tutte_barycentric.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "from utils import *\n",
    "\n",
    "np.random.seed(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tutte's 1963 Barycentric Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "It took 1 iterations to converge\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class Barycenter:\n",
    "    '''\n",
    "    Tutte's algorith for straight-line, crossings free drawings of\n",
    "    3-connected planar graphs.\n",
    "\n",
    "    William T. Tutte. How to draw a graph. Proc. London Math. Society,\n",
    "    13(52):743–768, 1963\n",
    "    '''\n",
    "\n",
    "    def __init__(self, G, N_fixed=3):\n",
    "        assert N_fixed == 3 # Currently only works with 3 fixed nodes\n",
    "\n",
    "        self.G = G\n",
    "        self.M = nx.to_scipy_sparse_matrix(G, dtype='f')\n",
    "        \n",
    "        self.N_nodes = self.M.shape[0]\n",
    "        self.N_fixed = N_fixed\n",
    "        self.N_free = self.N_nodes - N_fixed\n",
    "\n",
    "        nodes = np.arange(self.N_nodes)\n",
    "        self.pos = np.empty([self.N_nodes, 2])\n",
    "\n",
    "        thetas = np.random.random_sample((self.N_fixed)) * 2.0 * np.pi\n",
    "        np.sort(thetas)\n",
    "\n",
    "        # plot fixed points on perimeter of unit circle\n",
    "        # need to order k-cycle nodes in order\n",
    "        for i in range(self.N_fixed):\n",
    "            self.pos[i] = [np.cos(thetas[i]), np.sin(thetas[i])]\n",
    "\n",
    "        self.degree = self.M.toarray().sum(axis=1).flatten()\n",
    "\n",
    "    def run(self):\n",
    "        converged = False\n",
    "        self.iterations = 0\n",
    "\n",
    "        while not converged:\n",
    "            old_pos = np.copy(self.pos)\n",
    "\n",
    "            for i in range(self.N_fixed, self.N_nodes):\n",
    "                self.pos[i] = np.sum([self.pos[j] for j in self.M[i].indices], axis=0) / self.degree[i]\n",
    "\n",
    "            self.iterations += 1\n",
    "            converged = np.array_equal(old_pos, self.pos)\n",
    "\n",
    "    def display(self):\n",
    "        display_plot(self.G, dict(zip(G.nodes(), self.pos)))\n",
    "\n",
    "# make a 3-connected undirected graph\n",
    "G = nx.Graph()\n",
    "G.add_edges_from([(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), \n",
    "                  (2, 3), (3, 4), (4, 5), (5, 6), (6, 2)])\n",
    "graph = Barycenter(G, N_fixed=3)\n",
    "graph.run()\n",
    "print('It took {} iterations to converge'.format(graph.iterations))\n",
    "graph.display()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}