Curvas_e_Superficies_Part_I.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "78c78a19",
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils import vector_simplify, pretty_results, get_vector_arguments\n",
    "\n",
    "%display latex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ead3f869",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Curve definition\n",
    "curve_alpha(t) = (1/2 * cos(3 * t) + 1/3 * sin(t), \n",
    "                  1/2 * sin(3 * t) + 1/3 * cos(t))\n",
    "\n",
    "# Plot\n",
    "parametric_plot(curve_alpha, (t,0, 2*pi), thickness=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d12bea6f",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 31 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#ref: https://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/curve.html#curves-in-manifolds\n",
    "\n",
    "# Define dimention and variables\n",
    "M = Manifold(2, 'M')\n",
    "X.<x,y> = M.chart()\n",
    "\n",
    "# Define curve\n",
    "c = M.curve([1/2 * cos(t) + 1/3 * sin(4 * t), \n",
    "             1/2 * sin(t) + 1/3 * cos(4 * t)], (t, 0, 2*pi))\n",
    "\n",
    "# Vectors tangent\n",
    "v = c.tangent_vector_field() ; v\n",
    "\n",
    "# Plot\n",
    "show(c.plot(thickness=2, aspect_ratio=1) +\n",
    "     v.plot(chart=X, number_values=30, scale=.2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "72c2d1cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{align*} \\int_0^t || C'(x) || dx &= 2 \\, t \\\\ \\end{align*} \\\\\\]</html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{align*} \\int_0^t || C'(x) || dx &= 2 \\, t \\\\ \\end{align*} \\\\$$"
      ],
      "text/plain": [
       "\\begin{align*} \\int_0^t || C'(x) || dx &= 2 \\, t \\\\ \\end{align*} \\\\"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define curve\n",
    "curve_alpha(s) = (2 * cos(s), 2 * sin(s))\n",
    "\n",
    "# Calculate the derivative\n",
    "x = get_vector_arguments(curve_alpha).pop()\n",
    "curve_alpha_x = curve_alpha.derivative(x)\n",
    "    \n",
    "# Calcular comprimento de arco de 0 a t\n",
    "t = var(\"t\")\n",
    "assume(t>0)\n",
    "s = integrate(norm(curve_alpha_x), (x,0,t))\n",
    "s = s.simplify_full()\n",
    "\n",
    "# Plot equation\n",
    "pretty_results((r\"\\int_0^t || C'(x) || dx\", s))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9bb5139f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Curve definition\n",
    "alpha(t) = (cos(t) + sin(4 * t), sin(t) + cos(4 * t))\n",
    "\n",
    "# Reparametrization\n",
    "phi(x) = 2 * x + 1\n",
    "beta(t) = alpha(phi(t))\n",
    "\n",
    "# Plot\n",
    "parametric_plot(alpha, (t,0, 2*pi), thickness=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d8b04706",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parametric_plot(beta, (t,0, 2*pi), thickness=2, color='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b31599ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Curve definition\n",
    "alpha(s) = (2 * cos(s), 2 * sin(s))\n",
    "\n",
    "# Plot\n",
    "parametric_plot(alpha, (s,0, 2*pi), thickness=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f8460180",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Curva reparametrizada:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{align*} \\alpha(s) :& \\quad s \\ {\\mapsto}\\ \\left(2 \\, \\cos\\left(\\frac{1}{2} \\, s\\right),\\,2 \\, \\sin\\left(\\frac{1}{2} \\, s\\right)\\right) \\\\ \\end{align*} \\\\\\]</html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{align*} \\alpha(s) :& \\quad s \\ {\\mapsto}\\ \\left(2 \\, \\cos\\left(\\frac{1}{2} \\, s\\right),\\,2 \\, \\sin\\left(\\frac{1}{2} \\, s\\right)\\right) \\\\ \\end{align*} \\\\$$"
      ],
      "text/plain": [
       "\\begin{align*} \\alpha(s) :& \\quad s \\ {\\mapsto}\\ \\left(2 \\, \\cos\\left(\\frac{1}{2} \\, s\\right),\\,2 \\, \\sin\\left(\\frac{1}{2} \\, s\\right)\\right) \\\\ \\end{align*} \\\\"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Identify curve parameter\n",
    "x = get_vector_arguments(alpha).pop()\n",
    "\n",
    "# Calculate the derivatives\n",
