Visualization_helpers.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> LSH Hashing </b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "f1 = lambda x: x\n",
    "f2 = lambda x: -.5*x\n",
    "f3 = lambda x: 0.1*x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = 2\n",
    "n_samples = 100\n",
    "x = np.linspace(-rng, rng, num=n_samples)\n",
    "y1 = f1(x)\n",
    "y2 = f2(x)\n",
    "y3 = f3(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": [
    "fig = plt.figure(1)\n",
    "ax= fig.add_subplot(111)\n",
    "\"\"\"for direction in [\"xzero\", \"yzero\"]:\n",
    "    ax.axis[direction].set_axisline_style(\"-|>\")\n",
    "    ax.axis[direction].set_visible(True)\n",
    "for direction in [\"left\", \"right\", \"bottom\", \"top\"]:\n",
    "    ax.axis[direction].set_visible(False)\n",
    "\"\"\"\n",
    "ax.plot(x, y1)\n",
    "ax.plot(x, y2)\n",
    "ax.fill_between(x, y1, y2, color='g', alpha=0.2)\n",
    "x2 = -2*x\n",
    "x2 = np.clip(x2, -rng, rng)\n",
    "ax.fill_betweenx(y1, x, x2, color='r', alpha=0.2)\n",
    "#axs.plot(x, y3)\n",
    "ax.set_aspect('equal', 'box')\n",
    "#axs.axis('equal')\n",
    "#axs.set(xlim=(-rng,rng), ylim=(-rng,rng))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TThrGtGkLmDEjXUvqJ03gcMj3IXib2gwEfuRtagPscM61Aj8EVpnZXnIthplBrxs33d3ddJY59777jTdyL/bWdzcOi9Lc+3KrK0vNuKxXFagEU69Nbd4Grg7jWlHTX0dez+ddu+g8fJjue+7p8/vlzL2PUkdeNbUSfiFR6ypQCU7TwUrob+6913vfsX69bz09FM+9vyoSVXZBBS2iKt2SuIR58xQSUZO6cPD9S5/vve/IT9gpt/d+Yorm3odZXVkcEkuXrmXjxsf57GfVkoiSxIRDr7/0L7yQG6qrtPf+r3/t9z19WufeZzIZbrxxEWPHhltE5YVEV9dsnnpqtUY3IibW/9J37tzJd77znb7LZXm9908/rbn3AXnBcOxY7aorBw9uYtq0BVxzzSzuu+8+jW5ERKzDYfDgwbwz6B0GjR/EWeefxdDhQxkybEjP55ObTmbgCQP7/F5n/n9/evtPuRkY7fW/9zjYt2cf6+5ex2A7l9mzal92PWzYsF5vN1atWcODjz7KmRddxEWzZjFy/PiaXj9JolJb0TCTJk3ia9/6Grte3dXoW0kcLxjOGX8O/3zRSoYMqd9CLcV9EqvWrOHerVsVEnUW63AAmDp2KlPHTm30bSRKJpNh1fJVTJqQ21di3brGrODkN7rx0PbtGt2oE+14Jb30N/OxUbyQ8HYVf/jhrXzuc/HYCzTOYt9ykPBEMRgKaXSjvtRyECD6wVDIG93wWhJx2lU8ThQO0qtWIurBUKj47YYXEosXL1ZIhEDhkHJx31cC+obEtm3b1JIIgcIhxZIQDIVKtSRuvVUtiWooHFIqacFQqDgkWlu3aXSjChqtSKFa1UpEjUY3glHLIWXqUSsRNd7oRmtrK3PmzNHoRpkCtRzMrBm4H5gAvARc45z7m89xx4Df5x/uc85dHuS6hba3b9f06TLVu1Yiaop3FU9y7UYYtRVBWw63Ar90zk0Efpl/7Oewc+6D+Y/QgkHKV1grMXtWfWslosZ7u7Hp5z/nK/Pm8XpbG/cuWMD6JUvIvvxyo28vMoL2OVwBTMt//RPg18DXA56zIqqtOL6o1EpEjWo3+he05TDaOXcAIP95VInjTjSzHWa23cw+198JzWx+/tgd2RRuYxa2OM18bBS/2o0rr1SfxHFbDma2GXifz4++WcF1xjnn9pvZmcATZvZ759yf/Q7UpjbhUTBURqMbvR03HJxz00v9zMxeNbNTnXMHzOxU4LUS59if//yimf0a+BDgGw4SDgVD9bzRjbTvuxH0bYW3WQ35zw8XH2Bmw83svfmvW4AL6b3JroRMwRAOryXR2tqaygKvoOFwJ3CJmb0AXJJ/jJlNMTNvk4ZJwA4zexb4FXCnc07hUCMKhvB5y9elrQo00GiFc+4g8Cmf7+8A5ua//j/gn4JcR8pT7k5UUp1S+2586lPTmT8/eTt4aYZkQiS5ViJq0lK7odqKBGhra+OGG25OfK1E1CR9dEMth5jzgiFNtRJRk9SVqWLfckhzbUXaayWixm9J/UbVbkShtkIaxAuGcyecm/paiajxQuLRDRtiXbsR+5ZDGmsrvFqJyWdMZvny5aqViKjiHbziVruhlkPMFM5jUB9DPJSq3Yj6QrixbzmkiSY4xVvx6Ma2bWvZvHlzZEc31HKICQVDcsRldEPhEAMKhmQqtVp2VEJC4RBxCobki2pIKBwiLK47UUl1orbvhsIholQrkV5Rqd3QaEUEqVZCoHTtxvTp05k3r/ZVoGo5RIxqJaRY8ehGvfYCDbpvxdXA7eQWdLkgv46D33GXAt8FBgL3OOfuDHLdQkmqrVCthPSnktqNKNRWPAd8HthS6gAzGwgsAz4NTAauNbPJAa+bOKqVkHIV7ruxaO7cmtVuBF0JajeAmfV32AXAXufci/lj15Lb7yKUpeKSUFuhWgmpRlNTU68dvAprNzrmzeWUgH0S9ehzGAO8UvC4Pf89X2nbt0K1EhJU8ejG5s1buf766+nq6gp03kD7Vjjn+qw27XcKn++V3I8iTftWaIKThMkLife+dzbnn/9nBg0aFOh8gfatKFM7cHrB47HA/oDnjD0Fg9TKsWNNnH32hwOfpx5vK54GJprZGWb2HmAmuf0uUkvBIHEQKBzM7Eozawc+DjxiZo/lv3+amW0EcM4dBW4CHgN2Az9zzj0f7LbjS8EgcRF0tGI9sN7n+/uBzxQ83ghsDHKtJFAwSJxohmSdKBgkbhQOddDW1saNN6q6UuJF4VBjqpWQuIp9VWaUayte+eMrPPjfD6pWQmIp9uEQVV4wnDvhXC66ULUSEj+xD4co1lZkMhlWfV+1EhJv6nMImTcqoRWcJO4UDiFSMEiSKBxCoupKSRqFQwg0wUmSSOEQkIJBkkrhEICCQZJM4VAlbTgjSadwqII3JVqjEpJkCocKqVZC0iL2MyTrWVuhWglJk6ArQV1tZs+bWbeZTennuJfM7Pdm1mZmvhvfRF1hrYT2lZA0CNpy8Da1WVHGsRc75zoCXq+PetRWqFZC0qgem9rEmqZES1rVq0PSAb8ws2fMbH5/B0ZpUxsFg6RZPTa1AbjQObffzEYBj5vZHuec7/6aUdnURrUSknb12NTGW40a59xrZrae3P6ZJTffbTTNfBSpw9sKMzvZzIZ6XwP/Qq4jM5IUDCI5Nd/UBhgNbDWzZ4HfAY845zYFuW6tKBhE3lXzTW2ccy8C5we5Tj0oGER60/RpcsFw440KBpFCqQ8HLxiOHlUwiBRKdW3Fvj37WHf3unythIJBpFDsw6FaXjBoXwkRf7EPh2pqKzKZDKuWr2LShEmsWLFCtRIiPlLX51A4JVp9DCKlpSocCpd205Rokf6lJhza2tq4+WYt7SZSrlSEgxcMKqISKV/iw6GwxaA+BpHyJToc9FZCpHqJDYdMJqNgEAkgkeHgTYlWMIhUL3HhUFgroWAQqV7sZ0gW1laoVkIkPLEPB49qJUTCFXQlqLvMbI+Z7TKz9WY2rMRxl5rZH81sr5ndGuSaxaaOncpHB3yU3yz/DZMmTGLlCgWDSBiC9jk8DrzfOfcB4E/A4uIDzGwgsAz4NDAZuNbMJge8bg/VSojURtBl4n5R8HA7cJXPYRcAe/PLxWFma4ErgD8EuTbAs88+61srceKJlZ1Hx+v4pB0fxj5T5lw4W0OY2QbgfufcT4u+fxVwqXNubv7xF4GPOeduKnGe+cB8gHHjxn3k5ZdfLnnN9vZ2lixZwh133KEWg0gVzOwZ55zvPrehbGpjZt8EjgKr/U7h872SiVTJpjZjx45l2bJl/R0iIlUKvKmNmX0JuAz4lPNvhrQDpxc8Hgvsr+QmRaT+go5WXAp8HbjcOfePEoc9DUw0szPM7D3ATKA1yHVFpPaCjlYsBYaS2/+yzcyWQ+9NbZxzR4GbgMeA3cDPnHPPB7yuiNRY0NGKs0p8v2dTm/zjjcBGv2NFJJoSV1shIuFQOIiIL4WDiPhSOIiIr9BmSNaCmWWB0lMkc1qAjjrcTq0l4Xkk4TlAMp5Huc9hvHNupN8PIh0O5TCzHaWmf8ZJEp5HEp4DJON5hPEc9LZCRHwpHETEVxLCYWWjbyAkSXgeSXgOkIznEfg5xL7PQURqIwktBxGpAYWDiPhKRDiUu9Bt1JnZ1Wb2vJl1m1mshtJquYhwvZjZj8zsNTN7rtH3Ui0zO93MfmVmu/P/lr5S7bkSEQ6UsdBtTDwHfB7Y0ugbqUStFxGuox8Dlzb6JgI6CtzinJsETAUWVvvfIhHh4Jz7RX7dCMgtdDu2kfdTLefcbufcHxt9H1XoWUTYOXcE8BYRjhXn3Bags9H3EYRz7oBzbmf+6zfJraEypppzJSIcivw78GijbyJlxgCvFDxup8p/kBIeM5sAfAh4qprfj82OVyEsdBsJ5TyPGKpoEWGpPTMbAjwIfNU59/dqzhGbcAhhodtION7ziCktIhwhZjaIXDCsds6tq/Y8iXhbUeZCt1I7WkQ4IszMgB8Cu51zdwc5VyLCgRIL3caNmV1pZu3Ax4FHzOyxRt9TOZKyiLCZrQF+C5xjZu1m9uVG31MVLgS+CHwy/1poM7PPHO+X/Gj6tIj4SkrLQURCpnAQEV8KBxHxpXAQEV8KBxHxpXAQEV8KBxHx9f9Ca4urFBfwyAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(1)\n",
    "ax = fig.add_subplot(111)\n",
    "\"\"\"for direction in [\"xzero\", \"yzero\"]:\n",
    "    ax.axis[direction].set_axisline_style(\"-|>\")\n",
    "    ax.axis[direction].set_visible(True)\n",
    "for direction in [\"left\", \"right\", \"bottom\", \"top\"]:\n",
    "    ax.axis[direction].set_visible(False)\n",
    "\"\"\"\n",
    "a = 0.8\n",
    "ax.plot(x, y1, c='k', alpha=0.8)\n",
    "ax.plot(x, y2, c='k', alpha=0.8)\n",
