Sage plots in jupyter notebooks with standard ipython kernel

sage plots in jupyter with standard ipython kernel.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "aa10dc65-9498-430f-b3ac-400e813333d9",
   "metadata": {},
   "source": [
    "# Using sage plots in jupyter with standard ipython kernel\n",
    "\n",
    "[Sage](https://www.sagemath.org/) is a free mathematics software system. It works wonderfully from the native interface which is built on top of python. For use in projects that are not sage-centric this interface can be a bit too opinionated, and it is possible to instead use sage as a module from standard python.\n",
    "\n",
    "One reason to do so is to access the sage plotting tools which are superior to matplotlib for implicit plots: the sage implicit plots all support adaptive sampling in contrast to e.g. matplotlib which require grid-sampled input.\n",
    "\n",
    "There is one challenge in doing this: when used as a module, sage does not automatically attach to the jupyter display backend, so you need to save your plots to see them. This notebook demonstrates how to attach the sage backend to jupyter."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d05f089-162c-49ea-8207-136a58c3fb8a",
   "metadata": {},
   "source": [
    "There are [official instructions](https://doc.sagemath.org/html/en/installation/conda.html#installing-all-of-sagemath-from-conda-not-for-development)for installing sage with conda. Personally, I prefer to not add `conda-forge` to my default channels, and have found the following to work:\n",
    "\n",
    "    conda install -n jupysage -c conda-forge jupyterlab sage\n",
    "    \n",
    "Other incantations/channel settings apparently risk installing an incorrect version of libgsl?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be2c6132-f246-4157-863c-e3af4f351cde",
   "metadata": {},
   "source": [
    "### Attaching sage display manager to jupyter backend\n",
    "\n",
    "This is the code you need to copy to your notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "1487d881-44c5-4570-9fe6-edd24888ab55",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "IPython notebook"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sage.repl.rich_output\n",
    "import sage.repl.rich_output.backend_ipython\n",
    "import IPython\n",
    "sage.repl.rich_output.get_display_manager().switch_backend(\n",
    "    sage.repl.rich_output.backend_ipython.BackendIPythonNotebook(),\n",
    "    shell=IPython.get_ipython())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbc99fdb-05d6-4e98-8044-561247deb7cb",
   "metadata": {},
   "source": [
    "### Demonstration that this works"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "e140bc32-2ac7-4708-88ef-a5362c4a7668",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import sympy\n",
    "from sage.plot.plot import plot\n",
    "from sage.plot.contour_plot import contour_plot\n",
    "from sage.plot.plot3d.implicit_plot3d import implicit_plot3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "6aef80a7-74cf-4fda-abdf-fd983d8ef2d3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<iframe srcdoc=\"<!DOCTYPE html>\n",
       "<html>\n",
       "<head>\n",
       "<title></title>\n",
       "<meta charset=&quot;utf-8&quot;>\n",
       "<meta name=viewport content=&quot;width=device-width, user-scalable=no, minimum-scale=1.0, maximum-scale=1.0&quot;>\n",
       "<style>\n",
       "\n",
       "    body { margin: 0px; overflow: hidden; }\n",
       "\n",
       "    #menu-container { position: absolute; bottom: 30px; right: 40px; cursor: default; }\n",
       "\n",
       "    #menu-message { position: absolute; bottom: 0px; right: 0px; white-space: nowrap;\n",
