{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Examples of charts. Cartesian and spherical coordinates\n",
    "\n",
    "This notebook is part of the [Introduction to differentiable manifolds in SageMath](https://sagemanifolds.obspm.fr/intro_to_manifolds.html) by Andrzej Chrzeszczyk (Jan Kochanowski University of Kielce, Poland)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'SageMath version 9.6, Release Date: 2022-05-15'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "version()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "In every example of a manifold, some charts must be defined, so in the next four notebooks  we present examples of such definitions.\n",
    "\n",
    "In the present  notebook we are using the `EuclideanSpace` module, since some coordinate systems are predefined in this special case. \n",
    "\n",
    "Generally, in the `Manifold` module, the charts (or coordinate systems) and the transition maps must be defined by the user."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "### 2-dimensional case\n",
    "\n",
    "<br>\n",
    "\n",
    "**Example 2.1**\n",
    "\n",
    "First consider the case of 2-dimensional Euclidean space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "E.<x,y> = EuclideanSpace()  # number of variables determines dimension\n",
    "cartesian.<x,y> = E.cartesian_coordinates()  # Cartesian coordinates\n",
    "polar.<r,ph> = E.polar_coordinates()         # polar coordinates "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us check, that the domains of these maps are whole Euclidean space $E^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Euclidean plane E^2, Euclidean plane E^2)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cartesian.domain(), polar.domain() # domains of Cart.and polar coord."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us check the ranges of the coordinate  variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x: (-oo, +oo); y: (-oo, +oo)\n",
      "r: (0, +oo); ph: [0, 2*pi] (periodic)\n"
     ]
    }
   ],
   "source": [
    "print(cartesian.coord_range())           # Cartesian coord. ranges\n",
    "print(polar.coord_range())               # polar coord. ranges"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result: $r\\in (0,+\\infty),\\ \\ \\phi\\in [0,2\\pi]$ (periodic) shows that\n",
    "the predefined polar coordinates do not define a one-to one map onto an open subset of $R^2$ (the domain and the range of polar coordinates will be restricted below).\n",
    "\n",