    "alpha_x = alpha.derivative(x)\n",
    "    \n",
    "# Calculate arc length from 0 to t\n",
    "t = var(\"t\")\n",
    "assume(t>0)\n",
    "comp_arco = integrate(norm(alpha_x), (x,0,t))\n",
    "\n",
    "t = comp_arco.arguments()[0]\n",
    "    \n",
    "# Find t in terms of s\n",
    "s = var(\"s\")\n",
    "param_comp_arco = solve(s == comp_arco,t)[0]\n",
    "    \n",
    "# Replace original parameter in curve \n",
    "alpha_subs = alpha(t).subs(param_comp_arco)\n",
    "alpha_subs = vector_simplify(alpha_subs)\n",
    "    \n",
    "# Reset function argument\n",
    "alpha_param(s) = tuple(coord for coord in alpha_subs)\n",
    "\n",
    "# New curve plot\n",
    "print(\"Curva reparametrizada:\")\n",
    "pretty_results((r\"\\alpha(s)\", alpha_param), use_colon=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8d13043d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{align*} K(s) :& \\quad \\frac{1}{2} \\\\ \\end{align*} \\\\\\]</html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{align*} K(s) :& \\quad \\frac{1}{2} \\\\ \\end{align*} \\\\$$"
      ],
      "text/plain": [
       "\\begin{align*} K(s) :& \\quad \\frac{1}{2} \\\\ \\end{align*} \\\\"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Curve definition\n",
    "curve(t) = (2 * cos(t), 2 * sin(t))\n",
    "\n",
    "# Calculate the derivatives\n",
    "curve_t = curve.derivative(t)\n",
    "curve_tt = curve_t.derivative(t)\n",
    "\n",
    "# Calculate J(c'(t))\n",
    "curve_t_rotation(t) = (- curve_t[1], curve_t[0])\n",
    "\n",
    "# Calculate the curvature\n",
    "curvatura = curve_t_rotation.dot_product(curve_tt)/norm(curve_t)^3\n",
    "curvatura = curvatura.simplify_full()\n",
    "\n",
    "# Plot\n",
    "pretty_results((r\"K(s)\", curvatura), use_colon=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7b6f416f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{align*} T(t) &= t \\ {\\mapsto}\\ \\left(\\frac{2 \\, \\cos\\left(2 \\, t\\right)}{\\sqrt{4 \\, \\cos\\left(2 \\, t\\right)^{2} + \\sin\\left(t\\right)^{2}}},\\,-\\frac{\\sin\\left(t\\right)}{\\sqrt{4 \\, \\cos\\left(2 \\, t\\right)^{2} + \\sin\\left(t\\right)^{2}}}\\right) \\\\ \\end{align*} \\\\\\]</html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{align*} T(t) &= t \\ {\\mapsto}\\ \\left(\\frac{2 \\, \\cos\\left(2 \\, t\\right)}{\\sqrt{4 \\, \\cos\\left(2 \\, t\\right)^{2} + \\sin\\left(t\\right)^{2}}},\\,-\\frac{\\sin\\left(t\\right)}{\\sqrt{4 \\, \\cos\\left(2 \\, t\\right)^{2} + \\sin\\left(t\\right)^{2}}}\\right) \\\\ \\end{align*} \\\\$$"
      ],
      "text/plain": [
       "\\begin{align*} T(t) &= t \\ {\\mapsto}\\ \\left(\\frac{2 \\, \\cos\\left(2 \\, t\\right)}{\\sqrt{4 \\, \\cos\\left(2 \\, t\\right)^{2} + \\sin\\left(t\\right)^{2}}},\\,-\\frac{\\sin\\left(t\\right)}{\\sqrt{4 \\, \\cos\\left(2 \\, t\\right)^{2} + \\sin\\left(t\\right)^{2}}}\\right) \\\\ \\end{align*} \\\\"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Curve definition\n",
    "alpha(t) = (sin(2 * t), cos(t))\n",
    "\n",
    "# Diedro de Frenet\n",
    "T(t) = alpha.derivative(t)/norm(alpha.derivative(t))\n",
    "\n",
    "N(t) = (- T[1], T[0])\n",
    "\n",
    "# Plot\n",
    "pretty_results((r\"T(t)\", T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "22f327b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{align*} N(t) &= t \\ {\\mapsto}\\ \\left(\\frac{\\sin\\left(t\\right)}{\\sqrt{4 \\, \\cos\\left(2 \\, t\\right)^{2} + \\sin\\left(t\\right)^{2}}},\\,\\frac{2 \\, \\cos\\left(2 \\, t\\right)}{\\sqrt{4 \\, \\cos\\left(2 \\, t\\right)^{2} + \\sin\\left(t\\right)^{2}}}\\right) \\\\ \\end{align*} \\\\\\]</html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{align*} N(t) &= t \\ {\\mapsto}\\ \\left(\\frac{\\sin\\left(t\\right)}{\\sqrt{4 \\, \\cos\\left(2 \\, t\\right)^{2} + \\sin\\left(t\\right)^{2}}},\\,\\frac{2 \\, \\cos\\left(2 \\, t\\right)}{\\sqrt{4 \\, \\cos\\left(2 \\, t\\right)^{2} + \\sin\\left(t\\right)^{2}}}\\right) \\\\ \\end{align*} \\\\$$"
      ],
      "text/plain": [