       "                    display: none; background-color: #F5F5F5; padding: 10px; }\n",
       "\n",
       "    #menu-content { position: absolute; bottom: 0px; right: 0px;\n",
       "                    display: none; background-color: #F5F5F5; border-bottom: 1px solid black;\n",
       "                    border-right: 1px solid black; border-left: 1px solid black; }\n",
       "\n",
       "    #menu-content div { border-top: 1px solid black; padding: 10px; white-space: nowrap; }\n",
       "\n",
       "    #menu-content div:hover { background-color: #FEFEFE; }\n",
       "\n",
       "    .dark-theme #menu-container { color: white; }\n",
       "\n",
       "    .dark-theme #menu-message { background-color: #181818; }\n",
       "\n",
       "    .dark-theme #menu-content { background-color: #181818; border-color: white; }\n",
       "\n",
       "    .dark-theme #menu-content div { border-color: white; }\n",
       "\n",
       "    .dark-theme #menu-content div:hover { background-color: #303030; }\n",
       "\n",
       "</style>\n",
       "\n",
       "</head>\n",
       "\n",
       "<body>\n",
       "\n",
       "<script src=&quot;/nbextensions/threejs-sage/r122/three.min.js&quot;></script>\n",
       "<script>\n",
       "  if ( !window.THREE ) document.write(' \\\n",
       "<script src=&quot;https://cdn.jsdelivr.net/gh/sagemath/threejs-sage@r122/build/three.min.js&quot;><\\/script> \\\n",
       "            ');\n",
       "</script>\n",
       "        \n",
       "<script>\n",
       "\n",
       "    var options = {&quot;animate&quot;: false, &quot;animationControls&quot;: true, &quot;aspectRatio&quot;: [1.0, 1.0, 1.0], &quot;autoScaling&quot;: [false, false, false], &quot;autoPlay&quot;: true, &quot;axes&quot;: false, &quot;axesLabels&quot;: [&quot;x&quot;, &quot;y&quot;, &quot;z&quot;], &quot;axesLabelsStyle&quot;: null, &quot;decimals&quot;: 2, &quot;delay&quot;: 20, &quot;frame&quot;: true, &quot;loop&quot;: true, &quot;projection&quot;: &quot;perspective&quot;, &quot;theme&quot;: &quot;light&quot;, &quot;viewpoint&quot;: false};\n",
       "    var animate = options.animate;\n",
       "\n",
       "    if ( options.theme === 'dark' )\n",
       "        document.body.className = 'dark-theme';\n",
       "\n",
       "    var scene = new THREE.Scene();\n",
       "\n",
       "    var renderer = new THREE.WebGLRenderer( { antialias: true, preserveDrawingBuffer: true } );\n",
       "    renderer.setPixelRatio( window.devicePixelRatio );\n",
       "    renderer.setSize( window.innerWidth, window.innerHeight );\n",
       "    renderer.setClearColor( options.theme === 'dark' ? 0 : 0xffffff, 1 );\n",
       "    document.body.appendChild( renderer.domElement );\n",
       "\n",
       "    var b = [{&quot;x&quot;:-2.0, &quot;y&quot;:-2.0, &quot;z&quot;:-2.0}, {&quot;x&quot;:2.0, &quot;y&quot;:2.0, &quot;z&quot;:2.0}]; // bounds\n",
       "\n",
       "    if ( b[0].x === b[1].x ) {\n",
       "        b[0].x -= 1;\n",
       "        b[1].x += 1;\n",
       "    }\n",
       "    if ( b[0].y === b[1].y ) {\n",
       "        b[0].y -= 1;\n",
       "        b[1].y += 1;\n",
       "    }\n",
       "    if ( b[0].z === b[1].z ) {\n",
       "        b[0].z -= 1;\n",
       "        b[1].z += 1;\n",
       "    }\n",
       "\n",
       "    var rxRange = Math.sqrt( Math.pow( b[1].z - b[0].z, 2 )\n",
       "                            + Math.pow( b[1].y - b[0].y, 2 ) );\n",
       "    var ryRange = Math.sqrt( Math.pow( b[1].x - b[0].x, 2 )\n",
       "                            + Math.pow( b[1].z - b[0].z, 2 ) );\n",
       "    var rzRange = Math.sqrt( Math.pow( b[1].x - b[0].x, 2 )\n",
       "                            + Math.pow( b[1].y - b[0].y, 2 ) );\n",
