TurmellMetre.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sage.plot.plot3d.shapes2 import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# coordinates\n",
    "ar,ap,az=var('a_rho,a_psi,a_z')\n",
    "rt,Rb=var('r_t,R_t')\n",
    "l1,l2,l3=var('l_1,l_2,l_3')\n",
    "x,y,z=var('x,y,z')\n",
    "px=cos(2*pi/3)\n",
    "py=sin(2*pi/3)\n",
    "A1=rt*vector([1,0,0])\n",
    "A2=rt*vector([px,py,0])\n",
    "A3=rt*vector([px,-py,0])\n",
    "ABs=Rb*vector([1,0,0])\n",
    "BBs=Rb*vector([px,py,0])\n",
    "CBs=Rb*vector([px,-py,0])\n",
    "Ap=vector([x,y,z])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "c1=(Ap-A1)*(Ap-A1)-l1^2==0\n",
    "c2=(Ap-A2)*(Ap-A2)-l2^2==0\n",
    "c3=(Ap-A3)*(Ap-A3)-l3^2==0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "sln=solve([c1,c2,c3],x,y,z)\n",
    "snx=sln[1][0].rhs().subs(r_t==100)\n",
    "sny=sln[1][1].rhs().subs(r_t==100)\n",
    "snz=-expand(sln[1][2]).rhs().subs(r_t==100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Rotation matrix for the initial direction of the axis\n",
    "dtr=pi/180  # degrees to radians\n",
    "alpha = var('alpha') # rotation angle\n",
    "ux,uy,uz=var('u_x,u_y,u_z') # vector of rotation of the axis\n",
    "# angle functions\n",
    "va=(1-cos(alpha))\n",
    "ca=cos(alpha)\n",
    "sa=sin(alpha)\n",
    "# components of the rotation matrix\n",
    "sx=ux^2*va+ca\n",
    "nx=ux*uy*va-uz*sa\n",
    "ax=ux*uz*va+uy*sa\n",
    "sy=ux*uy*va+uz*sa\n",
    "ny=uy^2*va+ca\n",
    "ay=uy*uz*va-ux*sa\n",
    "sz=uz*ux*va-uy*sa\n",
    "nz=uz*uy*va+ux*sa\n",
    "az=uz^2*va+ca\n",
    "#assembly of the column vectors\n",
    "sv=vector([sx, sy, sz])\n",
    "nv=vector([nx, ny, nz])\n",
    "av=vector([ax, ay, az])\n",
    "#assembly of the rotation matrix\n",
    "R=matrix([[sv[0], nv[0], av[0]],[sv[1], nv[1], av[1]] , [sv[2], nv[2], av[2]]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.00000000000000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R1=R.subs(alpha=80*dtr, u_x=1, u_y=0, u_z=0)\n",
    "R2=R.subs(alpha=-6*dtr, u_x=0, u_y=0, u_z=1)\n",
    "vuz=vector([0,0,1])\n",
    "vtpa=R2*R1*vuz\n",
    "n(norm(vtpa))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.00000000000000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R1=R.subs(alpha=41*dtr, u_x=0, u_y=1, u_z=0)\n",
    "R2=R.subs(alpha=23*dtr, u_x=0, u_y=0, u_z=1)\n",
    "vux=vector([1,0,0])\n",
    "vac=R2*R1*vux\n",
    "n(norm(vac))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Anthropometric values\n",
    "vK=12;vL=11;vO=16;vP=1;vQ=5;vR=0.54 #anthropometric measurements\n",
    "H=1750 #heigth in mm\n",
    "d_m=0.246*H #knee ankle distance\n",
    "d_p=0.039*H #ankle sole of the foot distance\n",
    "z_p=-(d_m+d_p) # z initial position \n",
    "r_p=60 #platform radius \n",
    "ae=2*pi/3 #auxiliar angle\n",
    "O=vector([0,0,-d_m/2]) #middle shank reference point\n",
    "#initial position of the platform\n",
    "A0=vector([r_p,0,z_p]) \n",
    "B0=vector([r_p*cos(ae),r_p*sin(ae),z_p])\n",
    "C0=vector([r_p*cos(-ae),r_p*sin(-ae),z_p])\n",
    "PM0=(A0+B0+C0)/3 #center of the platform\n",
    "#marker representation\n",
    "dot=point3d((0,0,0),size=5,color='red',opacity=.5)\n",
    "dO=dot.translate(O)\n",
    "dA0=dot.translate(A0)\n",
    "dB0=dot.translate(B0)\n",
    "dC0=dot.translate(C0)\n",
    "dPM0=dot.translate(PM0)\n",
    "ptf=polygon([A0,B0,C0],color='red') #platform representation"
   ]
  },
  {
   "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; }\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",
       "</style>\n",
       "</head>\n",
       "\n",
       "<body>\n",
       "\n",
       "<script src=&quot;/nbextensions/threejs/build/three.min.js&quot;></script>\n",
       "<script src=&quot;/nbextensions/threejs/examples/js/controls/OrbitControls.js&quot;></script>\n",
       "        \n",
       "<script>\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( 0xffffff, 1 );\n",
       "    document.body.appendChild( renderer.domElement );\n",
       "\n",
       "    var options = {&quot;aspect_ratio&quot;: [1.0, 1.0, 1.0], &quot;axes&quot;: true, &quot;axes_labels&quot;: [&quot;x&quot;, &quot;y&quot;, &quot;z&quot;], &quot;decimals&quot;: 2, &quot;frame&quot;: true, &quot;projection&quot;: &quot;orthographic&quot;};\n",
       "\n",
       "    // When animations are supported by the viewer, the value 'false'\n",
       "    // will be replaced with an option set in Python by the user\n",
       "    var animate = false; // options.animate;\n",
       "\n",
       "    var b = [{&quot;x&quot;:-40.0, &quot;y&quot;:-61.96152422706632, &quot;z&quot;:-508.75}, {&quot;x&quot;:70.0, &quot;y&quot;:61.96152422706632, &quot;z&quot;:-205.25}]; // bounds\n",
       "\n",
       "    if ( b[0].x === b[1].x ) {\n",
       "        b[0].x -= 1;\n",
       "        b[1].x += 1;\n",
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       "        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 rRange = 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.aspect_ratio;\n",
       "    var a = [ ar[0], ar[1], ar[2] ]; // aspect multipliers\n",
       "    var autoAspect = 2.5;\n",
       "    if ( zRange > autoAspect * rRange && a[2] === 1 ) a[2] = autoAspect * rRange / zRange;\n",
       "\n",
       "    // Distance from (xMid,yMid,zMid) to any corner of the bounding box, after applying aspect_ratio.\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",
       "    if ( options.frame ) scene.add( new THREE.BoxHelper( boxMesh, 'black' ) );\n",
       "\n",
       "    if ( options.axes_labels ) {\n",
       "\n",
       "        var d = options.decimals; // decimals\n",
       "        var offsetRatio = 0.1;\n",
       "        var al = options.axes_labels;\n",
       "\n",
       "        var offset = offsetRatio * a[1]*( b[1].y - b[0].y );\n",
       "        var xm = xMid.toFixed(d);\n",
       "        if ( /^-0.?0*$/.test(xm) ) xm = xm.substr(1);\n",
       "        addLabel( al[0] + '=' + xm, a[0]*xMid, a[1]*b[1].y+offset, a[2]*b[0].z );\n",
       "        addLabel( ( b[0].x ).toFixed(d), a[0]*b[0].x, a[1]*b[1].y+offset, a[2]*b[0].z );\n",
       "        addLabel( ( b[1].x ).toFixed(d), a[0]*b[1].x, a[1]*b[1].y+offset, a[2]*b[0].z );\n",
       "\n",
       "        var offset = offsetRatio * a[0]*( b[1].x - b[0].x );\n",
       "        var ym = yMid.toFixed(d);\n",
       "        if ( /^-0.?0*$/.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 );\n",
       "        addLabel( ( b[0].y ).toFixed(d), a[0]*b[1].x+offset, a[1]*b[0].y, a[2]*b[0].z );\n",
       "        addLabel( ( b[1].y ).toFixed(d), a[0]*b[1].x+offset, a[1]*b[1].y, a[2]*b[0].z );\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 );\n",
       "        addLabel( ( b[0].z ).toFixed(d), a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*b[0].z );\n",
       "        addLabel( ( b[1].z ).toFixed(d), a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*b[1].z );\n",
       "\n",
       "    }\n",
       "\n",
       "    function addLabel( text, x, y, z ) {\n",
       "\n",
       "        var fontsize = 14;\n",
       "\n",
       "        var canvas = document.createElement( 'canvas' );\n",
       "        var pixelRatio = Math.round( window.devicePixelRatio );\n",
       "        canvas.width = 128 * pixelRatio;\n",
       "        canvas.height = 32 * pixelRatio; // powers of two\n",
       "        canvas.style.width = '128px';\n",
       "        canvas.style.height = '32px';\n",
       "\n",
       "        var context = canvas.getContext( '2d' );\n",
       "        context.scale( pixelRatio, pixelRatio );\n",
       "        context.fillStyle = 'black';\n",
       "        context.font = fontsize + 'px monospace';\n",
       "        context.textAlign = 'center';\n",
       "        context.textBaseline = 'middle';\n",
       "        context.fillText( text, canvas.width/2/pixelRatio, canvas.height/2/pixelRatio );\n",
       "\n",
       "        var texture = new THREE.Texture( canvas );\n",
       "        texture.needsUpdate = true;\n",
       "\n",
       "        var sprite = new THREE.Sprite( new THREE.SpriteMaterial( { map: texture } ) );\n",
       "        sprite.position.set( x, y, z );\n",
       "\n",
       "        // Set the initial scale based on plot size to accomodate orthographic projection.\n",
       "        // For other projections, the scale will get reset each frame based on camera distance.\n",
       "        var scale = midToCorner/2;\n",
       "        sprite.scale.set( scale, scale*.25 ); // ratio of canvas width to height\n",
       "\n",
       "        scene.add( 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+xRange), a[1]*(yMid+yRange), a[2]*(zMid+zRange) );\n",
       "\n",
       "    function createCamera() {\n",
       "\n",
       "        var aspect = window.innerWidth / window.innerHeight;\n",
       "\n",
       "        if ( options.projection === 'orthographic' ) {\n",
       "            var camera = new THREE.OrthographicCamera( -1, 1, 1, -1, -1000, 1000 );\n",
       "            updateCameraAspect( camera, aspect );\n",
       "            return camera;\n",
       "        }\n",
       "\n",
       "        return new THREE.PerspectiveCamera( 45, aspect, 0.1, 1000 );\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 ( !animate ) render();\n",
       "        \n",
       "    } );\n",
       "\n",
       "    var texts = [{&quot;text&quot;:&quot;A0&quot;, &quot;x&quot;:70.0, &quot;y&quot;:10.0, &quot;z&quot;:-488.75},{&quot;text&quot;:&quot;B0&quot;, &quot;x&quot;:-20.0, &quot;y&quot;:61.96152422706632, &quot;z&quot;:-488.75},{&quot;text&quot;:&quot;C0&quot;, &quot;x&quot;:-40.0, &quot;y&quot;:-61.96152422706632, &quot;z&quot;:-508.75},{&quot;text&quot;:&quot;M1&quot;, &quot;x&quot;:13.793869954397882, &quot;y&quot;:46.096261438066286, &quot;z&quot;:-426.89980358791473},{&quot;text&quot;:&quot;M2&quot;, &quot;x&quot;:-13.231815146338935, &quot;y&quot;:-40.748667150945344, &quot;z&quot;:-435.0483154621467},{&quot;text&quot;:&quot;N1&quot;, &quot;x&quot;:66.09966895651182, &quot;y&quot;:35.414672721518464, &quot;z&quot;:-480.3220864994704},{&quot;text&quot;:&quot;N2&quot;, &quot;x&quot;:-23.7101563299267, &quot;y&quot;:-2.707336360759232, &quot;z&quot;:-395.5093994676936},{&quot;text&quot;:&quot;O&quot;, &quot;x&quot;:10.0, &quot;y&quot;:10.0, &quot;z&quot;:-205.25},{&quot;text&quot;:&quot;r1&quot;, &quot;x&quot;:10.0, &quot;y&quot;:10.0, &quot;z&quot;:-420.5},{&quot;text&quot;:&quot;r2&quot;, &quot;x&quot;:-13.77354790111386, &quot;y&quot;:-10.0, &quot;z&quot;:-443.78029514495256},{&quot;text&quot;:&quot;PM0&quot;, &quot;x&quot;:10.0, &quot;y&quot;:10.0, &quot;z&quot;:-488.75}];\n",
       "    for ( var i=0 ; i < texts.length ; i++ )\n",
       "        addLabel( texts[i].text, a[0]*texts[i].x, a[1]*texts[i].y, a[2]*texts[i].z );\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",
       "        scene.add( mesh );\n",
       "\n",
       "    }\n",
       "\n",
       "    var lines = [{&quot;points&quot;:[[0.0, 0.0, -215.25], [0.0, 0.0, -430.5]], &quot;color&quot;:&quot;blue&quot;, &quot;opacity&quot;:1.0, &quot;linewidth&quot;:1},{&quot;points&quot;:[[3.793869954397882, 36.096261438066286, -436.89980358791473], [-3.2318151463389353, -30.748667150945344, -425.0483154621467]], &quot;color&quot;:&quot;blue&quot;, &quot;opacity&quot;:1.0, &quot;linewidth&quot;:1},{&quot;points&quot;:[[56.09966895651182, 25.414672721518464, -490.3220864994704], [-33.7101563299267, -12.707336360759232, -405.5093994676936]], &quot;color&quot;:&quot;blue&quot;, &quot;opacity&quot;:1.0, &quot;linewidth&quot;:1},{&quot;points&quot;:[[-3.77354790111386, 0.0, -433.78029514495256], [60.0, 0.0, -498.75]], &quot;color&quot;:&quot;blue&quot;, &quot;opacity&quot;:1.0, &quot;linewidth&quot;:1},{&quot;points&quot;:[[-3.77354790111386, 0.0, -433.78029514495256], [-30.0, 51.96152422706631, -498.75]], &quot;color&quot;:&quot;blue&quot;, &quot;opacity&quot;:1.0, &quot;linewidth&quot;:1},{&quot;points&quot;:[[-3.77354790111386, 0.0, -433.78029514495256], [-30.0, -51.96152422706631, -498.75]], &quot;color&quot;:&quot;blue&quot;, &quot;opacity&quot;:1.0, &quot;linewidth&quot;:1}];\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 transparent = json.opacity < 1 ? true : false;\n",
