{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Catmull-Rom splines ##"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Definition of this class of curves ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Catmull-Rom interpolation problem defined in [Catmull, E. and R. Rom, *A Class of Local Interpolationg Splines*, in Barnhill R.E. and R.F. Riesenfeld (eds.), Computer Aided Geometric Design, Academic Press, New York, 1974.] is formulated as follows:\n",
    "\n",
    "Given $n+1$  points, $P_0, P_1, \\ldots, P_n$, $n\\geq 3$, find a piecewise cubic curve, parameterized by\n",
    "$c:[1, n-1]\\to\\mathbb{R}^d$ (usually, d=2,3) such \n",
    "that $c(i)=P_{i}$, for $i\\in\\{1,2\\ldots, n-1\\}$, and the tangent vector at each interpolatory point, $P_i$, $i=\\overline{1, n-1}$, to be colinear with the vector $\\overrightarrow{P_{i-1}P_{i+1}}$:\n",
    "\n",
    "$$\\vec{\\dot{c}}(i)=s\\overrightarrow{P_{i-1}P_{i+1}},\n",
    "$$ where $s\\in(0,1]$. Usually one takes s=0.5.\n",
    "\n",
    "Hence given n+1 points, $P_0, P_1, \\ldots, P_n$, a CR curve interporlates only the points $P_1, P_2, \\ldots, P_{n-1}$.\n",
    "The first and the last point  influence  only  the direction of tangent at $P_1$, respectively, $P_{n-1}$.\n",
    "\n",
    "\n",
    "\n",
    "Since the distance between two consecutive knots, $t_i=i$, $t_{i+1}=i+1$ is constant, such a curve is called uniform parameterized Catmull-Rom curve.\n",
    "\n",
    "Being a cubic above each interval $[i, i+1]$,  an arc of CR curve on such an interval can be defined\n",
    "as a Bézier curve of control points ${\\bf b}_0, {\\bf b}_1, {\\bf b}_2, {\\bf b}_3$,\n",
    "with\n",
    "${\\bf b}_0=P_i, {\\bf b}_3=P_{i+1}$.\n",
    "\n",
    "But the  tangent at end  points, ${\\bf b}_0$ and ${\\bf b}_3$, of a Bézier curve, is\n",
    " $3\\overrightarrow{{\\bf b}_0{\\bf b}_1}$, respectively $3\\overrightarrow{{\\bf b}_2{\\bf b}_3}$.\n",
    "Thus we get:\n",
    "\n",
    "$$ {\\bf b}_1=P_i+s(P_{i+1}-P_{i-1})/3, \\:\\: {\\bf b}_2=P_{i+1}-s(P_{i+2}-P_{i})/3$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Below we illustrate the above stated properties of a CR curve, defined by 7 points.  Attached to the third arc, joining the points $P_3, P_4$,\n",
    "is  the Bézier control polygon defining that arc of curve. The tangent at $P_2$ is obviously parallel to \n",
    "$\\overrightarrow{P_1P_3}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAyAAAAJYCAYAAACadoJwAAAgAElEQVR4XuydC5xWVbn/nwEGhjuK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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(filename='Imag/Catmull-Rom-curve.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Catmull-Rom interpolating curves can be evaluated\n",
    "at a point using a recursive scheme similar to the [de Boor algorithm](http://nbviewer.jupyter.org/github/empet/geom_modeling/blob/master/FP-Bezier-Bspline.ipynb) for B-spline curves.\n",
    "\n",
    "Usually a cubic spline curve is $C^2$ at knots. Although the CR curves are only $C^1$ at each knot, \n",
    "they are sometimes called Catmull Rom spline curves, due to the similarities of the algorithms of\n",
    "evaluation, and other common properties.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Let us point out the drawback of the uniform parameterization, that led to defining CR splines with\n",
    "non-uniform knots.\n",
    "\n",
    "A $C^1$-parameterization,  $c:[a,b]\\to\\mathbb{R}^d$, of a curve can be interpreted as defining the motion of the point c(t), along the trace of $c$,  during the time from a to b.\n",
    "\n",
    "When the parameterization of a CR curve is uniform, the point $c(t)$ spends the same amount of time on each arc of ends $P_i, P_{i+1}$, $i=1,2, ...n-1$, irrespective of the distance between $P_i, P_{i+1}$.\n",
    "\n",
    "If the distance between two data points is large, the point c(t)\n",
    "moves with a high speed. If the next two interpolatory points, $P_{i+1}, P_{i+2}$, are closer, then the moving point will overshoot since it cannot abruptly change its  speed.\n",
    "\n",
    "Barry and Goldman [P. J. Barry, R. N. Goldman, *A recursive evaluation algorithm for a class of Catmull–Rom splines*, SIGGRAPH Computer Graphics, 22(4):199-204, 1988] extended the definition of uniform parameterized CR splines to curves whose parameterization incorporates the\n",
    "distance between any two adjacent interpolatory points. \n",
    "\n",
    "Namely, given the points $P_0, P_1, \\ldots, P_n$, one defines a knot sequence, $t_0, t_1, \\ldots, t_{n}$ as follows:\n",
    " \n",
    "$$\\begin{array}{lll}t_0&=&0\\\\\n",
    "            t_i&=&t_{i-1}+||\\overrightarrow{P_{i-1}P_i}||^\\alpha, \\quad \\alpha\\in[0,1]\\end{array}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " A $C^1$-piecewise cubic, that interpolates the given points, i.e. $c(t_i)=P_i$, $i=1,2, \\ldots, n-1$, is defined at any $u\\in[t_i, t_{i+1}]$ through a recursive scheme in which are involved only four points, $P_{i-1}, P_i, P_{i+1}, P_{i+2}$\n",
    " and the knots $t_{i-1}, t_i, t_{i+1}, t_{i+2}$:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$P_j^r=(1-\\omega^{r-1}_j)P^{r-1}_j+\\omega^{r-1}_jP^{r-1}_{j+1}, \\quad r=1,2,\\quad j=i-1, i, i+1, i+2,\n",
    "$$\n",
    "\n",
    "with $\\omega^r_j(u)=\\displaystyle\\frac{u-t_j}{t_{j+1+r}-t_j}$. The superscript $r$ points out the level of  recursion. $P_j^0=P_j$.\n",
    "\n",
    "\n",
    "The  last two points, $P^2_{i-1}$, $P^2_{i}$, are finally interpolated linearly, to get $c(u)$,  the point on the CR curve corresponding to the parameter $u\\in[t_i, t_{i+1}]$:\n",
    "\n",
    "$$c(u)=\\left(1-\\displaystyle\\frac{u-t_i}{t_{i+1}-t_i}\\right) P^2_{i-1}+\\displaystyle\\frac{u-t_i}{t_{i+1}-t_i} P^2_{i}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We note that in the first two steps, the points $P_j^r$, $r=1,2$, are computed via de Boor algorithm for B-splines, while in the last step, $c(u)$ is computed according to  the [Neville algorithm](https://en.wikipedia.org/wiki/Neville%27s_algorithm) for evaluating Lagrange polynomials."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The parameter $\\alpha$ in the definition of knots controls the geometry of the interpolating CR curve.\n",
    "For $\\alpha=0.5$ the corresponding CR curve is called centripetal Catmull-Rom curve, for $\\alpha=1$, chordal Catmull\n",
    "Rom curve, while for $\\alpha=0$ we get the initial uniform parameterized CR spline.\n",
    "\n",
    "For $\\alpha$ close to $0$ the corresponding CR curve can exhibit singular points (self intersections or cusps) within short curve segments(with small distance between  $P_i, P_{i+1}$).\n",
    "\n",
    "In [C Yuksel, S Schaefer, J Keyser,\n",
    "*Parameterization and Applications of Catmull-Rom Curves*,\n",
    "Computer Aided Design, 43, 7, 2011] it was deduced that the optimal parameter that corresponds  to CR splines with no singular points is $\\alpha=0.5$.\n",
    "Moreover a centripetal CR curve  follows  more tightly the interpolatory points than CR curves corresponding to $\\alpha$ close to 0 or to 1.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "That is why centripetal Catmull-Rom splines are now widely used in interactive generation of interpolating curves."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Python implementation of the Catmull-Rom spline generation ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of the above mixture of the de Boor and Neville algorithm we generate each segment of CR curve,\n",
    "as a Bezier curve.\n",
    "\n",
    "Over each interval $[t_i, t_{i+1}]$,  the CR curve is a cubic polynomial curve, hence it can be defined as\n",
    "a B&eacute;zier curve, parameterized over $[0,1]$. Theoretically, the standard polynomial parameterization\n",
    "is obtained applying (using a Computer Algebra System) the two steps of de Boor algorithm defined above, and a step of the Neville algo.\n",
    "Then this parameterization is converted to one in which the polynomial components are  expressed \n",
    "in Bernstein basis, to get the B&eacute;zier form of that polynomial segment of curve.\n",
    "\n",
    "The expression of the B&eacute;zier control points as combinations of four consecutive interpolatory \n",
