simpleMotion.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rapidly-exploring Random Trees (RRT)\n",
    "### Input: start: Tuple, goal: Tuple, obstacles: List[List[Tuple]], space_size: Tuple\n",
    "// rrt(start, goal, obstacles, space_size), nearest_point(point, tree), colliding(p1, p2, obstacle)\n",
    "// cost from all points to all points is constant (penalty on number of points traversed, not on the distance between points as d at each step is constant.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import Tuple, List, Dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def distance(p1, p2):\n",
    "    \"\"\"distance between 2 points\"\"\"\n",
    "    return (p1[0]-p2[0])**2 + (p1[1]-p2[1])**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nearest_point(point, tree):\n",
    "    \"\"\"point in the tree which is nearest to the given point\"\"\"\n",
    "    dist = [distance(point, x) for x in tree]\n",
    "    res = tree[numpy.argmin(dist)]\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 1)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nearest_point((0,0), [(1,1), (1,2), (2,2)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def onSegment(q, l1):\n",
    "    if ( (q[0] <= max(l1[0][0], l1[1][0])) and (q[0] >= min(l1[0][0], l1[1][0])) and\n",
    "           (q[1] <= max(l1[0][1], l1[1][1])) and (q[1]>= min(l1[0][1], l1[1][1]))):\n",
    "        return True\n",
    "    return False\n",
    " \n",
    "def orientation(p, q, r):\n",
    "    \"\"\"\n",
    "    to find the orientation of an ordered triplet (p,q,r)\n",
    "    Returns:\n",
    "    ========\n",
    "    0 : Colinear points\n",
    "    1 : Clockwise points\n",
    "    2 : Counterclockwise\n",
    "    \"\"\"\n",
    "    val = (float(q[1] - p[1]) * (r[0] - q[0])) - (float(q[0] - p[0]) * (r[1] - q[1]))\n",
    "    if (val > 0):\n",
    "        # Clockwise orientation\n",
    "        return 1\n",
    "    elif (val < 0):\n",
    "        # Counterclockwise orientation\n",
    "        return 2\n",
    "    else:\n",
    "        # Colinear orientation\n",
    "        return 0\n",
    " \n",
    " # The main function that returns true if\n",
    "# the line segment 'p1q1' and 'p2q2' intersect.\n",
    "def doIntersect(l1,l2):\n",
    "     \n",
    "    # Find the 4 orientations required for\n",
    "    # the general and special cases\n",
    "    p1, q1 = l1\n",
    "    p2, q2 = l2\n",
    "    o1 = orientation(p1, q1, p2)\n",
    "    o2 = orientation(p1, q1, q2)\n",
    "    o3 = orientation(p2, q2, p1)\n",
    "    o4 = orientation(p2, q2, q1)\n",
    " \n",
    "    # General case\n",
    "    if ((o1 != o2) and (o3 != o4)):\n",
    "        return True\n",
    " \n",
    "    # Special Cases\n",
    " \n",
    "    # p1 , q1 and p2 are colinear and p2 lies on segment p1q1\n",
    "    if ((o1 == 0) and onSegment(p2, [p1, q1])):\n",
    "        return True\n",
    " \n",
    "    # p1 , q1 and q2 are colinear and q2 lies on segment p1q1\n",
    "    if ((o2 == 0) and onSegment(q2, [p1, q1])):\n",
    "        return True\n",
    " \n",
    "    # p2 , q2 and p1 are colinear and p1 lies on segment p2q2\n",
    "    if ((o3 == 0) and onSegment(p1, [p2, q2])):\n",
    "        return True\n",
    " \n",
    "    # p2 , q2 and q1 are colinear and q1 lies on segment p2q2\n",
    "    if ((o4 == 0) and onSegment(q1, [p2, q2])):\n",
    "        return True\n",
    " \n",
    "    # If none of the cases\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def colliding(p1, p2, obstacle):\n",
    "    \"\"\"line segment p1p2 intersects the given obstacle or not\"\"\"\n",
    "    # identify boundary of the obstacle as the combination of line segments between the closest vertices.\n",
    "    lines = []\n",
    "    for point in obstacle:\n",
    "        temp = obstacle.copy()\n",
    "        temp.remove(point)\n",
    "        np1 = nearest_point(point, temp)\n",
    "        temp.remove(np1)\n",
    "        np2 = nearest_point(point, temp)\n",
    "        if (point, np1) not in lines and (np1, point) not in lines:\n",
    "            lines.append((point, np1))\n",
    "        if (point, np2) not in lines and (np2, point) not in lines:\n",
    "            lines.append((point, np2))\n",
    "    # given line segment intersects with any of the line segments in obstacle boundary\n",
    "    resp = [doIntersect((p1, p2), x) for x in lines]\n",
    "    return lines, resp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([((0, 0), (0, 2)), ((0, 0), (2, 0)), ((0, 2), (2, 2)), ((2, 2), (2, 0))],\n",
