{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.optimize\n",
    "import lmfit\n",
    "from math import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Circle Fitting Research"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "nbsphinx-toctree": {
     "hidden": true
    },
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. contents::\n",
    "    :local:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "This document is an exploration into the mathematics and algorithms of fitting lines and circles to a limited number of points which are a subset of an aircraft track."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_data(dataset):\n",
    "    x = []\n",
    "    y = []\n",
    "\n",
    "    for x_coord, y_coord in dataset:\n",
    "        x.append(x_coord)\n",
    "        y.append(y_coord)\n",
    "\n",
    "    plt.scatter(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### data1\n",
    "an aircraft travelling in more or less a straight line (perhaps with a slight curve)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY8AAAD7CAYAAACSXhiEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe21c84ac18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data1 = [[-7823.439561574536, -2568.6287717351497],\n",
    "[-5107.037760476856, -1043.730245427465],\n",
    "[-2762.7301083133757, 190.28046761840392],\n",
    "[-259.35055129732217, 1076.7365979969445],\n",
    "[2135.210021244198, 2041.7607403979657],\n",
    "[4013.295597771261, 2335.1731250977123]]\n",
    "\n",
    "plot_data(data1)\n",
    "plt.axes().set_aspect('equal', 'datalim')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### data2\n",
    "noisy data of an aircraft turning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe21c84a9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data2 = [[-2736.5842226839904, 9051.690473155024],\n",
    "[-1973.134855393139, 9237.219387656745],\n",
    "[-1307.9423416823379, 10095.120237700188],\n",
    "[-1212.8163721100887, 10729.934781668326]]\n",
    "\n",
    "plot_data(data2)\n",
    "plt.axes().set_aspect('equal', 'datalim')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Line Fitting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scipy Line Fitting\n",
    "\n",
    "This is a first foray into doing line fitting using minimization of perpendicular offsets using scipy's minimization function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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L9f6tZnZdFN9aM7u2ofpsilydOGpm/2Rme83s8JSyROrJzH4V1cNyM3vWzLqk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\niIhIbP8fGNlb0+wvLHMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe21c730dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def perpendicular_distance(m, c, point):\n",
    "    \"\"\"returns a positive if on the right side of the line\n",
    "    returns a negative if on the left side of the line\"\"\"\n",
    "    a = m\n",
    "    x1 = point[0]\n",
    "    y1 = point[1]\n",
    "    \n",
    "    d = (a*x1 - y1 + c)/(sqrt(a*a + 1))\n",
    "    return d\n",
    "\n",
    "def least_squares_distance(m, c, points):\n",
    "    distance_sum = 0\n",
    "    for point in points:\n",