       "    var xRange = b[1].x - b[0].x;\n",
       "    var yRange = b[1].y - b[0].y;\n",
       "    var zRange = b[1].z - b[0].z;\n",
       "\n",
       "    var ar = options.aspectRatio;\n",
       "    var a = [ ar[0], ar[1], ar[2] ]; // aspect multipliers\n",
       "\n",
       "    var autoScaling = options.autoScaling;\n",
       "    var autoAspect = 2.5;\n",
       "    if ( xRange > autoAspect * rxRange && autoScaling[0] ) a[0] = autoAspect * rxRange / xRange;\n",
       "    if ( yRange > autoAspect * ryRange && autoScaling[1] ) a[1] = autoAspect * ryRange / yRange;\n",
       "    if ( zRange > autoAspect * rzRange && autoScaling[2] ) a[2] = autoAspect * rzRange / zRange;\n",
       "\n",
       "    // Distance from (xMid,yMid,zMid) to any corner of the bounding box, after applying aspectRatio\n",
       "    var midToCorner = Math.sqrt( a[0]*a[0]*xRange*xRange + a[1]*a[1]*yRange*yRange + a[2]*a[2]*zRange*zRange ) / 2;\n",
       "\n",
       "    var xMid = ( b[0].x + b[1].x ) / 2;\n",
       "    var yMid = ( b[0].y + b[1].y ) / 2;\n",
       "    var zMid = ( b[0].z + b[1].z ) / 2;\n",
       "\n",
       "    var box = new THREE.Geometry();\n",
       "    box.vertices.push( new THREE.Vector3( a[0]*b[0].x, a[1]*b[0].y, a[2]*b[0].z ) );\n",
       "    box.vertices.push( new THREE.Vector3( a[0]*b[1].x, a[1]*b[1].y, a[2]*b[1].z ) );\n",
       "    var boxMesh = new THREE.Line( box );\n",
       "    var boxColor = options.theme === 'dark' ? 'white' : 'black';\n",
       "    if ( options.frame ) scene.add( new THREE.BoxHelper( boxMesh, boxColor ) );\n",
       "\n",
       "    if ( options.axesLabels ) {\n",
       "\n",
       "        var d = options.decimals; // decimals\n",
       "        var offsetRatio = 0.1;\n",
       "        var al = options.axesLabels;\n",
       "        var als = options.axesLabelsStyle || [{}, {}, {}];\n",
       "\n",
       "        var offset = offsetRatio * a[1]*( b[1].y - b[0].y );\n",
       "        var xm = xMid.toFixed(d);\n",
       "        if ( /^-0.?0*$/.test(xm) ) xm = xm.substr(1);\n",
       "        addLabel( al[0] + '=' + xm, a[0]*xMid, a[1]*b[1].y+offset, a[2]*b[0].z, als[0] );\n",
       "        addLabel( ( b[0].x ).toFixed(d), a[0]*b[0].x, a[1]*b[1].y+offset, a[2]*b[0].z, als[0] );\n",
       "        addLabel( ( b[1].x ).toFixed(d), a[0]*b[1].x, a[1]*b[1].y+offset, a[2]*b[0].z, als[0] );\n",
       "\n",
       "        var offset = offsetRatio * a[0]*( b[1].x - b[0].x );\n",
       "        var ym = yMid.toFixed(d);\n",
       "        if ( /^-0.?0*$/.test(ym) ) ym = ym.substr(1);\n",
       "        addLabel( al[1] + '=' + ym, a[0]*b[1].x+offset, a[1]*yMid, a[2]*b[0].z, als[1] );\n",
       "        addLabel( ( b[0].y ).toFixed(d), a[0]*b[1].x+offset, a[1]*b[0].y, a[2]*b[0].z, als[1] );\n",
       "        addLabel( ( b[1].y ).toFixed(d), a[0]*b[1].x+offset, a[1]*b[1].y, a[2]*b[0].z, als[1] );\n",
       "\n",
       "        var offset = offsetRatio * a[1]*( b[1].y - b[0].y );\n",
       "        var zm = zMid.toFixed(d);\n",
       "        if ( /^-0.?0*$/.test(zm) ) zm = zm.substr(1);\n",
       "        addLabel( al[2] + '=' + zm, a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*zMid, als[2] );\n",
       "        addLabel( ( b[0].z ).toFixed(d), a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*b[0].z, als[2] );\n",
       "        addLabel( ( b[1].z ).toFixed(d), a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*b[1].z, als[2] );\n",
       "\n",
       "    }\n",
       "\n",
       "    function addLabel( text, x, y, z, style ) {\n",
       "\n",
       "        var color = style.color || 'black';\n",
       "        var fontSize = style.fontSize || 14;\n",