       "\\begin{align*} N(t) &= t \\ {\\mapsto}\\ \\left(\\frac{\\sin\\left(t\\right)}{\\sqrt{4 \\, \\cos\\left(2 \\, t\\right)^{2} + \\sin\\left(t\\right)^{2}}},\\,\\frac{2 \\, \\cos\\left(2 \\, t\\right)}{\\sqrt{4 \\, \\cos\\left(2 \\, t\\right)^{2} + \\sin\\left(t\\right)^{2}}}\\right) \\\\ \\end{align*} \\\\"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pretty_results((r\"N(t)\", N))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "97dff70f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define curvature and theta_0\n",
    "curvatura(t) = 1/t\n",
    "theta_0 = 0\n",
    "\n",
    "# Identify the Curve Parameter\n",
    "t = curvatura.arguments()[0]\n",
    "    \n",
    "# Build Angle Function\n",
    "theta(t) = integrate(curvatura(t), t) + theta_0\n",
    "\n",
    "# Build Curve From Angle Function\n",
    "aux(t) = (cos(theta(t)), sin(theta(t)))\n",
    "\n",
    "curva_ang(t) = integrate(aux(t), t)\n",
    "\n",
    "curva_ang = vector_simplify(curva_ang)\n",
    "    \n",
    "# Export function with n-tuple\n",
    "curva_construida = tuple(coord for coord in curva_ang)\n",
    "\n",
    "# Plot\n",
    "parametric_plot(curva_construida, (t,0, 2 * pi), thickness=2)\n",
    "#pretty_results((r\"C(t)\", curva_construida))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "01e62bf0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<iframe srcdoc=\"<!DOCTYPE html>\n",
       "<html>\n",
       "<head>\n",
       "<title></title>\n",
       "<meta charset=&quot;utf-8&quot;>\n",
       "<meta name=viewport content=&quot;width=device-width, user-scalable=no, minimum-scale=1.0, maximum-scale=1.0&quot;>\n",
       "<style>\n",
       "\n",
       "    body { margin: 0px; overflow: hidden; }\n",
       "\n",
       "    #menu-container { position: absolute; bottom: 30px; right: 40px; cursor: default; }\n",
       "\n",
       "    #menu-message { position: absolute; bottom: 0px; right: 0px; white-space: nowrap;\n",
       "                    display: none; background-color: #F5F5F5; padding: 10px; }\n",
       "\n",
       "    #menu-content { position: absolute; bottom: 0px; right: 0px;\n",
       "                    display: none; background-color: #F5F5F5; border-bottom: 1px solid black;\n",
       "                    border-right: 1px solid black; border-left: 1px solid black; }\n",
       "\n",
       "    #menu-content div { border-top: 1px solid black; padding: 10px; white-space: nowrap; }\n",
       "\n",
       "    #menu-content div:hover { background-color: #FEFEFE; }\n",
       "\n",
       "    .dark-theme #menu-container { color: white; }\n",
       "\n",
       "    .dark-theme #menu-message { background-color: #181818; }\n",
       "\n",
       "    .dark-theme #menu-content { background-color: #181818; border-color: white; }\n",
       "\n",
       "    .dark-theme #menu-content div { border-color: white; }\n",
       "\n",
       "    .dark-theme #menu-content div:hover { background-color: #303030; }\n",
       "\n",
       "</style>\n",
       "\n",
       "</head>\n",
       "\n",
       "<body>\n",
       "\n",
       "<script src=&quot;/nbextensions/threejs-sage/r124/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@r124/build/three.min.js&quot;><\\/script> \\\n",
       "            ');\n",
       "</script>\n",
       "        <script>// fat_lines.js\n",
       "\n",
       "var _fatLines = [];\n",
       "\n",
       "function _createFatLine( lineStrip, geometry, materialOptions ) {\n",
       "\n",
       "    var vertexCount = geometry.vertices.length;\n",
       "    var positions = [];\n",
       "    for ( var i=0 ; i < vertexCount ; i++ ) {\n",
       "        var v = geometry.vertices[i];\n",
       "        positions.push( v.x, v.y, v.z );\n",
       "        // For a line strip, duplicate all but the first and last vertices.\n",
       "        if ( lineStrip && i > 0 && i < vertexCount - 1 ) {\n",
       "            positions.push( v.x, v.y, v.z );\n",
       "        }\n",
       "    }\n",
       "\n",
       "    geometry = new THREE.LineSegmentsGeometry();\n",
       "    geometry.setPositions( positions );\n",
       "\n",
       "    var material = new THREE.LineMaterial( materialOptions );\n",
       "    material.resolution = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "\n",