    "        distance_sum += perpendicular_distance(m, c, point)**2\n",
    "    \n",
    "    return distance_sum\n",
    "\n",
    "def func(x, *args):\n",
    "    return least_squares_distance(x[0], x[1], args[0])\n",
    "\n",
    "retval = scipy.optimize.minimize(func, [0,0], args=(data1))\n",
    "m = retval.x[0]\n",
    "c = retval.x[1]\n",
    "\n",
    "plot_data(data1)\n",
    "\n",
    "x = np.linspace(-10000, 5000)\n",
    "y = []\n",
    "for val in x:\n",
    "    y.append(val*m + c)\n",
    "\n",
    "    \n",
    "plt.plot(x, y)\n",
    "plt.axes().set_aspect('equal', 'datalim')\n",
    "\n",
    "\n",
    "# least_squares_distance(1, 1000, data1)\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Newton Line Fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gauss-Newton Line Fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Circle Fitting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### three point circle solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1/NfPiQjGmLz+wS+QO92NlUBdEaklIlFAL+B3K2+KSBPgbSDlSgVC+Uh0tHOb\n9NVXoUsXeP117X6EGE8PXhZYJIwxF4HBwDxgEzDJGJMuIs+JSNfsw14BSgKfichaEdHNL227805Y\nvtxpTdx+Oxw5YjuR8hFPD14W2N3wJO1uWPDLL/DMM87yeKNHQ/futhMpLzPGEPtqLBsGbqBqTFXA\n+90NFciiopxFdqdOhWHDoHdvbVUEORFxuhweak1okQgVrVvDunVQtarzwNjnn9tOpLyoaZWmrPth\nnUfOpUUilJQoAf/8p7YqQkD92PpsPbrVI+fSIhGKtFUR9OLLx5NxNMMj59KBy1C3eDHcfz80bQqj\nRjmPpKuAd/TMUer8qw7Hhx5HRHTgUhXBpVZFtWpw/fUwbpyufhUEypcoT3hYOIfPHC7yubRIqN/G\nKubPh4kToUULZ46FCmjx5ePZeqTo4xJaJNRvGjVydhJ7/HG44w7o318HNgOYp8YltEio3xNxHhZL\nT4dSpZwuyNix2gUJQPXK19MiobyoTBl44w1YsAD+/W/nCdNly2ynUlchvnw8Gce0SChvS0yEr792\ndjy/807nTsi+fbZTKTfomITyHRHo08fpglSu7Ixd/PWvcOyY7WQqH3WvqcvO4zu5mFW0rqIWCeW+\n0qXhpZdgwwY4eRLq1XPenzljO5nKQ4nIEsSWiGXfyaK1/LRIqKtXtaqzTN7ixbB2LVx3nfP+/Hnb\nyVQuVWOqcuD0gSKdQ4uEKrz4eJgyBaZPh2nToEED531Wlu1kKluVmCpFXu9Si4QqumbNnIlYY8Y4\nj6U3bw6zZ+uKWH6gaqmqHDilLQnlLzp2hJUrnY2Nhw2DJk1g0iSdY2FRlZgq2t1QfkYEevaE776D\nF16AkSOdAc533oFz52ynCzlVY6pqd0P5KRHo2tUZ3Bw/Hr78Eq69Fl57DU6dsp0uZFQppS0JFQhu\nvtkZo5g1C1atcorFP/6hz4X4QNUYHZNQgaRxY2eMYulS+OEH5+7IwIHOvAvlFXp3QwWmunWdMYqN\nG50ZnJ07OxsgT5rkrO6tPKZCiQocP3u8SOfQIqHsqVoVnn0Wdu92Hk9/912oWdPZAuD7722nCwrh\nYeFULFmxSOfQIqHsi4x0Hh5bsABSU52BzSZN4I9/hHnzdHJWEWmRUMElIQHeestpSXTp4jxIVq8e\nvPyyti4KKSYqpkjfr0VC+aeSJZ2VsdauhY8+crokTZqAy+V0S44XrZ8dSmKKaZFQwUwEbrrJeYAs\nMxOeeAIW1bdRAAAGiklEQVS++gri4pwuyhdf6CStApSKKlWk79cioQJHsWLOOMXUqbBnDyQnw7/+\n5QyAPvywsz6njl9cRrsbKjSVLQsPPugMdK5b59xWHTwYatSARx5xJm+dPWs7pV/QIqFUjRrOAOf6\n9bBwoVMwXn4ZKlVydlEfPx4OHbKd0hodk1Aqp3r14Mknna7Hjh3O1gCzZzuzO1u3hhEjYPPmkHqM\nvahjEhEeyqGU/4mNdbYHuOceZ3AzLQ1mznRmeEZFQYcO0K4d3HILVKliO63XFLW7oXuBqtBjjNM1\nSU11Csc33zhdE5frt49Klexm9KCJ6ydyT6N7Cr0XqBYJpS5edIpGWppTOBYtcloWLpfT0rj5ZucZ\nkwD15ZYvuSPhDi0SSnnMxYvOojmXWhqLF0Px4s4yfUlJv30ESOGYt2Menep28m6REJHOwJs4A53v\nG2NG5Pp6FPARkAQcAe4yxlw2h1aLhApIxsCuXbB69e8/AqRwLNi5gI51OnqvSIhIGJABdAAygZVA\nL2PMlhzHDAQSjTGDROQu4A5jTK88zhVwRSItLQ2Xy2U7htsCLS8EaObUVFy1al1eOMLDnTsp8fHO\nnZZLr+vWhehoK1lTd6XS/tr2hS4S7tzdaA5sM8bsARCRSUA3YEuOY7oBz2a/ngqMKkwYfxRov8CB\nlhcCNPPXX+MaPtxZZatnT+eTxsDBg7B1K2RkOB8ffuj8d9cuZ5zjUtGIj3cei69SxfmoXNl5GtYL\nwqRoMx3cKRLVgL053u/DKRx5HmOMuSgiP4rINcYY3QdOhQ4R5y975crObdWcLlxwppJfKiDp6c42\nBJmZcOAAHD7szCKtUsWZZp7zv1WqOF+LiXF2eo+J+