    "The transition from the polar coordinate system to the Cartesian coordinate system is given by  $x=r\\cos\\varphi,\\ \\ y=r\\sin\\varphi$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x = r*cos(ph)\n",
       "y = r*sin(ph)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polar_to_cart = E.coord_change(polar,cartesian)  # polar -> Cartesian\n",
    "polar_to_cart.display()                        # transition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 9 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "po1 = {'thickness': 2, 'linestyle': ':'}            # lines parameters\n",
    "po2 = {'fontsize': 16, 'color': 'black'}            # text parameters\n",
    "t = var('t')                                     # symbolic variable\n",
    "p0 = parametric_plot((0.5*cos(t), 0.5*sin(t)),    \n",
    "                     (t,0,pi/6), color='green')                # circular arc\n",
    "p1 = parametric_plot((cos(t),sin(t)),\n",
    "                     (t,0,2*pi-0.2), color='green', **po1)       # dotted circle\n",
    "p2 = parametric_plot((cos(pi/6),t),\n",
    "                     (t,0,sin(pi/6)), color='blue', **po1)       # vertical dot-line\n",
    "p3 = parametric_plot((t,sin(pi/6)),              \n",
    "                     (t,0,cos(pi/6)), color='blue', **po1)       # horizontal dot-line\n",
    "a = arrow((0,0), (cos(pi/6),sin(pi/6)), color='grey')      # arrow\n",
    "t0 = text(\"$y=r\\\\; \\\\sin\\\\phi$\", (-0.4,sin(pi/6)), **po2)     # y=rsin(phi)\n",
    "t1 = text(\"$x=r\\\\;\\\\cos\\\\phi$\", (cos(pi/6)+0.1,-0.1), **po2)  # x=rcos(phi)\n",
    "t2 = text(\"$r$\", (1,0.5), **po2)                            # r\n",
    "t3 = text(\"$\\\\phi$\", (0.4,0.1), **po2)                      # phi\n",
    "(p0+p1+p2+p3+t0+t1+t2+t3+a).show(ticks=[[],[]], figsize=[3,3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The polar coordinates defined on the entire $E^2$ are not homeomorphic.\n",
    "They do not define a one-to-one\n",
    "mapping of $E^2$ onto an open subset of $R^2$, since points of the form $(r, \\varphi)$ and $(r, \\varphi+2\\pi)$ pass to the same point. \n",
    "\n",
    "To obtain homeomorphic charts on an open set\n",
    " and smooth invertible transitions we can restrict ourselves \n",
    " to the  open subset of $E^2$ with half line {y=0, x>=0} excluded.\n",
    "\n",
    "With this restriction in mind the inverse transition is well defined. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "r = sqrt(x^2 + y^2)\n",
       "ph = arctan2(y, x)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cart_to_polar = E.coord_change(cartesian, polar) # transition\n",
