxTfD1Ldn6f+h2/tzqcRtryb6beUUty5nAmFM9ndL9xTJubanVISqkuLNoWzJKjRdRmGUoiunGy6u1OsQS0Jv9mKncdIzWvnoeSFzHm5mFWh6OU8gPhix+kIiisUy0Brd0+bnmlxTz6+uvkR26gYugbJMzI1hm8SqkOcdkS0BUllJ6zdmEDTf5u//nBFjbvDWPFoZ66RLNSyivGTZxESPrXeHHATby2e6ulsWi3D65+/tvLEzgZso/b7ZNIShptdUhKKT9kt9u5qxbMzr8xs89AMh3W9f9ryx9XP3/accMzcROYOWOk1eEopfxY0l1LeDT+Rsrt4Xz8t5Xs3bjekjg0+QNFMduoGPoG0VN2az+/UsqrGvr/K2ITqOmbQGUva9YKC+hun8bJXMWjyKk9RHppOjq+RynlC7kDh/HxuJmEB50DCyZ/BXTLXydzKaWsYvXkr4BO/kMKxjHh+HzSzqbz2LRUouza5aOU8o1oWzB3HzhBXZah5KDvU3HAJn+ns4z4mlyWlM1mZGhvq8NRSgWgk31i2V6RSF54tM9X/vRa8heRASLyoYgcEJH9IvKE+/gzIlIgItnuj3neiqEtR4+/TkH4TxkwpYSoyf2tCEEpFeBG3r6AAf/2JBWxCWzatInPdu/x2bW92fKvA75rjBkBTACWi8gI97lfGWPS3B+WjHPafOJGXsufyfu94wnSFTuVUhZoWPkzNz6RHSkjORTVx2fX9lryN8YUGmP2uB+fBw4C8d663tWqvuBkz8bj1Pc4yLaqi3SLOGJ1SEqpALfk3FbmOzdz59bnqSsv98k1fdLnLyLJwGhgl/vQ4yKyT0ReFZEWt8YSkaUikiUiWSUlJR0Wy4FtBex45yhpZ9N5ak46S0bptoxKKWtFj87ggfJzVL/yMSWrVvnkml5P/iISBrwNfMcYUwn8DkgF0oBC4PmWXmeMWWGMSTfGpMfExHRYPP2DahgR2o2hITbdllEp1TnYo8npO6dx20df8GryF5EQXIn/b8aYdwCMMUXGmHpjzCXg98B4b8bQXEXCJ0R87S0qEj7x5WWVUqpNFbEJHBz1NSpiE3xyPW+O9hHgD8BBY8wLHsfjPD5tIZDjrRiaK68p5zcHg3m51sYnpem+uqxSSl1Rw4zf3PhE2P5r16xfL/Lm8g6TgQeAL0Qk233sfwH3iUgaYIB84DEvxtDEm/vf5qPzv+em8O/obF6lVKeyJDmebqHTuOfIX+DTn1JfXU3QrKe8dj2vJX9jzKeAtHDKmiXscM3onVRwjK+njdDZvEqpTiXaFszyxL6cebeeouxwTHQ3Ymd573oBtbDb0BAbS8pmMzREE79SqnPKC4/mTEUiseHRxHrxOgG1vIMWe5VSnZ2vCr8BkfzLa8pZmbOSTcWjtNirlOrUfFX4DYjkr0s3K6W6iiXJ8cyfPo2MM+th00+8ttxzQCR/XbpZKdVVNBR+6w+6Cr/eWu45IAq+WuhVSnU13i78BkTLXwu9SqmuxtuF34Bo+W9y79E7qniU7tGrlOoScuMTXXv8xid65f0DouXfsHxzfY+DVoeilFJXJePMeuY7N7sKv17g98m/3lHLiH3DmHqhN6Mrx1kdjlJKXZWgvGDuXreeM+9/SVVlRYe/v98n/8pdx0jNq+ehPosYf7N2+iiluobwxQ9yKulOPsw/zt6NHd/69/vkXxSzjYqhbxA9ZTc9wnS0j1KqawiOjKR43h2c759EZa+ojn//Dn/HTkaLvUqprsqbRV+/b/lrsVcp1VV5s+jr98k/7Ww6Uy/0Ju2sruejlOpa6g/Wc/e