       "        var material = new THREE.LineBasicMaterial( { color: json.color, linewidth: json.linewidth,\n",
       "                                                      transparent: transparent, opacity: json.opacity } );\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.Line( geometry, material );\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        scene.add( mesh );\n",
       "\n",
       "    }\n",
       "\n",
       "    var surfaces = [{&quot;vertices&quot;:[{&quot;x&quot;:60,&quot;y&quot;:0,&quot;z&quot;:-498.75},{&quot;x&quot;:-30,&quot;y&quot;:51.9615,&quot;z&quot;:-498.75},{&quot;x&quot;:-30,&quot;y&quot;:-51.9615,&quot;z&quot;:-498.75}], &quot;faces&quot;:[[0,1,2]], &quot;color&quot;:&quot;#ff0000&quot;, &quot;opacity&quot;:1.0}];\n",
       "    for ( var i=0 ; i < surfaces.length ; i++ ) addSurface( surfaces[i] );\n",
       "\n",
       "    function addSurface( json ) {\n",
       "\n",
       "        var useFaceColors = 'faceColors' in json ? true : false;\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "        for ( var i=0 ; i < json.vertices.length ; i++ ) {\n",
       "            var v = json.vertices[i];\n",
       "            geometry.vertices.push( new THREE.Vector3( a[0]*v.x, a[1]*v.y, a[2]*v.z ) );\n",
       "        }\n",
       "        for ( var i=0 ; i < json.faces.length ; i++ ) {\n",
       "            var f = json.faces[i];\n",
       "            for ( var j=0 ; j < f.length - 2 ; j++ ) {\n",
       "                var face = new THREE.Face3( f[0], f[j+1], f[j+2] );\n",
       "                if ( useFaceColors ) face.color.set( json.faceColors[i] );\n",
       "                geometry.faces.push( face );\n",
       "            }\n",
       "        }\n",
       "        geometry.computeVertexNormals();\n",
       "\n",
       "        var side = json.singleSide ? THREE.FrontSide : THREE.DoubleSide;\n",
       "        var transparent = json.opacity < 1 ? true : false;\n",
       "\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: json.useFlatShading } );\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",
       "        scene.add( mesh );\n",
       "\n",
       "        if ( json.showMeshGrid ) {\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 material = new THREE.LineBasicMaterial( { color: 'black', linewidth: 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.LineSegments( geometry, material );\n",
       "            mesh.position.set( c.x, c.y, c.z );\n",
       "            scene.add( mesh );\n",
       "\n",
       "        }\n",
       "\n",
       "    }\n",
       "\n",
       "    var scratch = new THREE.Vector3();\n",
       "\n",
       "    function render() {\n",
       "\n",
       "        if ( animate ) requestAnimationFrame( render );\n",
       "        renderer.render( scene, camera );\n",
       "\n",
       "        // Resize text based on distance from camera.\n",
       "        // Not neccessary for orthographic due to the nature of the projection (preserves sizes).\n",
       "        if ( !camera.isOrthographicCamera ) {\n",
       "            for ( var i=0 ; i < scene.children.length ; i++ ) {\n",
       "                if ( scene.children[i].type === 'Sprite' ) {\n",
       "                    var sprite = scene.children[i];\n",
       "                    var adjust = scratch.addVectors( sprite.position, scene.position )\n",
       "                                    .sub( camera.position ).length() / 5;\n",
       "                    sprite.scale.set( adjust, .25*adjust ); // ratio of canvas width to height\n",
       "                }\n",
       "            }\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 = 'graphic.html';\n",
       "        a.click();\n",
       "\n",
       "    }\n",
       "\n",
       "    function getViewpoint() {\n",
       "\n",
       "        var info = '<pre>' + JSON.stringify( camera, null, '\\t' ) + '</pre>';\n",
       "        window.open().document.write( info );\n",
       "\n",
       "    }\n",
       "\n",
       "</script>\n",
       "\n",
       "<div id=&quot;menu-container&quot; onclick=&quot;toggleMenu()&quot;>&#x24d8;\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;getViewpoint()&quot;>Camera Info</div>\n",
       "<div>Close Menu</div>\n",
       "</div></div>\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": [
    "r_1=vector([0,0,-d_m]) #intersection point between the talocrural axis and the sagittal plane\n",
    "ap=0.039*H \n",
    "lp=0.152*H\n",
    "#points on the malleolar medial and lateral\n",
    "M_1=r_1-ap*vR*vtpa\n",
    "M_2=r_1+ap*(1-vR)*vtpa\n",
    "tht=41*dtr\n",
    "#intersection between the subtalar axis and the sagittal plane\n",
    "r_2=vQ*vector([-cos(tht),0,-sin(tht)])+r_1\n",
    "#points from the hindfoot to the midfoot\n",
    "N_1=r_2+0.6*lp*vR*vac\n",
    "N_2=r_2-0.3*lp*vR*vac\n",
    "#representation of the kinematic chain\n",
    "lrt=line([O,r_1])\n",
    "lm12=line([M_1,M_2])\n",
    "ln12=line([N_1,N_2])\n",
    "lrA=line([r_2,A0])\n",
    "lrB=line([r_2,B0])\n",
    "lrC=line([r_2,C0])\n",
    "#representation of the markers\n",
    "dr1=dot.translate(r_1)\n",
    "dr2=dot.translate(r_2)\n",
    "dM1=dot.translate(M_1)\n",
    "dM2=dot.translate(M_2)\n",
    "dN1=dot.translate(N_1)\n",
    "dN2=dot.translate(N_2)\n",
    "#labels of the markers\n",
    "lbl = Text('A0',color='black').translate(A0+vector([10,10,10]))\n",
    "lbl += text3d('B0',B0+vector([10,10,10]))\n",
    "lbl += text3d('C0',C0-vector([10,10,10]))\n",
    "lbl += text3d('M1',M_1+vector([10,10,10]))\n",
    "lbl += text3d('M2',M_2-vector([10,10,10]))\n",
    "lbl += text3d('N1',N_1+vector([10,10,10]))\n",
    "lbl += text3d('N2',N_2+vector([10,10,10]))\n",
    "lbl += text3d('O',O+vector([10,10,10]))\n",
    "lbl += text3d('r1',r_1+vector([10,10,10]))\n",
    "lbl += text3d('r2',r_2-vector([10,10,10]))\n",
    "lbl += text3d('PM0',PM0+vector([10,10,10]))\n",
    "#plotting and showing the initial position\n",
    "gr = dO+dA0+dB0+dC0+dPM0+ptf+lrt+lm12+ln12+lrA+lrB+lrC+dM1+dM2+dr1+dr2+dN1+dN2 + lbl\n",
    "gr.show(aspect_ratio=1,frame=true,figsize=(1024,1024), \n",
    "        projection='orthographic', axes = true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#finding the twist unitary vectors \n",
    "w1=n((M_1-M_2)/abs(M_1-M_2))\n",
    "w2=n((N_1-N_2)/abs(N_1-N_2))\n",
    "#the perpendicular component\n",
    "v1=n(-w1.cross_product(r_1))\n",
    "v2=n(-w2.cross_product(r_2))\n",
    "#angles for the talocrural and subtalar rotations\n",
    "theta1=var('theta_1')\n",
    "theta2=var('theta_2')\n",
    "#six dimensional vector xi mapping \n",
    "xi1=matrix([v1[0],v1[1],v1[2],w1[0],w1[1],w1[2]]).transpose()\n",
    "xi2=matrix([v2[0],v2[1],v2[2],w2[0],w2[1],w2[2]]).transpose()\n",
    "#transformation of exponential matrix of rotation\n",
    "Rexp1=R.subs(alpha=theta_1, u_x=w1[0], u_y=w1[1], u_z=w1[2])\n",
    "#rotation matrix component of the homogeneous transformation\n",
    "vexp1=(matrix.identity(3)-Rexp1)*(w1.cross_product(v1))\n",
    "#conformation of the homogeneous transformation matrix\n",
    "MTH1=(Rexp1.augment(vexp1)).stack(vector([0,0,0,1]))\n",
    "#components for the subtalar axis\n",
    "Rexp2=R.subs(alpha=theta_2, u_x=w2[0], u_y=w2[1], u_z=w2[2])\n",
    "vexp2=(matrix.identity(3)-Rexp2)*(w2.cross_product(v2))\n",
    "MTH2=(Rexp2.augment(vexp2)).stack(vector([0,0,0,1]))\n",
    "#transformation matrix representing the initial position\n",
    "gst0A=matrix([[1,0,0,A0[0]],[0,1,0,A0[1]],[0,0,1,A0[2]],[0,0,0,1]])\n",
    "gst0B=matrix([[1,0,0,B0[0]],[0,1,0,B0[1]],[0,0,1,B0[2]],[0,0,0,1]])\n",
    "gst0C=matrix([[1,0,0,C0[0]],[0,1,0,C0[1]],[0,0,1,C0[2]],[0,0,0,1]])\n",
    "gst0PM=matrix([[1,0,0,PM0[0]],[0,1,0,PM0[1]],[0,0,1,PM0[2]],[0,0,0,1]])\n",
    "#product of exponential matrices for all the points\n",
    "MTHA=MTH1*MTH2*gst0A\n",
    "MTHB=MTH1*MTH2*gst0B\n",
    "MTHC=MTH1*MTH2*gst0C\n",
    "MTHPM=MTH1*MTH2*gst0PM\n",
    "#components of the group of rigid movements for the central point\n",
    "f_xpm=MTHPM[0][3]\n",
    "f_ypm=MTHPM[1][3]\n",
    "f_zpm=MTHPM[2][3]\n",
    "#components of the three vertices of the plattform\n",
    "dp=10 #data points\n",
    "crvpm=parametric_plot3d([f_xpm, f_ypm, f_zpm], (theta_1, -pi/6, pi/6), (theta_2, -pi/6, pi/6),plot_points=[dp,dp])\n",
    "f_xA=MTHA[0][3]\n",
    "f_yA=MTHA[1][3]\n",
    "f_zA=MTHA[2][3]\n",
    "crvA=parametric_plot3d([f_xA, f_yA, f_zA], (theta_1, -pi/6, pi/6), (theta_2, -pi/6, pi/6),plot_points=[dp,dp])\n",
    "f_xB=MTHB[0][3]\n",
    "f_yB=MTHB[1][3]\n",
    "f_zB=MTHB[2][3]\n",
    "crvB=parametric_plot3d([f_xB, f_yB, f_zB], (theta_1, -pi/6, pi/6), (theta_2, -pi/6, pi/6),plot_points=[dp,dp])\n",
    "f_xC=MTHC[0][3]\n",
    "f_yC=MTHC[1][3]\n",
    "f_zC=MTHC[2][3]\n",
    "crvC=parametric_plot3d([f_xC, f_yC, f_zC], (theta_1, -pi/6, pi/6), (theta_2, -pi/6, pi/6),plot_points=[dp,dp],texture=\"red\")\n",
    "#representation of the vectors of position scaled\n",
    "ar1=arrow3d(O,r_1,50,color='cyan')\n",
    "ar2=arrow3d(O,r_2,50,color='magenta')\n",
    "aw1=arrow3d(r_1, r_1 + 50*w1,50, color ='red')\n",
    "aw2=arrow3d(r_2, r_2 + 50*w2,50, color = 'blue')\n",
    "av1=arrow3d(r_1, r_1 + 50*v1/abs(r_1),50, color ='orange')\n",
    "av2=arrow3d(r_2, r_2 + 50*v2/abs(r_2),50, color ='purple')\n",