       " [True, True, False, False])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obs = [(0,0),(0,2), (2,2), (2,0)]\n",
    "colliding((0,0), (1,1), obs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fixed_increment(p1, p2, d, space_size):\n",
    "    \"\"\"increment line p1p2 by a fixed distance of d such that result lies within space_size\"\"\"\n",
    "    # vertical line\n",
    "    if p1[0] == p2[0]:\n",
    "        return (p2[0], min(p2[1]+d, space_size[1]))\n",
    "    # horizontal line\n",
    "    if p1[1] == p2[1]:\n",
    "        return (min(p2[0]+d, space_size[0]), p2[1])\n",
    "    # any other orientation\n",
    "    m = (p2[1]-p1[1])/(p2[0]-p1[0])\n",
    "    c = p2[1] - m*p2[0]\n",
    "    a1 = (1+m*m)\n",
    "    b1 = 2*(m*c - m*p2[1] - p2[0])\n",
    "    c1 = p2[0]**2 + p2[1]**2 +c**2 - d**2 -2*c*p2[1]\n",
    "    under = b1**2 - 4*a1*c1\n",
    "    # in case of complex roots for x, considering x=0\n",
    "    if under < 0:\n",
    "        return (p1[0], min(p2[1]+d, space_size[1]))\n",
    "    x = (-b1 + numpy.sqrt(under))/(2*a1)\n",
    "    y = m*x + c\n",
    "    x = min(max(0,x), space_size[0])\n",
    "    y = min(max(0,y), space_size[1])\n",
    "    return (x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.1414213562373097, 2.1414213562373097)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fixed_increment((0,0), (2,2), 0.2, (5,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def goal_isvalid(goal, obstacles):\n",
    "    for obstacle in obstacles:\n",
    "        minx = min(obstacle, key=lambda x: x[0])[0]\n",
    "        miny = min(obstacle, key=lambda x: x[1])[1]\n",
    "        maxx = max(obstacle, key=lambda x: x[0])[0]\n",
    "        maxy = max(obstacle, key=lambda x: x[1])[1]\n",
    "        if goal[0]>= minx and goal[0]<=maxx\\\n",
    "        and goal[1]>=miny and goal[1]<=maxy:\n",
    "            return False\n",
    "    return True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "goal_isvalid((1,1), [[(0,0), (0,2), (2,2), (2,0)]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as ntx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rrt(start, goal, obstacles, space_size, d=0.1):\n",
    "    tree = [start]\n",
    "    connections = []\n",
    "    gph = ntx.DiGraph()\n",
    "    if not goal_isvalid(goal, obstacles):\n",
    "        return \"Path not possible\"\n",
    "    goal_reachable = not any([any(colliding(start, goal, obstacle)[1]) for obstacle in obstacles])\n",
    "    #print(goal_reachable)\n",
    "    while not goal_reachable:\n",
    "        new_point = tuple(numpy.random.uniform(space_size))\n",
    "        nearest = nearest_point(new_point, tree)\n",
    "        new_point = fixed_increment(new_point, nearest, d, space_size=space_size)\n",
    "        if not any([any(colliding(nearest, new_point, obstacle)[1]) for obstacle in obstacles]):\n",
    "            tree.append(new_point)\n",
    "            connections.append((nearest, new_point))\n",
    "            gph.add_edge(nearest, new_point)\n",
    "            goal_reachable = not any([any(colliding(new_point, goal, obstacle)[1]) for obstacle in obstacles])\n",
    "    tree.append(goal)\n",
    "    connections.append((new_point, goal))\n",
    "    gph.add_edge(new_point, goal)\n",
    "    return tree, connections, gph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as anim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "start = (0,0)\n",
    "goal = (5,5)\n",
    "space_size = (6,6)\n",
    "obstacles = [[(0,1), (1,1), (1,2), (0,2)], [(3,2), (3,3), (4,3)]]\n",
    "\n",
    "tree, collections, gph = rrt(start, goal=goal, obstacles=obstacles, space_size=space_size, d=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "shortest = ntx.shortest_path(gph, source=start, target=goal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 0),\n",
       " (0.1960049048186211, 0.22711688023359972),\n",
       " (0.465203980133449, 0.3595248023894948),\n",
       " (0.7341540428419714, 0.4924377956184557),\n",
       " (0.986320802832978, 0.6549552566976822),\n",
       " (1.1115340673346608, 0.9275752089991067),\n",
       " (1.3727335441428947, 1.0751381898415406),\n",
       " (1.4896411190786902, 1.3514217740854),\n",
       " (1.7416313632318021, 1.514212796109511),\n",
       " (1.9275049706336238, 1.7496931606230623),\n",
       " (2.1068000172627865, 1.990220261495802),\n",
       " (2.3932702427461465, 1.9011427115097848),\n",
       " (2.200522016260398, 1.705235723487326),\n",