       "        var fontFamily = style.fontFamily || 'monospace';\n",
       "        var fontStyle = style.fontStyle || 'normal';\n",
       "        var fontWeight = style.fontWeight || 'normal';\n",
       "        var opacity = style.opacity || 1;\n",
       "\n",
       "        if ( options.theme === 'dark' )\n",
       "            if ( color === 'black' || color === '#000000' )\n",
       "                color = 'white';\n",
       "\n",
       "        if ( Array.isArray( fontStyle ) ) {\n",
       "            fontFamily = fontFamily.map( function( f ) {\n",
       "                // Need to put quotes around fonts that have whitespace in their names.\n",
       "                return /\\s/.test( f ) ? '&quot;' + f + '&quot;' : f;\n",
       "            }).join(', ');\n",
       "        }\n",
       "\n",
       "        var canvas = document.createElement( 'canvas' );\n",
       "        var context = canvas.getContext( '2d' );\n",
       "        var pixelRatio = Math.round( window.devicePixelRatio );\n",
       "\n",
       "        // For example: italic bold 20px &quot;Times New Roman&quot;, Georgia, serif\n",
       "        var font = [fontStyle, fontWeight, fontSize + 'px', fontFamily].join(' ');\n",
       "\n",
       "        context.font = font;\n",
       "        var width = context.measureText( text ).width;\n",
       "        var height = fontSize;\n",
       "\n",
       "        // The dimensions of the canvas's underlying image data need to be powers\n",
       "        // of two in order for the resulting texture to support mipmapping.\n",
       "        canvas.width = THREE.MathUtils.ceilPowerOfTwo( width * pixelRatio );\n",
       "        canvas.height = THREE.MathUtils.ceilPowerOfTwo( height * pixelRatio );\n",
       "\n",
       "        // Re-compute the unscaled dimensions after the power of two conversion.\n",
       "        width = canvas.width / pixelRatio;\n",
       "        height = canvas.height / pixelRatio;\n",
       "\n",
       "        canvas.style.width = width + 'px';\n",
       "        canvas.style.height = height + 'px';\n",
       "\n",
       "        context.scale( pixelRatio, pixelRatio );\n",
       "        context.fillStyle = color;\n",
       "        context.font = font; // Must be set again after measureText.\n",
       "        context.textAlign = 'center';\n",
       "        context.textBaseline = 'middle';\n",
       "        context.fillText( text, width/2, height/2 );\n",
       "\n",
       "        var texture = new THREE.Texture( canvas );\n",
       "        texture.needsUpdate = true;\n",
       "\n",
       "        var materialOptions = { map: texture, sizeAttenuation: false, depthWrite: false };\n",
       "        if ( opacity < 1 ) {\n",
       "            // Setting opacity=1 would cause the texture's alpha component to be\n",
       "            // discarded, giving the text a black background instead of the\n",
       "            // background being transparent.\n",
       "            materialOptions.opacity = opacity;\n",
       "        }\n",
       "        var sprite = new THREE.Sprite( new THREE.SpriteMaterial( materialOptions ) );\n",
       "        sprite.position.set( x, y, z );\n",
       "\n",
       "        // Scaling factor, chosen somewhat arbitrarily so that the size of the text\n",
       "        // is consistent with previously generated plots.\n",
       "        var scale = 1/625;\n",
       "        if ( options.projection === 'orthographic' ) {\n",
       "            scale = midToCorner/256; // Needs to scale along with the plot itself.\n",
       "        }\n",
       "        sprite.scale.set( scale * width, scale * height, 1 );\n",
       "\n",
       "        scene.add( sprite );\n",