e11eHiBsXxRJPJqouTuM+Q+RvI4RqnQFREB\ndeo4H8nJl3/94kWnUBw44HxcKh4bNzrF5MQJZ52NU6fg9Gnnvz/95DzPkrNoxMQ4LZKwsF8/wkqf\nKFJ0d8YkWgLDjTGds98PA0zOwUsRmZN9zHIRCQcOGGMuW+lCRLRwKGWJN8ckVgJ1RaQWcADoBfTO\ndcxM4D5gOdATWOjJkEopewosEtljDIOBefx2CzRdRJ4DVhpj/gO8D3wsItuAoziFRCkVBHw6mUop\nFXi88hSoiHQWkS0ikiEiQ/P4epSITBKRbSKyVERqeiOHu9zI+z8isklE1onIfBGpYSNnrkz5Zs5x\nXA8RyRKRpr7Md4UsBWYWkT9l/6w3iMhEX2fMlaWg34saIrJQRNZk/27cZiNnjjzvi8hBEVmfzzH/\nyv57t05EGrt1YmOMRz9wCs92oBYQCawD6uc6ZiAwJvv1XcAkT+fwcN5bgOjs14/YzOtu5uzjSgFf\nA0uApv6eGagLrAZKZ7+P9fO844AB2a8TgF2Wf8ZtgMbA+it8/TZgVvbrFsAyd87rjZbEr5OvjDHn\ngUuTr3LqBnyY/XoqzmxOWwrMa4z52hhzaZmjZTjzQmxy52cM8DwwAvCHRSDdydwfGG2MOQlgjLG5\nD6A7ebOA0tmvywL7fZjvMsaYb4H8VgjuhvP4BMaY5UAZESnwcVdvFIm8Jl/l/kv1u8lXwI8ico0X\nsrjDnbw5PQjM8WqighWYObspWd0YM9uXwfLhzs85HqgnIt+KyBIR6eSzdJdzJ+9zwD0ishf4DzDE\nR9kKK/efaT9u/IPnjUVnAm3ylTt5nQNF+uI8xHZLXl/3oXwzi4gAb+Dcls7ve3zJnZ9zBE6Xoy1Q\nE1gkIg0utSx8zJ28vYHxxpg3sucTTQQaeD1Z4bn9u56TN1oS+3D+B19SHefBsJz2AjUAsidflTbG\n2NpIwZ28iEhH4Cng9uzmp00FZY7B+WVNE5FdQEtguuXBS3d+zvuA6caYLGPMbmArcJ1v4l3GnbwP\nAlMAjDHLgGgRifVNvELZR/bfu2x5/q5fxguDJ+H8NuAThTPgk5DrmEH8NnDZC7sDl+7kbZJ9TB1b\nOa82c67jU4Em/p4Z6ARMyH4dC+wByvlx3lnAfdmvE4B9fvC7EQdsuMLXkvlt4LIlbg5ceitoZ5x/\nBbYBw7I/9xzQNft1MZwKvA1nIDDO8g+2oLzzcWabrgHWAl/6wS9DvplzHbsQy3c33M0M/BPYBHwH\n9PTnvNmF4dvsArIG6GA576c4LYNzwPfA/cAA4OEcx4zKLn7fufs7oZOplFL50iX1lVL50iKhlMqX\nFgmlVL60SCil8qVFQimVLy0SSql8aZFQSuVLi4RSKl//DwkrRpvJPPwOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe21c86a208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class Circle:\n",
    "    def __init__(self, pos, radius):\n",
    "        self.pos = pos\n",
    "        self.radius = radius\n",
    "\n",
    "    \n",
    "    @staticmethod\n",
    "    def from_three_points(p1, p2, p3):\n",
    "        dy1 = p2[1] - p1[1]\n",
    "        dx1 = p2[0] - p1[0]\n",
    "        dy2 = p3[1] - p2[1]\n",
    "        dx2 = p3[0] - p2[0]\n",
    "        \n",
    "        slope1 = dy1/dx1\n",
    "        slope2 = dy2/dx2\n",
    "        \n",
    "        x = (slope1*slope2*(p1[1] - p3[1]) + slope2*(p1[0] + p2[0]) - slope1*(p2[0] + p3[0]))/(2*(slope2-slope1))\n",
    "        y = -1*(x - (p1[0] + p2[0])/2)/slope1 + (p1[1] + p2[1])/2\n",
    "        \n",
    "        x1 = x - p1[0]\n",
    "        y1 = y - p1[1]\n",
    "        r = sqrt(x1*x1 + y1*y1)\n",
    "        \n",
    "        return Circle([x,y], r)\n",
    "    \n",
    "    def get_plot(self, **kwargs):\n",
    "        return plt.Circle((self.pos[0], self.pos[1]), self.radius, **kwargs)\n",
    "    \n",
    "    def __str__(self):\n",
    "        return \"Circle([{0},{1}],{2})\".format(self.pos[0], self.pos[1], self.radius)\n",
    "    \n",
    "    def distance2(self, point):\n",
    "        return (sqrt((point[0] - self.pos[0])**2 + (point[1] - self.pos[1])**2) - self.radius)**2\n",
    "    \n",
    "\n",
    "\n",
    "c1 = Circle([1,1], 1)\n",
    "c2 = Circle.from_three_points([-1, 0], [0, 1], [1, 0])\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.add_artist(c1.get_plot(edgecolor=\"r\", facecolor=\"none\"))\n",
    "ax.add_artist(c2.get_plot(edgecolor=\"g\", facecolor=\"none\"))\n",
    "ax.set_aspect('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scipy Minimize Circle Fitting\n",
