{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Balancing a Ball on a Beam with Proportional-Derivative Control\n", "\n", "###### The latest version of this Jupyter notebook is available at [http://github.com/jckantor/Ball-and-Beam](http://github.com/jckantor/Ball-and-Beam) for noncommercial use under terms of the [Creative Commons Attribution Noncommericial ShareAlike License](http://creativecommons.org/licenses/by-nc-sa/4.0/).\n", "\n", "Jeffrey C. Kantor (Kantor.1@nd.edu)\n", "\n", "This notebook illustrates the principles of proportional-derivative feedback through an interactive simulation of a ball on beam apparatus. The task is to choose the control parameters to balance the ball at desired locations on the beam with acceptable dynamics and without rolling off the ends. \n", "\n", "\"Ball\n", "\n", "The simulation in intended for use in as in-lecture demonstration on PD control and the dynamics of second order systems, and for out-of-class reinforcement of key concepts in feedback control. Suggested exercises are included.\n", "\n", "Everything is included in a single, self-contained Jupyter notebook using standard python libraries.\n", "\n", "## Table of Contents\n", "\n", "* [Initialization](#Initialization). This section loads needed libraries and defines functions to display and update a diagram of the ball and beam apparatus, and to create plots of the ball position and beam angle. These cells need to be executed for subsequent simulations.\n", "* [Ball on Beam Dynamics](#Simulation/Animation). This section presents a model for the dynamics of the ball on beam system, and demonstrates the behavior with an open-loop simulation of the device.\n", "* [Proportional Control](#Proportional Control). This section introduces a proportional feedback control. Simulations can be run for different choices of setpoints and control parameters.\n", "* [Proportional-Derivative Control](#Proportional-Derivative Control). This section introduces a proportional-derivative feedback control. Simulations can be run for different choices of setpoints and control parameters.\n", "* [Theory](#Theory). A derivation of an approximate linear model for the dynamics of the ball on beam system under proportional-derivative control.\n", "* [Exercises](#Exercises). A short set of exercises to reinforce control concepts, and introduce methods to analyze the performance of the ball on beam control system.\n", "\n", "## How to Use\n", "\n", "This notebook can be downloaded to your laptop and run as a standard Jupyter notebook. This requires prior installation of a Python distribution with standard libraries such as [Anaconda](https://www.continuum.io/) available from Continuum Analytics.\n", "\n", "Once the notebook is loaded in an executable environment, either in the cloud or laptop, proceed through the notebook executing each cell, one at a time. You can use either the `run` button in the Jupyter tool bar, or press `shift-enter` for each cell. Be sure to run the Initialization cell first!\n", "\n", "This notebook can be run in the cloud from mybinder.org. This can be done from any browser (laptop, tablet, phone), and doesn't require any software installation. Click this button to get started:\n", "\n", "[![Binder](http://mybinder.org/badge.svg)](http://mybinder.org/repo/jckantor/Ball-and-Beam)\n", "\n", "Note that as a free service, the mybinder.org site is sometimes overloaded and unresponsive. " ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "\n", "## Initialization (Run this one first!)\n", "\n", "The following cell creates utility functions that display and update a figure showing the ball and beam apparatus. This cell must be executed in order to run the control simulations later in this notebook. The detail of these functions can be safely ignored by anyone primarily interested in the subsequent applications of feedback control." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%matplotlib notebook\n", "\n", "from pylab import *\n", "import time\n", "from ipywidgets import interact, interactive\n", "\n", "# limit on beam angle in radians\n", "ulimit = 0.2\n", "\n", "def draw_beam(fig,ax):\n", " # Draw the ball and beam diagram on a given figure and axis\n", " ax.axis('off')\n", " ax.axis('equal')\n", " ax.set(xlim = (-0.2,1.2), ylim = (-0.3,0.3))\n", " \n", " # draw ball, beam, and set point patch\n", " ax.plot(0.5,0.049,'r.',ms=50)\n", " ax.plot(array([0.0,cos(0.0)]), array([0.0,sin(0.0)]), lw=5)\n", " ax.add_patch(Polygon([[0.5, -0.01], [0.5-0.03, -0.05], [0.5+0.03, -0.05]]))\n", "\n", " # draw pivot patch\n", " ax.add_patch(Polygon([[0.0,0.0],[0.02,-0.25],[-0.02,-0.25]]))\n", " \n", " # beam hi and lo limit patches\n", " ulimit = 0.2\n", " xa = cos(ulimit)\n", " ya = sin(ulimit)\n", " ax.add_patch(Polygon([[xa-0.05, ya+0.01],[xa+0.05, ya+0.01], \\\n", " [xa+0.05, ya+0.02],[xa-0.05, ya+0.02]]))\n", " ax.add_patch(Polygon([[xa-0.05,-ya-0.01],[xa+0.05,-ya-0.01], \\\n", " [xa+0.05,-ya-0.02],[xa-0.05,-ya-0.02]]))\n", " fig.canvas.draw()\n", "\n", "def update_beam(fig,ax,x,u,SP):\n", " # Update the ball and beam diagram with current state values.\n", " \n", " # Limit beam angle\n", " u = -ulimit if u < -ulimit else ulimit if u > ulimit else u\n", " \n", " # Determine ball position, and if it rolled off the beam\n", " x = -0.05 if x < 0 else 1.02 if x > 1.0 else x\n", " y = 0.049/cos(u) + x*sin(u) if x >= 0.0 and x <= 1.0 else -0.2\n", "\n", " # update ball, beam, and setpoint positions\n", " ax.lines[0].set(xdata=x, ydata=y)\n", " ax.lines[1].set(xdata=[0.0,cos(u)], ydata=[0.0,sin(u)])\n", " ax.patches[0].set_xy([[SP*cos(u), -0.01 + SP*sin(u)], \\\n", " [SP*cos(u) - 0.03, -0.05 + SP*sin(u)], \\\n", " [SP*cos(u) + 0.03, -0.05 + SP*sin(u)]])\n", " fig.canvas.draw()\n", " \n", "def draw_plot(fig,ax,SP):\n", " \n", " # set up xplot to display ball position\n", " xplot = ax\n", " xplot.set(xlim=(0,tf),ylim=(0,1),xlabel='Time [dimensionless]',ylabel='Position')\n", " xplot.plot([],[],'b')\n", " xplot.plot([0,tf],[SP,SP],'b--')\n", "\n", " # set up second axist to display beam angle\n", " uplot = ax.twinx()\n", " uplot.set(xlim=(0,tf),ylim=(-ulimit,ulimit))\n", " uplot.set_ylabel('Beam Angle', color='r')\n", " for tl in uplot.get_yticklabels():\n", " tl.set_color('r')\n", " uplot.plot([],[],'r')\n", " uplot.plot([0,tf],[0,0],'r--')\n", " \n", " # return lines for updating\n", " return xplot,uplot\n", "\n", "def update_plot(ax,t,y):\n", " tdata = append(ax.lines[0].get_xdata(),t)\n", " ydata = append(ax.lines[0].get_ydata(),y)\n", " ax.lines[0].set(xdata=tdata, ydata=ydata)\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Run the following cell to see a diagram of the ball and beam apparatus." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. 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We choose to adjust the control using proportinal (P) feedback in the form\n", "\n", "$$u(t) = K_p (x(t) - x_{SP})$$\n", "\n", "where $K_p$ is the parameter determining the proportional control response.\n", "\n", "Running the following cell defines a function to perform a closed-loop simulation of PD control for fixed values of the setpoint (`SP`), proportional gain (`Kp`), and then runs the simulation for a choice of these parameters." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. 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');\n", " var titletext = $(\n", " '
');\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 = $('
');\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 = $('');\n", " canvas.addClass('mpl-canvas');\n", " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", "\n", " this.canvas = canvas[0];\n", " this.context = canvas[0].getContext(\"2d\");\n", "\n", " var backingStore = this.context.backingStorePixelRatio ||\n", "\tthis.context.webkitBackingStorePixelRatio ||\n", "\tthis.context.mozBackingStorePixelRatio ||\n", "\tthis.context.msBackingStorePixelRatio ||\n", "\tthis.context.oBackingStorePixelRatio ||\n", "\tthis.context.backingStorePixelRatio || 1;\n", "\n", " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", "\n", " var rubberband = $('');\n", " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", "\n", " var pass_mouse_events = true;\n", "\n", " canvas_div.resizable({\n", " start: function(event, ui) {\n", " pass_mouse_events = false;\n", " },\n", " resize: function(event, ui) {\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " stop: function(event, ui) {\n", " pass_mouse_events = true;\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " });\n", "\n", " function mouse_event_fn(event) {\n", " if (pass_mouse_events)\n", " return fig.mouse_event(event, event['data']);\n", " }\n", "\n", " rubberband.mousedown('button_press', mouse_event_fn);\n", " rubberband.mouseup('button_release', mouse_event_fn);\n", " // Throttle sequential mouse events to 1 every 20ms.