       "    var line = new THREE.LineSegments2( geometry, material );\n",
       "    line.computeLineDistances();\n",
       "    line.scale.set( 1, 1, 1 );\n",
       "\n",
       "    _fatLines.push( line );\n",
       "\n",
       "    return line;\n",
       "\n",
       "}\n",
       "\n",
       "function createFatLineStrip( geometry, materialOptions ) {\n",
       "    return _createFatLine( true, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function createFatLineSegments( geometry, materialOptions ) {\n",
       "    return _createFatLine( false, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function rescaleFatLines() {\n",
       "    var res = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "    var n = _fatLines.length;\n",
       "    for ( var i=0 ; i < n ; i++ ) {\n",
       "        _fatLines[i].material.resolution = res;\n",
       "    }\n",
       "}\n",
       "</script>\n",
       "<script>\n",
       "\n",
       "    var options = {&quot;animate&quot;: false, &quot;animationControls&quot;: true, &quot;aspectRatio&quot;: [1.0, 1.0, 1.0], &quot;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;:-9.830263050559644, &quot;y&quot;:-14.790272675948948, &quot;z&quot;:0.0}, {&quot;x&quot;:11.366056608780493, &quot;y&quot;:18.84955592153876, &quot;z&quot;:39.47841760435743}]; // 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 = [];\n",
       "    for ( var i=0 ; i < texts.length ; i++ ) addText( texts[i] );\n",
       "\n",
       "    function addText( json ) {\n",
       "        var sprite = addLabel( json.text, a[0]*json.x, a[1]*json.y, a[2]*json.z, json );\n",
       "        sprite.userData = json;\n",
       "    }\n",
       "\n",
       "    var points = [];\n",
       "    for ( var i=0 ; i < points.length ; i++ ) addPoint( points[i] );\n",
       "\n",
       "    function addPoint( json ) {\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "        var v = json.point;\n",
       "        geometry.vertices.push( new THREE.Vector3( a[0]*v[0], a[1]*v[1], a[2]*v[2] ) );\n",
       "\n",
       "        var canvas = document.createElement( 'canvas' );\n",
       "        canvas.width = 128;\n",
       "        canvas.height = 128;\n",
       "\n",
       "        var context = canvas.getContext( '2d' );\n",
       "        context.arc( 64, 64, 64, 0, 2 * Math.PI );\n",
       "        context.fillStyle = json.color;\n",
       "        context.fill();\n",
       "\n",
       "        var texture = new THREE.Texture( canvas );\n",
       "        texture.needsUpdate = true;\n",
       "\n",
       "        var transparent = json.opacity < 1 ? true : false;\n",
       "        var size = camera.isOrthographicCamera ? json.size : json.size/100;\n",
       "        var material = new THREE.PointsMaterial( { size: size, map: texture,\n",
       "                                                   transparent: transparent, opacity: json.opacity,\n",
       "                                                   alphaTest: .1 } );\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var mesh = new THREE.Points( geometry, material );\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "    }\n",
       "\n",
       "    var lines = [{&quot;points&quot;: [[0.0, 0.0, 0.0], [-0.15163293600881328, -0.1146775765409041, 0.007209353105251539], [0.27306286251546563, -0.30293435971756366, 0.028837412421006157], [0.08609703820115179, 0.7531792791590863, 0.06488417794726387], [-0.6494889490732475, -0.2983556325555305, 0.11534964968402463], [0.5875108290575933, -0.9194967409386123, 0.18023382763128845], [0.33943444273947515, 1.4410395515170005, 0.25953671178905535], [-1.1790826942439256, -0.22648116857372563, 0.35325830215732534], [0.7607406159245018, -1.6883285367520169, 0.46139859873609834], [0.7453648472486499, 2.0013966907691896, 0.5839576015253745], [-1.6966280932096136, 0.10810781527337252, 0.7209353105251537], [0.769420826506272, -2.5532267061564147, 0.8723317257354359], [1.2801803210868137, 2.3782100205376384, 1.0381468471562214], [-2.158056467190895, 0.6976451196866394, 1.2183806747875099], [0.5990580524965796, -3.451063624388353, 