Where is the point?

where_is_the_point.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## calc distance between two points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setup\n",
    "Let's assume that:\n",
    "\n",
    "* 9 points on grid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Place 9 sensors on the plane"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pos_sensors = [np.array([i*2, j*2]) for i in range(3) for j in range(3)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x106ce7610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(zip(*pos_sensors)[0], zip(*pos_sensors)[1])\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set a point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "point = np.array([[1,1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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R6xFxXtLnJb2945kaExEPSfpJ13O0JSIej4i18e1nJJ2U9GvdTtWsiPjp+OYLJW2T9FSH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\noMOqJmFvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106e0aa90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(zip(*pos_sensors)[0], zip(*pos_sensors)[1])\n",
    "plt.scatter(zip(*point)[0], zip(*point)[1], color='r')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate distances between the point and scanners"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.spatial import distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.41421356,  1.41421356,  3.16227766,  1.41421356,  1.41421356,\n",
       "         3.16227766,  3.16227766,  3.16227766,  4.24264069]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance.cdist(point, pos_sensors, 'euclidean')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pick min 4 from distance array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "distances = distance.cdist(point, pos_sensors, 'euclidean')[0]\n",
    "ind = distances.argsort()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 3, 4])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ind[:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Show euclidean distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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g/vhpCGI12Teus1tsfwpZYz1mJI2TtBzYCCyJiDVpuXNYkRzSoe6d8thD3TvZ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\nXGAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10710d4d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.scatter(zip(*pos_sensors)[0], zip(*pos_sensors)[1])\n",
    "plt.scatter(zip(*point)[0], zip(*point)[1], color='r')\n",
    "ax = fig.add_subplot(111)\n",
    "for index, pos in enumerate(pos_sensors):\n",
    "    ax.annotate('%s: %s'% (index, distances[index]),\n",
    "                xy=pos, textcoords='offset points')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Moving the point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nRMQZbfcHsmNGogzuafnr24c/28RB3VSsu8FmTdHfoM6d/oOSxhgz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\nF9sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10744fd90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "point = np.array([[0.5,2.5]])\n",
    "distances = distance.cdist(point, pos_sensors, 'euclidean')[0]\n",
    "ind = distances.argsort()\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.scatter(zip(*pos_sensors)[0], zip(*pos_sensors)[1])\n",
    "plt.scatter(zip(*point)[0], zip(*point)[1], color='r')\n",
    "ax = fig.add_subplot(111)\n",
    "for index, pos in enumerate(pos_sensors):\n",
    "    ax.annotate('%s: %s'% (index, distances[index]),\n",
    "                xy=pos, textcoords='offset points')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusion of this short experiment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can keep track of movement of point based on eucledean distance. We can calculate where the point is based on eucledean distances of seneors without position of "
   ]
  },
  {
   "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
}