       "\n",
       "        return sprite;\n",
       "\n",
       "    }\n",
       "\n",
       "    if ( options.axes ) scene.add( new THREE.AxesHelper( Math.min( a[0]*b[1].x, a[1]*b[1].y, a[2]*b[1].z ) ) );\n",
       "\n",
       "    var camera = createCamera();\n",
       "    camera.up.set( 0, 0, 1 );\n",
       "    camera.position.set( a[0]*xMid, a[1]*yMid, a[2]*zMid );\n",
       "\n",
       "    // camera is positioned so that the line from the camera to the center\n",
       "    // of the bounding sphere of the objects makes an angle of 60 degrees with x-axis\n",
       "    // and an angle of 30 degrees with z-axis and the field of view of the camera looking\n",
       "    // at the center has an angle of 45 degrees.\n",
       "    const sin8 = Math.sin(Math.PI / 8);\n",
       "    const sin5 = Math.sin(Math.PI / 5);\n",
       "    const cos5 = Math.cos(Math.PI / 5);\n",
       "    const sin3 = Math.sin(Math.PI / 3);\n",
       "    const cos3 = Math.cos(Math.PI / 3);\n",
       "    var r = midToCorner / sin8;\n",
       "    var offset = new THREE.Vector3( r * sin3 * cos5, r * sin3 * sin5, r * cos3 );\n",
       "\n",
       "    if ( options.viewpoint ) {\n",
       "\n",
       "        var aa = options.viewpoint;\n",
       "        var axis = new THREE.Vector3( aa[0][0], aa[0][1], aa[0][2] ).normalize();\n",
       "        var angle = aa[1] * Math.PI / 180;\n",
       "        var q = new THREE.Quaternion().setFromAxisAngle( axis, angle ).inverse();\n",
       "\n",
       "        offset.set( 0, 0, offset.length() );\n",
       "        offset.applyQuaternion( q );\n",
       "\n",
       "    }\n",
       "\n",
       "    camera.position.add( offset );\n",
       "\n",
       "    function createCamera() {\n",
       "\n",
       "        var aspect = window.innerWidth / window.innerHeight;\n",
       "\n",
       "        // Scale the near and far clipping planes along with the overall plot size.\n",
       "        var nearClip = 0.01 * midToCorner;\n",
       "        var farClip = 100 * midToCorner;\n",
       "\n",
       "        if ( options.projection === 'orthographic' ) {\n",
       "            var camera = new THREE.OrthographicCamera( -1, 1, 1, -1, -farClip, farClip );\n",
       "            updateCameraAspect( camera, aspect );\n",
       "            return camera;\n",
       "        }\n",
       "\n",
       "        return new THREE.PerspectiveCamera( 45, aspect, nearClip, farClip );\n",
       "\n",
       "    }\n",
       "\n",
       "    function updateCameraAspect( camera, aspect ) {\n",
       "\n",
       "        if ( camera.isPerspectiveCamera ) {\n",
       "            camera.aspect = aspect;\n",
       "        } else if ( camera.isOrthographicCamera ) {\n",
       "            // Fit the camera frustum to the bounding box's diagonal so that the entire plot fits\n",
       "            // within at the default zoom level and camera position.\n",
       "            if ( aspect > 1 ) { // Wide window\n",
       "                camera.top = midToCorner;\n",
       "                camera.right = midToCorner * aspect;\n",
       "            } else { // Tall or square window\n",
       "                camera.top = midToCorner / aspect;\n",
       "                camera.right = midToCorner;\n",
       "            }\n",
       "            camera.bottom = -camera.top;\n",
       "            camera.left = -camera.right;\n",
       "        }\n",
       "\n",
       "        camera.updateProjectionMatrix();\n",
       "\n",
       "    }\n",
       "\n",
       "    var lights = [{&quot;x&quot;:-5, &quot;y&quot;:3, &quot;z&quot;:0, &quot;color&quot;:&quot;#7f7f7f&quot;, &quot;parent&quot;:&quot;camera&quot;}];\n",