    "ax.plot(x, y3, c='k', alpha=0.8)\n",
    "ax.fill_between(x[:n_samples//2], y1[:n_samples//2], y3[:n_samples//2], edgecolor='g', alpha=a, facecolor='none', hatch='-', linewidth=0.0)\n",
    "ax.fill_between(x[n_samples//2:], y1[n_samples//2:], y3[n_samples//2:], edgecolor='m', alpha=a, facecolor='none', hatch='|', linewidth=0.0)\n",
    "ax.fill_between(x[:n_samples//2], y3[:n_samples//2], y2[:n_samples//2], edgecolor='r', alpha=a, facecolor='none', hatch='|', linewidth=0.0)\n",
    "ax.fill_between(x[n_samples//2:], y3[n_samples//2:], y2[n_samples//2:], edgecolor='c', alpha=a, facecolor='none', hatch='-', linewidth=0.0)\n",
    "x2 = -2*x\n",
    "x2 = np.clip(x2, -rng, rng)\n",
    "ax.fill_betweenx(y1[:n_samples//2], x[:n_samples//2], x2[:n_samples//2], edgecolor='b', alpha=a, facecolor='none', hatch='|', linewidth=0.0)\n",
    "ax.fill_betweenx(y1[n_samples//2:], x[n_samples//2:], x2[n_samples//2:], edgecolor='y', alpha=a, facecolor='none', hatch='-', linewidth=0.0)\n",
    "ax.set_aspect('equal', 'box')\n",
    "#axs.axis('equal')\n",
    "#axs.set(xlim=(-rng,rng), ylim=(-rng,rng))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Ratio test </b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IfOp7+wVCSa/WOlF3f+B1TM2VPUJhhvxeIvIcsA9mhflNm+upJFGy4nSi7hGYVBgesKeXiHxVbMMI+YPBb31w98C4Mb5eqlstJSlOJ+oehfmRJgF7e4nI90ExjJA/GPw2I/0+mFnVa6Xo8ldyz5xO1O2NceZ+BzjYS0TmB80wQv7g8DtRtwvwBiZV50FeIvKO7/3LE0pKnPYZ08V4uezvJSK/B9kwQv5g8NtttjeAdYD9SiX0rGTE6UTdPTDbJV8B1V4i8mspGEbIHwx+Gx/6NiYedfdSKMRUEuK0K25jgVmYZ8wfS8kwQv5g8DtRd0tMIMQcjEB/auKUoiLw4nSi7voYJ+1lmO2Sb0vRMEL+YPA7UXc30do3RPm0tqJiHy8R+cNPfj8RaHFaX9k3MYVmV/l9TIlLR0zgdGdMzp8HMSFU52GL5g74hAlXjmHQIcczc+ZaTMckb56oMX1R4tIFWATM1phmlxQ7wNcnU/6XuvZ69qzDL2uDyMtAH5uhPnAIbLC1Lej6H2AnoO+qJkyJSw9Mes8eQCuN6dGYvEYRTHb9HyzXD5jygkuALUdty+WjtuVITNmIthghb2RpY5gcQm0kLhMx9Ta7YiqYf6wx/dOv/meFAvEfPG1CX0Q2x4TQ3URqzuUAIbAjpxN1/47JwnaJl4hcXy6GkY5f4lKF2TTvA/ymMb1a4nI/JovBROB9jekHjdLH6/k11qTw2wCba0w/kricCAwBNsUk0joC+AlYutzoWobX34m612OyQJ7oJSIP+d5mjgikOJ2oOxBT3/EB4LRyjC6RuKyJKaY0E5M46xdMhP9TGtOpzaJvhjAb4WiNGaXfxmReuA6TXOy5b25kyca/8whldP0BbHb5VzCZCnt5ichHvredAwInTpta5ENgCrCvN7z37pSJMGUYYzFTybMxaSv/oTFNSFzaa0x/y4reB2E2wLsFcFhlLScc8SkLDv6S60/tx9ca0w/9asM0VNwR2Ym662DyNv0J9Mi6alweEChx2uTB44FNgO7e8N6bUgbC/Gg9TtrxLL4GpmGcKJ4HHtKYZlqSIj19noSZjh8QzBrAd5hEYU9oTBc3fHYmDQRjquxE3V0xC4+vA72DEqwdNHHehAmYPdwb3nsOAfjhcuGf3o4n/3Iib33VgX2AWzWmV/pGX0BhJvnts/GhmGTUgzB5chdqTH9pfgPBEGYSTtQ9E1MAOuolIsN9708WCIw4nah7GOaZ61ZveO+nCNAP11wsqpJ9F7bgvvX/j18WteBV4DaNNVCHJAsUQ5gNHHcaJlfTTcDNGtPMsg8ETJhQl3tqFGY1u6eXiEzxvV/NRCDEaR0NpgLfvHv7iUPX/ePXkQToh8uYOi5tdvqeW77sQP9lQt/5q/Gmxvy9wEERZsrxXYG/Y/Zbd2hy/zSAwkzCibodMSvWPwK72JqiRUPRQ8bsHesOYI2rXr7zphIWZt/KWrwPO9P/99U5549/6NhyFyaAxnSa3YPdW2NaK3G5T+LSJ30DwRUmgJeI/AycBuyASUReVBRdnJgcpH13nvnpiBM/dG8koD9cg7Rx2Vji0mbDubRbVkGlCv00po/4xZ/STjUBE2YqNKbJVc7HgBslLg9JXDrUNxBsYSbhJSI1mAyOQ2ywRdFQVHE6Ubc9cFubxfO/ePzRS48k4D/ccpRxEYnL6cCkilrOmrkW1wOHB1E4heTXmL6KKab0K8abqWSEmYKLMIWaRjhRN/eE2lmi2CPn9ah2fPTRyztV1S4rlR8OiUslJkXKmcCQ2gqGUgLCKRS/xnS+xnSwxvShjkPkb4ccxzNvb8SgUvl9vURkHua33Zwi1pEt2oKQE3X3A147/b2nFl7+xgOHlsoPJ3HZWGM6Q+KyH2bv7zFKSDjF4K+oZWxtBT2Bfr46MeR5RN7tnP+M/bFNh11UKrbyEpFv/OZvCkUZOZ2oW4XqbRvM/WnJiR/U9CsFYdpp7AXABInLWhi/11CYGfAvi+uRmJqjUf8ayP9UedQjQ7bDjF03+s6fAYo1rT0Vka17zPz0qo3m/Piy7+z+C3M1jJ/vKRgH9R0pE+EUil9jOgo4WuLSWeIyROKSve0V6Bl2o7k/9deKir8DRzhR9yDf22kCBRenE3XXrKhddnW7hfOmPLtt9TW+N5CfH64FJlJjD0w8ZVkJp1D8dmtpGSb6ZrSNjmlmAwVfXLoB43Z5qxN1W/reXiMoxsg5pLaisuOcVm1P873wqf8j5iYSFxdYrDEdionaKEvhFIpfY/oTsD/wG/CixEUyb6Dwq77WEeEiTNzrKb632QgKKk4n6m6E6v8BI71E5H1fyf0X5haYvEU1GtMlQTDscuG3DvOnAWdoTNWGqzXRQFG3Y1xgAnBFIbdWCj1yxhER4HJfWf0X5hqYOL9hGtM7g2TY5cKvMVWN6WcSl72B9yUu6zTcQHH3Se0M72/ABpgtloKgYOK0yX1PAO72EhHPN2L/hdlaY7oA2Etj+kAQDbuc+DWmbwKjgVeW8yiqayAYDgxeIvI6JvftZU7UbXqk9wGFHDkvBhS43jdG/4W5ATBV4rKd3cus4w+iYZcRfwz4LyvOqAIizBRcgUlMXZCcQwVxQnCi7rqYgkMjvUTkVF9I/RdmK+AtTJqQf5SQYZcFv10YqsKkbvlFh7E3wRImAE7UfQHYBdjYS0QW+N6vFBRq5LwAWA3wJ4g1P3fUKPAF8M9SM+xy4LfPoEuAO3aYxQMEUJgW/8TUXTne516thLyL04m67YBzgFFeIvJFzoT5cclrgQkaPhVTmaqkDLuc+IFHPlmHgUcN4LYAChNMArQPgAtsuGPeUIiR8zRM/tREzkz5EWYEk/d1ESZPbMkadpnw37usgvNGbcspGW2xNKuB3O3HrtzeDGwNHOhb39Igr+K0d5YzgHFeIpKbw3N+hNkV+DdmShv4EVNEVEQeSvl3lYjMFpGaxvhFpLuIHJoBf4OlCQos/PuAbTWm8+2sxocGfLWfJzB1ey7IkadR5HvkrMZ4VtydE0ue4jExQbXXYJ6HAy1Mi/nAdiLSyv77QOA72rB2E/zdMYm5skKRfHHnS1xOwtw8c2zAX/uxXkN3AIc4UXerXPkaQr7FeSbGTWt01gx5Wk63fp7nYfLjloIwk3iRZBAzHMOGvMu67AQMYBgLRGS8iHxo37cUkZbAVcBAEflIRAaKSBsR+beITBWRKSLSv66/IteIyGQReUdE1i3yVHk0sJvEpW/2DeRtO+ZuTK7bvDkl5G0rxYm6nbA5Tr1EJLvhP3+pRbYAjgXGUELCtNPO3YErgeNpyccMpCNP85nO014isiawQFWXisgBwF9Vtb+InAz0UNVzLc9wYDVVvcD+u72q/iYiCvRR1edF5FrWZ23OoI9f/V/p/5PB9ZG47AU8DmyXkgolwwbyu0+66zkPvjm7dbutaisq1/cSkaV+8+dz5DwZE81xT1Zn50+YlcC/UdpTQsJMQlWnAA5dGUYPOvM5w/iDZN7YtYBRIvIxJl3ltg3QHADcnsKZzDb/J1ADwNYspBPH+t3/JDK9PhrTtzCeZb83r4H8OzBc8dq93WorKjuRp4WhfIrzBGC8l4h82uwz83thz6+spTVSfMPLGuszhW8ZQmvO5T1S63v8HXhDVbfD5F9tyElbgHRTpiWqqhKXarbhAr5hbBCuj8b0NWBvicvBmTVQGM+int99eiTmse0E39sgT+K0FYS3x0xHmoc8X9jO8+i2rIKNKVFhSlyqOYq+rMvt+rKuuFiyFuZRAszMJYl5mO2sJF4mxQVNRNovxw+j+B83ModZfvZ9Of7srs/tEpfGYyoL6PK37rxfXsFkw+jnRN22jZ6XBfI1ch5p359q1ll5vrDPbSl9fmrNnsARpShMhEpgFO3or56el+aIa4F/isg4oDLl8zeAbZILQsDVQHsR+VhEJgP7LscPA/iET3zvfg7XR2P6Oibo+fSGGyiKL+5DQCtMild/oaq+v7oMrfmwy9Ca8c06D6oVZitU56NPD2/PwKorWMwwDskHP8OoZhizGZaf/of8CsPYkWG4xbCfhvi7DK2RLkNrpncZWpO+Xzm8fB85bQm/7jRn+6QAd7zHtuPOZRU8rjF90Xf68vDMCTy/zdzXe6XsCUWMXrEeQ88D+zlRdw0/m83HtDY5vD+Z0dEFuLBT1uWpF7oiKqSbCuZGXyKGXUb8LYFJEpeOpoFAhJW5mMW3ff1sOh/i7A18kFGezwJd2JltOb62gt6aYz3MlehLz7BLnt+mOHkHuDggwgSTzmY+9c4hvsBXcdoI8d0wKT4aR4EurNuVMyPHM0djOs5X+hI07DLiv6GylrMWVAVCmEl3vleBiJ+RKn6PnHtiAmZfb/SoAt7xeh9HN4w3kH/0pW3YJc8PbFRRy/yXuvLXYgszBS6wMQ07fjQbVX4RWewPLAEaHqUKKEwZxjhgJD56cJS6YZcL/5IqBvQfyHu+O59mb5/JhcYDMTU+c4bfI+d+wAQvEUlf4bjwzwh9gS80pr7s2ZWLYZcR/zsSl539ayB7+/QSkZmYymS9/OqOb+K05fx2oqEpbXEe3p8HTvSFvvwMuxz4HwXO9qcBX+xzAkEUJ6ZTglm5Wh5FEKbEZUPgII3pjJzpy9Owy4H/fuBIm2c4hwZ8s8/xwIZO1N0op/5Y+CnOnez7B8t9Wrzl7iMxNTlyoy9fwy55fjWlHa4Ashenv/Y53r7vniMP4K84dwSmeYlIfWhPcfeh+gDP5URfxoZdLvwa038BDaZXabwB3+1zCrCAAIpzJ6A+T1ARhSlxaY8pOvRq1vQBMLx884vIhiLyrIhME5HpInKbiKzmF38uyJTfJgL/UppbUjAP9uklIkuASZi8tjnDF3HaxSCHpDiL77kxF+ippqxC8+kDYnj55BdTs+Yp4BlV7YrJ9dQKE9niB39lus8zQXOuj8b0O0wgdo/MG8irfX6C6tZ+OCP4NXJ2t+8fBECYYPaafsyKPgDCKRD/fsAiVRMTqqrLgAuBE22OoZNF5LY6XpEaEamWuFTzBc+Q4CeGcaOIjBIxdTZFxBORK0XkbSAqIh+knN9VRCb52P9UPEem6wt5ts9dZ0xdgshawHq5cvklzh0ARjxxZWuKLEwbsTASaN1s+uAIpxD822KmYHVQ1d8xZTM2T3vGLnRnPqN5mm9YxC6quhMwEVO/MolFqrqnql4DzBWR5I37FGCEj/1PxUjg2yaPKsDAcda7o5Nbdzln5fNLnJtW1NYu2OfrD+6h+L6OmwIL7HQnc/pgCacQ/A2lKkk/HWvD2mzJMF7mBhayATBORD4CTgK6pByZmv3iPuAUO8UdiBGRX/2vg8Z0isb07kYPKtCMbmGL1ZPB4FvnSumXOJ1NfvuuSoovTICdWWFEaJI+eMIpBP8nrPCcZrP3rQt8DizF2ofEpZq12ZnPGcZkPgZeUdXu9rWNqp6aQpPqHfYkcAgmUmmSqv5CGviScDsuz0lcdkr/ZeEetc7ud+loTFqYYIizsnbZZvNWaz0xAMIE46URz5g+mMIpBP9rwBoiciLULeDcANymqgsx09vucoXsyxyeZAZLbDKxd4A9RGRze94aIrJFugZUdRGmtN+dNJAc2sfr8yvpFoUKvAZig6//B2yZK3XO4nSiriyTii4/tekwMVeulZDdhW2B2W9qmj64wsk7v6oqcDhwpIhMA34Bau2zIsA41mI+d/EKDzAZ5X173mxM8rBHRWQKRqyNPV89gpk+v+xn/9NgIiuKs3iLkzOB9XOl9yMqpQNmtc7zgaseWVxYuxg0CWMsja7WBlk4heJX1W+xq5wisjtGcDur6iSGsQ9mFf6AlTxzVF8Heqbhc9I0syfwgF0N9rX/K2ACqaNVcXcNZgF759qEH+J07LvnA5dB9hd2Y8xiUNGEabOrp07h3pBhdWssY1W1Ouc28tB/VR2PXdjxi19EngY2w2zb1H+ej/7HdBLJtYbib+f9AKztRN2WXiLyZ7bN+CHOte37Tz5w5XphN8KE7TRMn+cRjcF8TxW/8ANnMJLdMYsh1fbbrH+oJEphRE5CVQ/PJ38a7jtf+Q8vHWBWiYu5OJnM97sumWzxNAA/FoTa2fc5OTPlfsebTSPlHwpi2O15hLYcqY/oU3ASSm4AABmJSURBVBifz6WqOsu+mlfrIx1/iQizGPyVtezf9k9GUPxdgx/se+dcmvNj5ExmC89NnD5MRTSmn2O2AVamL3HDyzv/+jKCbTiSvehdkv2PS3UldLqjJ9fuOrPouwbJkTMnLyE/R87fGj2qMfj0jCBxiUlczkrzeR1/qRpeQ/zWR7bhc5v4vo5/cwbwBQ+V8vVRePvB7vzsN38W9pnM8phTiQa/xLkEWJjV2f4+vG+GKR9fT19cYf6OybOaF34RGQbc1JAA7ec32ePSfX+5tJQZ/JuXmcI7fMtXIrKZiLwkIpNE5C0R2coeOyBZvkFE3rSfVYrI9Sl1PlfKC1zI619bQX/M86aPDWRln0kbbKiQVEbwQ5ztgTl287V58H9VrTP18/1iCxPMfqsjIr1EpF2a77Pmt8JrBwwmjUCTwrTft0vz/c605FQuoRUH04+5dS549wDnqerOwMWYCs5gaoIepKrdqHcyPwPYBNhRVXfA7Glm1H8/kIZ/Y/xM7Jy9fQZGnC1ZYbTKCPlZ7v4WO99P/eEYxpsicrCYaAFfkKHhvQbcC7xAM+/oDfGLyI4isqV1IrgQuIUVBLqCMG8BLrTH16MLp7AL69KSAXqXvoCJ7FgdEyg8yvrN3k39osY4YISInE59kaQDgLtUdSlA6oJXkW6MuwGD/GkgJ/v0RZx+p8bMDHnah9KYDoKUH24pR3E1HYHJmGl3P+qfB7JGpoZnBXGOffnFvwVwq4i8jKnHeaH9fDCAiFxIE8KUuFSzBSfzMaP0reX4K4A5qtqdFaCqZ4nIrpis5h/ZaJO0zvNFnLEsxQ+bzt0+S1ScedwglrjEgE+BO3iQB5nOw5jn4Rfs50dksD7SOBy6siWD+JwH8NhOhsl2ufY7C/5rMR4oE4HPqC+5ONi+oDFhwiiWcCE/cJ6ItMLYwWGYkfJrERmgqqPsCLyDqk4Wkc1U9V3gXRE5DLOn/DJwloiMUVPqvgPD2IHiPUrkLk5/7DNZgv5U4JrGDmwMhRVnnj03Wi3h+IUt6AgcznQOwzhIeMCa+BBfx9pswNoczERe4hcqfeHMnr8K49TQBeiEGUEHp3zfsDBhgL6hY0RkHeAjjOPGW/aw44A7ReRvGD/lxzAzj+tEpCtmtHzNfvYxZiSfIiJLcBgDRa0YPo4cNv39sk8vEVEn6oJxQsgahRNnAVyq2l/EegtbcLHGdAwxxojIVcD59vUicK4NKG4+fb1hHJJnw2uUX0T2BG7HzAhOwpQBADOVTcVNIlIn0HSGbZ3c093ZVyrvrqpHpDluKSbQ+qIALL6B2Wsv+q6BE3WTuvpnLjz5qmy9PArk6zh3dWZg7ugAqOpcVf07JrL/Q6BNVvTBMLwk2gF/A3qqao39LPUZs4IVFokC1v988h+BuXE1swHf7TP5rNn8hdIU+DFyLqWxvbwCOiHPb8lUTKDrclDVuaw8smRGHxzDAyBFkA2uytpFIYDBdGNDlH2QYPQ/z/ytae7ImR/79EWcfoycc4D0WxSFjw7YALNQ4Q99sAxv+XMb2S6p22bpxpP8hf48w1iGpcnEnyMCeH2W2+duuoG82WegxLm6E3WXXzYuTtjOSdRX1s6NPniGtxysAOfQ0D7mMPahH/vwMk8ymY9X+j5HBPT6fAq8mVkDebXPwExrkz617Ug6/BYvnu57YMOc6YNpeCtBVYeJiDS4KisMYDJjVxFhojEdlVkD+bXPi998sPr6vU8Ek/09a/g1ckLSAb64ga4/kGOYTlANryE0ul0S0zGrijDtuY9LXBpPrFUA+9z6p6+vt/+a1eixTcBPcbYPQAT6WzQSz9kkfYANL+TPCHvQWN2UAtnnwzseepf9JPPn3zTwQ5y/Ahzx8WvVFFeYaEy/xXjNNJ8++IYX8jd+fkuMM0b6FDUFHDje2Kxn0kW06CPnDIBtf5x+GUWOQBdTzOY7iTcvAiTohhfyZ4QNgXEa05VTwRR+RtcZmOslItk5RFj4Ic5ZorWLH9/hLy8UO2+txrQWE6aVPrlwOvrSMLyQvwloTKdrTPdb6YviPGqtR46jJvggTi8RUUW+/qJTF/9dAbO7sJMwWd+bpi8Rwwv5M+I6XeISlLy1G5Dj8yb45b4n4lGfItMfZH9hn8VOtRulLyHDC/kzwhlAfW3R4i5ObglMy7UJv0a7r4FdfeLK6cJqTF9rkr70DC/kb5yvJaZq2kfmg+IJ04m6nTDRUJ/l2oxfju9fA+2dqNvsVBwrIccLK3ERicsHEpcODXxfx18KhhfyZ4StgK81pvMDsJ2X3GcNjDg/tu875MTiw4XVmCrGU+iglehL0/BC/iagMZ0C7BkAYUIAxfmhfc94lXQl+Hthn8NE9tfTl6jhhfwZcZ855Q52o/jCBCPOBeQS9G3hizi9RGQWZul4x6wI/L/j1ZCS26aUDS/kb5K7c0Ut1235Mw9SfGECbAN87iUitbk26+f2xwdkM3LmYSqiMf0ek26jpA0v5M8IF+39DUtb1hZfmE7UrcBUXxvtR9N+ZkL4ENjaibqtMj4jj88IEpc+VTG5nxI2vJC/af6KWk5rt4jbiy1Mi60wASDj/Wjeb3FWAttndHSeH97/+QodRTkWOKpUDS/kb5p/wCec+MzWueXqSd9AVva5u30PnDgn2Pemi4YWYFVtyDiGt6jlO/KQxKxcDLvk+ZV/PL49X2lMc4qbXLmBrO2zFyYQ5As/uuGbOL1E5Hvgf8D+jR5YoOXuChiwsAVXAZv6Sl8uhl0G/AinkGP87soN5GSfuwPjsypNkgZ+jyqvASc3WNG3wPtQySskcRG7/5kbfRkZdqnzU59Y7nX/GsjePp2ouzbmmfNBv7rjd2rM1zEZ0Hqu9E2RNoglLqdiivDkRl9Ghl0m/KcAd/px0zUN5Gyff7Hvb/jSH/wX5xjM/uLyU9viem6MB86y/pfZ0ZefYZcD/7mYIlE+NOCLfUaAn4H3fekTPovTS0R+xaza1ouzyC5VGtPPMFnZjsmKvjwNu6T5JS4nAlv7shDkg306UbcSkyX/RS8RWZZznyzykfH9RWAPJ+p2KrYwUxAji4pP5WjYpc4vcVkHk683+0rqdQ34Zp+7YiJR3KYObA7yIc7RQOXe0ycNIRjCRGP6tsb0bvvDZkZfhoZdJvyXA49oTL/OrQFfB44IsAz4b448yyEf4pyM6ldLKyrPJwDCrDslLpsCUyQubTM4to6/zAy7pPklLi2AXcihrJ4h8n1G1xsY5yUic5o8shnwXZxeIqKIjB7fpVuFM7Rmit/82V5Yjel04FVMVayG6cvUsMuEfymwu8Y0fYa9jBrwV5hO1N0GEyr5VK5cKyJfVcZGI1IF9PGVNfcLeyVwvsSlU1r68jbskuaXuOxArtsU+VkDOQEzpX3UJ7465EuckzAFWY/yjdGfQOzpmCrQKy0mlLNhlzq/xKUSU3X7saz3NfMgTBuFcjzwXy8R+ckPzlTkRZzWfekR4CAn6uZe9cvHC6sxfQPYQ+ISqaMvY8MuE/6LMKX9ssvmn79dg2pMvtyHfOSsQz6L594HCDAoJ5b8XNglwH0Sl44BMLyQv2n+icCpavISN7OBvG7nnYDqPEzGR98hPte5WQ5O1H0JkxVtEy8RWdpsgvzGe15fUUv32gq6Ud6GXbL8djp7GnC/xjRQ9uNE3TYVtctm1VZUPuElIrkNQA0g32Xn78EM+4c0+8w8OzBMv5mXt51NN6nl5HI07DLhvwg4GgjaiEmvbyZfXVtR2Rq/XAjTIN/ifB6TW+iMZp1VAM+iTebwyJQ7GaAVjJW4+FYNGwJj2CXNL3HZHbgEGNTs6Wye7WdxVct9Z6617tmovuslIhOaPiM75FWcXiKyBLgfONSJuptkdFLhXf76Ai9JXNb0hT4Ahl0m/L2Bk5vtCVQA+xm76U7PfNtuvRaI3Ow7fwryPXIC3InZB7q4ySOL44s7ElPX82ExVcqypw+OYZcsv8RlDYnL9hrTyzSmLzSvgcLYT/Tg878AvgOe9L2NFORdnF4i8h0wAjjVibrrNXhgkZzk7b7Z+UAbTPHV7OgDYNilzi9xEeABzO/RzAYKYz/39Dx8yK9rrNUDuM3ODPOGQoycANcCLYAL035b/LCyP4EDNaZvSVwavoE0RB8Awy4T/ksxaWWaJ84C2s8/9ju1GrPnmreFoLpm87mVkgon6j6KeY7Y2EtE6j10ghNWhsRlbeAT4CSNaUYRBgEy7JLmt8/8rwBHaEy/y7yBwtmPM7RmFsY+bvISkaYf03JEoUZOgH9ipo7n1n0SIGECaEx/AY4AHpK47NskfUAMu9T5JS77YEaj3YIqTMs/DNPP4b63lQYFE6eXiEzBbK1c5ETdDkETZhIa0/HAAGCofQZKTx8Qwy51fonL8Rin8Q2a5TdbYPtxou4OwEDgZi8Rme17e2lQyJET4DJgzc1/nnE3ARRmEhrTsRjHifb2rr48fUAMu9T5JS6nYUahAzSmXuYNFOXGfhUwF7jB9/YaQEHF6SUiHwMPfN1hg/6PdjvogiAKMwl7F98EGCVxObqOPiCGXSb86wLVGtNPM2+g8MJ0ou4umP3w65dbL8kzCrYglIQTdTujOg2RF71EZICv5Hn44SQu3YBnMPlI3yA4hl2S/BKX1YFbgbs0ppOa10BRhFkBjMOsIm/uJSLzfG+3ARR6WouXiPyAyLXAkU7U3b3JEzJFnn44jelkYJeDp7Gg5VL+BRxTrsLJN7/EpTMmfepamOoAzWigaGsUJwG7AUMKKUwogjgtbsBUn77JphXMDXn+4XQY2774CBefOZHbgZslLpv5yR8E4eSb3y6uPYGpnTpQYzo/8waKI0wn6rbHPBOPJ08xm42hKOL0EpH5wBBMsqazcyIr4A93627cA9wBjJO4HOELfQCEk09+iUuFxOU4jBPKIRrTq4O8KrvCt1dhUl6e40cx3Oai4M+cSThRV4AXgL2Abb1E5JtmkxTph7MRE3/FTHk029QZxRZOvvklLg4m8KENcLiaosbNaKB4wnSibndMup07vETkPN/bzgDFmtYmU5mcZf95pxVr5ijiD6cxHa8xPQEzGryfzShabOHkm98+X76PyeW6R4kJswUmFvkX4Arf284QRRMngB0tL8PsKR6b8YkBcWDQmC4GBgMJictjDWX1W4m+jIUpcdlU4jJQY/oDsL3G9NpmZzEo/u97GaYY11/9zkXbHBRVnBa3A+8CtzhRt+mM7MX/4ZaDxnQc0B2YCXSWuKwljSSuLldhSlzWkbjcghkt1wfQmM5qfgPF/X2dqNsDM1o+7CUieQ0JawpFF6ct/HIq5rlkhN1XSo+ACTMJjekCjenFGtMpwGHANInLebJCZbNyFKbEJVnj9W+AANtoTG/KroGiC7MVZlV2FlCU58xUFF2cAF4i8gkmX8whNJSRPaDCXBEa04cxFacOwZR/aAnlJ0yJS2uJy/nAdIlLR2CwxvR8zTYbezB+339iCuCeXMzpbBJFW61dEXZB6EnMyLOHl4i8V/dlMH645tPGZTON6VdrXSojf1+NCMJpGtNRfvGntFNNYYV5MCYv8ZvAMOuokUMDxf99nah7CGb34FYvEWl+sHceEBhxQt2m74eYbGs7eonI3CD8cLnyT12Hpw4/mte/6sB+wNMa01N9oy+cMP8F7INJNzMTaK0xbf7210oNFP/3daLuptRXKdjdS0Ryr/vpAwIlTgAn6vbC5PR5+str+9xepbUlLcxUfolLG8wK5gSJy73APOA54O1s8rLmU5gSl1bA7pXL+LcKrWsr+BTjgPGUXaX2oZFACHMNjAfQxkAPLxGZ7ns/skTgxAngRN0hwPDBb49ccOG4kZFyEOZKXxuH+r6YYk9/akx3l7hsA3yvMW3yeScfwrSZIPoAfUQ58OrX+N8hX/K3nc7iK43pND/aqG8sEMIU4D+YeicRLxF50fd+5ICqpg8pCq5DdYdb9jz2uFv2PHZtz2/2ABiGfU6bDFwlcVnDfnwacIbE5TtgAnAK0AlYpDH9vY7eB2FKXDoAPYCd7fvpwE7AoYd9zqf3P8tenRZwMapjfL99B+D6W5yDqRJ2ZdCECQEdOQGcqLs68DpmD3EvLxFpXnhRQwiOYaQ/3WxNbA1srjF9WuJyAaZY7CxgRocF3PZrK25BzHQY+AH4TGM6S+KyPWY7owXmxvurxnSaxGUQpoZkZ6BKY9pf4jIUs6I8EfO89ZzGdH7Qr49f/E7UPRCzAPQi0K8YvrNNIbDiBHCi7rrAexhD28Wm2cweATGMZtMawW7+1/c59Pr/culD3bjgrMPogRFbZ+A2jekoicuHQCWmyOwSwNWYXiVxORNojRHyTI3pW4Xsf9D4nai7EzAWmA7s7SUic33viw8ItDgBnKi7PeaB/QugOuuYuoAYRshfdGFuirGnxUAvLxFpns9vAREIJ4TG4CUiUzGJlboBNXZ1rXkIiGGE/EUXZifgJaAlcHCQhQklIE4ALxF5AbOithfwpBN1V8v45IAYRshfdGG2wQR6bwT09hKRz3zvi88oCXECeInIY5jVzIOBR52o2/RKc0AMI+QvujDbYhZ+egBHe4nIeN/7kgeUjDgBvETkAUyI1uEYJ/mGU5wExDBC/qILc01MTGkv4BgvEclLFep8oKTECeAlIv/CxNsdBzzkRN2WKx0UEMMI+YsuzHbAy5jYzIFeIvKE733JIwK/WtsQnKg7FEhgpitH1vlDBsQwQv6iC7M9RpjdgAGlNGImUbLiBHCi7unAXcA7QG9veO9uBMAwQv6iC3NDwMWEf/X3EpEa3/tSAJTctDYVXiJyL3AU0KP1nwvfn9Wmw5OUueGF/E0Kszsms8YmmFXZkhQmlPjImYQTdQ+Q2trnWtYunbO4quVBdm/UPwTE8EL+JoV5CCY37hyMI/sU3/tSQJT0yJmEl4i8qhUVey+uagkwwYm6vuSUBQJjeCF/k8I8E1PFbhqwa6kLE8pk5EzCibrrA08BuwJx4KqcHJoDYnghf6NhXy2B6zDVsF/ArMr+4XtfioCyEifURbPcCZyMKUB0Ylb+uAEwvJC/SWFujJnG7grcDFziJSLNDloPKspOnFAXRHsecCNmmnOMl4h8lDFBAAwv5G9SmIdiMuVVAYOKncYyHyhLcSbhRN19gYcxAcuXAjc1Oc0NgOGF/I2mr6zC1DC5FBOsfqSXiHzpez8CgLIWJ4ATddcG7sW4/L0KnNRgNEKZG3ap8ztRd2vg35hp7H3A+V4istD3fgQEZS9OqJvmngrcAiwCTvcSkaeWO6jMDbuU+a0P9f9hRsz5mKpfj/neh4BhlRBnEk7U3QIYicmb8yxwnpeIfFvOhl3q/CuMlk9j6pdkl7i6xLBKiRPqKkhdCAwDant++8l/Hn3ssqOqapeVnWGXMr9ddb8YU+bhD0wyridsdbpVAqucOJNwoq6D6m2IRFovXjBt/mprHL9clnk/UKbCySe/fQQ5ArgecIDRwLmrymiZilVWnLCcIfwLkyjrEeAKLxHxciYvQ+Hkm9+Jujtg1gWqganABV4i8rrvbZcIVmlxJmEDci/HeJlUYjKbX+MlIrOzIixD4eST34m6G2DK7p0O/Gb/vrecHAqyQSjOFNhQoxgwCLMqeD1wY7PcwcpMOPnkd4bWfAVEMelnKjA3xbiXiPzqe7sliFCcaeBE3a0wiZyPAH7FGM2tXiLyU6MnlpFw8sn/zDb7nHvBYZdUY7a3BLMa+w9fHifKCKE4G4ETdXfF3Nn7An9i6mrc4CUiX6x0cJkIJ5/8k9fr+vR5fYdMmNGu8wH20/uBhJeI5F6trAwRijMDOFF3S0xR35MwOU+fBW4D3vASkdpyEE6++J2ou9qBX0y4YlbbjpdM7dy1JbAAGAEM9xKRGX62VW4IxdkM2PIQ5wJnAx2Ab7ab9eWY259NHNZlzqz+pSacfPLbzOqDqpYtPXtpZVV7VKchcgcwIghVo0sBoTizgN0g74fqIOAARAR4DfPs9FzWJSNWRIkJ08bTDgSOBnZBVQVqVOQ24NUgFgsKMkJx5ggn6nbBTHdPwWyaL8YI9RngeS8RmZUVcYkI04m6nTE1PY/GVL4WTHXyR4HHw6lr9gjF6ROcqFuBKRfRD7OAtAmgmMyAz2IiYiZntHcXYGHaWcOewF+AgzClBQE+xwjyMS8R+dy3vq7CCMWZB1jPo+0xIu2HKUoLpsz8OOBN+5roJSKLlzs5YMJ0ou5amDIGu2BuPtVAK0yJwbcx2dRfAqasSn6vhUAozgLAPovtnfLa1n61COOmNhWYevwHbsUF40Ze1nHB3COLEP0hwPpAV8yNZRdMpvQtUw77HJOo+b/A2HLJ1RNUhOIsApyo2xEzNdwLU7l7e0y2hiR+BL4EvgVm2vfk3z9iRuA/vERkSYbtVT34+BW9O83/7YEndjgw/u8efWfa9rpgxNgV2BxILa84C1O4OPma6CUiv2X3Pw6RDUJxBgR2m2b7lNcmmHJ1GwINlTz8ExNONQ9YiPELrqK+7HwVZl92zQbOX4qp7jwt5fUl8CnwXThNLS5CcQYcdrrZkXqhroMpId8WaJPyWgMjtuRrScrfvwE/A7Pte/L146ruXB5khOIMESKgKIuM7yFClCNCcYYIEVCE4gwRIqAIxRkiREARijNEiIAiFGeIEAFFKM4QIQKKUJwhQgQUoThDhAgoQnGGCBFQhOIMESKgCMUZIkRAEYozRIiAIhRniBABRSjOECECiv8HJeGC7quMSCQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_circ(ax, circumference, **kwargs):\n",
    "    ax.plot(circumference * np.cos(x), circumference * np.sin(x), **kwargs)\n",
    "x = np.linspace(0, 2*np.pi, 100)\n",
    "tau = .65\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "plot_circ(ax, 1)\n",
    "ax.set_aspect('equal', 'box')\n",
    "ax.scatter([0], [0], c='k', marker='x', s=100)\n",
    "ax.annotate('Query \\ndesc', (0,0), xytext=(0.1, 0), size=10)\n",
    "ax.scatter([-.5], [np.cos(-.5)], c='r', marker='x', s=100)\n",
    "ax.annotate('Second nearest\\n neighbour', (-.5, np.cos(-.5)), xytext=(-1.1, np.cos(-.5)), size=10, c='r')\n",
    "#ax.arrow(0, 0, -tau, 0)\n",
    "ax.annotate(\"\", xy=(-tau, 0), xytext=(0, 0), arrowprops=dict(arrowstyle=\"<->\"))\n",
    "ax.annotate('τ', xy=(-tau/2, 0), xytext=(-tau/2, .025), size=14)\n",
    "#plot_circ(ax, tau, c='r', linestyle='dashed')\n",
    "ax.annotate('No match', xy=(-.2, (1-tau)/2+tau-.025))\n",
    "ax.annotate('Match', xy=(-.1, tau/2))\n",
    "n, radii = 50, [tau, 1]\n",
    "xs = np.outer(radii, np.cos(x))\n",
    "ys = np.outer(radii, np.sin(x))\n",
    "xs[1,:] = xs[1,::-1]\n",
    "ys[1,:] = ys[1,::-1]\n",
    "ax.fill(np.ravel(xs), np.ravel(ys), facecolor='none', hatch='/', edgecolor='r', linewidth=0.0)\n",
    "ax.add_artist(plt.Circle((0,0), tau, linestyle='dashed', edgecolor='g', facecolor='none', hatch='/'))\n",
    "ax.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "hfnet-pytorch",
   "language": "python",
   "name": "hfnet-pytorch"
  },
  "language_info": {
   "codemirror_mode": {
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