\n", " rubberband.mousemove('motion_notify', mouse_event_fn);\n", "\n", " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", "\n", " canvas_div.on(\"wheel\", function (event) {\n", " event = event.originalEvent;\n", " event['data'] = 'scroll'\n", " if (event.deltaY < 0) {\n", " event.step = 1;\n", " } else {\n", " event.step = -1;\n", " }\n", " mouse_event_fn(event);\n", " });\n", "\n", " canvas_div.append(canvas);\n", " canvas_div.append(rubberband);\n", "\n", " this.rubberband = rubberband;\n", " this.rubberband_canvas = rubberband[0];\n", " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", " this.rubberband_context.strokeStyle = \"#000000\";\n", "\n", " this._resize_canvas = function(width, height) {\n", " // Keep the size of the canvas, canvas container, and rubber band\n", " // canvas in synch.\n", " canvas_div.css('width', width)\n", " canvas_div.css('height', height)\n", "\n", " canvas.attr('width', width * mpl.ratio);\n", " canvas.attr('height', height * mpl.ratio);\n", " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", "\n", " rubberband.attr('width', width);\n", " rubberband.attr('height', height);\n", " }\n", "\n", " // Set the figure to an initial 600x600px, this will subsequently be updated\n", " // upon first draw.\n", " this._resize_canvas(600, 600);\n", "\n", " // Disable right mouse context menu.\n", " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", " return false;\n", " });\n", "\n", " function set_focus () {\n", " canvas.focus();\n", " canvas_div.focus();\n", " }\n", "\n", " window.setTimeout(set_focus, 100);\n", "}\n", "\n", "mpl.figure.prototype._init_toolbar = function() {\n", " var fig = this;\n", "\n", " var nav_element = $('
')\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 = $('');\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 = $('');\n", " nav_element.append(status_bar);\n", " this.message = status_bar[0];\n", "\n", " // Add the close button to the window.\n", " var buttongrp = $('
');\n", " var 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", " // 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", "\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= 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": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def ballbeam(IC, SP, Kp, Kd):\n", " # initialize\n", " t = 0.0 # time\n", " x = IC # ball position\n", " v = 0.0 # ball velocity\n", " u = 0.0 # beam angle\n", " \n", " # initialize graphics\n", " fig,ax = subplots(2,1,figsize=(8,6))\n", " draw_beam(fig,ax[0]) \n", " xplot,uplot = draw_plot(fig,ax[1],SP)\n", " \n", " # simulation loop\n", " while (t < tf) & (x <= 1.0) & (x >= 0.0):\n", " # calculate control\n", " u = max(-ulimit,min(ulimit,Kp*(x - SP) + Kd*(v)))\n", "\n", " # update state\n", " t += dt\n", " v += -sin(u)*dt\n", " x += v*dt\n", " \n", " # update graphics\n", " update_beam(fig,ax[0],x,u,SP)\n", " update_plot(xplot,t,x)\n", " update_plot(uplot,t,u)\n", "\n", "# run simulation for one choice of initial position, setpoint, and control gains\n", "dt = 0.05\n", "tf = 10.0\n", "ballbeam(1.0, 0.5, 2.0, 1.0) " ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Interactive Simulation\n", "\n", "Running the following cell will open a set of sliders with which you can adjust the initial position of the ball, the setpoint, and the control parameters $K_p$ and $K_d$. Adjust the sliders, then press the `Run ballbeam` button to perform the simulation. \n", "\n", "Try this out! For example, see if you can choose parameters to position the ball on the very tip of the beam without falling off." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", " 'Firefox 4 and 5 are also supported but you ' +\n", " 'have to enable WebSockets in about:config.');\n", " };\n", "}\n", "\n", "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", " this.id = figure_id;\n", "\n", " this.ws = websocket;\n", "\n", " this.supports_binary = (this.ws.binaryType != undefined);\n", "\n", " if (!this.supports_binary) {\n", " var warnings = document.getElementById(\"mpl-warnings\");\n", " if (warnings) {\n", " warnings.style.display = 'block';\n", " warnings.textContent = (\n", " \"This browser does not support binary websocket messages. \" +\n", " \"Performance may be slow.\");\n", " }\n", " }\n", "\n", " this.imageObj = new Image();\n", "\n", " this.context = undefined;\n", " this.message = undefined;\n", " this.canvas = undefined;\n", " this.rubberband_canvas = undefined;\n", " this.rubberband_context = undefined;\n", " this.format_dropdown = undefined;\n", "\n", " this.image_mode = 'full';\n", "\n", " this.root = $('
