{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Function graph as a manifold\n",
    "\n",
    "This notebook is part of the [Introduction to manifolds in SageMath](https://sagemanifolds.obspm.fr/intro_to_manifolds.html) by Andrzej Chrzeszczyk (Jan Kochanowski University of Kielce, Poland)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'SageMath version 9.6, Release Date: 2022-05-15'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "version()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The graph\n",
    "$$Γ(f)=\\{(x, f(x))\\in R^{m+n}: x ∈ U  \\},$$\n",
    "\n",
    "for a smooth function $f : U → R^{m}$ and an open subset $U\\subset R^n$  is a simple example of a smooth manifold having an atlas with a single chart \n",
    "\n",
    "$$(Γ( f ), φ ),\\quad \\phi: (x, f (x)) \\to x,\\quad x\\in U.$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "### One-dimensional function graph as a manifold\n",
    "\n",
    "<br>\n",
    "\n",
    "Since we don't use any predefined charts or transitions in this case, we can use general manifold (not the Euclidean space as previously).\n",
    "\n",
    "<br>\n",
    "\n",
    "**Example 3.1**\n",
    "\n",
    "Here we use an open interval $(0,2\\pi)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "J = manifolds.OpenInterval(0, 2*pi)  # open interval J as manifold\n",
    "c.<t>=J.chart()                      # chart on J"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we plot $U=(0,2\\pi)$  as a subset of $R^2$  defined as $x(t)=t,\\quad y(t)=0.$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R2 = Manifold(2, 'R^2')             # manifold R^2\n",
    "X.<x,y> = R2.chart()                # chart on R^2\n",
    "                                    # F1: J -> R^2 :\n",
    "F1 = J.continuous_map(R2,{(c, X):[t,0]}, name='F1')\n",
    "                                    # plot c\n",
    "p1=c.plot(X,mapping=F1,thickness=4,color='grey')\n",
    "p1.show(figsize=[4,3])              # show plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And next the image of $U$ under sinus function as a subset of $R^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "                                    # continuous map x=t,y=sin(t):\n",
    "F2 = J.continuous_map(R2, {(c, X): [t,sin(t)]}, name='F2')\n",
    "p=c.plot(X,mapping=F2,color='grey',thickness=2) # plot image of J\n",
    "p.show(figsize=[4,3])                           # under F2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "**Example 3.2**\n",
    "\n",
    "Below, we map the same open interval into $R^3$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# continuation\n",
    "po1={'thickness':5,'color':'darkblue'}         # param.\n",
    "po2={'fontsize':20,'color':'black'}\n",
    "\n",
    "ax =line3d([(0,0,0), (1+0.15,0,0)], **po1)     # axes\n",
    "ax+=line3d([(0,0,0), (0,1+0.15,0)], **po1)\n",
    "ax+=line3d([(0,0,0), (0,0,6.28+0.15)], **po1)\n",
    "ax+=text3d(\"x\",(1.25,0,0),**po2)\n",
    "ax+=text3d(\"y\",(0,1.25,0),**po2)\n",
    "ax+=text3d(\"z\",(0.,0.,6.9),**po2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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",
       "        <script>// fat_lines.js\n",
       "\n",
       "var _fatLines = [];\n",
       "\n",
       "function _createFatLine( lineStrip, geometry, materialOptions ) {\n",
       "\n",
       "    var vertexCount = geometry.vertices.length;\n",
       "    var positions = [];\n",
       "    for ( var i=0 ; i < vertexCount ; i++ ) {\n",
       "        var v = geometry.vertices[i];\n",
       "        positions.push( v.x, v.y, v.z );\n",
       "        // For a line strip, duplicate all but the first and last vertices.\n",
       "        if ( lineStrip && i > 0 && i < vertexCount - 1 ) {\n",
       "            positions.push( v.x, v.y, v.z );\n",
       "        }\n",
       "    }\n",
       "\n",
       "    geometry = new THREE.LineSegmentsGeometry();\n",
       "    geometry.setPositions( positions );\n",
       "\n",
       "    var material = new THREE.LineMaterial( materialOptions );\n",
       "    material.resolution = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "\n",
       "    var line = new THREE.LineSegments2( geometry, material );\n",
       "    line.computeLineDistances();\n",
       "    line.scale.set( 1, 1, 1 );\n",
       "\n",
       "    _fatLines.push( line );\n",
       "\n",
       "    return line;\n",
       "\n",
       "}\n",
       "\n",
       "function createFatLineStrip( geometry, materialOptions ) {\n",
       "    return _createFatLine( true, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function createFatLineSegments( geometry, materialOptions ) {\n",
       "    return _createFatLine( false, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function rescaleFatLines() {\n",
       "    var res = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "    var n = _fatLines.length;\n",
       "    for ( var i=0 ; i < n ; i++ ) {\n",
       "        _fatLines[i].material.resolution = res;\n",
       "    }\n",
       "}\n",
       "</script>\n",
       "<script>\n",
       "\n",
       "    var options = {&quot;animate&quot;: false, &quot;animationControls&quot;: true, &quot;aspectRatio&quot;: [1.0, 1.0, 0.3], &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;:-0.9999050314965978, &quot;y&quot;:-0.9999647963004263, &quot;z&quot;:0.0}, {&quot;x&quot;:1.25, &quot;y&quot;:1.25, &quot;z&quot;:6.9}]; // 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 = [{&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;x&quot;, &quot;x&quot;: 1.25, &quot;y&quot;: 0.0, &quot;z&quot;: 0.0}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;y&quot;, &quot;x&quot;: 0.0, &quot;y&quot;: 1.25, &quot;z&quot;: 0.0}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;z&quot;, &quot;x&quot;: 0.0, &quot;y&quot;: 0.0, &quot;z&quot;: 6.9}];\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 = [{&quot;points&quot;: [[0.999995500003375, 0.002999995500002025, 0.001], [0.9952320050128708, 0.09753592260321854, 0.032563745262208975], [0.9815514975837362, 0.19119795394073874, 0.06412749052441795], [0.9590765514016019, 0.28314690277594506, 0.09569123578662692], [0.9280085359699147, 0.37255893113301614, 0.1272549810488359], [0.888625812393073, 0.458632931164729, 0.15881872631104488], [0.8412812393354212, 0.5405977028643922, 0.19038247157325386], [0.7863990115020437, 0.6177188638115308, 0.22194621683546284], [0.7244708589677218, 0.6893054290418518, 0.2535099620976718], [0.6560516414070527, 0.7547160020876142, 0.28507370735988075], [0.5817543767002461, 0.8133645217183426, 0.3166374526220897], [0.5022447484569627, 0.8647255128926187, 0.34820119788429865], [0.41823514166930964, 0.9083387948738358, 0.3797649431465076], [0.33047825993294844, 0.9438136043264531, 0.41132868840871656], [0.23976038142430073, 0.9708320964509125, 0.4428924336709255], [0.14689431405849965, 0.9891521927879869, 0.47445617893313446], [0.05271211294797739, 0.9986097501769946, 0.5060199241953435], [-0.041942374588680796, 0.9991200314345934, 0.5375836694575524], [-0.13622106967289657, 0.9906784645772673, 0.5691474147197614], [-0.22927926042590235, 0.9733606837850762, 0.6007111599819703], [-0.3202831703611291, 0.9473218517396419, 0.6322749052441793], [-0.4084174287984047, 0.912795269408042, 0.6638386505063882], [-0.4928923763670535, 0.8700902857285782, 0.6954023957685972], [-0.5729511401425429, 0.8195895259270705, 0.7269661410308061], [-0.6478764150253469, 0.7617454632972253, 0.7585298862930151], [-0.7169968906026851, 0.6970763651610067, 0.790093631555224], [-0.779693265910176, 0.6261616493321223, 0.821657376817433], [-0.8354037982027535, 0.5496366926874636, 0.853221122079642], [-0.8836293360193375, 0.4681871383603194, 0.8847848673418509], [-0.9239377914463521, 0.38254275256138, 0.9163486126040599], [-0.9559680115098032, 0.2934708860687765, 0.9479123578662688], [-0.9794330140092796, 0.20176959897045518, 0.9794761031284778], [-0.9941225588016728, 0.10826051025934887, 1.0110398483906868], [-0.9999050314965975, 0.01378143634707066, 1.042603593652896], [-0.9967286226861096, -0.08082111554693447, 1.074167338915105], [-0.9846217921431372, -0.17469953187354825, 1.105731084177314], [-0.9636930138295304, -0.267012687144556, 1.137294829439523], [-0.9341298039983921, -0.3569334801919339, 1.1688585747017322], [-0.8961970410986287, -0.4436562447729804, 1.2004223199639412], [-0.8502345925349312, -0.5264039681242529, 1.2319860652261503], [-0.7966542695467772, -0.6044352527879978, 1.2635498104883593], [-0.7359361374899279, -0.6770509593349721, 1.2951135557505684], [-0.6686242145793061, -0.7436004704666385, 1.3266773010127775], [-0.595321597631372, -0.8034875203720533, 1.3582410462749865], [-0.5166850584780359, -0.8561755371099717, 1.3898047915371956], [-0.4334191594668003, -0.9011924501498514, 1.4213685367994047], [-0.34626994077066825, -0.9381349199974799, 1.4529322820616137], [-0.2560182360678327, -0.9666719520089095, 1.4844960273238228], [-0.16347267648087443, -0.986547862013891, 1.5160597725860319], [-0.06946244545829716, -0.9975845671776168, 1.547623517848241], [0.025170150487281603, -0.9996831815752667, 1.57918726311045], [0.11957722862008224, -0.9928249021834317, 1.610751008372659], [0.21291292678357857, -0.9770711773501716, 1.6423147536348681], [0.3043409820990639, -0.9525631562342611, 1.6738784988970772], [0.3930422236572604, -0.9195204241464983, 1.7054422441592862], [0.47822191207045583, -0.8782390351240813, 1.7370059894214953], [0.5591168601247416, -0.8290888593656593, 1.7685697346837044], [0.6350022707332176, -0.7725102692933328, 1.8001334799459134], [0.7051982309239345, -0.7090101939335943, 1.8316972252081225], [0.7690758036781788, -0.6391575769689063, 1.8632609704703316], [0.8260626630378525, -0.5635782791545567, 1.8948247157325406], [0.8756482219929016, -0.4829494707737757, 1.9263884609947497], [0.917388207204294, -0.3979935643732085, 1.9579522062569588], [0.9509086395742484, -0.30947174213981504, 1.9895159515191678], [0.9759091849988719, -0.2181771359121704, 2.021079696781377], [0.9921658452813608, -0.12492772093143653, 2.052643442043586], [0.9995329650959022, -0.03055898700209219, 2.084207187305795], [0.9979445370204155, 0.0640835472731384, 2.115770932568004], [0.9874147929453901, 0.1581519101137015, 2.147334677830213], [0.9680380765599556, 0.2508032741614466, 2.178898423092422], [0.9399879980576732, 0.34120750798821486, 2.2104621683546313], [0.9035158786356606, 0.42855461385129223, 2.2420259136168403], [0.8589484987239187, 0.5120619850564249, 2.2735896588790494], [0.8066851701201274, 0.5909814179043712, 2.3051534041412585], [0.7471941582627953, 0.6646058153958275, 2.3367171494034675], [0.6810084866982372, 0.7322755226313228, 2.3682808946656766], [0.6087211613322387, 0.7933842371425907, 2.3998446399278857], [0.530979857255832, 0.8473844412004367, 2.4314083851900947], [0.44848111574979727, 0.8937923074270762, 2.462972130452304], [0.36196410346118246, 0.9321920337599664, 2.494535875714513], [0.2722039896679489, 0.9622395689270168, 2.526099620976722], [0.18000500096967995, 0.983665695053917, 2.557663366238931], [0.08619321563245971, 0.9962784397842485, 2.58922711150114], [-0.008390837851332296, 0.9999647963004261, 2.620790856763349], [-0.10289971167338402, 0.9946917358345421, 2.652354602025558], [-0.19648663161503252, 0.980506503597288, 2.6839183472877672], [-0.28831308391766647, 0.9575361954735103, 2.7154820925499763], [-0.3775563281416168, 0.9259866192770929, 2.7470458378121854], [-0.4634167687003264, 0.8861404507680192, 2.7786095830743944], [-0.5451251190228343, 0.8383547009532067, 2.8101733283366035], [-0.6219492941555831, 0.7830575173634259, 2.8417370735988126], [-0.693200970047704, 0.7207443479659915, 2.8733008188610216], [-0.7582417507503108, 0.6519735020835614, 2.9048645641232307], [-0.8164888882733622, 0.5773611480920144, 2.9364283093854397], [-0.867420503851716, 0.4975757927166826, 2.967992054647649], [-0.910580263839203, 0.41333229139099154, 2.999555799909858], [-0.9455814683359823, 0.3253854433430721, 3.031119545172067], [-0.9721105159161632, 0.2345232287966611, 3.062683290434276], [-0.9899297134126578, 0.14155974887916814, 3.094247035696485], [-0.998879405584355, 0.04732793149341963, 3.125810780958694], [-0.9988794055843533, -0.04732793149345261, 3.157374526220903], [-0.9899297134126531, -0.14155974887920084, 3.1889382714831123], [-0.9721105159161555, -0.23452322879669318, 3.2205020167453213], [-0.9455814683359722, -0.32538544334310165, 3.2520657620075304], [-0.91058026383919, -0.41333229139101996, 3.2836295072697395], [-0.8674205038516996, -0.49757579271671126, 3.3151932525319485], [-0.8164888882733432, -0.5773611480920413, 3.3467569977941576], [-0.7582417507502892, -0.6519735020835864, 3.3783207430563666], [-0.6932009700476802, -0.7207443479660144, 3.4098844883185757], [-0.6219492941555572, -0.7830575173634464, 3.4414482335807848], [-0.5451251190228066, -0.8383547009532247, 3.473011978842994], [-0.4634167687002987, -0.8861404507680336, 3.504575724105203], [-0.3775563281415879, -0.9259866192771047, 3.536139469367412], [-0.2883130839176349, -0.9575361954735199, 3.567703214629621], [-0.19648663161500016, -0.9805065035972944, 3.59926695989183], [-0.10289971167335206, -0.9946917358345454, 3.630830705154039], [-0.008390837851299283, -0.9999647963004263, 3.6623944504162482], [0.0861932156324926, -0.9962784397842456, 3.6939581956784573], [0.18000500096971242, -0.983665695053911, 3.7255219409406664], [0.2722039896679798, -0.9622395689270081, 3.7570856862028754], [0.36196410346121155, -0.9321920337599551, 3.7886494314650845], [0.44848111574982674, -0.8937923074270613, 3.8202131767272935], [0.5309798572558599, -0.8473844412004191, 3.8517769219895026], [0.6087211613322643, -0.7933842371425711, 3.8833406672517117], [0.6810084866982614, -0.7322755226313002, 3.9149044125139207], [0.7471941582628173, -0.6646058153958029, 3.94646815777613], [0.806685170120147, -0.5909814179043446, 3.978031903038339], [0.8589484987239351, -0.5120619850563973, 4.0095956483005475], [0.9035158786356733, -0.42855461385126564, 4.041159393562756], [0.9399879980576826, -0.34120750798818883, 4.072723138824965], [0.9680380765599624, -0.2508032741614198, 4.104286884087173], [0.9874147929453944, -0.15815191011367505, 4.135850629349382], [0.9979445370204171, -0.06408354727311433, 4.167414374611591], [0.9995329650959015, 0.03055898700211454, 4.198978119873799], [0.992165845281358, 0.12492772093145871, 4.230541865136008], [0.9759091849988671, 0.21817713591219132, 4.2621056103982164], [0.9509086395742425, 0.3094717421398329, 4.293669355660425], [0.9173882072042873, 0.39799356437322414, 4.325233100922634], [0.8756482219928934, 0.48294947077379063, 4.356796846184842], [0.8260626630378434, 0.56357827915457, 4.388360591447051], [0.7690758036781702, 0.6391575769689166, 4.4199243367092595], [0.7051982309239263, 0.7090101939336025, 4.451488081971468], [0.6350022707332085, 0.7725102692933402, 4.483051827233677], [0.5591168601247326, 0.8290888593656655, 4.514615572495885], [0.4782219120704487, 0.8782390351240852, 4.546179317758094], [0.3930422236572545, 0.9195204241465008, 4.577743063020303], [0.3043409820990578, 0.952563156234263, 4.609306808282511], [0.2129129267835732, 0.9770711773501728, 4.64087055354472], [0.11957722862007944, 0.992824902183432, 4.6724342988069285], [0.025170150487280562, 0.9996831815752667, 4.703998044069137], [-0.0694624454582982, 0.9975845671776168, 4.735561789331346], [-0.16347267648087457, 0.986547862013891, 4.767125534593554], [-0.25601823606783025, 0.9666719520089102, 4.798689279855763], [-0.3462699407706642, 0.9381349199974813, 4.830253025117972], [-0.43341915946679643, 0.9011924501498533, 4.86181677038018], [-0.5166850584780315, 0.8561755371099744, 4.893380515642389], [-0.5953215976313658, 0.803487520372058, 4.9249442609045975], [-0.668624214579299, 0.7436004704666449, 4.956508006166806], [-0.735936137489921, 0.6770509593349794, 4.988071751429015], [-0.7966542695467709, 0.6044352527880061, 5.019635496691223], [-0.8502345925349245, 0.5264039681242637, 5.051199241953432], [-0.8961970410986221, 0.4436562447729938, 5.082762987215641], [-0.9341298039983865, 0.35693348019194826, 5.114326732477849], [-0.9636930138295262, 0.26701268714457127, 5.145890477740058], [-0.984621792143134, 0.17469953187356602, 5.177454223002266], [-0.996728622686108, 0.08082111554695467, 5.209017968264475], [-0.9999050314965978, -0.013781436347049944, 5.240581713526684], [-0.9941225588016751, -0.10826051025932783, 5.272145458788892], [-0.9794330140092843, -0.20176959897043228, 5.303709204051101], [-0.9559680115098106, -0.2934708860687525, 5.3352729493133095], [-0.9239377914463619, -0.38254275256135634, 5.366836694575518], [-0.8836293360193495, -0.46818713836029674, 5.398400439837727], [-0.8354037982027674, -0.5496366926874422, 5.429964185099935], [-0.7796932659101943, -0.6261616493320995, 5.461527930362144], [-0.7169968906027054, -0.6970763651609858, 5.493091675624353], [-0.6478764150253695, -0.7617454632972062, 5.524655420886561], [-0.5729511401425701, -0.8195895259270515, 5.55621916614877], [-0.49289237636708233, -0.8700902857285618, 5.5877829114109785], [-0.4084174287984352, -0.9127952694080284, 5.619346656673187], [-0.3202831703611609, -0.9473218517396311, 5.650910401935396], [-0.22927926042593505, -0.9733606837850686, 5.682474147197604], [-0.13622106967293338, -0.9906784645772623, 5.714037892459813], [-0.041942374588718134, -0.9991200314345918, 5.745601637722022], [0.05271211294793984, -0.9986097501769966, 5.77716538298423], [0.14689431405845874, -0.989152192787993, 5.808729128246439], [0.23976038142426057, -0.9708320964509224, 5.8402928735086475], [0.3304782599329092, -0.9438136043264669, 5.871856618770856], [0.4182351416692719, -0.9083387948738533, 5.903420364033065], [0.5022447484569265, -0.8647255128926397, 5.934984109295273], [0.5817543767002091, -0.813364521718369, 5.966547854557482], [0.6560516414070184, -0.7547160020876442, 5.9981115998196906], [0.7244708589676904, -0.6893054290418847, 6.029675345081899], [0.7863990115020132, -0.6177188638115696, 6.061239090344108], [0.8412812393353944, -0.5405977028644339, 6.092802835606316], [0.8886258123930502, -0.45863293116477316, 6.124366580868525], [0.9280085359698962, -0.37255893113306243, 6.155930326130734], [0.9590765514015877, -0.28314690277599314, 6.187494071392942], [0.9815514975837258, -0.19119795394079156, 6.219057816655151], [0.9952320050128656, -0.09753592260327226, 6.2506215619173595], [0.9999955000033748, -0.002999995500056164, 6.282185307179568]], &quot;color&quot;: &quot;#808080&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 3.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [1.15, 0.0, 0.0]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 5.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [0.0, 1.15, 0.0]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 5.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [0.0, 0.0, 6.430000000000001]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 5.0}];\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 = [];\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": [
    "J=manifolds.OpenInterval(0,2*pi)  # open interval as manifold\n",
    "c.<t>=J.chart()                   # chart on J\n",
    "R3 = Manifold(3, 'R^3')           # manifold R^3\n",
    "X.<x,y,z> = R3.chart()            # chart on R^3\n",
    "                                  # F: J -> R^3:\n",
    "F=J.continuous_map(R3,{(c,X):[cos(3*t),sin(3*t),t]},name='F')\n",
    "p=c.plot(X,mapping=F,color='grey',thickness=3,\n",
    "  plot_points=200,label_axes=False)  # plot image of J\n",
    "(p+ax).show(aspect_ratio=[1,1,0.3],frame=False)  # show plot\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two-dimensional function graph as a manifold\n",
    "\n",
    "<br>\n",
    "\n",
    "**Example 3.3**\n",
    "\n",
    "Now let $U$ be an open rectangle $(-\\pi,\\pi)\\times (-\\pi,\\pi)$ in $R^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "R2 = Manifold(2, 'R^2')                  # manifold R^2\n",
    "c_xy.<x,y> = R2.chart()                  # chart on R^2 \n",
    "U = R2.open_subset('U',                  # open subset of R^2\n",
    "    coord_def={c_xy: [x>-pi,x<pi,y>-pi,y<pi]})\n",
    "c_U.<x,y>=U.chart()                      # chart on U"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we plot the coordinate lines in the set $(-\\pi,\\pi)\\times(-\\pi,\\pi)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 30 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p=c_U.plot(number_values={x:15,y:15},color='grey')  # plot\n",
    "p.show(figsize=4)                        # coordinate lines on U"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The graph of the function $f(x,y)=\\cos(\\sqrt{x^2+y^2})$ as a subset of $R^3$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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",
       "        <script>// fat_lines.js\n",
       "\n",
       "var _fatLines = [];\n",
       "\n",
       "function _createFatLine( lineStrip, geometry, materialOptions ) {\n",
       "\n",
       "    var vertexCount = geometry.vertices.length;\n",
       "    var positions = [];\n",
       "    for ( var i=0 ; i < vertexCount ; i++ ) {\n",
       "        var v = geometry.vertices[i];\n",
       "        positions.push( v.x, v.y, v.z );\n",
