saraedum/Interactive Visualization in SageMath.ipynb Secret

## Interactive Visualization in SageMath.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3c242ff7",
   "metadata": {},
   "source": [
    "# Interactive Visualization in SageMath\n",
    "\n",
    "for [Sage Days 114](https://wiki.sagemath.org/days114)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c24a02c",
   "metadata": {},
   "source": [
    "## Non-Interactive Visualization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1edc3171",
   "metadata": {},
   "source": [
    "### matplot based plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "72e9b3a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "( x^2 ).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "874cec22",
   "metadata": {},
   "source": [
    "### graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0b1403b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 42 graphics primitives"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graphs.BalancedTree(4, 2).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7305a16",
   "metadata": {},
   "source": [
    "### 3d plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d76231a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics3d Object"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "var('y')\n",
    "plot3d(sin(x^2 + y^2), (x, -3, 3), (y, -3, 3), plot_points=256).show(viewer='tachyon')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efc6651e",
   "metadata": {},
   "source": [
    "## Somewhat Interactive Visualization\n",
    "\n",
    "\n",
    "### jsmol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "55a93ccb",
   "metadata": {},
   "outputs": [
    {
     "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;: false, &quot;axesLabelsStyle&quot;: null, &quot;decimals&quot;: 2, &quot;delay&quot;: 20, &quot;frame&quot;: false, &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;:0.94, &quot;y&quot;:-0.8189113760801243, &quot;z&quot;:-0.9955891312542251}, {&quot;x&quot;:2.6398193228073956, &quot;y&quot;:0.745431402398476, &quot;z&quot;:0.824909109236766}]; // 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",
       "    var offset = new THREE.Vector3( a[0]*xRange, a[1]*yRange, a[2]*zRange );\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;: 1.9950957740371293, &quot;y&quot;: -0.31301014775288016, &quot;z&quot;: -0.9955891312542251}, {&quot;x&quot;: 2.0100957740371292, &quot;y&quot;: -0.287029385639347, &quot;z&quot;: -0.9875506554812914}, {&quot;x&quot;: 2.0250957740371294, &quot;y&quot;: -0.31301014775288016, &quot;z&quot;: -0.9875506554812914}, {&quot;x&quot;: 1.9800957740371294, &quot;y&quot;: -0.287029385639347, &quot;z&quot;: -0.9875506554812914}, {&quot;x&quot;: 1.9650957740371293, &quot;y&quot;: -0.31301014775288016, &quot;z&quot;: -0.9875506554812914}, {&quot;x&quot;: 1.9800957740371294, &quot;y&quot;: -0.3389909098664133, &quot;z&quot;: -0.9875506554812914}, {&quot;x&quot;: 2.0100957740371292, &quot;y&quot;: -0.33899090986641334, &quot;z&quot;: -0.9875506554812914}, {&quot;x&quot;: 2.0210765361506624, &quot;y&quot;: -0.2680101477528802, &quot;z&quot;: -0.9655891312542251}, {&quot;x&quot;: 2.0470572982641957, &quot;y&quot;: -0.31301014775288016, &quot;z&quot;: -0.9655891312542251}, {&quot;x&quot;: 1.9691150119235963, &quot;y&quot;: -0.2680101477528802, &quot;z&quot;: -0.9655891312542251}, {&quot;x&quot;: 1.943134249810063, &quot;y&quot;: -0.31301014775288016, &quot;z&quot;: -0.9655891312542251}, {&quot;x&quot;: 1.969115011923596, &quot;y&quot;: -0.35801014775288015, &quot;z&quot;: -0.9655891312542251}, {&quot;x&quot;: 2.0210765361506624, &quot;y&quot;: -0.35801014775288015, &quot;z&quot;: -0.9655891312542251}, {&quot;x&quot;: 2.0250957740371294, &quot;y&quot;: -0.26104862352581387, &quot;z&quot;: -0.935589131254225}, {&quot;x&quot;: 2.055095774037129, &quot;y&quot;: -0.31301014775288016, &quot;z&quot;: -0.935589131254225}, {&quot;x&quot;: 1.9650957740371293, &quot;y&quot;: -0.2610486235258138, &quot;z&quot;: -0.935589131254225}, {&quot;x&quot;: 1.9350957740371293, &quot;y&quot;: -0.31301014775288016, &quot;z&quot;: -0.935589131254225}, {&quot;x&quot;: 1.9650957740371293, &quot;y&quot;: -0.36497167197994645, &quot;z&quot;: -0.935589131254225}, {&quot;x&quot;: 2.0250957740371294, &quot;y&quot;: -0.36497167197994645, &quot;z&quot;: -0.935589131254225}, {&quot;x&quot;: 2.0210765361506624, &quot;y&quot;: -0.2680101477528802, &quot;z&quot;: -0.905589131254225}, {&quot;x&quot;: 2.0470572982641957, &quot;y&quot;: -0.31301014775288016, &quot;z&quot;: -0.905589131254225}, {&quot;x&quot;: 1.9691150119235963, &quot;y&quot;: -0.2680101477528802, &quot;z&quot;: -0.905589131254225}, {&quot;x&quot;: 1.943134249810063, &quot;y&quot;: -0.31301014775288016, &quot;z&quot;: -0.905589131254225}, {&quot;x&quot;: 1.969115011923596, &quot;y&quot;: -0.35801014775288015, &quot;z&quot;: -0.905589131254225}, {&quot;x&quot;: 2.0210765361506624, &quot;y&quot;: -0.35801014775288015, &quot;z&quot;: -0.905589131254225}, {&quot;x&quot;: 2.0100957740371292, &quot;y&quot;: -0.287029385639347, &quot;z&quot;: -0.8836276070271587}, {&quot;x&quot;: 2.0250957740371294, &quot;y&quot;: -0.31301014775288016, &quot;z&quot;: -0.8836276070271587}, {&quot;x&quot;: 1.9800957740371294, &quot;y&quot;: -0.287029385639347, &quot;z&quot;: -0.8836276070271587}, {&quot;x&quot;: 1.9650957740371293, &quot;y&quot;: -0.31301014775288016, &quot;z&quot;: -0.8836276070271587}, {&quot;x&quot;: 1.9800957740371294, &quot;y&quot;: -0.3389909098664133, &quot;z&quot;: -0.8836276070271587}, {&quot;x&quot;: 2.0100957740371292, &quot;y&quot;: -0.33899090986641334, &quot;z&quot;: -0.8836276070271587}, {&quot;x&quot;: 1.9950957740371293, &quot;y&quot;: -0.31301014775288016, &quot;z&quot;: -0.875589131254225}], &quot;faces&quot;: [[0, 1, 2], [0, 3, 1], [0, 4, 3], [0, 5, 4], [0, 6, 5], [0, 2, 6], [2, 1, 7, 8], [1, 3, 9, 7], [3, 4, 10, 9], [4, 5, 11, 10], [5, 6, 12, 11], [6, 2, 8, 12], [8, 7, 13, 14], [7, 9, 15, 13], [9, 10, 16, 15], [10, 11, 17, 16], [11, 12, 18, 17], [12, 8, 14, 18], [14, 13, 19, 20], [13, 15, 21, 19], [15, 16, 22, 21], [16, 17, 23, 22], [17, 18, 24, 23], [18, 14, 20, 24], [20, 19, 25, 26], [19, 21, 27, 25], [21, 22, 28, 27], [22, 23, 29, 28], [23, 24, 30, 29], [24, 20, 26, 30], [26, 25, 31], [25, 27, 31], [27, 28, 31], [28, 29, 31], [29, 30, 31], [30, 26, 31]], &quot;color&quot;: &quot;#ff0000&quot;, &quot;opacity&quot;: 1.0}, {&quot;vertices&quot;: [{&quot;x&quot;: 1.9275369276271184, &quot;y&quot;: 0.43232031356315814, &quot;z&quot;: -0.714161684135268}, {&quot;x&quot;: 1.9425369276271183, &quot;y&quot;: 0.4583010756766913, &quot;z&quot;: -0.7061232083623343}, {&quot;x&quot;: 1.9575369276271184, &quot;y&quot;: 0.43232031356315814, &quot;z&quot;: -0.7061232083623343}, {&quot;x&quot;: 1.9125369276271185, &quot;y&quot;: 0.4583010756766913, &quot;z&quot;: -0.7061232083623343}, {&quot;x&quot;: 1.8975369276271183, &quot;y&quot;: 0.43232031356315814, &quot;z&quot;: -0.7061232083623343}, {&quot;x&quot;: 1.9125369276271185, &quot;y&quot;: 0.406339551449625, &quot;z&quot;: -0.7061232083623343}, {&quot;x&quot;: 1.9425369276271183, &quot;y&quot;: 0.40633955144962497, &quot;z&quot;: -0.7061232083623343}, {&quot;x&quot;: 1.9535176897406514, &quot;y&quot;: 0.4773203135631581, &quot;z&quot;: -0.684161684135268}, {&quot;x&quot;: 1.9794984518541847, &quot;y&quot;: 0.43232031356315814, &quot;z&quot;: -0.684161684135268}, {&quot;x&quot;: 1.9015561655135853, &quot;y&quot;: 0.4773203135631581, &quot;z&quot;: -0.684161684135268}, {&quot;x&quot;: 