{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cinématique & espace de travail d'un manipulateur 2 axes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "source : https://sajidnisar.github.io/posts/python_kinematics_dh"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Objectif\n",
    "\n",
    "Ce document fournit une base pour dériver et analyser la cinématique de manipulateurs robotiques séries en utilisant Python. L'objectif est de fournir un programme d’apprentissage, de calcul et de compréhension de la cinématique de robots série de manière agréable et interactive.\n",
    "\n",
    "Nous utilisons l’environnement Jupyter Notebook \\ Matplotlib qui offre un moyen flexible d’interagir avec le code et d’afficher des tracés en ligne. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prérequis\n",
    "\n",
    "**Côté technique**: la connaissance de la cinématique robot est recommandée. Pour une utilisation avancée, par exemple pour étendre cet exemple à des conceptions plus complexes, il est nécessaire de connaître la notation DH (Denavit Hartenberg classique). \n",
    "\n",
    "**Côté programmation** : des compétences de niveau débutant à intermédiaire avec Python et Jupyter notebook sont souhaitables. Les bibliothèques python utilisées sont:\n",
    "\n",
    "     Sympy (pour le calcul symbolique)\n",
    "     Numpy (pour la calcul numérique)\n",
    "     Matplotlib (pour les tracés)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Configuration de l'environnement\n",
    "\n",
    "Nous importons ici la bibliothèque Sympy qui nous permettra de développer et de manipuler des expressions symboliques."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans SymPy, nous initialisons l'impression afin que toutes les expressions mathématiques puissent être rendues en notation mathématique standard."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.physics.vector import init_vprinting\n",
    "init_vprinting(use_latex='mathjax', pretty_print=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Le manipulateur plan 2 axes "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 3,
     "metadata": {
      "image/png": {
       "width": 300
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image('fig/2rp_new.png', width=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pourquoi le manipulateur 2RP ?\n",
    "\n",
    "Presque tous les manuels de robotique commencent à enseigner la cinématique des robots à l'aide d'un exemple simple et fondamental : le *manipulateur plan à 2 axes* (2RP, R pour les liaisons *revolute* (-> rotoïde) et P le plan). Par souci de simplicité et comme point de départ, nous commençons également par l’exemple de ce manipulateur, qui devrait être facile à suivre et à comprendre.\n",
    "\n",
    "Maintenant, nous déclarons les symboles (longueur des liens, variables articulaire etc.) qui seront utilisés par la suite."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.physics.mechanics import dynamicsymbols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left ( \\theta_{1}, \\quad \\theta_{2}, \\quad l_{1}, \\quad l_{2}, \\quad \\theta, \\quad \\alpha, \\quad a, \\quad d\\right )$$"
      ],
      "text/plain": [
       "(theta1, theta2, l1, l2, theta, alpha, a, d)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta1, theta2, l1, l2, theta, alpha, a, d = dynamicsymbols('theta1 theta2 l1 l2 theta alpha a d')\n",
    "theta1, theta2, l1, l2, theta, alpha, a, d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cinématique utilisant la méthode DH\n",
    "\n",
    "Nous définissons les repères (*frame*) de notre manipulateur conformément à la convention classique DH. La méthode DH offre un moyen pratique d’exprimer la position et l’orienation d’un corps rigide sous forme de matrice en utilisant les longueurs de liaison, les angles de liaison, les angles de torsion et les décalages de liaison appropriés.\n",
    "\n",
    "### Table DH\n",
    "\n",
    "La table DH pour la manipulateur plan 2 axes décrit par la figure ci-dessous\n",
    "\n",
    "<img src=\"fig/2rp_DH_table.png\" alt=\"2rp_DH_table.png\" style=\"width: 200px\" align=\"left\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$i$: numéro corps , $\\alpha_i$: angle de torsion, $a_i$: longeur de la liaison $i$, $d_i$: offset liaison et $\\theta_i$: angle de la liaison."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transformation Homogène"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La matrice de transformation homogène standard est représentée par : <br /> \n",