    "scrws = ar1 +ar2+ aw1+aw2 + av1 + av2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0clrtdAf7VbEfGaiuRtkY782UvqyurqZqGZVSUlKya9cuhcu6YpFf3AHU1NQoXNwZy5YtYwu5ubnkxSuW1k8vY9V1z53djwnVoa4C5fnz58ttQiCKEHcFPtH0TH5+vt1uZ/l6ajqoNIrLyoAhAKDXy20LcdOsXr0aACtwlNuW3tLR0TFjxgy5rQhEEeKuRmJiYsRYDVsj+vWEvKz4/oJn0AkA0dGg9gPqgf0pqdFbevXVVxXYrkoR1TIKfKLpPcuWLWOyvnr1aofDIbc5BAr+7y7vEn0dKqG0tJQ57OQhhRBFeO4KfKK5WdiP0uFwrF692mQy0W9URgbZ4iEI4Dgm7uS5KxkxCKNGh13hKGWavSNHjmhA4hmlpaXV1dUWi4V+r7Kwk9u5qP0hAKipEWbM2L59++LFi+U2igjE4XDk5+cvWLBgypQpcttyS3R0dAAI4RTboUIRnjuA3bt3a0bcp0yZMmXKFObFQ50xRFUTj3i0tCA5GY2NIM9deWzdupW5Ptr407BYLMrULqWIu6rD7l0SHR3NfrvMQzGbzUuXLpXbqLChuRnJySyhSnXuimL16tXa0HSRPXv2KFPcFZFQ1TZM5U0m0+rVq5kvT/Q7o0eLixSTUQKlpaXbtm1zOp0aU3YloxTPfcaMGVoKuwfDYjVOp3P16tVms9lkMqk91KgCHA5QP3e52bZtW3V19YYNG7T6gx+YuaD7gFLEHQp+ugkher2eeS6rV6/etWvXwoULc3Jy5DZKi5w+jdGjWViG5lCVC/acumDBAm0HJBXbHUtB4h5WbNiwwel06vV6Srr2C8nJ4iIlVAce9qsOB99FmWNTGQqKuSut1X1/o9frAWzYsMFsNq9evZpFJOU2SoOQuA8kLPDIKmE0r+xQ3uxLUhTkuc+YMaOjo0OB5aL9DXtodTqdu3btslgsCxYsCIe/iv7l9GmkpLCYO1XLDAxr1qxhP116DFUIChJ3ALt371Zaw/sBQ6/XM5Xftm3brl27TCaTtiOV/QurljEY5LYjLGBzXYXnpChKjjcoS9yVNk+VLIiaHs5/M7fIIFt8IwCnE8CiRYvkNkebuFwuNvl4OP9EFRtwh9LEnZDC/mZI4vuAd4JsgwHAjh07qNQ9tJSVlbGHS7PZHM4hxFWrVimwGaSIssRdyVdKLqQST+H43lJSgqlTsXMnZsygyTpCC3kbakEpjcNEtD2U6VZwuVwbNmzo7Ox0uVy///3v5TZHufyQ+2HJZP7g48lwOIRf/7qysnLixIlyG6UFSNYDULhYKU7cCwoKVqxYIbcViub5558fNGgQ6M+sG/Zyex/9ALj7bhw8KDz0EM/zOp2CSn5VR2FhIYDq6mr6vQWg8Oo+ZYVliN7w9ttvAygsLGSeFEjlg5G46tXV1eS595k1a9aYzeYlS5bIbYjiUL4bqjhxV2yjBqUh/r2JKk8SLxJrg823TOLeB9xu9/r16xcuXEg/qu5Q/szPihN3JcewlAlTebfbTU6WiM3WDKSwCbKrqqrkNkdNlJeXU4GjNlBczB2KT1MoGabvYR4e3cvtfe0vpoPzBuHsWWHyZLnNURP0CNh7jh49On36dLmt6AnFee4Ij/aQ/YT4Z8n+ShcuXDg5LNXt4NwIAKirQ1h+/JuFBWHMZjPJeu9RuLJDUY3DiBCyfv16sUC+vLxcbnMGHNYV0mAAUFRUJLMxCqa8vHzNmjU7d+5cv349BfR6T0FBgdwm3Bgleu6K7Y+sOiZPnjx58uTCwsJwi6Iu+UNT4Qup1FumB9izHXnrfUP52VQoM+YOxReQqpHy8vJdu3YBmDhx4j333JOWlia3Rf3FXm7vo/9dh8WLUV4ufO1rVOceAKVMbx3l10FCseKu8KYN6qWiouJPf/pTSUlJWlraokWLNNlUay+399++yK6bmIKaGmHmzKKioqeeekpuoxRBRUXFjh07qKQqTFBiWIboPyZNmvT666/v379/x44db7311pUrV1544QW5jQo9w0866iYC7e0AFi5cKLc58rN9+/bq6moKwoSEzs7OuLg4ua24MQr13JVfZqQBqqqq3n//fbvdDmDNmjURERFyWxQa9nJ78z6+88gsDgcPCg8/HM69ZSoqKlgExmw2U2vMUKGWuIJCPXdS9gEgOzs7OzubLefl5UFDEl+XBQAYNAhA2Co7+05J1sMWhYo71HN71Abr1q2Dz9FbuHChquel00NfF9sCpLCwTBh67iwIo/bvUbHMnz9fbhN6hXLFnRh4Jk2aNGnSpIqKiry8PFVLwxBbch3C0XMXvXV2tyZCTmdnp1riCsoVd6p2lwsm8du3b2fhWtXFapxwjtl2uO4ns9gE2Xl5eeGgdEzWVX1LVgUWi8VkMlFC9ZZQS0pa23g8HlZfoaLQ7V5u77/9K7tukrcUUm5z+h2N5UsUjioq3BnK9dwJJRAREcHc3ry8vLy8PFVIvB76FrQAKXIb0u8wWYcvZUIQUpQr7nFxcZRTVQ5ixjUvL8/lci1dulSxj/9OOJNTbrMBLCyjPSoqKqqrqyllKgsqChfTsGziJpg0adK6deuMRuPOnTtFt1Fp6KGP/fwIBAHR0QAUG3jsG3l5eTt37mQpU1L2AUZF2VQo2XOHqm6SYcXPfvYzAJWVlb/4xS+qq6tHjx793e9+VyyZlxf+Jd4JZ1aM+TQgTtahgYIZnufF+Bi1ypELi8WiInFXbkIVQGdn5+7du9WSvghP9u/fv3btWgBpaWlms/n555+XvSXZx9zHL/8lteLJ0Th7VsjJEQSB4zh5TbpF2EMSBdZlR12BYkWLO6gPgUp46623qqur2YR2c+fOXbRokWyOfBH2Lt77aNudAHD8uDBzpnoHMYmBL1XkscMBdcmRosMyAHbv3q2iqxm2/OAHPxAX9u/fv3///uzs7Ly8PFm8eD30owsPn14yU9UJVfLWlUZBQYFaxqYyyHMnQkxVVdW6desaGhrYyx/84AcD2lj4PD4f8fnS6il1WV7PXXUtf3/0ox8ZjUaSdaWhupE3Shd31V1QQqShoUFUVdY7fiAc+QuoHF45aV8DZszA4cPn77tvqEpi7kVFRVVVVW1tbW+88YbcthBdoKLhSwylp93j4uJUMV0hEUxaWhpLt2ZnZ+/YseOpp57asWMHi8v3I8NQj/rR/G2+V1C+svM8n5eXV1VVtWjRIlJ2IlQoPeYOKohUOXPnzp07d25DQ8Pbb7/91ltvsTWswKY/4F/mU5AypvDw6VkPIisLgJKrZWiIqYpQ7K+oO1Qg7pRT1QBpaWlr165lEr9///65c+dmZ2c///zzIS+q0c3WWWGNvusBwFvnrkwqKyt37NgBknWVYLPZli9fLrcVN4fSY+6gnKoWkVbHL1q0KLQTdhdzxa/974T35+lQUyPMmqU0z1301mk4koo4duzYtGnT5Lbi5lCBuIPSqhpl//79VVVVO3bsSEtLGzx48KJFi+bOnXuLx/yA+yAVqQsOZtRNSmGDmKqqqhQyepbJenZ2trqqdwgAubm5+fn5cltxc6hD3FWXpyZ6D9P36urqhoaGtLS0559//lYknn+Z3/f6vueqZ9VlcSgvF+68UwmeO6uEIVlXL1u2bFFdWEYFMXcAFotFbhOI/oJN5VpVVXX16tW3336bhWuYF98Hj1s3W6eHHqdPI2sMUlMhdx5MTB1TbF292Gw2dQ1fYqhD3KlgRvMwHZ87dy4Lx+/YsWPHjh3Z2dk3G6s5/vpxAwyxNkAQUFcHk0kuz72yspJNZdV/pUHEwGCxWFQXcIdawjIUcw83GhoaXnjhBTbMNTs7m9VQ9ooiVC6u/NY/hx6ZyeH4cWHWrIGPuRcVFbFm6yrtaUMEoMaYDNTiuZOyhxtpaWlFRUUNDQ3MhWchGrPZLDax6Y7jrx9vQhOa42WZiYm8dU2i0rCwOjx3qDNbTYQEMRzPMq49Nxb+gPsgBSl3tJoBMM99AMIylZWVANgcGpQy1R5qrIOEWjx3IpwRw/HMHWZdJ//4xz+OHj06WLUffunhktdLZhSeOrJkzMB0hWRWmc1m8ta1ikpzfqoRd5VeXyKEMPWsqqqqqqpiHYeCPeWTh04aYEByFAA2zV51dXU/xdxZbB0UhNE0Kg24Q0VhmS1btphMJjU+HBH9hCAIrL7QbDazekoAKMJniz/7znbD6QdH4+xZYcqU/jgvK8yXc04SYqBQaUwGKhJ3qPkqE/2K6EHn5eUdvuNwRHHEloeaXy+cxWLuoe3nLgZhKLYeJqjXc1dNWAbA7t27SdyJYJjOFhUVrVu3bnfx7gfwwF9GxQGz4HBcAEI1VYg4uoq89bBCvQFhNYk7QfQAk3jhI2Fv8V7rAQGP7cfixcPuugu3ViojBn9I1sMT9TqUagrL2Gy22NhYua0gFM3xOcdRjIcmvFR7ZxaOHfvGhAn35eT87Gc/68OhpNEe2bvTELKg3pgMlD8TkxSLxWKz2eS2glA0J4tPWmGNePZb+M1vsHhxYlzc3r17i4qKbuoggiCsXbtWrIQhZQ9bVDp8iaGmsMy0adNoKBPRM2Nnj9UX60+nHAWAOXN2/OxnbJ4/sVqx57JFaQUOpUwJVaOmsAxonCpxI/7G/S0b2a98+9T2385EU5MwerTYW0Yq3IsWLQrwx8WtoLp1QhOoyXMHoMbGm8QAY4X1yJhWAGyEqijuHMcx1WZ1NfAF01lDeZC3Tvij9iSfysR92rRpar/iRL8ydvZYZ7EzlqVmnM4u92EKXlVVtW7dukOHDmVnZycmJpK3TgSg0k6/ImpKqDJ2794ttwmEoklAwgOnRoovu6tzZ4H4tLS03/3ud6TsRDCqzqZCjeKu9itO9DdOOP85phYA9Pob7jx69Oj+todQKeodvsRQn7gTRA8kjUnSQz/kkgAATU2Qe5o9Qr2oOiYDNYq72m+nRL/SdqoNQHILgOsJVVktIlTJsWPH5DbhVlGfuC9fvlwD153oJ04Wn2xHuy0rGQAMBrnNIdSKBsK/6hN3aOK6E/1HJjJb0AJ4Y+5Go1FmgwhCDkjcCa3hgOPA3dfj7P/6179kNIZQKeptKSOiSnGnsDvRA044F2/j2XIIW/4S4YM2Ar+qFHcN3FSJ/kMP/TGUAIDTOYyqZYibRxuDaVQp7tDKrZXoD5xwLjo1FYLAEqo9dE86ceKEy+UaQNMIdaCNNidqFXcKuxPdoYf+/buv95bpwXMfN25cQ0PDgBlGqAVtyItaxZ0gukMPvS0OAGAwXAB6buaelZU1MFYRKkIbgV+1ijvlVIkuESAAMCbfBgB6/es8T3PjEeGJWsVd7SODif7DCuvd7zYBgNP5O51af+GEXOTm5sptQmhQ8U+fcqpElyQgwbuk1wMwm81yWkMQMqFicddGuRLRH7Qkc4C3cRibiIMgeoPdbtdMyFfF4r5q1Sq5TSCUiBXW6Dhvy4ELAMXciZtCG9lUqFrcCaJLBAitaAUAvX5Yj10h1TWBMDEAaKMIkqFicafJ9oguSUDC2eRWwDvNXg/TotLgVSKAXbt2yW1CyFCxuENDeW0itJgvGQFg5MgL5J4TN0N+fr7cJoQMdYs7QXTJx6nHAKCurufeMj2PbyLCkJKSErlNCBnqFnfKqRJdcv9hIwQBmZk979ZDxIYIT6ZOnSq3CSFD3eJOYXeiS4bEjAKAEyfQY0KVPHdCypYtW+Q2IZSoW9yhue+DCAkfz2wDgNRU9FgKSa3eCSkaG++menHXUukSETJaWgCgvb3nvahahpCipZgMNCDumhlORoSQoeUtAG7Yz50gpGgpmwoNiPuCBQvsdrvcVhDKIjprFOBt+UvuOdEbcnNzyXNXFjExMdXV1XJbQSiLkS3e9gM9j1DtYRMRbmgvBqB6cQeF3Ql/BAityQAAh4N6yxBhixbEfc+ePXKbQCiFKEQBqI6tZS+H9bgz6T4hopl+YSJaEPd58+bJbQKhLF6Iv5stXKDGYUQv0GTeLlJuA0KAyWTasmWL9m68RJ/5x0M6CALa2w8BT8nqnl+5gvJyACgvR3l5I8BNnpz64x/LaBHRBRaLRWPZVGhD3KdNm0YTdxAMPfQAzAebMR8A5vS4c0gKaRoaUFCAl1/Gc8+1iAcUKl0iAAAgAElEQVQGeJ73BJ2IA1Be3gSk3vp5iRCya9cuEneCUC6OIgcT96iNjwBNN9y/b2GZjz9GeTkqKq4JghsAk+znnmMbOabjgqADPOIqto8PKs1UHAsWLJDbhNCjEXHXXhkT0Qei50Q3oxnAChdeiAUcjp4Tqr0pomVSDqC8vJWt8Rfr60rNcTrJMif11gEB3nuJAHD//CceeKB3H4kYELTntkMz4k4BdwIAdiADGQD+vMmCF9JgMBQBPTR+zM7O7nKGVRZpqai4Jgh8wCZ/Zdcx1RYddlxXcLbsEZ8NfNs5AJs3X33ggcE3/emI/sFut8fExMhtRejRiLhDu98QcRO8jOYfNw/H8MFTEwFAr+855h5QSPPcc63istQN73kl02tB8AgCL8Z52J5Byq6F4jTtkZ+fr6U5OkS082vT0vxYRB+54P13+eNZABAd3XNYxmicUFBw8LnnWtl/4nrRDZdmXAOU3afmHp538byL5z1M2TmO8+0pHoQt6yTv5f/zP/vy+Yj+QJMBd2hJ3GmcKgHACacAwZvLrKtDV3Xuv/sdPv4Yzz3XvGDB61ar3W5vlG4NDqmLei0IPCDwvNvjcQiChwXQu38vfIF3DhAEwSMIHkFw87wLEMrL60P6uYm+o8mAO7Qk7lq9/RI3wSFvKSQiAACZmUWSJt0NDV5NLy9vLihoFn/8MTGDxAMEVbYATJg9Do/HwfMuj8cpCB6OY554T8oOQBB4nvfwvJvnmZvPC4IgPgHUk7wrgK1bt8ptQn+hnZj71KlTS0pKtHoTJnrFU0hYnAD4qhCt1mKP56mIiOeeaw7aleM4rq3teA/KzvNuQXAHa71P2b2v/N8r8DyrjxTYKaTFlgHH37wZP/1pHz8oQdwQ7Xju0O7jFdF7WCkkyrzZzM0FB559tktl1wGIiRkUGztYXMWUl+fdPO/0eOyC4OY4XcBAJ39lZ2t0TNNZ8B0QRGX3bfU7PgvW87y7rOziRx+F+vMTN4mGe8pqStxfe+01uU0gZKUI6UgH8NayYgBwONKaDJLNnOQ/AKivP9jaWsNxHAuYeDwOpum+CsjAtGpXgRc3z7t88XfRS+ekb/ENa+KZ+rM0LFP+zZsvhfwaEDeFxqbWk6Ipcb/vvvsorRrO1F5GC1oAfJnDAYDBcDVVnGnveo5UVN4RI55gmi4Ibp53StRZ3I2T5FTFODsvCG6Px+7x2AXBA6CxsbSxsaS9vba9vdbpbHM628SjCIIgCLwguNmeEmNonKoiWLZsmdwm9BfaibkDiIqKoqGqciII4GTQrN/8Bjk5KChonLu33IxkABOajACg1w9uMgSFVbx+tCDwly9/DgQOU/LtJvV7ON8QU5cg8OfPfxgXl5GUNCYqylBR8Xp7+9nuDNPrjRMn/ig6OjmghMYXn+EFwb1s2bmtW0f0/cMTt8DWrVtJ3NUBxdxlo6gIYuzSbMZTPQwLDTFPP13PcbqKCq8WJyABQLGhFkhFe3tHrFO6M8dxPO8RAy8xMakOR3ALGi6opJ3neReAa9dOXbjwd7ZQX3/Q47F3dFwIeruXESOeyMy8hx2K43TsjJJby/W+NHV1GDKkzxeA6Dva9gU1FZYBkJubK7cJYYmo7FYbqqtRVNTfJ/zHP/D001eefvqKrwLdG1FhCdUhMbexl52xDvEtPO92u+0875Q2FYiJkTZo5KRBG0DgeZfHY+N57x3C5bLyvJvn3Z2d9e3ttV0qu15vzMy8Z/bs34nKLoWlUiXKzgH4yU/Offhh3y4DcUtoO4qrKc8dVO0uL/trcaUN996GvEX9d5Lf/OZvhw+P0euTcX3wpx8CBLS0AskA4mzRADweJvGBezocTXa7n+fOYiaCwEtD8Jcvf+ZwtAK4fPlTyZ5Ren2ywTCqqemYuDIlZcrIkY/r9UbfoXwmCYIv6ep3NnFp06bTDz88utfXgAgN2vbctSbuJpOJmszIxoxMVOk8e09FlHLohwhZVRUef3wRgCFDvj5y5HwAAXpti49OaIwDkNTpldGOWJvbbfP3x71wHGe3NyUljRdXAPB4mKYLDkdbU1Pp5cv7nc7rbQn0+mSed0dGxjD5Tky8LSvrgYyMr7EkampqDlvvO5pYJOP23YQ4ib4zp95bF89x3NKlp7dtI30fOOx2u7YDuVoTd5J1eVi7FmvXIiEatw+PeOKBte811PyqddGicaF6jvrsswvf/vbLqanT2Eufa4xAcY/TO+EE8MkkryIPv8AcfLHvrl9RY1LSeHYQQeDb2o47nW3NzWXt7bVSQU9IGAVg1KgnDYZRANraTl648Hfmi8fGpgNISBgRHH7xlVd6Aqoqxe0AfKH/65uWLj2zbdttfbtExM2iydmXpGhN3AHQlHvysHbt9UUASNuw4VptbeItTin30Uf44x+rjh1bCyA62usX19buNhhGRUenREcni3sKgtAZH23FVQBTT8YfAZCa2ph6tauiQ2+No8Ew4vLlzw4fXuV0tkg3JySMHDnySb3eGB2dHBBdSUgYMXbscoC7du10SspkdNMq0vcEID2duMyiNC7xpdj5XRD4ixcxdOjNXSKib2hy9iUpGhR3bSdJVMTq1YkAVqy4VFCQ1Ye3X76M8nJs3nypqamUramr+0TcWlHxW70+OSvrviFDvu5bJ0w+cjYBGQDa4gBBwOXLjalW/4CM0NRU5nC0trefbW8/W1f3idN5TcypjhjxhMEwknnoAPy7tPO+AAsXGZkAgCm7P6z9gCtwreT8zJ337ew9B/uXjW798Y+P5+SMWrlS3/sLRfQNDQ9fYmhQ3AlFUVCQ9ctfCiUlJ7ZvH3/jvX38+tcoL78E4OjRtdIgiRSns4UJMeu7CwgXhiennHcCyLQZAcBgmF46nO3c2FgKoLZ2j9RJj4xMSE7Onj37t12OKvKVLQo87xTb+XZZsQ7vpKluQfAEFMhzHBIaS51xmfrOy/GNR6I66gAu48SfE2IzPnn8gO+9gq8ghwO4srLaDz4Y9+ijvb9aRF/QcIU7Q4Pirsm++6rmF7/ggPF798Jmww2j8G++eXDfPs5gGAmgrm5/d8oOYMiQ+wyGUR6PTVTeYedbrNADOJBSCnwDev1XQz69VHS9zFCvN2Zk3B0dbUxIGGkwjDh8ONfhCO48wzrD6ATBw/NuyfwbCG5I4AuzuNh02AFp26cKb2sF/CI+QAqQEpvx/v1F8IbmPf6DVwFg06bjpaXDVq2K6/FSEURPaK3OnVAsjzyC8vIrv/0tzp3reocPP8Ty5ecPHkyurHyjtvZdAEOGzB0x4snuDhgfn+Xx2HC9NwDXNCg+GckABp/1NgCIbOlgC5mZ94wZs8Jsfn7EiG9mZt5jMHgHhfpKIaUTa8BX4e7yn0FbOtsGW6/jeZfHY2fKzg4Q72h+4GRBnKP5+4Wjo4BRAAuh64GxgBlISJ2y9fED1rhMADwvVXbxOUDgeVdZWe3f/tbdRydulZKSErlN6Hc06LmDcqpKZd26dAAXL2Lx4uMBUZply2qZSuv1xjlz3jhx4n8PHXoxIWHkpEkvXb78WUDCk5GamiN9WVn55jdapgEJACo6PwUWoakpyzps1h3/h+ddguAWBEEcIOrrCpkaPB6VDWENav0YeHZBEATBbzwUx3HP/uuFhxzNAL59puh/dHo770wFhgLxQCSQAByY8krp+G97z9OVs+9z5DkAmzZV5+SYh/U8mxTRJzSfTYVWxZ1yqj1zmuNGC8KN9+sfhg7F9u3j330XDQ3V3/ueua4OP/lJrbiVKe+4cc/V1r57+fL+o0fXpqZOaWoq9em7t1Q8IWFka+txj8d++fLnTmcri97Uxgyb3jFJgDBu3LfqWlqQmWkf2ea5aJM44GKC1Cv00vYDbPQpwObTEHylLH5v9O7IuwEh4AaQ6Gh+yNGMzsvwOGGrfwZgTWfqgERAB5SO+xZTdjYlU9Bz8/UQjaj4P/5xVVFRdt+uM9ED4RC81aa45+bm0lCmbnnpJQA4fx7Dh8toxZNP4t57j3zxRWZra01sbDrHRUiq0QFwI0fOGzVq/vHjf758+dPY2Ez2Lp1Oz/MugO/ouFhT8w5bqdcbU1KmGAwjh11L13foAbj1ApKTcfmyZNLqLjqatbWdTEoaB++8HB5f1fn1onjpFKrsH1/yFtIbAGPmvmW4dsr7QhcVBe7TMcsiO+szmkoTbPW77tteP2gaAN/Y14DbTJfBd4Hn3QsXlufkjFq92gAidITDxD7aFPeYmBi73S63FUqEnzPnXHExABw6JK+419UhM/Oejo5LOp0+KiqB510OR4tenwhAqn3jx3/r6tVJp06xudB0YpsXQXBzXGRqas6wYY9cb7tYUWOFNR7xyXwGACQkxHVau8qCXj9FW9sJj8chvQFIe8v43stcbN7jYXNx+O0zvvS16M769AsfpgMVwCRdFGIzEJeB6JRPpvyCHTbBVt8RN0QQeIAPnnkVvhk8fK+8W8VQflnZ2YULsXNncPEl0Re03QxSRJvijjAYftYHmLIzGXO/8Ubk4sVyWfKrX6Gs7ByAqChDVJTB6bwWFWWIjIzlebdOFynGxOEdvu/U6SI9HndAe15BcEdGJkgb6qY0WoEUADa0AYDBAEgnKg2Ibgt2e+PgwbOEwAiV36glX2Myt2/+vOukX/hwfMlr0bZ6IzAZqE/NqU0cM8l6HsCZpLG/yn5BPExHXAYgSDtBSs4izsznZ55vUidq+x56tN1SRkSz4h4OCZOb4qx/4u5ccbFy+pjodFE879DponQ6vcvVzvMuvT7xxIlN7e210lQqx0X69NFLff1n9fWfAUhNnaLXGy8b0oeLk3MIAjgurjPK916/M/K8UxA8giAElEIGt6Bh0RL/GwA3vuSX0bbLIy78PQdIAj4f9+x/jnu2NTYDwGZg6tXDArjW6BTJ6dxdKjXHcexpQBLk4TiOC96f3PYQEibioFlxJ/xgcXYAQZ0JB56ioqKnn36qrCxgNQuSnIyNTXM62xoavmpvP5uRcafVer65uRxAdHSqXm90OJq6rHxvaipNTp7UGpkQj3gAjecPAhPR3l4zvnHCcTYF9vXsJVN2AElJY4Lq3KVuOy8Jr3u5fd+S9KbSkYAAGGMz/nB/ES+4W2PTpW8sGTxT8hZBVOrg6Vh9XQqkgSBWZ+nXcyYnZxSIEGG328MhmwoNizs1dr/O9u1n33iDLfop+0sv4fXXB9KQoqKip5566qmgqTzq6w+0t59zOlut1loAM2e+mpmZnpIy6cqVQ0zZExJGmM3P2+1XIyPjT5z4X6u1i1L5lpYKp9PYgQ53bHxixiS0toLn+Ya6L7/8U0pKDoDU1MlRUUmRkTF6fRIAgLPbm5OSxohHkIovq54EAOgAIeeLl2Js9SOaSgGMj804N2jKX6esbI3LYM2EOe8EqjoE+f4ej1NcKQk3cRJl94M9JUgHSU2ZMio3l7KpISN8AraaFfeYmJhwSIjfgHPnakeOhKTVrFRLPMXFEQNoS2VlpVTWt24d8fjjn58791ertVavN+r1xtTUnOzsF3yTaQiNjUfHjFmSnGy+cGGv2fw8ANaFMTv7hcuXP29uLk9JmXT+vN84nxH2QfGIT7BxRv0IGI0A0nSjp0xZ1dFxoamptK5uv9N5zeVqi48f5nReGz78kc7OupiYlKCAieDxOFyujqTGI7xxwsgTfxl54i8ZQDpwfNxztalT/jloWmtchiAIvMcBPwT/knmBKTsASW2MV989ge9lW1nbdwjC9ep7UvbQQuKuBcIkstYtlZVVkybF+15xQV7i2eLiMYHv6SdDKidOnDhx4sSA9bGxB1JTJxsMI0aMeAIAzzs9Hm+N0/nzH165cvDq1cNjxizPzv4PllMV35iZeXdTU2lTU9mECd+7cOHvHR3nxU0XcMEE05n6D9C6mOm7Xp8YFTUhKWks28HpvNbSUgng/Pm9DkdzQ8OXhw+vHDbsUaezLTPzbkCIiIjlWqqfrHrLc3l/DDACGAmUDn3wnamvtMZmMp9a7DbjjyCpa+TFDmJdDVMKnokb8CZR2f6CIPAcx+XkUAdgoo9oWdzDHMukSQLg9v+OpRLvArB9O/qzZqY7WWds375q+fLzzKt1uzvF9adPFzL9jY8flpAwnOedsbFpbneny9XBJN7ttt1221M1NX8EYDZ//9SpwpaWCvbeZCQLEK7Vl8P4fQCCwLvdndIbg16fmJ5+B6BLT7/T47G1ttbk5PzM6bzW3NxWWvpqlr350fazsfZGg6s9AxgBtBtN6+58uzU2nWkuoON5h1Sd/fvMCIKALtvF+BA8HifH6cT4jLhB4uZ79xQEUHl7yAmTUhlou7dMOIfdLb42V9LiEulgHrbe5ovFh5zKykoA3cm6yOTJw3ne3aWyjx69dMyYpQA4LqKzs97jcUZGxlmt553Oa4Cg1yempGTX1LwjCAKLoX/9yii9BzroCmYcT07LBID29otDWspM57vyssFxcDiaY2PT9PqkLHvjxNjB33G2f6vuk7vaz97vah+jNw4fcl/W8EfTEm9ri8vwBc09Ho+9q9LJ690ied4plvSITW/YSzYASoy/Sw8R5OZzALdrVxg/d/Yb4fM0r2XPnQ1lCsNxqjUcx/lqwrt0IMWO42eLi0Pe07qXss74+c+xeLGLyV9Hx/n6+n8xZY+KSkpJmQRAEDwcFxkREQ0IDkdzUtJ4nS7Saj0fEREzbNjDTue1I0dyAXzr0h2pjpg4xE37nxIAqM9ASwsiIwGcHFnfbOwYd27IsHrWt/16UwG7vTlj0JScL36UceHvzE/v0BvPxGX8Z+qUn7ZaJtftw5CvF4325glYcwKJ0w3xaAxBEHjeIZYzdlNVeT1Z6ou/c9Lek+IxSdn7g7DKw2lZ3AHs3r07HIaiSakJ1hT/hKrUlw/tCJmbknWRnJyRZWW1TmfbqVOFLlcbgPT0O4cPf0SyCy8IOp53cFyEw9Gs00UaDCM7Oi5VVv6BdYb51qU7shxGAE4452w/f2jxcBiNOHsWY8fCbgfQZGx3bv0nRi/1HZADkNRYmtVSnXL1qynAeKA+ZXLBkK9/FZUw9coX804XngJOAWcThlVn3gOAjWKVRMMDH3nFtgS+JsA8oJMOZJWUzfhVWyLIiwfVPhKhQMthGQDV1dVymzCgSJVddAU9kpeuoLSqbc6ckJy6qKioh/B6D6xcqW9pqSwv/zVT9vj44f7KDkHgpcEQnnfX1PyPy2WdMWNdbGwGgA9TKz3wcOA60Tn9sAAAMTGoq8Nnn8HhAJDyUVVLS5XF8o7VeiGms35C6Wv3vH/P7H2L49xWG/DJvZt+M+u1H4975l/N5c+U5E+SzPc06sRfBMEj6U/gtUhc8uVX3RJlF0SzBcFbh8OiMcG+PLxhnEBxX7PGGLwnQdwUGvfcwyd5AsAukWmpFLmASECQRGOkO9QWF9/iNeJ5XqfTBVev957kZG8Xz/j44Wbz/yfZIng8TkHgdboI5oi4XNcslv92udquXv1Sp4uZNWuj09l27NiGrWnF9zQMS0TiXS3Z24TopvQIuFzQ6cDzKf/7sbGyIdHjNDSVzjnxv1mO5hhgLnA2ZbLBZb04/JFP2k4l1B+8p+2EueMi/AcUccDX9i37fO5f4D/GVYyowNt0zC15X8Csq3x3yVVJd182asnr6X/nO+ESNxh4wqcOEgDXZa6JUB3V/pEC3l/f44DAkmzJsqmwsG81M5WVldXV1bci6yKjRy+Kjx9uNn9fqq6SYAjHcRFnzhRZrReYgy9iMIyeMuUX9fUHBx3+W3bziGxkn8O5Vzcl16emAMg+e07Y9MXck6UzWyoBjAfiImI/TRhqNJr35Pxk376len3iEt41p+1kD7a9t0Cc2CGgybuOtYn3XxkwiMnBcZH+K6+nXqUvAU6niwDw859nxMU19+EZiCCkRKyVTFqvSUpKSjIzM+W2op956aX64mLpU1iXd2yumyD74KFD8dBDN3XCoqIik8mUnp6enR2abuMcl2G3zxUrTwSBF4f5MGW8cuWLhoZDPO93kzIaTZmZd3o8TlOr5Xv2snv5M/HOpKHcltXHPx/X2HhxUGrB79/4YdknkfaGCcCQiNj/f/CMP6Vkf5ow9HNdREPDl7yz1dx28kl7Y8+2tSeObk8cHXz9fMYENhUQlz0e9rAU0HvAG6iRvmQIAr9794ysLENaWhqAoqKiUF1eAmEiBRK077mHQ3vPYxwnsCmIfLLOS5aZisRK9heC1N/U658Bz/PV1dX94VcuWXKCCajHYw+Y4ejYsfXB+w8efHtW1n2sfOWJ6v9a3Fga5RbQ0X7acW50TBwyMhBpxaUzcOLDzAdLhz74PviGhmLx7WmtJ1uay5KAF4IPHcRHD//dHpfh38rRxZ4qxPiMaC0AQZD2bfd2EvY9XOl8k3V43yG+d8+eWcGnZlGvXthI3IDc3Nww6SrD0P6PRvM51bY5cyARa85/WZpNlSKNLDsBbN/em3Nt375dp9P1U8QgJ2cUIHg8Nqmyu1ztwcoeFZU4duyzWVn3AWBx7arolHfarny3+ezyhNSXp60tvW0BhGZEncFIXJmJTbN//nFcutV6gb092Xpx2pmdQ5vLmgErUNcL28acLPBXdqcg8F4Z90uHsscO1t3X76oLgsDyq/7K7vfGLk+t0+ny8vJYJRJxK5jNIa/7VTTa99y1XdnaNmfO2eJiDyAAcQDrFcP7++zMT4+R3MkFyYLYvGpKj7+EvLy8devWhdz+ABYtqpC+dDqvVVYGDrOKikrMzv4P8SWLdlwo/T+6lvqkicsSBmffcaX4hdI39Z02JLYefKz16iC02NP+/MVtzfbU21qbhjWVXfXY2Hs/AwYD04EhwA3DH+8tYH0seWnHGDHYwvx3juMEAYLg8k3q5N3of6SA2hivrO/ZM7NnA8iFJ24K7f9Wpk6dqtmZzl988Wzx9TiDzbfARNrj/zJ4YiqpsvfA9u3bAQyAsgN45plJbMHpvNbSUh2s7ElJE7Kz/eIoV658eenSvsyJ/zZmRu6Yc+d/VPX20I5L3737zTOZ2Xzr6Eu7F7d0IlHf8PLXixeM+OBRZ/Ecj20im9EDAOAAbMBp4Ahglww2Df5vzMnN/hNrcP5lMbxvwSVWQPr2BMd5/+N5B897gj2qZ5+9gbIDYMpOLnzf0KwIdI/2PXcA2hyn+uKLpb//PQBBouMGX1WdR+IfsgUOiPFJjujXS0Pzo2bPTjp0SHqG7du3Lx7w2Zr++lds2lRx5UrxpUv/CNg0ZMjXBw+eCYDjWIeZDo6LiI8f4rxy3F3615SmDuuj/+aO1gsCr9NFRUREl5QknzyZaow78v37nrt99HGHGw432j+G8ZRX0LcAiYD0Wf0uie4Hs+vJr6Qvg+rWOZ53BY1vur6Xx+MSG7X75oz1Nhu4odseQGVlpdlsJke+92j7Cb5LwuLHsWvXLrlNCD1M2QNw+8Q9cFSMb72IM2gf6UMAZFJ2AN/8Js6c2Rms7CNGPMGU3e3usFpr3e7O2Nh0nndaD2/p3PdGUtM1d0q6Sx/FPGied9ntTdOmtT344F6HkPOrv1a+9c9VHJAYi8EP4dzDiAUm+oeqGAeASskzUAC3f/VKD5YLgjuoBvV6dbxvAtXrvQdEZ/9mlR3AxIkTdTodz/Pbe5csISwWi9wmDDRhIe7a+17LgmZxFtuB8d30k4EkBN9tNOallwBUVFQAkEXZGWPG6APWjBjxhNE4weVq93jscXFDoqISz5wpqqp6C+DcJw8aYfQMGdt21+OSSUq5iIiYa9dOJyaOfuih6lmzzn1xZtUvCg+02xARgewJqLsXHUZEAhlAlv+5TgMHfFlWm7/QD63bxxZYjEUKz7t43s1aQgZfXZ73+Nc+elOxwXnXm0Kn08n4NakLzZfMBUNhGRXy4otlErc9QEuifAvSrKm4HO0/TjVgT9worTpgLF688ciRUgBxcUOGDLnX43EajeMBzulsqa19t6Pj4tixz8TpEh0f/joGMYkxQ6/d8zgfy2pBOY67PgdJVFT8tWtneN7NcUObv2o43HL/lBE7Vz25NFKH6kv47724x4r7gTrgcJANWcAlAL4q0m8AAL6c9dolb5UOJMOR3L5hqOJd19tfjOM4QRAkyg7451ffe++Ovl8mCXl5eWvWrImIGMj5VwhFExaeO5uVSW4rQkRh4b+6CsgwPBK3nZOURYpy0mXAIbTtw0LC9u2rAHBc5LBhj6Sm5mRkfA1AW9uJS5f2RUYmmM3Px8UNcZfv5cAZYWx9aJlP2QEI4nB/juPc7k6jcbzH0xkdbR9yd+I7MUNKzy386ZYDje0wZyHeCNsguGIwBHgCCCjwvORbYP57C8ABs796JdbW4NviHW8lOaP4bt7XFCxA2SHuyXEhU3YA69ati4iIyMvLC9UBtYTdHlxPoH3CQtyhoSYzh5Yu5SXet9QrZ0nU4ApqBuvt7u6moFqsCSnpqrmVLIwZ8/TUqbkGw4jOzisdHRebmkqvXTs1ePCMkSOfjIpKBMBfqjLCyMck+L+P2X89oWC1XszIuNvjsQH45O533okZ8lLjkp//8eypK1kAuDHoWAzbUHDAGOBJ/9FeUj733RpTmsrFEwmCuyvt9t5YBcHj6zHgv5kDgJyc0TdzPXoFK2oiiQ9Ae4HZ3hAu4q6RkWkvvsj+7UIwuu/7yBCzrGL3wmCVF7o58gCzcGHZsmXnjMbxTmerw9Hqdne2tp64fPnzrKwH4uKyAAjNF5x//60BhojkYS0PLpW8VUxXCqxs0e2263RRLS1V8fHDPB6HLTateGZ+Ki69iVH7tr547qrpXCOGpSDmMVwZ6T3Eg0FReJHTAICcijd8wUzeVxkpPbu0PtLD84EheFHZ161L78vV6QVM4lnuhAhbSNzVQ2HhIV9AJrgYhmkMS64GT70s+Hx2oXvXXlT2qyFqAnyz7N6NqVNfuXABO3fmLFo0wuFo4XvDrAUAACAASURBVLiIiIjoyMjYy5c/nTDh37wqabvmOXUozuaOR3zrXY8F98tleDwO0aeOjIy32xuio1PdbltTyqRPJ/4QwAr8NMNxuq31sbNXsxLjMHo+bN/1vndINxaeApqBWHtDZNtJnnf5RjNJb5QByu4GEKzvAPpP2UUmTZoE8uIBaOjB/aYIi4SqNihmo9196hwLRPn8cVGvxShNvP9Lp/8OXY5WdUiWbx/YX8XCheWRkbGFhd45rNesqSsvr3W77VFRBpfrWmtrzaBB0wGwNjKeio88pw5lIMN2W7Z14ixxPQCxjl/McEpnT3U625OSxjY3V8TGpo2rfDPndOFG4H5gLLLen/jiC9/4KYBrNlz7GMaT+Bxo7srUFGAm4IqIff+BHVFRCRwXGdxYBoB0gmxJb5kItvDss3fMmxeqi9crPB5P2OZatVZP0WvCxXMHsGXLFrlNuAUKCwNWsPiv4KudlqZP4VNzaRMCEa6r2IvD37ccGOc9P9+6bNm5X/6S37lzsqjsZ86gtPQ068l16dLHHR2XmLKDzdpxscJz6lAqUvmYeKbsvl4u1weF8rxLrF3h+esJZr0+0WZrSE2dzPMui+l7+8zPe4BEIAWXnqv86QcfLnS4kBiLod/E+cW4G7gHGBMUomkGPgf0Hlv7sXyg68JHAJJwjXeEqi/TK4OyA2DKHp5efHgG3BFWnruqe8IV+1xC6dBTlvqTRiVEJYsEon0TdEh3EL/sGInDKVX20DvvTFDOnUNrK/7wBwwdCmDevK/mzJm1ZAmGD/fbd82autLS0zzv0ukim5rKfONRfe6w7Zr7o9/HI94Aw9XHvwXA32vWcRwnNgoWt/o3bhQiImIiIqJttqsAyvZ+4xneJT6xuwchYhEMsQBwsRkH9g/9Wm1TKmw24BIQHMAuH/et8eOfg9/zAVNxj1TcA1LU779/T+8uXH9RUVHBIjZhgqr/8G+FMPLcc3Nz5TahjxRL5KHnHlQibl+4prsdxNtAdwOavgxV2UxnJ8rKEBcHLhmP/0fh9DV//zv27Jn1s58FKjuA0tLTRuO4xMTb3O6O1NQpguCWBDoET8U/IhBhgKHpgS6mB2Hz4XW1XpBM0eex25sEQejsrHc6WzuTzZ8mjBCfe6Iagb+g/ig8PIal4P77L346IXUvxsYCY4DgbrycvaG+/iC8de7i7Hoe/yyr39V9/XWZlR2+WHz4pFsXLFggtwnyEEbirtanM/+AjFSsO/13DNBou3/EJgCXryi+yxaFISuH/OADdHQgJwfF9TjWiMTEJYvSupsX5LHH9hkMo65cKW5trYmKMrDhPyzAIgiCp+LvQp0lFamdt5k8MdGimb7BogLPO6VdvfxzmzzPu3neKQgenS7KZruSlDTW7e4EcCl1yj7z8+Keuk4YPkPnO2ivRVIcnnvkYvIDF181zj6JlCwgwN2dcOmTpqaSpqZSeOfM46VNBXxc7yA2Zcro0aGvfuwjTOI9nu6GM2sEu90ebi1lRMJI3KdOnarGsQz7li71+KutuOzpvtOAEFQzE6zXzq5Gq0r3/+rWnfcZMzB4MADcPhLPTcM9I3FbWpc7/vnP5wcNmu5wNMXEpEZFeUvXOY4NEeL5pnPCmSNGGBFj6LzNDG8jFy+CwPO8k/nO3QXBBcEtOtQcF+F0tmRk3CkIQnS0seG2RUXT/ILRuk4If0dzPTw8Hphk+86jxWfvwoGYoaf8i+CjPLZk68X6+gOdnfXwPTpIxF1aQsMBWL9+6E1dvAEgIiKisLCwMCijQ2iAMBJ3qLGDWGEhfLnTLgMyAXWNopywrV0EKXx4etwaMtLTwSaKSzN413Q14ero0Yt++cu8xsZjDkcXJSput40/8m4EImIQ03znQ3xsHABAEAQ3x7EhoN4mur5ZkALF3ePxNtoVlZfjIjs66iIjY/X6JADO9DnvznldOnxX1wlDETreQUsHRqfj/onNKQ827Yn5+kX4CfTQpjIAZ8/uaGoq9XhcgsD7JssOvC9OmaIYp92fJUuWLFmyxO12u93dVcmqmPCMtjPCS9xVxydLl3ZZmS74/h/c3BGS8UrBXakCVMfVYxDGA3x+6867qObZ2QhqCr9///nRoxclJo4ZN+4ZdDVYXxA8+Nc22NtTkWo1z/Apu9h7i/nsHo6TdlfnpX69OEaU49gm79OOzVbP8+6IiJiOjksArEbTnnsLxJYDDF0nuN1obEd8NG4fY/vpo59ET4j9AI+K41ijPLYJg2clJo6trz/Q3FwOQBDE9pB+rF/f3dAoRRAZGRkZGVleXl5eXi63LURo0P4E2VImT54stwk3gScv7/xnn8En1nqA87WUFcWdA3RApG8TJMoOgAMigm7ggn8ndx2g60rixSYHI9rabnb67EDuvRf33ouguZ4XL84/cqTM4xnDWsdIZzUSfXC+8mPUn0xGst082zY6O8BSj8fO9u/qrALHcWymU99hr2/jOM5mu3LlyheZmXPT02e7XO0cxyEq/vygGUnuDqP1vBi2j+hE1DG0DoJhEDKN7uxhzbrIpr2Nd89zN+lhcwNCZ138xB+mpk45d+69xsajgwfPYGcHoNPpOA4A9/77d9/SBRwo0tPT09PTCwsLeZ5PT+/3YVYDQHJyclhNii0ljEohobbhDOdmzz7z5Ze8b3Bpki//KbYM5336nuAreJe6+Uy+dYD4gcUZmtySlxGAtMGueNuQBm3u7ocfye7dmD8fAB577BNpSQxbiIjQA/B4HPjg9UQkxsQMbrjvm4BOOijJV8/OSQYxST6IIPC8i+Miunn24Dgu8osvfjhu3DNDh36D5112e6O47e4vXhze2kX6nXsB8dEA8Jkl9v1jOSfrh/4QxbNx8aM7fn/VaAJw6dK+9vbTsbHpI0c+6TuLburUcQp327uERWkiIyNvuCehTMIrLBMTE6OanGph4Zkvv4TExXZJfHbpkCVpQ5jg/GrA5BHBncU8/mlVpoSB4ZqXXrqFTxLIjh14/XWvsv/kJ0elIRTOB8+7eN6FfX/UQx+P+MY77hfjMF6zPU5fgEVglSoBZ+F5l7RDpOTzeVs5dnbWAXA4Wjo66gA4ne3iTp/f8UZxdGpwB03hD2g8CQ+Pe0y2f7+/eGzGxTcxOw9fbz+2nR02K+t+k+n7LlfHyZNbbLYGZrAalR2+QI2qA/Ha6QXbJ8JL3KGeBMunS739sESFtfv3gJTi9v2/y61O30E83ZTHBOifdEwTe+PnbwTOZdpnVqy4eOHC9ZvFgQP/FATB43EG3E143sNX7oO93Qhjx6jxkiSqmBf1U/MAEfd4xA/BWhEEmsHzbqezFRCs1nMcxzkcrcnJJjZ7Hzv78bl/PjjiieD0bsz7aKtASwfGpOPVxcULZhafRMpu+5DW1iviPklJc93uiNraPRcv/vO55+4LOoaaYJ77mjVr5DakL6ivgCKkhFfMHWqJwb34Yu2XX7JF6TzXERL9kwq9AEQGabR0K3tXDz6YznefDy6hYaIb+dFHid/9btDGm2P58gvPPjtsxQrvyzvueMPlak9IGMbM5LiIiLrTXHsL53Y2Ve+2XvxyKIbqoW+d/jUhMkpyGGlFCid1xtlIVJ4PvM1xHCSDVJlTz+v1SZcu7Rs1akF0dDLAu1zXoqOTJP6+0D5o2ulB05IbjyV5/Jz4iDPgqtExDIZETB1xbfLw6upLGZaT5y5cOG63d3z1VXld3VWb7ZsTJqSOHRudmzv7Fi+aErj33nsBrFmz5q677lLRxK319fVhNRY3gPCKuUMlYfe9HCcWVEtb+PK+jmCMALGO8n8p9WyZdku/6YBlHRAN8Ddq+XtXX38t588jN7dh06brRe47duDtt//S2Hhs+PBH2Y9Qp4uM2VfA2a0OOOpRPwRDhmN43bSp9szrI1nFhlw6XVTwWXz7dFn9z7F4vRipt1rPVVf/V0rKpDFjVuh0EQAiIxM4Dp2dV6SR/YjW4+bad6dd+Zf3KJIjtt+DlCmIjkSbDb/bm3Os9lEgCjgOzALMRiPX0vKNvlwsZbNmzZr169fLbQVxY1RzEw4VKgi7FxZKQ95SVz1gfI50k1PixAZsBeAI8usDRkWxI/Ss7H++ic/gx9KlZ6uqIFV2AP/zP3+Ni8uEr+IFgNDZxtmtACIRGYEIF1w66Ix1DUyLvfv44uzB7jlYZzFPd1+u4Buk6p2lOiFhBICUlMm+0I3gdlsjI+MTE0ezwasAAM5jnFAx5Refj/+OPaigyPAZrO/C4UZSHFY+UfaTRzclxAwGkpNircNTLYKjQZOTVzNlV36gRul/5v1P2Ik7FN+HoOaNN/huBi4hqBhGDKZzgNW3KUDfBf+ka5cEj2iVYgX+DLQDOHfuhvYHsGJF3bZtox5+2H+tExyn83gccXGZ166dYdUyEa3e6esiEBGP+AhEAEiovzzsi0NMxyWD+zmfvvt9CObUB02gIcZt/GZNslrP+71Z8LjdNqv1fGRkXGxshu+9Xs6OfHLnpJf/lTQu4NNFn4NtKxpPIDoK95gu/uCBF/7jwai9P1/z0sMvvfLE0xt/uurmLpZ6WL9+vcvlUvLQVoX/mQ8A4SjuCk+znP7yS8G/A7tU4juDPHTe/2Uwbt9uPfQqcPnqLLmg4wP4EGgHvg38c+TI3n+Qc+ewYsWlgoLAqS8Wcdxj9/yWnVmn00dG+gYEnfW2skpAghFGPfQA3DEx5+fczmIpQWrup+M+4eZ86wOvCnPPWVQdQELCcP+tbHypp6Wl2mAIbGnG8y5n+h01M1/dPOnlgCxr5FXoP8bnNQkflmJoCpbMeZMDslIQHYnlX3vVGFfQi0ulSqKiopYsWQKgrKxMblu6QOF/5gNAOIq78rvE6bpq6ChGadySl2KlI/t/cPWedOfunHcxrB8w3pW9awdgBZ4CogEA/+zdmNXFi09UVqKgILAKcBHHuUY+6TFOAADoBIFvbq5ip9K1NgDQQ5+EpGQkN6P5wpzZZ+6dy97o8Ti6Go0reuuugOyR/0hXv3ANz18vnWTtBwTBLc5nLQiexsZjgwfPiIz05mak7cBcGXf8dearn/gXSuo6cecZ64o7MX2U96INTcHtYxAdhcemvfPQfcW9uWLqJScnB8qT+PCcfUlKOIq7krvEHZ89G75vRVSjgMJEu2RlgNoFtBILiNEL3fQqEGvnEZSkPQBcBqYCg6WPCD2WvVsseP11bN8+7tFH/dYfnTPnTxwHwJ1xp/fjcJzBMAIQHI6WiNarbGUa0jhwTenJkVO/aTMmey0XPP5zG/l/BG8kPXi997YlKbW83rfA6WwF4HS2CQIvmdODobt69Uhi4hinsyX4vB7juNq7/+/ucc9Jx+nz8egMCmzdloYZtx3gm3d3c6k0BZP4bdu2yW2Il+XLl8ttgsyEo7hDkbMylZWV/frb3z715ZfwKWywG84Q+/R2Wf3i9N9T3MpUzenTaPg6FgSMYJIOejoJlACPAFP9Rf/j7sve165tPHcuUPzbX3ppG8edKC5mnVuchtskI1FjEhJGcFyE3lIMIBWpAK6lD+7IuTMifYLXeEHwiS8naep7/aN7PE7pSKj/196Zx1dVnvv+t/aYvTMwj6IiASERgSRgota56nFoKyAWCMFjj+29PafH2NbTWyFQLyToVat4eu29tudYBcJYpKcO9Vhbqx4xUbITFBJEkUFFZsi4p7XWe/548y7ePWXc836+n3xg7zW+a2flt579vM8go+uqpoVOhfLDaoyx7OwJsnYbWVSMaefOtYwbdx1/BgBGbeFuvBff+cFNm7fkTf6Kf7At8PhxpgMdHqjicx+Vi4LxuP3yJ35wz5MVFV9H+tDSiUWLFiEJrPgk/AOPPxkq7snG7t27Z86c+bObb+Zvjd+KJ0J4TGeID93YRRPZTKF5pwhcHqlZNt/gU+A14FpgSri51oMhffj27sWSJUctlqygOjTtP/7xK+Jh8BXgH3MVun0s3Ua0pnlOnKhT3B1OOC32oZ9dd/VXs6ZDOMERXMXXqPwVED8TWnHMWKvrAS4uLtDnmzu5T4T7DABAVT1u9/GhQ6cFyroxPQvGWNvs//3ajbWvAbs70FUL71twH0GHFz7xyeY5kD8av3nqwvXrxz32mL5q1blIp0snZs6c6ff7/f4eSkrHluR3vcaBDC0ckTwz6fxrLLd3Xlu8WJGsbAa4IzSz1iUDXC4iJtecQeAGkPbl+KVtgg5+GngNKBY2e2hw+4G6uksOH8bFF/O3r7yC5mYEz51u2bJp4UJ5WvM0wLJGKIrCGDTNazbbFcXkdI51u49bvd5c+0WHy2b7s7IAKAqXdRUwSaGQjCcrAaqimEUAzPlnnK77eVEaUdu9+0mg65qiMB7MDshKzTo7v8jJmaAo5tDqNLruP3fukxEjirKyRrndJ4PmGnTdeOQpX9648UvgyHs/uunrM2iAA7j1wwcPNNcd+aQuy4qRuXh57cJvPfndn//cBAy97762+fPz7rwz5DNNL6zW7kQEn89ns9l63jjqtLS0JLP3NT5kXBITJ0lSmbjBbrx9WVG4/KiBNrWRuKQiYPpU7hwhW/E6YAn8UhZUt4DnNAV5qY0NOoENwKXAbRFKCht8kzGAh8QET5xuDjfv+jfgyxkP+cdeDUDXVbPZpigWVe1UGl8flX3piUvzTSabENnuIeu6qiim0AecSEYNtg0VxaQoZh5bqWndw+f3uKIocnaSx3P6o4+enDDh1jFjrjR2PP9pCFe7oljGjLny4MHfO50XGAXOpB7cMB5eJu9pAJfs+sUo75kHH3xw1NNPAwAOv/HziU47ury45bHuwb/8Mnbs6Hj++ZzIHy0xKJLkDzyxZKi4J5wgWedsVJShAERgIscHDBX5pUY1R+6TyZY0T/aVq2KtQZC4G7WCEbiQUwtkA/MAs/SMCb1LPgf+cPmPR8z82fr1Y+Xl7T/+8asRnPJuYPMtO7oHrKsAzGa7pnlPHvnL0HFX2Gx5jOlms11cLjOcLSaTNfR7CGNqoBwbuq8oioXXGAgZgsKlX9c1r/fMxx8/NXr0lRdeeKuxlqs/Y8yoAg+h78ePv8cYUxSTCNEJGzXENM1rP/lhXvP/2xb6l+XdAvt3jXcLF+6fMWPismXxtmoTRUJM+Ewmc33uLpcrIeflc02hyo5Nmww1MsxLJTD2MSitVHaFy06VUCEO0iE1sDqYvA2fh7oZ0KRwHePsxhi25V7y+txdYwr+Z82db5/faMuWzYoSSdkBOIA76n/efUDFBEDTvBaLwz50os/Xxg8vyj1yv3b3M07XfYDOa6MbV6zrmtyZOqCVdvi4Sb5S1XWNMdXnawMgKtsYx1SDlB0AY+rx4ztHjiw2mayMaSL2Jgya5gPgHXXFyet+t2dPyGpJ2QFs3nzpsmW2e+899cgjEf3+6QRXdp/P5/P1nFE3WGg2lZO54h5/tzt3r4eRdQDA1sWLzTwLVJjthn4YqaeyTwaAP1yVR0PS3BEmY31ieei+fwAAXAk4AX/kMpO/HDK1/c6/2k7UdWyd+tOFC49s2YLDh11XXrl54cKwlyYzuvWTO+t/DpzvsKGqbqs1V57YNJwecoCjrqu6rhnOHu5qZ0wLjXAHwJjf4znd0fFF4COp+1+506nVmhe0q6a5Q709jGmdnV/xvCdx0uCHh6Z5pbPgRz964frrX7j++hd6/kBefHHkVVeNLi8/cuRIzxumCTabzWazbdq0KXYSnzwzaoklc8U9nqxYsQJi1rQHTCGWO0cJDHCUlcwnbYNA94seEkypBO4bFNr9Z+A4MAPIl2Q96O/vI+DXc9aMn+9yf7pBe+9HfOFfFi7cPHHi/rq+puqMbv1k4rGdOG9rM5ttiM/Xyr3i3YPX/VKWafdmjPHivfw6dEVRRD6q3+ihqigKoJ84UX/Lpxu+81ntJQe2Bn5C3E2vM6ZZLE4AnZ1fBpYo6M5XCq1d09X1tap2DRkyBd2j4ZlQcvHNAXLLLaitvSiMpZ++LFq0yGazrVixIhYST+lLnIz2ucdh1qWpqQnArFmzet1ym6Jwb8loqVkSRKqqCRgiXjPxw9U5GzCL5YbBaViVhuediU4dsvlvFnmnx4AdwFXAjJCy7xbAAnQC6y/4