1.875575403400052, &quot;y&quot;: 0.43232031356315814, &quot;z&quot;: -0.684161684135268}, {&quot;x&quot;: 1.901556165513585, &quot;y&quot;: 0.38732031356315816, &quot;z&quot;: -0.684161684135268}, {&quot;x&quot;: 1.9535176897406514, &quot;y&quot;: 0.38732031356315816, &quot;z&quot;: -0.684161684135268}, {&quot;x&quot;: 1.9575369276271184, &quot;y&quot;: 0.48428183779022443, &quot;z&quot;: -0.654161684135268}, {&quot;x&quot;: 1.9875369276271184, &quot;y&quot;: 0.43232031356315814, &quot;z&quot;: -0.654161684135268}, {&quot;x&quot;: 1.8975369276271183, &quot;y&quot;: 0.4842818377902245, &quot;z&quot;: -0.654161684135268}, {&quot;x&quot;: 1.8675369276271183, 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{&quot;x&quot;: 2.2659196391691956, &quot;y&quot;: 0.5285018972876253, &quot;z&quot;: 0.6041625608215979}, {&quot;x&quot;: 2.572228042432939, &quot;y&quot;: 0.34652667357591643, &quot;z&quot;: -0.18269609538663978}, {&quot;x&quot;: 2.2770262034111983, &quot;y&quot;: 0.509401729957676, &quot;z&quot;: 0.6122008593484158}, {&quot;x&quot;: 2.593825498134311, &quot;y&quot;: 0.3529625089028975, &quot;z&quot;: -0.1759941303485859}, {&quot;x&quot;: 2.2986236591125704, &quot;y&quot;: 0.5158375652846571, &quot;z&quot;: 0.6189028243864697}], &quot;faces&quot;: [[0, 1, 2, 3], [1, 4, 5, 2], [4, 6, 7, 5], [6, 8, 9, 7], [8, 0, 3, 9]], &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;vertices&quot;: [{&quot;x&quot;: 2.0265367558658838, &quot;y&quot;: -0.2176994239835658, &quot;z&quot;: 0.7741759468045294}, {&quot;x&quot;: 2.047398448319235, &quot;y&quot;: -0.22605917992622782, &quot;z&quot;: 0.7672701034048449}, {&quot;x&quot;: 2.3005097461256647, &quot;y&quot;: 0.5247785178171644, &quot;z&quot;: 0.6229734843381216}, {&quot;x&quot;: 2.2796480536723136, &quot;y&quot;: 0.5331382737598265, &quot;z&quot;: 0.6298793277378062}, {&quot;x&quot;: 2.0462975743768226, &quot;y&quot;: -0.2301331313959758, &quot;z&quot;: 0.7441405249286794}, {&quot;x&quot;: 2.2994088721832524, &quot;y&quot;: 0.5207045663474165, &quot;z&quot;: 0.5998439058619561}, {&quot;x&quot;: 2.024755504409731, &quot;y&quot;: -0.22429121593013557, &quot;z&quot;: 0.7367515026846356}, {&quot;x&quot;: 2.277866802216161, &quot;y&quot;: 0.5265464818132567, &quot;z&quot;: 0.5924548836179124}, {&quot;x&quot;: 2.0125426469244534, &quot;y&quot;: -0.2166067621430947, &quot;z&quot;: 0.7553144142703531}, {&quot;x&quot;: 2.265653944730883, &quot;y&quot;: 0.5342309356002976, &quot;z&quot;: 0.6110177952036299}], &quot;faces&quot;: [[0, 1, 2, 3], [1, 4, 5, 2], [4, 6, 7, 5], [6, 8, 9, 7], [8, 0, 3, 9]], &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;vertices&quot;: [{&quot;x&quot;: 2.537726899428753, &quot;y&quot;: -0.41679117582441394, &quot;z&quot;: -0.4611327266854707}, {&quot;x&quot;: 2.5576586238948193, &quot;y&quot;: -0.41326541920078375, &quot;z&quot;: -0.4730944073591793}, {&quot;x&quot;: 2.5983305849065084, &quot;y&quot;: 0.3614728336687364, &quot;z&quot;: -0.17696538137709897}, {&quot;x&quot;: 2.578398860440442, &quot;y&quot;: 0.35794707704510614, &quot;z&quot;: -0.1650037007033903}, {&quot;x&quot;: 2.5520084133145695, &quot;y&quot;: -0.4048587451672031, &quot;z&quot;: -0.4943120735030322}, {&quot;x&quot;: 2.5926803743262585, &quot;y&quot;: 0.3698795077023171, &quot;z&quot;: -0.1981830475209518}, {&quot;x&quot;: 2.5285846666663145, &quot;y&quot;: -0.40318889150573933, &quot;z&quot;: -0.4954636316681724}, {&quot;x&quot;: 2.5692566276780036, &quot;y&quot;: 0.37154936136378086, &quot;z&quot;: -0.19933460568609207}, {&quot;x&quot;: 2.5197582056740764, &quot;y&quot;: -0.41056353922029687, &quot;z&quot;: -0.4749576676103988}, {&quot;x&quot;: 2.5604301666857654, &quot;y&quot;: 0.36417471364922327, &quot;z&quot;: -0.1788286416283184}], &quot;faces&quot;: [[0, 1, 2, 3], [1, 4, 5, 2], [4, 6, 7, 5], [6, 8, 9, 7], [8, 0, 3, 9]], &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;vertices&quot;: [{&quot;x&quot;: 2.090424434753732, &quot;y&quot;: -0.7413896691000248, &quot;z&quot;: 0.046249275363897946}, {&quot;x&quot;: 2.107792937463208, &quot;y&quot;: -0.7565044638534666, &quot;z&quot;: 0.05100999985627447}, {&quot;x&quot;: 2.553353494079114, &quot;y&quot;: -0.4073266419570295, &quot;z&quot;: -0.46592153616121185}, {&quot;x&quot;: 2.5359849913696384, &quot;y&quot;: -0.39221184720358776, &quot;z&quot;: -0.4706822606535884}, {&quot;x&quot;: 2.105529048205691, &quot;y&quot;: -0.7749455294962118, &quot;z&quot;: 0.036602074679840946}, {&quot;x&quot;: 2.5510896048215974, &quot;y&quot;: -0.4257677075997747, &quot;z&quot;: -0.48032946133764537}, {&quot;x&quot;: 2.086761384988305, &quot;y&quot;: -0.7712279400987545, &quot;z&quot;: 0.02293676272106321}, {&quot;x&quot;: 2.532321941604211, &quot;y&quot;: -0.4220501182023174, &quot;z&quot;: -0.49399477329642316}, {&quot;x&quot;: 2.077426220488065, &quot;y&quot;: -0.7504892778521645, &quot;z&quot;: 0.02889906064010156}, {&quot;x&quot;: 2.5229867771039713, &quot;y&quot;: -0.40131145595572737, &quot;z&quot;: -0.4880324753773847}], &quot;faces&quot;: [[0, 1, 2, 3], [1, 4, 5, 2], [4, 6, 7, 5], [6, 8, 9, 7], [8, 0, 3, 9]], &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;vertices&quot;: [{&quot;x&quot;: 2.031964288814563, &quot;y&quot;: -0.20691282892875662, &quot;z&quot;: 0.743599678386578}, {&quot;x&quot;: 2.0506184119356163, &quot;y&quot;: -0.2175640481646034, &quot;z&quot;: 0.7531580058487722}, {&quot;x&quot;: 2.1126990311361915, &quot;y&quot;: -0.7535174815689278, &quot;z&quot;: 0.034766942082399444}, {&quot;x&quot;: 2.094044908015138, &quot;y&quot;: -0.7428662623330811, &quot;z&quot;: 0.0252086146202052}, {&quot;x&quot;: 2.0428600883856056, &quot;y&quot;: -0.2356694462831923, &quot;z&quot;: 0.7659950374044235}, {&quot;x&quot;: 2.104940707586181, &quot;y&quot;: -0.7716228796875167, &quot;z&quot;: 0.047603973638050696}, {&quot;x&quot;: 2.019411057614926, &quot;y&quot;: -0.23620797846448183, &quot;z&quot;: 0.7643704317582767}, {&quot;x&quot;: 2.081491676815501, &quot;y&quot;: -0.7721614118688063, &quot;z&quot;: 0.045979367991903865}, {&quot;x&quot;: 2.012677083145415, &quot;y&quot;: -0.21843541153796553, &quot;z&quot;: 0.7505293386949917}, {&quot;x&quot;: 2.07475770234599, &quot;y&quot;: -0.75438884494229, &quot;z&quot;: 0.032138274928618885}], &quot;faces&quot;: [[0, 1, 2, 3], [1, 4, 5, 2], [4, 6, 7, 5], [6, 8, 9, 7], [8, 0, 3, 9]], &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;vertices&quot;: [{&quot;x&quot;: 1.4914613952429938, &quot;y&quot;: -0.6686886533682855, &quot;z&quot;: -0.47401913078472996}, {&quot;x&quot;: 1.4770792548746545, &quot;y&quot;: -0.6786126655361558, &quot;z&quot;: -0.45828844658418133}, {&quot;x&quot;: 2.0829808265642056, &quot;y&quot;: -0.7492757821514937, &quot;z&quot;: 0.051091801736285476}, {&quot;x&quot;: 2.0973629669325446, &quot;y&quot;: -0.7393517699836234, &quot;z&quot;: 0.03536111753573689}, {&quot;x&quot;: 1.477354216469113, &quot;y&quot;: -0.7018527410116016, &quot;z&quot;: -0.4618394594702744}, {&quot;x&quot;: 2.0832557881586635, &quot;y&quot;: -0.7725158576269394, &quot;z&quot;: 0.047540788850192424}, {&quot;x&quot;: 1.4919062924484283, &quot;y&quot;: -0.7062918853886697, &quot;z&quot;: -0.47976479032891733}, {&quot;x&quot;: 2.0978078641379794, &quot;y&quot;: -0.7769550020040076, &quot;z&quot;: 0.02961545799154947}, {&quot;x&quot;: 1.5006250084160577, &quot;y&quot;: -0.6857953520192199, &quot;z&quot;: -0.487292241173053}, {&quot;x&quot;: 2.1065265801056086, &quot;y&quot;: -0.7564584686345578, &quot;z&quot;: 0.022088007147413838}], &quot;faces&quot;: [[0, 1, 2, 3], [1, 4, 5, 2], [4, 6, 7, 5], [6, 8, 9, 7], [8, 0, 3, 9]], &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;vertices&quot;: [{&quot;x&quot;: 1.287983602543815, &quot;y&quot;: 0.03474375578496619, &quot;z&quot;: 0.7588192693819298}, {&quot;x&quot;: 1.2859925179318994, &quot;y&quot;: 0.02764163094363975, &quot;z&quot;: 0.781143735989364}, {&quot;x&quot;: 2.0352469751099993, &quot;y&quot;: -0.21189252849995877, &quot;z&quot;: 0.7717651251712065}, {&quot;x&quot;: 2.0372380597219153, &quot;y&quot;: -0.20479040365863227, &quot;z&quot;: 0.7494406585637723}, {&quot;x&quot;: 1.2788317898859995, &quot;y&quot;: 0.0052474798108956555, &quot;z&quot;: 0.7810325002193761}, {&quot;x&quot;: 2.0280862470641, &quot;y&quot;: -0.23428667963270283, &quot;z&quot;: 0.7716538894012186}, {&quot;x&quot;: 1.2763973011813547, &quot;y&quot;: -0.0014907418970156738, &quot;z&quot;: 0.7586392861253245}, {&quot;x&quot;: 2.025651758359455, &quot;y&quot;: -0.24102490134061416, &quot;z&quot;: 0.749260675307167}, {&quot;x&quot;: 1.282053432462556, &quot;y&quot;: 0.016738959196506836, &quot;z&quot;: 0.7449107544678354}, {&quot;x&quot;: 2.0313078896406562, &quot;y&quot;: -0.22279520024709165, &quot;z&quot;: 0.7355321436496779}], &quot;faces&quot;: [[0, 1, 2, 3], [1, 4, 5, 2], [4, 6, 7, 5], [6, 8, 9, 7], [8, 0, 3, 9]], &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;vertices&quot;: [{&quot;x&quot;: 0.9822430473788583, &quot;y&quot;: -0.16962710003172035, &quot;z&quot;: 0.054318951592674525}, {&quot;x&quot;: 0.9889634900161284, &quot;y&quot;: -0.19190132415312441, &quot;z&quot;: 0.05770731329837642}, {&quot;x&quot;: 1.2712152188172534, &quot;y&quot;: 0.0020972040737010714, &quot;z&quot;: 0.7731888217184931}, {&quot;x&quot;: 1.2644947761799834, &quot;y&quot;: 0.024371428195105127, &quot;z&quot;: 0.7698004600127912}, {&quot;x&quot;: 1.0109360143339312, &quot;y&quot;: -0.19416604485482697, &quot;z&quot;: 0.049653393771408094}, {&quot;x&quot;: 1.2931877431350565, &quot;y&quot;: -0.00016751662800148712, &quot;z&quot;: 0.7651349021915248}, {&quot;x&quot;: 1.017795338543697, &quot;y&quot;: -0.1732914951021006, &quot;z&quot;: 0.04128743605538332}, {&quot;x&quot;: 1.3000470673448221, &quot;y&quot;: 0.02070703312472488, &quot;z&quot;: 0.7567689444755}, {&quot;x&quot;: 1.0000621097273843, &quot;y&quot;: -0.15812559315336244, &quot;z&quot;: 0.0441709093654038}, {&quot;x&quot;: 1.2823138385285096, &quot;y&quot;: 0.035872935073463036, &quot;z&quot;: 0.7596524177855205}], &quot;faces&quot;: [[0, 1, 2, 3], [1, 4, 5, 2], [4, 6, 7, 5], [6, 8, 9, 7], [8, 0, 3, 9]], &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;vertices&quot;: [{&quot;x&quot;: 1.5036095414872346, &quot;y&quot;: -0.6849281775149569, &quot;z&quot;: -0.46060494366794436}, {&quot;x&quot;: 1.4971684023247085, &quot;y&quot;: -0.672077380831548, &quot;z&quot;: -0.47921018904097556}, {&quot;x&quot;: 1.0094831688344588, &quot;y&quot;: -0.16125143282578838, &quot;z&quot;: 0.042458225443904735}, {&quot;x&quot;: 1.0159243079969849, &quot;y&quot;: -0.17410222950919732, &quot;z&quot;: 0.061063470816935986}, {&quot;x&quot;: 1.4776218461540138, &quot;y&quot;: -0.6815741887913253, &quot;z&quot;: -0.48818399452923045}, {&quot;x&quot;: 0.9899366126637642, &quot;y&quot;: -0.17074824078556564, &quot;z&quot;: 0.03348441995564988}, {&quot;x&quot;: 1.4719825492400416, &quot;y&quot;: -0.7002943355785071, &quot;z&quot;: -0.47512486595637105}, {&quot;x&quot;: 0.9842973157497921, &quot;y&quot;: -0.18946838757274745, &quot;z&quot;: 0.04654354852850928}, {&quot;x&quot;: 1.488043828245249, &quot;y&quot;: -0.7023672146075953, &quot;z&quot;: -0.4580800751466342}, {&quot;x&quot;: 1.0003585947549996, &quot;y&quot;: -0.1915412666018357, &quot;z&quot;: 0.06358833933824616}], &quot;faces&quot;: [[0, 1, 2, 3], [1, 4, 5, 2], [4, 6, 7, 5], [6, 8, 9, 7], [8, 0, 3, 9]], &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}];\n",