       "        // For a line strip, duplicate all but the first and last vertices.\n",
       "        if ( lineStrip && i > 0 && i < vertexCount - 1 ) {\n",
       "            positions.push( v.x, v.y, v.z );\n",
       "        }\n",
       "    }\n",
       "\n",
       "    geometry = new THREE.LineSegmentsGeometry();\n",
       "    geometry.setPositions( positions );\n",
       "\n",
       "    var material = new THREE.LineMaterial( materialOptions );\n",
       "    material.resolution = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "\n",
       "    var line = new THREE.LineSegments2( geometry, material );\n",
       "    line.computeLineDistances();\n",
       "    line.scale.set( 1, 1, 1 );\n",
       "\n",
       "    _fatLines.push( line );\n",
       "\n",
       "    return line;\n",
       "\n",
       "}\n",
       "\n",
       "function createFatLineStrip( geometry, materialOptions ) {\n",
       "    return _createFatLine( true, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function createFatLineSegments( geometry, materialOptions ) {\n",
       "    return _createFatLine( false, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function rescaleFatLines() {\n",
       "    var res = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "    var n = _fatLines.length;\n",
       "    for ( var i=0 ; i < n ; i++ ) {\n",
       "        _fatLines[i].material.resolution = res;\n",
       "    }\n",
       "}\n",
       "</script>\n",
       "<script>\n",
       "\n",
       "    var options = {&quot;animate&quot;: false, &quot;animationControls&quot;: true, &quot;aspectRatio&quot;: [1.0, 1.0, 1.8], &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;:-4.2914953731462235, &quot;y&quot;:-4.2914953731462235, &quot;z&quot;:-0.9999999892205398}, {&quot;x&quot;:4.2914953731462235, &quot;y&quot;:4.2914953731462235, &quot;z&quot;:1.0}]; // 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",
       "    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 = [{&quot;points&quot;: [[-1.149536694152646, -4.290129347742439, -0.2676182393664917], [-1.076027693586496, -4.247688906477712, -0.32454346577871984], [-1.0025186930203462, -4.205248465212985, -0.37953445991563134], [-0.9290096924541964, -4.162808023948258, -0.4324222210316291], [-0.8555006918880466, -4.120367582683531, -0.48305971223931665], [-0.7819916913218963, -4.077927141418804, -0.5313222344165983], [-0.7084826907557464, -4.035486700154077, -0.5771076049931826], [-0.6349736901895966, -3.9930462588893496, -0.6203361430889544], [-0.5614646896234468, -3.9506058176246226, -0.6609504640392592], [-0.4879556890572969, -3.9081653763598956, -0.6989150878697893], [-0.41444668849114685, -3.8657249350951686, -0.7342158677646979], [-0.3409376879249968, -3.8232844938304416, -0.7668592459942795], [-0.26742868735884695, -3.7808440525657145, -0.7968713461221432], [-0.1939196867926969, -3.7384036113009875, -0.824296911585862], [-0.12041068622654727, -3.6959631700362605, -0.8491981019298744], [-0.04690168566039743, -3.653522728771534, -0.8716531590559641], [0.02660731490575219, -3.611082287506807, -0.8917549568367322], [0.10011631547190203, -3.56864184624208, -0.9096094483037411], [0.17362531603805165, -3.5262014049773533, -0.9253340253680231], [0.2471343166042015, -3.4837609637126263, -0.9390558066509223], [0.3206433171703511, -3.4413205224478993, -0.9509098694932744], [0.39415231773650095, -3.3988800811831723, -0.9610374425672924], [0.46766131830265056, -3.3564396399184453, -0.9695840757357926], [0.5411703188688004, -3.3139991986537187, -0.9766978038862478], [0.6146793194349501, -3.2715587573889917, -0.98252732141235], [0.6881883200010999, -3.2291183161242647, -0.9872201838241187], [0.7616973205672497, -3.186677874859538, -0.9909210526410193], [0.8352063211333995, -3.144237433594811, -0.9937699992640197], [0.9087153216995494, -3.101796992330084, -0.9959008829360005], [0.9822243222656992, -3.059356551065357, -0.9974398171904326], [1.055733322831849, 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       "    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;: -1.1499027195564306, &quot;y&quot;: -4.2914953731462235, &quot;z&quot;: -0.26625534204141565}, {&quot;x&quot;: -1.2304563773407844, &quot;y&quot;: -4.151972345128207, &quot;z&quot;: -0.3727097141275432}, {&quot;x&quot;: -1.0909333493227675, &quot;y&quot;: -4.0714186873438525, &quot;z&quot;: -0.4770949182830191}, {&quot;x&quot;: -1.0103796915384138, &quot;y&quot;: -4.210941715361869, &quot;z&quot;: -0.3727097141275432}, {&quot;x&quot;: -1.3110100351251381, &quot;y&quot;: -4.01244931711019, &quot;z&quot;: -0.47167803722521756}, {&quot;x&quot;: -1.1714870071071213, &quot;y&quot;: -3.9318956593258356, &quot;z&quot;: -0.5726087097224786}, {&quot;x&quot;: -1.391563692909492, &quot;y&quot;: -3.872926289092172, &quot;z&quot;: -0.5622060206139605}, {&quot;x&quot;: -1.252040664891475, &quot;y&quot;: -3.7923726313078188, &quot;z&quot;: -0.6583931671919214}, {&quot;x&quot;: -1.4721173506938456, &quot;y&quot;: -3.733403261074155, 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[1496, 1497, 1537, 1536], [1497, 1498, 1538, 1537], [1498, 1499, 1539, 1538], [1499, 1500, 1540, 1539], [1500, 1501, 1541, 1540], [1501, 1502, 1542, 1541], [1502, 1503, 1543, 1542], [1503, 1504, 1544, 1543], [1504, 1505, 1545, 1544], [1505, 1506, 1546, 1545], [1506, 1507, 1547, 1546], [1507, 1508, 1548, 1547], [1508, 1509, 1549, 1548], [1509, 1510, 1550, 1549], [1510, 1511, 1551, 1550], [1511, 1512, 1552, 1551], [1512, 1513, 1553, 1552], [1513, 1514, 1554, 1553], [1514, 1515, 1555, 1554], [1515, 1516, 1556, 1555], [1516, 1517, 1557, 1556], [1517, 1518, 1558, 1557], [1518, 1519, 1559, 1558], [1521, 1520, 1560, 1561], [1520, 1522, 1562, 1560], [1522, 1523, 1563, 1562], [1523, 1524, 1564, 1563], [1524, 1525, 1565, 1564], [1525, 1526, 1566, 1565], [1526, 1527, 1567, 1566], [1527, 1528, 1568, 1567], [1528, 1529, 1569, 1568], [1529, 1530, 1570, 1569], [1530, 1531, 1571, 1570], [1531, 1532, 1572, 1571], [1532, 1533, 1573, 1572], [1533, 1534, 1574, 1573], [1534, 1535, 1575, 1574], [1535, 1536, 1576, 1575], [1536, 1537, 1577, 1576], [1537, 1538, 1578, 1577], [1538, 1539, 1579, 1578], [1539, 1540, 1580, 1579], [1540, 1541, 1581, 1580], [1541, 1542, 1582, 1581], [1542, 1543, 1583, 1582], [1543, 1544, 1584, 1583], [1544, 1545, 1585, 1584], [1545, 1546, 1586, 1585], [1546, 1547, 1587, 1586], [1547, 1548, 1588, 1587], [1548, 1549, 1589, 1588], [1549, 1550, 1590, 1589], [1550, 1551, 1591, 1590], [1551, 1552, 1592, 1591], [1552, 1553, 1593, 1592], [1553, 1554, 1594, 1593], [1554, 1555, 1595, 1594], [1555, 1556, 1596, 1595], [1556, 1557, 1597, 1596], [1557, 1558, 1598, 1597], [1558, 1559, 1599, 1598]], &quot;color&quot;: &quot;#d3d3d3&quot;, &quot;opacity&quot;: 0.7}];\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": [
    "R3 = Manifold(3, 'R^3')                     # manifold R^3\n",
    "c_XYZ.<X,Y,Z> = R3.chart()                  # chart on R^3\n",
    "F = U.continuous_map(R3,                    # F: U -> R^3\n",
    "  {(c_U, c_XYZ): [x,y,cos(sqrt(x^2+y^2))]}, name='F')\n",
    "                    # plot the image of coordinate lines in  U:\n",
    "p1=c_U.plot(c_XYZ,mapping=F,number_values={x:15,y:15},\n",
    "  color='black',thickness=2,label_axes=False)\n",
    "s=plot3d(cos(sqrt(x^2+y^2)),(x,-pi,pi),(y,-pi,pi),\n",
    "         color='lightgrey',opacity=0.7)     # plot  image of U                 \n",
    "(p1+s).rotateZ(-pi/6).show(frame=False,aspect_ratio=[1,1,1.8]) \n",
    "                                            # show plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example 3.4**\n",
    "\n",
    "Now we show a similar example using  polar coordinates. We need two charts in this example. If we don't use the Euclidean space, **we need to define both Cartesian and polar coordinates and also the transition map**  \n",
    "\n",
    "$$\\ \\ x=r\\cos\\phi,\\ \\ y=r\\sin\\phi.$$\n",
    "\n",
    "First we plot the coordinate lines $r,\\phi$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kEsHT0xOhoaGMleQz0dnZiaSkJHR0dMDZ2RmrVq2as77rHxAqYvolgSAI5OfnIzU1FTweD9HR0fD29p6TDDo7O5GWloaWlhbo6+sjJCQEixYtgkwmw2effYaIiAhERkYyflcqlaKhoYGKochkMjg4OMDV1RVOTk4wMzP7wRqtPX/+HIWFhfjkk09AEAREIhFVrEmCdDlbW1spYtLS0oKWltYPsh8SiQR/+tOfsHLlSgQHB4MgCAwODqK5uRl1dXVUDI4sGXBxcXktS0osFqO0tBR5eXkYGRmBvb09li9fPufDhCAI1NTUICUlBePj41i+fDlCQkL+Wdw7FTH9UjAyMoL4+Hi0tbUhKCgI0dHRcwZJR0dHkZKSgqqqKpiZmWHJkiXw9PRUuLEfPXqEuro6fPjhh5TLNTPrVF1djampKVhYWFBZp+9rqUilUgwNDaG/vx9jY2NUoLq7uxuDg4PQ1dWFUChknJ6iLCvHZrMZs3E8Hg/6+vowMzNT2o5lJlpaWhAbG4t3332X0bXl8/mUPq67uxsaGhpU1tLR0fGVpCGXy1FXV4fMzEz09va+lvstkUiQlpaGvLw8aGlpYdOmTXB3d5/zd/4BoCKm+Q6CIFBcXIykpCRwuVxs2rQJjo6OSj//JoFUsuJ68+bNcHFxQWFhIYqLi8Hn82FoaEhJVb5Lnc3shmwzA87ktSaFtjweDzKZDF1dXQgLC4OBgQF4PB7NEuLz+fD19UVZWRl0dXVBEAQmJycVMnCzM3SkQJjFYsHIyIgmkTE2NqbOTVpaGoqKivDb3/72lRbY0NAQVec1PDwMHo+HgIAABAYGvtI1JhMWqampEAqFr5WwuH37NmpqaqCmpoYVK1YgKCjoH7kt8Lw5MBUxMWBsbAwPHz5Ec3MzFi9ejJiYGKUdHcnU8/PnzyGRSF479Xzp0iUMDg5CLBYDAHx9feHn5/fKyubZIAgCvb29VGaura2NKpDU1taGubk5LUU/0+p5Hb3cd4kxMenjBgYGqBYq6urqsLOzg6OjIyoqKmBoaIidO3e+0XH39PSgtLQUpaWlkMvl8PX1RWho6CvjQkwlHoGBgbQyg87OTly4cAHLly8Hn89HYWEhHBwcsHHjRhgaGr72vv6CoCKm+QiCIFBWVobExERoaGhg48aNcHZ2VvrZhoYGJCUlYWhoCH5+fli2bNkrF25HRwdycnJQW1sLAFi0aBFWrFjx2hXdZCcBMjPX2tqKyclJqKmpUQvdysrqtZv+v45e7ocMfguFQgwMDKCrqwutra0Ukaqrq2PBggVUUN/ExOS1CXpychJFRUUoKCiAQCCAq6srQkNDYW9vP+c2ZhbFGhgYYMWKFfDw8ACLxYJUKsU333wDTU1NHDlyBGw2Gy0tLYiPj8fk5CRWrlwJf3//fzTrad4cjIqY/gaRSIQHDx6grq4Ovr6+WL16tdIskEAgQEJCAurr6+Ho6IiYmJg5a2/IGEdOTg46OzthYmKCkJAQ5ObmwtTU9JWWAmkVkfGnsbExsNlsWFtbUwvZxsbmOxVlTkxM4NNPP8WOHTsUWt4CP165wEzU19fjxo0bCAwMRF9fHzo7OyGXy6GrqwsvL6836r4glUpRUVGB3NxcDAwMwNLSEmFhYbQY32z09/cjOTkZjY2NcHZ2xoYNG1BUVITs7GwcP34cZmZm1GenpqaQlJSEkpISODs7Y+vWrXO6gr8wqIhpPmFgYAA3b97ExMTEnEFOgiBQVVWFJ0+egM1mY926dXB3d59z0TQ3NyMpKQl9fX2wt7dHWFgYXFxcwGKxUFxcjEePHuGDDz5gDMQODw9TUpXBwUFwuVx4eXnBxcUFdnZ2bzQwQBkIgsD/+T//B2vXrkVAQADjZ37McoHU1FS8fPkSv/nNb8BisSAWi9He3o6GhgaFflVk3M3Y2Pi1jqmpqQm5ublobm6GqakpYmJilFq/JOrr65GQkACxWAyJRIIlS5Zg2bJljJ9taGjA/fv3oaWlhZ07d75RPdo8hoqY5gvq6upw79496OvrY9euXUozNUKhEE+ePEF1dTW8vLywdu3aOd2vgYEBJCcno6GhAba2tli5ciVsbW0VPiORSPDZZ59h4cKFWL16NfU7szs0khkoJyenH0w3x+fzqUB1QUEB9PT0oKWlRQWyZ94XIpEI//Ef/4Hf//73VGBcWTaOnCVnamr6Wvq4CxcuQF9fn7HyXC6Xo6WlhdLHicViWFlZwdvbG97e3q+lcevq6kJycjLa2tqwYMECrFy5ck4SEQgEOHXqFEQiEVxdXbFhwwalnURHRkZw69YtDA8PY/PmzfD09Hzl/sxzqIjp5wZBEMjMzERGRgbc3d2xefNmpRZITU0NHj9+DLlcjnXr1sHLy0vpdoVCIdLT01FSUkKLWzAhNTUVBQUF2LdvH4qLi6lWH87OzvDx8YGbm9t3mmo7OTlJa8zW39+v0E5XQ0MDPB4PfD4fOjo6cHJyoroFzAwECwQCREdHIzU1FTo6OpDJZJicnGTMyM2cR8ekjzM1NaUIXSwW409/+hPWrFmj1FojIZFIqNousie6l5cXQkNDYWlpOed3CYJAXV0dkpOTMTIyQsUDmYjtxYsXSE9PR3R0NHJzcyGXy7F27Vp4e3szblssFuPhw4eoqqqiLKxfcNxp3uz4PyUxTU1NIT4+HjU1NYiKisLSpUsZb6bJyUkkJiaivLwcbm5uWL9+vdKnp0QiQV5eHrKyssBms7F06VIEBgbOGfchCAKVlZW4d+8eAEBPTw/BwcHw8/N74/YmQqFQoZHcyMgIgOl0vb6+Pjo6OlBZWYmenh7o6uriL3/5C4KCggBM6+V0dHSwbds2xm2/iSsnlUoxNjZGy8YNDg5SNVIGBgZwdHQEl8tFdnb2KztozoZIJEJpaSny8/MxOjoKR0dHhIaGwtnZeU5SkMlkKCoqwvPnzyGVShEeHo7Q0FAqgzo4OIgzZ84gODgYK1euVLCSPT09sW7dOsbrQhAEsrOzkZqaChcXF2zduvWXOrxTRUw/F4aHh3Hz5k2MjY1hy5YtSuNJbW1tuHv3LsRiMdasWYOFCxcqvekbGxvx6NEj8Pl8BAYGYunSpXMSi0wmQ2VlJXJzc9HX1wctLS2w2Wz8+te/fm3raGpqitKZzRTwmpiYUB0tzczMwGazERgYiGXLluHEiRMwMzNDU1MTHBwcKD3YXHo54IeJMZH6uP7+fnR0dKClpYUaHUUKeUm93+suarlcjpqaGuTk5KC7uxumpqYIDQ2Fj4/PnA+EmTVnXC4X69atg4uLC7799lsIhUK8++67CtehsrKSiitu27ZNaT1bQ0MD7t69Cx0dHezateuXKGdREdPPgebmZty5cwdcLhe7du1iLGAkCAJFRUVITEyEra0ttm7dqnQxTk1N4dmzZ3j58iUWLFiANWvWzBmclclkKCwsRE5ODvh8PlxcXKgn9vnz5xkzY7N/r7a2FpWVlWhqalIQ8JJ/s92Tf/u3f0N2djZevHihdLuz9XJvOiL8u+Kbb76BmpoaTE1NKSEvi8WCo6MjfHx84OHh8VoBfoIg0N7ejtzcXNTV1UFHRwehoaEICgqak6BGRkbw9OlTNDQ0wMrKCt3d3UrLJgQCAe7fv4+WlhasWrVKaaHl0NAQbt68ifHxcWzfvh0uLi5vdlJ+XqiI6adGbW0t4uLi4ODggO3btzM+laVSKZ4+fYqSkhIEBQUhJiZGaW+fmTUtMTExWLx4sVKLaqb+anR0lCoEnJmGvnTpElgsFg4dOqTwXZlMRvUeqqurg1QqpYZXOjs7w9DQcE73xdPTE6tWrUJnZyeeP38Oa2trnDx5EseOHaM+8/z5cxQVFeE3v/kNAOB//a//hT/84Q+0bf2QxDQ1NYU//elPWLduHfz9/QFME0VTUxMqKyvR1tYGNTU1uLq6wsfHB87Ozq9VDjE0NIScnBy8fPkS+vr6WLFiBTw9Pee8Njk5OUhJSYG6ujp27NihNHsnl8uRkpKC3Nxc+Pr6Yv369Yz7NDU1hXv37qGxsRFbt26dMyY5z6Aipp8S9+/fR3l5OTw9PbF161ZGshEIBLh9+za6u7uxbt06LFq0iHFbYrEYKSkpVBXwpk2b5myr0dXVhaSkJLS3t8PZ2RkrV65UICQS1dXVuHPnDt555x1YWlqis7MTpaWlqK6uxuTkJMzMzCjd3Js05ycJ+OOPP8Zbb72FgoIC/OY3v8Hnn3+O6OhoCIVC1NTUoLq6GosXL4ZQKIRAIFBorzs5OUl9hwyMz87EkX86OjowMjJ6JYk0NDTg+vXreP/99xmtzLGxMVRWVqKyshK9vb3Q1NSEp6cn/Pz8YGtr+1qFo2Q7YxsbG8TExNCyosA0MV29ehUDAwMwNjZGa2vrK6v9y8vLkZCQADMzM+zcuZORrGUyGeLj41FZWYlNmzbB19d3zv2dJ1AR00+F0tJSxMfHAwCWLFmC5cuX0z7T1dWFW7dugSAI7Ny5U+lMsvb2dsTHx2N8fPyVuqnR0VGkpaWhoqICZmZmiImJmbPHj1wuxxdffAEDAwPI5XJ0dHRAX1+fqt/5LnUycrkcVlZWCA0NxYcffkgFpAcGBhT2m81mQy6Xw8LCgpo7N5NYJiYmsHPnTty6dQtcLhdSqZSmjSM7VQLM+rjZ8+OSkpJQWVmJjz766LVIhtTHjY6OvtFoppaWFiQlJaG3txeenp5YsWKFgpykpKQECQkJ2Lt3LxYsWPDa+sju7m7cunULMpkMO3bsYOxYIJfL8ejRI7x8+RLr1q17ZeZxHkBFTD8FCgsL8eTJE/j7+0NfXx9paWlYvXo1goODqc+Ulpbi0aNHsLS0xI4dOxhTyHK5HBkZGXjx4gVsbGywefNmpbEkqVSK58+fIzc3F9ra2li2bBn8/PzmXEASiQRlZWVIT0/HxMQErK2tsWTJEri6ur5R6pkU5JIB8c7OTmrcN5fLpQiipqYG165dQ3JyMng8Hnp6enD58mWl2bHXCX6LxWIIhULw+XwFAuzv76f0cRwOh6pWr6yshIWFxZydM2eDaTRTcHAwFi1aNKc2kZQapaWlQSgUIiQkBFFRURCJRDh16hRVLkJiZkeJsLAwREdHM14/oVCIO3fuoKOjQ2nJA0EQSExMREFBAWJiYhAaGvrax/szYN4Q0z/slJScnBwkJycjJCSEGplEpv+5XC68vb2RmpqK7OxsLFq0CGvXrmV0P0QiEe7du4eGhgYsX74c4eHhSkmmq6sLDx48wMjICMLCwhARETHngpk94snV1RVNTU1wcnKCm5vbK4+RHPRI6uZI3ZmmpiYcHR0RHR2NCxcuoLm5GWlpadT3kpKSoKmpSRWTkqp8oVD4nTNJGhoa0NDQgKGhIc16IPVxfX19aG1tRV5eHqampjA6OoqrV69SgftXSU+YRjM9e/YMGRkZc45mYrFY8PPzg5eXF3JycpCVlYXa2lro6OhAXV0dq1atUvi8oaEhDh48iNzcXKSkpKCvrw/btm2jSU94PB7279+PZ8+e4fHjxxgcHMSqVasUjoHFYmH16tXQ0NBAUlISxGKx0vIUFf6OfziLaWbh5OyCN4Ig8PDhQ5SVlcHZ2RkNDQ2IiYlBSEgI440yODiImzdvQigUYtu2bUqDojKZDM+fP0dWVhYsLCywefNmxjgSCbFYTKnbAVAtYA0NDfH06VNUVFTgo48+Ulo6MHPq7NjYmIKAl1zgJHkWFhYiLCwMf/jDH7Bjxw4UFBTg2LFjOHv2LDXtdi69HPDDS1Jqampw+/ZthIeHo7e3F+3t7ZBIJNDT01NwXV9n8Y6OjiI/Px8lJSWQy+UICwtDeHj4nA+EwcFB3LhxA8PDw3Bzc8P27duVxsSam5sRFxcHLS0t7Nq1S+l1Ja3zRYsWYf369YwPr8zMTKSnpyM8PBzR0dHzkZzmzQ79wxFTamoqsrKysHz5cixZsoT2vlQqxZdffonx8XGEh4djxYoVjNupr6/HvXv3oKenh507dyp13Xp7e/HgwQMMDAxg6dKliIiIUJrJm+lSTExMICgoCEuWLFF4Eg8PD+PLL7/E+vXrqWwVML0ASd1cf38/tLW14enpCS8vL9ja2s4ZbH706BF+97vfoaGhAY6Ojvj4448VsnKv0sv90MT07Nkz1NTU4MMPPwSLxYJMJkNHRweqqqpQVVWFyclJmJqaUiT1Oi1GRCIRsrKyqMZuy5Ytw6JFi5S6YKdOnYKuri6GhoZgZGSEzZs3w8rKinHbM6UnW7ZsUVrSUVZWhvj4eHh7e2Pz5s2Mv52Xl4dnz54hODiYZl3NA8ybnfmHIibyoq9cuRJhYWG092UyGe7fv4/q6moYGRlBKBTi0KFDCoFlgiAoWYKbmxu2bNnCmJ2Ry+XIysrC8+fPYWJigs2bN88pjZgZhPXy8kJ0dLTSBXfz5k0MDw/jnXfeQXV1NYqLi9He3g41NTW4u7vD29sbzs7OrxxTNBfINrpk8PrGjRuws7ODlZUVhEIh1ScKmLao9u3bh6tXr4LL5VJSFqasHDlEcy588803MDc3V4jrkJDJZGhubkZFRQVqa2shkUhgY2ODgICA1xrNNDvpsHLlSpqle/fuXTQ1NeHkyZOYmJjAgwcP0NvbS7U7ZvqN15WeVFVV4d69e3B1dcW2bdsYHxikdRUdHY2IiIg5j+cnhoqYfmiQ6fawsDCsXLmS9r5UKkVcXBwaGhqwfft2ODo64vLlyxAIBDhy5AgMDQ0hFovx4MED1NTUIDIyEpGRkYw33/j4OFVaEB4ejsjISKUWy+DgIJKTk1+Ztp4JshUIl8vFxMQEnJycsHDhQri7u3+njgKTk5OM8+Zm6uaA6XiIjo4OeDweNDQ00N3dje7ubojFYpw/fx6nT5+GlpYWFehmasWrpaWloIsj/5ushJ+cnMR//dd/YePGjUpLMkiIxWLU1dWhrKwMTU1NbzSaaWaZxoIFC7Bq1SqYmpqirq4ON2/exJYtW7Bw4UIA02SYlZWFzMxMqgSAqSRjpvTE1dUVW7ZsYdyP+vp63L59G46OjtixYwejS56eno7MzExs3boVPj4+cx7LTwgVMf2QaG9vR2xsLDw8PLB161YamUgkEty6dQttbW3YsWMHVY0rEAhw6dIlEASBPXv2UC7ZXFKV9vZ23L59GxwOB2+99ZbS0gK5XI68vDykpaVBV1f3lYV+wHTtTn5+PoqLiyEWi6Grq4u9e/e+canA6OgolZlrbW0Fn88HMF0WYGxsTJGFsbExRUQPHz6Erq4u3nrrLdr2lLlyBEFgamqKIimBQIDBwUGK+Gbq43R1dWFvbw9tbW0UFhbiww8/fKN6rIGBAeTm5qK8vPy1RzMRBIHa2lqkpKRgbGwM4eHhKCkpgYWFBfbs2UO7Fj09Pbh9+zampqbw1ltvvVJ6YmRkhH379jHKj5qbm3Hz5k1YW1tj165dtAcKQRCIj49HRUUF9u3bN2fb5p8QKmL6oTA4OIiLFy/CzMwM+/bto1kuU1NTuHHjBrq7u7F7927aDTAyMoILFy5gamoKampq2L9/v9JYQ1FREZ4+fQpbW1u89dZbSntMDw8P48GDB+jo6EBISAiWL18+pwZueHgYz58/R2VlJdTV1REQEAAej4ekpKTXErhOTk6iubmZys6RAl5LS0sqGE4SkTJXaC693HeNMclkMgwPD6O/vx/d3d1obW1Fd3c3gL8LeR0dHbFgwYLXFi3PHs3k5eWFqKioOaVAUqkUGRkZyM7OBovFwv79+5USwcTEBOLi4tDa2jqn9KSvrw9XrlwBl8vFgQMHGMXd7e3tuH79OkxNTbF3716adSWTyXD9+nV0dXXh8OHD86Gnk4qYfggIBAJcuHAB6urqOHz4MC2dS174zs5O7N27l7EIjs/n49KlSxgZGYGFhQWOHDlCIxGZTIYnT56gpKQEgYGBWLVqFeMCJwgChYWFSElJgY6ODjZt2qS0XS0wTSikmJTH4yEsLAyLFi2CpqYmpFIpPv/8c3h4eGDdunW070okEtTV1aGiogKNjY2Qy+WUgJcUw75JZ8W55sv9kMHv06dPQ0dHh9LHDQwMgM1mY8GCBVSbl9cZ1S0Wi1FWVoasrCwIBIJXiqebm5tx5coV8Hg8iESiOccyyeVyJCcnIy8vb07pyeDgIGJjY6Guro4DBw5AX1+f9pnu7m5cuXIFFhYW2Lt3L+OD89KlS5icnMTRo0d/tLl9rwkVMX1fiMViXL58GePj4zh69CjNpH8dU3l0dBSxsbGQyWRYuXIlHj58CEdHR+zcuZO6YWdKVdauXYvFixcz7s/o6CgePnyIlpYWBAQEYOXKlUoXGFP7jbCwMBohZmRkICcnBx999BG0tbUhl8sVAsNisRjW1taU4PX73NQz58vNxg9FTGRZwubNmymJBp/PR01NDSorK9HR0QF1dXW4ubnBx8cHCxYseGWwe3a7mSVLltDEu2KxGF9//TX09fWxZ88epKWlIT8/H7a2tti8ebPS5oCvIz0ZGRlBbGwsCILAgQMHGLf1qlADn8/H+fPnoaWlhcOHD/+cLVNUxPR9IJfLcfPmTbS1teHQoUOM2TAyuDgzyDkTw8PDuHz5MthsNg4ePAgDAwM0Njbixo0b8PHxwaZNm9Db24sbN26AIAjs2LFDadC6uroa8fHx0NbWxsaNG+Hk5MT4uTdpWAZMp7U/++wzhIWFgcPhoLCwkGo16+PjAx8fn1eOJn8VCIKg6qqeP3+OHTt2YGJiQiEwLhQKsXr1aiQmJlKZt9kZOU1NzVdm48gExa9//WtG62JkZIQqiRgYGACXy6UKJ181mkkoFCIjIwPFxcUwMDBAdHQ0FdNLTExEcXExTpw4QZ2vtrY2xMfHQyAQYMOGDUoD0DOlJ7t372ac5js+Po7Y2FhMTU3hwIEDjF0ryGNXVqLS39+PS5cuwdLSEnv37v1eGdfvARUxfR8kJycjNzcXe/bsYSx6JPVPytKxAwMDiI2NhaamJg4cOKDwJKyoqMC9e/fg5eWFxsZGGBkZYffu3YzkQRAE0tPT8eLFC3h5eWHDhg1Ks2bj4+NISEhAY2MjnJycEBMT88qYwtDQEG7cuIGhoSGoqanBz88PixcvhoWFxRvXv8jlcireMzMzNzIyQslWZmLmbDmRSIR///d/xx/+8AdoampiamoKs+8bDocDAwMDWjbOyMiIWmRPnjxBY2MjfvWrX825rwRBoL+/HyUlJXj58uUbjWaa2dLYyckJAQEBuH37NqMcRCwW4/HjxygvL0doaChWrFjB6NoJBALcunUL/f392LNnj9K2KFeuXIFAIMD+/fsZh1Pk5uYiKSkJa9asoZr0zURrayuuXr2KxYsXY+3atXMe548EFTF9V5CqdGW6o8bGRly/fh3+/v5Yu3YtbQEPDw/j4sWLlJyAKWj59OlTFBQUQF9fHydOnGAkG5FIhPv376O+vh7R0dEIDw9nJAtyyGJiYiLU1NSwfv36V2rgyN5CtbW10NbWxuTkJK3g8lWQSCRob2+nMnO9vb2MujkjIyPweDwIBAI8e/YMR44cgbW1NdhsttIpKXK5nDbwUigUKhAfqY9js9mwsLCAg4MDqqqqYG9vjy1btrz2cXzX0UwNDQ1ISEiAQCCAvr4+3n//faVxwby8PCQnJ8PJyYlRegJMk9iNGzfQ2dmJXbt2MQqyJyYmcPXqVYyMjODo0aOMJErq5nbs2MGY+S0oKMDTp08RGBj4c5CTipi+C8bHx3HmzBnY2Nhg9+7djOneS5cu0eJEJCYmJnDhwgWwWCwcOXKEMVDa2NiIW7duQUdHB6Ojo4yEQEpVBAIBtm3bprQZmEAgoMaB+/j4YM2aNXMGpPv6+pCcnIympiaYmJggNDQUCxcuxPXr1yEWi/H2228r/S5BEOju7kZTUxNaWlrQ0dEBmUwGHo8HR0dHWFtbw9zcnJo3NxuDg4M4deoUY6O07xJjIvVx/f396OzsRHNzM4RCIVgsFmxtbeHo6AhnZ+fXHvAplUqprp/9/f2vNTbr2bNnyMvLAwC4uLhgw4YNSt3m15GeSCQS3LlzB83NzXjrrbcY9YyTk5O4dOkSJBIJjh49SnvwEQSBuLg41NfX4+DBgwrlJjKZDE+fPkVxcTE4HA7ef//9Nyqp+AGgIqY3hVwuR2xsLIaHh/Huu+/SSGV0dBQXLlyAnp4eDh48SAs8SyQSxMbGUk8zpqrr2tpa3LlzB87Ozti+fTuSk5NRWFiI7du3U82+SKmKrq4udu3apTRNXVVVhcePH4PFYmH9+vVzdqacOXjR0NAQ0dHRCgMMyILLI0eO0OJcg4ODVEuQkZERaGpqwsHBgcrOmZqavtbCn0sv90MEvysrK3H37l0sX76cKh0QiUQwMDCgpCdz6QtJEASB+vp6JCcnzzlotKenB+fOnUNkZCQsLS2RkJAAqVSKNWvWwMfHh/GcvI70RCaT4e7du6irq8OWLVsYhxSMjY3h/Pnz0NXVxaFDh2j3olQqRWxsLIaGhnDkyBEYGxtjfHwcd+7cQU9PD6Kjo5Gfn099/yeMN6mI6U2RkZGBzMxMHDx4kPZEl0qluHDhAkQiEeNTSi6X486dO2hqasLBgwcZA5gVFRW4f/8+lTnhcDggCAL3799HVVUV9u7di8HBQTx9+nROqYpEIsHjx49RVlZGpfqVBW5njqrmcDjUAIPZNyJBEPjqq69gaWmJ7du3g8/nUyLenp4eaGpqwsPDAwsXLoS9vf13GvE0l17uhyCmx48fo6WlBe+//z6A6WvS3t5ODfEUiUQwNzengvqv+h2ZTIaSkhJkZGRAIpEgNDSUEu/KZDKcP38eBEHg2LFj4HA4mJycpATS3t7e2LhxI2Nt2UzpiTJpk1wupzK+GzduhJ+fH+0zvb29uHTpEuzs7LB7925G6/3ixYvgcDhYsWIFHjx4ADU1NezYsQPW1tbo7OzEpUuXEBISwqhk+JGgIqY3QUtLC2JjYxEVFYXIyEja+2SN0dtvv00z7cl+OIWFhdi1axdcXV1p3y8vL8f9+/excOFCbNq0SeEmkslkuHnzJlpaWiCTyag2KsqkKmSQdP369XMOMKirq8OTJ08gEAgQFBSEpUuXzunmkbEHDw8P1NXVUS1AfHx84OLi8p2m8M7Gp59+ShHDxMQEVbUtEAgQEBCAoqIi6OnpURk5Ujf3Ojh16hTs7OywYcMG2ntSqRRNTU1U+2C5XP7ao5lmine1tbWxdu1aDA4OIj09HW+//TatWLayshIPHz6EsbHxnNKTtLQ0ZGVlKZ2iQxAEHj16hJKSEqXymqamJly/fh2+vr7YsGEDbRt9fX04e/Ys5HI5Fd+a6QlkZ2cjJSUFe/bs+al6h88bYpr3/ZiEQiHu3bsHBwcHxm4BNTU1KCwsxJo1a5RmQgoKCrBu3TpGUmpubkZ8fDx8fX2xadMm2s3DZrNhbm6OxsZGqKmpYdGiRYxkM1OqcuTIEaULSiQSITExEWVlZXBxccHBgwfnTPkTBIHm5mbU1NQAmL7ZV6xYgUWLFn2nepfZurn+/n6Mj49DKBRCIpEgPz8f+fn5tH0GQMVgZkJdXR1cLhf6+voK2biZ+jhSqsL0UAEANTU1uLm5wc3NDVNTUygtLUVeXh4qKirg4OCA0NBQanrxbGhpaWHFihUICAhAYmIibt++DRaLhYCAAMYKfm9vb5iamuLmzZs4d+4c3nrrLTg4OCh8hsViITo6GhoaGkhLS4NYLMaKFStofZbWr18PFouFhIQE6Ojo0MhjwYIF2LBhA+Lj46Gvr69w/CKRCBkZGRT5+/r60sITYWFhaG1txYMHD3D8+PGfu/jyJ8W8tpgIgsD169fR3d2Nd999lxa4HB0dxTfffAMHBwfs2LGDduNWVVUhLi5Oae1IX18fLl26RAXTmVwosjRh6dKlqK2thUgkwpEjRxTqcIqLi/HkyRPY2Nhgx44dSl23xsZGJCQkYGpqCqtWrYKfn98rBxg8f/4c/f39sLS0hI6ODtrb2/Hxxx+/lqVCEASGhoYoqUpnZycEAgGAacI1MTGBmZkZ9PX1wePxUFJSAh6Ph9WrV4PL5VLnY3x8nJoiwuPxqGzczKzc6OgoBgYGMDAwQC02Ho8HGxsbaGlpoaysDB9//PFrTc8F/j6aKTc3F11dXTAxMcHSpUvh7e2t9JzJZDKcOnUKo6Oj4HK52LhxI+PDCHh96QnZsSIwMBBr1qyhfUYul+PWrVtoaWnBoUOHGMnw+fPnyMjIwKZNm+Dn54f+/n7cvn0bAoEAmzZtQnV1Nerr63H8+HHaQ0ooFOKbb76BkZERDhw48L0mMb8G5o3FNK+JiXRf9u7dS6tXkslk+Pbbb8Hn83H8+HGaGzQwMICzZ8/C3d2dsdp2fHwc58+fB4/Hw6FDhxhFlk+ePEFRURHVjpfP51NxAbJCNzExEUVFRQgICMDq1asZA5VTU1NISkpCSUkJnJycsHHjRsYCQxKdnZ1ISkpCR0cHFixYgPDwcDg4OGB8fBx//etfsWbNGgQGBjJ+VyQSoa6ujiIjPp8PNpsNGxsb2NnZUZk5Jt3cbL2csnKBuTBTH9ff34+2tja0t7eDIAgqQ+jk5AR3d/fXkswQBIGOjg5kZ2ejvr4eVlZWWLVqFaO8iCSRHTt2oKSkBI2NjfDz88OqVasYrcuZ0hM/Pz+sW7eO0SUuLi7Go0eP4Ofnhw0bNtDIQSwWIzY2FqOjo3j77bcZVQgJCQkoLy9HZGQkXrx4AUNDQ+zYsQPGxsaYmprC2bNnoampiSNHjtD2obW1FbGxsVixYgVjzOsHhIqYXgU+n49Tp05RhYuzQY7ROXz4ME3hL5FIcO7cOQDAsWPHaEFOkUiES5cuYWpqCkePHqU9xclOl6WlpdiwYYOCDGVoaAiXLl2Cnp4eeDwempubsXbtWqU1Rn19fbh16xYEAgFiYmLg7++v9Ik/MjKC1NRUVFVVwdzcHDExMbQq8jt37qC3txfvv/8+tR2pVIr6+npUVlaivr4eMpmMEvA6OjrCzs7utSwsZXq57xv8/vLLL6muBi0tLejp6QGLxYKLiwt8fHzg6ur6WoM+W1tbkZSUhJ6eHnh4eGDFihWUhTEyMoKvv/4afn5+WLt2LQiCQGlpKRITE6GtrY2dO3cqda/LysqQkJAwZ5uS8vJyPHjwAF5eXtiyZQuNnIRCIS5cuAA2m42jR4/SSHdqagpffPEFJiYm4OXlhU2bNin8Tk9PDy5cuAB/f3+sWbOG9vtPnz7Fy5cv8d577835UPuemDfENG