       " (2.6906950764468536, 1.8619193983133182),\n",
       " (2.7860981148262836, 2.146345593077392),\n",
       " (2.9712017522920076, 2.3824316862657815),\n",
       " (2.185290105390636, 1.700670082656865),\n",
       " (2.1875167046936705, 1.7012828697131095),\n",
       " (2.6503676884158023, 2.055741881721459),\n",
       " (2.1120450196229466, 1.6902661150844693),\n",
       " (2.7557181551604772, 1.7748481666677334),\n",
       " (2.835531533886689, 1.819703007104521),\n",
       " (3.1120306059805745, 1.7033060005656075),\n",
       " (2.2762229541479906, 1.742640237145698),\n",
       " (2.2225402568696055, 1.7134456294650642),\n",
       " (3.4090988444080814, 1.745144520108966),\n",
       " (5, 5)]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def obstacle_boundaries(obstacle):\n",
    "    lines = []\n",
    "    for point in obstacle:\n",
    "        temp = obstacle.copy()\n",
    "        temp.remove(point)\n",
    "        np1 = nearest_point(point, temp)\n",
    "        temp.remove(np1)\n",
    "        np2 = nearest_point(point, temp)\n",
    "        if (point, np1) not in lines and (np1, point) not in lines:\n",
    "            lines.append((point, np1))\n",
    "        if (point, np2) not in lines and (np2, point) not in lines:\n",
    "            lines.append((point, np2))\n",
    "    return lines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
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       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\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 toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\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",
       "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",
       "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], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.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,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\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",
       "        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.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\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",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\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",
       "                img.type = 'image/png';\n",
       "            }\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",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\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(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\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(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\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",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\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",
       "        }\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",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\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",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, 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",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\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\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "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.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\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",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(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 = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\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;\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",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\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.innerHTML =\n",
       "        '<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 / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<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 () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('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",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\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",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\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(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img 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width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = plt.figure()\n",