       "    for ( var i=0 ; i < surfaces.length ; i++ ) addSurface( surfaces[i] );\n",
       "\n",
       "    function addSurface( json ) {\n",
       "\n",
       "        var useFaceColors = 'faceColors' in json ? true : false;\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "        for ( var i=0 ; i < json.vertices.length ; i++ ) {\n",
       "            var v = json.vertices[i];\n",
       "            geometry.vertices.push( new THREE.Vector3( a[0]*v.x, a[1]*v.y, a[2]*v.z ) );\n",
       "        }\n",
       "        for ( var i=0 ; i < json.faces.length ; i++ ) {\n",
       "            var f = json.faces[i];\n",
       "            for ( var j=0 ; j < f.length - 2 ; j++ ) {\n",
       "                var face = new THREE.Face3( f[0], f[j+1], f[j+2] );\n",
       "                if ( useFaceColors ) face.color.set( json.faceColors[i] );\n",
       "                geometry.faces.push( face );\n",
       "            }\n",
       "        }\n",
       "        geometry.computeVertexNormals();\n",
       "\n",
       "        var side = json.singleSide ? THREE.FrontSide : THREE.DoubleSide;\n",
       "        var transparent = json.opacity < 1 ? true : false;\n",
       "        var depthWrite = 'depthWrite' in json ? json.depthWrite : !transparent;\n",
       "        var flatShading = json.useFlatShading ? json.useFlatShading : false;\n",
       "\n",
       "        var material = new THREE.MeshPhongMaterial( { side: side,\n",
       "                                     color: useFaceColors ? 'white' : json.color,\n",
       "                                     vertexColors: useFaceColors ? THREE.FaceColors : THREE.NoColors,\n",
       "                                     transparent: transparent, opacity: json.opacity,\n",
       "                                     shininess: 20, flatShading: flatShading,\n",
       "                                     depthWrite: depthWrite } );\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.Mesh( geometry, material );\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        if ( transparent && json.renderOrder ) mesh.renderOrder = json.renderOrder;\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "        if ( json.showMeshGrid ) addSurfaceMeshGrid( json );\n",
       "\n",
       "    }\n",
       "\n",
       "    function addSurfaceMeshGrid( json ) {\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "\n",
       "        for ( var i=0 ; i < json.faces.length ; i++ ) {\n",
       "            var f = json.faces[i];\n",
       "            for ( var j=0 ; j < f.length ; j++ ) {\n",
       "                var k = j === f.length-1 ? 0 : j+1;\n",
       "                var v1 = json.vertices[f[j]];\n",
       "                var v2 = json.vertices[f[k]];\n",
       "                // vertices in opposite directions on neighboring faces\n",
       "                var nudge = f[j] < f[k] ? .0005*zRange : -.0005*zRange;\n",
       "                geometry.vertices.push( new THREE.Vector3( a[0]*v1.x, a[1]*v1.y, a[2]*(v1.z+nudge) ) );\n",
       "                geometry.vertices.push( new THREE.Vector3( a[0]*v2.x, a[1]*v2.y, a[2]*(v2.z+nudge) ) );\n",
       "            }\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 gridColor = options.theme === 'dark' ? 'white' : 'black';\n",
       "        var linewidth = json.linewidth || 1;\n",
       "        var materialOptions = { color: gridColor, linewidth: linewidth };\n",
       "\n",
       "        var mesh;\n",
       "        if ( linewidth > 1 && window.createFatLineSegments ) {\n",
       "            mesh = createFatLineSegments( geometry, materialOptions );\n",