    "cart_to_polar.display()                          # Cartesian -> polar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://en.wikipedia.org/wiki/Atan2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The nonvanishing of the Jacobian determinants of the one-to-one smooth mapping $f$ at all points of its domain  means that the mapping $f^{-1}$ inverse to $f$ is smooth. This follows\n",
    "from the local inverse  function theorem. So let us check the Jacobians of the transition maps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r\n",
      "1/sqrt(x^2 + y^2)\n"
     ]
    }
   ],
   "source": [
    "print(polar_to_cart.jacobian_det())   # det(Jacobian(polar->Cart))\n",
    "print(cart_to_polar.jacobian_det())   # det(Jacobian(Cart->polar))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows (again) that the point (0,0) should be excluded from the domain of transition maps. \n",
    "\n",
    " As was mentioned  above, to obtain homeomorphic charts on an open set\n",
    " and smooth invertible transitions we can restrict ourselves \n",
    " to the subset of $E^2$ with  half line $\\{y=0, x\\geq 0\\}$ excluded.\n",
    " \n",
    " In the definition of the open set $U$, below we show how to make the corresponding restrictions.\n",
    " The round brackets in `(y!=0, x<0)` denote the inclusive OR (true if  at least one of two inputs is true).  Thus  `(y!=0, x<0)` is equivalent to $\\ \\ \\neg(y=0\\ \\&\\  x\\geq 0)\\ $ i.e., the half line $\\{y=0, x\\geq 0 \\}$ is excluded."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "r: (0, +oo); ph: (0, 2*pi)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# U is the open subset of E^2 with {y=0,x>=0} excluded\n",
    "U = E.open_subset('U', coord_def={cartesian: (y!=0, x<0)})\n",
    "polarU = U.chart(r'r:(0,+oo) ph:(0,2*pi):\\phi')    # polar coord.\n",
    "cartU = cartesian.restrict(U)        # Cartesian coordinates on U\n",
    "polarU.coord_range()                 # ranges of polar on U"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The command `coordinate_chart.plot` allows to plot coordinate lines of the chart `coordinate_chart`. \n",
    "\n",
    "<br>\n",
    "\n",
    "**Example 2.2**\n",
    "\n",
    "In our next example, coordinate_chart is polar (try polar.plot? to see more information).\n",
    "As the first  argument one can use both `polar` and `cartesian`. In polar coordinates the set \n",
    "$\\ \\ \\varepsilon < r < r_0$, $\\ \\ \\varepsilon < \\varphi < 2\\pi-\\varepsilon\\ \\ $ is an open rectangle. \n",