pm16paKYvK93pyfNAKb0dl2R8lnrp9639+Jv67rKVfLYsXeHD5/hcIwBdH5P6rpqMllCHluKyWSV3SZBzZsAuN0nF+z519sV00jAA7ic454u+L7IXdIMq/zs2ZaDB7dPmrRg+HCjKiwLMcmNOVgFYJrmGT78crf7uNt98vwWiqIolqC4HYOioqlPPx0cNtoD3/3uJ4sXT/3Od/q+R8rT1NRUUFBgt9ujcjSaSjUgyz2GNDU1zZo1qy/KjoMHjZenAbO0xigzoIYs5NZmp1iohXjGAXRKr0Pzf7iOHwd2ALcAM8S0rRK41+9tQx6/+tmssifUQzu6/roYwARgZoiyK+F+IlH6ye+mH/4j30RRTCaTLdDTzQDGm18HjpppmiesRcJVW9N8Nu/pWVkjLrAPc9qHjbQPm615hKAzw5sPKNnZFwCwWnMkz74a4mwx5J7XKVPOnNkzcuRsq/V8oAtjTFW7pPYgATxd1j9vy5YtU0tKcN99bZnjWpg1a5bdbvd6vV5vD8Xr+gqVlDHIaHGP3X2wceNG9M1g5zQtWgTRi0OT5FXWR3+gX0WRXnD3S6SvYFy6gorGGLu3Ai8B+cAkcZYg/mof/vV1v5sw/HJ11yP6J8+bfa03AKXA5D7reCSu+OR3lx95hb/Oy5vc2fmVprn5PSkJrp8xvzyVypgm1xuQ51FV1a3r/rFMHwVkAVbxkQ7xd3I/T+BTQQFgtebxRCfGtMBC8Oc/YMZ0VXUbSbBHj/4lLy9f/lUwpjPGSwoHGP5j2w5s7cM8RBATJuB3v8t77TVkSMYTx263c4lP9EDSh4wW91j45rh7ffHixf3a69P6ekj2eKu0ypAQT48FCUJrV8tPBRbiYYdQ5G3AZQBvKuELfEK8DfxbXv6pb71tbt2vvbnAdvg/pgC3AyMGquahlO5/YdLxOgA2W57f384Y4xpqhMCAt9zrDj1UGGOMMe46D3WD8PpfR3Mu/CBvkrHwa8cYBjCmad0mfPehbbY88a8C6KraJdUTVgJfQDwAVACa5vN4Tg0ffjn3GknZTMaWfsbUmV/+563Nzw74U/rpT7F48dCKiq+/+GKgh0hBuHOGOzMHRmFhYfSGk9pktM89uqxYsaKqqmpgrsPNImDbaBKRJbzhcvlfPzBE2isoCF0+sTyzyqPaZVePscs2oBO4Hrg0pBrBDrPjdMH3c4tXdmyZYvKeHQHcMIAL6xsbr362M2vEiRN1w4fPMJlskGJpeLS7oig81N2oJcAYv0TFSEllTBMPBgbAbLaN9nedsHZPOkhuE+5GV/z+to8/fmbq1PuysyfIThVFMcvh84H7QoxNcTrHOZ3jTp78MGzNMgDXfL511ldv8tcLBvFX9sYb2L0b8+YhP3/Ax0hJGhsbKct0MGS05R4tmpqampqaVq9ePeBJoTbxwiT+NSzxoG55hpUoqwVvjxepRSqfaA1VoL8BncDfAxMBt/QI2Qv8YczVrfM+zC1e2bWt8CLv2UujrexB/pwrP12f7T1jMtl57Dmg67pRx5F7aZiIjwzyxjAjVEb2p/PHgKHskklu7KLzc2VnTwgMegmYdEV3CYQAaeZVDTo6Duu6b+zYb4T1h+X4zhrKPkhuuQX/8i9YterUmjWxDQ9PNriy86/CxADIdHGvqqoa5BEaGxv7OmsamdA6X6qYKT3f1xkwSZ4ZY6EurQprH3JFDPJldgGHgOvFW57U2gV8CLx9Y23b9S9g/7qudSMvdZ8oA2YM4tKM0fbgnZ90oq78v/7xwrYDXV1HAfCaXEYFdm7F89SkcBHouq4HVIXkus8YE/lQck0xw82iGqGQhs9HnrYVz5LQfk/GWcwnT+6yWrOHDQvjB7jmfAgmAHT2WCS5L7z44shly2xLl56Qpt4zgtWrV6PPEt/Y2Bjj4aQSmS7uA8br9fJZ02h9c+wAFBHhzr0oASkxEu7I/m4tRD0Ng10OgzkJbAWuByYCEDb7QWDH2G98fPsboy66Q9syZfjux+8ekKz3K2ZGpuTg74eeblIUBWCKYmJMF+5sxbDTGdM1zSd8iecPrKruQM+JuHxdU1VPUHQj/8/nawMY9wKFg/HGe1K4jnwpfBJVO3ZsZ3b2BXb7MHky9prPt04+1SAf67XIWbv9Yt260du346mnonKwVGL16tWNjY29andzc3N8xpMSZLq4D2xOdePGjXa7vb+zpj1gBTyitwbXD57QFBQtwVcZmfWKHP4thc3IyIGERunbV4DLhLLz3T8B3rbkeItX2NoPtm+ePKE/fphBxswYjAKKv3xjTOtn/K3JZGFM1zS3UQGTT6XyqVHuiOdb6rqqKEqgXa+IOr089Sk0xhHo9tSrgSGY5y+Fy7fw0uiBG3SXl/F4Th058qdx46612YYYoTKTTzaEnmt3SJHkgfHQQ/jJT/Dkk7jnnowJlgQAFBUVFRUV9azvVOlXhsS9wO2OFIQShqqqKo/HE0VZ53BTvRWwSuIOYWsHbQmg3fAfBy5XhLPeUHMZHfAAzwOjgcvEwlbgCPBe2ZPOe5pN9T8b8+7/uMlzqqzHoUZLzYPIA7zAbQ2/GNP2mXE2USiGSd52M0SJAj63KZabGNM0zSvHCBhyr+t+KVRGCfr8dN0b2u4jqCmrHGkT9Kj4+uu3R4yYZTbbGdMWND2a6zsb+il92ucM3r7w0EPYurXgH/6hq/dN0wv+Rdnj8fDvzUGQ5S5D4l7w0kt96oLW2Njo8Xiqq6tjlP/GdTmonACAcyG/JEWSutDkd784iBIuKP5NIBu4DMgGFMAPvGVx7rynZUzhP1o2XlR6encZMDzwXDGS8lDsgB3IAua7Vuef/ADgZXh5ALuH1+TqHpWiZ7HPYAAAIABJREFUMKaLuHUWaFZDWOIKn2c19hIune6NOzvlGENF1Pg15D404p874v2MqUFr3e6TZ858fOGFf5fnbx/XHtEpHi3j3eDf/925YMHHzzwT3aOmAFlZWdzACqoRVlxcnKARJSOZLu4Oh6OPZYaKiopil9ZshCq2SjGLXEn9IflHnPbA0HVZdr0ifiaIL4BTwCzhkNkD/H7SPe3zXNi/fuzzzhuACXGUcoR7ckwAuNF+695nhb6buYOFe2PEruenWFW1yziA4ajhLhrZXS6XYucibrFkA/D7O6QRMWNtYEKTtAVjuu4LLRzm8Zzq6Phi9OjSHq43usY7Z9u2yysrce+9p6N+5JSAN0r1eDygYpAhZLq4A5g3b14Pa+M2/8771qhS2IxRPqxDkj+5aYU3shCHeppOAzuBkcAEwAs0mR3vX/OcpeQR5a2K25rWzASccVfzULzAl+L1rXufnedaJW+rKIqmuQGmKHJeqi5VeTx/1JDuqef3kYJh4HSODxkL8/s7g6r+nl/X3bePMebnUTqGytsP/WHU2b1/vP7FHj6BrkGHzYTlxRdHAPje98SDSlWxciVWrozFuZKQrKwsl8tF4h4EiXvEr3L8XolbGoXRbchwoxpu9GC/AwAh7pFi272BNQwA7AScwE0AgLesua67djq6vp7y6k3zTn7ojPKldI9zAC6dIYFvx7YdWPr+g4piNsJjRECkCpjkXk+GvkvZTzpjuqZ55JZJomwkNM2XlTWKMdba+okYr0H35y1OxIKeGdIlMsZ0PmELYMHu/zO94RH3yKKW/IglB6IVNhMW3trp4btexsJ/7l6UMfre0tLy2muvJXoUyQWJOxDSuKO2ttblcvFvfPGBR/wZDhle1V2R9P2sFCEjExTnweFVJOW20I1AF/BNwA38ftr9pxfsvfjt+69peGRK19dRGX+0XPOjAEgpXQByvGfnu1Ybki1CaPj8pyKUV+HRMprm43Y9AMa6awLruj8oxZQHsB879i7A7PYRYirVcOl0f6i8erBw1ADdzUPCFMlnTL/m860Asj2nZr/z/Y+LV+665O6IF7llywA/nb5xy4mXD7tOYutudHqBjND3qqqqeP61pgok7gEYsh7nmRk5xMUkSjkGZSR1Br5lgBnwB3pg+BG4phuNWLuAfUARsP/Cv3vp1j8OnV5Z/PodpacaRgx0tDGdZR0VKO4AxrR9du/7Py0SCZ88WkbTfCJHyRgUGNNU1SPXnDEC5MVUanfoCwCncxwAqzVH11UjWkauUiANQdd1H/8JO+Zc77mpp7vLoeSfqL9nW+Gxa59zO8aE/fqyvf+lxPrFDd8ce/HcfEwahezoFNFNcqqqqqqrqxM9imSExL2b06dPu93u+Ms6xwN0SU52E3AasEjSaQoXSMPxRzDqAXiBduAPwEXAuWn3nyx9fKr75MxXb7rwzMf9HWHcZlmHAG0hgpjrO3vN59uu+XwbpIYePMnI0GJpuRrYAbW747au++RYeKdzHKD4/R08rkaUJ4N0lQHXqmluTfPxgpRBFZlKvv5brq9VHvDo+of/c17D6RHh85Y/inbYTAB3341sO2aPP/82fSFl7wESdwDIy8tzOp0OhyNRA/hfGzeek0QlK8Tfwpe3ihdMWsgCS0JqQDvwEbAHOAS8B6iWbG1OzbE5a6589ebid/5hhLv3jp0xtc17Pt0oINL4ir56s+irP49rO2AyWbhJrigmTfMYiax8M154QFXlsu/npyp4WWDGdB4nI82yQtd9vHKkFAljHFPjvZ54lRseMMM3yPWdK/n67aChlu77jeXcJx8VhS9uEYuwmfPMmAGjMmJhIWYMvnhEkkLK3jNUFTI5+PzzR/PzeQlyK8CEE8YIOWfCLz8kcH5VFwGRPEhcE+I+GygCjgDbnBc0fue/hp3cVfLuD3K8ZyOdP9by3a8TvQVcBoyOvMG2WT8/mnMxn8yE6NlkMtkUReE+GW65M6YpikWUjexODBAudeZ2nzx4cPu0afdbrTk8Xl40QeUd+0y8DqXYS86NCqgQWb732fEdh8OO85VvvZ391Zs3uFaHrpp/8CAmTuzDh0GEhzou9QpZ7gEEzazGjcPPPGMD2gCbMGD5LyY0kaY98K0hMzwsUgPMwA1ACWACRmdfeOvIWfn711335oJQZY+DYT6wbwBDpIDIsCxoeuzag+cbrSiKWddVXpCd5zcZaxhTVbVL11XunJHd8T5fK2O6xeIAeBx9gLXOp22NkPbQLh+cS0/vjqTsAK5/466jF3/r/an3ha7afsklPV4i0Quk7L1C4h5AcXHx4OtEDoCLKyttgAk4DgBQRAshYxJVEbE0OiBn3chyyTc2A5fy9xfc7BxWOONkwy0NvzA2jrWgR+UUE4C83rYp+urN+z9cPq79EHisjGIGoKpuTfNIITT8U+SdPfyi+XX309NqzVUUHkvjkxzuxnUAorqv39/BmAroPJ1KDsGcc+zdHgaZ4z175c7KU2VPHRp3Xeha94MP9uHDIIJJyF9oKkJumTDU1tbGP7LqV4rSAfiAYUAWoAI8A8cO8KkAn+SNsQG8mKHcYUMHeMT6lYBsFr4PHAR08bUgusTiIXES2ANcFdh+JNJ594+Y9fbEue32YbzRNgBd95lMVkXh89PMMMm5UhtlIN3uYwcPbp8ypcJqzeF9nUwmi6KYjArD/HuRKCnc3RvEZLIoillRFMbYtDMff/uz3hNnDo+/oeH6F65+9ZtjWz8NWjWP/vr6SUL+NlMUstzDUF5eHn/rQAFyAYipVCNypkuq2G4oWocUISPLK+/P9z7wqgiRPAZ8CWiAT8TV8PLuemC3pr4PMg7mvxHtHjaUMOi8l55uWvjx0wCEnc4ARdN8qsq/4ShGWyWu/prGrfuAwgOMaYoCXfdrmocHSvIYeYi4SfGW8W1U1ZPjPfPtz2p7GKHxM/HoW0P2Ptt046b9I4IT4sh47xeNjY2k7H2HLPeIxN9G+L+KchawAH5gLOAWPnQVGBrYhskPWIBcdDdHZeKFDpiF/Q6p+Iyh6TnS6eRywRD7KoEP/LhNtAadqwHIA6b0Z/e3J85tGH+9rqsiiVTnE6omk1VUh+ezrN11Y06e3HX27J7Cwh8azVEhlXtUFJPJZJdqyvO15/9YCs7unft5QEeOnnmv7JcAZjU9mu05JS8n472PkM3eX8hyj0h5eXmcq1VMLS3NFkKsAVZRk0ANmUc1CS/N+RA/8dovhVGez8QXL0L7aEOE3/B8KK+w63WxnA3Ixu+Vnr8EXBjSOqpXrju04yc7K6V5YxNgYkzVNHdgi9RuX3xuLo+30UQgvDyTzSdU3araIc+mynGTVxzf2a/hzXCtMlsc9d/4/yfswwNWbN7czwvNREjZBwBZ7r3gdrvjGf/+57KyXfX1NqALGA24AbPwqAwXQg+hxQCGCf3VxHL+NhuwSgv5XkzktRrXw8S/fknBzSG9tg28wl/E/dZ9tOuVoPosfeAEsAe4sT+7GLTbhtQW/lObbQgAYZIzXdcUxWQydbu7GNPOnNlz4kT9pEn3mEwWHkkpVp1/lmmamzEAuqKYTCYbfzQwxu7d99sLOnuO6Al3UUOn7St7ynJg81WfrpOXk/HeM9Qpe2CQ5d4LDoeD1ySIz+lurqvjvxIvcFr8enjByDPSb8uoMtYuVaSBWKgI6VeE7sumsRZiv+uB/pnwtW7FE4LXrewUbVf1QA++nDUkm+T9de+MBrIiZzP1gALk+lp/2LTmxiOvzDn2rsnUnefL67/7/e28HJiimHNzJwFwu48riknXNVXt0jQfb+rED8Vd8zxZitcgE/56NgBlBzD63L6LP3ri2BU1h8ffNIDdM5Pa2lpS9oFhfuSRRxI9hmRnxowZ48aNc7lc48aNi8Ppxp89u6++3gp0Ag4xj8rV0xLoh+FuE2tgwXdd/KuKfCh5LRNrTYBZHCQ0mt4vPT8UaaEMnw+QSxAbR/MGfl1A4HH6yAmgDRgfeYNIE6383ws6jlzSun9i6/7DQ6d6zTZAUxQeEe9nTGNMdbuPt7cfHD/+OlFrjPGmeoypjGmKohiFa2RvDMBKj7+fH7kjRw8owND2Q45TDR9c+1u/xTnu+Ht8zOrrr4+5//4BHDDtIW/MYCDLva+0tLTExwU/6ZlnmPB+GCW0+NtWSSuN31xHYOFf2UJXIzf08AjRj2Sn+wLlMmz5SW/gkwPSs0QV0ZxuoAvwiokELWSXSAyR3O49B8z0wAUdR5Y0/3rOsf+6oKPb1lYUKwDGdKs1hzHd6z0nlp8PgmRMV9VOv79L1DBQ5H5+Nx/9S+iJ+hI2w7nk63fG7VpxeObPPh/SnZDwWX19364mYTz5ZAKq6VKtx0FCPvd+4Ha7X3rppfjccL9UFC/QBQwBsgAGdAkTfhgAyeJmgAmwS3JvaD0DgtL4dOnxwNOmtJANDEyAA2CBIfZBKIBVuIb4lvL9FJTWKQ/m9srKHLm4+aFD7rVrXxMt4xTAA+wcqNs9LF9lT3hp0oJ2Wx4PmGlvP3zs2DuTJt3DmGo2O/hEq5g+1XXdz1/w+Bmz2c5DKr+3f92ErqODH8yO299wO8cu/n134ZfbKiuzYlnqfTA8+eRrDz10e5xPSn72wUPi3m/i81Xx1bKy5vp63jLbATgAt9BxFRgeOAvKlxsRkHJakwY4JL+8odH8t+6X9jKWyzeEBbCGdOwLumMU8ZzwhqwK2tgkpmqnlJYW9Vo869Chc3V1e9auPRFVw7bdmlc/5sr60WXt7QeOHn07P/+7ABhTGQOvQmMy2aQa7kBAyz3Tqj1Rk+C6b/yaMXble//E385Nyr/Et98+ft11Y+J8UlL2qEDiPhDio++/VBQeAakBvPa6V4i7E8gSSUmGp9uIsFOFpKpiba5YJWu3KvzmskEdGvWoixldBG4mowCWyG2hZMyAFbhnYHfd5s0fr107uazss7q6Tweh+NxDsiYv/1PVfcHEuby8DGOaHPKoaV5FMZtM3ZfO9f2y1k+/+0XUHBTH8ia/det/TGn57WzxwEhOfY8z5GePFiTuAyQ+t+ATitIh5kVzAa/IafIBYwLdIFxYcwCL5NfmC7mCZ4tjGsa7T0h5duA8LaTXRrH4UAM/6K0XyOqbK3xpdG+5Q4c8a9cCMFw6Bj0PZg+wBfiBc/wb429otea2WXMBxvvq8fKQPKPVbLYzppvNtjx/x0OfPB/NkQMHRpfVXfPc9M+3zmysQZKJ+69+9f4//3Ms686Hg6r4RhES94HjcrkKCwtjWp3uQGVl7b/+qwVwA04pOoX3WR0jeUJ4dIoJGCpiE+XMVQDOwOAZw2XPM6HsUsEDubKt8QAINfBlDKd8r/p+Z2Xl8Ng7lz8uK/usvv62yso/hSi+wU7gT8BDonFrmzW3zZr7+vjrj2SNErV/IUJoGIBrzjbffuL96I5TARouuOmza35zx44rcrynAdyVHH+P77xz8tAh89Klw3vfNHqQzR5dSNwHRRyKSm8vK/ukvl4FOoBRQjp9ItIxJ9AShyhL4JeWG30/nSKzSQ5/ZNJak1jC8QZu4wgMrjI206SoR/6ciKTvl5aWlsW0T0WPeB588NO6OiM0hVvuYUqtAwC+cIx5b/iMI86xrZZsbsIvPvrXy/scAdmvuM/3p33/eOljV798w6gzHyWDuBcVPXzrrUsfe6wgniclP3vUIXEfLB6PBzGuLl2tKCagDdBFCwsm6oI5RLIopI7YFmkhJOPdBGSLt5q01rgDsgGT5NKRt4E4XZBsya4hIxPKJk3hyrdXlB0yg2ZuWdmOzZs9a9f2YOC3WbLz1M5WS/YQNaCLbXSr7rx31TNHJ961YOPFSLTxXlKycuvWVfn5cT0peWNiAcW5D5asrKysrKyYhsBXMQYgB1CAsyLjlKunW7LQ5VDIsI2cdaBdeOTDBowbvbZZhPh3tzi7gSrJtyL2DRs2c2dlZc+XGX8uv+UWTJyYtXbtXMbO/xw8eFtl5ZTS0imlpQowRO1UgKFq5wCi7PvO1TsrL933b69f/2K0D9wP1q5958YbaxsaSNnTBBL36DB//vyYVgl+uLbWJJUTgKjgqACtwsci/y49UuxKkBK5A9/KUqUDbp4zGbKNgRdQxRI1cg6UW6zix4+Pqz06TJyYtXbt9Lq66XV1dzHGf26rrLxr06bJpaWxO+1M1+rOCbf+x5VP7ykri91ZQnn88T8WFHy/uHj5n/505q9/jbfLm5Q9dpBbJprEdEaIbdxYXV7Oi7oMARyA0XNIFZlNRuQ7n1DNE4qvSaY0t7Xl2r9Bwe+st9hH7lgPW7dA3t4k4t8BVCTlbbZ58+aFCxcO5gjeBx/swaXTX04Ou6zu2t/Meeve50fMmlxWdsUVxWVlV5WV9dCzZOA8/vgfn3tuPYC8vMk/+cnPKiqGxeIsPUN+9phC4h5lYq3vy8vLLUA7cIHI/udlwlRgpHhtOM0tYprUCJIxCgDYpdKPstud+9AtIV2QQjNU++idyEo+VztHVdVVq1atWrUq6kcejOKfGFr4t9teGbbzx2/ahwKwWnNttqFGH/APPnjit7/94Ec/uqK/h21tRXHxgpKSmQ0NuwFYLNkWS3ZW1sjhwy//85/vHthQBwkpe6whcY8+Mf2mubGsrKW+XhdZS36hsG7ACgwHfFKlXw0wiVA/vtCoWKABOeEyV43EKFNgbHtQcpNPPCEsCCD0ZppWWnpt4iJkemblypWxEPdgDh1CXd3etWv7WEOmecqSlrKnrts0aWrW8P3mrFdGX3HAMYYxzWSy8xJmuq56vWcslmyf7xzPpDWajZSUzOQvuIjLKIoVYHb7MIdjjMXifO65f5k5M2qX2F9I2eMAiXtMiKn9XqUoJqHmecI/zl00TsAu+cFVsTBLqtsFyZB3CA+MUUvSUH/unDFigOS7RJViH60hkTkyU0tLr0tWZUfcxD0ce8vKLtu0ae+iRaGKvx9QL7z9ZrDppxoVxXwK+N7wyz6z9dozPBheIs1mG2KxODXNraqeceO+8atffe/yy6NzCQOG4tnjA4l7rIhpCPxKRdGATsACDAUAaMLhLmuAkarKM1flql7GA4Bvzzfzh/jf5U7cBp7AbSLpe5IrO6Lhc48yBw+ivn7z4iXXKKZRw2ea7cNM/rZOKPdcdMcpRVEUi6KYVbXL7T6mqm7GVP7Ha7E4zWabopjNZrum+XXdazZnAXA4xvr9bTbbUJPJ+pvfVE6fnuirA0DKHkdI3GNL7L5+rlQUt7CgRwRmkxr2OJPiXoK6ScnlIXOlAjUQO8oBjtliIQIrRBrbyPpuLPxB0t9aCbTce+HBB3Haj73HcFEuzrJbzg6f/I1v7tq122rN6ej4wmrNsVpzGdMZ061Wp6p6zGZ7V9dRu324xeJ0OEbPmjX53Xf/XFf3s0RfRjCk7PHE0vsmxOCIkb6vYmylonQAADqEA50HKXYKU12RkpI6A13kcrHfrkBnDkTMJYcBnZK+h639y780yHOwP/j88yhcZMaSl4c84BJeLw5vAFh1B3BHfw6RdB5tUvY4Q3HusaWoqKi5uTl2KU5m0SzbJ/VpMkkdPII0OmzhRu7hCcp7Cmg+JKLje9hGFe4aBfh2ZSUuuWQg1xNHNm/eXFhYmOhRRGD+/J7epiDUeSP+kFsmTsTIbNlYVuaqr+fJR6MACH8Lt695nDt3tqhSkIxV2hJS9Ud7oPUdZKTrgb51BD45OFZgetK72jl+v3/16tVJ6pbh7N6NBEa0RA+y2RMCiXv8iJF/pmvjxl+Ul/POpSOFu5wJV8lo4YvnXheezTRUuGvkhqt8rV2KkJHFXRVVJ3uu/QugMnXuqKSbUE1H4lBcjwgLuWXiR1FRUW1tLS80FkWcixf/orbWCtiBU8Jzoggr+xRgEYmsRkWaNqHUHMPbznul+qW3HCZKynAHTg+kkLIDaG5uTvQQ0pzGxkZS9kRB4h5XysvLW1paon7YnMWLnzhwgPcy7ZSkHIAOnJO2NBa2idnXoMAYAB6h78ZBZLnXgc7A54HBd5KvNFjPzE99X3YyU1tbS5lKCYTEPd4UFRXFpMTYpEm/qK3NEsLN7XfuW1eBs5JAGwEzbaIUe1CxQz59aky9htZ95LlOQSXDppWWTkyV0mCCWDxoCQ7NoCYcEvcEUF1dXVVV1djYGN3D5ixePL20lDthzgFuqbqAAngle9ygNTAARl7VBXgkv7y8DS9V5pX0/TuVlbemwiSqzO7dwQn6RLRobGykWo8Jh8Q9MfBbP+om/N/X1f2KMQBWoFWUKOD4gbPitexMd4umfaH4AHe4KVOOLtYqQMrZ7ABaWlpoNjUWVFVVkTcmGaBomUTS2NjY3Nwc/W+vBw780+TJALpEfKQq/tWAIYBdWPFGlKRTBMmwwARUn+jfhHCBjxwn8GBq3kW7d++emRaxhskDVQRLHshyTyRFRUWFhYXRd8Hn5z/L2PTSUidwUioFYxLNPXQpcxWAAnQBHeK1Yddzj40auCqozO/cBx5IUWUHRctEG5pBTSpI3BNMUVFRjLo4/bCubnppqQloF931TOL3fSqwjSp3zfuArsDavxweAdkaofBAQfRaVcQZv99PE6pRpLGxkWZQkwoS98RTVFRUXV0dixIFP6yre6K2lnfw4PHpRqjM2UCx5veBBzgnlQXmGKZ6h9jFWLIsZW12kNkePTweD9nsSQj53JOIWGVpHzjwvcmTebGBEVKxAT/gAOxC2Y3YR4to0Gogx8I7ASugA3MfeCB1zXYiipCfPTkhyz2JKC8vj0kIfH7+84wBUICjQJtovGcCvECbsMeNW8EHtEqeeoSESPLt00DZV65cmeghpDxksyctJO7JBQ+Bj8WRX2AMQBbQBbRKyzXgFHAG+BI4ApwTaU1dgamtMheWlqa0Q8agoKAg0UNIYWpra8nPnsyQuCcd3P8eCxf8C4y9wJgN8AKngHNAF+AH3ELTIZXtNYnSBUy85RSWllakWr5SWDZt2pToIaQwHo+npaWFbPZkhnzuSQqvLxajoktfbNz40/LySL/4XBHYrglX+zBRVQbAo2l0w1CcO5HGkOWepGRlZbW0tMTIRXPh4sVbP/ss0tp2ETBjEt72s4AXUIBHDxyIxXgSgs/n630jIoQYfa0kog6Je/LCQ+Bj9YeUn7+NsccjHLxV1Pg1frqA2x54AJMmxWQwiWD79u2JHkLq0djYWFhYSH72lIDEPakpKioqLy+PnaF0yeLF2xhb8sADQct5wIxfuj8uKy29JvXDY4hBsn37dvKzpwrkc08N4hBKvEAJqCzADfYcwAHowK/T7j7ZtGnTokWLEj2KlCGmk0BELCDLPTXgXZxieoptjG2TFJwnLnUA59JR2QEsWrSIAmb6BSl7akHinjLEKsUpEC7x3BfPFX1DOio7gN27d5Pl3hc8Hk9VVRUpe8pBbpkUI97xxQcOID8/TueKL5s2bSooKJg1a1aiB5LsxKoqBhFjSNxTD/J+RgWfz2ez2RI9iqTG4/HQbZa6kFsm9cjKympubqZY48HT1NSU6CEkLx6Ph6JFUxqy3FMYl8tVXFyc6FGkKitWrFixYgUZ72FpbGxkjNHdldKQ5Z7axGGKNV2ZP38+WaZhcblczc3NpOypDol7ClNcXBy7KpJpT0tLC1WFDMXlcgGgGdQ0gMQ95SF9Hxik7KFwZSebPT0gcU8HSN+JaEHKnjaQuKcJ1dXV3Owi+khhYSH53A1cLldVVRUpezpB0TJphdvtdjgciR5FarBixYqCgoLFixcneiBJAYW0px9kuacVDofD5XLxLCeC6Asul8vtdpOypx8k7ulGcXFxVlYWueB7hcx2AC6Xq6Wlhb7tpSUk7unJvHnzKIW1VzZu3JjoISQSt9vd0tJCUY/pCvnc05mqqqrq6upEjyJJaWpqKigosNvtiR5IwqAZmvSGLPd0prq6muz3SDQ3N2essvPAKlL29IbEPc2JTxX4VKSwsDDRQ0gM3M+e6FEQMYfEPf2hFCfCgN8J5GfPBMjnninU1tYWFBRQlopBHNrSJiFUSTRzIMs9UygvL6cv4zItLS1erzfRo4gfLpeLlD2jIHHPIMrLy2tra6lKgUHmTKhSRbAMhMQ9sygvLy8oKCB95zQ2NiZ6CPGAR0yRsmcaJO4ZBw+AoylWAJngp3K5XOXl5aTsGQiJeybCu3xkuP3e0tIyf/78RI8itlCWQyZD4p65FBcXZ/IfP2MsvX3u/MsZ2ewZC4l7RsNTnNxud6IHkgDSO4nJ5XLNmzeP4tkzGRL3TKe6ujoTXM8ZBc9BJZs9wyFxJ1BcXJzh/vd0wu12FxcXk81OkLgTgPC/Z5R/prm5OdFDiD70kCYMSNyJbsrLyx0ORyZPsaY6vAkq1XokOCTuRDAZEgJfUFCQ6CFEk6qqqnnz5iV6FEQSQYXDiGDcbvdLL72U9k7bdCocVltbm/a/L6K/kOVOBONwODKhCvz27dsTPYTokPa/KWJgkOVORCS9u/Slh7VLhR6JSJDlTkSEd/nIqBCa1IJHPSZ6FESSQuJO9ER1dXVNTU2iRxETUr2wDHljiJ4hcSd6IV1LjKW0x6m2tra6upqiHokeIHEneoenOKVZCHzqBg663W6aKiN6hcSd6BPl5eW8kVOiBxI1UrSiTkNDA2NsyZIliR4IkeyQuBP9YNq0aWnjoklFcd+wYUNJSYnT6Uz0QIgUgMSd6AclJSWMsQ0bNiR6IJnI8uXL0yyrlogpJO5E/ygpKVmyZMny5csTPZDMoqGhYd68eSUlJYkeCJEykLgTA6Gmpob0PW40NDSUlJSQshP9gsSdGCCpru+p4uJYvnw5yToxAEjciYHD9b2hoSHRAxkIKTGhunz58nRNIiNijSXRAyBSm5qamq6urq6uLgrhiDoNDQ2k7MSAIcudGCxOp7OlpaWrqyvRA0kryBtDDBISdyIKlJSUvPTSSxQiGS2WL18NZeF3AAAEHElEQVSe0vMZRDJA4k5EB54zSfo+eDZs2FBTU0NuLmKQkLgTUWPJkiVLlixJFX1PzvIsGzZsSN2iN0RSQeJORBlKcRowy5cvX7JkCdnsRFQgcSeiT6qHwCeEDRs20IdGRBESdyImkL73iw0bNpDNTkQXEnciVtTU1KSK/z2xcGVP9CiIdIPEnYgh3P9OEt8D3M+e6FEQaQiJOxFbampqaIo1EjzqMdGjINITEnciHpD9HgrZ7ERMIXEn4oHT6ST7XYZsdiLWkLgT8YNCaDg0g0rEARJ3Iq6QvpOyE/GBxJ2IN5ms76TsRNwgcScSQE1Nza5du3bt2pXogcQVUnYinpC4E4lh9uzZs2fPzhx9p9gYIs6QuBOJZN++fZmg79Qtj4g/JO5EIlmyZElBQUF66/uuXbtI2Yn4Q+JOJJjs7OyWlpb169cneiAxYf369bNnz070KIhMhMSdSDwVFRXz5s1LP31fvnx5RUVFokdBZCgk7kRSkJ2dXVFRkU4hkuRnJxILiTuRRKRNCDwpO5FwSNyJ5CIN9J2UnUgGSNyJpKOmpmb9+vUpGkJDyk4kCZZED4AgwlBRUdHR0ZHoUfSbZcuWrVmzJtGjIAiALHciacnJyUkt+339+vXLli1L9CgIohsSdyJ54XGEMQqRZIxF8WjLli2rqKjIycmJ4jEJYjCQuBNJzezZs+fOnZvkFvH69evJG0MkGyTuRLKTk5OzbNmypNX3ZcuWzZ07N9GjIIhgSNyJFCAnJ2fNmjVJqO/cZidvDJGEkLgTKQPX9+SpUsD97IkeBUGEh8SdSCXWrFnT0tKSDFGS5GcnkhwSdyLFWLNmzY4dOz788MMEjoFsdiL5IXEnUo+Kiop9+/Ylyn6nTCUiJSBxJ1ISbjjHf4qVlJ1IFUjciVSFh9AMeH61oKCgv7uQshMpBIk7kfIMzH5vaWnp71lI2YkUgsSdSG0qKioefvjhmPpn2tvbSdmJlIPEnUh5cnNzY5ri9Oijj5KyEykHiTuRJsRI38lmJ1IUJbq18QgisfBKL3PmzOl1yw8//LDXzUjZidSFLHcireAprO3t7YM/FCk7kdKQuBPpxtKlS/ft29ervvccLUPKTqQ6JO5EGjJnzpzBlCggZSfSABJ3Ij1ZunTpnDlzBqDvpOxEekDiTqQzc+bMWbduXdhV+/btC1pC8exEOkHiTqQ5S5cuDRsiOW3aNPlte3s7xbMT6QSJO5H+hA2BD7LcSdmJNIPEncgI1qxZs27durAhNO3t7evWrSNlJ9IMEnciU1i6dKms4Dx974MPPtixY8fSpUsTNy6CiAkk7kQG8eijj65bt86YYv3ggw/27dtHyk6kJVR+gMhEysvLOzo6CgsLH3300USPhSBiAlnuRCZy9913OxwOUnYijflvDGfFjj3G6nIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "Graphics3d Object"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#all the plots in one figure\n",
    "allgr = crvpm+crvA+crvB+crvC+scrws+gr\n",
    "allgr.show(viewer='tachyon', camera_center=(4,-4,3),viewdir=(-4,4,-3), raydepth=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sage.interfaces.maxima_lib import *\n",
    "from sage.symbolic.expression_conversions import *\n",
    "m = InterfaceInit(maxima) #create the interface with maxima\n",
    "maxima_lib.set('thmax','%pi/6')\n",
    "maxima_lib.set('thmin','-%pi/6')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#parametric surface for the middle point\n",
    "maxima_lib.set('fxpm',m(f_xpm))\n",
    "maxima_lib.set('fypm',m(f_ypm))\n",
    "maxima_lib.set('fzpm',m(f_zpm))\n",
    "maxima.plot3d (\"[fxpm, fypm, fzpm]\", \"[theta_1,thmin,thmax]\", \"[theta_2,thmin,thmax]\", \"[grid,50,1]\", '[plot_format, openmath]')   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "#parametric surface for the A point\n",
    "maxima_lib.set('fxA',m(f_xA))\n",
    "maxima_lib.set('fyA',m(f_yA))\n",
    "maxima_lib.set('fzA',m(f_zA))\n",
    "maxima.plot3d (\"[fxA, fyA, fzA]\", \"[theta_1,thmin,thmax]\", \"[theta_2,thmin,thmax]\", \"[grid,50,1]\", '[plot_format, openmath]')"
   ]
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  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "#parametric surface for the B point\n",
    "maxima_lib.set('fxB',m(f_xB))\n",
    "maxima_lib.set('fyB',m(f_yB))\n",
    "maxima_lib.set('fzB',m(f_zB))\n",
    "maxima.plot3d (\"[fxB, fyB, fzB]\", \"[theta_1,thmin,thmax]\", \"[theta_2,thmin,thmax]\", \"[grid,50,1]\", '[plot_format, openmath]')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#parametric surface for the C point\n",
    "maxima_lib.set('fxC',m(f_xC))\n",
    "maxima_lib.set('fyC',m(f_yC))\n",
    "maxima_lib.set('fzC',m(f_zC))\n",
    "maxima.plot3d (\"[fxC, fyC, fzC]\", \"[theta_1,thmin,thmax]\", \"[theta_2,thmin,thmax]\", \"[grid,50,1]\", '[plot_format, openmath]')"
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  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
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    "allgr.save_image('good.png',figsize=[50,50],viewer='tachyon',aspect_ratio=1, camera_center=(4,-4,3),viewdir=(-4,4,-3), raydepth=10)"
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  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "allgr.save('bad.png',figsize=[25,25],viewer='jmol', aspect_ratio= [1,1,1], frame_aspect_ratio= 'automatic', zoom=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
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       "  'draw point_33 DIAMETER 5 {1.873112204565473 0.8733645877566716 -2.4070987654051255}',\n",
       "  'color $point_33 translucent 0.5 [255,0,0]',\n",
       "  'draw point_34 DIAMETER 5 {-1.2730731909174051 -0.5723267817937058 -0.7984159197029959}',\n",
       "  'color $point_34 translucent 0.5 [255,0,0]',\n",
       "  'select atomno = 1',\n",
       "  'color atom  [0,0,0]',\n",
       "  'label &quot;A0&quot;',\n",
       "  'select atomno = 2',\n",
       "  'color atom  [0,0,0]',\n",
       "  'label &quot;B0&quot;',\n",
       "  'select atomno = 3',\n",
       "  'color atom  [0,0,0]',\n",
       "  'label &quot;C0&quot;',\n",
       "  'select atomno = 4',\n",
       "  'color atom  [0,0,0]',\n",
       "  'label &quot;M1&quot;',\n",
       "  'select atomno = 5',\n",
       "  'color atom  [0,0,0]',\n",
       "  'label &quot;M2&quot;',\n",
       "  'select atomno = 6',\n",
       "  'color atom  [0,0,0]',\n",
       "  'label &quot;N1&quot;',\n",
       "  'select atomno = 7',\n",
       "  'color atom  [0,0,0]',\n",
       "  'label &quot;N2&quot;',\n",
       "  'select atomno = 8',\n",
       "  'color atom  [0,0,0]',\n",
       "  'label &quot;O&quot;',\n",
       "  'select atomno = 9',\n",
       "  'color atom  [0,0,0]',\n",
       "  'label &quot;r1&quot;',\n",
       "  'select atomno = 10',\n",
       "  'color atom  [0,0,0]',\n",
       "  'label &quot;r2&quot;',\n",
       "  'select atomno = 11',\n",
       "  'color atom  [0,0,0]',\n",
       "  'label &quot;PM0&quot;',\n",
       "  'draw line_35 diameter 1 curve {-3.0 -3.0 -3.0}  {-3.0 3.0 -3.0} ',\n",
       "  'color $line_35 translucent 0.5 [0,0,0]',\n",
       "  'draw line_36 diameter 1 curve {-3.0 3.0 -3.0}  {3.0 3.0 -3.0} ',\n",
       "  'color $line_36 translucent 0.5 [0,0,0]',\n",
       "  'draw line_37 diameter 1 curve {3.0 3.0 -3.0}  {3.0 -3.0 -3.0} ',\n",
       "  'color $line_37 translucent 0.5 [0,0,0]',\n",
       "  'draw line_38 diameter 1 curve {3.0 -3.0 -3.0}  {-3.0 -3.0 -3.0} ',\n",
       "  'color $line_38 translucent 0.5 [0,0,0]',\n",
       "  'draw line_39 diameter 1 curve {-3.0 -3.0 -3.0}  {-3.0 -3.0 3.0} ',\n",
       "  'color $line_39 translucent 0.5 [0,0,0]',\n",
       "  'draw line_40 diameter 1 curve {-3.0 -3.0 3.0}  {-3.0 3.0 3.0} ',\n",
       "  'color $line_40 translucent 0.5 [0,0,0]',\n",
       "  'draw line_41 diameter 1 curve {-3.0 3.0 3.0}  {3.0 3.0 3.0} ',\n",
       "  'color $line_41 translucent 0.5 [0,0,0]',\n",
       "  'draw line_42 diameter 1 curve {3.0 3.0 3.0}  {3.0 -3.0 3.0} ',\n",
       "  'color $line_42 translucent 0.5 [0,0,0]',\n",
       "  'draw line_43 diameter 1 curve {3.0 -3.0 3.0}  {-3.0 -3.0 3.0} ',\n",
       "  'color $line_43 translucent 0.5 [0,0,0]',\n",
       "  'draw line_44 diameter 1 curve {-3.0 -3.0 3.0} ',\n",
       "  'color $line_44 translucent 0.5 [0,0,0]',\n",
       "  'draw line_45 diameter 1 curve {-3.0 3.0 -3.0}  {-3.0 3.0 3.0} ',\n",
       "  'color $line_45 translucent 0.5 [0,0,0]',\n",
       "  'draw line_46 diameter 1 curve {3.0 -3.0 -3.0}  {3.0 -3.0 3.0} ',\n",
       "  'color $line_46 translucent 0.5 [0,0,0]',\n",
       "  'draw line_47 diameter 1 curve {3.0 3.0 -3.0}  {3.0 3.0 3.0} ',\n",
       "  'color $line_47 translucent 0.5 [0,0,0]',\n",
       "  'select atomno = 12',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;-83.0&quot;',\n",
       "  'select atomno = 13',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;2.6&quot;',\n",
       "  'select atomno = 14',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;88.3&quot;',\n",
       "  'select atomno = 15',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;-76.7&quot;',\n",
       "  'select atomno = 16',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;2.4&quot;',\n",
       "  'select atomno = 17',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;81.5&quot;',\n",
       "  'select atomno = 18',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;-521.6&quot;',\n",
       "  'select atomno = 19',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;-363.4&quot;',\n",
       "  'select atomno = 20',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;-205.2&quot;',\n",
       "  'isosurface fullylit; pmesh o* fullylit; set antialiasdisplay on;',\n",
       "].join('\\n');;\n",
       "    var Info = {\n",
       "      width: '100%',\n",
       "      height: '500',\n",
       "      debug: false,\n",
       "      disableInitialConsole: true,   // very slow when used with inline mesh\n",
       "      color: '#3131ff',\n",
       "      addSelectionOptions: false,\n",
       "      use: 'HTML5',\n",
       "      j2sPath: '/nbextensions/jupyter_jsmol/jsmol/j2s',\n",
       "      script: script,\n",
       "    };\n",
       "    var jmolApplet0 = Jmol.getApplet('jmolApplet0', Info);\n",
       "  </script>\n",
       "</body>\n",
       "</html>\n",
       "\"\n",
       "        width=\"100%\"\n",
       "        height=\"500\"\n",
       "        style=\"border: 0;\">\n",
       "</iframe>\n"
      ],
      "text/plain": [
       "Graphics3d Object"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "allgr.show(viewer='jmol')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "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/build/three.min.js&quot;></script>\n",
       "<script>\n",
       "  if ( !window.THREE ) document.write(' \\\n",
       "<script src=&quot;https://cdn.jsdelivr.net/gh/sagemath/threejs-sage@r122/build/three.min.js&quot;><\\/script> \\\n",
       "            ');\n",