       "        } else {\n",
       "            var material = new THREE.LineBasicMaterial( materialOptions );\n",
       "            mesh = new THREE.LineSegments( 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",
       "    function render() {\n",
       "\n",
       "        if ( window.updateAnimation ) animate = updateAnimation();\n",
       "        if ( animate ) requestAnimationFrame( render );\n",
       "\n",
       "        renderer.render( scene, camera );\n",
       "\n",
       "    }\n",
       "\n",
       "    render();\n",
       "    controls.update();\n",
       "    if ( !animate ) render();\n",
       "\n",
       "\n",
       "    // menu functions\n",
       "\n",
       "    function toggleMenu() {\n",
       "\n",
       "        var m = document.getElementById( 'menu-content' );\n",
       "        if ( m.style.display === 'block' ) m.style.display = 'none'\n",
       "        else m.style.display = 'block';\n",
       "\n",
       "    }\n",
       "\n",
       "\n",
       "    function saveAsPNG() {\n",
       "\n",
       "        var a = document.body.appendChild( document.createElement( 'a' ) );\n",
       "        a.href = renderer.domElement.toDataURL( 'image/png' );\n",
       "        a.download = 'screenshot';\n",
       "        a.click();\n",
       "\n",
       "    }\n",
       "\n",
       "    function saveAsHTML() {\n",
       "\n",
       "        toggleMenu(); // otherwise visible in output\n",
       "        event.stopPropagation();\n",
       "\n",
       "        var blob = new Blob( [ '<!DOCTYPE html>\\n' + document.documentElement.outerHTML ] );\n",
       "        var a = document.body.appendChild( document.createElement( 'a' ) );\n",
       "        a.href = window.URL.createObjectURL( blob );\n",
       "        a.download = suggestFilename();\n",
       "        a.click();\n",
       "\n",
       "        function suggestFilename() {\n",
       "            if ( !document.title ) {\n",
       "                return 'graphic.html';\n",
       "            } else if ( /\\.html?$/i.test( document.title ) ) {\n",
       "                return document.title; // already ends in .htm or .html\n",
       "            } else {\n",
       "                return document.title + '.html';\n",
       "            }\n",
       "        }\n",
       "\n",
       "    }\n",
       "\n",
       "    function getViewpoint() {\n",
       "\n",
       "        function roundTo( x, n ) { return +x.toFixed(n); }\n",
       "\n",
       "        var v = camera.quaternion.inverse();\n",
       "        var r = Math.sqrt( v.x*v.x + v.y*v.y + v.z*v.z );\n",
       "        var axis = [ roundTo( v.x / r, 4 ), roundTo( v.y / r, 4 ), roundTo( v.z / r, 4 ) ];\n",
       "        var angle = roundTo( 2 * Math.atan2( r, v.w ) * 180 / Math.PI, 2 );\n",
       "\n",
       "        var textArea = document.createElement( 'textarea' );\n",
       "        textArea.textContent = JSON.stringify( axis ) + ',' + angle;\n",
       "        textArea.style.csstext = 'position: absolute; top: -100%';\n",
       "        document.body.append( textArea );\n",
       "        textArea.select();\n",
       "        document.execCommand( 'copy' );\n",
       "\n",
       "        var m = document.getElementById( 'menu-message' );\n",
       "        m.innerHTML = 'Viewpoint copied to clipboard';\n",
       "        m.style.display = 'block';\n",
       "        setTimeout( function() { m.style.display = 'none'; }, 2000 );\n",
       "\n",
       "    }\n",
       "\n",
       "    function getCamera() {\n",
       "\n",
       "        function roundTo( x, n ) { return +x.toFixed(n); }\n",
       "\n",
       "        var pos = camera.position;\n",