9jTElJSVTGYjYaGxuRnZ2NFStWMLYdSUxMxMjICCMpyWQy3L59G+Pj4zhy5Aija5GcnIzS0lJGOQsZNL106RIAYOfOnUr7c1dXV+PBgwcwMjLCu+++qzSWJJFI8Pz5cyqAu3HjRvj6+jKa7SEhIbh48SIaGhrA5XJRXFyMmpoaTE1NwdLSEtHR0fD29n5tl2kmeDweVRj5Q4HP52N4eBjLly+nSi74fD6qqqpQWVmJuLg4aGhowN3dHf7+/nOOZnJwcMCxY8dQUVGB1NRUnDp1CkFBQYiKikJCQgK4XC6io6MBTMeAFi1aBEdHR9y+fRsXL17Exo0bGaUnvr6+0NXVxc2bN3H9+nXGNiULFy6Empoa4uLioK2tTXPreDwe9u7diwsXLuDmzZvYv38/Zfnw+XzcuXMHk5OT4HA4YLPZNKvI0tISK1euRGJiIhwdHWnFl8uWLUN1dTUSExOxc+fON7wKvzzMS2Iihx5u3ryZ9uQhJ6IuWLCA0aytrKxESUkJNmzYQKuLIU3q9vZ27Nu3j1HTVFBQgNzcXKxevZpRYzc1NYWUlBRwOBzI5XIqiD2TRGZLVTZu3KjUYuno6MCDBw8wPj6OiIgIhIWFzWndWFlZwcjICPfu3cPU1BQ1KcTHx+d7j6QmG9OR45nIkUzj4+MApqvmyc+9bhawpaUFABQCzLq6uggJCUFISAiGhoZQWVmJ8vJylJeXw9raGqGhofDw8GAkZhaLhYULF8LDwwN5eXl48eIFysvLqS6bswnFwMAAhw8fxqNHj3Dv3j309vYyTj1xcnLCvn37cP36dVy9epWxTYmnpyfWrl2Lx48fw8DAgHb/GRsbY8+ePbh8+TLu37+P7du3o62tDXFxcWCz2Th8+DBGRkZw//59ODk50coMgoKC0Nraivj4eFhZWSlYp1paWli9ejXi4uJQV1f3WsMqfsmYd66cVCrF119/DV1dXRw8eJD29CQnnL733nu0IPPw8DC++eYbuLq6MsaVyJamyroG1tbW4tatWwgJCaFNzgCmM1rXrl3D4OAg9u7di4mJCdy6dYtqQM9isagprK+SqkilUqSnpyM3NxdWVlbYvHnznMQikUiobBVJEKtXr55zth0T/t//+3/4/e9/jw8//BBHjx6lGrrx+XyMjIxQwfGZEIlE+OMf/4h/+7d/oxarpqamwpBLZfq4hw8forOzEydPnpxzv8jRTLm5uWhtbYWBgQFCQkJeOZqpvb0d3377LQiCmLP31etKT7q7u3H16lXo6+tj3759jIkMsq/8tm3bGAssyWELbm5uqK+vh729PbZv305tKz4+HlVVVTh27Bjt4Tg5OUmVVuzYsYN2DOT9d/Lkydcu1XgDzBtXbt4REzm/7d1336VdNLKeicxuzIRUKsXFixchEolw/Phx2pOzt7cX58+fVyqQ7OjoQGxsLNzc3LBt2zbaYhcKhbhy5QrGx8exf/9+Kl5BDtQMDw9HQEAArl27Bj6fP6dUpbu7Gw8ePMDQ0BCWLVuGsLAwpdkWuVyO0tJSpKenQygUwsPDA8HBwYiLi8OCBQuwadOmOc8nME0s5NgkcnQ2SRw8Hg+mpqbQ19eHVCpFVVUVoqOjYW5uruCK+Pr6oqysDNra2lQmjszKjY+PY2BgQCHjZ2pqCjs7O1RXV8PV1RUbN2585X6S6OnpQW5uLiorK8HlchEVFYXFixfTzhFBELh58ya6uroQFBSEzMxMGBgYYPPmzUo7i86Unuzbt4/RvZ7ZBG7//v2MMcgHDx6gqqoK+/bto5UbkMHs4eFh+Pj40AYTiMVinDt3Dmw2G2+//TaNSEkh+e7du2lZxeHhYZw+fRohISFKB2l8D6iIiQlDQ0P4+uuvERoaSsUKSEilUpw5c4bKos0mDrKI8ujRo7SUrVgsxtmzZ6Guro6jR4/S3JChoSFcuHABpqamCrEBElNTU1QG8MCBAzQXkVSNa2lpQVtbG3v37mWUqhAEgfz8fCQlJVHN+OfqMNDU1ITk5GT09fXB29sby5YtoxZSVlYWMjIy8NFHH9Ge6gRBoKenBzU1NWhubkZPTw8IgoBAIICTkxOysrJgaWmJP/zhDwrfHRgYwOnTp2l6udcNfk9MTFDZuN7eXjQ3N2NsbAzAdAzFyckJHh4esLKyeu3RTOnp6SgvL4epqSk1WID8LrmAd+7cCXd3dwwODuLBgwfo7u5GdHQ0wsLClEpPrl27NmebkqGhIcTGxirtkSSTyXDt2jX09PTg8OHD1D0xMDCA27dvY2xsDLq6upDL5Th+/Djt+/39/Th37hwWLlxIS+6QY8uHh4dx8uRJGnFlZmbi+fPnOH78+GvJeN4A84aYftSiiDcBmZ7X1dXF0qVLae9nZ2djZGQE69ato91sra2tyM/Px8qVKxnrSJ48eYLx8XHG+WETExO4du0aeDwedu3aRXtfJpMhLi4Ow8PD2L9/P+ONsGDBAqirq0MkEiEwMJCRlKRSKeLj46nRPW+//bZSUhoYGMC1a9dw9epVaGho4OjRo9i2bZvC053M7hUVFVGvkS16T506hXPnzqGkpARGRkZYv3492tvbIZVKceLECXR1dUEqldIIjfz/sbExjI+PK/y9DrhcLhwcHBAUFISNGzdi2bJlAKZdThMTE5SWluL8+fP46quvkJGRgaGhoTm3Z2BggC1btuCdd94Bj8ej4j99fX0QCoVITEyEl5cXFSg2MTHBkSNHEB4ejpSUFNy7dw8SiYS2XUNDQxw6dAhcLhfffvstent7aZ8xNjbGvn37qMETs1vDcDgc7NixA3p6erh27RoEAgGqqqpw/vx5sFgsvPPOO9i3bx8mJyfx6NEjWpsYMzMzrF69miprmAkWi4W1a9eCz+cjMzOTtm9hYWEwNDTE48ePadv9R8G8CX5XVVWhubkZe/bsoT0hhoeH8eLFC4SGhtKIQSqV4tGjR7C1tVUY/U2itLQUZWVl2LJlC40wyC6XIpEI77zzDi3mQBAEHj9+jObmZqVDAXp6enDlyhUYGRnBzMwMycnJMDIyUghOkjd3X1+f0sZ1wLTblp2djYyMDOjr6+Ott95SEPPOhLa2Nnx9fan2LMXFxejs7KQyXKtXr4aTkxPYbDZu3ryJgoICFBYWMv7uzG2yWCzcu3cPf/jDH+b87OugtbUVZmZm1HWRy+VobW1FRUUF1ZjOysoKgYGB8PHxUSpWtbS0xIEDByjx7tmzZ2FiYgK5XE5LrbPZbERHR8PCwgLx8fG4ePEio/RER0cHBw8exLVr13D58mXs3buX5v6Zmppi165duHLlCuLj47FlyxaFa6GlpYW9e/fi7NmzOH/+PMbGxmjJjo0bN+LOnTtwcHCgaRAXL16MqqoqPHnyBCdOnFC4742NjREREYEXL15g4cKFCladmpoa1q1bh9jYWJSVlTFq9X7pmBcWk1gsxrNnz+Dq6kqLy5CWlI6ODqMllZOTg+HhYUZLanBwEE+ePIGfnx8jGeTn56O+vh6bN29m1ExlZmbi5cuXSrtSdnR04PLly9RI6c2bN8PDwwN37txBa2sr9Zlz586Bz+fj8OHDSkmJHKqQnp6O0NBQnDx5cs6pKiKRCJqampiYmEB8fDw0NTWxbds2fPLJJ9iyZQucnZ3BZrPR0dGBDz/8EFevXn2lhIXFYoHL5WLp0qUYGxuj/jo6Oub8njK0trYqxF/YbDacnJywadMmfPLJJ9RAh/j4eHz++efIysqijZSauW9ubm44ceIE3N3d0d/fDy0tLaXlDV5eXjhy5AhEIhHOnTtHXY+ZIGNIpqamuHLlCuNnyP5RFRUVCmPWZx4Tj8fD2NgYXFxcsG3bNoWgtKenJwICAvDs2TP09fXRjmnt2rUYHx/HixcvaNuOiIiAgYEBo2Xk6OgILy8vZGRkMDb6+6VjXsSYEhISUFJSAktLS6xdu1bhyUXKSpgCgSMjIzh9+jSCgoJoCmyZTIZz585BJpPh2LFjtAxGd3c3Lly4gODgYMTExND2iQxqL1u2jJEQu7u7cfnyZWoUEBlsl0qluHHjBrq6urB06VKkpaXB2toab731FmNTOjJblJaWBj09PWzevHnOuXOTk5PIyspCUVER5Y5paGjgvffeYySxBw8eYMuWLQrWiEwmA4vFAo/HQ1lZGQYHBzE4OAihUIiGhgaoqalRGUZgmgT/8z//E//jf/wP6Ovr09rqktIWU1NTyh0cHR3FX//6Vyr+MxdmjmZis9lYvHgxlixZwpgRE4lEOHXqFAwNDTE5OYmRkRFERUUpTSCQ0pO2tjalbUrEYjFu3bqF9vZ2HDhwgPH8k3HEdevWUZZPe3s77ty5A2C63KCiogKHDh2iVaVLpVKcP38eMpkMx48fp4UL0tPTkZWVhRMnTtAys+QQBaaEDxkTnLlP3xPzJsb0sxOTTCbDV199BV1dXUxNTaG/vx+enp5Yvnw5dHR08NVXX8HGxoZWVEbq6Pr7+/Hee+/RiCcrKwtpaWk4duwYreJXJBLh7Nmz4HK5OHz4MM2FaGlpwdWrV+Hn50eVAcwEOfLJwMAABw4coP321NQUzpw5g9HRUbi4uGDnzp2Mbsrk5CQ1FTY4OBjR0dFKK6BlMhkKCgqQmZkJuVyOwMBABAcHo7+/H1evXsXBgwdp2SFgOqPW1tYGgiAwOjqK/v5+pKWlwcjIiFog5Lw5XV1d9PX1QUtLC76+vhTZCgQCREdHIzU1Ferq6goZOT6fj6GhIQV9nIWFBTQ1NVFdXY1PPvnklf26SQgEAhQWFlIi4iVLliA4OFhhIT98+BDV1dU4efIkuFwu0tPTkZOTAwcHB4WU/EzMbFOyYcMGxk4AUqkUV65cwcDAAI4ePcro9pMJlt27d2NoaAjJycmwsbGhfvfy5csYHR3F8ePHaYLcgYEBnDlzBkuWLEFUVBTtt0+fPg19fX0cOHCAsUSmqakJ77//Pi3ccO/ePbS1teGDDz74ITpMqIiJBNmfmywPKC8vR3p6OgQCASwsLNDX18fYyY9s7s70RCYtqcDAQJo1RBAE7t69i8bGRhw/fpzWME4gEODMmTPUnDplfXQIgsCRI0cYFwJ5TJqamtDU1GQcy9Pf34+bN29CJBJh27ZtjK1ayf2tqalBSkoKRkdHsXjxYkRFRVHWF0EQ+Prrr6mK9JmYmppCbW0t6urq0NLSApFIBHV1dfT29lJuzOy6I6b5cq/KypH6OLJjZVdXF5qbmyGXy6GlpQUHBwe4ubnBw8PjtSYJT0xMICMjg2qzsmLFCnh5eaGlpQVXrlyhWQitra24c+cO1NXVsWvXLsYuE2S8sLi4WGnP7cnJSVy8eBFSqVRpX6/r16+jtbWVaoGzYsUK6tyNjY3hm2++gZ2dHXbu3EkjmLS0NOTk5ODEiRM04mtqasLVq1cZY5B8Ph9ffPEFwsLCqIQCicHBQZw+fZqqafuemDfE9LPGmGQyGV68eAFPT0+Ym5uDzWbDz88PH3zwAZYuXYru7m4QBIGXL19SbgUwveASExPh5uZGIyWCIPD06VOq/mU2SkpKUFVVhQ0bNtBIiaxPAYCtW7fSSEkikeDmzZuYnJzE3r17GUkpPz8fCQkJCAgIwLvvvgsAuHr1qkLspKamBufPn4e6ujqOHTumlJTGxsZw9epV3LlzB8bGxnj33Xexfv16hQXDYrEQHByM2tpaDA8PQyaToa6uDnFxcfjzn/+MBw8egM/nIygoCIcOHcK//uu/ory8nBoWaWpqqmDNcbncN5alcDgcmJqawtPTE1FRUdizZw94PB68vLwQEhJCxcE+/fRT3LlzBzU1NVRVORO4XC7Wrl2LkydPwsLCAnfv3sW3336LBw8ewMHBgaZLdHBwwDvvvAMul4sLFy6gsrKStk0Wi4V169YhJCQET58+RXZ2Nu0zZKkH6Y6LxWKF90dGRjA6OgqZTAYTExOsXLlS4dzp6+tj06ZNqKuro7WOAaYtQD09PcaY0YIFC+Dt7Y1nz57R4my6uroIDAxEXl4e7T0TExP4+PggKytrznP6S8PPSkylpaUYHR2l9ekhTVIOh4PFixcjOzsbX3zxBQoKCiCTyZCRkQGRSITVq1fTtllbW4uGhgasXr2a5mKNjo7i2bNnWLx4MaXbmons7Gw0NTVhy5YtjL2a79+/j56eHuzevZuxMC83NxeJiYkIDQ3F2rVrYWBggP3790MgEOD69euYmppCRkYGbt++DRcXF6Utfkky/vrrrzEwMIA9e/Zg7969SmtWFi5cCC0tLdy7dw9/+ctfcPPmTar/0a9//WscPXoUy5Ytg729PTgcDjIyMvD5558zbuuH0MuNjo6Cz+fDx8cHkZGROHz4MD766CMsX74cw8PDuH37Nv7yl79QlrEymJiYYNeuXdi/fz96e3vB5/OVTtDV19fH4cOH4enpibt37yI5OZm2+FksFmJiYrBkyRKkpKQwpuINDAywZ88eDA4O4u7du5SLWlNTg7NnzwIANm/ejKGhITx//pz2fTc3NwQHByMlJYWq0Cehrq6OtWvXoqWlhZE8Y2JiIJPJkJqaSnsvPDwcBEEgJyeH9t7SpUshEAhQXFzMeG5+ifjZygVIa8nLy4u24EQiEfLy8iildUREBDIyMpCYmIicnByMj48jMjKS5t6JxWIkJibC1dWVMeCamJgILS0txmB3R0cH0tLSEBERwWjBpKamora2Fjt27GCsKq6oqEBSUhLCw8MRHR1NmfEmJibYu3cvLl++jNOnT2N8fBzLli3DkiVLGIPVfD4fCQkJaGhomLNlB4mhoSHk5uZCLBajq6sLixcvRlBQ0HceN03q5QiCwOnTp6m2J28CUh83s0hTT08PYWFhCAsLw8DAAIqLi6m2wgsXLkRoaChjoSMwvaDJ4Z7p6elob2/Hhg0baCp7dXV1bN68GRYWFkhKSsLExAStTQmLxcLy5cvBZrORnp4OXV1dWszJ0tISb731Fq5fv45nz55BXV0d2dnZ8PT0xMaNG6GpqYnR0VFkZGRQ/dVnIjo6mupQunfvXoXr7OzsDE9PTzx79gzOzs4KMSNdXV1ERkYiOTkZYWFhCg8/Ho+HwMBAFBQUIDQ0VCGGZWxsjIULFyIrKwuLFy9+rU4N8x0/m8X08uVLjI2NMXY1zMvLg1QqpWbCkSYy6RoRBIHa2lpqAZDIyMjAxMQEY0MvMtayevVqWpxjcnIScXFxsLGxofnwwPQooOzsbERHRzMSXktLCx48eABfX18FUiJhaWkJW1tbjI+Pw9raWikptba24syZM+ju7sauXbuwadMmpaTE5/MRHx+Pr776CrW1tQgJCQGLxYKpqekbkZJMJsPAwACqqqrw4sULNDQ0gCAIXL58Gerq6vjwww+pNiiXLl3ClStXcPfuXSQmJuLFixeoqqpCf3+/Anm1tbXB0tJS6b6bmppi9erV+OijjxAVFYWGhgacPn0a9+/fpyrFSUilUjx8+BDW1tY4cuQI9u7di/7+fpw5cwZNTU20bbNYLISGhmLLli0oKyvDvXv3GIk1MjISixcvpmb9zYazszOWLVuGgoICZGdnY+XKldi+fTt17yxZsgSOjo64d+8ezcJUV1fHmjVr0NTUhKqqKtq2V61aBYlEwlh+EBAQAB6Px1g+EB4eDgBKrSahUPgPYzX9LBYTaS2RbU5nYqa1NFujpKGhAT6fD39/f/T29iI2NhbOzs4UGeTl5WH58uWMltTTp0/h7OzMOPni0aNHEIvF2LZtGy2uND4+jvv378PFxYWxm0F/fz9u3boFBwcHxr7OMpkM9+7dQ0tLC4KDg1FQUIAnT54ozLwjCAIFBQV49uwZlV1iGi1FHktOTg5ycnKgpqaG1atXw9/fH2pqahAIBMjPz0dQUJBS7Z1AIEBLSwtaWlrQ3d2NwcFBauFqa2tT7q+amhpMTEzAYrEwMTEBYJpgWSwW+Hw++vr6IBAIqJgH2RHTysoK9fX1jK7ybGhrayMiIgIhISF4+fIlMjIyUF1dTQ0W0NTUxPPnzzEyMoLjx4+DzWbD2dkZJ06cwL1793Dt2jWsWLECoaGhtPO+cOFCqKurIy4uDlKplFb1T8acyJYksyc6d3Z2oqCgABwOBxwOh1ZTxmazsWXLFpw5cwbx8fG0cWKurq7w8PCgLKOZJK2np4dly5bh2bNn8PPzUxiOoa6ujoiICDx79gwREREKQXIul4ugoCDk5+cjNDRUIcZpZGQEX19fZGVlISAg4AfpAf9z4mfJypEZtXfffZf2dCfTvx9++CEtzpOQkIDa2lp8+OGHUFdXR01NDdLS0jA0NAQ9PT2w2WzGwYbJyckoKCjAyZMnaTGduro63Lx5k1Ep/qqRUeTMeW1tbRw+fJhmiUmlUmo6y/bt2+Hu7k51Q4yMjERUVBSkUikeP36M0tJSaiKGMlKpqanB06dPMTExgeDgYCxZskThhu/u7sa5c+doI5j6+vpQUVGBhoYG9Pf3A5i2WmxtbamOlmSPbqb5cnNl5SYmJqhsXF9fH1pbWympiampKdUMztzc/JX6uKmpKWqwgKamJkJCQpCWlkYNBJh9bdLS0pCdnQ0fHx9s2LCB0YVpaGjA7du3YWdnh127dtE+IxaLcfnyZYyPj+Po0aPQ19dHUVEREhMTYW1tjfXr1+P69etKRymRHSneeusteHp6Krw3Pj6OU6dOwdfXlyYcl8vlOHPmDHR1dbF//36F96RSKb744gs4OjrShoNOTEzgr3/9KwICAmi1e+S1U9Y94zUwb7JyPwutlpSUwMbGhkZKk5OTyM/PR0BAAI2URkdHUVpaiuXLl1NPdU9PT7i5uSEjIwNZWVlgsVhISUnBkiVLKBLp6+tDXl4eIiMjaaREWlILFixgfMJnZmaivb0dBw8epJESmbkBoFBgSYKUuzQ1NWHXrl1Ua2B/f39MTk4iNTUVHA4H9fX16OnpwebNm+Hr68t4vmaOHnJzc8OqVasYg+ZWVlaws7NDXl4erK2tUVZWhsrKSvT390NbWxtubm6IiIiAo6MjY7EnAOo4SSvpVeByubC3t6dIjCTejRs3oqOjA6WlpcjJyaGyR76+vko7MGpqaiI6OpoaLJCamgpNTU1GyQWbzcaKFStgaWmJ+Ph4qhXN7Eypi4sL9uzZg+vXr1M9kmYSv4aGBnbv3o0LFy7g+vXrMDc3R2VlJYKCghATEwMOh4Pt27fj0qVLSEtLo5GBu7s73NzckJiYiAULFijcB3p6eoiKikJSUhL8/PwUdJxsNhtRUVG4c+cO2tvbFYoy1dTUEBERgcTERCxZskSh6JLL5SI4OBi5ubkIDQ1VuI4mJiZwcHBAcXHxdyWmeYOfPMY0MjKCpqYmxla0RUVFkMlklC89E5mZmdDW1qb1uuZwOOjr64ORkREiIyNRUlKCL774AllZWRCLxXjy5AmMjIwY3bDMzEwIBALGUeKtra3IzMxEZGQk46z65ORk9Pf3Y9euXYy1PampqaisrMTWrVtp/crDw8Ph7++PtLQ09Pf34/Dhw0pJqb6+HqdPn0ZDQwO2bNmCnTt3MpISCXd3d7S3t+Pzzz9HZmYmzMzMsHv3bvzmN7/Bpk2b4OPjo5SUgL/r5b5rZq61tRXW1tZYtGgRNm7ciI8//hh79uyBpaUlsrKy8Ne//hV3795FT0+P0m3o6+sruFVnz56lpsTMBik9GR8fpzpAzIajoyO2b9+O2tpaJCUl0d7X0dHB2rVrqVjb1q1bsWbNGso6srGxQXR0NHJychjjUWvWrIFIJEJ6ejrtveDgYJibmzMKeT08PGBubo6MjAza9xYvXgxdXV3GzGFoaCjYbDYKCgpo7/n7+6OtrQ0DAwO0935J+MmJqbi4GJqamjQLRS6Xo7i4GN7e3rSFMzIygrKyMsbujl1dXWhoaKBmzv3qV7+Cr68v0tPT8fnnn6O9vR2rVq2i+dz9/f3Izc3FkiVLaKl/iUSC+Ph42NnZMY6Mqq2tRUFBAWJiYhj7SBcWFiI7OxsxMTE08x6YdgFbW1uhpqYGiUTCaJ2QjfJv3LgBCwsLnDhxYs45dR0dHbhy5QqSkpLAYrFgYWGBTz75BNu2bYOrq+trT3Ml9XLfhZgIgqDp4zgcDlxcXLB161Z88sknWLVqFTo7O3H27FlcvnwZbW1ttO0MDAwgMzMT4eHheP/992FjY4Pbt2/j6dOnjIFsCwsLHD58GGKxGJcuXcLo6CjtM25ublizZg3y8/ORm5ur8F5dXR3u3r0LHo8HgiAYz3FoaCgWLFhATbmZCX19fURFRaGgoIBGuGw2G2vWrEFPTw+qq6sV3mOxWIiMjERLSwvtPJBWU0VFBY1ktLW1sXDhQrx8+ZJ2Ptzd3amWy79k/KTEJJPJUFpaCl9fX5qv39TUhLGxMUZL6sWLF4zWEjCdiTMxMaGIjsfjYc2aNTh58iT1hEpMTERtbS31/2QVsKGhoVLrjM/nM07EGB0dRXx8PNzd3Rn3p66uDk+fPkVwcDBCQ0Np74+OjuLbb7+FVCrF8ePH4erqitu3bysIZScnJ3H9+nXk5uYiJiYGe/bsUdoHaXh4GHfu3MHFixchFAqxbds2REdHo6+vj1YgOBcmJibQ2tqK0tJSANPk+8c//hGHDx+msnKPHz9GUlISsrOzUVpaipaWFgUCGxoagkAgYJTGANNuU3BwMD744ANs376d6nN169YtKi4ll8vx8OFDGBgYUBXuO3fuxJo1a1BUVISrV68ykqaxsTEOHz4MYDp7yNRSJTAwEOHh4UhKSkJVVRUVp7p58yYcHBzw3nvvwdvbGwkJCbQaJHKOHFmVPhvBwcEwNTXFo0ePqNonEvb29liwYAGeP39Oe8/d3R0WFhaM21y0aBH09fUZrSZ/f38IBALU19crvK6mpgY/Pz+UlZUxtnz5peAnjTHV1tZCKBQykk9JSQnMzc1p47snJiZQXl6OqKgoGpl1dnaisbGRMZs2MDAAkUiEdevWobq6Grdu3YKtrS1WrlyJoaEhtLe3MzaFGxgYQE5ODpYsWUKTDZBz6zU1NbFx40bak3VgYAB3796Fu7s7Y62UQCDA5cuXwWKxcOjQIRgYGGDbtm24du0arl+/TjXAI6Uq+/btY+xqAEzHxzIyMpCfnw8dHR1s3ryZsqhEIhEyMzNRWFiI5cuX074rk8ko2UhHRwfV34gEi8WCRCKBmZkZLCwsKKIcGhrC4OAgJiYmqCGYwPTDwMzMjDqXr5qey2az4eXlBU9PT1RWViI1NRWnT59GQEAAdHV10dnZicOHD1PbY7FYCAoKgpmZGe7cuYNz584xTj0xMDDAoUOHcOXKFcTGxjJKgaKjo6lMa25uLtVUjmyBvH79epw9exZxcXG0UUoGBgaIjIxEWloafH19FaQvHA4H69evx8WLF1FSUkIT1UZFReHChQuorq5WSLKwWCxERUVR055n1kSpqakhNDQUSUlJWLVqlYInYWFhAWtraxQXF9Myzf7+/sjJyUF1dbXSEMF8x0+alYuNjYVUKsWRI0cUXufz+fjss88Y56Xl5uYiJSUFH3/8MS2wefXqVYyPj+Pdd9+lDQP45ptvoK2tjYMHD4IgCDQ1NSElJQV9fX1QU1ODvb099u3bp3ggf6vf4fP5OHHiBKMK/MWLFzh8+DBNgS6RSHD+/HkQBME4nWV29mdmSYNIJMLly5cxNjYGmUwGAwMD7Nq1S2ksqa2tDfHx8eDz+ViyZAlCQ0Npv0cGyz/66COoq6tDIpGgrq4OlZWVaG5uhkQigZaWFuzt7RUyc4aGhnjw4IGCXo4pKyeVSilRMNmxsrGxETKZDGpqanB0dIS3tzfc3d1f2ZtaKpUiLy8PmZmZkEgkcHNzw65duxg/OzY2hps3b2JoaAh79uxRKlyeK1va1taG2NhYEATBOOWGHKUUHBzM2LXim2++oRr4zX44PXjwAE1NTfjVr35FuybXrl3D6OgoTpw4Qbtfz507B3V1dVp31snJSfzlL3/B0qVLaWGFly9f4uHDh/jVr35Fu1euXLkCiURCW2uvwLzJyv1krtzw8DBaWlqUWktqamq0TAJBENQTYTYp9fT0oKmpCUuXLqVZS7W1tejr66O0ciwWC87Ozjh+/Dh8fX0hlUrR1NSEhIQEhWBpeXk52traGAcfDg4OIisrCxEREYxtMRITEzE8PIzt27fTbki5XI64uDgqczS7zkpLSwtLlizB5OQk5HK50gC3RCLBs2fP8O2330JHRwcnTpzA0qVLGdPkwcHBmJycxPPnz3H//n18+umnuHv3LoRCIZYuXYpjx47ht7/9LXbt2oVly5ZRujk1NbXXijGRdU6kPm7nzp1UBi0qKgoikUjhd8mhl8q2FR4eDnNzc3A4HKpqmskVJaUntra2uHbtGmMwWldXF3v37sXo6KhC90nyfrpy5QpMTEygpqbGGFS3tLREZGQkcnNzaT2UOBwO1q1bh66uLsY4TmRkJCYmJhQ6i5KIiorC4OAgTY5CWk3t7e203lfa2trw9vZGSUkJ7fx5e3tDU1MTJSUltN/y9/dHR0cHVR7yS8NPRkzFxcXQ0tKiBYPlcjlKSkrg7e1NqxRua2vD0NCQ0gyenp4ebXsEQSAjIwOOjo60bJpMJkNzczO8vb2xatUq1NTU4IsvvkBqaipGR0eRlJQEb29vmvtExqT09fUZg+HkyKg1a9Ywjox68uQJmpqasGPHDkble0NDA+7fvw87Oztoamri9u3bCq4SMB2bunjxIgoLC7Fy5UocOnRI6Zw6uVxOtS/Jzs5GZ2cnIiIi8Ktf/QpHjx5FREQErKyslNZLkWPA3wSki+ft7Y3w8HAcOXIEH374ISIjI9Hb24tLly7hwoULVGxnNkpKStDZ2Yldu3Zh9erVePnyJS5cuECL9QB/T/E7OTnhxo0bjORiZmaGXbt2oa2tDQ8fPoRYLMbDhw+pibrHjh3D+vXrUVZWRsXVZiIsLAzGxsaMglt7e3v4+fkhNTWVRuCGhobw9fVFdnY2jVitra3h6upKta6ZCRcXFxgaGjKSnb+/P0ZHR2mV7urq6kqD4G5ubuDxeIwE+UvAT0JMBEGgsrIS3t7etKd7Y2MjxsfHGcmnuLgYxsbGjFMoKioqsGjRItriqqmpQX9/v9LOAgKBAFFRUQgJCcGvfvUrhISEIC8vD6dOncLU1BRjTKaiogKtra1Yu3Ytbf9HRkaQkJAAb29vxj4/xcXFKC4uxvr16xk1eI2Njbh58yYWLFiA/fv348CBAxgbG8ONGzeo4GVrayvOnTsHkUiEt99+e86pKo2NjThz5gxu375NuV1r1qzB0qVL5ywzmImZernXRUtLC9hstoI1aWBggIiICJw8eZJqmRwXF4evv/4adXV11PbHx8eRnJwMPz8/ODs7Izg4GO+88w6kUinOnTvHKD1RU1OjCknv3LmD2tpa2mccHBywadMmlJeX46uvvqJmFa5fvx5qampYuHAh/Pz88OTJEwwODip8l7SMOjo68PLlS9q2V65cCYIgGLsULF26FJOTk4ytjKOiojA0NISKigqF11ksFtVqd3YHAWtra5ibmzOSVkBAAIRCIerq6hRel0gksLCwQElJyS+y68BPQky9vb0YHx9nlIOUlJTAwsKCNkRgYmICNTU1WLx4Mc2Pr6iogFQqVRjdTSI/Px8ODg6MXQSzsrLg4+NDBbW1tLQQHR2Nt99+G3K5HDKZDLGxsSgvL6cWzeTkJJKSkuDl5UWrRyIHaHK5XMaGcr29vUhMTERgYCAjafX09OD27dtwdnbGW2+9BTU1NZiZmWHPnj3o6elBXFwcCgoKcOXKFZibm+PYsWOMFhcAqmHctWvXwOVycfToUaqynqkFBxNI3ZxAIIBcLseLFy/w4sULSptVUFCA8vJyNDU10fRxZP0SUzyJHAd+8OBBHDt2jJp6Gxsbi56eHjx+/Bjq6uoKs/xMTU3x9ttvw8bGBteuXUNeXh5tuxwOB1u3boW7uzvu3r2Lzs5O2me0tLTA4XCoLOvsYPCaNWugp6eHhIQEGhE7ODjA19cXycnJNMuILHQsLCykdUgwMDCAn58fcnJyaFaTpaUlnJ2dGWuQFi1aBIIgUFZWRjt//v7+qKuro9VpmZmZwdbWFsXFxRCLxaisrMStW7fw5z//GU1NTZDJZIzEPt/xk2Tl6urqoKmpSXOtJicnUV9fj9WrV9MWNWlez676JeMELi4ujM3X2tvbsX37dto+FBcXQyAQMLbJraioAIfDwcGDB5GTk0NlbFasWIHa2lpIJBLGAZiVlZVoaWnB3r17aQFWsViMuLg4mJqaMmboRkdHcf36dZiammLbtm0KdUa2trbYsWMHrl+/jvr6egQFBWHVqlWMVpJMJkNWVhY1U40M5pLnMyQkhKqMnt22dXR0FM3NzWhra0Nvby8GBwcVXIwXL15AQ0ODciszMzMV9pPsfGlubo6mpiYsXLhQaR0QCSsrK+zfvx8NDQ1ITk7GuXPnQBAEtm/fTnPltbW1sXv3bqSmplJ9iqKiohg1a1euXMGNGzdw5MgRGBsbgyAIPH/+HM+fP4ezszMEAgHS09Ph6uqq8DsaGhpUY//S0lLaA2TlypWoq6tDSkoKbYZfSEgI8vPzkZWVRWvBs3TpUpSWlqKgoIASo5MICAjAzZs30dPTo5BZ5PF48PDwQFFREYKDgxWO08fHB8nJySgpKVEQvkulUlhaWqKgoACffvoppFIprKysEB0dDQ8PD5w7dw4dHR2/uMm9Pwkx1dfXw8XFhVbk19jYCIIgGJu9kUHv2VKQ7u5u9Pb2MnYBKCkpAZfLpW1PJpNR7TVmlwAIhUIUFBQgKCgIdnZ2sLOzQ3t7O1JSUnD16lUA04Hk2YJikUiEZ8+ewdPTk2ZJAX8fGcXU45mc6Kuuro7du3fTrAyCIBSCxSwWi3GxDwwM4P79++jt7UVERAQiIyNp59jb2xspKSnIz8/HunXrMDAwgIqKClRVVVHxG7L7gb+/P8zMzCCTyXD16lXweDycPXuWsow++eQTaGlpYWJiAmNjY1RGrq2tDWKxGEVFRWhqaoKXlxd8fHyU9o9isVhwdXWFhYUFvvzyS0ilUrx48QLGxsY0i5DNZmPlypXQ1tZGamoqxGIxYmJiFM4H2bny4sWLuHbtGvbu3YvExEQ0NjZSOrvR0VF88803SEhIwPbt2xW+7+joiIULFyI5ORlubm4K9xyPx8Py5cvx5MkThIWFKYjOtbW1ERISgqysLISHhyvcI/r6+li8eDFycnIQEhKicA+4uLhAV1cXRUVFtJly/v7+iI2NRVtbm0IIQ0tLiwqCh4eHo62tDZWVlaipqaEKPp2dnRETE6Pgsru6uqK+vv7HGI75o+JHd+XGxsbQ09NDGyQATFtSs2e0A9PV3MPDw4yuWnFxMfT19WlkIJFIqFE2sxdnfX09+Hw+Y8FjTk4OWCyWgmTFzs4Ohw8fhoODA9hsNvLz83H37l2MjIxQn0lNTVVqSVVVVaGsrAzr169n7B394MEDCAQC7N27l7EhXUpKCl68eIGVK1dS1cpZWVkKn6usrMTZs2chkUhw9OhRLF++nLG6W01NDf7+/igpKcGZM2dw+vRpFBQUwN7eHjt37sS//Mu/4J133sH69esRFBQEBwcH6im+atUqVFdXK8RKNDQ0YGBgAHt7ewQGBmLdunXw9/cHm83G9u3b4ejoiKKiInz99df45ptvUFpaqjTGkZSUBHV1dezfvx8EQeD8+fM0N4ZEREQE1qxZg7y8PDx9+pTmdnG5XOzduxcikQhnzpxBZ2cn9u3bh8jISLBYLBgaGmLjxo2orq5GeXk5bfsxMTEgCALJycm09xYvXgx9fX3GxnAhISFQV1enXR/g75nR2RXf5MCFyspKWhW5g4MDjI2NafEkgiBgaWmJ8fFx/PnPf8bVq1fR3t6O4OBgnDx5EnZ2diAIghZHdHNzw8DAAGMSYT7jR7eY6uvrwWazaWOZZDIZGhoaGDVsdXV10NbWprl+IpEIlZWVCA8Pp7k11dXVEIlESoPoTKJhoVCIwsJCBAcH0yyz4eFhtLW1ISYmBhoaGsjIyMBXX32FgIAAuLq6oqioCKtWraKRqkgkQmJiIjw8POYcGbV7927GwZi5ubnIycnB6tWrqXlsExMTSEtLA5fLxaJFi5CamoqcnJw5VfXAtJlfWFiIkpISyOVySCQS7NixAy4uLnO2xXhTvVxraytsbGzg5eUFLy8vrF27Fo2NjSgpKUF8fDxSU1MREhKCoKAgal9ra2spXZqTkxOOHTuGx48f48GDB+jp6UFMTAztGgcFBYHD4eDRo0eM47xaW1sxNTUFuVyOoKAgWrLB09MTPj4+SEpKgqurq0KTNh6Ph+joaDx+/Bh+fn4K9x6Hw8HSpUuRkJCAJUuWKNxHWlpaCA0NpSQ0M++HmaLa2ffC4sWLkZmZiYqKCoViTDIInpaWBqFQiNHRUVRWVqKqqgp8Ph8sFosaYkq2oQGmLaOMjAxIJBKF+8HJyQlqamqora1lXGvzFT+6xVRXVwd7e3ta/KC1tRVisZix8Vp9fT1cXV0Z65MkEonS7JeTkxMthT6XaLi4uBgEQTBaUpmZmdDR0UFAQAAWL16MDz74AFFRUSgrK6Mm9zKp3tPT0yEWixnb/nZ3dyM5ORkhISGMFmRlZSWSk5MRERGhMLwzMjISgYGBePToEc6fP09JVbZs2cJISgRBoKqqCqdOnUJSUhJqampQX1+PtrY2/O53v3tlMPRN9HIEQdDcDg6HAzc3N+zevRsnT56Ei4sL0tLScOrUKZSXl2NychKPHz+Gq6srVQWtpqaGjRs3Ys2aNSgsLMT169cZ65j8/f0RFRWF9PR0Kg4plUqRkJCAhw8fwtfXF2FhYcjNzUV7ezvt+2T72pSUFMZtW1paIjU1lWaR+fr6wsDAgNFqCg4OBofDYUzN+/v7o729naZ309PTg4uLC3UPzoS1tTVkMhlOnz6N8+fPo6KiAu7u7jh8+DAWLVqEqakpBVICpqUtZH3eTGhoaMDJyYkmXZnv+FGJaWpqCi0tLYyBt7q6Oujr69PiECMjI+jv71fq+tnY2DAGvTs6OpSSjzLRMFk/NdtaGhwcREVFBSIiIijLQl1dHUuWLMHWrVtBEAQmJydx6tQpqiMCME08hYWFiIqKou3j1NQU4uLiYGFhwejvt7W14cGDB/Dx8aGVLLBYLERHR4PH46GnpwfLli1jbI4GTAe0Y2NjERcXBzMzM5SWliIiIgLvvfcedHV1oaenh5iYmDlJZ3JyEpqamujp6UFtbS11U7e2tqK/v1+hxqmvrw+Tk5NKe3Gbmppi48aNOHnyJCwtLXH//n2cOnUKYrGYNqSUlJ7s27cP7e3tuHbtGs3VAaYDy4sWLUJCQgLKy8tx8eJFlJWVYePGjdi4cSOio6NhY2ODu3fv0lLvOjo6iI6ORklJCa2YkcViYdmyZejo6EBzc7PCe6TVVFNTQxsprqmp+Z1EtQEBAejt7UV3dzeGhoaQmZmJ06dP49tvvwWbzQaHw8H+/fvx8ccfY+3atbCzs4ObmxuGh4dp5Q3GxsYwNjamlQ0A0+5ce3v7G9em/Zz4UV25xsZGyOVyGjERBIG6ujq4u7vTFlddXR04HA7NDJdIJFSl92yUlZWBy+XSfue7ioazsrKgq6vLGOPKzc2Fubk5du7ciYyMDDx+/Bh5eXlYtmwZcnJyFEZizwTZeH///v20WJBAIMCdO3dgY2ODTZs20c7J1NQUrl27BolEAmtra7x48QJOTk4KukKCIFBSUoKkpCRoa2tj3759WLBgAXbv3k19prGxEebm5rhy5QqKi4uxdOlSiMVitLe3o6WlBT09Pejv76dIa3h4GHV1dVRW7saNG5Tly+VyqYcKm81WGugmQY6Xys7ORkpKCjgcDmpraxEYGEg7XkdHR+zfvx/Xrl1DbGws9u3bp+B2kZq23t5e3L9/H3p6ejh69CgVG2Oz2di2bRu+/vprpKamYv369Qrb9/f3R1lZGR49ekR1xiTh7OwMa2trZGRkwMnJSWHffH19qRKKt956i7bNoqIi1NfXK5TFkKLakpIS2txAExMTaGpq4vr165iYmICGhgbc3NywYsUKDA0NITU1FdbW1gr75+TkBHV1ddTV1dG6v7q5uaG0tBRyuVzhO66uriAIAvX19b+YceI/qsXU0NAAc3NzmgSDrGtSZkk5OjrS0u8tLS2UjorpO25ubozdBZWJhouLi5WKhslGYbPjMK2trWhtbaWazm3ZsgXHjx+HgYEB4uLi0N3djcWLF9Nc0J6eHhQUFCAqKmrOkVHbt2+nHYNMJsOtW7fQ399PFWCam5vj2rVrlHsgkUhw//59PHr0CF5eXjhx4gRjMWdISAj6+vpgb2+PiYkJ3Lp1C//1X/+Fa9euoby8HFpaWggICMCmTZtga2sLCwsLHD9+nNJbkf+9fft2BAYGQltbGx0dHZDL5fjv//5v3Lx5E5WVlUpV7WTmzt7eHosXL8bTp08RFxfH6LLZ2tri4MGDGBkZwc2bNxUC6ARBICsrCz09PeBwONDT06PFD/X19bF8+XIUFxfTLCM2m421a9eiv7+fFggn5SGdnZ00t4jNZlOjsmbXLs0U1c6Gv78/RCIRqqurIRAIUFBQgIsXL+KLL76AWCym2jp/8skn2Lp1KzVMg6kGSU1NDc7OzoyWkbu7OyYmJmj1XDo6OrC2tkZDQwPtO/MVPyoxdXR0MDZZm6uuqa2tTSn5GBkZ0WpxBgcHMTQ0xPidsrIy2NjY0J7m4+PjqK+vh7+/P+1pTWaFmJ4sz58/h4WFhUJcjBwRrq+vD01NTTx9+hQ3btygNEpyuRyPHj2CqakpoyX1qpFRDx8+RHt7O3bt2gUbGxtoaGhgz5490NXVxdWrV9HR0YGLFy+ipqYG27Zto6Z4MMHS0hISiQQHDx5Efn4+xsfHsXz5cpw8eRIff/wxduzYgaioKDx48ABxcXEoKyuDpaUl5VYbGRnB1tYWXl5eiIqKovpoBwYGYuXKlRAIBLh79y4+++wzpKWl0RZvamoqBAIBNm7ciLVr12Lnzp1obGzEhQsXFDKeM/d39+7d6O7uxv3790EQBEQiEW7evIn09HRERkZi37596OrqYoz9BAQEwNLSEo8fP6ZJQKysrODu7o7MzEya+7VgwQLY2NggIyODMdbEZrMZq8H9/f3R1NREOxZtbW2YmJggMTERf/nLX/Ds2TNoaWlhy5Yt2LFjB6RSKUxMTBSsKUNDQ5iZmTESkKurKzo7O2nn19raGlwul/E79vb2jAWo8xU/GjFNTExgeHiYcdRRS0sLFixYQLMOyAkds+NLpBk6s3CQRF1dHdTU1Gj6NrFYjObmZsZGbS9fvnxj0XB3dzdaW1uxdOlS2j5UVVVhbGwM+/btw7Zt26hx0PHx8cjOzkZ3dzfWrVtHO97e3t45R0ZlZGSgvLwcmzdvVgguk64aQRD49ttvMTExgaNHj9J6ls88F+np6fjv//5vsNlssNls7N+/H8eOHaNqc2Ye0+9+9zv8+te/hqOjI8bGxmgWB4m+vj5MTU1Rgy3ffvttfPDBB1i4cCHy8vLw+eefIyUlBVNTU2hvb0dBQQGWL19OJSjc3d1x9OhRSCQSXLhwgVFwamtri23btqG6uhoPHjzA2bNn0d7ejj179iAqKgoODg6IjIxEZmYmbeGx2WysX78efX19jNXvkZGRGBkZYbSaIiMj0dXVRTv2mfVEykS1xcXFmJqaQnl5Oa5fv44///nPGBwchEgkQkxMDH7zm99gz549WLhwIVxcXKCpqak0NlRfX08jTldXV7BYLFpAmxzWMHt6EDDdhXN8fJyxw+d8xI9GTF1dXQBAc5VkMhm6u7sZCauhoQGWlpa0wHF3dzcEAoFSS2rBggWMMSSZTMYY3yorK4OXl5dS0bCy+ik9PT3a9uRyOTIzM+Hi4gIbGxt4e3vjvffew+rVq1FXV4e0tDSYmprS4gGkMNjExIRR19fQ0IDMzEwsX76ckXAmJiYglUpBEAS0tbWV6uCqqqrw5Zdf4vnz5ygvL8dbb70FLS0tRlU+CU1NTRgaGmJycpIKmDOhpaUFampqCtfYyMiIGs0UHh6O/Px8fPHFF7hz5w6sra1pVqOZmRk1jvvbb79lbLnr7u4Ob29vSir0zjvvKJSfLFmyBBYWFkotI39/f2RmZtIC6RYWFvDw8FBqNb2pqBaYJoD8/Hx8+umnuH//PkVGx44dAzBdljAz2cLhcJS6Zm5ubhCJRDRy5HK5sLOzY8y02djYoK+vj+ZOk9fol2I1/WjE1NnZCS6XS1sw/f39kEqljMTU3t7OmN0h65pmtxsRCoVKy+3J4ODs8oH+/n6MjIwwDh8oKSl5Y9FwdXU1NfWWBIfDQVBQEDXrbWRkBF988QWys7OpWAmppmeypPh8Ph48eABnZ2eanAGY7hQZGxsLfX197N+/H6Ojo7h165ZCHGZiYgJxcXGIi4vD0NAQbty4gT/96U/w8fHB4sWLUVJSMmeHSy6XC4Ig0N3dTRXnTU5OKlgJbW1tsLW1ZayJ0tbWxrJly/DBBx+Ay+VCIBBAQ0ODliUDphfrwYMHYWRkhNjYWIXUOjlFprKyEvr6+hCJRDSLlbSMent7GTVoS5cuhUQiUWo1jY6OMlpN/v7+rxTVkvV49+/fp/RppI7zww8/xJEjRxAcHAwrKytYWloqJaCenh6Mj48rvG5lZQVdXV1GgbK9vT06OjpoVpuNjQ3kcjktc6inpwc9PT0VMXV1dcHa2pp2E3V2doLNZtOkB+Pj4xgfH2ckrKamJjg7O9NIgXxizC7elMvlVC3UbNTV1UFDQ4ORfKqrq99YNFxYWAgHBweaZSgWi5Gfn49Fixbhww8/hLe3N1JTU/Hll18iPz8fKSkptEI+YNqSunfvHjgcDjZv3kzbF6FQSAl1Dxw4AEdHR+zevRsdHR24d+8edVOeO3cOzc3NGB0dxenTp3H27Fno6uqit7cXDg4OEIvFVB0QQRAYGBhAQUEB7t69i6+//hr37t0DAJw/fx7ffPMNAODzzz/Hf/zHf+D06dPUWCoTE5M5uxAIhUIMDQ3B29sbfX19OHv2LLq7u2mfI91TPT09XLt2DXw+H2NjY/j222/x8uVLrFu3Du+88w40NTUVRneTsLa2RkBAANLT02kLXE9PD/7+/sjNzaW1kzE3N4ezszNjDZKfnx+jqJYgCNjb26O2thZ//vOfcf36dXR3dyM0NBQnTpyAlpYWtLS0aEkfNzc3qpneTLi4uIDNZtNIi+wjNrt0AZgmoImJCVp/c7KTKBMBWVtbU57MfMePQkwEQVDENBtdXV