Annulus (interactive).ipynb

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       "<div id=\"interact-js-shim\">\n",
       "    <script charset=\"utf-8\">\n",
       "(function (IPython, $, _, MathJax) {\n",
       "    $.event.special.destroyed = {\n",
       "\tremove: function(o) {\n",
       "\t    if (o.handler) {\n",
       "\t\to.handler.apply(this, arguments)\n",
       "\t    }\n",
       "\t}\n",
       "    }\n",
       "\n",
       "    var OutputArea = IPython.version >= \"4.0.0\" ? require(\"notebook/js/outputarea\").OutputArea : IPython.OutputArea;\n",
       "\n",
       "    var redrawValue = function (container, type, val) {\n",
       "\tvar selector = $(\"<div/>\");\n",
       "\tvar oa = new OutputArea(_.extend(selector, {\n",
       "\t    selector: selector,\n",
       "\t    prompt_area: true,\n",
       "\t    events: IPython.events,\n",
       "\t    keyboard_manager: IPython.keyboard_manager\n",
       "\t})); // Hack to work with IPython 2.1.0\n",
       "\n",
       "\tswitch (type) {\n",
       "\tcase \"image/png\":\n",
       "            var _src = 'data:' + type + ';base64,' + val;\n",
       "\t    $(container).find(\"img\").attr('src', _src);\n",
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       "\n",
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       "\tfunction initComm(evt, data) {\n",
       "\t    var comm_manager = data.kernel.comm_manager;\n",
       "        //_.extend(comm_manager.targets, require(\"widgets/js/widget\"))\n",
       "\t    comm_manager.register_target(\"Signal\", function (comm) {\n",
       "            comm.on_msg(function (msg) {\n",
       "                var val = msg.content.data.value;\n",
       "                $(\".signal-\" + comm.comm_id).each(function() {\n",
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       "                delete val;\n",
       "                delete msg.content.data.value;\n",
       "            });\n",
       "\t    });\n",
       "\n",
       "\t    // coordingate with Comm and redraw Signals\n",
       "\t    // XXX: Test using Reactive here to improve performance\n",
       "\t    $([IPython.events]).on(\n",
       "\t\t'output_appended.OutputArea', function (event, type, value, md, toinsert) {\n",
       "\t\t    if (md && md.reactive) {\n",
       "                // console.log(md.comm_id);\n",
       "                toinsert.addClass(\"signal-\" + md.comm_id);\n",
       "                toinsert.data(\"type\", type);\n",
       "                // Signal back indicating the mimetype required\n",
       "                var comm_manager = IPython.notebook.kernel.comm_manager;\n",
       "                var comm = comm_manager.comms[md.comm_id];\n",
       "                comm.then(function (c) {\n",
       "                    c.send({action: \"subscribe_mime\",\n",
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       "                    toinsert.bind(\"destroyed\", function() {\n",
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       "                               mime: type});\n",
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       "\t\t    }\n",
       "\t    });\n",
       "\t}\n",
       "\n",
       "\ttry {\n",
       "\t    // try to initialize right away. otherwise, wait on the status_started event.\n",
       "\t    initComm(undefined, IPython.notebook);\n",
       "\t} catch (e) {\n",
       "\t    $([IPython.events]).on('kernel_created.Kernel kernel_created.Session', initComm);\n",
       "\t}\n",
       "    });\n",
       "})(IPython, jQuery, _, MathJax);\n",
       "</script>\n",
       "    <script>\n",
       "        window.interactLoadedFlag = true\n",
       "       $(\"#interact-js-shim\").bind(\"destroyed\", function () {\n",
       "           if (window.interactLoadedFlag) {\n",
       "               console.warn(\"JavaScript required by Interact will be removed if you remove this cell or run using Interact more than once.\")\n",
       "           }\n",
       "       })\n",
       "       $([IPython.events]).on(\"kernel_starting.Kernel kernel_restarting.Kernel\", function () { window.interactLoadedFlag = false })\n",
       "   </script>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Plots.GRBackend()"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using IntervalConstraintProgramming, ValidatedNumerics, Interact, Plots\n",
    "gr()  # GR backend for Plots.jl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-∞, ∞] × [-∞, ∞]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = @constraint 1 <= x^2 + y^2 <= 2\n",
    "X = IntervalBox(-∞..∞, -∞..∞)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "Interact.Slider{Float64}(Signal{Float64}(0.5, nactions=1),\"\",0.5,0.5:0.5:10.0,\"horizontal\",true,\".3f\",true)"
      ]
     },
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    "@manipulate for n in slider(0.5:0.5:10, value=0.5)\n",
    "\n",
    "    paving = pave(C, X, 2.0^(-n))\n",
    "    plot(paving.inner, aspect_ratio=:equal, label=\"inside\")\n",
    "    plot!(paving.boundary, c=\"gray\", alpha=0.1, ann=[(0, 0, string(Vol(paving))), (0, 0.5, \"eps = 2^(-$n)\")], label=\"boundary\")\n",
    "        \n",
    "end"
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