1.4130332086293014], [1.912140486028575, 2.524342934693655, 1.6221044486815959], [-2.5211237634605967, 1.5196062764600127, 1.8455943949443934], [0.24482358801753912, -4.314703419813144, 2.083503047417694], [2.602856124409229, 2.4039631122524643, 2.335830406101498], [-2.7474592424320345, 2.537516618488541, 2.6025764709958046], [-0.28802775060872865, -5.076121670368423, 2.8837412421006148], [3.308974939541978, 1.994483237853973, 3.1793247194159275], [-2.804472712841995, 3.7023696375505484, 3.4893269029417437], [-0.9841668005299377, -5.669604525780926, 3.8137477926780625], [3.984104247121629, 1.2879602209601138, 4.152587388624886], [-2.6670423355975954, 4.954604209453333, 4.505845690782212], [-1.818631044469346, -6.034899487278817, 4.873522699150041], [4.580895851665957, 0.291891101238148, 5.2556184137283735], [-2.3189128581068488, 6.226567482393089, 5.652132834517209], [-2.757684732726382, -6.120190945726003, 6.063065961516548], [5.05321154675966, -0.9706335796019585, 6.488417794726391], [-1.7537446208204235, 7.445371016171278, 6.928188334146736], [-3.76006930596877, -5.884779142006877, 7.382377579777583], [5.358283829854171, -2.4614339685837354, 7.850985531618935], [-0.9757664329459371, 8.536031830469765, 8.334012189670789], [-4.778600094020937, -5.301351295056787, 8.831457553933147], [5.458785696317052, -4.128392755473234, 9.343321624406007], [7.20486771292243e-13, 9.424777960769386, 9.869604401089372], [-5.76205156833525, -4.357747908553344, 10.41030588398324], [5.324725819051111, -5.907220014493454, 10.96542607308761], [1.1479605093495067, 10.042390388787616, 11.534964968402482], [-6.657261728001107, -3.058145233692655, 12.118922569927859], [4.9350909640829785, -7.723772623885518, 12.717298877663739], [2.4326135063006817, 10.327450119204594, 13.330093891610122], [-7.411376935247697, -1.4235959167473067, 13.957307611767007], [4.279165964574061, -9.496848019231392, 14.598940038134396], [3.809642552605579, 10.229360863930282, 15.25499117071229], [-7.974152038085124, 0.508106731787328, 15.925461009500685], [3.35747269748038, -11.141352899592684, 16.610349554499578], [5.227402977772501, 9.711024250527078, 17.30965680570898], [-8.300217181503069, 2.6832504603358975, 18.023382763128886], [2.1822829055214625, -12.571731774558287, 18.751527426759292], [6.628753684900524, 8.751055506935531, 19.494090796600204], [-8.351222466462376, 5.0336957907770135, 20.25107287265162], [0.7776749266416026, -13.70552850999501, 21.022473654913536], [7.95317149125169, 7.345442842990588, 21.808293143385956], [-8.097774609271884, 7.4789963492330305, 22.60853133806888], [-0.8208790892377654, -14.466946760549654, 23.423188238962307], [9.139073642545622, 5.508572752164019, 24.25226384606624], [-7.521085911710651, 9.929082209798043, 25.09575815938067], [-2.5673916535597354, -14.790272675948948, 25.953671178905605], [10.126264961434869, 3.2735655616019805, 26.826002904641044], [-6.61426499227936, 12.287418439447533, 27.71275333658699], [-4.406682915448016, -14.623025680712002, 28.613922474743433], [10.858419796541686, 0.6918900177445768, 29.529510319110383], [-5.383190563459448, 14.454531655557819, 30.459516869687835], [-6.2761100813805974, -13.928710428200667, 31.40394212647579], [11.285505787762759, -2.1677483277835004, 32.36278608947425], [-3.8469236843765637, 16.33178158386157, 33.33604875868321], [-8.107649440998062, -12.689055024948178, 34.323730134102675], [11.366056608780493, -5.221223569728426, 35.325830215732644], [-2.037629904089261, 17.825242940099603, 36.34234900357311], [-9.830263050559644, -10.90563694982649, 37.373286497624086], [11.069204328641169, -8.371463087492605, 38.41864269788556], [2.468521160029876e-14, 18.84955592153876, 39.47841760435743]], &quot;color&quot;: &quot;#6666ff&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 2.0}];\n",
       "    for ( var i=0 ; i < lines.length ; i++ ) addLine( lines[i] );\n",
       "\n",
       "    function addLine( json ) {\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "        for ( var i=0 ; i < json.points.length ; i++ ) {\n",
       "            var v = json.points[i];\n",