    "(cf https://en.wikipedia.org/wiki/Denavit-Hartenberg_parameters)\n",
    "<img src=\"fig/DH_matrix.png\" alt=\"DH_matrix.png\" style=\"width: 650px\" align=\"middle\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "soit, avec les notations adoptées :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\operatorname{cos}\\left(\\theta\\right) & - \\operatorname{sin}\\left(\\theta\\right) \\operatorname{cos}\\left(\\alpha\\right) & \\operatorname{sin}\\left(\\alpha\\right) \\operatorname{sin}\\left(\\theta\\right)\\\\\\operatorname{sin}\\left(\\theta\\right) & \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\theta\\right) & - \\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\theta\\right)\\\\0 & \\operatorname{sin}\\left(\\alpha\\right) & \\operatorname{cos}\\left(\\alpha\\right)\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[cos(theta), -sin(theta)*cos(alpha),  sin(alpha)*sin(theta)],\n",
       "[sin(theta),  cos(alpha)*cos(theta), -sin(alpha)*cos(theta)],\n",
       "[         0,             sin(alpha),             cos(alpha)]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R = sp.Matrix([[sp.cos(theta), -sp.sin(theta)*sp.cos(alpha), sp.sin(theta)*sp.sin(alpha)],\n",
    "                 [sp.sin(theta), sp.cos(theta)*sp.cos(alpha), -sp.cos(theta)*sp.sin(alpha)],\n",
    "                 [0, sp.sin(alpha), sp.cos(alpha)]])\n",
    "R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}a \\operatorname{cos}\\left(\\theta\\right)\\\\a \\operatorname{sin}\\left(\\theta\\right)\\\\d\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[a*cos(theta)],\n",
       "[a*sin(theta)],\n",
       "[           d]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = sp.Matrix([a*sp.cos(theta),a*sp.sin(theta),d])\n",
    "T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}0 & 0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "Matrix([[0, 0, 0, 1]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "last_row = sp.Matrix([[0, 0, 0, 1]])\n",
    "last_row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\operatorname{cos}\\left(\\theta\\right) & - \\operatorname{sin}\\left(\\theta\\right) \\operatorname{cos}\\left(\\alpha\\right) & \\operatorname{sin}\\left(\\alpha\\right) \\operatorname{sin}\\left(\\theta\\right) & a \\operatorname{cos}\\left(\\theta\\right)\\\\\\operatorname{sin}\\left(\\theta\\right) & \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\theta\\right) & - \\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\theta\\right) & a \\operatorname{sin}\\left(\\theta\\right)\\\\0 & \\operatorname{sin}\\left(\\alpha\\right) & \\operatorname{cos}\\left(\\alpha\\right) & d\\\\0 & 0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[cos(theta), -sin(theta)*cos(alpha),  sin(alpha)*sin(theta), a*cos(theta)],\n",
       "[sin(theta),  cos(alpha)*cos(theta), -sin(alpha)*cos(theta), a*sin(theta)],\n",
       "[         0,             sin(alpha),             cos(alpha),            d],\n",
       "[         0,                      0,                      0,            1]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = sp.Matrix.vstack(sp.Matrix.hstack(R, T), last_row)\n",
    "M"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transformation du repère $R_0$ au repère $R_1$\n",
    "\n",
    "En déduire $M_{01}$, la transformation du repère $R_0$ au repère $R_1$ : <br>\n",
    "*indication* : substituer respectivement *alpha*, *a*, *theta* et *d* dans M par *0*, *l1*, *theta1* et *0*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\operatorname{cos}\\left(\\theta_{1}\\right) & - \\operatorname{sin}\\left(\\theta_{1}\\right) & 0 & l_{1} \\operatorname{cos}\\left(\\theta_{1}\\right)\\\\\\operatorname{sin}\\left(\\theta_{1}\\right) & \\operatorname{cos}\\left(\\theta_{1}\\right) & 0 & l_{1} \\operatorname{sin}\\left(\\theta_{1}\\right)\\\\0 & 0 & 1 & 0\\\\0 & 0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[cos(theta1), -sin(theta1), 0, l1*cos(theta1)],\n",
       "[sin(theta1),  cos(theta1), 0, l1*sin(theta1)],\n",
       "[          0,            0, 1,              0],\n",
       "[          0,            0, 0,              1]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M01 = M.subs({alpha:0, a:l1, theta:theta1, d:0})\n",