0wNzenuV7KXD+JRILe3l7G5mz19fWwsbGhBY07OzsxOTmptHjT2dmZ9pQnb5jZltTriIaZsn6FhYUQiURYsmQJdHR0sG7dOrz33nuwsbFBYmIipqam4OTkRFvUL1++RGtrKzZv3kyLc5EjoyQSCfbu3Uul0O3t7akpIFevXsWFCxegra2N48eP4/PPP8fY2BiioqJgaWlJBbO1tbWRm5uLjIwMnDp1CqdPn8azZ88wNjYGOzs7qkqY7DkOAFu2bMGqVavg4OCAoaEhyGQyFBYW4ssvv0R6ejptkchkMsTHx8PMzAybN2/G8ePHoauri4sXL9KapQHT8Zu9e/eCIAhcunQJ33zzDfh8Pg4fPoyAgABwuVxs27YNnZ2djEQSHR0NDofDOMU2IiKC6pQ5GwEBAeju7qa5kaSotri4GHK5HB0dHXj69Ck+++wzyjKztbXFu+++i5MnTyIqKgpmZmZwdXVVahlNTU2htbWVdtz29vaMrpmtrS0GBgZobqgy14zD4cDKyoqRgGxsbNDd3c3YD2u+4UchpuHhYYhEIkbrp7Ozk5GwOjs7KXNzJnp7eyGXy2nbIiuOmXpi19bWgsfj0X6Hz+ejq6tLqetnYWFBm3nW29uL3t5epZ03uVwurZ2LTCZDXl4e/Pz8FJ6axsbGWL16NZXivnfvHi5fvkzdREKhECkpKfD19WU8ruTkZPT29mL37t2MT+NFixahpaWF6vKor68PgiBof4ODg7C0tMTo6Ciys7NhY2ODPXv24F//9V9x5MgRrFu3jqqGJ3VxwHSsJygoCGvXroWPjw/U1NSwe/du2NvbU7Gku3fvUq5YdnY2+vv7sWnTJuqYDx06BC8vL9y9e5ex86Kuri7c3d0xMjICNTU1HD9+XOE6kmLj1NRUWiBXS0sLYWFhKCkpoZEkWZdWUFBA0+7NFNXOBEEQcHR0xODgIP7yl7/g4sWLqK6uhpeXF44ePQpra2twOBzaME83NzcqZDAT5ubm0NfXZ3TNHB0d0d7eTiMN8r6fTTRcLhdGRkZKLSNlr0skkl9EV8sfhZjIkzKbGCYnJzE0NMRIWMosrM7OTqpP0UyMjIxgcnKScVuNjY1wcXGhuUH19fVUb6CZIOMETK5fbW0ttLS0GAs+5xINCwQCBAUF0baXnZ1NLbg9e/ZgcnIS58+fx507d6huibP7TJP7QY6Mmt27CphuE1NSUgJra2sMDQ0xNimbmppCYmIiTp8+jYGBAejr68Pa2hqbN2+Gi4uLQpcD0hr7l3/5F8ZpMK2trbCzs4Orqys2bdqEjz/+GKtXr0ZHRwe+/vpr3L17F8+fP0d4eLhCaw81NTVs3rwZAQEBSEhIUCADkUiE27dvo6CgAC4uLuDz+YxuTHR0NNTU1PDs2TPae0FBQdDS0mK0mgIDA19LVDswMEBZko8ePQIwXQt08OBBfPTRR1i9ejVsbGzg5uaGpqYmWqCZzDgzuWaurq5Kg+ZisZhW0U0WYTJZQMpcMxsbG4yNjdHKCaysrMBisX4RcaYfjZiMjY1pWS8ytjCbgORyObq7u5W6fpaWlrTFr8z1I2+s2Y3igGmryM7OTqGKGJgOuotEIkZLSlnLltra2jcWDQsEAhQXFyM0NBTa2tpwcXHB8ePHsWnTJrS1taGmpgZmZmY0925iYgIPHz5UOjKK7F++aNEiqnVucnKyQsvY1tZWnDlzBiUlJYiKisL777+P6OhotLW10fpaA9OLiMfj4ZNPPqGRnEwmQ3t7u0KcTkNDA0FBQdR2q6qqAIDRBWexWFi7di0CAwPx5MkT1NXVob+/H+fOnUNLSwt27dqF3bt3w9vbG48ePaItMG1tbaxcuRJVVVW0eJWGhgbCwsJQWlqKsbExhfdmimpnw8nJCWKxGKdPn8bp06eRl5dHWZK+vr6QyWRUtwkS7u7ukEgktPS8pqYmHB0dGd05W1tbjIyM0CRB5MNmNtGwWCylFpCNjQ16e3tpFqAyN09dXR3m5ua/iDjTj0JM1dXVkEqlyMjIQHV1NQYGBiCTydDZ2QktLS2aqr6/vx8SieSNLSkjIyOazo086bO3JZfL0dbWxlgvVFdXB11dXdo4oNHRUfT29iq1pKytrd9INEy6LjMtKTabDT8/P9ja2kJLSwt9fX344osvkJ6eTsUVkpOTQRAETVsGTPdkun37NhYsWEB10Vy+fDkWL16Mhw8fora2Fjk5OVQW78SJE1iyZAnU1dXh6ekJXV1dxrgLoLz3d09PD8RiMeOEEjU1NbDZbBAEAXNzc9y4cQMvXrygkS2LxcLq1avh5uZGjWRSV1fHO++8Q9WrrV27FhwOh3F6Ltlbi6mwMjAwEGpqakpT/aSols/nIy8vD+fPn8elS5cAgBoG8cknn1CWpIeHB1XIOxMmJiYwMjJiJCAnJyd0dnbSAt3KXDNNTU2YmZnNGbRWJvZlysDp6OgwEpCVlRXt8/MRP4pWjmy9UFhYSN3YbDYbampqUFdXx/Pnz2FmZkal87u6usBisWjEIBAIMDo6+kaE1dXVBU1NTcYKcbFYrLR+iixamwmyZcvs3k9SqRSNjY2MwzJfvnz5StHwbIutr68PtbW12LBhAzw8PJCVlYXs7GwUFRVh4cKFKC0txbp162hBfolEgri4OOjr62P79u3U05zFYmHdunWYmJjA7du3QRAEwsPDsXz5coUnPlnWkJGRgRUrVkBNTQ0tLS1obW1FX18fhoaGMDAwQPUaOn36NCwtLSGVSsHhcBiHIQwPDyMtLQ1BQUFYvXo1MjIykJaWhqGhIWzcuJE2tkhHRwcymQyamprYv3+/QsCftIzi4+Ph5+enEHdjs9lYunQp7t+/T7sXNDQ0KFHt7OZ59vb20NDQoEZ/kXVEW7duxejoKDIzM6lWISRmtg6Zec1J14y0DmfCxsYGUqkUfX19Cq63gYEBuFwuurq6aA+8uVyzFy9eYGxsTCG2aGFhAQ6Hg87OToX7mrSymGrCDA0Naa7sfMQPTkwSiQQSiQTLli2Dr68vhEIhBgYG0N/fj4yMDLBYLBphaWhoQENDgxLBziQsgG79SKVS9Pb20iq3gWliIn3p2a8DoMVnhEIhhoeHGYsc6+rq4ODg8EYtW2pra+Hh4UHLOjY3NysVDefk5MDAwAC+vr7gcDhYuXIlgoKCkJ6ejry8PHA4HGhqatLa1iYlJWF4eBjHjh2jdcFksVhQU1MDQRBQU1ODl5cXY2tef39/ZGRkIDY2FsPDw5BKpTAwMIClpSUMDQ0hl8vh7e2N//t//y88PT0xNTVFVSN/9tlncHNzo7p/AkBCQgKl4CfV+iYmJrh//z4kEgk1nJTP5+POnTvo6urC0qVLqfmBs9vX+vr6oqSkBCkpKTh27JjC8Xt7eyMzMxPZ2dnYsWMH7bhIUa2joyPV/6mpqQkEQUAul2PDhg3w9PSkru/Q0BDS0tLQ1NSkkNBQV1fHggULUFdXR3sY2dnZIS8vD+Pj4wqJG0tLS7DZbOp+nHldbGxslLpmpaWlEIvFCtdzpms2k5g4HA4sLCyUEhCTNs7Q0BAikQiTk5O0B+R8wg9OTGQ2hDyBPB4PPB4P9vb2SE1NRXh4OMLDwxUIKysri0o9zyQsspH8y5cvFQirr68PMpmMMVPX2dnJ2K+ps7MTpqamNB2ZMvIj4yhMU1Pq6upgYGBAq+YeHh7GwMCA0ra/ykTDVVVVWLZsmcKTXV9fHz4+PigrK4OFhQXu3buH3NxcrFy5Eo6Ojujo6EBRURFWr17NqOx/9uwZqqqqsGnTJhQWFuLatWs4fPiwghvd29uL5ORkagjBsmXL4O3tTRXFPnnyBG1tbRSZRkVFgcfj4U9/+hPCw8PB4/Hw8uVLfPvtt7C3t4etrS1aW1uxb98+hYXl4+MDdXV13L59G0+ePKGycmw2G4cPH4aNjQ309fWRkJCAhQsXKhTZkuQWGxtLyZJIsNlsBAYGIikpCQKBQMGiNDIygpGRER4/fgyRSASZTAY7OzusWbMGWlpauHfvHmxsbBQeOsbGxjAxMaF1CACmA9qJiYm0RmzkfdPZ2akgf1JTU4OFhQU6OztpcUFra2vk5OTQHjTW1tZUUetMN5nH40FfXx/d3d00FYCRkREtAwlMr7/R0VHab5DrcnR09J+bmEhMTk5CLBZTNz1JWA4ODsjLy4O3tzfVJ4gkrPz8fEbC4nK5lFZobGwMZmZmMDIywvj4OIRCoVLXT9nrXC6Xtr99fX1KK9QbGhqU6vaUtWxpaGigNdIHpkXDBEEwioYzMjJgbW2No0ePoq2tDSkpKYiNjYWTkxNGR0dhZWXFGAwvKipCfn4+1qxZAz8/P7i6uuLSpUu4cuUKjhw5Ah6Ph8zMTLx48QJGRkZYs2YNnj59Cj09PYVKfR6PRwvSdnd3QyKRwMPDA9bW1ggJCUFDQwOSkpKQlZUFc3NzxtiTu7s71q9fj4SEBBQXF8PBwQHbt2+nXLdFixahrKwMjx8/xrvvvqvgSjk6OsLBwQEZGRk0l9vX1xcpKSl4+fIlQkND0dTUhMrKStTV1VHZsuXLl8PX11dhirCGhgbq6upopO7m5oaXL1/SFjRZUd3T06OQWCElO11dXTRdprW1tdLiyKmpKQwNDSmEHExNTaGurk4jJmCaNJUR0Oy6KGDaMpLJZODz+QqWHHl9R0ZGXjnK/efED05MIyMjYLPZtOb9yghLLpcr+M4zCauyshI2NjbYsmULhEIh+vv7MTAwgJKSEohEIhQWFlJyATabTT0x29raIJPJqJHXMpkM/f39jItYWYV6V1cX2Gw27eKNj49jbGxMqXTGycmJ5lY1NzdDKpUy6vZKSkqUiobJAZAsFgsODg44evQoampq8OTJEwiFQjg7O2N8fFzhnPb19SExMRH+/v5UkJ3L5WLfvn24ePEiYmNjwePx0NHRQY2d5nA4aGhoQF5eHhYuXEidC6b5cq2trdDU1KTOC1l+UVhYCD6fj4GBAcTGxmLHjh0KxzQ1NUWlyWc2viNBxsW+/vprvHz5knatIiIiqG4KM4lBQ0MDdnZ2yMrKQlZWFsRiMczMzBAREQE7OztcvnwZRkZGCotzZuuQ2QNM7e3tkZ2djZGREYUYmrm5OVVRPTvjO5drRt6jM60T0rXr7u5WICY2mw1DQ0PGTgsGBgaMFfOGhobg8/mQSqUKZD7TMpp57Nra2tDQ0GAkufmEH8ViMjAwoMUzyJM9m5j4fD7kcjmjCHVkZIQiAB6PB0dHRzg6OqKlpQU6OjrYu3cvZWENDAygvLwcfD4fpaWlyM3NBTB9sfX09EAQBHp7e1FdXU25hGQMICQkhPbbnZ2dsLCwoFWIK6vRkkgk6OjoYGypW1dXR7kJMzE0NITBwUHGuiVSNDyz5orFYsHNzQ3JyckwNzdHT08PvvrqKwQGBmLJkiXQ0tLCgwcPYGJiQtsPfX19bN26FZcvX8bIyAj27NmjENQPCQnB1atXFdrkktm0mXo9sn5p5vWtqKhAY2Mjdu3aBS6Xi1u3buHSpUs4cOAA9PT0qMzh+Pg4tm3bhtzcXMTHx+Pdd99VcF/NzMzg4+ODrKwsLFq0iBaAJkW1tra2aG9vR2VlJaqrqylretGiRQgJCVGwgszNzVFXV0dLRjg7O+Phw4cQiUQK7tzMeM5MYmKz2UorqsnGcrMbtJHb6u7uVrCitbS0wOPxGAcEGBoaKrWMmILW5HoaGxtTcNPJ10dGRhSIlMViwcDAgJH85hN+NGJiel1DQ4Pm1yqzpCQSCQQCASNhjY6OUlaOjo4OdHR04OjoSA1hfOeddxQIq6amhmrqThb0sdlsGBgYQCQSYXh4GNXV1ZRLSBIWU/V1V1cX9PT0aBZhT0+P0gr1hoYGxkB9bW0t1NXVadYXObgwNDSUUTQ8OjqKd999F4aGhtTwgpcvX8LOzg69vb04duwYjVCnpqbw9OlTaGtrU4JWR0dHihicnJxgamqK3NxcaGtro7GxEcbGxuDz+Th48CB++9vf4t69e+jo6EBQUBDl6giFQiQmJsLb25uyCI8cOYLY2FhcuXIFYWFhSExMhL6+Po4dOwYTExOYmprim2++QU5ODs1iWbp0KdUbfLY2kdS0tbS0UC6Kr68vvLy8cOXKFejp6TG6ZgUFBTTSIK9Td3e3wnWeWVE9e4CAtbU1IznY2NhAIpFgYGBAoXbN0NAQLBYLw8PDNPd+LgJi6vxABq1nE+lM12wmMWloaIDH4zH+hrLfnk/4UYiJyXcdHR2lLtRMKLOkyOI4JpJT1h2AJMXZhCUUCjE4OIiPP/5YgbAaGhqo9rGkupzD4cDQ0BBDQ0MwNTVlJCxlsSo1NTVaUeXIyAgEAgEjydXX1ytt2SIWi2lTY4Hp+JGjoyP1O5GRkQgICEBaWhpKSkqgrq6O3t5eWFhYUAuRFAaPjo7iyJEjEAgEuH79Oh48eICtW7dS18TW1hYlJSWor6+Huro6ZeGRN/zIyAjkcjny8vLQ3NyM8PBwqoZnpoVmZGSEPXv24Ny5c3j48CG8vLywceNGysU1NzdHUFAQsrKy4O/vr1CLZmJiQjXpX7x4Mfr7+1FZWYnKykrqXjExMcH27dtha2tL7buLiwvq6upo2VVHR0dkZmZicHBQgbTIiurOzk7atbGxsVGats/NzaUF2snzMzw8rHD92Ww29PX15wxOzwZJGnMFrWcK4PX09MBisd7oNwwMDOb9dN4fJcbENAp8LkuKx+PRFudcQfSpqSmlltRsuQn5OkmKMwkLmI7//Pa3v8Xk5CRFWK2trRgcHERLSwulayLrdgYHB+Ho6IiamhqaS2hlZUWzcJS5flNTU+jo6KANPARABWVnH+PAwADa29uxbds2hdd5PB709PTA4XDg5OSEhIQE5ObmIjo6Gm5ubigsLER9fT127doFMzMzmJmZYevWrYiLi6OGNsbHx6O9vZ2q29qxYwempqbw6aefUpkgNzc3lJeXY+vWrSgqKsL9+/cBTAt9Z8aLBAIBnjx5QhUXWlpa0uJuS5YsQUlJCbWfM+Hq6orHjx/jr3/9K0ZHR6GlpQUPDw+sX78eKSkp0NbWpsV5XF1dUVlZCaFQqLAvM2UYM4mJrPVR5ppVVlZCJpMpuJokUQ8PDysQE5fLhbq6OqN7NJdlxDTFxcDAADKZDAKBQMEqn2kZzSQmkvyU/bayeBUT+c0n/KDEJJVKIRKJGBuLjY6OMloNJGnMBhlEn70tZYRFEMSc5DfX6xwOR4GweDweampq8MEHHwAANXG2q6sLAwMD6OzspLItHA4HxsbGGBkZgbm5OSNhGRkZ0VxYckHMlmyQLVuY6p2qq6uhoaHBOGm4qKgIfn5+WL9+Pbq7u5GSkoJbt27BysoKAwMD8Pf3Vwi+e3p6Yt26dXj06BFevnwJHR0dHDhwAC0tLcjPz4dEIqHNlyNlKK6urrC1taWm6D5//hzm5uZwcnJCe3s77ty5AwA4dOgQampqkJGRAS8vL4VrwOPx4O/vj+LiYkRGRkIoFKKqqgqVlZVUXQ45qXhmt1N3d3dkZ2fTSIM8j7MLFzU0NGBqaorOzk6aa2htbc0oJDY1NYVcLsfo6Ohrx23mIiCmSmtDQ0OMj4/TjmMmAc0kJpL83sQ1MzAwYOw+qqenB6lUiqmpKVqN3nzBD0pMZOMxpp7Tk5OTNPkIAFo6kwSZTXiTILpMJlNKcky9x18VDyPLEsige1tbGyoqKnD06FFwuVyqrKGvr4/69/bt2wD+Tljk8TERlrIK9cnJSaWuH9OwSlI0TGayrKyssH//fjQ3N+Pu3buQSCQYGxvDwMCAQu0V6e5JpVL4+/vD0dERJiYmyM7OptLvZGYOmLb+SPcyKSkJcrkcx44dw7Nnz3D9+nWqqNHW1hbbt2+Hjo4OLCwsUFlZiYyMDGzevFlhvz08PJCXl4czZ85gaGgIHA4Hrq6uiIiIQG1tLaMcyMnJCenp6ejt7VWwQvX19cHj8dDZ2Un7jrKsmampKYRCIS1uM9Ntmh234XK5b+yaMXUTmBm0nhlkn/nbrxu01tPTYwyka2lp0fpPAaC8E7FY/IMRE4vFMgTw75jmFGcAtwFcB/ApABYAQwD/SRDEa5Wd/yjExDSEUSKR0Mx58jtMxKSMyMbHx6GmpkZ7T5klJZVKwefzlbp+/z977x0WVZ5uC6+iyBnJUTJIlCCCGDCiYE5gwmzb7UxPd5+eOzPnnnvPzDlzJ3VP93QwpzYLIqCIiARJSs45g+QcCygq7O8P7v5NVe1dqD0d7Pv1+zw8du+qHWqHd79hrfV+m3qYnp4elJSUSIQ1MDCAkpIS7NmzB4aGhsRh0dAGgUDAcFj076utrZVyWB0dHeBwOKwI9a6uLlbFgurqapiYmEjVNzgcDoyMjIgmd2dnJ86ePQsvLy8EBQVBQUEBd+/ehZmZGczMzJCamkpAnW5ubsjPz8fixYuhoaFBIBkikQg2NjZoampCaWkpNm7cCENDQ2zfvp2MHvf29iYcN2D2YV66dCmSkpIQFBQEFRUV1NTUoKqqipBfp6ensXXrVjg7O0u91CoqKjA6OiolRUM7U1kaylypmaGhIcGLSV5T+p6Qrdvo6OgQ5VFZmys6YcMs6erqkvKD5G+TjIwkHZOysjJUVVUZYnfAbNTENmdPSUmJdTKNsrKy3OUA5lQwfRPjcDjKAM4A+DeKoro4HM58AC0AtgD4AIADgAQAwwB+8Trb/E4dE30SZB0TRVGYmZlhdVjyls/lyJSVlRlOg354ZPFANDOdzfl91/UwPT09qZRwamoKRUVF2LJlC6ytraUcFv2gyDosgUAAdXV1NDc3kzoT/SACYNRWaMkWNshDSUkJkZ1VVFREQUEBsrKyUF5eTmoZu3fvhqamJmZmZhAXFwdVVVUsXrwY5eXl+OSTTzA0NETe+EpKSlBXV8fdu3dhY2MDb29vDAwMICoqirx9eTweQ4nBxcUFKSkpuHHjBkZGRiAWi2FtbY3Q0FCMjY3hxYsXcHFxkTqvkqmZpGOiEdVsDsjIyIghkUtfF7a6jWRqxla3keeA5nJYss6PPvaxsTGpaJV+sbJFNPIcipKSEqszUVZWZl2upKQEsVjMSBfp8yxvzNa3sJMArlIURQOtpjEbJbVSFNXC4XCcATQAuPO6G/xeHJOsQ6FlGdgcjTwHJAv9f9X35UVr9BtGNr0Ui8WYnp5mODJgNrxmQy9/23qYrMOiKAqlpaVYu3YtXF1dpRxWZWUlhEIhw2FRFAUlJSV0d3dDJBKRCKunpwd8Pp9VNaG6uhoLFiwg4XpAQAC8vLzw5MkTlJWVQUlJCZWVlVi0aBE2bdqEqakpREVFYenSpVBQUMD09DR0dXXJuRUIBPjqq69AURQOHjyI2tpaxMXFQVtbG8ePH0dvby/u37+Ply9fwtTUFI2NjaisrER9fT2EQiHGxsawbt06omoAzNJiMjMz0dXVJZVua2lpQUdHh0H1AGa7emxSLbq6uqx1G0kHJOmY6JfMm6RmNDVE1tTV1SEUCiEUCqXuQXnRiWQ6JWvyHI2ysvIbR0z0PiRrnN91xARgmKIoSQkI3//77xMAoCgqEUDim2zwB0nl5EVS9DrylrOlcnM5rLn2/SbOUl7uPTk5KdeRaWlpfat6mGyXsL6+Hn5+fvDz8yPOqr+/H9XV1RCJRKSwzOVyYWBgAAUFBXA4HIyOjpLhDwoKChgbG0Nvby9jmIGqqiooioKOjg5sbW2RnJyM/Px8rFy5Etu3b8fZs2eRnp5OHn57e3vSPXJ3dyfE0NjYWLS3t2PBggXYsmULmayio6ODmJgYQkEyMTFBUFAQ1NTUEB8fT9QiaTMyMoKSkhI6OzsZdUBjY2OGcBp9PtnqNvRLQ7ZuI5myydZtdHR0GLpNgHzJFxUVFblOA2Dez/KcAD0CXF6kI2852/iluRwZANLIYFv+XRhFUTdkFq0EIAKQ/W23+YNETHM5pjeNmF6VEsqmePKc5Vz1sLn2wZYSynNkPB4PHA6H4WDpB0FWxleyHkY7LLoI3tXVBVNTU6xcuVLKYdE4ovv37wP4p8OSfCAGBweJwxIKhaipqcHSpUuxfPlyBAQEIC0tDbGxsSQd0dDQIGnPwMAASYfpSGhqagrt7e2kC0ijsGtqakhKvXTpUnh6epLi/tTUFOLj41kR1UZGRlKTUWiTV7ehR0vJ1m3o8ynrmJSVlaGkpPRGjmYu5yBvOcB82OdKm+aqAclL5d50OfBm0dp3ZKsAFFEU9a2H2P0gERO9XNYBURQ1ZwT0XTiyVznLN93Wt1ku6yzpcFzWmdEPjqzuEjD7tnd2dmY4rNHRUSgoKGDTpk3EYfX19RH0cHx8PIB/Oix1dXUIBAIoKipicHAQ+vr6CAsLQ3t7O27evAlgFiA5OjpK9KHpOgitXwTMggrr6urQ0NAAHo8HXV1deHt7w9zcHFFRUbC2tpbqOKqpqUFXV5dVb1pe3UZXV5c1mqHPD4/Hk3JM9PmUl+7IcyjfxmnI1pLkRUZzpU3f5pjkRUZstSR5kdF3HTFJ2v/tznkC+FRm+TGKoi697nZ+kOK3vOUikYjUTmRNVpNGcltvGuWw7VvecoqiCPv8Tfb9pvUztn3P5SzlYU4mJiZgbm7OcFgPHjxAf38/wsLCSHTV19dHOmHJyclITk4mDouuJTk7O6O3t5d0P2WNy+WCw+EQNUd3d3f4+fkRihB9Pfv6+hh1L3l1Gy0tLdaakaqqKgQCAYNO8m2cwFwP9beJjGRrSd91xCSvzf+qyEgyZZMXGXG5XCgoKHwnEROHwzHEbMctgaKoPwBYj1ll3HyZ7ywB8MM4Jg6Hw5F8ow0NDWFmZoYhlTE4OIjp6Wnw+XypNujk5CSmp6cxMzPDaI+Oj4+zLh8dHYWamhpj+cjICEQiEWP58PAwEcaSvNj0JJfp6WmpdWZmZliPFZiNGOQdE13Xkd032zFJ7ltSr5k+T7LHJBKJMDk5ybrvsbExGBkZse6bnopiYGAAAwMDLFiwABwOB+Xl5Th48CCRi6UR5dPT00QnnMPhkPNFRyDT09MYHByEpqYmdHR00Nvbi4aGBobk7Pj4OJKSkhgjmui0TDY66u7uxtTUFC5evMj4DdPT0zh//ryUk6TP0Z07d6SiS4qiMD09jYSEBMZwy56eHgwNDTH0uWklClld8d7eXvB4PMYxjY6OYnp6mkgB08bn8zE9PY3IyEhSQ6NVGaanp/HkyRPGFJaOjg709vaira2NLONwOGhvb4dAIMCFCxekvj8wMIDx8XHG8vHxcUxPT+Py5ctSLzWBQIDp6Wncu3dPqgRBURQmJyeRl5cnBbrV0dHRBjBOzTUokGkrACwC8JjD4agBCAPQBUDz//4eDQBfAvjNG2wTnDc7BpmVORxtAMxY+2f72X62n6rpUBTFBFHJMQ6HowXgcwAzmHVGfwagDeBPANoAKAP4G0VRTBzHXNv9Fx0TZ3R0lAzCys3NxbNnz/Dee+9JFXY7Ojpw48YNHDt2DCEhIWTqBp/Px2effYYtW7bAxcUFixYtIp+dOXMGrq6uZPQ2/VlkZCQUFRWl+GJjY2OIiIhAcHAw3n33XaljrKiowKNHj/DrX/9a6q3b09ODq1evIi0tDcnJyWS5SCTC3/72N4SGhsLDw0PqmM6dOwcHBwesXr0aY2NjsLS0RHt7O5KTkyEUChEWFka2s2jRInz66aeorKzEqVOnpI6puroaDx48wEcffSRVI+nv78elS5eQnp4uNZqIoij85S9/QVBQEBmRRL8BL126hPnz5xPpFPp4Hzx4AB6PR4ZVUhSFlStX4uOPP0ZNTQ2cnZ3R39+PwcFBqaiNJrfSAyLo6/T555/jo48+gpqaGkQiEQGSbt68GYcOHZKapPLVV19h4cKFWLZsmdT5i4qKgoKCAnbu3Cl1nv7617+ivr4eJ0+elLqm69evx6ZNm+Reu0OHDkkBZOlrV1hYSJoBtEleO8ljun//Prl2kte0tLQUFRUVUtdu0aJFuH79OuLi4vDhhx9KpdYDAwO4ePEi9u/fTzBYdMT6t7/9DcXFxYiMjJQ6psuXL8PExAT79u1DW1sbuaYPHz4Ej8dDeHg4gFmYR05ODnJyclBUVCR1TIGBgbh27RpiY2Px7rvvQlNTk0RqwcHBWLt2LXbt2iXV8aQoCl988QWSkpIQExND9qsz+9C+acT0vdi/lMrJ/gBdXV2oqqpCXV1dKnSkRzmpqKiQwYfALJZIVVUVysrKhIRKf6alpUWWAyCf0VIlst0xsVgstT5tenp6UFVVhZqamlT+TXfSVFRUGOuoq6uT5ZLb1NHRkTomYBa4qaOjw9B8plUK2I5p3rx55JgkUxH6fKiqqjLWoc8HvU/6c1r7SvI80aJh4+PjSE1NRV9fHwYGBrBlyxY0NDRAUVERPB4Ptra2WLx4MYyMjBAeHo5t27ZBJBJhcHAQJiYmjE6ZlpYWOBwOXFxcMDQ0BFVVVTx9+hRr1qxBXV0dXFxcyP4tLCwY509yueR54nK50NXVZfxm+prJovBpYq+sABxNLeFwOIxtKSoqkn1IHpOSkhIhQUteUyUlJaJOKXmsNDKbhmrQNj4+TiYASa4jFAqhoqJCoAmyx0Qvk/z9ysrKUFRUJDAHWkCOviclO44cDgdqampQVVWFiYmJVCqnpKQEVVVVGBkZSVFraB14kUgkdS+9SaT0fdt3Wvx+nQKgpLensRz09yU/ky0+0p/Jw3IIBALGfC3g1ViObdu2sf4Oet+yx/S6iNxTp069soAq+xkdPbEpDmhqakrV7iiKIsDOly9fIjY2Fn19fQgLC8NXX31Fvjc4OAhTU1N4eHggNzcXu3fvxqVLlxAYGEikY9rb27F161ZyDj08PFBeXg4jIyNMTExIRU5ubm6k4+fp6Qlra2s8fvwYiYmJSExMJLQYGuVMnz+xWIyhoSGGxtGpU6cYtBPatLS0CF9R0ujalyxolj6fGzZsYGxLskEheU1nZmZYu6BsjYtTp05BIBCQ4rHs9wH5TRY2McDXxfDRx8vWfKGPiW3fYWFhGB0dlduR/h7hAv+yfaeOiQ63X9cxAdKdCcnPZDsWko6J7YTOzMx8KyxHcHAw6zrynOXrdldOnTqF0tJSiEQihuwp/SCMj49Lvf3o6FGSXkI7IGVlZbS2tmLbtm24desWmWhCm4aGBnFAhoaGEIlEuHv3LpkaC4CM/aaJtcbGxkhNTUVtbS0BQiYkJKC8vBxOTk5EKpj+bba2tmhuboaamhqmpqbQ2NgIb29v/Pu//zsmJydRXV2N9PR0AMCVK1dgb2+P5cuXY2ZmBsPDwxAIBAwO4KlTp/DFF1+wUoNowKasjYyMSEkp00YXsCVTamDWKc7MzBBHJnlN3wQCcurUKWRnZ8/Z/ZV1AvRy2ekvb7Jv+njZur+nTp1Cbm4uKyxl8+bNuHHjhlxn+f8bx0R7edkT9F1iOdiWq6ioIDQ09I2wHN+mjauioiL1tv7P//xPqKioEECirEkC/tjkM0ZGRkjuTzsgNTU1VFdXo7e3l7T5aQfE4XDg4eEBExMTLFy4EIaGhhgfH8fDhw+xc+dOKYQ5PautsbGRIWzn4uKCtLQ01NbWQldXF9u2bYO7uzvq6+sxPj4OdXV11NXVkZYy7VSHhoYgFoshEAhw5MgRJCcn49q1a1i3bh38/Pzg4OCAxMRErFixAqqqqqisrERMTAyUlJRIWss2nZhWJJU91+7u7qyz64aHh0kKK7scAIM2ND4+TtDusjYxMUHuW8lrKgvepO3bQkDk8UfV1NTIPml7U6jMt8Xw7dmzh/U3vg32nTommq4h65i+SywH2/dVVFSwe/du3Lt3742wHFwulxWMp66uzupotLW1SRqjoqKC3//+9wBA6l6vI3tKURQmJiagqqqKsrIyNDc3MxzQ2NgYOBwOjI2N4e7uDkNDQ/T29iI1NRX//u//LnWj0eldW1ublGPicrlwcHBAVVUVVqxYQdr/L168wIsXL8DhcGBgYIDjx49DSUkJbW1tiI6OxoIFCxASEoJ//OMfUFVVRUdHB7kOExMTCAwMRF5eHjo6OhAREYGUlBQ8efIEHR0dEAqFUFNTw5IlS0jkNzw8jMrKSmRmZkIkEuGLL76As7Mz3NzcYGNjQ+guss6Ty+VCUVGRVS10aGhIrlqEiooKA+8ljxokK98seU1H5AxalXRkkkbfR/IiJnmUKHV1dbJPyeP6NsR2tuWA/PTy2LFj//9wTD8EL0je9+kTzOfzpRwTfRPJYqvoAikbslietMWbyJ5SFAWRSAQOh4PCwkJUVFQwHFBbWxvMzMykHFBzczNKSkpw5MgRqX1oamoiJSWFdeaYmZkZGhoaGFK8Xl5euHHjBnF+mZmZEAgECAgIgKGhIWJjY4lW+J07d2BhYUHUKSmKwokTJxAZGUnOrVAoxPLly0FRFNLS0uDk5ITg4GBYWFggNjYWIpEI69atk3pI9PT0YGNjg7S0NISEhGBiYgJVVVUoKysjxW1dXV2GhvpcswO7urpYx13RDkv2xShPEkeefDMtOig7w41eh015YnR0FJqamowojkbzywoFynNY9Gfylr8Jf/RNmRhvk/0gxW/gzXlB8pjUtCaNbN2G7izI3jhzjauZi0EuCXqT/L6sfIakk3rx4gUUFBRIF4z+XQ0NDTAzM4OJiQlxQJWVlejo6MDRo0el9sHhcJCTk8OYOWZkZAQ1NTU0NTUxlA+cnJzw/Plzxg1tbW0NbW1t3L17FyKRiGgx0cfe2dmJJ0+eQFlZGfPmzUN4eDgUFBSQn59PBP5bW1ul9KFbW1uxevVq1NXVIT4+HgcOHCATf1VUVJCRkQE9PT0plc2srCzo6+vDx8cHCgoKCAoKQm9vL0pLS5Gfnw+KovCPf/wDLi4ucHNzg7m5OZqamqCsrCwlRwLMXt+JiQm5uuts+lq0FK7sAyov9aMBtvKUJGSF6IBXK0/IOl7aKbJ1l6emplhR/jMzM6zp6KtSP1lHPRd39W2x7yViehNHo6amxkqu1NbWZhXLklT+e1XdBphb+e9VsqeSzo+iKPI2zMjIgFAoZDig6upqmJqaSjmg/Px8zMzM4NChQ1L74PF4KCsrY8wco2stL1++ZMwcc3R0RH19PUMj29PTE+np6aioqCCSvE1NTUhJSSHncMOGDQyRuSVLlqCkpAR8Ph/29vZQUlJCfX09hoeHsWPHDpibm+NPf/oT3nvvPULybW1thYuLCzZt2oSbN28iOjqa4KI2btyIR48eITIyEoGBgVi1ahVaWlpQX1+P7du3k/PH4XBgYmICU1NTUBSFHTt2oL29HVVVVcjLy4Ouri6BFshGILRUrGxNamZmRu7sQJoALWvynIY8h0VRFEZHR+U6oLnkm2V/h7wobq5xZmNjY6zyNnM5sjcp1L9N9p07JgUFBVZHo6WlxepodHR0WMfVvEndBvgnHuVNNJHZZE9pjAcAPHv2jAzalHRApaWlRDGSdkDPnj2Drq4udu3aJbW9vr4+1plj9Bu/s7NTar6bqqoqLC0t0dDQwNCodnJyQllZGUMiV0dHBw4ODsjLy4OpqSlSU1PR3NwMS0tLHDp0CNnZ2Xj+/Dnc3d2JE5yamsLt27ehqqoKLy8vZGVloampiTgEc3NzCAQCIlwHzIrUtba2knOkoaGB6upq+Pj4ICQkBAoKCti1axdycnKQkpKCjo4O8qKQTYsoikJeXh5sbW3h5uYGNzc3BAcHo62tDUVFRaiqqsLExAQB2rq7u0NfXx/19fUwMTFhdOS6u7tBURRr6idvdmBXVxeMjY3fWK5GngOSp+HF9n260/q648xo5Ql5+5Z11MCsI5N1uoB8uMXbZN+pY6JBZG/qHOaq28iOMv4242p0dHQY8hk02XRqagoZGRkYHh5mOKD8/HwYGxvD2NgYbm5uMDIyQkJCAhwdHRlYmebmZtaZY/QD3tfXJ5WWzJs3DxoaGmhpaZFyTMDsxA+6HiT5xnNwcIC6ujqKi4sZMAdPT0/cu3cPFy9ehIGBAcLCwsgYc11dXZw/fx6xsbEIDw+HSCTCnTt3MD4+jsOHD8PQ0BCurq6Ij4/HwMAAtLS0kJqaSl4CYvEsuF9VVRX9/f04c+YMBgYGCCxhfHycXDsOh4MlS5bAxMQEt2/fJnUntnHq3d3dOHjwIFmmoKAAGxsbNDc3Q0VFBVu2bEFtbS1ycnLIwIPBwUHWQQ3Nzc1QVVWVctjAP/mHbKlfR0cH60Tlrq4uaGtrM+o58iKpueSbh4eHGRAJevmbjDOTFB1k25a8cWbyvq+pqclK0n5b7Ds/MknnUF9fj1//+td4/vw5Fi1ahIULF+LZs2dYuXKl1PfnGlcjq8s9l+wpPa4mISEB//Vf/4Xy8nJoaGhg165dMDc3R3Z2NgYGBhgOKDs7W8oBGRoaIjo6GoGBgVi+fLnUPiwtLeWO/MnJycHixYuRn5+PkpISLFy4kIwPam9vl3JMHA4Hjo6OqKurY4DvnJ2dkZqaisbGRil8j6KiIjw9PVFcXIx79+4hNTUVo6OjWLduHZydnaGoqAhlZWVGt4Wewnv79m0kJCRgbGwMPT09OHjwIHmQraysYGZmhsnJScyfPx/FxcUk8k1ISAAA5OXlEcQ6Pcm3rq4OkZGRqKysJEM9KYpCfX09RCIR9PX1cf/+ffB4PPj6+oLD4UAoFCIlJQXW1tZSUcaf//xnxMXFYcWKFWhqakJubi7++te/YuPGjWSEuVAoRF5eHjo7O+Hm5gZXV1doamqirq4ODg4OclM/WecwNTWFwcFBxsDNP//5z6ivr2d1Jl1dXVBUVGRAGOZyGiMjI3KdhqqqKvbv34/ExERMTU3B0dER/+N//I8562GyDmuucWay9TChUIjf//73aGtrg6qqKmxtbXHo0CH8x3/8B+O8/dj2nR+NZD0nNDQUQqEQaWlpeP/998lbULKuIxkZSdpc42rYIiOKokh7+x//+Ae2b9+Ov/3tb/jwww9hYmICkUhEBh8aGxsjKCgIu3fvBjBbfzl27Bi2bNmCJUuWwMHBARYWFqwSqubm5ujp6WGgzOk3smz0o6SkBCsrK6L8KGlOTk5kTLikGRgYyB0ttGjRIszMzEBDQwP/63/9L3z88cdwc3NDXl4eRkdHMTMzg6ysLMZ69vb22LhxI4qLi9HY2EicNW3j4+OorKxEYGAgduzYgY8//piAAjdv3gwAePfddzFv3jwYGxvDwcEBHA4Hzs7OcHV1RWJiIng8HsRiMR4/foy8vDyEhITg3XffhY+PDx4/foy4uDgIBAJkZ2djeHiYEXVmZGRg//790NDQwIcffgihUIh169ZhZmYGLi4u0NDQgKGhIbZu3Qp1dXU8ffoUn332GS5fvoze3l7WVKqhoQHm5uaMlIm+tpKRVEFBAS5evAgLCwtWFgFdXJfVNKfHTclOAaYVLdjSr8HBQTx+/BhKSkpITExEdXU1/v73v8+ZKr7pODPZethf//pXnDt3DgsXLsTy5cvxt7/9DZ988okUU+Btse88YqLrNgMDA2hsbMSVK1fg4eEBTU1N5OfnQ0lJCVVVVSR6mEv2lK1oTVEU1NXV0d3djefPn5MWfH9/P4mAli5dCn19fRgaGsLQ0BBqamp4+PAhduzYISXzAMzeTJ2dnXJnjsmmmBYWFhCJROjp6ZG6qZ8/fw4ej4eQkBDcvn1baltOTk5ITU1ldE9sbW2hpKSEmpoaxpvbx8cHDx8+ZNQotLW1pepTfn5+WLZsGVRUVHD27Flcu3YNaWlpsLOzk0pTKIoimkccDgfPnz+HsbExudELCwvB5XLJeZD8zfQ509XVhbW1NVpbW6WOdcOGDTh9+jTi4+MhEAjQ0tKCjRs3kpQrJCQElpaWiI+PR3t7O0ZGRrB06VLGg/zo0SN89dVXcHd3x9KlS3H16lUYGRmhqKgIXl5eqKurw/r16+Hp6QlPT09MTU2hpqYGz58/J+vX1taSceVcLheNjY2McwsALS0tZBw4MItP2rdvHz7//HOUlpYSJU5JY9Mfp5fPmzePkfrRL2BZUCkNplVUVMTVq1fJcmtra1y9elVu9KOjo/NGoFJZJ5eTk4MtW7aQiTKrVq3CnTt3GHIsb4N9LxHT1NQUNDU1sWDBAly/fh08Ho+kaTY2NlI1AnmzuiiKgqamJjo7O/H8+XPExcXh4sWL+POf/4zq6moMDQ1JjX4OCgoiLWpjY2OcPn0aJ0+exH//939DSWl2uoe8FEzech6Px8A5mZiYgMvlSs0p6+3txYkTJ7BgwQLWLp+TkxNEIhFjLLOSkhJcXFxQUlJCGOG0ubq6QkVFhegKURSF6upqnD17lqQnvr6+CA4Ohrq6OpGTDQwMhI2NDWJiYqSOPTMzE/n5+QgNDcXBgwcxODiIs2fPorCwEDMzM2RgpmSjITk5GTMzM4TKAoCMq5LEmKmpqcHZ2Rl1dXXo7OzEgQMHGHUgd3d3hIeHk2Ni65LR47fp9Jn+7rx581BQUABFRUUprp2amhq8vLxIx3L9+vXg8/mIjY3Fp59+iuvXr0MgELDO6Kurq4OjoyNxwKdOnUJoaCjMzc0hFosZEdPExARGR0dZi8yyo6Ro6+joYJ0d2N/fT5zDrl27YGRkBC8vL1y8eHHOCT3ylrMV0dkc1tKlS/Hs2TNSDysrK0N2djZCQkIY2/2x7XtxTMDsTZWcnIySkhJoaWmRC/4f//EfUieYoihoaWmhra2N4YBaWlrQ1dWFzMxM9Pf3EwdEvwHfe+89qRRMJBJBJBIhLi4O//Ef/4FHjx5BT08PQUFBJDKSNQsLC/T19TFAm3RUIjsokcvlYv78+SQ1oygKhw4dwsmTJ7Fs2TJMTEwwIoF58+bB0NAQNTU1jP37+PhgeHiYUZxXVlbG4sWLUVhYiJqaGly5cgX37t2Drq4u3nnnHSxbtgyFhYUYGBhAU1MTvvrqK5w8eRIKCgrYvn07FBUVcevWLUxNTaGgoADp6elYuXIlfH19MX/+fLz33ntwcnJCQkICvvzyS0xOTsLLy0vqGBYuXAhjY2MpSRM6XWptbYVAIEBJSQnOnTtHrrOioiKr0+Hz+UhOToa6ujpsbGwQFRWFtLQ0UlgfHh5GZmYm/P39YWBgAIqi8NFHH2Hp0qWwtbVFXl4eFi1axGiLv3z5EgMDA1i8eDH8/Pxw+PBhfPDBB1i5ciVJka9du4aYmBhS96LTZzoSvHv3LoqLi/HnP/8ZDQ0NrN1j+j6QLaILhULG8E3aaIclW+Du7OwERVE4f/48HBwckJSUhJMnT+I3v/kNY8wTbXN193R1dV8LVPqb3/yGSKns2rULXl5e+OCDD7Bnzx7Gdn9se+NUjsPh/B6zEzdZTVNTEx9//DGGh4fxm9/8BkZGRsjKyoKqqioePHiA2NhYMiFUNgVrb2+HoaEhjIyM4OrqipGRERQWFoLP5+PEiROMfQQEBJCHnX54enp6sGrVKqLXdPXqVVhYWJBit2xqZm5uTtDEkjWKTz75BMPDw/jtb39Lir+0+fn5ITg4GDk5OSgoKMDY2Bh+97vfkU6fbLoIAB4eHsjIyGDgliwsLGBkZITCwkLcuHEDf/jDH6Q+O3z4MKKiotDV1YXk5GRERUXBxMQEBgYGqKysxL179/D5559j165dOHbsGDk/+/btw5UrV3DhwgWMjIxg8eLFUimNmpoatm7dSjSG6HNlb28PW1tbmJqaYmxsTCo9oRU3NTU1kZaWRlI3R0dHbN68Gdra2jhz5gySkpKkSKs0NGF4eBiHDx+GkZERnj9/jrS0NHR1dWHr1q14+PAhNDQ0iP7WL37xC5SXlyM7Oxs5OTmgKApLlixhnNfCwkLMmzdPKm3V0dGBj48PMjIysGjRImhqaqKyshIVFRVELoXL5cLa2hrt7e341a9+hadPn4LL5aK5uRkDAwNSUBRgFqUvK4MCzN5v8hDqbGPJgVkn19/fDzc3N/zpT38CMIvSr6+vJ9dd0kQiEfr7+0lzQdLm6rzJzkCMjIxEWloaNmzYgJs3b6KhoQEffPABzMzMpLqjb4N9mxrT1wDu0v9TIxMGUBSFmJgYpKenY3BwEL/61a9QXV2N/v5+cLlc8vYzMzODkZERXFxciETrr3/9a6kcuqenBwUFBdi+fTvx9LTFx8fjf//v/02oCdbW1hgfH0dHR4dUAVpFRQW2trYYHh6GkpISA1FtaGgIZWVldHR0SDmmX/ziF3j69CnMzc3xySefSDkzHo+HR48eQVVVFWlpacjNzSVdsB07dmDBggXw9fXFvn37cO3aNQAgHcmysjIpTA2Hw4Gfnx8ePXqEPXv2IDw8HJOTk6isrERrayshLR85cgQffvghOUZFRUUsXboUcXFxCAkJwWeffSZ1fgwMDLBy5Uo8fvwYKioqWLRoEeOtCsxGMjMzM9i+fTtGRkbQ0NCAx48fS6WWn346qyv/+eefk4iFy+Vi2bJlDKLt2rVr8ejRI7i5ucHOzg4jIyMEmhAREUHqLUuXLoWZmRnu37+Pr7/+GjMzM4iIiICysjJ++ctf4uHDh8jMzISGhgZyc3PJVGBJGxoaQlVVFSscobKyEgKBAIGBgdDR0cHy5cvR19eHiooK5OTkQCQS4euvvyaaXD4+PnB0dERYWBgSExMxNDSEr7/+Gnw+HwoKCmQ8u+x+Ojo6wOVyWRHqPB5PbiQ1PDzMqFeZmJhgcHCQERn19vYSfJms9fb2vrbD+vWvf41f/epXmJychJ+fH/z9/dHW1oY///nPP33HRFHUAADmsC8JE4vF6O3txfLlyzE0NAQTExO4urqipaUFJSUl0NPTw/Hjx8n3GxsbUVFRgZGREambnJ45NjExwXhbVlRUYGJiQor64OPjg97eXkxNTZHIRCAQoLW1FRYWFujt7UVHRwcDUT1//nw0NjZKzWAzMDBAQEAArl+/Dl1dXUZ6UlhYiJaWFnz55Zf44x//SJZXVlairq4O33zzDYKCgshyTU1NODs7o6ioCIsXL5a6wRcuXIisrCyUlJRAX18f+fn5UFZWxvr16+Hh4YELFy6grq4OBw4cIOt1dnYiLCwMa9euhZGREWpra6Vu9I6ODiQnJ8Pa2hpjY2O4dOkStm7dyojmcnNzCUyCw+Fg2bJlEAgE6O/vR3R0NDQ0NGBtbY3//u//xpYtW2BpaYmBgQHExcXB29ubAeDz9vZGVVUV4uPjERwcjPj4eKioqODQoUOMFNfW1hZr1qzBw4cPyYCDTz/9FLGxsUhPT4e1tTXu3LkDdXV1BmwDAHFcsvUsiqJQWFgIBwcHKQqHkZERPDw8kJ2djZUrV2JqagqVlZU4evQo1NTUoKSkBKFQCBsbG2zYsAG/+c