    "The following two cells demonstrate using scipy's minimize function to solve for circles using the conventional parameterization:\n",
    "\n",
    "$$d_i = \\sqrt{(x_i - a)^2 + (y_i - b)^2} - R$$\n",
    "$$F =  \\sum_{i=1}^{n}d_i^2$$\n",
    "\n",
    "Where F is the function we are trying to minimize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Guess(green): Circle([-2676.9263298024503,10469.756101355182],1419.3199745179995)\n",
      "Answer(red): Circle([-2744.1154157915385,10576.023919859705],1530.7115839583885)\n"
     ]
    },
    {
     "data": {
      "image/png": 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F0hSQiBTrcP5hfvlAU76YcIzorduhVq1gR5JSKvMisIhEtne+fYexn1Un+s5btfM/w2gK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\n/90sKSEYrGNxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe21c7a2198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "def circle_ri(a, b, radius, points):\n",
    "    r_sum = 0\n",
    "    c = Circle([a, b], radius)\n",
    "    for point in points:\n",
    "        r_sum += c.distance2(point)\n",
    "    \n",
    "    return r_sum\n",
    "\n",
    "def func(x, *args):\n",
    "    return circle_ri(x[0], x[1], x[2], args[0])\n",
    "\n",
    "c1 = Circle.from_three_points(data2[0], data2[1], data2[2])\n",
    "\n",
    "retval = scipy.optimize.minimize(func, [c1.pos[0],c1.pos[1],c1.radius], args=(data2))\n",
    "a = retval.x[0]\n",
    "b = retval.x[1]\n",
    "r = retval.x[2]\n",
    "\n",
    "c2 = Circle([a,b], r)\n",
    "\n",
    "\n",
    "plot_data(data2)\n",
    "\n",
    "print(\"Guess(green):\", c1)\n",
    "print(\"Answer(red):\", c2)\n",
    "\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.add_artist(c1.get_plot(edgecolor=\"g\", facecolor=\"none\"))\n",
    "ax.add_artist(c2.get_plot(edgecolor=\"r\", facecolor=\"none\"))\n",
    "\n",
    "plt.axes().set_aspect('equal', 'datalim')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Guess(green): Circle([45793.89384213992,-94898.80121838693],106769.28015751315)\n",
      "Answer(red): Circle([12107.017055118396,-33336.20943681085],36638.49292318794)\n"
     ]
    },
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LU3W5NWYOk/4yRcEhIgUumF1DdwNT/emqwKIcr/3otxmwJUf7VqCFmZ0NpOYI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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe21c7b0588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c1 = Circle.from_three_points(data1[0], data1[1], data1[2])\n",
    "\n",
    "retval = scipy.optimize.minimize(func, [c1.pos[0],c1.pos[1],c1.radius], args=(data1))\n",
    "a = retval.x[0]\n",
    "b = retval.x[1]\n",
    "r = retval.x[2]\n",
    "\n",
    "c2 = Circle([a,b], r)\n",
    "\n",
    "\n",
    "x = []\n",
    "y = []\n",
    "\n",
    "for x_coord, y_coord in data1:\n",
    "    x.append(x_coord)\n",
    "    y.append(y_coord)\n",
    "\n",
    "plt.scatter(x, y)\n",
    "\n",
    "print(\"Guess(green):\", c1)\n",
    "print(\"Answer(red):\", c2)\n",
    "\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.add_artist(c1.get_plot(edgecolor=\"g\", facecolor=\"none\"))\n",
    "ax.add_artist(c2.get_plot(edgecolor=\"r\", facecolor=\"none\"))\n",