69dQfrO/w9/b7bh+d3auU6qq8OcvXspa/iMwVkcMikisiXtuuRmf3KqW6Km/O8rWk5S8iQcCLwGzgFJApIu8ZYw509LW04KuU6qr8seA7Hsg1xuQZY5zAamCBNy7ULeII26ou0i3iiDfeXimlvGbJua3Md25mybmtHf7eVvX5xwMnPZ6fAm7y/AQRWQosBUhMvPbfeouSZiBhh1iYNOOa30MppazQe+jdPHg0ip5DOz5/ddrRPsaYFcaYdGNMekxMzDW/z6nN24h97RNObd7WccEppZQPlO2tIWtvHGV7azr8va1K/gXAAI/nCe5jHW7A2TNMjjjBgLNnvPH2SinlNftrzrEqahP7a851+HtblfwzgcEiMlBEbEAG8J43LhQ0PIi37phH0PAgb7y9Ukp5TXafLD4OO0d2n6wOf29L+vyNMXUi8jjwARAEvGqM2e+Na62Once604lcih3Ft71xAaWU8pKg6uFM77mfoOrhHf7elk3yMsasB7yzULWHQQUnmJq5hUH9wmFUx99ApZTyltl9c5ic76Rn3xxgUoe+d6ct+HaUiDOnGJ7zBRFnTlkdilJKtUvEqSlUfHE3EaemdPh7+33yT6ksZXLECVIqS60ORSml2uVwrZNVUZs4XOvs8Pf2++SvBV+lVFfldwVfX3ojeRHPXSqmylHMvzgc2O12q0NSSqkrcjrL6FNdQEj5VKge2eHv7/ct/4zEASw/X4hz89/J3PGZ1eEopdRVKcxbw4j8Yv7j5hM8OGFIh7+/37f8o23BTL5QypmcL7Cl6wbuSqmuwXZsEhVfpDKpfz+i7B2/JL3ft/xBi75Kqa7Hm8VeCJDkr0VfpVRX481iLwRI8l8dO4/3bLNYHTvP6lCUUuqquGb3dvfK7F4IkOTfOMu34ITVoSil1FWZ3TeHx0KczO6b45X3D4jkH36+jNDiU0ScOUXpH/5AXXm51SEppVSLqi842bPxOBGnptD3y3vpVzLdK9fx+9E+AKPnzMNmszHg+FHqtvyWyvoLRC19wuqwlFLqMp9/eoi/fv46X0+7h7G3DaRnej+vXCcgWv49wyMYN/+uxsJvfUqd1SEppVSL9oZnNhZ6e01LIMge4pXrBETyb6CFX6VUZ+ftQm+DgEr+WvhVSnV23i70NgiIPv8G4efL6HX6OH3Xr6Nu/HiCIyOtDkkppQBXoffgZ4XE1U8h7Mvh2Ad6p6+/gVda/iLynIgcEpF9IrJGRHq7jyeLSLWIZLs/XvLG9Vszes48bklOIuH4Wirf/LMvL62UUm36/NND/G7nCg7XOom4bSDhNw306vW81e2zCRhljLkBOAL80OPcUWNMmvtjmZeu36Ke4RHE3jZYi75KqU7HV4XeBl5J/saYjcaYhuy6E0jwxnWuhRZ9lVKdka8KvQ18UfD9JvC+x/OBIrJXRD4SkVb3JhORpSKSJSJZJSUlHRbMsLKzTMzbz6CCE2S+9zZVlRUd9t5KKXUt6h213HaugPuStzAr8R8+ueY1F3xFZDMQ28Kpp40x77o/52mgDvib+1whkGiMKRWRscBaERlpjKls/ibGmBXACoD09HRzrXE2N2nsGHoGdUNyD3Hyj6+Cw8G4+x7sqLdXSql2K9t+mpOfxJAw6SckJd3ik2tec/I3xsxq67yIPATcAcw0xhj3ay4CF92Pd4vIUWAI4J1l61pgt9uZPHkyZ/ZsJzXiBObsGV9dWimlWrS/5hyrojbx9dB7GGyL8sk1vTXaZy7w78B8Y0yVx/EYEQlyP04BBgN53ojhSmKGXyI4XXhrRCKlTi3+KqV8