       "            geometry.vertices.push( new THREE.Vector3( a[0]*v[0], a[1]*v[1], a[2]*v[2] ) );\n",
       "        }\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var transparent = json.opacity < 1 ? true : false;\n",
       "        var materialOptions = { color: json.color, linewidth: json.linewidth,\n",
       "                                transparent: transparent, opacity: json.opacity };\n",
       "\n",
       "        var mesh;\n",
       "        if ( json.linewidth > 1 && window.createFatLineStrip ) {\n",
       "            mesh = createFatLineStrip( geometry, materialOptions );\n",
       "        } else {\n",
       "            var material = new THREE.LineBasicMaterial( materialOptions );\n",
       "            mesh = new THREE.Line( geometry, material );\n",
       "        }\n",
       "\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "    }\n",
       "\n",
       "    var surfaces = [];\n",
       "    for ( var i=0 ; i < surfaces.length ; i++ ) addSurface( surfaces[i] );\n",
       "\n",
       "    function addSurface( json ) {\n",
       "\n",
       "        var useFaceColors = 'faceColors' in json ? true : false;\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "        for ( var i=0 ; i < json.vertices.length ; i++ ) {\n",
       "            var v = json.vertices[i];\n",
       "            geometry.vertices.push( new THREE.Vector3( a[0]*v.x, a[1]*v.y, a[2]*v.z ) );\n",
       "        }\n",
       "        for ( var i=0 ; i < json.faces.length ; i++ ) {\n",
       "            var f = json.faces[i];\n",
       "            for ( var j=0 ; j < f.length - 2 ; j++ ) {\n",
       "                var face = new THREE.Face3( f[0], f[j+1], f[j+2] );\n",
       "                if ( useFaceColors ) face.color.set( json.faceColors[i] );\n",
       "                geometry.faces.push( face );\n",
       "            }\n",
       "        }\n",
       "        geometry.computeVertexNormals();\n",
       "\n",
       "        var side = json.singleSide ? THREE.FrontSide : THREE.DoubleSide;\n",
       "        var transparent = json.opacity < 1 ? true : false;\n",
       "        var depthWrite = 'depthWrite' in json ? json.depthWrite : !transparent;\n",
       "        var flatShading = json.useFlatShading ? json.useFlatShading : false;\n",
       "\n",
       "        var material = new THREE.MeshPhongMaterial( { side: side,\n",
       "                                     color: useFaceColors ? 'white' : json.color,\n",
       "                                     vertexColors: useFaceColors ? THREE.FaceColors : THREE.NoColors,\n",
       "                                     transparent: transparent, opacity: json.opacity,\n",
       "                                     shininess: 20, flatShading: flatShading,\n",
       "                                     depthWrite: depthWrite } );\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var mesh = new THREE.Mesh( geometry, material );\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        if ( transparent && json.renderOrder ) mesh.renderOrder = json.renderOrder;\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "        if ( json.showMeshGrid ) addSurfaceMeshGrid( json );\n",
       "\n",
       "    }\n",
       "\n",
       "    function addSurfaceMeshGrid( json ) {\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "\n",
       "        for ( var i=0 ; i < json.faces.length ; i++ ) {\n",
       "            var f = json.faces[i];\n",
       "            for ( var j=0 ; j < f.length ; j++ ) {\n",
       "                var k = j === f.length-1 ? 0 : j+1;\n",
       "                var v1 = json.vertices[f[j]];\n",
       "                var v2 = json.vertices[f[k]];\n",
       "                // vertices in opposite directions on neighboring faces\n",
       "                var nudge = f[j] < f[k] ? .0005*zRange : -.0005*zRange;\n",
       "                geometry.vertices.push( new THREE.Vector3( a[0]*v1.x, a[1]*v1.y, a[2]*(v1.z+nudge) ) );\n",
       "                geometry.vertices.push( new THREE.Vector3( a[0]*v2.x, a[1]*v2.y, a[2]*(v2.z+nudge) ) );\n",
       "            }\n",