    "\n",
    "plt.axes().set_aspect('equal', 'datalim')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### SciPy Levenberg-Marquardt Least-Squares Circle Fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Guess(green): Circle([45793.89384213992,-94898.80121838693],106769.28015751315)\n",
      "Answer(red): Circle([12051.872411956107,-32914.71010089948],36234.900858877416)\n"
     ]
    },
    {
     "data": {
      "image/png": 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tN7G9bQsGNT+bs76azaBHpyo4RCTXBbM/40Fguj99EbA502u/+G3Ht28BLjKz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\n/wNqR9e7aMzJKgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe21c70eef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def circle_ri(a, b, radius, points):\n",
    "    residuals = []\n",
    "    c = Circle([a, b], radius)\n",
    "    for point in points:\n",
    "        residuals.append(c.distance2(point))\n",
    "    \n",
    "    return residuals\n",
    "\n",
    "def func(x, *args):\n",
    "    return circle_ri(x[0], x[1], x[2], args)\n",
    "\n",
    "c1 = Circle.from_three_points(data1[0], data1[1], data1[2])\n",
    "\n",
    "retval = scipy.optimize.least_squares(func, [c1.pos[0],c1.pos[1],c1.radius], args=(data1), method=\"lm\")\n",
    "a = retval.x[0]\n",
    "b = retval.x[1]\n",
    "r = retval.x[2]\n",
    "\n",
    "c2 = Circle([a,b], r)\n",
    "\n",
    "\n",
    "plot_data(data1)\n",
    "\n",
    "print(\"Guess(green):\", c1)\n",
    "print(\"Answer(red):\", c2)\n",
    "\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.add_artist(c1.get_plot(edgecolor=\"g\", facecolor=\"none\"))\n",
    "ax.add_artist(c2.get_plot(edgecolor=\"r\", facecolor=\"none\"))\n",
    "\n",
    "plt.axes().set_aspect('equal', 'datalim')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Guess(green): Circle([-2676.9263298024503,10469.756101355182],1419.3199745179995)\n",
      "Answer(red): Circle([-2749.8969143634604,10575.118314312538],1533.689331374633)\n"
     ]
    },
    {
     "data": {
      "image/png": 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i1llt4Sc/8TuOVCJdDE5EijXly//y8EeOOs/8we8oUsk0AhCRYq0b9zhNYuPhqqv8jiKV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\nKgAiIhFKBUBEJEKpAIiIRKj/DzLDU4PSnAkrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe21c5a02b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c1 = Circle.from_three_points(data2[0], data2[1], data2[2])\n",
    "\n",
    "retval = scipy.optimize.least_squares(func, [c1.pos[0],c1.pos[1],c1.radius], args=(data2), method=\"lm\")\n",
    "a = retval.x[0]\n",
    "b = retval.x[1]\n",
    "r = retval.x[2]\n",
    "\n",
    "c2 = Circle([a,b], r)\n",
    "\n",
    "plot_data(data2)\n",
    "\n",
    "print(\"Guess(green):\", c1)\n",
    "print(\"Answer(red):\", c2)\n",
    "\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.add_artist(c1.get_plot(edgecolor=\"g\", facecolor=\"none\"))\n",
    "ax.add_artist(c2.get_plot(edgecolor=\"r\", facecolor=\"none\"))\n",
    "\n",
    "plt.axes().set_aspect('equal', 'datalim')"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Edit Metadata",
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}