    "points, $P_{0}, P_1, P_{2}, P_{3}$, involved in the definition of a CR segment, is given in the function  `ctrl_bezier(P, d)`.  `d` is a  list of values involved in knot definition, $d_j=||\\overrightarrow{P_{j}P_{j+1}}||^\\alpha$, $j=0,1,2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the function `knot_interval`, that computes the values \n",
    "$d_j=||\\overrightarrow{P_{j}P_{j+1}}||^\\alpha$, $j=\\overline{0, n-1}$. If we want  define a closed curve, then we extend the list of points $P_0, P_1, \\ldots, P_n$ with $P_0, P_1, P_2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def knot_interval(i_pts, alpha=0.5, closed=False):\n",
    "    if len(i_pts)<4:\n",
    "        raise ValueError('CR-curves need at least 4 interpolatory points')\n",
    "    #i_pts is the list of interpolatory points P[0], P[1], ... P[n]\n",
    "    if closed:\n",
    "        i_pts+=[i_pts[0], i_pts[1], i_pts[2]]\n",
    "    i_pts=np.array(i_pts)\n",
    "    dist=np.linalg.norm(i_pts[1:, :]-i_pts[:-1,:], axis=1)\n",
    "    return dist**alpha\n",
    " \n",
    "\n",
    "def ctrl_bezier(P, d):\n",
    "    #Associate to 4 consecutive interpolatory points and the corresponding three d-values, \n",
    "    #the Bezier control points\n",
    "    if len(P)!=len(d)+1!=4:\n",
    "        raise ValueError('The list of points and knot intervals have inappropriate len ')\n",
    "    P=np.array(P)    \n",
    "    bz=[0]*4\n",
    "    bz[0]=P[1]\n",
    "    bz[1]=(d[0]**2*P[2]-d[1]**2*P[0] +(2*d[0]**2+3*d[0]*d[1]+d[1]**2)*P[1])/(3*d[0]*(d[0]+d[1]))\n",
    "    bz[2]=(d[2]**2*P[1]-d[1]**2*P[3] +(2*d[2]**2+3*d[2]*d[1]+d[1]**2)*P[2])/(3*d[2]*(d[1]+d[2]))\n",
    "    bz[3]=P[2]\n",
    "    return bz\n",
    "\n",
    "def Bezier_curve(bz, nr=100):\n",
    "    #implements the de Casteljau algorithm to compute nr points on a Bezier curve\n",
    "    \n",
    "    t=np.linspace(0,1, nr)\n",
    "    N=len(bz) \n",
    "    points=[]# the list of points to be computed on the Bezier curve\n",
    "    for i in range(nr):#for each parameter t[i] evaluate a point on the Bezier curve \n",
    "                       #via De Casteljau algorithm\n",
    "        aa=np.copy(bz) \n",
    "        for r in range(1,N):\n",
    "            aa[:N-r,:]=(1-t[i])*aa[:N-r,:]+t[i]*aa[1:N-r+1,:]# convex combination\n",
    "        points.append(aa[0,:])                                  \n",
    "    return points \n",
    "\n",
    "def Catmull_Rom(i_pts, alpha=0.5,  closed=False):\n",
    "    #returns the list of points computed on the interpolating CR curve\n",
    "    #i_pts the list of interpolatory points P[0], P[1], ...P[n]\n",
    "    curve_pts=[]#the list of all points to be computed on the CR curve\n",
    "    d=knot_interval(i_pts, alpha=alpha, closed=closed)\n",
    "    for k in range(len(i_pts)-3):\n",
    "        cb=ctrl_bezier(i_pts[k:k+4], d[k:k+3])\n",
    "        curve_pts.extend(Bezier_curve(cb, nr=100))\n",
    "    \n",
    "    return np.array(curve_pts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we give a list of points and define the CR curve corresponding to $\\alpha=0,0.5,1$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f75070e8b50>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAigAAAFwCAYAAACSOICCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7509614dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=[[-0.72, -0.3], [0,0], [1., 0.8], [1.1, 0.5], [2.7, 1.2], [3.4, 0.27]]\n",
    "\n",
    "curve0=Catmull_Rom(P, alpha=0, closed=False)\n",
    "curve1=Catmull_Rom(P, alpha=0.5, closed=False)\n",
    "curve2=Catmull_Rom(P, alpha=1.0, closed=False)\n",
    "xp, yp=zip(*P)\n",
    "\n",
    "fig=plt.figure(figsize=(9,6))\n",
    "plt.plot(curve0[:,0], curve0[:,1], 'r', xp, yp, 'go' )\n",
    "plt.plot(curve1[:,0], curve1[:,1], 'g')\n",
    "plt.plot(curve2[:,0], curve2[:,1], 'b')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The green curve is the centripetal CR spline interpolating the central 4 from 6  points. It folows closely\n",
    "the given interpolatory points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to get more insights into  CR curves properties we give the possibility to generate them interactively.\n",