1vwOVy0d/fj6GhIVaJnKamJlhaWjI6dfJSPxqhrqOjw9BEHx0dlcKE0dbZ2QkFBQWG8xsbG8P4+Dirw+rr62Oc78nJSaKyQAcAXC6XpNNvk30v4AUrKysYGxvjwoULePr0KRnlU1lZCU1NTcYFpt8qsvUcBQUFmJqayi1Od3d3S51UbW1tkgo8fPgQdXV1RGo3LCwMhoaGrBw4JycnvHz5koFYt7KygqqqKutwRScnJ8KBo5HLbm5u8PPzI9NgZW8YHx8fDAwMMATxKYqCmZkZ6urqkJ+fjyVLluD999+Hn58fVFVVERISgpaWFjL+uqurC0FBQbC0tMTvfvc72NnZISYmhgwS6Ovrw61bt2Bqaoq9e/fi+PHjsLKywt27dxEXF0d+58DAABoaGhiOUklJCWZmZqAoCvPnzyc0DxcXF5ibm5OIVLY7B8xGgGvWrMHY2BiioqJgZmaG48ePMx4SYPaBS0xMhKOjI7y8vPDo0SP09vbixo0b0NLSQk5ODhoaGrB69WoGfWJwcBDl5eVYunQpA/PT3t6Onp4eViBmUVER1NXVsWTJEgQHB+Ojjz7CoUOH4OLigrGxMUxOTmLVqlUwNzcn0V1tbS2UlJQYRXQ+n4+WlhbW1P3ly5fQ09NjRHldXV2gKAo7d+5Ebm4u/vSnP6GxsRG3bt2CSCSSetHS1tHRARMTE8bvpJ8L2ftMIBCgt7eXEa1t2rQJtbW1EIvFaG1tRWxsLD777DNWscQf274Xx2RnZ4fh4WEkJiZiYmICq1atgq+vLwoKCsDhcBgANTU1NcybN4/hmIDZky7PMdGIakn7y1/+AoqicOPGDSxatAhtbW1IS0uDnp4eHBwc0NDQwOiAOTo6gqIoBtaIlg6hc39Jc3Nzw/T0NKOgraCggOLiYnR0dDAK6jY2NjAzM0NGRgYoioJYLEZpaSm++uor1NTUQEVFBebm5ggKCpICSNrb28Pd3R2PHz/G0NAQnj59isbGRqSlpRHaSVNTE+7evYva2lrcuHEDOjo62LNnD5FXDQ8Px+bNm1FbW4svv/wSz58/x4sXL6ChocGaCgCzKSvb5GEaTyTrYAUCAXJycnDjxg3yRl62bBkrI76npwe3b9+GsbExdu7ciU2bNiE2NhZOTk6IioqCn58fHj58iOrqahQVFTHWT05OhpaWFqvzycjIgJGRERwcHBjHV1ZWhoULFxLUM4fDwfz584mzDQkJwejoKFRUVHDmzBnSubSysmIgpZuamiASiRiOiQaYymLagFkno6ysjJUrVyI2NhZ37tyBm5sbvvjiC6iqqiI0NJSxzlxdP21tbUbUSr+wZR3Wl19+CQsLC2RkZGDBggX4+OOP8c477+C///u/Gdv+se17cUwWFhaYmZmBlZUVkpKSMDg4iLGxMSQnJ0NFReWNHRAd4koajaiW3ZaysjIWLFiAbdu2kX3SyFsnJyfweDzGfuiuIZsDcnR0RE9PDwNPZWBggPnz5zMeGmtra8TFxUEkEqGiokLqMw6HgxUrVuDly5fIzs7G+fPn8eDBA5ibm+MXv/gFduzYgba2NlRVVTGOIzQ0FBoaGoiOjsb+/fuJ0D09B+/s2bOws7Mjgvf79++X6mBxOBx4eXnhl7/8JTw8PJCWlkbS6qGhIcb+aJ7cf/3Xf7ESYyXxTAMDA0hNTcXnn3+O5ORkuLi44P3334eFhQXi4+MZrfeOjg5cu3YNurq6xHkCsxzEX/ziF3B2dsaxY8dgYGCAb775BocPH5Zav7a2FnV1dQgODmY4i7a2NjQ3NxMNKkmrrq7G9PQ0qzMrLCyEubk5Fi1ahHPnzuF//a//hfDwcELobmpqwqVLl5CTk0O6dnV1dTAyMmLUcnp7ezE6OsoaSdEcRgUFBWzcuBEVFRWYnp4mI5nkIdTlqSnIW66oqMjATwmFQigoKOCTTz7B1NQUmpqa8Mc//vGtJPN+L46JdhqyDoDGbshzQHMhqmXXUVJSgrGxMcH0SJqjoyM6OjoYYm8WFhZEnZFtncbGRsb+HR0doaysTNIkSfPx8UFbWxsDua2jowMnJye8ePGCkb+rq6tDWVkZaWlpUFVVxdGjR7F7927o6+vDwcEBCxYsQFJSEkMkT0VFBTt37kRfXx8ePXrEiPqA2RuPy+VicnKSlRgNzEY7ISEhWLJkCTgcDvr7+3H27FmcOXMGT548QW1tLUZGRsi5++qrr6TgArRWkYqKCoaHh3H69GmcPn0aBQUF8PDwwC9/+Uts2rQJ2tra2Lx5M0ZGRojcLjBbG7x27RqMjIxw4MABRjRlbGwMGxsbUBQFHo+HvLw8qd86MzODxMREcq5kLT09HcbGxozPKIrCixcvYGdnx4jYh4eH0dTUJOWwFBUV4eTkBHNzcygqKmLTpk3Q1NQkDvjq1auoqamRi5FSUVFhINGnpqbQ2trK6rDa29thYGDAgEPQ971sxCQWi9HV1SU3kjIzM2OAMemXONs6b5t9Lyw+ZWVlGBkZsbZLzc3NUVRUxIqoFovFDEQ1Hap2dHQw8m97e3sUFRUxmPs0P6ihoUEKm0MD8erq6hjSIc7Oznj27BlaWlqkUgBlZWW4u7ujpKQEK1askNrPggULoK6ujqKiIkbdbPny5bhw4QLKy8uxcOFCDA4OIi0tDdXV1dDR0cHMzAz8/PwYb7z169fj9OnTSExMZOT+ZmZm2Lx5M2JjY6Gjo0M4hwKBAHfv3sXY2BiOHDmCwsJCPHjwAF1dXVi7di3rBOTy8nJ4eHhg48aNaGxsRF1dHWpqagigky7mJiUlEed69uxZCIVCKeetpqaG3bt3w8HBgRG9GBoaYvny5UhPT4eTkxOqq6uRm5tL9ssmyfH8+XOUlpZi06ZNGB8fR3p6Ojo7O7F9+3aoqanh6dOnmJycxIYNG1iJwa2trQgLC2ONlvr6+rBx40bGPouLi6GiosLgtFEUheLiYri6usLb2xve3t6Ynp5GbW0tCgoKIBAIkJubi/7+fri6umLBggVQVVVFXV0d7O3tGQXxxsZGUBTFmvo1NDSwcuo6OjpIqUPS6PFa8iImNoR6Z2cnK0L9bbTvjV5sbm4uN2XLyspitDONjY0Jolr2ZFtZWTHqGcBsapadnY329nYpDSYNDQ1YWlqirq6OARp0dHREaWkphoaGpC42TV8pLS1l1CZ8fX1RVFSE+vp6KedIk2pLSkoYdSFTU1M4OzsjIyMDHR0dKCkpgaamJrZs2QIPDw/cu3cPT548gb29vdR62traCA0NRWxsLGxsbBhKjR4eHhgbG0Nqaio0NDTg6+uL+/fvE8S1mZkZNm3aBDMzMyQlJaG5uZl002irqanB2NgY/P39oaioCGdnZzg7O4OiKIyNjaG/vx81NTUoLi6GqakpwZktWLCAjAIyNDTEnTt3oK+vzxq50BYYGIjy8nICmwgODmYU22krKSlBamoqVqxYQV5o5ubmiImJwYULF+Dj44OioiJs3LiRkT7RkZSdnR3jwReLxUhPT4ednZ3UeQBAQKIeHh6MlKapqQkjIyPYvn07WaaqqoqFCxeitbUVPB4PgYGBqKqqwsOHD5GQkID58+eju7ubNf2tq6uDqakpAwvV1dWF8fFx1kiqpaUFlpaWrDAFDofD6BaPj49jdHT0jVK/t9G+N0qxubk5+vv7GQVgOoyUTc24XC7MzMxYUzMnJyd0dXUxELnm5uaEWc62TlNTE0O0zs7ODlwul9Fp43A48PHxQW1tLSMFNDExIZGerC1evBgCgQD5+flSy/l8PtGHKisrw6pVq/CLX/wCCxcuhIKCAqFPPHv2jLFNDw8PLFy4EI8fP2bMdgNmH3Z/f38kJibi8uXLaGhowO7duwnXkMPhwNfXFxs3bkRXVxcuX76MnTt3wt3dHf/5n/+JnJwcWFtbM9rPtGyNvb09eYA3b95MyLZBQUHw9/eHg4ODXN6cpI2PjyMhIQFDQ0MQiUTw9vaGv78/q1PKz8/Hw4cP4evrSzqrwGxUfOLECSgpKSE1NRXm5uasoMXMzExMTEwgJCSEsf2qqioMDAxIwTdoKywsxOTkJKteU1FREYyMjBgPMw0z8PX1xaJFi3Do0CF8+OGHWLNmDRmX/vjxY0RHR6O2thZCoRAikQgNDQ2szqeurg5qampSXFFgtr3f3t7OqpjZ0dEBY2NjuZ062XRNKBSiu7v7J5HGAd+jY7KwsCCIaknT0NCAnp4eazRla2tLOh2SZm9vDw6HwyhOS0qHyNZcnJycIBQKWakejo6OKCsrY6zj4eEBBQUFufWkxsZGRhFcR0cHXl5eyMnJAZ/Ph0gkQn5+Pr788kuUlpaSYZ++vr5SN5GOjg6CgoKQn5/PWnPbsGEDdHR0cPfuXQaMgcPhYO3atTA3N0dXVxccHBxYO0Dd3d3o7u6Gra0tfH19sWvXLjQ1NaGrq4v1QZS0yclJMnhRntnY2GBkZITBcxwZGUFSUhK++uor1NbWIjg4GEuWLEFxcTHD0VIUhaysLCQmJsLf35/VsaioqICiKCgrK6OzsxOPHj2SSid7enqQk5OD5cuXM1IegUCAtLQ0ohgh+9nz58/h6enJWG98fBx1dXXw8fFhHA9970hGs9ra2vD394eGhgbmz5+PFStWYGBgAJGRkfj0009x+/ZtzMzMMKJxAHIlW+rr61lTP7FYjIaGBtb6VkdHh1yEOlun7m21780xGRgYEES1rNFKiLLm7OwMPp/PwBqpqalh/vz5ciOjoaEhVukQfX19VgySj48P+vr6GMempqYGV1dXoiogaa6urlBTU0NOTg5je8uWLcPMzAzi4+NJfcjR0RG//OUvsX//fvD5fKkCMG2LFy8m6GfZYreysjL27t0LPp+PO3fuMCK/Fy9eoLOzkzjme/fuMaSL169fj6tXryIiIgIffPABli1bBgcHB1AURVQi2WSQAflQAUmj0+fW1lYIhUJUV1cjMjKSOOXFixfj/fffx+LFi7Fy5Uro6uriwYMHpGYlEAgQExODtLQ0rFixghXBLRQKERkZCR6Ph+PHj2PTpk0oKyvD1atXicxLdHQ0DA0NWSkrmZmZGB8fZwVHFhQUYGpqihW8Sc9qkx3QSZ87Z2dnVhVN2ukvXboUJ0+exHvvvYfFixeTl8/Nmzfx6NEjtLa2QiwWE4FCeZGUhYUFYz+dnZ2YnJxkxTy1tbXJTf3YOnVvq31vjklBQUFuncnBwQG9vb2MNy0twyHPAbW0tDAePhsbGygpKbGu4+LigpqaGkY6aWtrCz09PdbUbC5SbUBAAIqLixmKA4ODg1BVVUVVVRX09PRw8uRJbNmyBTo6OtDV1cXy5cuRl5fHUB7gcrnYsWMHJicnWTttenp62LNnD3p7exETE0MiyeLiYqSmpmL58uXYs2cPwsLC0NTURHSJ2ExVVRXe3t4kip2cnER0dDQ++eQT3L59Gzk5Oejo6ACfzwefzydCZmNjY6yk1pmZGQwNDUFLSwvPnj3DJ598gnv37mF0dBTr16/Hhx9+iNWrV5Muk6KiIjZv3ozOzk7k5eVhYGAAV65cQV1dHXbt2oWgoCDGwyQWixEXF4eOjg6Eh4fDwMAA3t7eOHLkCHg8Hs6fP4/IyEiMjY1h586djOiuv78fL168IDI4ssdPR0uy9aqJiQnk5+dj8eLFcknD8sCbWlpaUqmXoaEhli1bBgUFBbi7u8Pb2xuNjY24du0a/vGPf+DBgwdQUFBgRD9CoRBNTU2sDqu2thbq6uqMtGxiYgIdHR2sUVlHRwerltTbat+rtqaNjQ2ysrIYE03ojkVdXR0WL15MlnM4HDIBdv369QxNoKSkJDQ1NUl1HJSUlGBnZ4e6ujopSgkwS4/IyspCZWWlVF2Cw+HA29sbGRkZCA4OZiXVFhQUMITf/fz8kJOTg+zsbISGhqKnp4coTZqYmGB6epooYUpaQEAAysvL8ejRIxw9elTqd+np6WHTpk2Ijo6GtbU1fH19pdY1NzfHzp07ERkZiejoaLi6uuLRo0fw9fUlNRMa90NL665YsQKBgYGM1CA5ORl8Ph++vr44duwYBgcHUVNTg+bmZqSlpZH0iKIoQtg9ePAgcez3798HRVEYHx8nLxUOhwMFBQUsX74cLi4uDIkPSbOyssKiRYuQkpKC1NRU6Orq4ujRo6xvcZFIhNjYWFRXV2PXrl1S9RczMzOcOHEC165dQ3NzMxYsWMBwPBRFISEhAbq6uoz7Apjt/vH5fNZo6fnz5+ByuVJyL7QVFBQwSMPAbE2xoqIC/v7+jPNeU1NDIjMDAwOsXr0aHR0dqKysRGFhIcRiMc6fP0/YA0ZGRmhuboZAIGB1TPX19XB0dGTsp66ujpQ3JE0sFqOpqYm1IP+22vfqmJycnJCWlsZowdMYD1nHRK9TUFCA3t5eqeKsnp4ejIyMUFdXx2iFuri4ICYmBoODg4zJKTSkQLZgOhepNiAgAA8ePEBPT4/UMaioqGDJkiV49uwZJiYmUFtbi3nz5mHXrl1YsGABYcx7enpKPWxcLhehoaH45ptv8Pz5c8aD4urqitbWViQmJkJfX59x0zs6OiI8PJwguymKwqZNmxgRlqKiIoKCgiAQCFBYWIjt27eTdKutrQ3FxcWYmZkhSg36+vpYunQpli5dCqFQiP7+fvT19aGnpwelpaVQVFSEo6Mjpqam8PjxYwiFQhgaGsLS0pKoQAwPDyM6Ohpubm6sU3Mlrb29HZ2dnRCLxdDW1saJEydYwX1CoRD37t0jSptsXb+BgQEMDg7C2NgYNTU1uHv3LrZt20YinLy8PLS1tZHxUrLrZmdnY+nSpawDBwoLC7FkyRKGxlF/fz+qqqpY62A0aZitMF9UVIT58+cTp83hcGBpaQltbW0UFBQgICAA09PTKCwsRHZ2NgwMDKCkpAQdHR2Go6clW9asWcPYT319PSwtLRlwgJcvX2J6epo19Xtb7XsV+jU0NISenp7c1KytrY1RW7G2toaysrLcdRoaGhigxQULFkBNTU1uatbV1UXkT2mTJNWyFcHnzZvHqAtNTk5ibGwMYrEYjY2NCAkJwXvvvQcXFxfi0AwMDFjTsvnz52Pp0qVIS0tj7TyuX78eNjY2iIyMZE3HNDQ0oKCgQEYfFRUVoaamRuqvoqICX331FdauXQsNDQ188803RI/7vffeg7KyMv7n//yfjG0DIDpKnp6eCA4OJm3xEydOEOR1WFgYtm7dirVr1xI9czs7O3A4nDm7cwMDA7h37x6uXLkCsViM4OBgjI2NMZDxwGxt6+bNm2hubkZ4eLhcp3Tnzh1YWlri2LFj2LNnD16+fIkLFy6gp6eHSMT4+/szUiQ6ktLR0WFVtpwrWsrMzIS2tjYDggLMOh9Z0jAw68za2toYkTAwm5IrKSkhKCgImzdvxscff4w9e/bA1NQU3d3dGB0dxcWLF/H8+XMSodbW1kJRUZHxu2ZmZtDc3Cw39dPS0mLVyXpb7Xt1THRqRncXJM3JyYk84JI2Fz9twYIFmJqaYnDaaDxRWVkZK3JbS0uL1Wn5+voSCWBJo1OTuro6dHV1EZ3qL7/8EmVlZbC1tYVYLIaVlZVUzs7lchESEkJwS7K2cuVKWFhYIDo6miHdyuVysWvXLujp6eH27dtSdZ2BgQHcunULxsbGiIiIAI/Hw7Nnz6ClpUUwSJJ/S5cuxfHjx7Ft2zZ0dHTg/v378PHxgZWVFat2D5vxeLzXAuKpqqrCxMSE4ZgoikJbWxvu3r2L06dPo729HVu2bMGJEyfg7+8PLy8vJCcnS/3O7u5uXLx4EQMDAzhw4ABrrWRiYgK3bt2ClpYWwsLCSFRHR1+XLl3CrVu3YGJiwhpVVFRUoLW1FaGhoYxIanBwEIWFhQgICGDUlvr6+lBZWYnly5cz1mttbUV3dzer86FJw7LRilgsRklJCdzd3UnUyOVy4ejoSLp9K1euhJ6eHtLT0/HFF1/gypUrJPqShQk0NzdDKBQy9kNRFEOt86dg3/toBCcnJ4yPjzMiFm1tbZiamsqlh7DhlkxNTWFqaio3MpqcnGQl1Xp5eaGiooJRBLe2toalpSXS09MZjpPWGXr48CG++uorPHv2DJ6ennj//fexZ88e6OnpISEhgbGetbU1PD09GQ8dfSw7duyAQCDAgwcPGOuqqKhg79694HA4uHbtGkZHRzE6OoobN25AQ0MD+/btg7W1NU6cOAEdHR1cvXoVBQUFrPQUDocDAwMDXLhwAe3t7eByuWhvb8c//vEPxMfHE7wNm9E8uVd15SR/Mz1vbmhoCBkZGTh9+jS++eYbDA0NYfPmzXj//fexcOFC8nCsW7cOSkpKePToEcRiMYqLi3HlyhWoq6sTNQRZGx8fx7Vr1yASibBv3z7GvMEjR45AU1MTk5OTrGklj8fD06dPiVaUpNGRlJaWFmt3LyMjAzo6OgzAK0VRSE9Ph6mpKQOywUYapq2+vh7j4+NynRldNN+1axc+/vhjbNu2DUpKSoQ+c/36dRQXF5MXXF1dHQwNDRm/u7+/HyMjIz+pNA74ARzT60iHyOKWHB0dweVyWUN9Gk8k2xmTR6oFZovgAoGAyIbQxuFwEBQUhK6uLqkojGaHz8zMoLe3F4aGhjh16hQ2bNgADQ0NKCoqIjQ0FO3t7ayYJ/qhi4mJYaSdOjo62Lp1K+rq6pCcnMxYV0tLCwcPHoRYLMaVK1dw7do1cDgc7N+/n9Q86O94eXnh8ePHuHnzJuN8AMDTp0/J7+js7MS1a9eQkZGBFy9e4Ouvv8ZXX32F+Ph4VFVVYXh4mDg4Ho8HAK90TDRvTkFBAePj4/jyyy/x1Vdf4cWLFzA3N8f+/fvx7rvvwsvLi/FgqqqqkrFMFy5cQHx8PNzd3XH48GHWMdgjIyO4evUqZmZmcPDgQdbvPH/+HKOjo/D29kZNTQ2uXr1KXg4URSE2NhYAWKEDlZWVaGlpQWhoKCMa6e3tRXV1NZYvX87oarW0tKCtrY21q1hVVSWXNFxUVARzc3MGyJWuXUrip1RUVODh4QEnJycoKCgQWMWjR4/w6aef4tatW6iurmad0ltbWwtlZWXWCTJvs33vE+8kR1uvWrVK6jMnJyekp6ejra1NKmdWVVWFq6srioqKCNmUNnd3dzx9+hTFxcVS8+mAWacVExODgYEBqaKhjo4OXFxckJ2dDS8vL6mby8bGBlZWVkhPT4eDgwMRWGtvb4e1tTUUFRUhFAoZKZCNjQ08PDyQnJwMJycnqbRHXV0dO3bswLVr15CZmclAHNPC+U+ePIGuri5jdLeenh727t2L8+fPQywWIzw8nAGYo52jk5MTHj58iLNnzxJ5Gbpbc+jQIYSEhODs2bPYtm0bYbALBAI0NTWhqakJLS0tZEyUkpISDA0NCUWmpqYGvb29xFFlZWWBw+GQIQ2yyH4dHR2sXbsWDg4OrDw4SROLxZiYmICCggJ6e3uxbds2BmaItsHBQVy/fh1cLheHDx9m1b4uLi5GZmYmVq9ejaVLl8Lb2xtRUVE4f/48du7cic7OTjQ1NWH//v0MXND09DSSkpLg4uLCiHooikJycjL09PTg6enJ+Cw9PR1mZmaMtFMsFiM7OxuOjo6spOHGxkYyFkvSSkpKoKCgIBc/5eTkhICAAAQEBGBiYoLIwszMzKCgoACjo6Nwc3Mj14CWX3mbh1uy2Q9ytI6OjigvLyfTR2kzNjaGrq4uKioqGMU8Hx8flJeXo6WlReqzf4VUe/bsWZSWlkq9weio6fr167h8+TI6OzthbGyMffv2wc7ODi0tLbhx4wYJySVt7dq1qK+vR3JyspTGNQCC/s3IyGAMdgRmwZUjIyNITEyEtra2VKgtFArx5MkTMtzz/v372L59O2th097eHu+99x6ePn2KxMREFBQUEOfA4XCQm5sLLS0tKYKokpISqUcBsylSb28v+vr60N/fT/BWxcXFBNcEgCDZNTQ0YGBgQLhzxsbGiIqKgpaWFit5VNYaGxuRnJyMvr4+uLi4oKWlBfX19ayOqbGxEffv34empiYOHDjAcNDALFmbhlAEBgYCmIVZvPPOO7h//z6uX78ODoeDwMBA1qgiNTUVAoGANZKqrq5GU1MT9uzZw4iWmpub0d7eTtJvSauoqMDg4KAUz442mjTMNjadJg3LdgQ7OjrQ19eHdevWkWWamprw8/NDf38/eDwe/P39UV1djXv37kFZWRm2trbo7OxkTRffdvtBHJO9vT3RTZbFLXl7eyMzM5N0gmiztLSEgYEBioqKWJ2WPFLtwoULUVRUhBUrVkhtjx5wkJWVhYULF5KbjB70CMwWX7du3QoPDw9yo9na2pIozdHRUSoy0tTUxJo1a/Do0SM4OjoyOkjLli1Da2sr7t+/jxMnTjAEvdatW4exsTHcv38fYWFhsLe3h1gsRmxsLNra2rB//36YmpoiLi4Od+/excqVK7Fs2TLGQ6CqqorNmzdj0aJFSE5Oxp07d2BlZUWc+4oVK+YE1mlpaUFLS4tEC6WlpXjw4AH+/d//HYqKihgbG8Pf//53/PKXv2R1DMBsnYmmarAVWSmKQlNTE168eIGWlhZYWVnh2LFjMDc3R0VFBWJiYuDm5kauJy1TkpqaCnt7e2zfvp1RkAZmC8/37t0jY9sl962uro6tW7fi9OnT4PP5GBgYAJ/PlyJNNzY2orCwEOvXr2f8tunpaTx58gQLFixgYIPoaElS0ZM2sViMzMxMODk5MfSVZmZmUFxcDE9PT0ZUyUYapq2oqAh6enqs3biKigr4+fkR6Mfg4CDBSAFMjaefgv0gc4FVVFRgZ2fHWjPy8vKCWCxmrf/II9WamprCzMyMtZ4UEBAAkUjESh1ZsWIFRkdHUVJSgunpaaSmpuLLL79ETU0NfH19ST1I9sFat24dxGIxUlJSGNv09vaGs7MzGU4pafQoJQ6Hgzt37jCK7xwOB9u2bYONjQ3BKCUkJKCmpgY7d+6EtbU1VFRUsHv3bqxYsQLPnj0j9Aw2MzU1xYEDB7Bnzx7i4EQiEbhcLgOWMZdNTk5CRUXljcJ/a2trTExMMIrqfD6fjHi6desWpqensXv3bhw6dIggl93c3ODo6IiEhASi137//n2kpKQgMDAQ4eHhrE6JlqS1tLTEjh07GIBDgUCAyMhIoqfU2tqKCxcuENXT8fFxxMbGwt7enpFOA8CzZ8/A5/PlRlIdHR1YuXIl434pLy/H0NAQK2k4Pz8f09PTrAX2V5GGvb29WfFTfD5fCj+lr6+PFStWwMDAgACGf2r2gw0s9/LyQmdnJ4OWoampCScnJ1Y8kaen5xuTajU1NeHr64u8vDxGS97Q0BCurq5ITU3FF198gdzcXPj7++P9999HaGgo3Nzc8PTpU8Z6mpqaWL16NUpKSvDy5UupzzgcDjZv3gwVFRXcv3+fUcjX0tLCvn37MDg4iHv37jE+V1RURFhYGJycnBAZGYni4mJs2rRJKhKk082wsDC8fPkSZ86cYZ1RR3/X0dERhw4dgpqaGnR1dZGcnIxPP/0UUVFRqKmpkcuPo+11oQKSZmVlBQUFBcKbq6urQ3R0ND799FM8fPgQurq6OHjwII4fP44FCxZIPWAcDgehoaEQCAS4d+8ezpw5g6amJuzatQurV69mOBxgtqh7584d2NraSqlg0iYWi3H//n309fVh79698Pb2xokTJ6CoqIhLly6hvLwcMTEx4HK52Lp1K+OB7+rqQkFBAVauXMkotPP5fCQlJcHJyYmRGtKj6J2dnRmFbT6fjxcvXsDb25uxzbGxsVeShuXhp+zt7Rl1t8HBQbS2tv6k0N6S9oM5JkdHR2hqaspt9b8pqdbd3R0aGhrIyspibC8wMJARNVEUhfLycoKCNTQ0xPvvvy/F5woODoZIJEJqairrMZqZmeHRo0eMB1tNTQ07duxAZ2cnq4yJsbExdu/ejebmZlaIAS35QpssFos2Z2dnvPfee7C0tERUVBRiYmLkRk+VlZWYmprC3r178eGHH2LVqlUYHh5GVFQU/vrXv5LC/MuXLxn8w8nJydeGCgAg3UtNTU2kp6fjr3/9K+7evUukRuihitbW1nKxNEpKSjAyMkJLSwu0tbXx7rvvyq1XlZSUICoqCgsWLMDu3bsZkR1FUXjy5Anq6+uxa9cucm7nzZuHY8eOYcGCBYiNjUVrayu2bt3K+K1CoRDx8fEwMjJiMBOA2UhqenqayMFIGl1LlRctzczMyAV20t032d9SVFSEBQsWMI6TJg3L6/qpqam9Vs3vbbQfrFTP5XLh5eWF/Px8rF27VoqKIEmqlRXy8vHxQVlZGZqbm6XeTkpKSliyZAlSUlKwbNkyqaK6pqYmFi1ahLy8PAQEBKCrqwspKSno6emBk5MTKIoiusiSpqmpiVWrViExMRGenp5Sx6KgoIAtW7bg4sWLePLkCTZt2iS1rqWlJVatWoXU1FRYWloyCtV2dnbYtGkTHjx4AE1NTakUoKysDCkpKSQNffz4MXp6ehASEsKoDWlqaiIsLAzl5eV48uQJ6urqsGzZMiL6BszezLm5ubCzsyNTXZcsWYIlS5YQQGlraytevHhBHKmOjg7Rr6ZxT7W1teByuSSVrq+vh4KCAng8Hng8HmHG0yksfayrV6+GnZ3da6UQQqEQBQUFyMzMBEVRMDAwwMTEhFQdiDaRSISnT58iPz8f3t7eCA0NZY2msrOzUVBQgI0bNzK6ZbRiQHl5OTgcDtLT02FoaChV/0tOTkZ/fz+OHj3K2H53dzfy8/OxZs0a1kgqPT0dLi4uDP7f9PQ0iZZka1ljY2MoKirC8uXL5ZKG2cZ4s5GGgdlzWlpaCk9Pz59cN462H/Sovy2p1tjYmDxokrZo0SK8ePECmZmZjK5YYGAgCgoKyCRaS0tLHD58GFZWVhgfH8fXX3+NtLQ0xlQKX19flJWVISEhASdOnJC6MY2MjLBhwwbEx8fDxsaG0VUJDAxEZ2cn7t+/j0OHDjGKjgsXLgSPx0NKSgpEIhHWrFmD+vp6PHjwAF5eXli7di04HA6MjY2JSNzu3bsZ7W0OhwNPT084ODggIyMDz549Q2FhIVatWgU3Nzcyvmjfvn2Ma2BgYAADAwP4+/uT+X99fX3kr6WlBcPDwxCLxWSwAV2fun//PlRVVaGmpgYNDQ3o6OiQzpyRkRF4PB5u3779Wk5JLBajuroaaWlpGBkZgY+PD4KCgjAzM4OzZ88iNTVV6mHk8XiIjo7Gy5cvERISAl9fX0b0RRekaYgGWyTR29uLe/fuwd7eHkuXLsX9+/cJpMDa2hq1tbXIz8/H+vXrGRQOsViMR48ewdDQkDWSSk9Px9TUFNauXcv4LC8vDwKBgJVQnJ2dTUbCs603b948RleXJg0HBATIJQ2z/f6fiv2gjokm1RYXF8sl1ZaXlzM6d/QNJCu7q6SkhMDAQCQnJ2PZsmUELzI8PEzY8qOjo4xOm5aWFlatWoUnT55g4cKFUvIRCgoKCA0NxaVLl5Cbm8soUnp5eaGlpQXx8fEwMzOTwqhwOBxs374d165dw+3bt3H06FEG/ikwMBBcLhdJSUkYGhoiqoYbN24kx+ft7Q1DQ0NERUXhwoUL2Lp1K6somLq6OjZs2AA/Pz8kJycjNjYWaWlpUFFRwbx581hb45JGz+2TfQC/+OILuLi4oLa2FlevXiV1sffffx/GxsasUQowm9LRdSZ5jmlmZgalpaXIzc3F8PAwHBwcsGfPHhLZaWhoYNWqVUhKSoKbmxusrKzQ1taG2NhYCAQCRERESMko00bjjXJycrBmzRoCG5C00dFR3Lp1ixCvlZWVceLECQIpCAwMRGFhIZydnVmL4YWFhejq6sLhw4cZkWxPTw/y8vKwatUqRr1nenoaubm58PHxYURLo6OjKC4uxooVKxhRYk9PD2pqarB582ZWOMJcpGF6luNP1X6wGhNtPj4+covgzs7OKCwsZNRgXFxcYGhoyCq25uvrCw0NDWRmZoLH4yExMRFff/012traCAKb1keWtEWLFsHU1JRQIiTNzMwMfn5+SEtLYxwnh8PBxo0bySgl2XqQkpIS9uzZA2VlZdy6dYuhPgkA/v7+WL58OWpra6GmpoZt27YxHnZLS0ucOHEC+vr6uHHjBh4/fszo6tGmr6+P8PBwvPPOOzAxMUFfXx/Gxsbw9OlTdHd3s1JW5jIejwdNTU388pe/RHFxManj0URieaasrAxzc3NWQm9vby+Sk5Pxj3/8A0+ePIGZmRmOHTuGvXv3EqdEGz2k4cGDB0hMTMQ333xD1AjkOaWEhATk5ORgw4YNrE5penoat27dgoKCAvbu3UtKCTQ+avHixcjOzoZIJEJwcDDjfunv70dKSgq8vb0ZdBmKovDo0SMyvVnWMjMzIRQKWaOlrKwsKCsrszrCjIwM6Onpya07OTg4MBwdTRr+KUdLwI/gmGhSLY2xkDQ/Pz8MDAww6CsKCgpYsWIFmpqaGMx8JSUl+Pv7o6ysDF988QXKysqwcuVK/PKXv0RAQABWrlyJwsJChnwtHRn19PQw9LoBYM2aNTA0NER0dDTDIdCjlHp7e/HkyRPGg6+hoYH9+/djamoKd+/eZRTLh4aGUFRUBB0dHZKisLXztbS0EBERgfXr15OWu2xXUNJMTEygq6sLFRUVgmG6cOECzpw5g8zMTAwMDLzSSdE8uW87SYPmzYnFYgwODiIrKwtnz57FuXPniOj/+++/j507d8rVn1ZQUICfnx+GhoYIYPTQoUOsNBQ+n4979+6hqKgImzdvZn3AaRXM8fFx7Nu3j5Ea086Ww+GAoijcunVLSgJYIBAgOjoaOjo6rNCBoqIidHZ2IjQ0lBFJ9fb2Ijc3F8uXL2fg2EZGRlBSUoIlS5YwoqXu7m7U1tay0mCamprQ09PD+lvlkYZ/avaDO6a5SLXz58+HjY0NmVQraS4uLjAyMpKKmkQiEQoLC0n3TUdHB++//77U2Gg/Pz+YmJggISGBERmZm5vD19cXz549YxBuFRUVsXPnToyNjeHx48eM32FmZobQ0FAUFRXhxYsXjM/nzZuHPXv2oKenB7du3SKdr/Hxcdy4cQOqqqo4fvw49u7di/b2dly6dIkhDwzMPiyLFy/GyZMnoampiatXryImJoaVG0djhhYtWoT169fjo48+wr59+2BmZobs7GycPn0an3/+OWJjY8mkGNnz/Lo8OVmjKIrUpqampvD555/j66+/RlZWFoyMjLBnzx7827/9G9avX89KKaFtbGwMDx48QExMDLS0tEBRFKytrVkjtaGhIVy+fBlNTU0ICwtjbafPzMzgzp07RAVTNjoDZus4ubm5CA4OxjvvvAMOh4NLly6RwaN02r1z506GftTExARSU1OxcOFCRjRHR3L6+vqsuKWsrCyoqqrKjZbmzZvHGi2lp6fDwsKCkd7PRRr+qdmPcvR0Eby0tJRxUYKCgsgwQclWJz3F9t69e2hra8Pk5CRSU1MxODhI9JMyMjIwMjIi9banI6PLly+joKCAUWBcvXo1ampq8OjRI+zZs0cqhNfX10doaCji4uJgY2PD4Ep5e3tjdHQUKSkp0NbWZozatrCwwIEDB3Dr1i3cuHEDO3bswN27dyEWi3Hw4EFoaGjA3t4ex44dQ2RkJC5duoTt27ezTsXQ19fHoUOHUFJSgmfPnqGmpoZoS9Nv25KSEgiFQoJd4XK5sLe3h729PTZu3Eim1La0tBBAK82Po8cy0dEdj8fD0NAQFBQUiNMeHh7GxMQE6crxeDwMDAygv7+fwZvT19fHpk2biL7Wq4yWus3JyYGSkhI2bNgALy8vXLlyBQ8fPsTx48elIoempiZER0dDXV0dx44dY3U4fD4ft2/fRnd3N/bt28eaBtbU1ODJkycICAgg98axY8fw8OFDREdHo6ysDA0NDdi4cSOj00ZRFBITE8lwCFkrKSlBe3s7Dh48yIh6+vr6UFpaitWrVzPOT1dXF+rq6lhT/MbGRnR2dmL//v2sdSd5pOGfmv0ojklHRwfu7u7Izs6Gt7e3lHe3srKCra0tma8uefIXLFgAPT093LlzB3w+H3Z2dti5cydMTEwgFotRU1ODhIQERpvXwsICPj4+SEtLg4uLi1RITdM57ty5g7y8PMb0EE9PT7S0tCAhIQHm5uaMgmJQUBBGR0cRFxcHLS0tRvfE0tISERERuHnzJs6ePQsul4sjR45IRQ36+vo4evQomWW/dOlSrFixgvHWU1BQgI+PD9zc3MhDXFxcDH9/f3h7eyMvLw+urq6stBElJSXipIBZrFJXVxfhx/X19aG2tpaklHFxcWRdetm5c+ek2tl0kd3IyIhEtKamprh37x7U1NRYHaysTU9Po6ioCLm5uZiamsLixYuxbNkysp/Nmzfj4sWLyM7OxooVKyASiZCdnY2MjAzY2dlhx44drKjwqakp3Lx5E4ODg4iIiGCdDtLe3o6YmBi4urpKORZlZWXs2LED8+bNQ1ZWFtTV1Vl/S1FREZH+lU19eTwekpOT4enpybgn6EhKT0+PNVpKT0+Hvr4+K5cuPT0dlpaWjGhJJBIhKysLCxYseKWS6E/BfrR4b/ny5aioqEBRUREjigkKCsKVK1dQXV1NyKd9fX1ITU0lSO9169ZJFRrpyIgW05JFvNKRUVJSEnbu3Cn1maOjI/z9/ZGcnAwrKytGmz8kJASdnZ2IiorCkSNHpB4EDodDpsbevXsXR44cYXSkjI2NYWBggPb2dmhoaLBidFRUVBAWFobs7Gykp6ejoaEBW7duZaCH6e/SSgKZmZnIyMhARkYGKdy+jqmrq0s5KtqKi4sRHx+Po0ePkghofHwcf/nLXxAeHg4jIyNoaGhAXV1dbrpgbW1NRnvLA1SOjIwgNzcXJSUlEIlEcHd3x4oVKxhpnqmpKQIDA5GZmQljY2NkZmaip6cHy5YtY5C4aZuYmMDNmzcxPj6OgwcPsio30iqY5ubmrMjvmZkZNDQ0QEtLC2KxGBcuXJDSHqfri76+vqwgRpq+xBZJlZaW4uXLl4iIiGCcw87OTjQ0NGD79u2s45y6uroQERHBig4fGRlBeHg4Y38/RfvBa0y06evrw8PDA9nZ2YzisKWlJezs7JCRkYHh4WE8ePAA586dQ39/P7Zv3w4TExNUVVUxakaWlpbw9vZGamoqg1+npqaG4OBgVFVVMRQrgdlit4mJCWshWllZGWFhYRgfH0dkZCSjE8flcrF7927o6urixo0bhIsFzL7lHjx4gM7OTmzZsgUUReHChQusRWwOh4Nly5bh+PHjAICLFy8Sh8Nm2tra2LhxIz788ENoampCQUEBUVFRuHXrFsrLy+V28eay6elpqKiokBqGra0t0SC3sbEhk2TnqmFYW1tjenqaIRFME07v3LlD1EAXL16MDz74AFu2bJFbe6IjqMjISAgEAhw9ehQrV65kdUqdnZ24cOECJicn5TqlwcFBIr5Hq2BKmkgkQnR0NIaHh7Fv3z6cPHkS+vr6uHbtGnJzc0nB3cDAgPVF0NraitLSUiJxLGmTk5NITk6Gh4cHQ9udhjwYGBiwjitPT0/H/PnzGREYTYNxdXX9yYxnepX9aI4JmI2aeDyeXDJuf38/vvrqK9TX1yM4OBinTp2Cu7s7NmzYgM7OTqIjJGlr1qwhOCFZc3d3h52dHeLi4hiOi8vlYufOnXJHKRkYGGDPnj1ob2+Xqz554MABorVNt+mfPHmCiooK7NixAwsXLsTx48dhYGCAa9eusXYmgdnu2vHjxxEYGIiMjAxcvHiRdUQ6bWNjYxgdHcWWLVsQGhoKPp+P2NhYfPLJJ7h//z5qampem8QryZM7ffo0XFxc3phvZWFhAS6XS8Zt1dXVISYmBp9++iliYmIwOTmJDRs2EKqMbJdM0l6+fIlr164R/qKnp6fcbl5paSmuXr0KHR0dHD9+nBVL1dfXh6tXr0JZWRkREREMeRG69d/c3Izdu3fD2NiYQAr8/PyQlJSEc+fOyR0ZNTU1hdjYWFhZWbEW45OTk0FRFGskVV5ejra2NmzYsIF1AkpPTw+rIF1JSQlGR0elJhj/1O1HLd3PmzcPnp6eyM7Oho+PD5SUlCAUCpGfn09EyVRVVfGLX/xC6gaiL3pKSgpj8KCamhrWrl1L0NSSuTiHw8HWrVtx7tw5xMXFYd++fXJHKdnY2DCKiFZWVti2bRtpHctqSmtoaODgwYO4efMmrl27BhcXF5SUlCA0NJSE+xoaGjhw4ACSkpKQkJCAnp4ebNiwgVEc5XK5WLVqFZydnfH48WNcv34djo6OWLt2LaPOlZeXBx0dHbi5uZE61MjICCoqKlBRUYHKykpwOByYmZnBxsYGNjY2MDc3Z00pJXlyp06dwqlTpzA2NsbaqmczWi1TU1MTmZmZ5EE0MDDA0qVL4e7u/lq640NDQ0hJSUFNTQ1MTU1x+PBhVFZWIiMjAy4uLlJ1FEmqipeXF0JCQlgjuu7ubty4cQM6OjrYv38/a+cxIyMDpaWlDFArl8slXMqCggJG6x/4Z3QsEAiIqoSktbW1obS0FKGhoQxnPDU1RWR/2QYopKens+p6CYVCZGVlwc3NjbUB8FO1H72nuGzZMpSVlaGgoADq6up49uwZxsfHiZzIrVu3UFVVxRC7WrNmDWpra5GcnIxt27ZJfebp6YnS0lIkJCTg3XfflbpJNTU1sW3bNty8eVPuKKWWlhYkJibC0NCQAaZzdXUl4EUdHR1GNKGmpoaIiAicP38eJSUlWLhwIePY6aEFNIyht7cXW7duZcxGA2ZhCUePHkVVVRVSUlJw5swZ+Pr6YtmyZdDS0sL4+DgqKioYLHxdXV0sW7YMS5cuxfDwMFpaWohaZXZ2NoB/8uMMDQ0JX2xoaAgqKipELkXWRCIRJicnSVduYmKCdOUkeXOKiooQi8XYsGEDbG1tMW/evNcSw+fxeMjKykJBQQG5Vu7u7oSqU19fj4cPH+LgwYPgcDgYHh4mQzHlUVWA2UL3rVu3YGBggH379jEiJWA28sjIyMCqVasYHVhgtltWWloKJycnDAwM4OLFi9i6dSvR4crLy0NdXR3Cw8MZjlwkEiEhIYE0YmSNpimxpYYVFRXo7e3FoUOHWI95fHz8/6loCXgLHNO8efPg4OCAlJQUUBQFFxcXrFq1ijykCxcuRGpqKoNdra6ujrVr1+Lhw4dYuHChVL5Oy2icO3cOaWlpUqp/wCyhlh6lNH/+fAZxeP369RgcHCTFbNkIJSAgAKOjo0hMTISqqioDJtDQ0IDh4WFoa2ujsrISDg4OrAVSb29vGBkZISYmBufOncOaNWvg5+fHeLA4HA4RUcvLy0NWVhaKi4vh7u4OLpcLLpfLSk2g1503bx40NDRw9OhRlJeXIz09Hbq6uoQfV1VVxcBF/fGPf4SioiI4HA5JAz/55BPWSERbW1uqM2diYoKpqSlcu3YN5ubmrA5X1gYGBpCTk4OysjJwuVwEBQXB399fSs5EWVkZmzZtwo0bN1BYWAgOh4OnT59CXV1dLlUFmC0aR0dHw8zMDHv27GGNFGtqahAfHw8fHx9WhPbw8DBu374NY2Nj7NixA2KxGA8ePEBUVBSWLFmCBQsWkJFRbEqjNMD1xIkTjOvb3t6O4uJihISEsEZSSUlJcHV1Zfw+yWjpp0w/YTPOm9IVWOxf3kBDQwNu374NPz8/hpTE5OQkvv76azg6OmLr1q3SO6YofPPNN+DxeDh58iTjoXnx4gWSk5Oxd+9eVk3mb775BmNjY3jnnXcYb9Dp6WlcuXKFFFtlbxixWIyHDx+irKwMmzZtIo6hsbERd+7cgZubGzZu3IgHDx6gqqoKy5YtYxUVA2bTn5SUFBQUFMDa2nrOQjB9bEVFRcjLy8P4+Dh0dHSwZcuWOWVFfvWrX6GhoQGJiYkkkpM0gUAAHo+Hy5cvw9LSEo6OjgQUyuPxsHr1aqSkpBAnJ/nHpu8tFArx17/+FStXrmQFFwL/HPGUk5OD+vp6aGhoYPHixfD19WWNaGiLjo5GdXU1KIqCt7c31q1bx+psKIpCVlYWnj17BmdnZ2zfvp31WCsqKhAbGwsXFxfWbtjk5CSuXLkCiqJw5MgR8oKkKAo5OTlITk6GoqIi9PX1GXgrYHZgwfXr1xEUFMSIbEQiES5cuABFRUVWNYNHjx6hsrISp06dYqSP+fn5ePLkCU6dOvVazv817K2Z7/SjFr9pc3BwgLe3N8rLyxn6Qurq6lizZg3KysoYBWA6MhoeHmZFXwcEBMDBwQFxcXFyRynx+Xw8fPiQUcxWVVXFvn37IBQKWdUnaRkUX19fxMfHIz8/H+3t7YiKioK9vT02b94MJSUl7NixA6tXr0ZWVhbu3r3LWoRWVlZGSEgIDhw4gOHhYZw9exZ5eXlyu3GqqqoIDAwk460VFRVx/fp1fPHFF0hNTZXqCgJAYmIinj59ik8//ZR1e8AszklXVxd8Ph+WlpZYuHAhFi9eTBwFMMsv9PLygqOjI8zNzaGrqyt36ICioiIsLS1ZeXP9/f1IS0vDl19+iWvXrmF4eBibN2/GBx98gGXLlsl1SmKxGAUFBWSijZmZGTZu3MjqlGZmZnDv3j08e/YMK1aswO7du1mPtbi4GDExMfD09GR1SgKBAHfv3sXU1BT27dsnFbXTQ06tra0hFAoxMTHBGFPG4/EQExMDGxsbVh2mvLw89Pf3Y+PGjYx9d3R0oKioCKtWrWI4penpaWRmZsLDw+O7ckpvlb0VjgkAmaDCJl/r5eUFS0tLPH78mPGwGhkZISAgAJmZmQxZV7rYzeVyERsbK3eUUm1tLStBWEdHB/v27cPAwACio6MZ63M4HISEhCAgIACJiYm4fv06TE1NsXPnTvLWpNUR9u7di7a2NrnUE2BWl+rdd9+Fu7s7njx5grNnz5KR4LJGURTy8/Ph6OiIU6dO4dChQ7C3t0dhYSHhpmVlZaGqqgrHjx/HjRs3Xsl/o3lyysrKGBsbk/r7NmZtbY2XL19CJBKhp6cHz58/x/nz53HmzBnk5+fDxsYGERERckc8Sf7WhoYGnDt3Do8fP4aLiwu2bduGrq4uVrlmWaoKWycLAHJzcxEfHw9fX19s3ryZ4RhoeeLu7m7s3buXFbj4/PlztLa2IiQkBPPmzZOa9UePjKIoihXFPTIygvT0dPj5+cmVWDE1NWUdJkAPUJCdPPT/ir01jklDQwNr1qxBaWkp2trapD6jI6PBwUHWyGj58uXQ0dFhZfurq6tj+/btaGtrQ2ZmJmNdJycnrF69GpmZmazwAxMTE+zevRtNTU2sMAIOh4NFixZBWVkZQqEQFhYWrA+Yg4MDjh8/TnhYtFyqrKmoqGDjxo04efIkdHR0EBkZiWvXrqGrq0vqey0tLejv74e/vz84HA7mz5+PjRs34uOPP0Z4eDgMDAyQlZWF6OhoHD9+HM3NzaitrYWBgYFcIi8drcbHx0NHR4f8ydbgXmUURWFwcJBMWPn0009x/vx5pKenY968edi9ezc+/vhjbN68GTY2NnMWxXt6enDz5k3cvn0bGhoaOHHiBLZs2QJ3d3e4ubnhyZMnUtCPyspKXLx4EUKhEMeOHZNLZs3KykJSUhKWLFmCkJAQVm2nJ0+eoLa2Vi7huLy8HKmpqVi+fDkWLVqEgwcPwtfXF48fP0ZcXByysrLQ1NSEbdu2MSIekUiE+/fvQ11dnTGGDJiNpPr6+lgjqc7OThQWFmLlypVyh0P81O2tqDGRDVEUrly5Aj6fj3feeYeRqz99+hQFBQV47733GC3nnp4eXLp0CT4+PqySp7SAWEREBCtF4PHjxygqKsLevXsZaGhgFlkbFxcHT09PqbfrxMQErl69Coqi4ObmhqysLHh6emLjxo2sDorP5+Px48coLy8nOkzycDwURZFRR/39/XBxccGSJUtw8eJFNDQ0QFtbG+fOnWNdt6CgAM+fP0dycjI++ugjtLa2oqOjAxRFgcvlwtjYmHTkjIyMoK2tjfHxcdy8eROHDh2SOr9jY2OwtLTE6OgoeRBosi6Px8PY2BjpytH/CgQC8rDPnz8fy5cvh6Wl5WuTS7u7u5GTk4OKigro6+tj7dq1jDHXPB4PZ86cgbW1NUJDQ5GQkIDq6mq4uLhg48aNrCmhSCRCYmIiioqKEBQUhOXLl7M6pYSEBBQVFWHjxo2sXbSWlhbcvHkTHh4eDL2kiooKPHjwACKRCD4+Pti4cSNj/ZSUFOTk5ODw4cMMuszo6ChOnz6NhQsXMpQrxWIxLl68CAA4fvz4nDI038LemhrTW+WYgFkHc+HCBaxatYrRHZmZmcHp06dhZGTEOssrPz8fiYmJCAsLY50Vf+PGDQwMDODkyZMMDAut2Nja2opDhw6xIoYli6Tbtm2DUCjEN998g4mJCRw5cgR6enooLy8netFhYWFy32g0cZiiKISGhjKQvrLHVlJSgufPn2N4eBhGRkbo6+uDr6+vXDE4a2trhIeHIz4+npwnZWVlmJqawsTEBAEBAXByckJ/fz+rhrmmpiapyUxNTeFXv/oVvvjiCygqKoLH42Fqakoq8lJUVCROjv6ztLTEvXv3wOFwWNU0ZY12xDk5OWhpaYGOjg4CAwPh7e0td/xUZWUl7t+/DxUVFSgoKCAkJITBMaNtYmICUVFR6OrqQkhICGsnk+62VVRUYNOmTawgyd7eXly9ehXm5ubYu3cv49impqZw5swZTE9Pk0k5kp06erqLPEG7qKgotLe349SpUwweYG5uLpKSksjoq+/YfnZMc1lSUhIKCwtx6tQpRneqtrYWkZGR2Lx5M+OmoSgKUVFRaG1tJamQpI2Pj+P8+fPQ09NDREQEoxg6MzODa9euYWxsDEePHmXtjNXU1CA6Ohp2dnbg8/no6+vDoUOHpKgAXV1diIyMhEgkQlhYmNxUiMfjkXFNrq6uWL9+/ZwoaLFYjLq6OiQkJIDH40FfXx+LFy+Gq6sra/3o5cuXUvWhrq4uBAcHIzo6GosXL4aFhQUoisLo6CiZr5efn48VK1ZgamqKpMWTk5MIDw/H3bt3oa2tzejKaWpqQldXlzUly8rKQnZ2Nn7zm9/IfbtPT0+jqqqKFILNzMxIC36uiGBycpIg67lcLt555x25IMPOzk5ERkaCoijs3r2b9ZqIRCLExMSgpqYG27dvZ3VwY2NjuHz5MtTV1XHo0CFG4V0oFOLWrVsEd/Ts2TPU1tZi2bJlCAoKAo/Hw7lz52BmZsb6cqUd7Y4dOxj7Hxsbw+nTp+Hh4cGQhP6O7GfHNJfx+XycOXMGJiYmCA8PZ1y8Bw8eoLKyEidOnGDciFNTUzh//jy0tbVZ5SY6Oztx7do12NnZYdeuXYwbn26Z0yoAbOlAfX097t69CwDYv38/q+wtj8dDVFQUAf7Jk6KgKApVVVWksB8YGIiAgAC53S5a68jV1RXT09Ooq6sDh8OBvb093N3d4eTkJHfd1tZW2NjYsMIFgFl4RUZGBn73u99JLaeR35Kp3OtaR0cHLl++jKNHj0qlLAKBAA0NDaioqEBDQwNEIhEcHR2xZMkSWFlZzVl3EgqFBM9Fj7ailSNktd+BWaoKXUjevXs3K2pbKBQiKioKzc3N2LlzJ2ttanp6GlevXgWfz8fRo0cZ26Eoiji2iIgIWFlZgaIoPH/+HGlpaaR7NzIygnfeeYcRtQ8NDeH8+fNwdHRkRY7Tkj+/+MUvWBUVvgN7axzTjw6wZDMVFRWsX78eUVFRqKurY9wkNFcuOjoax44dk3oQ6VFKV69exbNnzxi0EXNzc+zcuRN3795FUlIS1q9fL3UDaGhoYN++fbhy5QquXbtG+G+0URRFZrpxuVxkZGTA1NSU4cA0NDQQERGBJ0+e4NGjR2hvb8f69esZNxQNnrSzsyNKAXSLWFKnnLbi4mKIxWKsXr0ampqamJiYQFVVFSoqKnD//n0oKyvD2dkZDg4OsLGxeSPBN1pS97s0U1NTKCsro6WlBfPmzUNLSwsaGhpQW1sLPp8PMzMzrF69Gm5ubqwOQ9JoJ56amorR0VH4+vpixYoVBEsVHx8PV1dXUiOk57/Rjjg0NJS1xjU9PU3Spz179rCmx7SMytjYGA4fPsx6rCkpKaisrJRSIaC7smZmZkTNNDQ0lHVkVHR0NDQ1NaX032lraGhAdXW13InE/6/ZWxkxAbM34Z07d9Db24t3332XcTH6+vpw8eJFeHh4MEYpAbOTJ1JTU7Fv3z7WYnZhYSESEhKwdu1aVgBgX18fUZo8cOAAtLW1pQTvt23bRrShVFVViSQIm5WVlSExMRHKysrYvHkz6/HQJssRW7t2LQFOikQifPnll7C1tWWNDIaGhlBRUYGqqioiDWtkZET4cfPnz5/zpn7w4AEGBgZw9OhRqeXfNmLi8/loa2tDYmIiJicnCRaMZs+/CWK5ra0NycnJ6OzshJOTE9asWSO1LkVRRH/p3XffRVdXFx48eIDJyUkEBwezTrEFZhHnd+/excTEBMLDwxmNEWC2NnXjxg1MTEzgwIEDrFI0dH0zODiYoekFzBbLb9y4AU1NTUxOTmL9+vVSwy2fPHmCwsJCHD16lFHfpCfHzJs3j1Ug7ju0tyZiemsdEzCL8zh//jxsbGywa9cuxgUpKirCo0ePsHPnTlaZiDt37uDly5c4fPgwqxxEamoqsrOzWdcHZuUxrl+/Di6Xi4iICFRWViI1NRXr168nGlLDw8OIjIzE0NAQtm3bRnhTsjY6OoqHDx+iubl5TrQybW1tbXj69Cm6urpgZmaGgIAAgquhhw7MZePj44Qf19LSQignkvw4ukitq6sLVVVV3LlzBxwOB3v27AEwqy5w+vRpiEQi1NfXszomiqLA5/MxPDxMOnL0H71PFRUVzMzMYNOmTbCzs3tt5yYWi1FbW4ucnBx0dHQQRy0rF0Lb8PAwzpw5g3nz5qGvrw/W1tbYvHmzXNJwfX09kfANDw9nBSqOjY3h+vXr4PP5iIiIYK1h0XVPf39/Vq7bwMAALl++DFNTU4SHhyM5ORmFhYWk69bU1ITIyEip+4o2iqIQFxeHmpoanDx58vsWgfvZMb2u1dTUICoqCiEhIQzCLEVRuH//PhobG3HixAnGRePz+YSycuzYMdaHKjY2FtXV1Thw4AAr12pkZATXr1/H1NQUpqensXz5cgbuZGZmBg8ePEB1dTWWL18uF9BHT7d4+vQpNDQ0CI5HnlEUhaamJuTk5KC5uRlcLhc6Ojo4ceLEnE6NbTvDw8Po6OiQaunThFvgn4L8KioqMDU1hbq6OqnPTU5OYt++fbh16xZUVFQIiZf+VxJ4Kuv4LCwsMDU1hcuXL+PIkSOvhYmSHfE0f/58LFmyBA4ODnNGCy9fvkRkZCQmJyexePFi1mkn9PmgqSpOTk7Ytm0b6/kcHh7G9evXQVEUIiIiWJ1Ce3s7UX7YuXMnY38TExO4fPkylJSUpEQGy8rK8OjRI+jp6WFsbAw2NjbYvXs3Y/3S0lI8ePAA27ZtY+h/fw/2s2N6E0tISEBJSQmOHTvGOg/+/PnzUFNTw5EjRxjF7vHxcVy+fBkqKio4fPgwI5URiUS4efMm0YVme3DoyExJSQlHjx5ljb4oikJ2djbS0tLmvNkBEPG7trY2uLm5YfXq1XNy44B/4qg4HA6UlZXh6ekJd3d3mJubf+vQns/no7+/H2NjY+DxeEhLS4Ouri7mzZsHHo9H4ABTU1M4deoUTp8+DXV1dairq0t15dTV1aGjowNDQ0PW3ywWi/G3v/0NS5YsITQaWaMoCt3d3aioqEBpaSn4fD5cXV0REBDAUBSVtbGxMaSlpaGsrAwWFhYQCoWYmZnByZMnWTuvdASyYsUKrFixQm6Kd/36dSgpKSEiIoJV9qWrqws3b96EoaEhDhw4wKhfzczM4JtvvsH4+DiOHTvG2EZnZyeZ28fWhevv78fFixfh6urKmrp/D/azY3oTEwqFuHTpEoRCIU6cOMEq3n758mX4+vqygiv7+/tx5coVmJqaYt++fQznJSlav2fPHqkopqWlBbdu3YK9vT2Gh4cxPj6OXbt2yY106PRAQ0MDW7dulRshUBSF0tJSpKWlsWpdy1p0dDS6u7sRERGB/Px8lJeXY2JiAvPmzYObmxvc3d3/ZYb5n/70J6xcuZIxG+1f6crRdvv2bQiFQkREREgtHxwcJJpRg4OD0NDQgLu7OxYvXvxKZ83n84n2ubKyMlauXAlvb28MDQ3h3Llz8Pf3l2p+dHV1ITY2FmNjY9i2bZtcVPjLly8RFRUFdXV1HDhwgLXQ/fLlS9y+fVuujIpYLJYqJbCl3nS90sLCAu3t7VKOUiAQ4NKlSxCLxTh+/PhrDXT4Duxnx/SmNjAwgAsXLsDFxYWhMgDMIp0fP35MJtPKWmtrK27evAlXV1dWjWearPny5UuEhYXB3t4eXV1duHbtGiwtLbFnzx5CDG1tbUVwcDCrRAkw+7DFxsaiq6uLzLaTh3iemZnBixcv8OLFCygpKWHFihXw8fGRcp6jo6P44osvEBwcTGoQYrEYra2tqKioQE1NDfh8PkxNTeHk5ESE4OSBEtlMIBDgT3/6E2vK8F04lZDfDAAAJ5ZJREFUphcvXuDZs2f49a9/jd7eXrS0tKCurg5dXV1QVlbGggUL4O7uDhsbm1eimWnA6bNnz8Dn8xnTYgCQVO3YsWMwNjZGRkYGsrOzYWJigm3btsnFOxUVFeHx48ewsLBAWFgYKz6spaUFd+7ckSujQlEU4uPjUVZWhr1797J2+Wht9bVr1yIgIIAcr729PbZv347U1FSUlZWR4/+B7GfH9G2MTme2bt3KKuSVlJSE3Nxc7N69m7UITYPXli1bxkp+FAqFuHfvHhobGxEcHEwmoUZERJA3llgsRnJyMnJzc+dsQYvFYrx48YLww7Zu3TpnSjI2NoZnz56htLSUzCHz8PCAoqIikpOTUVRUhI8++oj1zSkUCtHQ0IDKyko0NTWBz+dDSUmJzOmztbWFsbHxnCnfyMgIvvjiC9Yu5r/imCiKIqOKcnNzoaSkBIFAABUVFdjY2MDd3R0ODg5ysVeSJhKJUFlZiefPn6O/vx8eHh5YtWoVa5olEolw6dIl8Pl8KCsro7+/H8uXL8fSpUvlCuDRVJVFixYhODiY9Xv19fWIioqCtbU1wsLCWI87MzMTz549w5YtW1jxYg0NDbhz5w58fHykeHpNTU24f/8+OBwOJicn5dJhvkf72TF9W4uLi0N1dTVOnDjBSF0oikJ0dDTq6+sRERHBmkY9f/4cKSkpctu6IpEIkZGRZELGu+++ywqyLCsrQ3x8PExMTBAWFiYXg9PX14fY2Fj09vZi2bJlrJNVJa2npwfp6emoq6uDhoYGfHx8kJeXRzp5rzKxWIzu7m7SjXv58iWEQiErZcTIyAhaWlrgcDjo6urCxYsXceLECUa7+nUcE0VRGB8fJx05Se6cQCAAl8sFRVGYP38+Vq1aBTMzs9fmecnqTzk4OCAoKGhORy8SiUgLnsamsdGMgH9SVehpuvJE96qrq3H//n04Ojpix44drC8kuh65cuVK1npaV1cXvvnmG9ja2mL37t2Mc9Da2orr169DQ0MDH3300fcJDWCznx3Tt7WZmRlcuHCBILPZKAE3btxAf38/jh49ymgBUxSFlJQUvHjxAqtXr2bw8WhRsLGxMQgEAikROFmjqSdisVguzQH458yvrKwsMlmDDS0uaQMDA2S8kVgshqenJ1asWPFaetmSJhQK0dHRge7ubgbJFpjluGloaIDL5WJoaAguLi7Q1dWFmpoaeSh4PB6Cg4ORlJQEdXV1TE1NScnr0n80hUVyiKahoSFMTU1haWmJ6Oho8Pl8HDx48LWOXXbEk4eHBwICAl6pbd3W1oYnT56gt7cXFhYW6OjowMmTJ1lxZq9DVQFmlQTi4uJIKYDt5ULz2Pz8/BjAXWC26XH58mXo6uri4MGDjGhLIBDg6tWrmJ6eRkRExCtrbN+D/eyY/hXr6+vDlStXYGlpifDwcFYS5ZUrVyASiXD06FEGypaiKDKLTbK9PzMzg+vXr2N4eBiHDx9GXl4eCgsLERAQgDVr1sidYXbv3j10dHQgKCgIgYGBciOB7u5uJCYmor29HQ4ODli7du2cDxlFUfjqq6/A5XIxOTmJyclJkv4sWLDgWyOAKYrCyMgIgQzweDy8fPkSbW1tsLCwwOTkJIFHTE9Pg8/n47PPPsMf/vAHqKqqQk1NTaozR/+3np4ewUXJ0z9KSUnBb3/7W7k1Nz6fj9raWlRUVKC5uRmqqqrw9fWFn5/fK1Hpg4ODSElJQW1tLczMzBASEgJjY2OcP38eysrKUgqRYrEYeXl5SE1NnTPqpQcBZGZmwsvLi1WGBJitaaWlpWHJkiVYs2YN4/fTkAmxWMx6T4rFYty7dw9NTU04fPiw3Ojue7afHdO/as3Nzbh16xar7AQw+7a9dOmS3LcT8M+0zt/fH6tWrcLdu3fR0dFB1AUoikJeXh6ePn0KW1tb7NixQ66UxrNnz/DixQuYmZlh69atcjtkNKUlJSUFIyMj8Pb2xsqVK1mpI7TkMH2jVlZWoqKiAi0tLeByuXB0dCQ1mn91Vv2LFy+QmZmJ3/72t4zPvoviNzCbpp4/fx4HDx6UQlgLhUI0NjaioqIC9fX1EAqFmD9/Ptzd3eHu7v7KjtTk5CQyMjJQWFgILS0tQnGh74n29nZcuXKFoPyHhoYQFxeH9vZ2LF68GGvWrJErURMTE4P6+nqsXr0agYGBrBIpaWlpyM7OliujIhQKcf36dQwODuLo0aMMPBQ9arywsBDh4eGvNcH4e7KfHdN3YXQxnE1LGfhnPk+D19jCb5pKoKenh9HRURw4cIBBS2hubkZ0dPQrqScdHR2Ii4vD6OgoVq1ahcWLF8uNniTHVInFYixduhSLFy+Weghv3LiB6elpHDt2TOpmHxsbI/y47u5uqKiowNHRkVBPvk0KkJycjJqaGrz//vuMz74rx0RRFD755BP4+fnB29sbzc3NaGlpQX19Paanp2FiYgI3Nze4ubm91rgogUCAgoICIgC4dOlS+Pv7szoZut4UGBiInJwcaGpqYsuWLXIHGAwMDCAyMhLj4+PYsWMHQzOe/j1JSUnIy8uTS20Si8W4f/8+6uvrcfDgQdZR5fQLMjQ0lFWt8ge0nx3Td2Wv0wGJjIwkagKyNy1FUbh27Rra2tpgbW2NAwcOsDqT4eFh3L17F8PDw3NSTwQCAVJTU5GXlwcrKyts2bJlThrB5OQkMjMzUVBQAGVlZZK2TE5O4ty5c9i+fTtjCoukDQwMoKKiAo2NjUTlUk9Pjzip1yXyyuPJAd+NY5qcnERLSwtSUlIwMTFB6lEmJiZwcHCAu7v7a89F4/F4yM/PR0FBAaanp+Hj44OgoKA5fyfNrRQKhfD19cXatWvlRmKvQ1URi8VISEgg003YhoLSMiq1tbXYvXs36/SUV3WKf2D72TF9V0ZPTi0tLZWLGWlsbERkZCSsrKwQFhYmdUPSfDlvb2+UlJTA2dkZ27ZtY039JKknc6GGgdkCbFxcHHg8HlauXAk/P785u3Gjo6PIzc1FcXExRCIRdHR0MD09jY8++ui18UhTU1NobW0lHTlaW5weryT5Z2BgIPUbb9++DQUFBYSHhzO2+yaOSSAQYGBggNGdo3lzGhoamJycxLZt22BnZ/dKHXJJkxzxpKCgAC8vL/j7+8/ZEBCJRCgqKkJqaiqUlJTA4/HkRiavi94XCoVk+s3mzZtZX4iSMiq7du1idUo0ts7NzQ1btmz5oTtwbPajHwBtP3nHBMy+ve7evYu2tja5KNvW1lbcvn0bpqam2Lt3L1RUVJCTk4OnT5+SMLy2thYxMTHQ19dHWFgYa0okybOysbHBli1b5KYd9FimwsJC6OnpYc2aNXB2dp7zBpyenkZOTg5JT+zt7eHv7/9awENZGxsbQ1tbG3p7e1n5cbq6utDU1ISGhgba29uhpaWFhQsXQkNDA8rKyuQ4JyYm4OPjg6KiImhqaoLP50t14+gO3cTEBEZHRwmVhebN0X/W1taYmprCuXPncODAgVd2JoHZ893a2orc3FzU19dDU1MTfn5+rxzxRFEU6uvrkZKSgoGBAQK3ePr0KSorK/Hee+9JXbfx8XHEx8ejoaFhzpfO2NgYoqKi0NPTg23btrGSv2dmZnD37l20t7cjPDyc9WVJN3DkqWD+SPazY/quTZKXJE99sqOjAzdv3oS+vj4WLlyIx48fIzAwUIq20NPTg8jISMzMzGDXrl2sMhjALBju4cOH4PP5CA4OxsKFC+U6nL6+PiQnJ6OxsRFWVlZYt27dnLKoGRkZyMrKQnBwMIqKitDb2wstLS24urrC3d0dpqam/zI/rq+vD0NDQ8S5NDc3Q1FRESKRiDHQYXp6Gn/5y1/w29/+lnQCaZiBLGdOX1+fwATkzXr79NNP4ePjIzd1oUGZ5eXlqKysxNjYGJmG4+bm9spCf3d3N54+fUqE8dauXUu6XNPT0zhz5gyMjY2xd+9eALOSyYmJiVBUVMSmTZvkFp9pqgqXy0VYWBgrjmp6ehq3b99Gb28v9u7dy1rDGh8fx6VLl6CmpoZDhw69TfpKPzum78NoJjcAREREsIb43d3d+OabbzAzMwM3NzdWpcDJyUlER0ejtbUV69evx6JFi1gdwfT0NJKSklBaWgoHBwds2rRpTrGzpqYmPH36FH19fXB3d8fq1asZ0ZZQKMQXX3xBBhVQFIWOjg6iszQ5OQl9fX3SsfquZDBonpy/vz8EAgFmZmZw9epVQjItLy9HZ2cntLS0oKKiAiUlpW/tHO/du4fx8XEcOXJEavnw8DDpPPb390NNTY04Y0tLy1fuT5LMa2BggLVr17IqEtTX1+POnTtYv349WltbUVtbC3d3d2zYsEFuFCZJVdm1axcrdGFychI3b97E8PAw9u/fz/ryoWVU6EGqb9mUk58d0/dltEwJTRiVbdu3tbXhxo0bAGZTmYiICNabQywW4+nTp8jLy5uTegIAdXV1ePToEYRCITZs2AB3d3e5D5Ekz4su3ErWSehO43vvvccoBotEIrS0tBB+nEAggKmpKWxtbWFjYwMrK6vXonbI2lw8OeC768rRlp+fj6SkJPzbv/0bent7SXeus7MTSkpKcHZ2hru7O2xtbV8rxRkdHUVeXh5pIAQFBc05wAAArly5gvb2dqipqWHTpk1ymxmSVBVfX1+sX7+edbuvIyb3OjIqP7L97Ji+TxsfHycaSgcOHCAkyJ6eHnzzzTcwNTXFhg0bcOvWLXA4HISFhckFtL0u9WRychKJiYmorKyEs7MzQkJC5oye+Hw+cnJykJ+fj+npabi4uMDf3x8JCQnQ1NR85VQRgUCAuro61NXVoaWlBTweD1wuFxYWFoQfZ2Zm9loP9lw8OeC7c0xisZgMqczPz4eCggLEYjHU1dVhY2MDJycnODk5vTaTnh7xVFVVBSUlJSxatAiBgYFzpkY8Hg+JiYmoqqoCl8uFnZ0dEcaTNUnw7Fy67X19fbh7967clyHwejIqb4H97Ji+b+PxeLh58yZGR0exf/9+qKqq4sqVK2RIgYqKCkZHRxEZGYn+/n5s3rxZbluepi2IRCJs3LhR7tsVmOVTJSQkQCAQkMECcz1oMzMzKCsrQ05ODoaHhwHglR0/WaMoCv39/aQb19raCj6fT/hxMzMzyM7ORkVFBXg8Hry9vRETE0PWn4snB7y5Y3oVb05ZWRkikQhWVlYIDg6GkZHRG/1W2RFP/v7+8PLymlM8TyAQIDc3F9nZ2eByuQgJCSHDA9hI3/X19YiPjweAOakqNTU1iI2NhZ6eHsLDw1nLB729vWQSsjwZlbfEfnZMP4RNTU3h1q1b6O/vh7KyMhGLk8S7CAQCxMfHo6KiAkuWLMHq1atZu188Hg+PHj16rXoEPVc+Pz8f6urqWLVqFTw9Ped8+MRiMa5cuYLe3l4IhULo6+tj0aJFcHNze6OBAvS2uru70d7ejvz8fFRXV8PMzIx0yxQUFGBmZgYtLS2oq6uDz+ejsrISoaGhMDAwgIaGhlTaOjY2Bmtra7S2tkJbWxtCoVCqGyfZnaOHX/L5fABM3pyVlRXMzMwQExOD0dFRVtwUm01OTqKqqgoFBQVvNOKJoihUVFQgLS0N4+PjWLRoEZYvXw51dXVQFIXIyEh0dHTg1KlTUFNTk6ob2tvbY/Pmza+kqtDTWdheQJ2dnbh58yb09PSwf//+N4JH/Aj2s2P6oYzP5+PLL7/E5OQkq0ogMHuT5eTkICUlBXZ2dti+fTur06Fv8tfp4ACzNYXU1FRUVVXBxMQE69atm1Ov+ssvv0RoaCiMjY2Rk5ODuro6UBQFW1tbuLu7w9nZ+Y0kdYVCIaytrfGHP/wBR44cwejoKIliBgYGMDExAR6Ph5GREUxPT8vdDltXjjYFBQUpvpympiYMDAyk9MTZHHJhYSEeP36M3/72t3IjypmZGdTV1aGiogJNTU2gKAqOjo4ICAh45YgnQFo33dnZGWvWrGGAJcfHx3HmzBk4OTnB3d0dDx8+xPT0NIKDg+Hl5cW6D0mqCj2Yle17L1++xK1bt2BkZIR9+/a9Td03efazY/ohbXR0FPfv30d3dzd27dol15k0NTUhOjoa6urqCA8Pl4tEHhsbQ3x8PBobG7Fw4UIEBwfPedO1t7fj6dOn6OjogKOjI9asWcPY9pMnT1BeXo4PP/yQFLAnJydRXV2NiooKvHz5EoqKiuQBsre3f2X9KD8/H4sXL8aVK1fw5ZdfoqenBwsXLsSnn34qhb95/vw5MjIy8NFHHxFHNTU1RT6fmJhAQEAAysrKoKWlBS6XSyACKioq36o7NzAwgNOnTzPqWiKRCM3NzaioqEBtbS0EAgEsLS3h5uYGV1fX14oeBwYGkJqaSsi869atk0s9Af4pMggAtra22Lx5s9wa0OtQVQCQAQPm5ubYs2fPD6VA+a/az47phzahUIj79++jrq4Oq1evxpIlS1gfqKGhIURGRmJkZGRO+VWKolBSUoKkpCSoqqpi8+bNcsd109+nZ6KNjIyQN//8+fMxMzODzz77DH5+fli9ejXr+iMjI6SV3tfXB1VVVVhbW5NCt76+PuP33L17F3v27IGVlRU+++wzWFtb4+9//zuePn2K+vp60hWS5cn9/ve/xx/+8AfGMXxXXTn6fHz22Wfw8PCAt7e31ESXqakpGBoawt3dHW5ubq8l9UJRFNrb25GTk4Pa2lpoa2tj9erVc3ZIgVk1yocPH2J0dBQqKir41a9+Jfcl8zpUFYqiUFBQgCdPnsDOzg67d+/+Vp3SH8l+dkw/honFYjx79gzZ2dlwd3fHpk2b5FJPaMH6V/GqRkZG8PDhQ7S0tMDFxQVr1qx5JUWioqICOTk56Ovrg5mZGQwMDFBRUYEPPvjgtR783//+90hPT4etrS0sLCzA5XIxNjZGHuzm5makpqaivr4e+/btw/nz53HixAkAs2mIhYUF/vjHP+Kdd94BwOTJ8fl8UiMCZiNES0vL78wx0ceanp6O8fFxiEQiKCgowNzcHDY2NliwYMErFTdpE4vFqKmpQU5ODjo7O2FgYAB/f394enrOCcQcHR1FamoqKioqMH/+fAQFBeH27dvw9PRkjN8WCARIS0tDbm7uK6kqCQkJKC0thb+/P9auXfvGaP0f2X52TD+mVVVV4cGDB9DX10d4eDhr2E6/+VJSUl7JRKcoCmVlZUhLS8Pk5CT8/PywbNmyV1ImJEczKSkpYdWqVa/sLgGz6QTNgxMKhaTr1dvbSzp7WlpaUFRUxKNHj3D8+HEEBgbC0NAQSkpKROrj//yf/wNgbp4c8O3hAq/izWlra2NsbAy7du2CnZ3dG9XPZmZmUFJSgtzcXIyMjMDa2hoBAQGvHPHE5/ORlZWF3NxcqKqqkgEGHA4HeXl5ePLkiZQsC60YMTIyglWrViEgIOCVVJVNmzaxSj//BOxnx/RjW09PDxnZvHv3brlOR1K7h9ZtkheaCwQCvHjxAs+fP4eioiJWrFgBX1/fOWtB9Nw8e3t74qDoqSevU+CVNZrI29XVha6uLhQVFUlFcHp6eigqKoKbmxsWL14MdXV1vHjxgihrstWNZB0TPeSSrTPH4/EwNjaGvr4+DA8Pk06grq4u6cyZmZkR3tzXX3+NvXv3yq3VSJokCr6iouKNRjyJxWIUFRUhPT0dMzMzWLJkCZYsWSLlDCmKwtWrV8kcwufPn7+WxlZ7ezuioqKgoKAgl6ryE7GfHdPbYJOTk7h37x5evnyJ4OBgudQTsViM3NxcMndt69atrLo6tI2Pj5PBAnp6eli7di2cnJxYt3316lUAwOHDhzE2NoaCggKUl5cTZ0A7qW87KeODDz5AXFwc/v73v0NdXR2pqakYHh6Gl5cXpqenMTk5Cdl7QEFBQSoFmZ6exh//+Ef8x3/8B1RVVSEWi6WGXNJGd+a0tLSk9MXn4s19/vnncHNzm1PPvL+/n/DmRkZGoKWlBXd3d/j5+b0SqEhRFBoaGpCcnIyBgQF4enpi1apVciO/gYEBnD17FioqKuDz+a9UJX0dqspPyH52TG+LiUQiPH36FPn5+fDy8kJISIjc2kR/fz/i4uLQ3d2NwMBArFixYs46Rm9vL54+fYrm5mZYWVkhMDBQKtWggY27du2Ci4sLWY+iKLx8+RIVFRWorq7G1NQUjIyMSDH4TYTgBAIBfve73+HGjRtkft0//vEP0pUTi8X485//DD8/Pzg4OJAoSNLx8Hg8rF69GqmpqdDQ0ACHw5GCCGhoaEBNTe1b1VNiYmIwMDBAamC0jY6OkmJ/b28vVFVV4eLiQiLJV+2Loig0NzcjOzsbra2tsLa2xrp16+aUrBWJRMjMzERWVhYoippTC0uSquLj44MNGza8LQoB/4r97JjeNispKUFCQgL09fWxbds2Vq4TMPsgP3/+HOnp6dDX18e6detYaRy00UjljIwMUpwNCAiAh4cH4uPj0dbWhvfff1/ugyYSidDU1ETa50KhEIaGhkQEztra+l/Cx7yKJwd891w5SSsuLsajR4/wq1/9isyba2lpQW9vL4FHuLm5wd7e/rXkg2WbC6amplixYgUcHR1f2Z1LSkpCf38/li5divr6eojFYpw4cYLhcPr6+hAXF4fe3t45qSo/QfvZMb2N1tPTg7i4uFfOIANmo6HExES0tbXBzs4O69atkyu5C/yznf3ixQvU1dWRaSM0/eR1bGZmBvX19YT0OjIyAg6HQ2o2tra2sLS0fKP29Kt4csD345iEQiHa29tRXV2NwsJCcDgcUBQFbW1tQkp2cnJ67YL41NTU/9femcW0cW9h/BsWY3bM5rAZQ3Aoi1GSElJIaENF0BUihZeKl6qqVN2XqNGt1EXtU9urPlVVSyuhqGofq0pUSRPURKogokWEpSxpLpiYpcEYMNjB2AUbY4/tmfuQzv/aeMFwITHk/5MswDK2BzGfz5xzvnPIiier1QqFQoHq6mrI5fKggmQ0GtHd3Y2ZmRnk5uaisbERWVlZ0Ov1+Pbbb1FbW4sLFy4A8N4VKJFI0NLSEnR8zSGEClO44na7vba2trS0BBQcnucxNTWFO3fukLxNXV3djnkGo9GI69evQ6/XIyoqikxi3K3b3Gw2e/X/CEZez9yO8H1SUpLfE1Sn0+G7777z65Nrb29He3s73G43ZmZm9rzw0tM3J1TnDAYD3G434uLiwLIs8vLy0NTUBIlEsquEv9ls9lpzFeqKp83NTfz2228YGxtDcnIy6uvrUVpa6vXaPT096O/vJ1HTzZs3odPpUFNTE3S78iGGClO4o9PpcPPmTZjNZtTV1aG6ujro5dbIyAh6e3vBcRwx7war3rW1taG4uBhJSUkYGRmBzWaDTCaDUqlEaWnprj1VwnC1+fl5GAwGIgAsywIAYmJiiFhJJBKSG1pbW0NXVxfeeustvw2DQPCIiWVZv5U5s9lM2gM8fXPCe5BKpSgoKEBmZiY6OzthMBhIX9VObG1tQa1WY2JiAvPz84iNjQ15xZPL5SJmXgB48cUXUVVV5VdkXC4XvvnmG3KMSUlJaGlpCWjoPQJQYToMuFwuspYpNzcXLS0tAU9e4PEJI5h3ExIS8PLLL0OpVPoImrC3/sqVK0hNTYXT6STWk7m5OTAMg6KiIiiVShQXF++5c5jneS9/nHDb2NjwspwIREdHIz4+HmKx2Cty2Nrawttvv422tjbExsaC53my9FJYnOmJWCz2GqsrRG6BfHP3799HZ2cn3n///YC9X06nEzMzM5iYmMDs7Cx4nkdBQQGxquxk+eA4jnTeWywWVFZW4qWXXgr6AWAymfDjjz/CYDBAoVDg1VdfPUxd3HuBCtNhYmFhAZ2dndjY2MCFCxdw9uzZoGG8yWTCnTt3oFarkZKSQsZyiEQi8DyPq1evIjU11W9Do9VqxeTkJFQqFZaWlhAdHY2SkhIolUoUFBTsW+XH7XbDZrNhYGAAY2NjuHTpEol2touWzWZDa2srOjo6yIkcGxvrU5kTft7texTyXK2trV4WIGEwnkqlglqtBsuyyM7OhlKpRFlZWUjjQ5xOJ+7fv4+hoSGYTCYUFxfj4sWLQT9ghAi4p6cH8fHxqK2tDWjoPWKEzQFSYQoRlmXR09OD4eHhgDmJ7QiDzFQqFWJiYlBZWYnMzEz89NNPeP311wNOGhAwmUykZG40GhEdHQ2ZTEb8cVKp9P+2PATbJydwkFU5ga+++gonTpzAqVOnMDc3h/n5eWi1WrAsi7S0NNLPFUxQPLFarRgZGSErnkpKSlBdXR20/4zneUxPT6O7uxsmk2lHO9IRhArTYWV1dRXd3d2YnZ1FXl4eGhoagv6zA/8b/To2NgaWZSEWi/HGG2+E3DTJ8zwMBgMePnwIjUaDhYUFOJ1OiMVir/1x/oy8OxFsn5zAQQkTz/MwmUzQaDS4e/cuNjY2wPM8oqKiIJPJIJfLUVRUhGPHjoV8XKurqxgcHMT4+HjIK56Axz1lXV1d0Gq1KCwsRENDw56bWg8xVJgOO3Nzc+jq6oLBYEBZWRnq6+t3bHwUKmBisRh2ux1FRUWoqqrC8ePHdxX5uN1uLC0tkWrc0tISOI5DQkICpFKp18okwR8XiB9++AEMwwQcLwvsjzD5883p9XpYLBYwDAOJRAKTyYTW1taQe5YEOI6DRqPB8PAwWfF09uxZPP/880H9isDjD42enh6Mj48jIyMDDQ0NOH78+LNw2eaPsDloKkz/BxzHEfOu0FVdW1sbsOHx9u3bUKvVuHLlCqanpzE4OAi9Xo+4uDiUlZWhoqICOTk5uz4pWJaFVqvFwsICqYQJZl7gsT9OEKrU1FSySy4+Ph4dHR2QSqV45ZVXfJ53N+0CbrfbpzK3trbmtSpKICUlhSTE8/PzIZPJYLfb0dbW5nfMrT94nsfKygomJiagUqlgtVrJiielUrljnsvhcODu3bsYGhpCTEwM6urqcOrUqcM2DWC/ocJ0lGBZFgMDAxgYGEB0dDReeOEFn4WMW1tb+PLLL1FTU0Ma9nieh16vJyeXxWKBRCJBeXk5KioqAppGQ31Pgih4OvstFovPYyMjI5GcnEzEantOxWaz4bXXXsP3339Pkt8sy3qJkOeYFAF/nrlAvjkA+Prrr1FUVITGxsaAx7W2tkZMvCaTCfHx8ST/lJ2dvaOo2+123Lt3DwMDA3A4HKiursa5c+d2NdngCBM2wnTkOsSeBp4rg3p7e8nCSs/8xtjYGDiO89pxzzAMsrKykJWVhfr6emi1WrJBpK+vD8eOHYNSqURJSUlIw9K2v6ecnByfzmRhXrdw6+joQGFhITIyMgJW5YSfNzY24HQ6wfM8RCIRUlNTkZub67P4UqjO7ba0LpfLodVqfe5fX1/HgwcPoFKpsLy8DJFIhNLSUjQ2Noa8odhzBbvL5UJFRQXq6urCba8b5W9oxHQA+KsIabVaKBQKNDc37/j7LpcLs7OzmJiYwMzMDNxuN1JSUrwS3fvhYg/FJwc8maocAIyPj+PGjRu4fPkyHj16RKpzJpMJkZGRUCgUUCqVUCgUIYveysoKBgYGMDk5SSqjVVVV4byp5GkSNhETFaYDROih6e3txebmZsiGUk8cDoeX7WR1dRUAiJG3sLAQ+fn5ezLyhuKTAw5emBwOB7RaLaampvDHH3+Q+9PT073GB4d6jMKok8HBQczPz/v0klECQoXpWcJut6Ovrw+Li4tYXFxEWloaTp8+jfLy8l2f6FarlYzP1Wg0WF9fB8MwyMzMhFQqJTkdqVQa0B8nEMwn58l+CRPP82SInGfeS6/XEwOvw+Egg9n28reZnJzE6OgojEYjcnJyUFNTg+eee+5ZT2qHStgIE80xPQHEYjEuXrwI4PG0Q2HoXHd3N+RyOfHHhRIRJCQkQKlUQqlUgud5/PXXX5ibm8Py8jIePXqEqakp4o8TiURerQPp6emkIhcXFwebzQYAu95bFwyO42Cz2WCz2WCxWHxaBLb75qRSKU6fPo3CwkJIJBLcunULCwsLIYuSw+EgvjmNRgOGYVBcXIxLly4hLy/vWS37H3poxPSUsNvtXieUZw7lxIkTe3auC1GJp5FX+Op2u70eKxKJwLIsZDIZEhISiL1EeO3BwUEMDg7C6XTi1q1b+OWXX4iIBVp6uT1xHhkZ6bXwUhDJ5ORkv6KhUqlw/fp1vPPOOwHzaEIOTqVSYXp6Gm63G3K5HOXl5SgtLd2xd4kSkLBRcSpMYYDFYiHWk5WVFcTExKCkpASlpaXIz8/fl7wIx3FYX1/3EhG1Wk22u3jev13A7HY7PvroI3zyySckqvPcLbfdM+f5fUpKyq4uoywWC7744guf5aROpxMLCwuYnJzEgwcP4HA4SNVyL5fEFL9QYaL4x2g0kj4ds9mMiIgI5ObmkgRwTk7Ovhl5Q/HJAU+uKifQ3t4OmUyGkydPkqT/4uIi3G43JBIJEaOdZi5Rdg0VJkpweJ6H0WgkJ+b8/Dzsdjuio6ORn59P2gZ24yPbTig+OeDJCJPgB9RoNPj999/JiqeYmBhSmSsoKEBGRgbNGx0cYfOHpcnvMIVhGNIpXVVVBY7joNfriVD9+uuv6O7uRmxsLLKzs8nwNSHJLVz+zczM4L333kN/fz9YloVSqcSnn36Kuro6bG5u7mviO1ScTqdPV7pOp8PW1haioqKQnp6OxMRENDQ0ICcnh1bUnkGoMB0SIiIikJ2djezsbJw7dw4ulws6nQ4ajQZ6vR7T09MYGhoijxf8cdeuXUNSUhJu3LgBiUSCq1evoqmpCQ8fPsTm5uaBOeh5nofdbiftAZ5C5OnjE/bNnTlzBgUFBcjNzT2KI2spu4Reyh0hWJb1Ks/rdDqoVCqvyy+GYbCxsQGpVAqWZSGRSFBYWBh0DZPVakVlZSVGR0dJpYzjOGxtbXklzT0rdNtXQCUmJvpU5jIyMmjDY3hBL+Uo+49IJCJRFfA4aikrK8P58+fx7rvvgmVZ/Pzzz1Cr1Th//jz+/PNPsn9NEBN/2O12AMC1a9d8eq22V+PS0tK8KnOJiYlIT0+nJXzKrqAR0xFHp9OhubkZ9+7dQ0REBKRSKW7fvo2TJ0/6PJbjONjtdnz22Wf4/PPPyf08z8Nms2F5eZlEXwzDQCwW0/zP0SJsIib6X3UI+fjjj8EwTNDb6OgoeJ7H5cuXkZmZib6+PgwPD6O5uRlNTU1YWVnxed6IiAjExcXhww8/xPLyMrlNT08DgE/fEhUlykFBI6ZDiNFohNFoDPoYuVyO/v5+NDQ0wGw2e+WZFAoF3nzzTXzwwQchvd6T7mOiPDXCJmKiOaZDSHp6ekhD5ISc0fbIJiIiwisxTaGEG/sRMVHCFIZh0gFMAegF8G8AWwD+CeBfAM7wPP+fEJ8nCcA6gGSe5zcO6O1SKASaJDjC8DxvBPAPAAkAegCMAjgPoDlUUfobC4Dkv79SKAcOjZgoFErYQSMmCoUSdlBholAoYQcVJgqFEnZQYaJQKGEHFSYKhRJ2UGGiUChhBxUmCoUSdlBholAoYQcVJgqFEnZQYaJQKGEHFSYKhRJ2/Be+ZF+CNj1vGwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "Graphics object consisting of 40 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reset()\n",
    "R2 = Manifold(2, 'R^2')                  # manifold R^2\n",
    "c_cart.<x,y> = R2.chart()                # Cartesian coordinates\n",
    "                    # the complement of the segment y=0 and x>=0:\n",
    "U = R2.open_subset('U', coord_def={c_cart: (y!=0, x<0)}) \n",
    "c_pol.<r,ph> = U.chart(r'r:(0,+oo) ph:(0,2*pi):\\phi') # polar coord.\n",
    "                                         # transition map:\n",
    "pol_to_cart = c_pol.transition_map(c_cart, [r*cos(ph), r*sin(ph)])\n",
    "                                         # plot coordinate lines\n",
    "g = c_pol.plot(c_cart,number_values={r:20,ph:20},color='grey')\n",
    "g.show(figsize=[3,3])                    # show plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And next the image of these lines as a subset of $R^3$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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, 4.0], &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;:-8.0737341958871, &quot;y&quot;:-8.093430885189715, &quot;z&quot;:-0.9999828922480782}, {&quot;x&quot;:8.1, &quot;y&quot;:8.093430885189715, &quot;z&quot;:1.0}]; // 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",