       "</script>\n",
       "        \n",
       "<script>\n",
       "\n",
       "    var options = {&quot;animate&quot;: false, &quot;animationControls&quot;: true, &quot;aspectRatio&quot;: [1.0, 1.0, 1.0], &quot;autoPlay&quot;: true, &quot;axes&quot;: false, &quot;axesLabels&quot;: [&quot;x&quot;, &quot;y&quot;, &quot;z&quot;], &quot;axesLabelsStyle&quot;: null, &quot;decimals&quot;: 2, &quot;delay&quot;: 20, &quot;frame&quot;: true, &quot;loop&quot;: true, &quot;projection&quot;: &quot;perspective&quot;, &quot;theme&quot;: &quot;light&quot;, &quot;viewpoint&quot;: false};\n",
       "    var animate = options.animate;\n",
       "\n",
       "    if ( options.theme === 'dark' )\n",
       "        document.body.className = 'dark-theme';\n",
       "\n",
       "    var scene = new THREE.Scene();\n",
       "\n",
       "    var renderer = new THREE.WebGLRenderer( { antialias: true, preserveDrawingBuffer: true } );\n",
       "    renderer.setPixelRatio( window.devicePixelRatio );\n",
       "    renderer.setSize( window.innerWidth, window.innerHeight );\n",
       "    renderer.setClearColor( options.theme === 'dark' ? 0 : 0xffffff, 1 );\n",
       "    document.body.appendChild( renderer.domElement );\n",
       "\n",
       "    var b = [{&quot;x&quot;:-83.00635967155165, &quot;y&quot;:-76.72361426248445, &quot;z&quot;:-521.5809185214538}, {&quot;x&quot;:88.26738423823053, &quot;y&quot;:81.49276532675242, &quot;z&quot;:-205.25}]; // 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 rRange = 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",
       "    var autoAspect = 2.5;\n",
       "    if ( zRange > autoAspect * rRange && a[2] === 1 ) a[2] = autoAspect * rRange / 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;: 14.0, &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;A0&quot;, &quot;x&quot;: 70.0, &quot;y&quot;: 10.0, &quot;z&quot;: -488.75}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 14.0, &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;B0&quot;, &quot;x&quot;: -20.0, &quot;y&quot;: 61.96152422706632, &quot;z&quot;: -488.75}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 14.0, &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;C0&quot;, &quot;x&quot;: -40.0, &quot;y&quot;: -61.96152422706632, &quot;z&quot;: -508.75}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 14.0, &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;M1&quot;, &quot;x&quot;: 13.793869954397882, &quot;y&quot;: 46.096261438066286, &quot;z&quot;: -426.89980358791473}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 14.0, &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;M2&quot;, &quot;x&quot;: -13.231815146338935, &quot;y&quot;: -40.748667150945344, &quot;z&quot;: -435.0483154621467}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 14.0, &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;N1&quot;, &quot;x&quot;: 66.09966895651183, &quot;y&quot;: 35.41467272151847, &quot;z&quot;: -480.3220864994704}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 14.0, &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;N2&quot;, &quot;x&quot;: -23.710156329926704, &quot;y&quot;: -2.707336360759234, &quot;z&quot;: -395.5093994676936}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 14.0, &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;O&quot;, &quot;x&quot;: 10.0, &quot;y&quot;: 10.0, &quot;z&quot;: -205.25}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 14.0, &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;r1&quot;, &quot;x&quot;: 10.0, &quot;y&quot;: 10.0, &quot;z&quot;: -420.5}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 14.0, &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;r2&quot;, &quot;x&quot;: -13.77354790111386, &quot;y&quot;: -10.0, &quot;z&quot;: -443.78029514495256}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 14.0, &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;PM0&quot;, &quot;x&quot;: 10.0, &quot;y&quot;: 10.0, &quot;z&quot;: -488.75}];\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 = [{&quot;point&quot;: [0.0, 0.0, -215.25], &quot;size&quot;: 5.0, &quot;color&quot;: &quot;#ff0000&quot;, &quot;opacity&quot;: 0.5}, {&quot;point&quot;: [60.0, 0.0, -498.75], &quot;size&quot;: 5.0, &quot;color&quot;: &quot;#ff0000&quot;, &quot;opacity&quot;: 0.5}, {&quot;point&quot;: [-30.0, 51.96152422706632, -498.75], &quot;size&quot;: 5.0, &quot;color&quot;: &quot;#ff0000&quot;, &quot;opacity&quot;: 0.5}, {&quot;point&quot;: [-30.0, -51.96152422706632, -498.75], &quot;size&quot;: 5.0, &quot;color&quot;: &quot;#ff0000&quot;, &quot;opacity&quot;: 0.5}, {&quot;point&quot;: [0.0, 0.0, -498.75], &quot;size&quot;: 5.0, &quot;color&quot;: &quot;#ff0000&quot;, &quot;opacity&quot;: 0.5}, {&quot;point&quot;: [3.793869954397882, 36.096261438066286, -436.89980358791473], &quot;size&quot;: 5.0, &quot;color&quot;: &quot;#ff0000&quot;, &quot;opacity&quot;: 0.5}, {&quot;point&quot;: [-3.2318151463389353, -30.748667150945344, -425.0483154621467], &quot;size&quot;: 5.0, &quot;color&quot;: &quot;#ff0000&quot;, &quot;opacity&quot;: 0.5}, {&quot;point&quot;: [0.0, 0.0, -430.5], &quot;size&quot;: 5.0, &quot;color&quot;: &quot;#ff0000&quot;, &quot;opacity&quot;: 0.5}, {&quot;point&quot;: [-3.77354790111386, 0.0, -433.78029514495256], &quot;size&quot;: 5.0, &quot;color&quot;: &quot;#ff0000&quot;, &quot;opacity&quot;: 0.5}, {&quot;point&quot;: [56.09966895651183, 25.414672721518468, -490.3220864994704], &quot;size&quot;: 5.0, &quot;color&quot;: &quot;#ff0000&quot;, &quot;opacity&quot;: 0.5}, {&quot;point&quot;: [-33.710156329926704, -12.707336360759234, -405.5093994676936], &quot;size&quot;: 5.0, &quot;color&quot;: &quot;#ff0000&quot;, &quot;opacity&quot;: 0.5}];\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, -215.25], [0.0, 0.0, -430.5]], &quot;color&quot;: &quot;#6666ff&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 1.0}, {&quot;points&quot;: [[3.793869954397882, 36.096261438066286, -436.89980358791473], [-3.2318151463389353, -30.748667150945344, -425.0483154621467]], &quot;color&quot;: &quot;#6666ff&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 1.0}, {&quot;points&quot;: [[56.09966895651183, 25.414672721518468, -490.3220864994704], [-33.710156329926704, -12.707336360759234, -405.5093994676936]], &quot;color&quot;: &quot;#6666ff&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 1.0}, {&quot;points&quot;: [[-3.77354790111386, 0.0, -433.78029514495256], [60.0, 0.0, -498.75]], &quot;color&quot;: &quot;#6666ff&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 1.0}, {&quot;points&quot;: [[-3.77354790111386, 0.0, -433.78029514495256], [-30.0, 51.96152422706631, -498.75]], &quot;color&quot;: &quot;#6666ff&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 1.0}, {&quot;points&quot;: [[-3.77354790111386, 0.0, -433.78029514495256], [-30.0, -51.96152422706631, -498.75]], &quot;color&quot;: &quot;#6666ff&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",
       "    var surfaces = [{&quot;vertices&quot;: [{&quot;x&quot;: 43.94255103949445, &quot;y&quot;: -19.908869640075118, &quot;z&quot;: -477.3596124880449}, {&quot;x&quot;: 41.652464568990126, &quot;y&quot;: -16.593150511447867, &quot;z&quot;: -481.0137125774061}, {&quot;x&quot;: 35.290541563500625, &quot;y&quot;: -16.738107262885094, &quot;z&quot;: -485.6027136203864}, {&quot;x&quot;: 37.91124443828144, &quot;y&quot;: -20.145389195706585, &quot;z&quot;: -482.26905450197233}, {&quot;x&quot;: 39.329702093596666, &quot;y&quot;: -12.848848673453027, &quot;z&quot;: -484.20368359205406}, {&quot;x&quot;: 32.699030116587664, &quot;y&quot;: -12.90780464536374, &quot;z&quot;: -488.46693901726593}, {&quot;x&quot;: 37.00567499113231, &quot;y&quot;: -8.72659938515983, &quot;z&quot;: -486.8863866463593}, {&quot;x&quot;: 30.17175584416597, &quot;y&quot;: -8.70627961522203, &quot;z&quot;: -490.82299695765056}, {&quot;x&quot;: 34.71181174132673, &quot;y&quot;: -4.282148996540371, &quot;z&quot;: -489.0255427836465}, {&quot;x&quot;: 27.742895795271718, &quot;y&quot;: -4.19035059084419, &quot;z&quot;: -492.63902579967606}, {&quot;x&quot;: 32.479132909548184, &quot;y&quot;: 0.4243989252823894, &quot;z&quot;: -490.59222358684644}, {&quot;x&quot;: 25.44529613539603, &quot;y&quot;: 0.5789122347185867, &quot;z&quot;: -493.8904668686223}, {&quot;x&quot;: 30.33783164687193, &quot;y&quot;: 5.32939639367288, &quot;z&quot;: -491.5652423857117}, {&quot;x&quot;: 23.310027958443438, &quot;y&quot;: 5.537012763344052, &quot;z&quot;: -494.5603965708588}, {&quot;x&quot;: 28.316865379507785, &quot;y&quot;: 10.366511732315246, &quot;z&quot;: -491.9314407701856}, {&quot;x&quot;: 21.365967103489023, &quot;y&quot;: 10.616901190924139, &quot;z&quot;: -494.6397552564164}, {&quot;x&quot;: 26.443564209286816, &quot;y&quot;: 15.467626597344548, &quot;z&quot;: -491.6858665353256}, {&quot;x&quot;: 19.63940365859119, &quot;y&quot;: 15.749880740942572, &quot;z&quot;: -494.1274697352113}, {&quot;x&quot;: 24.74326132091826, &quot;y&quot;: 20.563757161091672, &quot;z&quot;: -490.83184065137954}, {&quot;x&quot;: 18.15368643245017, &quot;y&quot;: 20.866536670529044, &quot;z&quot;: -493.03046779010043}, {&quot;x&quot;: 28.44693067370667, &quot;y&quot;: -16.698990236153563, &quot;z&quot;: -489.4390487474773}, {&quot;x&quot;: 31.357733532835677, &quot;y&quot;: -20.20005138137681, &quot;z&quot;: -486.46235017051373}, {&quot;x&quot;: 25.627259376801273, &quot;y&quot;: -12.781743422044215, &quot;z&quot;: -491.94814580023524}, {&quot;x&quot;: 22.936850859309597, &quot;y&quot;: -8.501284982235646, &quot;z&quot;: -493.95571009546507}, {&quot;x&quot;: 20.41208828107815, &quot;y&quot;: -3.915500774068917, &quot;z&quot;: -495.4345927700177}, {&quot;x&quot;: 18.087114724788048, &quot;y&quot;: 0.9135943378794877, &quot;z&quot;: -496.36479447271927}, {&quot;x&quot;: 15.993371469333393, &quot;y&quot;: 5.920695126455328, &quot;z&quot;: -496.73373582128687}, {&quot;x&quot;: 14.15917280046133, &quot;y&quot;: 11.03808914309377, &quot;z&quot;: -496.53642751689387}, {&quot;x&quot;: 12.609323108630345, &quot;y&quot;: 16.196572412526834, &quot;z&quot;: -495.77553781587824}, {&quot;x&quot;: 11.36478145217998, &quot;y&quot;: 21.3263852978303, &quot;z&quot;: -494.46135644615197}, {&quot;x&quot;: 21.214179996788513, &quot;y&quot;: -16.4763284219353, &quot;z&quot;: -492.4708381072558}, {&quot;x&quot;: 24.370643315710875, &quot;y&quot;: -20.072116984796757, &quot;z&quot;: -489.8827923632834}, {&quot;x&quot;: 18.210023441984557, &quot;y&quot;: -12.47236976528378, &quot;z&quot;: -494.60022659117675}, {&quot;x&quot;: 15.398799715120571, &quot;y&quot;: -8.114387686946841, &quot;z&quot;: -496.24216148873285}, {&quot;x&quot;: 12.818525794493379, &quot;y&quot;: -3.461316418486007, &quot;z&quot;: -497.37443844714755}, {&quot;x&quot;: 10.504095458461176, &quot;y&quot;: 1.423919233461632, &quot;z&quot;: -497.9817453629611}, {&quot;x&quot;: 8.486807406950813, &quot;y&quot;: 6.475254837246496, &quot;z&quot;: -498.05586945196234}, {&quot;x&quot;: 6.793942000233781, &quot;y&quot;: 11.624379744312222, &quot;z&quot;: -497.5958083130062}, {&quot;x&quot;: 5.448392338852753, &quot;y&quot;: 16.80166087353156, &quot;z&quot;: -496.6077834837698}, {&quot;x&quot;: 4.4683546737089275, &quot;y&quot;: 21.93708437917418, &quot;z&quot;: -495.10515630512765}, {&quot;x&quot;: 13.69010007798422, &quot;y&quot;: -16.073132939294723, &quot;z&quot;: -494.65708194961695}, {&quot;x&quot;: 17.04446219585295, &quot;y&quot;: -19.763316099210698, &quot;z&quot;: -492.4841254673372}, {&quot;x&quot;: 10.547627704006992, &quot;y&quot;: -11.983867423064638, &quot;z&quot;: -496.38731654699467}, {&quot;x&quot;: 7.659541621918678, &quot;y&quot;: -7.550819851558316, &quot;z&quot;: -497.6514308047306}, {&quot;x&quot;: 5.06489824151435, &quot;y&quot;: -2.83393958835876, &quot;z&quot;: -498.4323297460564}, {&quot;x&quot;: 2.79878566344511, &quot;y&quot;: 2.1029856527063657, &quot;z&quot;: -498.7194530524103}, {&quot;x&quot;: 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[12, 13, 50, 49], [13, 14, 51, 50], [14, 15, 52, 51], [15, 16, 53, 52], [16, 17, 54, 53], [17, 18, 55, 54], [18, 19, 56, 55], [19, 20, 57, 56], [20, 21, 58, 57], [21, 22, 59, 58], [22, 23, 60, 59], [23, 24, 61, 60], [24, 25, 62, 61], [25, 26, 63, 62], [26, 27, 64, 63], [27, 28, 65, 64], [28, 29, 66, 65], [29, 30, 67, 66], [30, 31, 68, 67], [31, 32, 69, 68], [32, 33, 70, 69], [33, 34, 71, 70], [34, 35, 72, 71], [35, 36, 73, 72], [36, 37, 74, 73], [37, 2, 39, 74], [39, 38, 75], [38, 40, 75], [40, 41, 75], [41, 42, 75], [42, 43, 75], [43, 44, 75], [44, 45, 75], [45, 46, 75], [46, 47, 75], [47, 48, 75], [48, 49, 75], [49, 50, 75], [50, 51, 75], [51, 52, 75], [52, 53, 75], [53, 54, 75], [54, 55, 75], [55, 56, 75], [56, 57, 75], [57, 58, 75], [58, 59, 75], [59, 60, 75], [60, 61, 75], [61, 62, 75], [62, 63, 75], [63, 64, 75], [64, 65, 75], [65, 66, 75], [66, 67, 75], [67, 68, 75], [68, 69, 75], [69, 70, 75], [70, 71, 75], [71, 72, 75], [72, 73, 75], [73, 74, 75], [74, 39, 75]], 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{&quot;x&quot;: 4.727718225768459, &quot;y&quot;: -27.884006820092146, &quot;z&quot;: -433.57475576288596}, {&quot;x&quot;: 4.815201089665057, &quot;y&quot;: -27.849006510582974, &quot;z&quot;: -433.07472042353487}, {&quot;x&quot;: 4.97929027130497, &quot;y&quot;: -27.78166905339989, &quot;z&quot;: -432.597799024277}, {&quot;x&quot;: 5.215265223688842, &quot;y&quot;: -27.68393162458506, &quot;z&quot;: -432.1577117254403}, {&quot;x&quot;: 5.516337377075099, &quot;y&quot;: -27.558605952015395, &quot;z&quot;: -431.76711903734747}, {&quot;x&quot;: 5.8738454337715105, &quot;y&quot;: -27.409297427110847, &quot;z&quot;: -431.4372576004846}, {&quot;x&quot;: 6.277504537900201, &quot;y&quot;: -27.24030138428757, &quot;z&quot;: -431.17761692781306}, {&quot;x&quot;: 6.7157021519756706, &quot;y&quot;: -27.05647953200727, &quot;z&quot;: -430.99566640875895}, {&quot;x&quot;: 7.175832128465354, &quot;y&quot;: -26.86312009027645, &quot;z&quot;: -430.89664042847903}, {&quot;x&quot;: 7.644657365702178, &quot;y&quot;: -26.665785658185055, &quot;z&quot;: -430.8833877841298}, {&quot;x&quot;: 8.108690615198805, &quot;y&quot;: -26.470153188058458, &quot;z&quot;: -430.95628973016017}, {&quot;x&quot;: 7.478084858993894, &quot;y&quot;: -26.724946926153333, &quot;z&quot;: -433.87817551356596}], &quot;faces&quot;: [[0, 1, 2], [0, 3, 1], [0, 4, 3], [0, 5, 4], [0, 6, 5], [0, 7, 6], [0, 8, 7], [0, 9, 8], [0, 10, 9], [0, 11, 10], [0, 12, 11], [0, 13, 12], [0, 14, 13], [0, 15, 14], [0, 16, 15], [0, 17, 16], [0, 18, 17], [0, 19, 18], [0, 20, 19], [0, 21, 20], [0, 22, 21], [0, 23, 22], [0, 24, 23], [0, 25, 24], [0, 26, 25], [0, 27, 26], [0, 28, 27], [0, 29, 28], [0, 30, 29], [0, 31, 30], [0, 32, 31], [0, 33, 32], [0, 34, 33], [0, 35, 34], [0, 36, 35], [0, 37, 36], [0, 2, 37], [2, 1, 38], [1, 3, 38], [3, 4, 38], [4, 5, 38], [5, 6, 38], [6, 7, 38], [7, 8, 38], [8, 9, 38], [9, 10, 38], [10, 11, 38], [11, 12, 38], [12, 13, 38], [13, 14, 38], [14, 15, 38], [15, 16, 38], [16, 17, 38], [17, 18, 38], [18, 19, 38], [19, 20, 38], [20, 21, 38], [21, 22, 38], [22, 23, 38], [23, 24, 38], [24, 25, 38], [25, 26, 38], [26, 27, 38], [27, 28, 38], [28, 29, 38], [29, 30, 38], [30, 31, 38], [31, 32, 38], [32, 33, 38], [33, 34, 38], [34, 35, 38], [35, 36, 38], [36, 37, 38], [37, 2, 38]], &quot;color&quot;: &quot;#800080&quot;, &quot;opacity&quot;: 1.0}, {&quot;vertices&quot;: [{&quot;x&quot;: 60.0, &quot;y&quot;: 0.0, &quot;z&quot;: -498.75}, {&quot;x&quot;: -30.0, &quot;y&quot;: 51.96152422706631, &quot;z&quot;: -498.75}, {&quot;x&quot;: -30.0, &quot;y&quot;: -51.96152422706631, &quot;z&quot;: -498.75}], &quot;faces&quot;: [[0, 1, 2]], &quot;color&quot;: &quot;#ff0000&quot;, &quot;opacity&quot;: 1.0}];\n",
       "    for ( var i=0 ; i < surfaces.length ; i++ ) addSurface( surfaces[i] );\n",
       "\n",
       "    function addSurface( json ) {\n",
       "\n",
       "        var useFaceColors = 'faceColors' in json ? true : false;\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "        for ( var i=0 ; i < json.vertices.length ; i++ ) {\n",
       "            var v = json.vertices[i];\n",
       "            geometry.vertices.push( new THREE.Vector3( a[0]*v.x, a[1]*v.y, a[2]*v.z ) );\n",
       "        }\n",
       "        for ( var i=0 ; i < json.faces.length ; i++ ) {\n",
       "            var f = json.faces[i];\n",
       "            for ( var j=0 ; j < f.length - 2 ; j++ ) {\n",
       "                var face = new THREE.Face3( f[0], f[j+1], f[j+2] );\n",
       "                if ( useFaceColors ) face.color.set( json.faceColors[i] );\n",
       "                geometry.faces.push( face );\n",
       "            }\n",
       "        }\n",
       "        geometry.computeVertexNormals();\n",
       "\n",
       "        var side = json.singleSide ? THREE.FrontSide : THREE.DoubleSide;\n",
       "        var transparent = json.opacity < 1 ? true : false;\n",
       "        var depthWrite = 'depthWrite' in json ? json.depthWrite : !transparent;\n",
       "        var flatShading = json.useFlatShading ? json.useFlatShading : false;\n",
       "\n",
       "        var material = new THREE.MeshPhongMaterial( { side: side,\n",
       "                                     color: useFaceColors ? 'white' : json.color,\n",
       "                                     vertexColors: useFaceColors ? THREE.FaceColors : THREE.NoColors,\n",
       "                                     transparent: transparent, opacity: json.opacity,\n",
       "                                     shininess: 20, flatShading: flatShading,\n",
       "                                     depthWrite: depthWrite } );\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var mesh = new THREE.Mesh( geometry, material );\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        if ( transparent && json.renderOrder ) mesh.renderOrder = json.renderOrder;\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "        if ( json.showMeshGrid ) addSurfaceMeshGrid( json );\n",
       "\n",
       "    }\n",
       "\n",
       "    function addSurfaceMeshGrid( json ) {\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "\n",
       "        for ( var i=0 ; i < json.faces.length ; i++ ) {\n",
       "            var f = json.faces[i];\n",
       "            for ( var j=0 ; j < f.length ; j++ ) {\n",
       "                var k = j === f.length-1 ? 0 : j+1;\n",
       "                var v1 = json.vertices[f[j]];\n",
       "                var v2 = json.vertices[f[k]];\n",
       "                // vertices in opposite directions on neighboring faces\n",
       "                var nudge = f[j] < f[k] ? .0005*zRange : -.0005*zRange;\n",
       "                geometry.vertices.push( new THREE.Vector3( a[0]*v1.x, a[1]*v1.y, a[2]*(v1.z+nudge) ) );\n",
       "                geometry.vertices.push( new THREE.Vector3( a[0]*v2.x, a[1]*v2.y, a[2]*(v2.z+nudge) ) );\n",
       "            }\n",
       "        }\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var gridColor = options.theme === 'dark' ? 'white' : 'black';\n",
       "        var linewidth = json.linewidth || 1;\n",
       "        var materialOptions = { color: gridColor, linewidth: linewidth };\n",
       "\n",
       "        var mesh;\n",
       "        if ( linewidth > 1 && window.createFatLineSegments ) {\n",
       "            mesh = createFatLineSegments( geometry, materialOptions );\n",
       "        } else {\n",
       "            var material = new THREE.LineBasicMaterial( materialOptions );\n",
       "            mesh = new THREE.LineSegments( geometry, material );\n",
       "        }\n",
       "\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "    }\n",
       "\n",
       "    function render() {\n",
       "\n",
       "        if ( window.updateAnimation ) animate = updateAnimation();\n",
       "        if ( animate ) requestAnimationFrame( render );\n",
       "\n",
       "        renderer.render( scene, camera );\n",
       "\n",
       "    }\n",
       "\n",
       "    render();\n",
       "    controls.update();\n",
       "    if ( !animate ) render();\n",
       "\n",
       "\n",
       "    // menu functions\n",
       "\n",
       "    function toggleMenu() {\n",
       "\n",
       "        var m = document.getElementById( 'menu-content' );\n",
       "        if ( m.style.display === 'block' ) m.style.display = 'none'\n",
       "        else m.style.display = 'block';\n",
       "\n",
       "    }\n",
       "\n",
       "\n",
       "    function saveAsPNG() {\n",
       "\n",
       "        var a = document.body.appendChild( document.createElement( 'a' ) );\n",
       "        a.href = renderer.domElement.toDataURL( 'image/png' );\n",
       "        a.download = 'screenshot';\n",
       "        a.click();\n",
       "\n",
       "    }\n",
       "\n",
       "    function saveAsHTML() {\n",
       "\n",
       "        toggleMenu(); // otherwise visible in output\n",
       "        event.stopPropagation();\n",
       "\n",
       "        var blob = new Blob( [ '<!DOCTYPE html>\\n' + document.documentElement.outerHTML ] );\n",
       "        var a = document.body.appendChild( document.createElement( 'a' ) );\n",
       "        a.href = window.URL.createObjectURL( blob );\n",
       "        a.download = suggestFilename();\n",
       "        a.click();\n",
       "\n",
       "        function suggestFilename() {\n",
       "            if ( !document.title ) {\n",
       "                return 'graphic.html';\n",
       "            } else if ( /\\.html?$/i.test( document.title ) ) {\n",
       "                return document.title; // already ends in .htm or .html\n",
       "            } else {\n",
       "                return document.title + '.html';\n",
       "            }\n",
       "        }\n",
       "\n",
       "    }\n",
       "\n",
       "    function getViewpoint() {\n",
       "\n",
       "        function roundTo( x, n ) { return +x.toFixed(n); }\n",
       "\n",
       "        var v = camera.quaternion.inverse();\n",
       "        var r = Math.sqrt( v.x*v.x + v.y*v.y + v.z*v.z );\n",
       "        var axis = [ roundTo( v.x / r, 4 ), roundTo( v.y / r, 4 ), roundTo( v.z / r, 4 ) ];\n",
       "        var angle = roundTo( 2 * Math.atan2( r, v.w ) * 180 / Math.PI, 2 );\n",
       "\n",
       "        var textArea = document.createElement( 'textarea' );\n",
       "        textArea.textContent = JSON.stringify( axis ) + ',' + angle;\n",
       "        textArea.style.csstext = 'position: absolute; top: -100%';\n",
       "        document.body.append( textArea );\n",
       "        textArea.select();\n",
       "        document.execCommand( 'copy' );\n",
       "\n",
       "        var m = document.getElementById( 'menu-message' );\n",
       "        m.innerHTML = 'Viewpoint copied to clipboard';\n",
       "        m.style.display = 'block';\n",
       "        setTimeout( function() { m.style.display = 'none'; }, 2000 );\n",
       "\n",
       "    }\n",
       "\n",
       "</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;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": [
    "allgr.show(aspect_ratio=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 9.3",
   "language": "sage",
   "name": "sagemath"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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