    "ax = f.add_subplot(autoscale_on=False, xlim=(0, space_size[0]), ylim=(0, space_size[1]))\n",
    "ax.grid()\n",
    "for obs in obstacles:\n",
    "    bounds = obstacle_boundaries(obs)\n",
    "    for b in bounds:\n",
    "        ax.plot([b[0][0], b[1][0]], [b[0][1], b[1][1]], color='red')\n",
    "ax.scatter(start[0], start[1], s=20, color='orange', marker='o')\n",
    "ax.scatter(goal[0], goal[1], s=20, color='green')\n",
    "path, = ax.plot([], [], '-', lw=2, color='purple', marker='o', markersize=2, markerfacecolor='orange')\n",
    "history, = ax.plot([], [], '-', lw=1, color='purple')\n",
    "txt = ax.text(goal[0]-0.5, goal[1]-0.5, 'G')\n",
    "time_text = ax.text(0.05, 0.9, '', transform=ax.transAxes)\n",
    "final_path, = ax.plot([], [], '-', lw=2, color='cyan')\n",
    "def animate(i):\n",
    "    path.set_data([collections[i][0][0], collections[i][1][0]],\n",
    "    [collections[i][0][1], collections[i][1][1]])\n",
    "    xs = []\n",
    "    ys = []\n",
    "    for x in collections[:i+1]:\n",
    "        xs.extend([x[0][0],x[1][0]])\n",
    "        ys.extend([x[0][1], x[1][1]])\n",
    "    history.set_data(xs, ys)\n",
    "    time_text.set_text(i)\n",
    "    \n",
    "    final_path.set_data([x[0] for x in shortest[:min(i+1, len(shortest))]], [x[1] for x in shortest[:min(i+1, len(shortest))]])\n",
    "    return path, history, time_text, final_path\n",
    "ani = anim.FuncAnimation(f, animate, len(tree)-1, interval=1000, repeat=False, blit=True) \n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "Writer = anim.writers['ffmpeg']\n",
    "writer = Writer(fps=4, metadata=dict(artist='Me'), bitrate=1800)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "ani.save('rtt_motion.mp4', writer=writer)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "*----*-----*------*------*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dijkstra's Algorithm for shortest path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "input: graph:->{Tuple:List(Tuple(Tuple(int, int), int)...)}, start:->List[Tuple(int, int)...], goal->List[Tuple(int, int)...]\n",
    "output: path:-> list[nodes]\n",
    "visited, unvisited, neighbours, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dijkstra(graph, start, goal):\n",
    "    graph[start[0]]=start[1:]\n",
    "    graph[goal[0]]=goal[1:]\n",
    "    for neighbor in goal[1:]:\n",
    "        if neighbor[0] in graph:\n",
    "            graph[neighbor[0]].append((goal[0], neighbor[1]))\n",
    "    unvisited = [node for node in graph]\n",
    "    g_n = {start[0]: (start[0], 0)}\n",
    "    frontier = [(start[0], 0)]\n",
    "    \n",
    "    while len(unvisited)>0:\n",
    "        frontier = sorted(frontier, key=lambda x:x[1])\n",
    "        current_node = frontier[0][0]\n",
    "        current_cost = frontier[0][1]\n",
    "        frontier.remove(frontier[0])\n",
    "        if current_node in unvisited:\n",
    "            unvisited.remove(current_node)\n",
    "            neighbors = graph[current_node]\n",
    "            for neighbor in neighbors:\n",
    "                cost = current_cost+neighbor[1]\n",
    "                if neighbor[0] in g_n:\n",
    "                    if cost < g_n[neighbor[0]][1]:\n",
    "                        g_n[neighbor[0]] = (current_node, cost)\n",
    "                        frontier = [(y[0], g_n[y[0]][1]) for y in frontier]\n",
    "                else:\n",
    "                    g_n[neighbor[0]] = (current_node, cost)\n",
    "                    frontier.append((neighbor[0], cost))\n",
    "                    \n",
    "    shortest_path = [goal[0]]\n",
    "    y = goal[0]\n",
    "    while g_n[y][0]!=y:\n",
    "        y = g_n[y][0]\n",
    "        if y in shortest_path:\n",
    "            shortest_path = []\n",
    "            break;\n",
    "        shortest_path.append(y)\n",
    "    shortest_path.reverse()\n",
    "    return shortest_path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = {(1,1):[((8,1), 11), ((1,2), 18)],\n",
    "     (1,2):[((1,1), 18), ((8,3), 11), ((9,0), 32)],\n",
    "     (8,1):[((8,3),18),((9,0),37),((9,4),20),((10,3),31),((1,1),11)],\n",
    "     (8,3):[((1,2),10),((8,1),18),((9,4),15),((9,0),22)],\n",
    "     (9,0):[((1,2),32),((8,3),22),((8,1),37),((9,4),20),((10,0),11)],\n",
    "     (9,4):[((8,1),20),((8,3),15),((9,0),20),((10,3),11)],\n",
    "     (10,3):[((8,1),31),((9,4),11),((10,0),20)],\n",