    "Choose the interpolatory points, by clicking the left mouse button at the desired position. When the   right button is pressed, the corresponding curve is generated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#enable interactivity in notebook:\n",
    "%matplotlib notebook "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def curve_plot(i_pts,  alpha=0.5, closed=False):\n",
    "    curve_pts=Catmull_Rom(i_pts, alpha, closed=closed)\n",
    "    # plot the interpolating curve\n",
    "    plt.plot(curve_pts[:,0], curve_pts[:,1], 'b') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class catrom(object): \n",
    "    \n",
    "    def __init__(self,  alpha=0.5, closed=False):\n",
    "        self.interp_pts=[]     # list of interpolating points\n",
    "        self.alpha=alpha\n",
    "        self.closed=closed# boolean value\n",
    "    def callback(self, event):  #select interpolating points with  left  mouse button click\n",
    "        if event.button==1 and event.inaxes:\n",
    "            x,y = event.xdata, event.ydata\n",
    "            self.interp_pts.append([x,y])  \n",
    "            plt.plot(x, y,  'bo') \n",
    "       \n",
    "        elif event.button==3:   #press right  button to plot the curve\n",
    "            curve_plot(self.interp_pts,  self.alpha, self.closed)\n",
    "            plt.draw() \n",
    "            \n",
    "        else: pass\n",
    "        \n",
    "    def caxis(self):#define axes for plot\n",
    "        fig = plt.figure(figsize=(8, 6))\n",
    "        ax = fig.add_subplot(111)\n",
    "       \n",
    "        ax.set_xlim(0,10)\n",
    "        ax.set_ylim(0,10)\n",
    "        ax.grid('on')   \n",
    "        ax.set_autoscale_on(False)\n",
    "        fig.canvas.mpl_connect('button_press_event', self.callback)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "curve=catrom()\n",
    "curve.caxis()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cv=catrom(closed=True)\n",
    "cv.caxis()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cv2=catrom(alpha=0)\n",
    "cv2.caxis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The advantage of defining a segment  of a CR curve as a Bezier curve,  not via de Boor plus Neville algorithm, is that we can compute the tangent direction at any point of the curve.\n",
    "\n",
    "Namely, if $r:[0,1]\\to\\mathbb{R}^d$ is the B&eacute;zier parameterization of a segment of CR curve, then\n",
    "the tangent vector at a point corresponding to the parameter $t\\in[0,1]$ is $\\vec{\\dot{r}}(t)=3({\\bf b}_1^{2}(t)-{\\bf b}_0^2(t))$, where ${\\bf b}^2_0, {\\bf b}^2_1$ are points computed in the second level of recursion of the de Casteljau schema ([for details see this notebook](http://nbviewer.jupyter.org/github/empet/geom_modeling/blob/master/FP-Bezier-Bspline.ipynb)):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def tangentBezier(bz,t):\n",
    "    #bz is the list of Bezier control points and t is value in [0,1]\n",
    "    if t<0 or t>1:\n",
    "        raise ValueError('The parameter t must bi in [0,1]')\n",
    "    a=np.copy(bz) \n",
    "    N=a.shape[0] \n",
    "    for r in range(1,N-1): \n",
    "        a[:N-r,:]=(1-t)*a[:N-r,:]+t*a[1:N-r+1,:]\n",
    "            \n",
    "    return (len(bz)-1)*(a[1,:]-a[0,:])     \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above functions are independent on the dimension of the space of points. They work well on points in  any space $\\mathbb{R}^d$, $d\\geq 2$.\n",
    "\n",
    "Here is an illustration of a Plotly plot of a (2,3)-[torus knot](https://en.wikipedia.org/wiki/Torus_knot) resulted from a centripetal Catmull-Rom interpolation of a set of points on torus:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe src=https://plot.ly/~empet/13914/ width=900 height=600></iframe>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import HTML\n",
    "HTML('<iframe src=https://plot.ly/~empet/13914/ width=900 height=600></iframe>')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "    /*body {\n",
       "        background-color: #F5F5F5;\n",
       "    }*/\n",
       "    div.cell{\n",
       "        width: 900px;\n",
       "        margin-left: 13% !important;\n",
       "        margin-right: auto;\n",
       "    }\n",