       "    for ( var i=0 ; i < lights.length ; i++ ) {\n",
       "        var light = new THREE.DirectionalLight( lights[i].color, 1 );\n",
       "        light.position.set( a[0]*lights[i].x, a[1]*lights[i].y, a[2]*lights[i].z );\n",
       "        if ( lights[i].parent === 'camera' ) {\n",
       "            light.target.position.set( a[0]*xMid, a[1]*yMid, a[2]*zMid );\n",
       "            scene.add( light.target );\n",
       "            camera.add( light );\n",
       "        } else scene.add( light );\n",
       "    }\n",
       "    scene.add( camera );\n",
       "\n",
       "    var ambient = {&quot;color&quot;:&quot;#7f7f7f&quot;};\n",
       "    scene.add( new THREE.AmbientLight( ambient.color, 1 ) );\n",
       "\n",
       "    var controls = new THREE.OrbitControls( camera, renderer.domElement );\n",
       "    controls.target.set( a[0]*xMid, a[1]*yMid, a[2]*zMid );\n",
       "    controls.addEventListener( 'change', function() { if ( !animate ) render(); } );\n",
       "\n",
       "    window.addEventListener( 'resize', function() {\n",
       "\n",
       "        renderer.setSize( window.innerWidth, window.innerHeight );\n",
       "        updateCameraAspect( camera, window.innerWidth / window.innerHeight );\n",
       "        if ( window.rescaleFatLines ) rescaleFatLines();\n",
       "        if ( !animate ) render();\n",
       "\n",
       "    } );\n",
       "\n",
       "    var texts = [];\n",
       "    for ( var i=0 ; i < texts.length ; i++ ) addText( texts[i] );\n",
       "\n",
       "    function addText( json ) {\n",
       "        var sprite = addLabel( json.text, a[0]*json.x, a[1]*json.y, a[2]*json.z, json );\n",
       "        sprite.userData = json;\n",
       "    }\n",
       "\n",
       "    var points = [];\n",
       "    for ( var i=0 ; i < points.length ; i++ ) addPoint( points[i] );\n",
       "\n",
       "    function addPoint( json ) {\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "        var v = json.point;\n",
       "        geometry.vertices.push( new THREE.Vector3( a[0]*v[0], a[1]*v[1], a[2]*v[2] ) );\n",
       "\n",
       "        var canvas = document.createElement( 'canvas' );\n",
       "        canvas.width = 128;\n",
       "        canvas.height = 128;\n",
       "\n",
       "        var context = canvas.getContext( '2d' );\n",
       "        context.arc( 64, 64, 64, 0, 2 * Math.PI );\n",
       "        context.fillStyle = json.color;\n",
       "        context.fill();\n",
       "\n",
       "        var texture = new THREE.Texture( canvas );\n",
       "        texture.needsUpdate = true;\n",
       "\n",
       "        var transparent = json.opacity < 1 ? true : false;\n",
       "        var size = camera.isOrthographicCamera ? json.size : json.size/100;\n",
       "        var material = new THREE.PointsMaterial( { size: size, map: texture,\n",
       "                                                   transparent: transparent, opacity: json.opacity,\n",
       "                                                   alphaTest: .1 } );\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var mesh = new THREE.Points( geometry, material );\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "    }\n",
       "\n",
       "    var lines = [];\n",
       "    for ( var i=0 ; i < lines.length ; i++ ) addLine( lines[i] );\n",
       "\n",
       "    function addLine( json ) {\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "        for ( var i=0 ; i < json.points.length ; i++ ) {\n",
       "            var v = json.points[i];\n",
       "            geometry.vertices.push( new THREE.Vector3( a[0]*v[0], a[1]*v[1], a[2]*v[2] ) );\n",
       "        }\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var transparent = json.opacity < 1 ? true : false;\n",