    "    (10,0):[((10,3),20),((9,0),11)]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "g2 = {(1,1):[((8,1), 11), ((1,2), 18)],\n",
    "     (1,2):[((8,3), 11), ((9,0), 32)],\n",
    "     (8,1):[((8,3),18),((9,0),37),((9,4),20),((10,3),31)],\n",
    "     (8,3):[((9,4),15),((9,0),22)],\n",
    "     (9,0):[((9,4),20),((10,0),11)],\n",
    "     (9,4):[((10,3),11)],\n",
    "     (10,3):[((10,0),20)],\n",
    "    (10,0):[]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 0), (1, 2), (8, 3), (9, 4), (10, 3), (11, 1)]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dijkstra(g2, [(0,0), ((1,1),11),((1,2),10)], [(11,1),((10,3),11),((10,0),10)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probabilistic Roadmaps (PRM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "def explore(obstacles, space_size, tree=[], graph={}, num_points=10):\n",
    "    for i in range(num_points):\n",
    "        new_point = tuple(numpy.random.uniform(space_size))\n",
    "        if goal_isvalid(new_point, obstacles):\n",
    "            graph[new_point]=[]\n",
    "            for point in tree:\n",
    "                if not any([any(colliding(point, new_point, obstacle)[1]) for obstacle in obstacles]):\n",
    "                    cost = round(numpy.sqrt(distance(point,new_point)))\n",
    "                    graph[new_point].append((point, cost))\n",
    "                    if point in graph:\n",
    "                        graph[point].append((new_point, cost))\n",
    "                    else:\n",
    "                        graph[point]=[(new_point, cost)]\n",
    "            tree.append(new_point)\n",
    "    return tree, graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "def join_nearest(start, tree, obstacles):\n",
    "    distances_start = sorted([(p, distance(start, p)) for p in tree], key=lambda x: x[1])\n",
    "    for pt in distances_start:\n",
    "        pt0 = pt[0]\n",
    "        if not any([any(colliding(start, pt0, obstacle)[1]) for obstacle in obstacles]):\n",
    "            start_n = [start, (pt0, round(numpy.sqrt(pt[1])))]\n",
    "            break;\n",
    "    return start_n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "def prm(start: Tuple[int,int], goal: Tuple[int,int], obstacles: List[List[Tuple[int,int]]],\n",
    "        space_size: Tuple[int,int], num_points: int =10):\n",
    "    tree = []\n",
    "    graph = {}\n",
    "    connections = []\n",
    "    if not goal_isvalid(goal, obstacles):\n",
    "        return \"Path not possible\"\n",
    "    goal_reachable = not any([any(colliding(start, goal, obstacle)[1]) for obstacle in obstacles])\n",
    "    #print(goal_reachable)\n",
    "    while not goal_reachable:\n",
    "        tree, graph = explore(obstacles, space_size, tree, graph, num_points)\n",
    "        start_n = join_nearest(start, tree, obstacles)\n",
    "        goal_n = join_nearest(goal, tree, obstacles)\n",
    "        path = dijkstra(graph, start_n, goal_n)\n",
    "        if path!=[]:\n",
    "            return path, graph\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "collections, graph = prm(start, goal=goal, obstacles=obstacles, space_size=space_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\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(\n",
       "            '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",
       "\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 = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(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 (fig.ratio !== 1) {\n",
       "            fig.send_message('set_dpi_ratio', { dpi_ratio: fig.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 = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\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 toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\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",
       "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",
       "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], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.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,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\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",
       "        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.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\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",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\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",
       "                img.type = 'image/png';\n",