    "In Cartesian coordinates its image is the circle with a small sector and some small neighborhood of (0.0) excluded."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics Array of size 1 x 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# To define a set with some neighborhood of the half line {y=0, x>=0} \n",
    "# excluded it is sufficient to use appropriate ranges of parameters r,ph\n",
    "E.<x,y> = EuclideanSpace()  # number of variables determines dimension\n",
    "cartesian.<x,y> = E.cartesian_coordinates()     # Cartesian coordinates\n",
    "polar.<r,ph> = E.polar_coordinates()            # polar coordinates \n",
    "p0 = polar.plot(polar, ranges={r: (0.5,7), ph: (0.2,2*pi-0.3)},\n",
    "                number_values=10, color='grey')  # plot coordinate lines r,ph\n",
    "                                                 # in polar coordinates\n",
    "t0 = text(\"$\\\\varepsilon < r < r_0$\", (4, 4), fontsize=16, color='black')\n",
    "s0 = text(\"$\\\\varepsilon < \\\\varphi < 2\\\\pi-\\\\varepsilon$\", (4, 3), \n",
    "          fontsize=16, color='black')               # textual description\n",
    "r0 = p0 + t0 + s0                                   # combine previous plots\n",
    "p1 = polar.plot(cartesian, ranges={r: (0.5,7), ph: (0.2,2*pi-0.3)},\n",
    "                number_values=10, color='grey')         # plot r,ph lines in Cart.coord.\n",
    "p2 = point2d((0,0), size=50, color='orange')   # plot excluded neighb. of (0,0)\n",
    "p3 = plot(0*x,(0,7), thickness=5, color='orange') # plot excluded halfline\n",
    "p = p1 + p2 + p3                                    # combine plots\n",
    "graphics_array([r0,p]).show(figsize=(8,3))          # plot graphics array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "    \n",
    "**Example 2.3**\n",
    "\n",
    "The same plot with maps restricted to an open subset $U$ of $E^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics Array of size 1 x 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# continuation\n",
    "U = E.open_subset('U', coord_def={cartesian: (y!=0, x<0)})\n",
    "polarU = U.chart(r'r:(0,+oo) ph:(0,2*pi):\\phi')   # polar coord. on U\n",
    "cartU = cartesian.restrict(U)                     # Cart. coord. on U\n",
    "p0 = polarU.plot(polarU, ranges={r: (0.5,7), ph: (0.2,2*pi-0.3)},\n",
    "                 number_values=10, color='grey') # plot coord.lines r,ph in polar coord.\n",
    "                                    # transition from polarU to cartU:\n",
    "FU = U.continuous_map(U, {(polarU, cartU): [r*cos(ph), r*sin(ph)]}, name='FU')\n",