       "        }\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var gridColor = options.theme === 'dark' ? 'white' : 'black';\n",
       "        var linewidth = json.linewidth || 1;\n",
       "        var materialOptions = { color: gridColor, linewidth: linewidth };\n",
       "\n",
       "        var mesh;\n",
       "        if ( linewidth > 1 && window.createFatLineSegments ) {\n",
       "            mesh = createFatLineSegments( geometry, materialOptions );\n",
       "        } else {\n",
       "            var material = new THREE.LineBasicMaterial( materialOptions );\n",
       "            mesh = new THREE.LineSegments( geometry, material );\n",
       "        }\n",
       "\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "    }\n",
       "\n",
       "    function render() {\n",
       "\n",
       "        if ( window.updateAnimation ) animate = updateAnimation();\n",
       "        if ( animate ) requestAnimationFrame( render );\n",
       "\n",
       "        renderer.render( scene, camera );\n",
       "\n",
       "    }\n",
       "\n",
       "    render();\n",
       "    controls.update();\n",
       "    if ( !animate ) render();\n",
       "\n",
       "\n",
       "    // menu functions\n",
       "\n",
       "    function toggleMenu() {\n",
       "\n",
       "        var m = document.getElementById( 'menu-content' );\n",
       "        if ( m.style.display === 'block' ) m.style.display = 'none'\n",
       "        else m.style.display = 'block';\n",
       "\n",
       "    }\n",
       "\n",
       "\n",
       "    function saveAsPNG() {\n",
       "\n",
       "        var a = document.body.appendChild( document.createElement( 'a' ) );\n",
       "        a.href = renderer.domElement.toDataURL( 'image/png' );\n",
       "        a.download = 'screenshot';\n",
       "        a.click();\n",
       "\n",
       "    }\n",
       "\n",
       "    function saveAsHTML() {\n",
       "\n",
       "        toggleMenu(); // otherwise visible in output\n",
       "        event.stopPropagation();\n",
       "\n",
       "        var blob = new Blob( [ '<!DOCTYPE html>\\n' + document.documentElement.outerHTML ] );\n",
       "        var a = document.body.appendChild( document.createElement( 'a' ) );\n",
       "        a.href = window.URL.createObjectURL( blob );\n",
       "        a.download = suggestFilename();\n",
       "        a.click();\n",
       "\n",
       "        function suggestFilename() {\n",
       "            if ( !document.title ) {\n",
       "                return 'graphic.html';\n",
       "            } else if ( /\\.html?$/i.test( document.title ) ) {\n",
       "                return document.title; // already ends in .htm or .html\n",
       "            } else {\n",
       "                return document.title + '.html';\n",
       "            }\n",
       "        }\n",
       "\n",
       "    }\n",
       "\n",
       "    function getViewpoint() {\n",
       "\n",
       "        function roundTo( x, n ) { return +x.toFixed(n); }\n",
       "\n",
       "        var v = camera.quaternion.inverse();\n",
       "        var r = Math.sqrt( v.x*v.x + v.y*v.y + v.z*v.z );\n",
       "        var axis = [ roundTo( v.x / r, 4 ), roundTo( v.y / r, 4 ), roundTo( v.z / r, 4 ) ];\n",
       "        var angle = roundTo( 2 * Math.atan2( r, v.w ) * 180 / Math.PI, 2 );\n",
       "\n",
       "        var textArea = document.createElement( 'textarea' );\n",
       "        textArea.textContent = JSON.stringify( axis ) + ',' + angle;\n",
       "        textArea.style.csstext = 'position: absolute; top: -100%';\n",
       "        document.body.append( textArea );\n",
       "        textArea.select();\n",
       "        document.execCommand( 'copy' );\n",
       "\n",
       "        var m = document.getElementById( 'menu-message' );\n",
       "        m.innerHTML = 'Viewpoint copied to clipboard';\n",
       "        m.style.display = 'block';\n",
       "        setTimeout( function() { m.style.display = 'none'; }, 2000 );\n",
       "\n",
       "    }\n",
       "\n",
       "    function getCamera() {\n",
       "\n",