');\n", " this._root_extra_style(this.root)\n", " this.root.attr('style', 'display: inline-block');\n", "\n", " $(parent_element).append(this.root);\n", "\n", " this._init_header(this);\n", " this._init_canvas(this);\n", " this._init_toolbar(this);\n", "\n", " var fig = this;\n", "\n", " this.waiting = false;\n", "\n", " this.ws.onopen = function () {\n", " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", " fig.send_message(\"send_image_mode\", {});\n", " if (mpl.ratio != 1) {\n", " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", " }\n", " fig.send_message(\"refresh\", {});\n", " }\n", "\n", " this.imageObj.onload = function() {\n", " if (fig.image_mode == 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function() {\n", " 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", " '
');\n", " var titletext = $(\n", " '
');\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 = $('
');\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 = $('');\n", " canvas.addClass('mpl-canvas');\n", " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", "\n", " this.canvas = canvas[0];\n", " this.context = canvas[0].getContext(\"2d\");\n", "\n", " var backingStore = this.context.backingStorePixelRatio ||\n", "\tthis.context.webkitBackingStorePixelRatio ||\n", "\tthis.context.mozBackingStorePixelRatio ||\n", "\tthis.context.msBackingStorePixelRatio ||\n", "\tthis.context.oBackingStorePixelRatio ||\n", "\tthis.context.backingStorePixelRatio || 1;\n", "\n", " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", "\n", " var rubberband = $('');\n", " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", "\n", " var pass_mouse_events = true;\n", "\n", " canvas_div.resizable({\n", " start: function(event, ui) {\n", " pass_mouse_events = false;\n", " },\n", " resize: function(event, ui) {\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " stop: function(event, ui) {\n", " pass_mouse_events = true;\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " });\n", "\n", " function mouse_event_fn(event) {\n", " if (pass_mouse_events)\n", " return fig.mouse_event(event, event['data']);\n", " }\n", "\n", " rubberband.mousedown('button_press', mouse_event_fn);\n", " rubberband.mouseup('button_release', mouse_event_fn);\n", " // Throttle sequential mouse events to 1 every 20ms.\n", " rubberband.mousemove('motion_notify', mouse_event_fn);\n", "\n", " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", "\n", " canvas_div.on(\"wheel\", function (event) {\n", " event = event.originalEvent;\n", " event['data'] = 'scroll'\n", " if (event.deltaY < 0) {\n", " event.step = 1;\n", " } else {\n", " event.step = -1;\n", " }\n", " mouse_event_fn(event);\n", " });\n", "\n", " canvas_div.append(canvas);\n", " canvas_div.append(rubberband);\n", "\n", " this.rubberband = rubberband;\n", " this.rubberband_canvas = rubberband[0];\n", " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", " this.rubberband_context.strokeStyle = \"#000000\";\n", "\n", " this._resize_canvas = function(width, height) {\n", " // Keep the size of the canvas, canvas container, and rubber band\n", " // canvas in synch.\n", " canvas_div.css('width', width)\n", " canvas_div.css('height', height)\n", "\n", " canvas.attr('width', width * mpl.ratio);\n", " canvas.attr('height', height * mpl.ratio);\n", " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", "\n", " rubberband.attr('width', width);\n", " rubberband.attr('height', height);\n", " }\n", "\n", " // Set the figure to an initial 600x600px, this will subsequently be updated\n", " // upon first draw.\n", " this._resize_canvas(600, 600);\n", "\n", " // Disable right mouse context menu.\n", " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", " return false;\n", " });\n", "\n", " function set_focus () {\n", " canvas.focus();\n", " canvas_div.focus();\n", " }\n", "\n", " window.setTimeout(set_focus, 100);\n", "}\n", "\n", "mpl.figure.prototype._init_toolbar = function() {\n", " var fig = this;\n", "\n", " var nav_element = $('
')\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 = $('