       "    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 = [{&quot;points&quot;: [[0.0009999995000000417, 9.999998333333416e-07, 0.9999995000000417], [0.10909454004730183, 0.00010909457641216306, 0.9940550844079163], [0.21718908059460362, 0.0002171891529909928, 0.9765069955935162], [0.3252836211419054, 0.0003252837295698225, 0.9475600736018965], [0.43337816168920723, 0.0004333783061486522, 0.9075522178400924], [0.541472702236509, 0.0005414728827274819, 0.8569504427541497], [0.6495672427838108, 0.0006495674593063117, 0.7963454263374453], [0.7576617833311126, 0.0007576620358851414, 0.7264446151059327], [0.8657563238784144, 0.0008657566124639711, 0.6480639660264086], [0.9738508644257161, 0.0009738511890428008, 0.5621184217948407], [1.081945404973018, 0.0010819457656216305, 0.46961123064748533], [1.1900399455203197, 0.00119004034220046, 0.37162223537537203], [1.2981344860676214, 0.00129813491877929, 0.26929526824529515], [1.4062290266149233, 0.0014062294953581197, 0.16382479896726188], [1.514323567162225, 0.0015143240719369493, 0.05644199156759094], [1.6224181077095268, 0.001622418648515779, -0.05159966707326126], [1.7305126482568285, 0.0017305132250946087, -0.15903899925908313], [1.8386071888041304, 0.0018386078016734385, -0.26462185829171025], [1.9467017293514322, 0.0019467023782522683, -0.36711576821150527], [2.0547962698987337, 0.0020547969548310977, -0.465324310573819], [2.162890810446035, 0.002162891531409927, -0.5581010903236061], [2.270985350993337, 0.002270986107988757, -0.6443631177435788], [2.3790798915406386, 0.002379080684567586, -0.7231034502675023], [2.48717443208794, 0.0024871752611464156, -0.7934029465898774], [2.5952689726352416, 0.0025952698377252454, -0.85444099586548], [2.703363513182543, 0.0027033644143040748, -0.9055050967560758], [2.8114580537298446, 0.002811458990882904, -0.9459991745074406], [2.919552594277146, 0.0029195535674617335, -0.975450538970875], [3.027647134824448, 0.0030276481440405633, -0.9935154023477507], [3.1357416753717495, 0.0031357427206193927, 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0.9793671801669825], [6.5947669728854, 0.006594769171141937, 0.9518488672267573], [6.702861513432701, 0.006702863747720766, 0.9132195571340248], [6.810956053980003, 0.006810958324299596, 0.8639301724766263], [6.919050594527304, 0.006919052900878425, 0.8045560716243969], [7.027145135074606, 0.007027147477457254, 0.7357903325314284], [7.135239675621907, 0.007135242054036084, 0.6584356623895442], [7.243334216169209, 0.007243336630614914, 0.5733950275721601], [7.351428756716511, 0.007351431207193743, 0.48166111324583644], [7.459523297263813, 0.007459525783772573, 0.3843047356882012], [7.567617837811114, 0.007567620360351402, 0.2824623425760511], [7.675712378358416, 0.0076757149369302315, 0.17732274715362556], [7.783806918905717, 0.007783809513509061, 0.07011325113401908], [7.891901459453019, 0.00789190409008789, -0.037914681677945906], [7.99999600000032, 0.00799999866666672, -0.14550003380860035]], &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 1.0}, {&quot;points&quot;: [[0.0009455263425728176, 0.00032554559665409543, 0.9999995000000417], [0.10315181302149129, 0.03551526488903395, 0.9940550844079163], [0.20535809970040975, 0.0707049841814138, 0.9765069955935162], [0.3075643863793282, 0.10589470347379365, 0.9475600736018965], [0.4097706730582467, 0.1410844227661735, 0.9075522178400924], [0.5119769597371652, 0.17627414205855335, 0.8569504427541497], [0.6141832464160837, 0.2114638613509332, 0.7963454263374453], [0.7163895330950021, 0.24665358064331308, 0.7264446151059327], [0.8185958197739206, 0.2818432999356929, 0.6480639660264086], [0.920802106452839, 0.31703301922807275, 0.5621184217948407], [1.0230083931317575, 0.3522227385204526, 0.46961123064748533], [1.125214679810676, 0.38741245781283246, 0.37162223537537203], [1.2274209664895943, 0.4226021771052123, 0.26929526824529515], [1.3296272531685127, 0.45779189639759216, 0.16382479896726188], [1.4318335398474313, 0.492981615689972, 0.05644199156759094], [1.5340398265263497, 0.5281713349823519, -0.05159966707326126], [1.6362461132052681, 0.5633610542747317, -0.15903899925908313], [1.7384523998841868, 0.5985507735671116, -0.26462185829171025], [1.8406586865631052, 0.6337404928594914, -0.36711576821150527], [1.9428649732420233, 0.6689302121518712, -0.465324310573819], [2.0450712599209417, 0.704119931444251, -0.5581010903236061], [2.14727754659986, 0.7393096507366308, -0.6443631177435788], [2.249483833278778, 0.7744993700290106, -0.7231034502675023], [2.3516901199576963, 0.8096890893213903, -0.7934029465898774], [2.453896406636615, 0.8448788086137701, -0.85444099586548], [2.556102693315533, 0.8800685279061499, -0.9055050967560758], [2.6583089799944513, 0.9152582471985297, -0.9459991745074406], [2.7605152666733694, 0.9504479664909095, -0.975450538970875], [2.8627215533522876, 0.9856376857832893, -0.9935154023477507], [2.964927840031206, 1.020827405075669, -0.9999828922480782], [3.0671341267101244, 1.0560171243680487, -0.9947775132183874], [3.1693404133890426, 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-0.1455000338086153], [7.999996000000335, -0.007999998666614523, -0.1455000338086153]], &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 1.0}];\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",
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[1171, 1172, 1211, 1210], [1172, 1173, 1212, 1211], [1173, 1174, 1213, 1212], [1174, 1175, 1214, 1213], [1175, 1176, 1215, 1214], [1176, 1177, 1216, 1215], [1177, 1178, 1217, 1216], [1178, 1179, 1218, 1217], [1179, 1180, 1219, 1218], [1180, 1181, 1220, 1219], [1181, 1182, 1221, 1220], [1182, 1183, 1222, 1221], [1183, 1184, 1223, 1222], [1184, 1185, 1224, 1223], [1185, 1186, 1225, 1224], [1186, 1187, 1226, 1225], [1187, 1188, 1227, 1226], [1188, 1189, 1228, 1227], [1189, 1190, 1229, 1228], [1190, 1191, 1230, 1229], [1191, 1192, 1231, 1230], [1192, 1193, 1232, 1231], [1193, 1194, 1233, 1232], [1194, 1195, 1234, 1233], [1195, 1196, 1235, 1234], [1196, 1197, 1236, 1235], [1197, 1198, 1237, 1236], [1198, 1199, 1238, 1237], [1199, 1200, 1239, 1238], [1200, 1201, 1240, 1239], [1201, 1202, 1241, 1240], [1202, 1203, 1242, 1241], [1203, 1204, 1243, 1242], [1204, 1205, 1244, 1243], [1205, 1206, 1245, 1244], [1206, 1207, 1246, 1245], [1207, 1208, 1247, 1246], [1208, 1209, 1248, 1247], [0, 1210, 1249], [1210, 1211, 1250, 1249], [1211, 1212, 1251, 1250], [1212, 1213, 1252, 1251], [1213, 1214, 1253, 1252], [1214, 1215, 1254, 1253], [1215, 1216, 1255, 1254], [1216, 1217, 1256, 1255], [1217, 1218, 1257, 1256], [1218, 1219, 1258, 1257], [1219, 1220, 1259, 1258], [1220, 1221, 1260, 1259], [1221, 1222, 1261, 1260], [1222, 1223, 1262, 1261], [1223, 1224, 1263, 1262], [1224, 1225, 1264, 1263], [1225, 1226, 1265, 1264], [1226, 1227, 1266, 1265], [1227, 1228, 1267, 1266], [1228, 1229, 1268, 1267], [1229, 1230, 1269, 1268], [1230, 1231, 1270, 1269], [1231, 1232, 1271, 1270], [1232, 1233, 1272, 1271], [1233, 1234, 1273, 1272], [1234, 1235, 1274, 1273], [1235, 1236, 1275, 1274], [1236, 1237, 1276, 1275], [1237, 1238, 1277, 1276], [1238, 1239, 1278, 1277], [1239, 1240, 1279, 1278], [1240, 1241, 1280, 1279], [1241, 1242, 1281, 1280], [1242, 1243, 1282, 1281], [1243, 1244, 1283, 1282], [1244, 1245, 1284, 1283], [1245, 1246, 1285, 1284], [1246, 1247, 1286, 1285], [1247, 1248, 1287, 1286], [0, 1249, 1288], [1249, 1250, 1289, 1288], [1250, 1251, 1290, 1289], [1251, 1252, 1291, 1290], [1252, 1253, 1292, 1291], [1253, 1254, 1293, 1292], [1254, 1255, 1294, 1293], [1255, 1256, 1295, 1294], [1256, 1257, 1296, 1295], [1257, 1258, 1297, 1296], [1258, 1259, 1298, 1297], [1259, 1260, 1299, 1298], [1260, 1261, 1300, 1299], [1261, 1262, 1301, 1300], [1262, 1263, 1302, 1301], [1263, 1264, 1303, 1302], [1264, 1265, 1304, 1303], [1265, 1266, 1305, 1304], [1266, 1267, 1306, 1305], [1267, 1268, 1307, 1306], [1268, 1269, 1308, 1307], [1269, 1270, 1309, 1308], [1270, 1271, 1310, 1309], [1271, 1272, 1311, 1310], [1272, 1273, 1312, 1311], [1273, 1274, 1313, 1312], [1274, 1275, 1314, 1313], [1275, 1276, 1315, 1314], [1276, 1277, 1316, 1315], [1277, 1278, 1317, 1316], [1278, 1279, 1318, 1317], [1279, 1280, 1319, 1318], [1280, 1281, 1320, 1319], [1281, 1282, 1321, 1320], [1282, 1283, 1322, 1321], [1283, 1284, 1323, 1322], [1284, 1285, 1324, 1323], [1285, 1286, 1325, 1324], [1286, 1287, 1326, 1325], [0, 1288, 1327], [1288, 1289, 1328, 1327], [1289, 1290, 1329, 1328], [1290, 1291, 1330, 1329], [1291, 1292, 1331, 1330], [1292, 1293, 1332, 1331], [1293, 1294, 1333, 1332], [1294, 1295, 1334, 1333], [1295, 1296, 1335, 1334], [1296, 1297, 1336, 1335], [1297, 1298, 1337, 1336], [1298, 1299, 1338, 1337], [1299, 1300, 1339, 1338], [1300, 1301, 1340, 1339], [1301, 1302, 1341, 1340], [1302, 1303, 1342, 1341], [1303, 1304, 1343, 1342], [1304, 1305, 1344, 1343], [1305, 1306, 1345, 1344], [1306, 1307, 1346, 1345], [1307, 1308, 1347, 1346], [1308, 1309, 1348, 1347], [1309, 1310, 1349, 1348], [1310, 1311, 1350, 1349], [1311, 1312, 1351, 1350], [1312, 1313, 1352, 1351], [1313, 1314, 1353, 1352], [1314, 1315, 1354, 1353], [1315, 1316, 1355, 1354], [1316, 1317, 1356, 1355], [1317, 1318, 1357, 1356], [1318, 1319, 1358, 1357], [1319, 1320, 1359, 1358], [1320, 1321, 1360, 1359], [1321, 1322, 1361, 1360], [1322, 1323, 1362, 1361], [1323, 1324, 1363, 1362], [1324, 1325, 1364, 1363], [1325, 1326, 1365, 1364], [0, 1327, 1366], [1327, 1328, 1367, 1366], [1328, 1329, 1368, 1367], [1329, 1330, 1369, 1368], [1330, 1331, 1370, 1369], [1331, 1332, 1371, 1370], [1332, 1333, 1372, 1371], [1333, 1334, 1373, 1372], [1334, 1335, 1374, 1373], [1335, 1336, 1375, 1374], [1336, 1337, 1376, 1375], [1337, 1338, 1377, 1376], [1338, 1339, 1378, 1377], [1339, 1340, 1379, 1378], [1340, 1341, 1380, 1379], [1341, 1342, 1381, 1380], [1342, 1343, 1382, 1381], [1343, 1344, 1383, 1382], [1344, 1345, 1384, 1383], [1345, 1346, 1385, 1384], [1346, 1347, 1386, 1385], [1347, 1348, 1387, 1386], [1348, 1349, 1388, 1387], [1349, 1350, 1389, 1388], [1350, 1351, 1390, 1389], [1351, 1352, 1391, 1390], [1352, 1353, 1392, 1391], [1353, 1354, 1393, 1392], [1354, 1355, 1394, 1393], [1355, 1356, 1395, 1394], [1356, 1357, 1396, 1395], [1357, 1358, 1397, 1396], [1358, 1359, 1398, 1397], [1359, 1360, 1399, 1398], [1360, 1361, 1400, 1399], [1361, 1362, 1401, 1400], [1362, 1363, 1402, 1401], [1363, 1364, 1403, 1402], [1364, 1365, 1404, 1403], [0, 1366, 1405], [1366, 1367, 1406, 1405], [1367, 1368, 1407, 1406], [1368, 1369, 1408, 1407], [1369, 1370, 1409, 1408], [1370, 1371, 1410, 1409], [1371, 1372, 1411, 1410], [1372, 1373, 1412, 1411], [1373, 1374, 1413, 1412], [1374, 1375, 1414, 1413], [1375, 1376, 1415, 1414], [1376, 1377, 1416, 1415], [1377, 1378, 1417, 1416], [1378, 1379, 1418, 1417], [1379, 1380, 1419, 1418], [1380, 1381, 1420, 1419], [1381, 1382, 1421, 1420], [1382, 1383, 1422, 1421], [1383, 1384, 1423, 1422], [1384, 1385, 1424, 1423], [1385, 1386, 1425, 1424], [1386, 1387, 1426, 1425], [1387, 1388, 1427, 1426], [1388, 1389, 1428, 1427], [1389, 1390, 1429, 1428], [1390, 1391, 1430, 1429], [1391, 1392, 1431, 1430], [1392, 1393, 1432, 1431], [1393, 1394, 1433, 1432], [1394, 1395, 1434, 1433], [1395, 1396, 1435, 1434], [1396, 1397, 1436, 1435], [1397, 1398, 1437, 1436], [1398, 1399, 1438, 1437], [1399, 1400, 1439, 1438], [1400, 1401, 1440, 1439], [1401, 1402, 1441, 1440], [1402, 1403, 1442, 1441], [1403, 1404, 1443, 1442], [0, 1405, 1444], [1405, 1406, 1445, 1444], [1406, 1407, 1446, 1445], [1407, 1408, 1447, 1446], [1408, 1409, 1448, 1447], [1409, 1410, 1449, 1448], [1410, 1411, 1450, 1449], [1411, 1412, 1451, 1450], [1412, 1413, 1452, 1451], [1413, 1414, 1453, 1452], [1414, 1415, 1454, 1453], [1415, 1416, 1455, 1454], [1416, 1417, 1456, 1455], [1417, 1418, 1457, 1456], [1418, 1419, 1458, 1457], [1419, 1420, 1459, 1458], [1420, 1421, 1460, 1459], [1421, 1422, 1461, 1460], [1422, 1423, 1462, 1461], [1423, 1424, 1463, 1462], [1424, 1425, 1464, 1463], [1425, 1426, 1465, 1464], [1426, 1427, 1466, 1465], [1427, 1428, 1467, 1466], [1428, 1429, 1468, 1467], [1429, 1430, 1469, 1468], [1430, 1431, 1470, 1469], [1431, 1432, 1471, 1470], [1432, 1433, 1472, 1471], [1433, 1434, 1473, 1472], [1434, 1435, 1474, 1473], [1435, 1436, 1475, 1474], [1436, 1437, 1476, 1475], [1437, 1438, 1477, 1476], [1438, 1439, 1478, 1477], [1439, 1440, 1479, 1478], [1440, 1441, 1480, 1479], [1441, 1442, 1481, 1480], [1442, 1443, 1482, 1481], [0, 1444, 1483], [1444, 1445, 1484, 1483], [1445, 1446, 1485, 1484], [1446, 1447, 1486, 1485], [1447, 1448, 1487, 1486], [1448, 1449, 1488, 1487], [1449, 1450, 1489, 1488], [1450, 1451, 1490, 1489], [1451, 1452, 1491, 1490], [1452, 1453, 1492, 1491], [1453, 1454, 1493, 1492], [1454, 1455, 1494, 1493], [1455, 1456, 1495, 1494], [1456, 1457, 1496, 1495], [1457, 1458, 1497, 1496], [1458, 1459, 1498, 1497], [1459, 1460, 1499, 1498], [1460, 1461, 1500, 1499], [1461, 1462, 1501, 1500], [1462, 1463, 1502, 1501], [1463, 1464, 1503, 1502], [1464, 1465, 1504, 1503], [1465, 1466, 1505, 1504], [1466, 1467, 1506, 1505], [1467, 1468, 1507, 1506], [1468, 1469, 1508, 1507], [1469, 1470, 1509, 1508], [1470, 1471, 1510, 1509], [1471, 1472, 1511, 1510], [1472, 1473, 1512, 1511], [1473, 1474, 1513, 1512], [1474, 1475, 1514, 1513], [1475, 1476, 1515, 1514], [1476, 1477, 1516, 1515], [1477, 1478, 1517, 1516], [1478, 1479, 1518, 1517], [1479, 1480, 1519, 1518], [1480, 1481, 1520, 1519], [1481, 1482, 1521, 1520], [0, 1483, 1522], [1483, 1484, 1523, 1522], [1484, 1485, 1524, 1523], [1485, 1486, 1525, 1524], [1486, 1487, 1526, 1525], [1487, 1488, 1527, 1526], [1488, 1489, 1528, 1527], [1489, 1490, 1529, 1528], [1490, 1491, 1530, 1529], [1491, 1492, 1531, 1530], [1492, 1493, 1532, 1531], [1493, 1494, 1533, 1532], [1494, 1495, 1534, 1533], [1495, 1496, 1535, 1534], [1496, 1497, 1536, 1535], [1497, 1498, 1537, 1536], [1498, 1499, 1538, 1537], [1499, 1500, 1539, 1538], [1500, 1501, 1540, 1539], [1501, 1502, 1541, 1540], [1502, 1503, 1542, 1541], [1503, 1504, 1543, 1542], [1504, 1505, 1544, 1543], [1505, 1506, 1545, 1544], [1506, 1507, 1546, 1545], [1507, 1508, 1547, 1546], [1508, 1509, 1548, 1547], [1509, 1510, 1549, 1548], [1510, 1511, 1550, 1549], [1511, 1512, 1551, 1550], [1512, 1513, 1552, 1551], [1513, 1514, 1553, 1552], [1514, 1515, 1554, 1553], [1515, 1516, 1555, 1554], [1516, 1517, 1556, 1555], [1517, 1518, 1557, 1556], [1518, 1519, 1558, 1557], [1519, 1520, 1559, 1558], [1520, 1521, 1560, 1559]], &quot;color&quot;: &quot;#d3d3d3&quot;, &quot;opacity&quot;: 0.5}];\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": [
    "# continuation\n",
    "R3 = Manifold(3, 'R^3')                  # manifold R^3\n",
    "c_XYZ.<X,Y,Z> = R3.chart()               # chart on R^3\n",
    "F = U.continuous_map(R3,                 # F: U->R^3\n",
    "  {(c_pol, c_XYZ): [r*cos(ph),r*sin(ph),cos(r)]}, name='F')\n",
    "                     # plot images of coordinate lines in U:\n",
    "p=c_pol.plot(c_XYZ,mapping=F,number_values={r:20,ph:20},\n",
    "  color='black',thickness=1,label_axes=False)\n",
    "                                         # plot image of U:\n",
    "s=parametric_plot3d([r*cos(ph),r*sin(ph),cos(r)],\n",
    "    (ph,0,2*pi),(r,0,8.1),color='lightgrey',opacity=0.5)\n",
    "(p+s).show(aspect_ratio=[1,1,4],frame=False)  # show plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Three dimensional function graph as a manifold"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "**Example 3.5**\n",
    "\n",
    "First we show the coordinate lines $x,y,z$ in the three dimensional rectangle:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
       "<script src=&quot;/nbextensions/threejs-sage/r122/three.min.js&quot;></script>\n",
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       "        <script>// fat_lines.js\n",
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       "        var v = geometry.vertices[i];\n",
       "        positions.push( v.x, v.y, v.z );\n",
       "        // For a line strip, duplicate all but the first and last vertices.\n",
       "        if ( lineStrip && i > 0 && i < vertexCount - 1 ) {\n",
       "            positions.push( v.x, v.y, v.z );\n",
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       "    }\n",
       "\n",
       "    geometry = new THREE.LineSegmentsGeometry();\n",
       "    geometry.setPositions( positions );\n",
       "\n",
       "    var material = new THREE.LineMaterial( materialOptions );\n",
       "    material.resolution = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
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       "function createFatLineSegments( geometry, materialOptions ) {\n",
       "    return _createFatLine( false, geometry, materialOptions );\n",
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       "\n",
       "function rescaleFatLines() {\n",
       "    var res = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
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       "<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;:0.1, &quot;y&quot;:0.1, &quot;z&quot;:0.1}, {&quot;x&quot;:1.0, &quot;y&quot;:1.0, &quot;z&quot;:1.0}]; // 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",
       "    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 = [{&quot;points&quot;: [[0.1, 0.1, 0.1], [0.11216216216216217, 0.1, 0.1], [0.12432432432432433, 0.1, 0.1], [0.13648648648648648, 0.1, 0.1], [0.14864864864864863, 0.1, 0.1], [0.16081081081081078, 0.1, 0.1], [0.17297297297297293, 0.1, 0.1], [0.18513513513513508, 0.1, 0.1], [0.19729729729729722, 0.1, 0.1], [0.20945945945945937, 0.1, 0.1], [0.22162162162162152, 0.1, 0.1], [0.23378378378378367, 0.1, 0.1], [0.24594594594594582, 0.1, 0.1], [0.25810810810810797, 0.1, 0.1], [0.2702702702702701, 0.1, 0.1], [0.28243243243243227, 0.1, 0.1], [0.2945945945945944, 0.1, 0.1], [0.30675675675675657, 0.1, 0.1], [0.3189189189189187, 0.1, 0.1], [0.33108108108108086, 0.1, 0.1], [0.343243243243243, 0.1, 0.1], [0.35540540540540516, 0.1, 0.1], [0.3675675675675673, 0.1, 0.1], [0.37972972972972946, 0.1, 0.1], [0.3918918918918916, 0.1, 0.1], [0.40405405405405376, 0.1, 0.1], [0.4162162162162159, 0.1, 0.1], [0.42837837837837806, 0.1, 0.1], [0.4405405405405402, 0.1, 0.1], [0.45270270270270235, 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       "    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 = [];\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": [
    "M = Manifold(3, 'M')                   # manifold M\n",
    "c_xyz.<x,y,z> = M.chart()              # coordinates x,y,z\n",
    "p1=c_xyz.plot(ranges={x:(0.1,1),y:(0.1,1),z:(0.1,1)},\n",
    "    number_values={x:4,y:4,z:4},thickness=2,\n",
    "    color='grey',label_axes=False)     # plot coordinate lines\n",
    "p1.show(frame=False)                   # show plot\n",
    "# adjust manually the figure after plot \n",
    "# (figsize does not work in 3d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And next the image under the map $F(x,y,z)=(x,y,(x^2+y^2)+z)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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",
       "        <script>// fat_lines.js\n",
       "\n",
       "var _fatLines = [];\n",
       "\n",
       "function _createFatLine( lineStrip, geometry, materialOptions ) {\n",
       "\n",
       "    var vertexCount = geometry.vertices.length;\n",
       "    var positions = [];\n",
       "    for ( var i=0 ; i < vertexCount ; i++ ) {\n",
       "        var v = geometry.vertices[i];\n",
       "        positions.push( v.x, v.y, v.z );\n",
       "        // For a line strip, duplicate all but the first and last vertices.\n",
       "        if ( lineStrip && i > 0 && i < vertexCount - 1 ) {\n",
       "            positions.push( v.x, v.y, v.z );\n",
       "        }\n",
       "    }\n",
       "\n",
       "    geometry = new THREE.LineSegmentsGeometry();\n",
       "    geometry.setPositions( positions );\n",
       "\n",
       "    var material = new THREE.LineMaterial( materialOptions );\n",
       "    material.resolution = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "\n",
       "    var line = new THREE.LineSegments2( geometry, material );\n",
       "    line.computeLineDistances();\n",
       "    line.scale.set( 1, 1, 1 );\n",
       "\n",
       "    _fatLines.push( line );\n",
       "\n",
       "    return line;\n",
       "\n",
       "}\n",
       "\n",
       "function createFatLineStrip( geometry, materialOptions ) {\n",
       "    return _createFatLine( true, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function createFatLineSegments( geometry, materialOptions ) {\n",
       "    return _createFatLine( false, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function rescaleFatLines() {\n",
       "    var res = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "    var n = _fatLines.length;\n",
       "    for ( var i=0 ; i < n ; i++ ) {\n",
       "        _fatLines[i].material.resolution = res;\n",
       "    }\n",
       "}\n",
       "</script>\n",
       "<script>\n",
       "\n",