    "                                   \n",
    "p1 = polarU.plot(cartU, mapping=FU, ranges={r:(0.5,7), ph:(0.2,2*pi-0.3)},\n",
    "                 number_values=10, color='grey') # plot the image of coord lines r,ph\n",
    "t0 = text(\"$\\\\varepsilon < r < r_0$\", (4, 4), fontsize=16, color='black')\n",
    "s0 = text(\"$\\\\varepsilon < \\\\phi < 2\\\\pi-\\\\varepsilon$\", \n",
    "          (4, 3), fontsize=16, color='black')         # textual description\n",
    "r0 = p0 + t0 + s0                                     # combine plots\n",
    "graphics_array([r0, p1]).show(figsize=(8,3))     # graphics array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using coordinate lines one can easily plot images of any rectangle \n",
    "      $ r_0< r <r_1, \\ \\    \\phi_0< \\phi <\\phi_1$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PggULXjaB57AITt+rYV1zczNXr14lMTERlUqFKIqEhoYyZ86cIXuPhoaGboJMURQfE2TGxMSQlJTU77KVwTJt2jR+/etfExERweLFi9HT06OoqIilS5f2+pqeLFMGQ1NT0zNZ3yYIAubm5tTW1jJr1ixCQkK6CS9v3bqFQqFgzJgxjB8/ngkTJjyx8FIQBKmXe/bsWRITE0lNTSUjI4Pg4GCCg4NlzdQQ8r0ITk1NTcTHx5OUlATAlClTCAkJ4dy5c6SlpREaGvpEw7impiZJkJmfn49CocDV1ZUlS5Ywbtw4zMzMuu3v5ubG5cuXKSsreyzXMhRMmzaNvXv3snHjRlpbW6V2/P73v+/1NX/84x/57W9/+8Tv3dTU9JhX1NOiqKiIjo4O3NzcehVeZmZmEhERQUREBK6urnh7e2ulSeuLjo4Obt26hb+/P7NmzeLKlSvEx8eTkJAgXVtykHpyXurg1NraypUrV7h27RoAU6dOZerUqdKU8/Tp07l16xYZGRn4+PgM6NgdHR3cu3ePtLQ07t+/D3QGnRUrVvSrOnZ2dkZPT4/s7OynEpxu377Nj3/8Y/7jP/6DWbNmkZSURFFRET/72c945ZVXaG5ufkwh7uzszD//+U+pR9nS0sIvf/lLPv/8c0xMTBAEoZtFr56eXjeLXmNjY4yMjKirq0OlUtHQ0ICJiclTXXibnZ2NsbFxj8HQwsJC6s00NzdLwstTp05x+vTpbsLLnhxD++LGjRu0tLQwbdo0zMzMWLRoEdOnT+fKlSskJCSQmJjItGnTCA4OftmGe8+UlzLn1NHRQWJiInFxcSiVSqZMmcL06dN71MHs3buX+vp63n33Xa1mYDSCzFu3btHW1saoUaMkQeZAdDZ79+5FrVazZcuWAX22rjknURRpaGigurpaMm6rra0lJSUFHR2dHpO1enp6mJiYYGhoKHmA6+npSUJMHR0dBEGgpaWFNWvWcOTIEcmmV6lUSja9HR0d3Sx6W1paerTp7erQ2dWe19raWjKmGyw7d+7E0tKSdevWaf2axsZGMjIySEtLo7S0FCMjI3x8fPDz89NKeKlWq/nHP/6Bk5NTj+/b2NhIXFwcSUlJGBgYEBoaSmBg4IumPJdzTkONWq3m5s2bxMTE0NjYiL+/P6GhoY8Nq7oyffp0vv76a+7fv9+riVt7ezu3bt2SJAAaQebkyZP7nZrvDTc3Ny5cuEBHR4dWMz4tLS2UlZUxdepUCgoK2LlzJ1VVVVJAEAQBCwsLLC0tpQTxm2++Kfk/RUdH86c//Yns7Owe9UaPosk5zZs3T+sc0oMHD/j73//OokWLsLKyesyet6ioqFs1FwMDA0khbm9vj52dHfb29lolsVtaWigpKSEgIECrtmkwNTWVelQVFRXcuHGDmzdvcu3aNZycnAgICMDb27vX7yQjI4Pa2lo2bNjQ6/HDwsIICQkhNjaWc+fOce3aNebOncvEiRNlCcIAeGmCU35+PmfPnqWsrAwvLy/mzp2rVeAYPXo0o0aNIi4u7rHgVFVVxfXr10lLS6O9vR1PT0/mzJmDu7v7Ew9X3NzcOH/+PIWFhY9pdDo6OigtLZXEmMXFxdKPet68edTV1WFqasqkSZPw8PDg66+/pqioSDKaU6vVbN++nYkTJ7Jo0SJJha3RTvXFk+icNKJRjViyJ5RKJQ8ePKC6ulpaglNWVsatW7ek97SyspI0XqNGjcLBweGxoVdeXh4AY8eOHXA7Ndja2rJw4ULmzZvHvXv3SElJ4cSJE5w/fx4/Pz+CgoKwtLSU9hdFkfj4eMaOHdvvcNzCwoIVK1YwdepULly4wOHDh0lISCAsLGzIZ4VfVl744FRbW0tkZCS3b9/GycmJN998E2dnZ61fLwgC06dPJzw8nMLCQkaNGkVOTg7Xrl0jKysLY2NjgoKCCAgIGPC0f1/Y2tpiampKdnY2Tk5O3YzTSktLUavV6Onp4ejoiJmZGbt376a0tJSamhrUajUA27Zt46uvvqKkpISCggLp2K+//joNDQ188skn/OxnP8PNzY3169fzt7/9rd92/ehHP+JHP/qRJCUYCBprlv4sem1sbLCxsWH8+PHSdpVKRXV1NWVlZZL4MjMzE6VSiY6ODo6OjpLjpbOzM9nZ2VhZWQ3JjKeOjg4TJkxgwoQJ1NTUkJycTGpqKlevXmX8+PFMnToVFxcXsrOzKS8vZ9GiRf0f9CG2trZs2rSJ3Nxczp07x65du/Dx8RlQj/T7ygubc1IqlcTHxxMXF4eRkRHz589n0qRJg+o2i6LIp59+ip6eHmq1moqKCuzt7QkODsbb23vACdP+UKlUFBcXc/r0aR48eIBSqUQURczMzCQxprOzM3Z2dkOSUG5sbORvf/sbGzdu7BYQ+mIwOqe0tDSOHTvG//k//2dIxIkqlYry8nIKCwspKCggPz+fpqYmaXGyra0tixcvxtHRccgT7x0dHdJwr7KyEgcHB5RKJbq6umzfvn1Q15larebGjRtER0fT0dHBrFmzCA4OHo75qGEx9nwhe073798nIiKCuro6QkJCCA0NHfTiTKVSSUpKCs3NzbS0tODi4sLWrVtxdXUd0vxAc3MzWVlZZGVlcf/+fdra2tDT06Ojo4OFCxfi6emJlZXVU8lJaBL1T9t0rqmpSXI5GAo0PSaNTkwURaqrq8nIyODixYtUVlaya9cuSXipcbwcCuGlnp4eAQEB+Pv7k52dTXR0NJWVlZiampKSksLkyZMHHFQUCgX+/v54eXlx8eJFoqKiSE1NZenSpbi6uj5xm182Xqjg1NjYyLlz50hPT2fMmDFs2rQJGxubQR2ro6OD5ORk4uPjaWpqwsvLi9zcXKysrBgzZsyQtLe+vl4SZObn50uCzKlTp+Lh4YGJiQkff/wxZmZmg06sa4NCocDY2Fir4PQkOaempqanajInCAIjR46UZvnef/99qqurpaCvEV66uroyYcIExo8f/8TtEQQBd3d3kpOTaW5uxsHBgVOnTnHp0iVmzJiBn5/fgHvWhoaGhIWFMXnyZCIiIvj666+ZPHkyCxYskKvJdOGFCE6iKJKamkpkZCQKhYLVq1cPeginVCpJTk7m8uXLNDc34+vry4wZM7C2tubq1atERUUxe/bsQecyGhsbJUFmQUGBZA+7dOlSxo0b99iPZeTIkeTk5PRa422oMDExobGxsd/9njTn9Czsb3NycnBycsLY2BhjY2NJeFlfX/+Y8HL06NFMnDgRLy+vQf/wq6qqyMzMZPny5fj7+1NZWcnly5c5c+YMcXFxhIaGDqonZW9vzxtvvEFKSgqRkZHcu3ePsLAwvL295Vk9XoDgVFtby8mTJ8nJycHX15eFCxcO6iLTjPdjY2NpaGjA19eX0NDQbrMx/v7+XLp0iYSEhAElPTs6Oro5ZAqCwNixY1m1ahXjxo3rc5jh5ubG3bt3EUXxqV6QGrte+J/KvF2FmBoTOaVSiVqtlnyjbt26hbm5eTcRpp6enqSRMjAwwNDQEB0dnWcSnERRJDc3l8DAwMeeMzc3Z8qUKUyZMoWWlhZJeBkREcGZM2fw8PDA19d3wMLLK1euYGZmJgl1bWxsWLNmDaGhocTGxnLq1Cni4+OZPXv2gG+agiAQEBCAp6cnZ8+e5ciRI2RkZLB06dI+JTDfB4ZtQlwURZKTk4mMjMTQ0JBly5ZpVUyyp+Pcu3ePqKgoqqqqmDhxIrNnz+7Vmyc6OpqEhAR+8pOf9LsEoSdBpq+v74Du0nfv3mX//v38r//1v554aCeKIo2NjdTU1HSz621sbCQ/P5+Ojg4UCkWPYslHGahNr4GBAUqlEkNDQ1xcXDA1Ne1mz2tlZSUpzZ+EkpISdu7cybZt27TO0zQ1NUmOlyUlJZLw0t/fH1tb2z5fW19fz8cff8zcuXOZPn16j/uUl5cTExPD3bt3sbe3Z/78+YOWOGh8zlUqFWFhYfj4+DyPXtSw6LYNy+BUWVnJ+fPnuX//Pn5+fixcuHBQSc7S0lLOnTtHfn4+Y8aMYf78+f3qfJqamvjoo4+YMWMGs2bNeuz5jo4O0tPTuX79OqWlpZiamjJ58uRBCzLb2tr485//zOLFi3vsDfSEZtq9oqJC0gppLHu7WuIaGRlhbm6OmZkZtbW1NDU1MWPGDGmpSU9WvTo6OigUChobG7GysqK6urqbTa+mGIKm16VRh7e0tBAbG4ulpSWmpqaSAFOjfYL/sejVVPu1sbHB1tYWa2trrWfb4uLiuHTpEr/85S8HNctVWVlJamoqaWlpNDc3M2rUKIKCgvDy8uqxN3X+/HlSUlL4yU9+