    "M01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transformation du repère $R_1$ au repère $R_2$\n",
    "\n",
    "En déduire $M_{12}$, la matrice de transformation homogène du repère $R_1$ au repère $R_2$ :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\operatorname{cos}\\left(\\theta_{2}\\right) & - \\operatorname{sin}\\left(\\theta_{2}\\right) & 0 & l_{2} \\operatorname{cos}\\left(\\theta_{2}\\right)\\\\\\operatorname{sin}\\left(\\theta_{2}\\right) & \\operatorname{cos}\\left(\\theta_{2}\\right) & 0 & l_{2} \\operatorname{sin}\\left(\\theta_{2}\\right)\\\\0 & 0 & 1 & 0\\\\0 & 0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[cos(theta2), -sin(theta2), 0, l2*cos(theta2)],\n",
       "[sin(theta2),  cos(theta2), 0, l2*sin(theta2)],\n",
       "[          0,            0, 1,              0],\n",
       "[          0,            0, 0,              1]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M12 = M.subs({alpha:0, a:l2, theta:theta2, d:0})\n",
    "M12"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrice de transformation homogène  du repère $R_0$ au repère $R_2$\n",
    "\n",
    "En déduire la matrice $M_{02}$ de transformation homogène du repère $R_0$ au repère $R_2$ :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}- \\operatorname{sin}\\left(\\theta_{1}\\right) \\operatorname{sin}\\left(\\theta_{2}\\right) + \\operatorname{cos}\\left(\\theta_{1}\\right) \\operatorname{cos}\\left(\\theta_{2}\\right) & - \\operatorname{sin}\\left(\\theta_{1}\\right) \\operatorname{cos}\\left(\\theta_{2}\\right) - \\operatorname{sin}\\left(\\theta_{2}\\right) \\operatorname{cos}\\left(\\theta_{1}\\right) & 0 & l_{1} \\operatorname{cos}\\left(\\theta_{1}\\right) - l_{2} \\operatorname{sin}\\left(\\theta_{1}\\right) \\operatorname{sin}\\left(\\theta_{2}\\right) + l_{2} \\operatorname{cos}\\left(\\theta_{1}\\right) \\operatorname{cos}\\left(\\theta_{2}\\right)\\\\\\operatorname{sin}\\left(\\theta_{1}\\right) \\operatorname{cos}\\left(\\theta_{2}\\right) + \\operatorname{sin}\\left(\\theta_{2}\\right) \\operatorname{cos}\\left(\\theta_{1}\\right) & - \\operatorname{sin}\\left(\\theta_{1}\\right) \\operatorname{sin}\\left(\\theta_{2}\\right) + \\operatorname{cos}\\left(\\theta_{1}\\right) \\operatorname{cos}\\left(\\theta_{2}\\right) & 0 & l_{1} \\operatorname{sin}\\left(\\theta_{1}\\right) + l_{2} \\operatorname{sin}\\left(\\theta_{1}\\right) \\operatorname{cos}\\left(\\theta_{2}\\right) + l_{2} \\operatorname{sin}\\left(\\theta_{2}\\right) \\operatorname{cos}\\left(\\theta_{1}\\right)\\\\0 & 0 & 1 & 0\\\\0 & 0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[-sin(theta1)*sin(theta2) + cos(theta1)*cos(theta2), -sin(theta1)*cos(theta2) - sin(theta2)*cos(theta1), 0, l1*cos(theta1) - l2*sin(theta1)*sin(theta2) + l2*cos(theta1)*cos(theta2)],\n",
       "[ sin(theta1)*cos(theta2) + sin(theta2)*cos(theta1), -sin(theta1)*sin(theta2) + cos(theta1)*cos(theta2), 0, l1*sin(theta1) + l2*sin(theta1)*cos(theta2) + l2*sin(theta2)*cos(theta1)],\n",
       "[                                                 0,                                                  0, 1,                                                                        0],\n",
       "[                                                 0,                                                  0, 0,                                                                        1]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M02 = M01*M12\n",
    "M02"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simplifier la matrice $M_{02}$ avec `sp.simplify` :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\operatorname{cos}\\left(\\theta_{1} + \\theta_{2}\\right) & - \\operatorname{sin}\\left(\\theta_{1} + \\theta_{2}\\right) & 0 & l_{1} \\operatorname{cos}\\left(\\theta_{1}\\right) + l_{2} \\operatorname{cos}\\left(\\theta_{1} + \\theta_{2}\\right)\\\\\\operatorname{sin}\\left(\\theta_{1} + \\theta_{2}\\right) & \\operatorname{cos}\\left(\\theta_{1} + \\theta_{2}\\right) & 0 & l_{1} \\operatorname{sin}\\left(\\theta_{1}\\right) + l_{2} \\operatorname{sin}\\left(\\theta_{1} + \\theta_{2}\\right)\\\\0 & 0 & 1 & 0\\\\0 & 0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[cos(theta1 + theta2), -sin(theta1 + theta2), 0, l1*cos(theta1) + l2*cos(theta1 + theta2)],\n",
       "[sin(theta1 + theta2),  cos(theta1 + theta2), 0, l1*sin(theta1) + l2*sin(theta1 + theta2)],\n",