       "        function roundTo( x, n ) { return +x.toFixed(n); }\n",
       "\n",
       "        var pos = camera.position;\n",
       "        var pos_r = [ roundTo( pos.x, 4 ), roundTo( pos.y, 4 ), roundTo( pos.z, 4 ) ];\n",
       "   //     var up = camera.up; // up is always (0,0,1)\n",
       "        var textArea = document.createElement('textarea');\n",
       "        var cam_position = JSON.stringify(pos_r);\n",
       "        textArea.textContent = ',camera_position=' + cam_position;\n",
       "        textArea.style.csstext = 'position: absolute; top: -100%';\n",
       "        document.body.append( textArea );\n",
       "        textArea.select();\n",
       "        document.execCommand( 'copy' );\n",
       "\n",
       "        var m = document.getElementById( 'menu-message' );\n",
       "        m.innerHTML = 'Camera position '+ cam_position+' copied to clipboard';\n",
       "        m.style.display = 'block';\n",
       "        setTimeout( function() { m.style.display = 'none'; }, 2000 );\n",
       "\n",
       "    }\n",
       "                                       \n",
       "</script>\n",
       "\n",
       "<div id=&quot;menu-container&quot; onclick=&quot;toggleMenu()&quot;>&#x24d8;\n",
       "<div id=&quot;menu-message&quot;></div>\n",
       "<div id=&quot;menu-content&quot;>\n",
       "<div onclick=&quot;saveAsPNG()&quot;>Save as PNG</div>\n",
       "<div onclick=&quot;saveAsHTML()&quot;>Save as HTML</div>\n",
       "<div onclick=&quot;getCamera()&quot;>Get camera</div>\n",
       "<div onclick=&quot;getViewpoint()&quot;>Get viewpoint</div>\n",
       "<div>Close Menu</div>\n",
       "</div></div>\n",
       "\n",
       "\n",
       "</body>\n",
       "</html>\n",
       "\"\n",
       "        width=\"100%\"\n",
       "        height=\"400\"\n",
       "        style=\"border: 0;\">\n",
       "</iframe>\n"
      ],
      "text/plain": [
       "Graphics3d Object"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Curve definition\n",
    "alpha(t) = (2 * t * sin(50 * t), 3 * t * cos(50 * t), t^2)\n",
    "\n",
    "# Plot\n",
    "parametric_plot(alpha, (t,0, 2*pi), thickness=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e377bc35",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{align*} K(t) &= \\frac{4}{5} \\\\ \\end{align*} \\\\\\]</html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{align*} K(t) &= \\frac{4}{5} \\\\ \\end{align*} \\\\$$"
      ],
      "text/plain": [
       "\\begin{align*} K(t) &= \\frac{4}{5} \\\\ \\end{align*} \\\\"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Curve\n",
    "alpha(t) = (sin(2 * t), cos(2 * t), t)\n",
    "\n",
    "# Calculate the derivatives\n",
    "alpha_t = alpha.derivative(t)\n",
    "alpha_tt = alpha_t.derivative(t)\n",
    "    \n",
    "# Apply General Curvature Formula\n",
    "curvature = norm(alpha_t.cross_product(alpha_tt)) / norm(alpha_t)^3\n",
    "curvature = curvature.simplify_full()\n",
    "\n",
    "pretty_results((r\"K(t)\", curvature))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e4de205c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{align*} \\mathcal{T}(t) &= -\\frac{2}{5} \\\\ \\end{align*} \\\\\\]</html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{align*} \\mathcal{T}(t) &= -\\frac{2}{5} \\\\ \\end{align*} \\\\$$"
      ],
      "text/plain": [
       "\\begin{align*} \\mathcal{T}(t) &= -\\frac{2}{5} \\\\ \\end{align*} \\\\"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Curve\n",
    "alpha(t) = (sin(2 * t), cos(2 * t), t)\n",
    "\n",
    "# Calculate the derivatives\n",
    "alpha_t = alpha.derivative(t)\n",
    "alpha_tt = alpha_t.derivative(t)\n",
    "alpha_ttt = alpha_tt.derivative(t)\n",
    "    \n",
    "# Get Vector Product of Velocity and Acceleration Vectors\n",
    "prod_veloc_acel = alpha_t.cross_product(alpha_tt)\n",
    "    \n",
    "# Apply General Twist Formula\n",
    "torcao = (prod_veloc_acel * alpha_ttt) / norm(prod_veloc_acel)^2\n",
    "torcao = torcao.simplify_full()\n",
    "\n",
    "pretty_results((r\"\\mathcal{T}(t)\", torcao))"
   ]
  }
 ],
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