d2207197/star.ipynb

## star.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/site-packages/matplotlib/__init__.py:1318: UserWarning:  This call to matplotlib.use() has no effect\n",
      "because the backend has already been chosen;\n",
      "matplotlib.use() must be called *before* pylab, matplotlib.pyplot,\n",
      "or matplotlib.backends is imported for the first time.\n",
      "\n",
      "  warnings.warn(_use_error_msg)\n"
     ]
    }
   ],
   "source": [
    "import matplotlib \n",
    "import matplotlib.pyplot as plt\n",
    "matplotlib.use('nbagg')\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.lines as lines\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x104c0ae50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "fig.set_size_inches(6,6)          # Make graph square\n",
    "\n",
    "line1 = [(0.2,0.2), (1,0.2)]\n",
    "line2 = [(0.3,0.2), (0.2,1)]\n",
    "\n",
    "# Note that the Line2D takes a list of x values and a list of y values,\n",
    "# not 2 points as one might expect.  So we have to convert our points\n",
    "# an x-list and a y-list.\n",
    "(line1_xs, line1_ys) = zip(*line1)\n",
    "(line2_xs, line2_ys) = zip(*line2)\n",
    "\n",
    "ax.add_line(lines.Line2D(line1_xs, line1_ys, linewidth=2, color='blue'))\n",
    "ax.add_line(lines.Line2D(line2_xs, line2_ys, linewidth=2, color='red'))\n",
    "plt.plot()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "https://gist.github.com/f30414102ec666d632cd\r\n"
     ]
    }
   ],
   "source": [
    "!gist -u f30414102ec666d632cd star.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import division\n",
    "import cmath\n",
    "from cmath import pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def to_xy(r, phi):\n",
    "    coord = cmath.rect(r, phi)\n",
    "    return coord.real, coord.imag"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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H0snA5sDBtv/cZawjgLcBO6aAdy+zUIaE7ZsoS5wvlHSUpEljjaHiZcDVwKkp3tE4HngM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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1049853d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "plt.ylim(-3, 3)\n",
    "plt.xlim(-3, 3)\n",
    "for circle in [plt.Circle(to_xy(2,i*2*pi/7-0.5*pi/7), 0.2, fc='none', ec='black') for i in range(7)]:\n",
    "    ax.add_artist(circle)\n",
    "for circle in [plt.Circle(to_xy(1.384042944,i*2*pi/7+0.5*pi/7), 0.2, fc='none', ec='black') for i in range(7)]:\n",
    "    ax.add_artist(circle)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "https://gist.github.com/aeaca530943b6b19aee3\r\n"
     ]
    }
   ],
   "source": [
    "!gist -u aeaca530943b6b19aee3 star.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1.9498558243636472, -0.4450418679126288),\n",
       " (1.5636629649360596, 1.246979603717467),\n",
       " (1.2246467991473532e-16, 2.0),\n",
       " (-1.5636629649360594, 1.2469796037174672),\n",
       " (-1.9498558243636472, -0.44504186791262856),\n",
       " (-0.8677674782351166, -1.801937735804838),\n",
       " (0.8677674782351159, -1.8019377358048385)]"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[to_xy(2,i*2*pi/7-0.5*pi/7) for i in range(7)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1.3493420977639046, 0.30797852853452695),\n",
       " (0.6005137276419932, 1.2469796043840113),\n",
       " (-0.600513727641993, 1.2469796043840113),\n",
       " (-1.3493420977639046, 0.30797852853452706),\n",
       " (-1.0820883467069364, -0.8629366609185379),\n",
       " (-2.5424456418781187e-16, -1.384042944),\n",
       " (1.0820883467069362, -0.8629366609185384)]"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[to_xy(1.384042944,i*2*pi/7+0.5*pi/7) for i in range(7)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "line1 = (1.9498558243636472, -0.4450418679126288), (1.2246467991473532e-16, 2.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "line2 = (1.5636629649360596, 1.246979603717467), (-1.5636629649360594, 1.2469796037174672)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def line_intersection(line1, line2):\n",
    "    xdiff = (line1[0][0] - line1[1][0], line2[0][0] - line2[1][0])\n",
    "    ydiff = (line1[0][1] - line1[1][1], line2[0][1] - line2[1][1]) #Typo was here\n",
    "\n",
    "    def det(a, b):\n",
    "        return a[0] * b[1] - a[1] * b[0]\n",
    "\n",
    "    div = det(xdiff, ydiff)\n",
    "    if div == 0:\n",
    "       raise Exception('lines do not intersect')\n",
    "\n",
    "    d = (det(*line1), det(*line2))\n",
    "    x = det(d, xdiff) / div\n",
    "    y = det(d, ydiff) / div\n",
    "    return x, y\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.6005137273210023, 1.2469796037174672)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "line_intersection(line1, line2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}