       "            }\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",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\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(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\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(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\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",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\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",
       "        }\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",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\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",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, 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",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\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\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "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.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\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",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(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 = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\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;\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",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\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.innerHTML =\n",
       "        '<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 / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<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 () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('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",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\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",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\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(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = plt.figure()\n",
    "ax = f.add_subplot(autoscale_on=False, xlim=(0, space_size[0]), ylim=(0, space_size[1]))\n",
    "ax.grid()\n",
    "for obs in obstacles:\n",
    "    bounds = obstacle_boundaries(obs)\n",
    "    for b in bounds:\n",
    "        ax.plot([b[0][0], b[1][0]], [b[0][1], b[1][1]], color='red')\n",
    "ax.scatter(start[0], start[1], s=40, color='orange', marker='o')\n",
    "ax.scatter(goal[0], goal[1], s=40, color='green')\n",
    "tree = [y for y in graph]\n",
    "ax.scatter([x for x,y in tree], [y for x,y in tree], s=5, color='brown')\n",
    "path, = ax.plot([], [], '-', lw=2, color='purple', marker='o', markersize=2, markerfacecolor='orange')\n",
    "history, = ax.plot([], [], '-', lw=1, color='purple')\n",
    "txt = ax.text(goal[0]-0.2, goal[1]-0.2, 'G')\n",
    "ax.text(start[0]+0.2, start[1]+0.2, 'S')\n",
    "time_text = ax.text(0.05, 0.9, '', transform=ax.transAxes)\n",
    "final_path, = ax.plot([], [], '-', lw=2, color='cyan')\n",
    "def animate(i):\n",
    "    up_bound = len(collections)-1\n",
    "    path.set_data([collections[i][0], collections[min(i+1,up_bound)][0]],\n",
    "    [collections[i][1], collections[min(i+1, up_bound)][1]])\n",
    "    time_text.set_text(i)\n",
    "    \n",
    "    final_path.set_data([x[0] for x in collections[:min(i+1, up_bound+1)]], [x[1] for x in collections[:min(i+1, up_bound+1)]])\n",
    "    return path, time_text, final_path\n",
    "ani = anim.FuncAnimation(f, animate, len(collections)-1, interval=1000, repeat=True, blit=True) \n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "Writer = anim.writers['ffmpeg']\n",
    "writer = Writer(fps=4, metadata=dict(artist='Me'), bitrate=1800)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, 0)\n",
      "(2.237547290239835, 1.1053959162687548)\n",
      "(0, 0)\n",
      "(2.237547290239835, 1.1053959162687548)\n",
      "(2.237547290239835, 1.1053959162687548)\n",
      "(3.547945869477475, 5.340390520217939)\n",
      "(3.547945869477475, 5.340390520217939)\n",
      "(4.872140459241358, 5.673904234363674)\n",
      "(4.872140459241358, 5.673904234363674)\n",
      "(5, 5)\n"
     ]
    }
   ],
   "source": [
    "ani.save('prm_motion.mp4', writer=writer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "2db524e06e9f5f4ffedc911c917cb75e12dbc923643829bf417064a77eb14d37"
  },
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "base"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}