       "        var pos_r = [ roundTo( pos.x, 4 ), roundTo( pos.y, 4 ), roundTo( pos.z, 4 ) ];\n",
       "   //     var up = camera.up; // up is always (0,0,1)\n",
       "        var textArea = document.createElement('textarea');\n",
       "        var cam_position = JSON.stringify(pos_r);\n",
       "        textArea.textContent = ',camera_position=' + cam_position;\n",
       "        textArea.style.csstext = 'position: absolute; top: -100%';\n",
       "        document.body.append( textArea );\n",
       "        textArea.select();\n",
       "        document.execCommand( 'copy' );\n",
       "\n",
       "        var m = document.getElementById( 'menu-message' );\n",
       "        m.innerHTML = 'Camera position '+ cam_position+' copied to clipboard';\n",
       "        m.style.display = 'block';\n",
       "        setTimeout( function() { m.style.display = 'none'; }, 2000 );\n",
       "\n",
       "    }\n",
       "                                       \n",
       "</script>\n",
       "\n",
       "<div id=&quot;menu-container&quot; onclick=&quot;toggleMenu()&quot;>&#x24d8;\n",
       "<div id=&quot;menu-message&quot;></div>\n",
       "<div id=&quot;menu-content&quot;>\n",
       "<div onclick=&quot;saveAsPNG()&quot;>Save as PNG</div>\n",
       "<div onclick=&quot;saveAsHTML()&quot;>Save as HTML</div>\n",
       "<div onclick=&quot;getCamera()&quot;>Get camera</div>\n",
       "<div onclick=&quot;getViewpoint()&quot;>Get viewpoint</div>\n",
       "<div>Close Menu</div>\n",
       "</div></div>\n",
       "\n",
       "\n",
       "</body>\n",
       "</html>\n",
       "\"\n",
       "        width=\"100%\"\n",
       "        height=\"400\"\n",
       "        style=\"border: 0;\">\n",
       "</iframe>\n"
      ],
      "text/plain": [
       "Graphics3d Object"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = graphs.BidiakisCube().show3d()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e795ef04",
   "metadata": {},
   "source": [
    "### d3.js"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c32fb1f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "graphs.BidiakisCube().show(method='js')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99e656ab",
   "metadata": {},
   "source": [
    "### THREE.js"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2f729197",
   "metadata": {},
   "outputs": [
    {
     "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;:-3.0, &quot;y&quot;:-3.0, &quot;z&quot;:-0.9999997595436875}, {&quot;x&quot;:3.0, &quot;y&quot;:3.0, &quot;z&quot;:0.9999999907502205}]; // 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",
       "    var offset = new THREE.Vector3( a[0]*xRange, a[1]*yRange, a[2]*zRange );\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;: -3.0, &quot;y&quot;: -3.0, &quot;z&quot;: -0.750987246771676}, {&quot;x&quot;: -3.0, &quot;y&quot;: -2.976470588235294, &quot;z&quot;: -0.8361240484433559}, {&quot;x&quot;: -2.976470588235294, &quot;y&quot;: -2.976470588235294, &quot;z&quot;: -0.9047539076887452}, {&quot;x&quot;: -2.976470588235294, &quot;y&quot;: -3.0, &quot;z&quot;: -0.8361240484433559}, {&quot;x&quot;: -3.0, &quot;y&quot;: -2.9529411764705884, &quot;z&quot;: -0.9042817299589553}, {&quot;x&quot;: -2.976470588235294, &quot;y&quot;: -2.9529411764705884, &quot;z&quot;: -0.955194778122791}, {&quot;x&quot;: -3.0, &quot;y&quot;: -2.9294117647058826, &quot;z&quot;: -0.954536983589107}, {&quot;x&quot;: -2.976470588235294, &quot;y&quot;: -2.9294117647058826, &quot;z&quot;: -0.9868952418613239}, {&quot;x&quot;: -3.0, &quot;y&quot;: -2.905882352941177, &quot;z&quot;: -0.9863537849072523}, {&quot;x&quot;: -2.976470588235294, &quot;y&quot;: -2.905882352941177, 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