r8zh5OWPjpLdJ4udSe9xJD7TZ9f21jj//wG6A5tEBGCne2TPVOCnIlILXAKWGWPKvBRDm4ImfotVDGRdQTdMfgHfHpJkRRhKqQD2dmYOew79lVGD7+bJsU9y56A7fXZtryR/Y8ygVo6/DbztjWu2mz2aQfW9mZq5hkH9wkGTv1LKx6ZEZzE2xEnPvjkMG7XUp9cOqOUdmtOlnpVSVqm+4KT0k7FEHL7Ha8s2tyWglndoTpd6VkpZ5fNPD/HXs++wOGUeyV6ezduSgG7561LPSimrNMzoPXDDIa/P5m1JQLf8G7yRvIjnLhVT5SjmXxwO7Ha71SEppfyU01lGYeFbBFWP4mJxLFRbU2/U5A9kJA6g6h//wLltA5n2UKbPmm11SEopP1WYt4bS7fuYPR5st81kcfoAS+LQ5A9E24KZfKGUMzlfYEsfZ3U4Sik/Zjs2iYovUonr34/Hbku1LI6A7vP3NPBCDcMLy0ipLIXtvwZHqdUhKaX8THlNOa9cWM/uukpO14daGosmf7eYJUvo+/3vETQ8iBcPHqB072qrQ1JK+ZlVOe/y15N5nJtyjBHT4y2NRbt93IIjI4l+5BFezD3mKv6WavFXKdUxGoq8lypGcbE4hj43JtEjzGZpTJr8m9Hir1Kqo3WWIq8n7fZpJtoWzCRTTWjxKWwFJ3Tmr1LqulRfcHJqa1rjTN7HpqUSZbe21Q/a8m+RzvxVSnUUq2fytkZb/i1omPnbsOzzqtR+uuyzUqpdGpZr3hueyc6k98gfd9CSmbyt0eTfhqCJ32LVhOf4vwVBrMovsDocpVQX8nZmDnsOvkhQ9XCeHPski0feZXVITWi3T1vs0Qyz9ac0bwuD+oWTeSiLkdNn0TM8wurIlFKdWL2jlltKjzI4eQv9EgczfPA/Wx3SZbzW8heRZ0SkQESy3R/zPM79UERyReSwiNzqrRg6wqSxY5g9ezYRZ05x8lcvsP/v71odklKqk2vYkze+8iekJt1rdTgt8nbL/1fGmF96HhCREUAGMBLoD2wWkSHGmHovx3JNGvb8LczOpk9pCbGn/g6O28EebXVoSqlOprymnLW5axlYM4YDNZcI7zkGm4/25G0vK/r8FwCrjTEXjTHHgFxgvAVxtEvMkiX0eHQqf4nszaldq9i+fTsOh8PqsJRSnYTTWcaG3T/gt1s+I7tPFhMXpVo+i7ct3k7+j4vIPhF5VUQi3cfigZMen3PKfawJEVkqIlkiklVSUuLlMK8sODKS9+Y9zbOp/8xr55PZ/P561v/hJaoqK6wOTSlloXpHLec/OkVh3hr6XtzCuO69oPomxsyxfhZvW64r+YvIZhHJaeFjAfA7IBVIAwqB59vz3saYFcaYdGNMekxMzPWE2WEyEgfw49T+3DdtGl/r1ZOgNe9oDUCpAFe2/TRZa3KxHZtE/wHfI33Y/Tw4YYjVYV3RdfX5G2NmXc3nicjvgXXupwWA59zmBPexTi/aFszyxL4ABIX15lxhGZFnz7hWAU27X+sASgWY8ppyXqp4ix51gwmvT2Ls4H9m+GCro7o63hztE+fxdCGQ4378HpAhIt1FZCAwGPjcW3F4i64CqpTqTKt0tpc3R/v8QkTSAAPkA48BGGP2i8gbwAGgDljeWUf6tMVzFdBngyq41Ls7Y7ZvJy0tTVcCVcrPdcZVOtvLa8nfGPNAG+f+C/gvb13blzISB4DNzpD8w2zeuIHTu3dy+0OP6kQwpfxUvaOWM5u2ciz0RWalLsN225xOsUpne+kM3+vUUAdwRNs5l/05J7Z/yP6YGFKqaolYtIjgyMgrv4lSqtOrvuDk4GeFDAC67exHyoQfE5s0g+GDO+c4/ivRtX06iN1u5/aHHmXq1x9mwNkz1P3fZ6h8889Wh6WU6iCff3qI3+1cwf6ac0TcNpD42Qs67QSuq6HJvwPpaqBK+acyh5M/le3ns/jNHInPpNe0hE61Que10G4fLwia+C1W2wbzn/WpmPwCxpSc0kKwUl1QQ2F347F0tu4LZ9boJ1k8co7VYXUITf7eYI8mY8ICOFOmhWCluijPwu7Nqcv4obuwGxnatUb1tEaTv5d4FoLP7/gY1rzD/pgYxt33oNWhKaWuQtn20xzd1oeEST8hKemWLlvYbY32+XuZ3W5nYlhvhheWMaBhNrCj1OqwlFKtKK8pZ2XOSvbXnONAzSUqO/HKnNdDW/4+ELNkCbbQUHonlVD64fOsrk8gY8ICom16+5XqTMocTv593UZ2XHiJJ9K+xcRFsxk+Ke7KL+yCNPv4QMNsYBylrLYN5tn6VC5pIVipTsOzsLt5b1hjYTcy1H/n6Wjy9yUtBCvVqdQ7aqnKKqKs3wfknv45Nw/4nt8Vdlujyd/HdEawUp1D9QUn2X89RN+8c0TNncKg1B8QF3e33xV2W6PJ3yINM4L3JyeTcPIMpS//mtDKrQQv/Y0uDa2UFzVstZhyaiw52WcZk9aH5JsGEmnv/GvwdyRN/hZqmBFcV15OuPMz7BXrKN07idWJi8mIjdKCsFIdrLWCblefrXstNLt0AsGRka4Wf/Z4Vvebx0v7jtJjw3YWL5xBrxitBSh1vc44SngldwdhZQkBU9C9Ek3+nYU9GiY/QYazjh5bszlx+h/sWi8Mnl5MXNzdfjnOWCmfcJTySuZr/I+ZymMRx/nhbaMCoqB7JZr8O5loWzCLF84gc0N34m84Re7Rn7Mzr5TZ479LlD2wf1iVao+68nIq3nmH3kklPJr1O5gAjw69j1h759gT3GpeSf4i8jow1P20N3DOGJMmIsnAQeCw+9xOY8wyb8TQlfWKiWDGA/NwOsvI3l7Ks1tTKLx0hIh+mdw56M6A/lNVqatRVVnBkWf/g+7rP0CeXEbslCf5UdrXdTCFB68kf2PMvQ2PReR5oMLj9FFjTJo3rutvbLYoZo//Lue6naTO/gkv7H6BgiPlfHfO411uyzilfMHhcJCdnQ2FJ9h9/DBT591K+OIHQYdQX8ar3T4iIsA9wAxvXsefRdltPDYtlfKaKMpPlBG6dRAHbAUM6RVCz/R+ATlKQamWlDrreHXbpzgydzD95slM/MajDJk+i2CdQNkib/f5TwGKjDFfehwbKCJ7gUrgR8aYT1p6oYgsBZYCJCYmejnMzi8yNJLvznmcg2GubeQq3j9GeflOYufN0GKwCmyOUsj+K6v7zefFkN4sHzeRcRMn6bIpV3DNyV9ENgOxLZx62hjzrvvxfcBrHucKgURjTKmIjAXWishIY0xl8zcxxqwAVgCkp6eba43Tn/QIszFmThL1jloKqjLJC30Wx/ESPj7tmo6uBWEVaOrKy7n4x3/FXrGOjFnBMMw1R8auc2Su6JrvkDFmVlvnRSQYWASM9XjNReCi+/FuETkKDAGyrjWOQBRkDyF23gxMYRkbj6Xzsw2HyDyTxbOzplO4u4bhk+K0JqD8lsPhIHPHZ4ScO0tKURnnV2YS//AdRI/OYLkWdK+aN389zgIOGWNONRwQkRigzBhTLyIpwGAgz4sx+C2bLYqkpKXc1cfJrqIv2XHhBf7wUQGRG9MwzktaE1B+p9RZx2r3ooifv/s2ocWnsN15DylP/IDuixaBXYu67eHN5J9B0y4fgKnAT0WkFrgELDPGlHkxBr8XZbfx3II5rM2tYm7cPArDarQmoPyPo5TVu7fxbH0qT8cnMnnBXYScO8vIOfN0RdxrJMZ0/u709PR0k5WlPUNXq95RS8Gmd8kLfZZ+qcv44MQUQiKyWDJqgc4RUF1GVWUF+//+Lgll5+k79Dzndv7/rJ76K90IqR1EZLcxJr2lc3oH/VDzmsB/bzpO976ZhEgd6aWztSagOjXPsfpFK14mrLCM7k8uI/qW77I8bTpo4u8Qehf9lGdNwFFvIyRiHENLxrBj7VEu5lUw/oHhWg9QnU7zsfoDlj5G77LzhC9eohO1Opgmfz8XZbfxnZmjgFFUX3Biy3dtXlG56xhnBmzh04KbuGvcKB0mqixTV15O5Zt/JiKlmtXJ9+pYfR/R5B9AeoTZGP/A8MZt606f/CVZRxbgqP8mPXvvZGjJeMbfPEy7hJRXNXTrDE1N4djnn5Fw8gzdNv2SoLRKMkJ76Vh9H9G7G2CC7CH0mpZAd+dCqoKcpHe7CWdYFr/N+TUTjs8nrO5RHSaqvMazW+f07l6c2P4hU++8h9R536M+pVrH6vuQJv8AZbNFMXzwPzN8MJTXDCRE6hjabzyJ3bo1DhMNnT6FNf+4oLOH1XVprVvnlrE3cCw5mZHTZ+lwTQto8ldEhkaydOyjAE2Wjijam8HPPrhBZw+rdms+C7elbp1oWzB95t9ldagBS5O/asJzmOiIiAXMKt7WZPbwxbwKRt8bS1HlWt1hTDXlKKV072pWx85jyOlTTWbhardO56PJX12mYZgo0GT2cH5xEX3zzlH80RFyw107jI274RE+Kvy7bjIToJpPxFqdf4xnayfrLNwuQJO/alNkaCQPj3oYgL4PRFGVVUTIDcPYkf0oz25NYULxh+yqcW0y853JyzCHyrRY7OdKnXWsyi9g2JkT9Cw+1WQiVsaIGyA2gozEeKKHJFkdqmqDJn911RpGCgGNO4zNHtWLVR8VELp1EF8U5zIgv0KLxX6oedF23c4sSvP2XzYRKzgykuVWB6uuiiZ/dU0adhgDGjeZGXJjDGU71jcpFlfXVTfOIRg7epD+ZdAFNKyeuSA8lNysXS0WbS9NuINhybGMGztGJ2J1UZr81XVr2GQGwOZRLP5htwvU2T9pnENgy7+3yV8Gq3aX6IJznYBnv33Mwrmszs3m2fpUqqqKcG5Y02LR9tv2aNBunS5Nk7/qUJ7F4sem9aO8JqpxDsHXRg9q8pfBf2+6oXHBubGFM0m0daPXuB46ksib3Fselo68j1XF1Zf124c7PyPD8QlM/RULJs8mt3s3Ldr6KV3SWfmU01lGYeFb9IhY0NjyH3V2DDlrzzIitBup08/yZfgPOCuPMu6GR9ic/54uO3GNmiyj8OGmxhE5QZ/+jBdnvMp7+ZeY6O63t5cUNrb8g4+tg7T7QYdkdnltLemsyV9ZrvqCkwPbChpb/u9m/8E1kmgU7Kr5TyYcn8+yMY+S0rOWyv6f0CP2Du0y8lBVWcH+bZsZlpZO7Ya1RKRUcy79m7y6fS+OzB2MjOpF0Jp3GF5YRr8nlxE1kiYt/0nab++3vLaev4gsBp4BhgPjjTFZHud+CDwC1AP/aoz5wH18LvBrIAh4xRjzf64nBtX19QizMfaOgY3PPUcSbc4/37jshGNjEaWD9/JlSnGrXUbHzr7NpwU3MfNrCX41/6B5v3xF3gZWx85jQZ9odvz5FU5s/5CQbZ8Ql/c2QWmVrLYN5sWQhK+WUYiJabI0cjTw7d5ov30Au94+/xxcm7S