       "    var options = {&quot;animate&quot;: false, &quot;animationControls&quot;: true, &quot;aspectRatio&quot;: [1.0, 1.0, 0.3], &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;:0.1, &quot;y&quot;:0.1, &quot;z&quot;:0.12000000000000002}, {&quot;x&quot;:1.0, &quot;y&quot;:1.0, &quot;z&quot;:6.000000000000001}]; // 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 = [{&quot;points&quot;: [[0.1, 0.1, 0.12000000000000002], [0.11216216216216217, 0.1, 0.12258035062089118], [0.12432432432432433, 0.1, 0.1254565376186998], [0.13648648648648648, 0.1, 0.12862856099342587], [0.14864864864864863, 0.1, 0.1320964207450694], [0.16081081081081078, 0.1, 0.1358601168736304], [0.17297297297297293, 0.1, 0.13991964937910883], [0.18513513513513508, 0.1, 0.14427501826150474], [0.19729729729729722, 0.1, 0.1489262235208181], [0.20945945945945937, 0.1, 0.1538732651570489], [0.22162162162162152, 0.1, 0.1591161431701972], [0.23378378378378367, 0.1, 0.16465485756026293], [0.24594594594594582, 0.1, 0.17048940832724613], [0.25810810810810797, 0.1, 0.17661979547114676], [0.2702702702702701, 0.1, 0.18304601899196488], [0.28243243243243227, 0.1, 0.18976807888970043], [0.2945945945945944, 0.1, 0.19678597516435345], [0.30675675675675657, 0.1, 0.20409970781592393], [0.3189189189189187, 0.1, 0.21170927684441188], [0.33108108108108086, 0.1, 0.21961468224981726], [0.343243243243243, 0.1, 0.2278159240321401], [0.35540540540540516, 0.1, 0.2363130021913804], [0.3675675675675673, 0.1, 0.24510591672753818], [0.37972972972972946, 0.1, 0.2541946676406134], [0.3918918918918916, 0.1, 0.2635792549306061], [0.40405405405405376, 0.1, 0.2732596785975162], [0.4162162162162159, 0.1, 0.2832359386413438], [0.42837837837837806, 0.1, 0.2935080350620889], [0.4405405405405402, 0.1, 0.30407596785975133], [0.45270270270270235, 0.1, 0.3149397370343313], [0.4648648648648645, 0.1, 0.32609934258582873], [0.47702702702702665, 0.1, 0.3375547845142436], [0.4891891891891888, 0.1, 0.349306062819576], [0.501351351351351, 0.1, 0.36135317750182583], [0.5135135135135132, 0.1, 0.3736961285609931], [0.5256756756756753, 0.1, 0.3863349159970778], [0.5378378378378375, 0.1, 0.39926953981007995], [0.5499999999999996, 0.1, 0.41249999999999953], [0.5621621621621617, 0.1, 0.42602629656683666], [0.5743243243243239, 0.1, 0.4398484295105912], [0.586486486486486, 0.1, 0.4539663988312632], [0.5986486486486482, 0.1, 0.46838020452885265], [0.6108108108108103, 0.1, 0.4830898466033595], [0.6229729729729725, 0.1, 0.49809532505478393], [0.6351351351351346, 0.1, 0.5133966398831258], [0.6472972972972968, 0.1, 0.5289937910883851], [0.6594594594594589, 0.1, 0.5448867786705618], [0.6716216216216211, 0.1, 0.561075602629656], [0.6837837837837832, 0.1, 0.5775602629656676], [0.6959459459459454, 0.1, 0.5943407596785968], [0.7081081081081075, 0.1, 0.6114170927684432], [0.7202702702702697, 0.1, 0.6287892622352074], [0.7324324324324318, 0.1, 0.6464572680788888], [0.744594594594594, 0.1, 0.6644211102994878], [0.7567567567567561, 0.1, 0.6826807888970041], [0.7689189189189183, 0.1, 0.701236303871438], [0.7810810810810804, 0.1, 0.7200876552227893], [0.7932432432432426, 0.1, 0.7392348429510581], [0.8054054054054047, 0.1, 0.7586778670562443], [0.8175675675675669, 0.1, 0.778416727538348], [0.829729729729729, 0.1, 0.7984514243973692], [0.8418918918918912, 0.1, 0.8187819576333077], [0.8540540540540533, 0.1, 0.8394083272461639], [0.8662162162162155, 0.1, 0.8603305332359373], [0.8783783783783776, 0.1, 0.8815485756026283], [0.8905405405405398, 0.1, 0.9030624543462368], [0.9027027027027019, 0.1, 0.9248721694667627], [0.9148648648648641, 0.1, 0.946977720964206], [0.9270270270270262, 0.1, 0.9693791088385668], [0.9391891891891884, 0.1, 0.992076333089845], [0.9513513513513505, 0.1, 1.0150693937180408], [0.9635135135135127, 0.1, 1.0383582907231539], [0.9756756756756748, 0.1, 1.0619430241051846], [0.987837837837837, 0.1, 1.0858235938641327], [0.9999999999999991, 0.1, 1.1099999999999983]], &quot;color&quot;: &quot;#808080&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 2.0}, {&quot;points&quot;: [[0.1, 0.1, 1.4200000000000002], [0.11216216216216217, 0.1, 1.4225803506208914], [0.12432432432432433, 0.1, 1.4254565376186998], [0.13648648648648648, 0.1, 1.428628560993426], [0.14864864864864863, 0.1, 1.4320964207450695], [0.16081081081081078, 0.1, 1.4358601168736305], [0.17297297297297293, 0.1, 1.4399196493791089], [0.18513513513513508, 0.1, 1.444275018261505], [0.19729729729729722, 0.1, 1.4489262235208182], [0.20945945945945937, 0.1, 1.453873265157049], [0.22162162162162152, 0.1, 1.4591161431701973], [0.23378378378378367, 0.1, 1.4646548575602631], [0.24594594594594582, 0.1, 1.4704894083272462], [0.25810810810810797, 0.1, 1.4766197954711469], [0.2702702702702701, 0.1, 1.483046018991965], [0.28243243243243227, 0.1, 1.4897680788897005], [0.2945945945945944, 0.1, 1.4967859751643535], [0.30675675675675657, 0.1, 1.504099707815924], [0.3189189189189187, 0.1, 1.511709276844412], [0.33108108108108086, 0.1, 1.5196146822498173], [0.343243243243243, 0.1, 1.5278159240321403], [0.35540540540540516, 0.1, 1.5363130021913805], [0.3675675675675673, 0.1, 1.5451059167275383], [0.37972972972972946, 0.1, 1.5541946676406135], [0.3918918918918916, 0.1, 1.5635792549306062], [0.40405405405405376, 0.1, 1.5732596785975164], [0.4162162162162159, 0.1, 1.583235938641344], [0.42837837837837806, 0.1, 1.593508035062089], [0.4405405405405402, 0.1, 1.6040759678597516], [0.45270270270270235, 0.1, 1.6149397370343315], [0.4648648648648645, 0.1, 1.6260993425858288], [0.47702702702702665, 0.1, 1.6375547845142437], [0.4891891891891888, 0.1, 1.6493060628195761], [0.501351351351351, 0.1, 1.661353177501826], [0.5135135135135132, 0.1, 1.6736961285609933], [0.5256756756756753, 0.1, 1.686334915997078], [0.5378378378378375, 0.1, 1.69926953981008], [0.5499999999999996, 0.1, 1.7124999999999997], [0.5621621621621617, 0.1, 1.7260262965668367], [0.5743243243243239, 0.1, 1.7398484295105914], [0.586486486486486, 0.1, 1.7539663988312633], [0.5986486486486482, 0.1, 1.7683802045288528], [0.6108108108108103, 0.1, 1.7830898466033596], [0.6229729729729725, 0.1, 1.798095325054784], [0.6351351351351346, 0.1, 1.8133966398831258], [0.6472972972972968, 0.1, 1.8289937910883851], [0.6594594594594589, 0.1, 1.8448867786705618], [0.6716216216216211, 0.1, 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5.20945945945946], [1.0, 1.0, 5.262162162162163], [1.0, 1.0, 5.314864864864866], [1.0, 1.0, 5.367567567567568], [1.0, 1.0, 5.4202702702702705], [1.0, 1.0, 5.472972972972974], [1.0, 1.0, 5.525675675675677], [1.0, 1.0, 5.578378378378379], [1.0, 1.0, 5.631081081081081], [1.0, 1.0, 5.683783783783785], [1.0, 1.0, 5.736486486486488], [1.0, 1.0, 5.78918918918919], [1.0, 1.0, 5.841891891891892], [1.0, 1.0, 5.8945945945945954], [1.0, 1.0, 5.947297297297299], [1.0, 1.0, 6.000000000000001]], &quot;color&quot;: &quot;#808080&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 2.0}];\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 = [];\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": [
    "c_XYZ.<X,Y,Z> = M.chart()                 # new chart X,Y,Z\n",
    "                                          # F: R^3 -> R^3\n",
    "F=M.continuous_map(M,{(c_xyz,c_XYZ):[x,y,(x^2+y^2)+z]}, name='F')\n",
    "                               # plot images of coordinate lines:\n",
    "p=c_xyz.plot(c_XYZ,mapping=F,\n",
    "    ranges={x:(0.1,1),y:(0.1,1),z:(0.1,4)},\n",
    "    number_values={x:4,y:4,z:4},color='grey',\n",
    "    thickness=2,label_axes=False)\n",
    "p.show (aspect_ratio=[1,1,0.3],frame=False)   # show plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example 3.6**\n",
    "\n",
    "Finally  let us show  3-dimensional example in spherical coordinates.\n",
    "\n",
    "First we show some coordinate lines of the open set defined by: $0<r<1,\\ 0<\\phi<\\pi/2,\\  0<\\theta<\\pi/2,$\n",
    "\n",
    "(the transition map $\\ \\ x=r\\sin\\theta\\cos\\phi,\\ y=r\\sin\\theta\\sin\\phi,\\ \\ z=r\\cos\\theta\\ \\ $ must be defined by the user).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "M = Manifold(3, 'R^3')               # manifold R^3\n",
    "U = M.open_subset('U') # the domain of spherical coordinates\n",
    "c_spher.<r,th,ph>=U.chart(r'r:(0,+oo) th:(0,pi):\\theta\\\n",
    "ph:(0,2*pi):periodic:\\phi')          # spherical coordinates\n",
    "c_cart.<x,y,z> = U.chart()           # Cartesian coordinates\n",
    "spher_to_cart = c_spher.transition_map(c_cart,  \n",
    "[r*sin(th)*cos(ph), r*sin(th)*sin(ph), r*cos(th)]) # trans.map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "po1={'thickness':5,'color':'darkblue'}         # param.\n",
    "po2={'fontsize':20,'color':'black'}\n",
    "\n",
    "ax =line3d([(0,0,0), (1+0.35,0,0)], **po1)     # axes\n",
    "ax+=line3d([(0,0,0), (0,1+0.35,0)], **po1)\n",
    "ax+=line3d([(0,0,0), (0,0,1.3+0)], **po1)\n",
    "ax+=text3d(\"x\",(1.45,0,0),**po2)\n",
    "ax+=text3d(\"y\",(0,1.45,0),**po2)\n",
    "ax+=text3d(\"z\",(0.,0.,1.40),**po2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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",
       "        <script>// fat_lines.js\n",
       "\n",
       "var _fatLines = [];\n",
       "\n",
       "function _createFatLine( lineStrip, geometry, materialOptions ) {\n",
       "\n",
       "    var vertexCount = geometry.vertices.length;\n",
       "    var positions = [];\n",
       "    for ( var i=0 ; i < vertexCount ; i++ ) {\n",
       "        var v = geometry.vertices[i];\n",
       "        positions.push( v.x, v.y, v.z );\n",
       "        // For a line strip, duplicate all but the first and last vertices.\n",
       "        if ( lineStrip && i > 0 && i < vertexCount - 1 ) {\n",
       "            positions.push( v.x, v.y, v.z );\n",
       "        }\n",
       "    }\n",
       "\n",
       "    geometry = new THREE.LineSegmentsGeometry();\n",
       "    geometry.setPositions( positions );\n",
       "\n",
       "    var material = new THREE.LineMaterial( materialOptions );\n",
       "    material.resolution = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "\n",
       "    var line = new THREE.LineSegments2( geometry, material );\n",
       "    line.computeLineDistances();\n",
       "    line.scale.set( 1, 1, 1 );\n",
       "\n",
       "    _fatLines.push( line );\n",
       "\n",
       "    return line;\n",
       "\n",
       "}\n",
       "\n",
       "function createFatLineStrip( geometry, materialOptions ) {\n",
       "    return _createFatLine( true, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function createFatLineSegments( geometry, materialOptions ) {\n",
       "    return _createFatLine( false, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function rescaleFatLines() {\n",
       "    var res = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "    var n = _fatLines.length;\n",
       "    for ( var i=0 ; i < n ; i++ ) {\n",
       "        _fatLines[i].material.resolution = res;\n",
       "    }\n",
       "}\n",
       "</script>\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;:-2.0289971893223505e-15, &quot;y&quot;:-0.4959292078222196, &quot;z&quot;:-2.1592137092929455e-15}, {&quot;x&quot;:1.858483507961787, &quot;y&quot;:1.3625543001395672, &quot;z&quot;:1.4}]; // 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 = [{&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;x&quot;, &quot;x&quot;: 1.3625543001395672, &quot;y&quot;: -0.4959292078222196, &quot;z&quot;: 0.0}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;y&quot;, &quot;x&quot;: 0.4959292078222196, &quot;y&quot;: 1.3625543001395672, &quot;z&quot;: 0.0}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;z&quot;, &quot;x&quot;: 0.0, &quot;y&quot;: 0.0, &quot;z&quot;: 1.4}];\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 = [{&quot;points&quot;: [[0.0, 0.0, 0.0], [0.0, 0.0, 0.013513513513513514], [0.0, 0.0, 0.02702702702702703], [0.0, 0.0, 0.04054054054054054], [0.0, 0.0, 0.05405405405405406], [0.0, 0.0, 0.06756756756756757], [0.0, 0.0, 0.08108108108108109], [0.0, 0.0, 0.0945945945945946], [0.0, 0.0, 0.10810810810810811], [0.0, 0.0, 0.12162162162162163], [0.0, 0.0, 0.13513513513513514], [0.0, 0.0, 0.14864864864864866], [0.0, 0.0, 0.16216216216216217], [0.0, 0.0, 0.17567567567567569], [0.0, 0.0, 0.1891891891891892], [0.0, 0.0, 0.20270270270270271], [0.0, 0.0, 0.21621621621621623], [0.0, 0.0, 0.22972972972972974], [0.0, 0.0, 0.24324324324324326], [0.0, 0.0, 0.2567567567567568], [0.0, 0.0, 0.2702702702702703], [0.0, 0.0, 0.28378378378378377], [0.0, 0.0, 0.29729729729729726], [0.0, 0.0, 0.31081081081081074], [0.0, 0.0, 0.32432432432432423], [0.0, 0.0, 0.3378378378378377], [0.0, 0.0, 0.3513513513513512], [0.0, 0.0, 0.3648648648648647], [0.0, 0.0, 0.3783783783783782], [0.0, 0.0, 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[[0.0, 0.0, 0.0], [0.4617271934896528, 1.2685850380609764, 0.0]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 5.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [0.0, 0.0, 1.3]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 5.0}];\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 = [];\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": [
    "                                    # plot the coordinate lines:\n",
    "pp=c_spher.plot(c_cart,ranges={r:(0,1),th:(0,pi/2),ph:(0,pi/2)},\n",
    "    number_values={r:2,th:10,ph:2},thickness=2,\n",
    "    color={r:'red', ph:'green',th:'blue'},label_axes=False)\n",
    "(pp+ax).rotateZ(pi/9).show(frame=False)   # show plot  frame=False\n",
    "# adjust manually the figure after plot "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And next the image of these lines under the mapping which triples the $\\phi$ coordinate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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",
       "        <script>// fat_lines.js\n",
       "\n",
       "var _fatLines = [];\n",
       "\n",
       "function _createFatLine( lineStrip, geometry, materialOptions ) {\n",
       "\n",
       "    var vertexCount = geometry.vertices.length;\n",
       "    var positions = [];\n",
       "    for ( var i=0 ; i < vertexCount ; i++ ) {\n",
       "        var v = geometry.vertices[i];\n",
       "        positions.push( v.x, v.y, v.z );\n",
       "        // For a line strip, duplicate all but the first and last vertices.\n",
       "        if ( lineStrip && i > 0 && i < vertexCount - 1 ) {\n",
       "            positions.push( v.x, v.y, v.z );\n",
       "        }\n",
       "    }\n",
       "\n",
       "    geometry = new THREE.LineSegmentsGeometry();\n",
       "    geometry.setPositions( positions );\n",
       "\n",
       "    var material = new THREE.LineMaterial( materialOptions );\n",
       "    material.resolution = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "\n",
       "    var line = new THREE.LineSegments2( geometry, material );\n",
       "    line.computeLineDistances();\n",
       "    line.scale.set( 1, 1, 1 );\n",
       "\n",
       "    _fatLines.push( line );\n",
       "\n",
       "    return line;\n",
       "\n",
       "}\n",
       "\n",
       "function createFatLineStrip( geometry, materialOptions ) {\n",
       "    return _createFatLine( true, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function createFatLineSegments( geometry, materialOptions ) {\n",
       "    return _createFatLine( false, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function rescaleFatLines() {\n",
       "    var res = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "    var n = _fatLines.length;\n",
       "    for ( var i=0 ; i < n ; i++ ) {\n",
       "        _fatLines[i].material.resolution = res;\n",
       "    }\n",
       "}\n",
       "</script>\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;:-1.4210965378698004, &quot;y&quot;:-1.1785151154886662, &quot;z&quot;:-2.1592137092929455e-15}, {&quot;x&quot;:1.1787359086363027, &quot;y&quot;:1.7091670675226391, &quot;z&quot;:1.4}]; // 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 = [{&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;x&quot;, &quot;x&quot;: 0.28807052965283875, &quot;y&quot;: 1.4210965378698004, &quot;z&quot;: 0.0}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;y&quot;, &quot;x&quot;: -1.4210965378698004, &quot;y&quot;: 0.28807052965283875, &quot;z&quot;: 0.0}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;z&quot;, &quot;x&quot;: 0.0, &quot;y&quot;: 0.0, &quot;z&quot;: 1.4}];\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",
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-0.6877678056906368, 0.17364817766693041], [0.7471952352759264, -0.6415181920833637, 0.17364817766693041], [0.7865055821305275, -0.592667933728892, 0.17364817766693041], [0.8226275211799384, -0.5414150642439717, 0.17364817766693041], [0.8554146180249381, -0.48796735716869777, 0.17364817766693041], [0.8847339573526977, -0.43254148367525286, 0.17364817766693041], [0.9104666817609566, -0.3753621342066181, 0.17364817766693041], [0.9325084735929603, -0.3166611076060358, 0.17364817766693041], [0.9507699778298581, -0.25667637142979327, 0.17364817766693041], [0.9651771643261986, -0.19565109725271707, 0.17364817766693041]], &quot;color&quot;: &quot;#008000&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 2.0}, {&quot;points&quot;: [[0.19866933079506122, 0.9800665778412416, 6.123233995736766e-17], [0.13589725961011134, 0.9907229354519164, 6.123233995736766e-17], [0.07257427576403189, 0.9973630103915657, 6.123233995736766e-17], [0.008957083723427933, 0.99995988452096, 6.123233995736766e-17], [-0.054696419357179255, 0.9985030303957538, 6.123233995736766e-17], [-0.11812818912227455, 0.9929983539435965, 6.123233995736766e-17], [-0.18108108009900822, 0.9834681705221459, 6.123233995736766e-17], [-0.24329988813688214, 0.9699511144550435, 6.123233995736766e-17], [-0.30453238497752827, 0.9525019824125818, 6.123233995736766e-17], [-0.36453034076054425, 0.931191511271984, 6.123233995736766e-17], [-0.4230505303202602, 0.9061060913578204, 6.123233995736766e-17], [-0.4798557191940189, 0.8773474162250612, 6.123233995736766e-17], [-0.5347156253448011, 0.8450320704045016, 6.123233995736766e-17], [-0.5874078526994735, 0.8092910567817944, 6.123233995736766e-17], [-0.6377187927182014, 0.7702692655260492, 6.123233995736766e-17], [-0.6854444903401606, 0.7281248867208956, 6.123233995736766e-17], [-0.730391470795098, 0.6830287690791461, 6.123233995736766e-17], [-0.7723775239289359, 0.6351637273407591, 6.123233995736766e-17], [-0.8112324428638563, 0.5847238011618308, 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-0.32468099845967835, 6.123233995736766e-17], [-0.9232444326669231, -0.3842131147547302, 6.123233995736766e-17], [-0.8969225506359537, -0.44218767300852596, 6.123233995736766e-17], [-0.8669646424583521, -0.4983696506881825, 6.123233995736766e-17], [-0.8334921542248156, -0.5525312921868555, 6.123233995736766e-17], [-0.7966407797500695, -0.6044530321201151, 6.123233995736766e-17], [-0.7565599104849532, -0.653924385420057, 6.123233995736766e-17], [-0.7134120298997778, -0.7007448006187977, 6.123233995736766e-17], [-0.6673720547940689, -0.7447244728622409, 6.123233995736766e-17], [-0.6186266262029474, -0.7856851133582454, 6.123233995736766e-17], [-0.5673733527747422, -0.8234606721399316, 6.123233995736766e-17], [-0.5138200096870902, -0.8578980112141296, 6.123233995736766e-17], [-0.4581836963490412, -0.8888575253660902, 6.123233995736766e-17], [-0.4006899563037426, -0.9162137081037942, 6.123233995736766e-17], [-0.34157186289952823, -0.9398556604475742, 6.123233995736766e-17], [-0.2810690744359957, -0.9596875405024765, 6.123233995736766e-17], [-0.21942686261541366, -0.9756289519908459, 6.123233995736766e-17], [-0.1568951182380047, -0.9876152701700612, 6.123233995736766e-17], [-0.09372733817190892, -0.9955979038141894, 6.123233995736766e-17], [-0.030179597704543787, -0.999544492197517, 6.123233995736766e-17], [0.033490487558668985, -0.9994390362813944, 6.123233995736766e-17], [0.09702480603985528, -0.9952819635725991, 6.123233995736766e-17], [0.16016579654486032, -0.9870901263902658, 6.123233995736766e-17], [0.22265749238822463, -0.9748967335484243, 6.123233995736766e-17], [0.2842465590541945, -0.9587512157310937, 6.123233995736766e-17], [0.3446833211872051, -0.93871902510568, 6.123233995736766e-17], [0.4037227747485268, -0.914881369987033, 6.123233995736766e-17], [0.4611255802359033, -0.8873348856278004, 6.123233995736766e-17], [0.5166590329397759, -0.8561912424696574, 6.123233995736766e-17], [0.5700980063027841, -0.8215766934435217, 6.123233995736766e-17], [0.6212258645582613, -0.7836315621539504, 6.123233995736766e-17], [0.6698353409479955, -0.7425096740225561, 6.123233995736766e-17], [0.7157293779590473, -0.6983777326965367, 6.123233995736766e-17], [0.758721926173406, -0.6514146442502785, 6.123233995736766e-17], [0.798638698492027, -0.6018107919196541, 6.123233995736766e-17], [0.8353178766757139, -0.5497672643091591, 6.123233995736766e-17], [0.8686107673386017, -0.49549504020065205, 6.123233995736766e-17], [0.8983824047349169, -0.4392141332683953, 6.123233995736766e-17], [0.9245120978953849, -0.3811527001676286, 6.123233995736766e-17], [0.9468939198952473, -0.3215461156123842, 6.123233995736766e-17], [0.9654371372704577, -0.260636018192082, 6.123233995736766e-17], [0.980066577841243, -0.19866933079505486, 6.123233995736766e-17]], &quot;color&quot;: &quot;#008000&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 2.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [0.26820359657333265, 1.3230898800856763, 0.0]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 5.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [-1.3230898800856763, 0.26820359657333265, 0.0]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 5.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [0.0, 0.0, 1.3]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 5.0}];\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 = [];\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": [
    "                                   # F1(r,th,ph)=(r,th,3ph)\n",
    "F1 = U.continuous_map(M, {(c_spher, c_spher): [r,th,3*ph]}, \n",
    "    name='F1')                     # define F1\n",
    "p1=c_spher.plot(c_cart,mapping=F1,ranges={r:(0,1),th:(0,pi/2),\n",
    "    ph:(0,pi/2)},number_values={r:2,ph:2,th:10},\n",
    "    color={r:'red', ph:'green',th:'blue'},\n",
    "    thickness=2,label_axes=False)  # plot image of coord. lines\n",
    "(p1+ax).rotateZ(3*pi/2+0.2).show(frame=False)       # show plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What's next?\n",
    "\n",
    "Take a look at the notebook [Spheres as manifolds](https://nbviewer.org/github/sagemanifolds/IntroToManifolds/blob/main/04Manifold_Spheres.ipynb)."
   ]
  }
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