gistfile1.txt

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 },
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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We define our square function as a lookup in a 4x2 array whos values are dependant on the input size and origin. It returns an array of absolute vectors, length depending on the number of points required (N)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from collections import namedtuple\n",
      "Point = namedtuple('Point', ['x', 'y'])\n",
      "\n",
      "def createSquare(origin, size, N):       \n",
      "    o = Point(*origin)\n",
      "    s = size/2\n",
      "    square = []\n",
      "    getPoint = lambda n: [[o.x - s, o.y + s], [o.x - s, o.y - s], [o.x + s, o.y - s], [o.x + s, o.y + s]][n % 4]\n",
      "    for n in xrange(1, N+1):\n",
      "        square.append(getPoint(n))\n",
      "    return array(square)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We want to plot two periods at a rate of 50Hz"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "PERIODS = 2\n",
      "N = PERIODS * 4 # 4 points per period\n",
      "\n",
      "RATE = 50.0 #Hz\n",
      "T_PERIOD = 1/(RATE*4) #that's 200Hz per vector\n",
      "t = [n * T_PERIOD for n in xrange(N)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 63
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We create a square of size 2 with orign -2,0 and plot X."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "s = createSquare(origin=(-2,0), size=2, N=N)\n",
      "\n",
      "X = s[:,0]\n",
      "Y = s[:,1]\n",
      "\n",
      "xlabel(\"time (seconds)\")\n",
      "ylabel(\"X\")\n",
      "plot(t, X)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 76,
       "text": [
        "[<matplotlib.lines.Line2D at 0xdeded8c>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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UhMTE209aPB4P9u/fj9GjR8f1YAsWLMDVq1fh8/mQk5ODef99rt7Q0ICCggIAQGJiItau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\nVf4fjyZszNSGfXcAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 76
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Y is 90 degrees out of phase with X and DC offsets will vary according to the origin."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xlabel(\"time (seconds)\")\n",
      "ylabel(\"Y\")\n",
      "plot(t, Y)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 65,
       "text": [
        "[<matplotlib.lines.Line2D at 0xd6fffcc>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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RQrR91Pa0adO6fZ0dO3aIJUuWBG673e7AO5UvXrwohBBi8+bNYs2aNUIIIa5d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\nCIOEiIgiwiAhIqKIMEiIiCgi/w/IMTSXrwoAewAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Of course we can plot X against Y to see our square."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(8, 8))\n",
      "axis(ymax=4, ymin=-4, xmax=4, xmin=-4)\n",
      "ylabel(\"Y\")\n",
      "xlabel(\"X\")\n",
      "plot(X,Y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 74,
       "text": [
        "[<matplotlib.lines.Line2D at 0xde1ae4c>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can mess with the inputs to show they work. Note: a rectangle function with a rotation parameter would be a more sensible primitive. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "s = createSquare(origin=(0,1), size=4, N=N)\n",
      "\n",
      "figure(figsize=(8, 8))\n",
      "axis(ymax=4, ymin=-4, xmax=4, xmin=-4)\n",
      "ylabel(\"Y\")\n",
      "xlabel(\"X\")\n",
      "plot(s[:,0],s[:,1], )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 77,
       "text": [
        "[<matplotlib.lines.Line2D at 0xe01812c>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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     ],
     "prompt_number": 77
    }
   ],
   "metadata": {}
  }
 ]
}