       "[                   0,                     0, 1,                                        0],\n",
       "[                   0,                     0, 0,                                        1]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M02 = sp.simplify(M02)\n",
    "M02"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Évaluation de la position de l'outil"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Déduire la position du poignet dans la direction x :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$l_{1} \\operatorname{cos}\\left(\\theta_{1}\\right) + l_{2} \\operatorname{cos}\\left(\\theta_{1} + \\theta_{2}\\right)$$"
      ],
      "text/plain": [
       "l1*cos(theta1) + l2*cos(theta1 + theta2)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "px = M02[0,3]\n",
    "px"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Déduire la position du poignet dans la direction y :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$l_{1} \\operatorname{sin}\\left(\\theta_{1}\\right) + l_{2} \\operatorname{sin}\\left(\\theta_{1} + \\theta_{2}\\right)$$"
      ],
      "text/plain": [
       "l1*sin(theta1) + l2*sin(theta1 + theta2)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "py = M02[1,3]\n",
    "py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour évaluer numériquement la position de la pointe, utiliser la fonction `lambdify` de Sympy avec les arguments *l1*, *l2*, *theta1* et *thetat2* :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "fx = sp.lambdify((l1, l2, theta1, theta2), px)\n",
    "fy = sp.lambdify((l1, l2, theta1, theta2), py)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Espace de travail du manipulateur"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En prenant $l_1 = 50\\ mm$ et $l_2 = 20\\ mm$ tracer les courbes des fonctions `fx` et `fy` pour *theta1* et *theta2* variant de 0 à $2\\,\\pi$ :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f69ac742be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "d2r = np.deg2rad\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "theta11 = np.linspace(d2r(0),d2r(360),100)\n",
    "theta22 = np.linspace(d2r(0), d2r(360),100)\n",
    "theta1, theta2 = np.meshgrid(theta11, theta22)\n",
    "\n",
    "l1, l2 = 50, 20\n",
    "X = np.array(fx(l1, l2, theta1, theta2))\n",
    "Y = np.array(fy(l1, l2, theta1, theta2))\n",
    "\n",
    "ax.plot(X, Y, 'b')\n",
    "plt.grid()\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\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",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\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",
       "        fig.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 backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\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 * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\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'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\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 * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\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",
       "    var width = fig.canvas.width/mpl.ratio\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 + '\" width=\"' + width + '\">');\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 width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\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": {
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\" width=\"670\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This import registers the 3D projection, but is otherwise unused.\n",
    "from mpl_toolkits.mplot3d import Axes3D  # noqa: F401 unused import\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "import numpy as np\n",
    "d2r = np.deg2rad\n",
    "\n",
    "%matplotlib notebook\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "theta11 = np.linspace(d2r(0),d2r(360),100)\n",
    "theta22 = np.linspace(d2r(0), d2r(360),100)\n",
    "theta1, theta2 = np.meshgrid(theta11, theta22)\n",
    "\n",
    "l1, l2 = 50, 20\n",
    "\n",
    "X = np.array(fx(l1, l2, theta1, theta2))\n",
    "Y = np.array(fy(l1, l2, theta1, theta2))\n",
    "Z = Y*0\n",
    "\n",
    "ax.plot_surface(X, Y, Z, shade=False,cmap=cm.coolwarm )\n",
    "\n",
    "ax.set_xlabel('X')\n",
    "ax.set_ylabel('Y')\n",
    "ax.set_zlabel('Z')\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}