       "    #notebook li { /* More space between bullet points */\n",
       "    margin-top:0.8em;\n",
       "    }\n",
       "\n",
       "    h1 {\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "    }\n",
       "    .text_cell_render h1 {\n",
       "        font-weight: 200;\n",
       "        font-size: 40pt;\n",
       "        line-height: 100%;\n",
       "        color: rgb(8, 66, 133);\n",
       "        margin-bottom: 0em;\n",
       "        margin-top: 0em;\n",
       "        display: block;\n",
       "    }\n",
       "    h2 {\n",
       "        font-family: 'Fenix', serif;\n",
       "        text-indent:1em;\n",
       "        text-align:center;\n",
       "    }\n",
       "    .text_cell_render h2 {\n",
       "        font-weight: 200;\n",
       "        font-size: 28pt;\n",
       "        line-height: 100%;\n",
       "        color: rgb(8, 66, 133);\n",
       "        margin-bottom: 1.5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\n",
       "    h3 {\n",
       "        font-family: 'Fenix', serif;\n",
       "        %margin-top:12px;\n",
       "        %margin-bottom: 3px;\n",
       "    }\n",
       "    .text_cell_render h3 {\n",
       "        font-weight: 300;\n",
       "        font-size: 18pt;\n",
       "        line-height: 100%;\n",
       "        color: rgb(8, 66, 133);\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 2em;\n",
       "        display: block;\n",
       "    }\n",
       "    h4 {\n",
       "        font-family: 'Fenix', serif;\n",
       "    }\n",
       "    .text_cell_render h4 {\n",
       "        font-weight: 300;\n",
       "        font-size: 16pt;\n",
       "        color: rgb(8, 66, 133);\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\n",
       "    h5 {\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "    }\n",
       "    .text_cell_render h5 {\n",
       "        font-weight: 300;\n",
       "        font-style: normal;\n",
       "        font-size: 16pt;\n",
       "        margin-bottom: 0em;\n",
       "        margin-top: 1.5em;\n",
       "        display: block;\n",
       "        }\n",
       "    div.text_cell_render{\n",
       "        font-family: 'Alegreya Sans',Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
       "        line-height: 145%;\n",
       "        font-size: 130%;\n",
       "        width:900px;\n",
       "        margin-left:auto;\n",
       "        margin-right:auto;\n",
       "        %text-align:justify;\n",
       "        %text-justify:inter-word;\n",
       "    }\n",
       "    \n",
       "    \n",
       "    code{\n",
       "      font-size: 78%;\n",
       "    }\n",
       "    .rendered_html code{\n",
       "        background-color: transparent;\n",
       "        white-space: inherit;   \n",
       "    }\n",
       "    .prompt{\n",
       "        display: None;\n",
       "     }\n",
       "    .rendered_html code{\n",
       "    background-color: transparent;\n",
       "    }\n",
       "\n",
       "    blockquote{\n",
       "      display:block;\n",
       "      background: #f3f3f3;\n",
       "      font-family: \"Open sans\",verdana,arial,sans-serif;\n",
       "      width:610px;\n",
       "      padding: 15px 15px 15px 15px;\n",
       "      text-align:justify;\n",
       "      text-justify:inter-word;\n",
       "      }\n",
       "      blockquote p {\n",
       "        margin-bottom: 0;\n",
       "        line-height: 125%;\n",
       "        font-size: 100%;\n",
       "      }\n",
       "   /* element.style {\n",
       "    } */\n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ [\"$\",\"$\"], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ [\"$$\",\"$$\"], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: \"center\", // Change this to \"center\" to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {\".MathJax_Display\": {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import HTML\n",
    "def  css_styling():\n",
    "    styles = open(\"./custom.css\", \"r\").read()\n",
    "    return HTML(styles)\n",
    "css_styling()"
   ]
  }
 ],
 "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": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}