{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## This notebook plots a parametic curve its osculating circle at a pair of slected points.\n",
    "\n",
    "Start by importing the required libraries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *  #python symbolic math package.\n",
    "import numpy as np   #numerical mathmatics library.\n",
    "import matplotlib.pyplot as plt    #plotting library.\n",
    "init_printing()            #to get good looking output."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Declare $t$ to be a symbol, give the domain $[a,b]$ of \n",
    "the curve, and define $x$ and $y$ as functions of $t$.\n",
    "Also give the values where the osculation circles\n",
    "are to be drawn.\n",
    "These should all be edited as needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = symbols('t')\n",
    "a = 0\n",
    "b = 4*pi \n",
    "x = (1+2*cos(t))*cos(t)\n",
    "y = (1+2*cos(t))*sin(t)\n",
    "s1 = 0   # should be between a and b\n",
    "s2 = pi/2   # should be between a and b\n",
    "s3 = pi   # should be between a and b\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Divide the domain into pieces of length $h$ to be used in plotting\n",
    "and compute the $x$ and $y$ values at these the subdivsions of the domain\n",
    "and store in them in lists."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "h = .05   #edit if need be.\n",
    "t_dom = np.arange(a,b,h)\n",
    "x_vals = [x.subs(t,s) for s in t_dom]\n",
    "y_vals = [y.subs(t,s) for s in t_dom]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left( -0.281162476302927, \\  3.1562458322049, \\  -1.9361487103523, \\  1.93570913070675\\right)$"
      ],
      "text/plain": [
       "(-0.28116247630292657, 3.156245832204901, -1.9361487103523003, 1.9357091307067\n",
       "45)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_vals,y_vals)\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the deriviatives of $x$ and $y$ with respect to $t$ and use\n",
    "them to compute the speed, $v$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIwAAAAaCAYAAABl/7RgAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAGcElEQVRoBe2a3VEcORCAx9QFQOEIjDPAdgTGGWBfBMYZ+IoneHPZGWBHcAcZ4IvABRlABgYy4L5PO5rTzEoz+wO7yxZd1bSmpZa6W61WzyzP7u7uqidYbw8cHR19rS38DX3O8199FtO/Tf8n8Kwe5/M1/NONmvFE1tQDbPI+pv02SMBvtM+gMRBKVhsgyjnuGHyJzCm0+sM/T7DWHjC7vI0WsvE/DRhwG7yK/Ax9S/9Fl/8UMF2PrNGzQYE5m2A3MG7h7WT4sP4H5Hd5Ut4gU6Z6upL0wvqCm52Da5hbuY6Ed0DbQPsJ/iBg9uwbC5g6Ku1bG5jUpknHrYpj5tDXYCkFU8W8ZpT34BVoZvkCnmh3K2Do/AzPVLU2MKVN3uv6YOmAHmP7AG8T9JqJMKRvuEbi4IQaLN1rqulmjZBNGkY9Fv5uEzD1IF+5QjWcDG416d8BrZxXHia1KRrCeNNvBfUNYdnwL3rcgec1XqLQOeh1EgB+r770GxQGTRpkI+GqGitoYwf0BNk0YM1IwlUIGDqNuANo7/t5EBmlpjhBzVo9MmST/eAl2HImz756frJ/yVYZGG62G6cuHuRX6CWvgQn09TqxeA3AeNun0JBhoPohfqepR1XfaaQZyIwTZOJbkgKDWYOJVyJdR6sG6JBNOs5gaU5sMp++UN6PVzMBvgrzQ3X+LHCB7PsJBYv6Msc38KvIXH64ewl+TObVB/v0H4MxSEwcJpDwoc+xtEe6+KX38PDwRtqHjNkB98Fz8KRv7Cr0oWOvTfQfg5clXZUHN0v9Q3xk98DPQ+NK/chO5WPGz6VvSY8uf4PIMd3EyDKYSvAnY2c9LaU5H4Q/oU0hNfcooE8+9PSvWtdC9PVKegeG4qnkATbAq2jwykrlkfHeNQ2md+4v+E1RnYyxoBNMlxZcjT60vcPdXOdxTsHgfTVqZv9mbULGebxmnMdUbAHv66J6WbukoA7Os7RDgk4W3+r6HFTfL/BKxepC9DVgXoPFYEBBFb2FTpKFGBruO2Ws6D8iFwIE6mYZDL7bez8bCG7WO3nQALT9bO1GevfqLO9fN64Bnodqi6xNyOlUvzGYVXe78zYLjBoGsTovC7T9H3S8VQGoPrVI11/NgbKvhoXou8FiKpYr/KIivjFMe8oMBAOjySb1Os4ZHAB1TFOt21GDBZdBYkC58a9pq2MKxQCvBw3ZZACWTmpcR5+4SUsBbDYwoq8q2h4qA6Vk+0L0NcNsgY1itBtASVNiScFmXNpAxs1ys1spHr7BE7ON/W7GL7AFjDP7yPPa8RdWHXED1Vn+emqQteaG14WiTfVAM0cazF15n90gbekFdNE/uUykDhX9uWw4zRtQur46mRlzPxxOpG862SxtAyYLKkWH7+gqMg3EU+krWQnimGyg1kIGlWCtcgB6jVgTmX2+g7mNoLsfkDMIXH/oJ/6hoAsLlfSAr75u7FBwh3nSP8io2xa0VKflAnkifdN1ZmkbMJ7gnAI69Q1Ke3Wk4EbqiHjtdD/2xQCzgC1BHJNbN8p4panDNdQ1wjq0Q9aD+t3gIg7u0JJNDgvZANmmDqDtwbjtzKFuzrMM8CrOrW1QVOias3sh+howbl488eoTAKV0aOPUmq2yN/Kh2Y9K8C2QNUijx4C+PdBrxQ2ylmhdDfDDhsI3IENwQptTSr/ZRTnnzzkOdt4mO4BW/cJcZgJ90J3LzYmBTXOhoI3dg6gC+mZsT2rNFqLvBovpqDf1opMQI1nsA4PJLNT6TYZnr5S4Mf5Tzwd4BkUKjvENKTrGL47d9XyO/alsbPfZ1Di2nlc9o05RXup1kOOnYx6qbfZs1Y48x6/s2YO6KH3NMH+D3WtnzBG1ATETWXgpk/t+UdHndfKCfusNDY/fWXREOLVQCz83xcL2Fio4v88xGOT7hrYPDxLgOX+dt+/099nkyVWPEMzQJnuNpm/+eppnqpOaGWZsaBsYfecsBvk1+AJ+9JX8FBai7zM//aKEG+r/PyzrRKWG30t7HpuQNXD9HtRXh/XqiaxX3UxFb+/Emc770DczbZbllSR4DSzlNIXVH+bPPDaZhZSfB8wEpWwwz7w52fvQNzfvOC/+uMSPV2fgdnxeBzqLTfpAucdi/6L1jRnGSLKYahVa4+H16Diz2KQPHlO2Xai+oYaJYVDfhb72lgrBOPTR0GlsYqxvIrmfK1bS3mXo+x/qZJuHAEpSWgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle \\left(4 \\cos{\\left(t \\right)} + 5\\right)^{0.5}$"
      ],
      "text/plain": [
       "              0.5\n",
       "(4⋅cos(t) + 5)   "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dx = diff(x,t)\n",
    "dy = diff(y,t)\n",
    "v = (dx**2 + dy**2)**(1/2)\n",
    "v.simplify()  # simplfy v if possible."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the components of the unit normal $\\mathbf n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "n1 = -simplify(dy/v)\n",
    "n2 = simplify(dx/v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the second derivatives of $x$ and $y$ and use them to \n",
    "compute the curvature and the components of the evolute\n",
    "and make lists of the values of the components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "ddx = diff(dx,t)\n",
    "ddy = diff(dy,t)\n",
    "num = simplify(dx*ddy - ddx*dy)\n",
    "curvature = simplify(num/v**3)\n",
    "curvature.simplify()\n",
    "r_1 = 1/curvature.subs(t,s1)\n",
    "c_1x = x.subs(t,s1) + r_1*n1.subs(t,s1)\n",
    "c_1y = y.subs(t,s1) + r_1*n2.subs(t,s1)\n",
    "r_2 = 1/curvature.subs(t,s2)\n",
    "c_2x = x.subs(t,s2) + r_2*n1.subs(t,s2)\n",
    "c_2y = y.subs(t,s2) + r_2*n2.subs(t,s2)\n",
    "r_3 = 1/curvature.subs(t,s3)\n",
    "c_3x = x.subs(t,s3) + r_3*n1.subs(t,s3)\n",
    "c_3y = y.subs(t,s3) + r_3*n2.subs(t,s3)\n",
    "osc_1x = [c_1x + r_1*cos(2*l*pi/200) for l in range(0,201)]\n",
    "osc_1y = [c_1y + r_1*sin(2*l*pi/200) for l in range(0,201)]\n",
    "osc_2x = [c_2x + r_2*cos(2*l*pi/200) for l in range(0,201)]\n",
    "osc_2y = [c_2y + r_2*sin(2*l*pi/200) for l in range(0,201)]\n",
    "osc_3x = [c_3x + r_3*cos(2*l*pi/200) for l in range(0,201)]\n",
    "osc_3y = [c_3y + r_3*sin(2*l*pi/200) for l in range(0,201)]\n",
    "\n",
    "#E1 = simplify(x + n1/curvature)\n",
    "#E2 = simplify(y + n2/curvature)\n",
    "#E1.simplify()\n",
    "#E2.simplify()\n",
    "#E1_vals = [E1.subs(t,s) for s in t_dom]\n",
    "#E2_vals = [E2.subs(t,s) for s in t_dom]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( -0.78, \\  3.18, \\  -1.98, \\  1.98\\right)$"
      ],
      "text/plain": [
       "(-0.7799999999999996, 3.18, -1.9799999999999998, 1.9799999999999998)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_vals,y_vals,osc_1x,osc_1y,osc_2x,osc_2y,osc_3x,osc_3y)\n",
    "plt.axis('equal')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "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": "3.9.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