       "        var materialOptions = { color: json.color, linewidth: json.linewidth,\n",
       "                                transparent: transparent, opacity: json.opacity };\n",
       "\n",
       "        var mesh;\n",
       "        if ( json.linewidth > 1 && window.createFatLineStrip ) {\n",
       "            mesh = createFatLineStrip( geometry, materialOptions );\n",
       "        } else {\n",
       "            var material = new THREE.LineBasicMaterial( materialOptions );\n",
       "            mesh = new THREE.Line( geometry, material );\n",
       "        }\n",
       "\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "    }\n",
       "\n",
       "    var surfaces = [{&quot;vertices&quot;: [{&quot;x&quot;: 0.9743589743589742, &quot;y&quot;: -0.1538461538461539, &quot;z&quot;: -0.16185897435897478}, {&quot;x&quot;: 0.9759615384615383, &quot;y&quot;: -0.1538461538461539, &quot;z&quot;: -0.1538461538461539}, {&quot;x&quot;: 0.9743589743589742, &quot;y&quot;: -0.16185897435897478, &quot;z&quot;: -0.1538461538461539}, {&quot;x&quot;: 0.9862179487179488, &quot;y&quot;: -0.1538461538461539, &quot;z&quot;: -0.05128205128205135}, {&quot;x&quot;: 0.9743589743589742, &quot;y&quot;: -0.16185897435897478, &quot;z&quot;: -0.1538461538461539}, {&quot;x&quot;: 0.9759615384615383, &quot;y&quot;: -0.1538461538461539, &quot;z&quot;: -0.1538461538461539}, {&quot;x&quot;: 0.9743589743589742, &quot;y&quot;: -0.21314102564102644, &quot;z&quot;: -0.05128205128205135}, {&quot;x&quot;: 0.9743589743589742, &quot;y&quot;: -0.16185897435897478, &quot;z&quot;: -0.1538461538461539}, {&quot;x&quot;: 0.9862179487179488, &quot;y&quot;: -0.1538461538461539, &quot;z&quot;: -0.05128205128205135}, {&quot;x&quot;: 0.9862179487179488, &quot;y&quot;: -0.1538461538461539, &quot;z&quot;: 0.05128205128205121}, {&quot;x&quot;: 0.9743589743589742, &quot;y&quot;: -0.21314102564102644, &quot;z&quot;: -0.05128205128205135}, {&quot;x&quot;: 0.9862179487179488, &quot;y&quot;: -0.1538461538461539, &quot;z&quot;: -0.05128205128205135}, {&quot;x&quot;: 0.9743589743589742, &quot;y&quot;: -0.21314102564102644, &quot;z&quot;: 0.05128205128205121}, {&quot;x&quot;: 0.9743589743589742, &quot;y&quot;: -0.21314102564102644, &quot;z&quot;: -0.05128205128205135}, {&quot;x&quot;: 0.9862179487179488, &quot;y&quot;: -0.1538461538461539, &quot;z&quot;: 0.05128205128205121}, {&quot;x&quot;: 0.9759615384615383, &quot;y&quot;: -0.1538461538461539, &quot;z&quot;: 0.15384615384615377}, {&quot;x&quot;: 0.9743589743589742, &quot;y&quot;: -0.21314102564102644, &quot;z&quot;: 0.05128205128205121}, {&quot;x&quot;: 0.9862179487179488, &quot;y&quot;: -0.1538461538461539, &quot;z&quot;: 0.05128205128205121}, {&quot;x&quot;: 0.9743589743589742, &quot;y&quot;: -0.16185897435897478, &quot;z&quot;: 0.15384615384615377}, {&quot;x&quot;: 0.9743589743589742, &quot;y&quot;: -0.21314102564102644, &quot;z&quot;: 0.05128205128205121}, {&quot;x&quot;: 0.9759615384615383, &quot;y&quot;: -0.1538461538461539, &quot;z&quot;: 0.15384615384615377}, {&quot;x&quot;: 0.9759615384615383, &quot;y&quot;: -0.1538461538461539, &quot;z&quot;: 0.15384615384615377}, {&quot;x&quot;: 0.9743589743589742, &quot;y&quot;: -0.1538461538461539, &quot;z&quot;: 0.16185897435897464}, {&quot;x&quot;: 0.9743589743589742, &quot;y&quot;: -0.16185897435897478, &quot;z&quot;: 0.15384615384615377}, {&quot;x&quot;: 0.9743589743589742, &quot;y&quot;: -0.05128205128205135, &quot;z&quot;: -0.21314102564102608}, {&quot;x&quot;: 0.9759615384615383, &quot;y&quot;: -0.1538461538461539, &quot;z&quot;: -0.1538461538461539}, {&quot;x&quot;: 0.9743589743589742, &quot;y&quot;: 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