/7HlQREbg2sZxJNAf2CwiQ9ynXwRmA6eATBF5zxhz4DrjUH7EcyTR0uivlp2oDL5IdP/RJMTewXculTTuUbBz3TEqQ7uRWnWW0+GulUp3Fd3ErpoXqL1Y3+ovh4YuJatGIbU0quaG8ZOatN5b65df3SuMZ2snU3X4CFXFZYyYfAupd95N7YaB1KdUk3HDFKjkq2UU7nvQZ1+X6hquK/kbYw4CiEjzUwuA1caYi8AxEckFxrvP5Rpj8tyvW+3+XE3+qk1B9hAiZwwhElcb4jsz+9GwR0FYXUOX0QgcZ79HereGln8VKafGtvHLoe1RSIsG3sbpHVVt/uIYf/MwLkntZX3rzVvnx/d/cdn5lkbV2D/b1aT1vi7/0mXj6bsvnEtG3gaIjWBBnxSO9w4jLS3N1XWz9AkAooHlvS37dqkuwFujfeKBnR7PT7mPAZxsdvymlt5ARJYCSwESExO9EKLyB827jIZHulYqBUiJfpjq5NZ/OTR0KbU2Cqn8RBmRG9Pa/MXRq9tSqu2n2LRpE6d3u/rWW2qdNyxh7Hm+pVE1qeMnNWm9X4qtbnE8fXT/5Y2TqRImT/bhHVf+4orJX0Q2A7EtnHraGPNux4fkYoxZAawAV8HXW9dR/q2tXw4NXUrQdH5CQ5fSooG3cdpW1eYvjuGT4rgkfQBcLXt333pLrfPm5+3H1rn2pLWHkzBr9ldBe7TetV9eeUuHjPYRkW3A9xoKvu5iL8aYn7mff4CrMAzwjDHm1pY+rzU62kcppdqvrdE+3bx0zfeADBHpLiIDgcHA50AmMFhEBoqIDVdR+D0vxaCUUqoV1zvUcyHwWyAG+LuIZBtjbjXG7BeRN3AVcuuA5caYevdrHgc+wDXU81VjzP7r+gqUUkq1m07yUkopP2VFt49SSqlOTJO/UkoFIE3+SikVgDT5K6VUAOoSBV8RKQGOX8db9AHOdlA4HUnjah+Nq300rvbxx7iSjDExLZ3oEsn/eolIVmsVbytpXO2jcbWPxtU+gRaXdvsopVQA0uSvlFIBKFCS/wqrA2iFxtU+Glf7aFztE1BxBUSfv1JKqaYCpeWvlFLKgyZ/pZQKQH6V/EVksYjsF5FLIpLe7NwPRSRXRA6LyK0ex+e6j+WKyFM+iPF1Ecl2f+SLSLb7eLKIVHuce8nbsTSL6xkRKfC4/jyPcy3eOx/F9ZyIHBKRfSKyRkR6u49ber/cMfj0Z6eNOAaIyIcicsD98/+E+3ir31MfxpYvIl+4r9+w30eUiGwSkS/d/0b6OKahHvckW0QqReQ7Vt0vEXlVRIpFJMfjWIv3SFx+4/6Z2yciY675wsYYv/kAhgNDgW1AusfxEcA/gO7AQOAoriWlg9yPUwCb+3NG+DDe54GfuB8nAzkW3rtncG3I0/x4i/fOh3HNAYLdj38O/LyT3C9Lf3aaxRIHjHE/7gUccX/fWvye+ji2fKBPs2O/AJ5yP36q4Xtq4ffxDJBk1f0CpgJjPH+eW7tHwDzgfUCACcCua72uX7X8jTEHjTGHWzjVuKG8MeYY0LCh/HjcG8obY5xAw4byXieuXe/vAV7zxfWuQ2v3zieMMRuNMXXupzuBBF9d+wos+9lpzhhTaIzZ4358HjjIV3tmd0YLgD+5H/8JuNO6UJgJHDXGXM8KAtfFGPMxUNbscGv3aAHwZ+OyE+gtInHXcl2/Sv5tiOfyjePj2zjuC1OAImPMlx7HBorIXhH5SESm+CgOT4+7/5R81eNPcSvvUXPfxNXqaWDl/epM96WRiCQDo4Fd7kMtfU99yQAbRWS3iCx1H+tnjCl0Pz4D9LMgrgYZNG2AWX2/GrR2jzrs567LJX8R2SwiOS18WNLqaslVxngfTX/oCoFEY8xo4ElglYiE+zCu3wGpQJo7luc78trXEVfD5zyNa1e4v7kPef1+dTUiEga8DXzHGFOJhd9TDzcbY8YAtwHLRWSq50nj6suwZLy5uLaSnQ+86T7UGe7XZbx1j65rG0crGGNmXcPLCoABHs8T3Mdo4/g1u1KMIhIMLALGerzmInDR/Xi3iBwFhgAdtoXZ1d47Efk9sM79tK1755O4ROQh4A5gpvs/gk/u1xV4/b60h4iE4Er8fzPGvANgjCnyOO/5PfUZY0yB+99iEVmDq7usSETijDGF7i6LYl/H5XYbsKfhPnWG++WhtXvUYT93Xa7lf40624bys4BDxphTDQdEJEZEgtyPU9wx5vkglobre/YbLgQaRh60du98Fddc4N+B+caYKo/jlt4vrPvZuYy7fvQH4KAx5gWP4619T30Vl11EejU8xlW8z8F1n77h/rRvAO/6Mi4PTf76tvp+NdPaPXoPeNA96mcCUOHRPdQ+vq5se7lqvhBXH9hFoAj4wOPc07hGZxwGbvM4Pg/X6IijwNM+ivOPwLJmx+4C9gPZwB7gn3x87/4CfAHsc/+AxV3p3vkorlxcfZzZ7o+XOsP9supnp5U4bsbVLbDP4z7Na+t76qO4UnCNgvqH+3v1tPt4NLAF+BLYDERZcM/sQCkQ4XHMkvuF6xdQIVDrzl+PtHaPcI3yedH9M/cFHqMa2/uhyzsopVQACpRuH6WUUh40+SulVADS5K+UUgFIk79SSgUgTf5KKRWANPkrpVQA0uSvlFIB6P8BdkZ96nQAWKsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#import warnings\n",
    "#warnings.filterwarnings('ignore')\n",
    "#%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "r = 100\n",
    "\n",
    "p = 1 - r\n",
    "x = 0\n",
    "y = r\n",
    "\n",
    "while x < y:\n",
    "    x += 1\n",
    "    \n",
    "    _y = y\n",
    "    y = y - 1 if p >= 0 else y\n",
    "\n",
    "    p = p + 2 * (x + 1) + (y**2 - _y**2) - (y - _y) + 1\n",
    "    \n",
    "    plt.scatter(x, y, s=1)\n",
    "    plt.scatter(y, x, s=1)\n",
    "    plt.scatter(-y, x, s=1)\n",
    "    plt.scatter(-x, y, s=1)\n",
    "    plt.scatter(-x, -y, s=1)\n",
    "    plt.scatter(-y, -x, s=1)\n",
    "    plt.scatter(y, -x, s=1)\n",
    "    plt.scatter(x, -y, s=1)\n",
    "\n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "07a54a9d",
   "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": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}