0u9SlIKCAqKioigsLGTs2LEsWrRoUDnR5uZmyTVjwoQJLFiwoFsP/xkgB6eeSExM5MyZMxgaGrJ69Wo8PT0HfIzGxkaio6NJTU3FxsaGBQsW4O7urvUd6PTp09y+fZv3339fmnmqra2VVqG3trbi4eFBQEAAHh4eTzyN/eWXX2JiYtKj6litVnPmzBkOHTpES0sLI0aMwNHRUaplZ2pqKjljWltbS/XcjIyM+NOf/sS3335LWVkZYWFhBAYG8h//8R99tqVrQvzevXtaSwlEUeR3v/sdixYtYsqUKdL2trY2amtrJXve6upqSYCpSdDr6up2s+Z1cnLCxsamx/O6Z88edHV12bx5c79t6guVSsXdu3dJTk4mJycHY2Nj/P39CQoKkj5vS0sLH330EUFBQcyfP1+r44qiSGZmJlFRUTx48IDAwEBmz549qFTE7du3OX78OB0dHaxcuVKq0fcMGBbBadjknNrb2zl79iypqamYmpqiVqt7VRn3hlqtJjExkYsXL6JQKKTeyECDx7Rp0yQhnoODA1evXiUzMxMDAwP8/f0JDAwc0jvZmDFjSEhIQK1Wo1QqKSwsJD8/n8LCQoqLi+no6JBcH69cuUJAQAALFy7E1ta216HnypUrKS8vZ9euXdJsU3p6ercSUT0x2IR4a2srarX6sZyTgYEBdnZ2Pa5ba25ulrzRy8rKKCwsJCUlBVEU0dfXZ9SoUYwaNQpXV1dJVV1QUKB1oOgLHR0dvLy88PLyoqqqiqSkJBITE7ly5QpeXl6EhISQnZ2NSqVi6tSpWh9XEAQmTJiAh4cHiYmJXLp0ifT0dObNm4efn9+ArkUnJyfJ5vjYsWOUlJSwYMGCIdfdDVeGxacsKyvj0KFD1NfXs3z5cjw8PPjss884efIkGzdu1KrHU1BQwOnTp6moqCAwMJC5c+cO2rZixIgRODs7c/78eVQqFdbW1ixZsgQfH58hN7tXq9WYmprS1tbG559/TlVVFWq1GmNjY1xcXJg9e7a0hENPTw9BEHjjjTcYPXp0r8c8e/YssbGx5OTkYGVlBXT2YNLT02lqanoqiVZt1OGPYmxszJgxY7pJN9rb26WlO0VFRVL1Xh0dHaytrVGpVJiYmPQbZAfCyJEjCQsLY86cOaSmppKYmMjOnTtRKBSMHTt2UEl+XV1dpk2bhq+vL1FRUZw6dYqUlBSWLl2q1dpGURQ5fvw4BgYGvPPOO9y6dYvIyEjy8/NZu3btoCU0LxLPdVinSXqfPXuWkSNHsm7dOilRnZmZSXh4uDR92xstLS1ERUWRkpKCk5MTS5Ys0erL7wm1Ws2dO3e4dOkSFRUVQOd6tIULFw5pUrKpqYn79+93E2RC5yxQUFAQrq6ujBw5ssf31MYJ84c//CH37t0jMDCQb775BhMTE1atWoWJiQnvvPNOjxYjPZnNOTs7az2s05Q8/9GPfjSkhQBEUaSiooK8vDwSExOpqakB6Ca8dHd3H1L/JLVazalTp0hNTQXAwcGB0NBQxo0bN+jroLCwULp5TpkyhTlz5vSZw7p69Srnz59ny5Yt0trLsrIyDh8+TF1dHcuWLRuwzc8A+H4P69rb2zl16hS3bt0iMDCQRYsWdeuujh8/Hj8/P86ePYurq6vUA+jK7du3iYiIQKlUsmTJEgIDAwe9fCUjI4PY2FiqqqoYO3YsS5YsIS4ujtzc3Cf6nBrq6uokQWZBQcFjgsxLly7R3t5OUFDQE79XTk4OcXFxGBoacvToUaqqqvjFL37B+vXrexViPqnZ3GB6TtogCII0LLxx4waTJk0iKCiom/BSEARcXV0lx8uh6Bnm5eXh5eVFQEAAly5dIjw8HDs7O2bNmsX48eMHfJ05Ozvzgx/8QCrUcOfOHZYuXdpjTrW8vJwLFy4wderUbovC7e3t2b59O6dPn+bo0aPk5+cTFhb2svqYP5/gVFVVRXh4OPX19axdu7ZXAeKiRYvIy8vj6NGjvPHGG1I3vrGxkYiICO7cucP48eNZvHjxoBZRiqLI3bt3iYmJoaKiAnd3d1auXCnlN0RR7NdOpS803kEZGRkUFhaio6ODm5sby5Ytw9PTs5sgU+NS0N7e/sRDR7VajSAI7N27V8obNTc3k5GRwYMHD3p8za9+9St++tOfSn9rek7a0tjYiEKhGFLP7q40NTVJljFdHS/r6+u5d+8ed+7c4dy5c5w5c0YSXg7UY0vD7du3efDgAevXr8fBwQE3Nzfy8/OJjY3lwIEDODg4MHfu3AFXYVEoFEybNg0vLy9Onz7Nvn378PHxISwsTOr5KZVKjh49irW1NfPmzXvsGPr6+qxatYrRo0dz5swZSkpK2Lhx45AuSh8uPPPglJmZybFjxzAzM+Ptt9/uc+xsYGDA6tWr+fLLLyUlbnp6OhEREQiCoFX56d4oKCggMjKSoqIiXF1de3QzGD16NE5OTsTHx2sdnDSCzLS0NLKzs6XlD6tXr2bcuHG9duXHjh2LWq0mPz9/UIGwKw4ODjg5OXVLaE+cOJHU1FRKSkp6fI1GVjBYNALMp6XJ0fRgH7WXMTc3JzAwkMDAQFpaWsjMzCQjI4MzZ85w9uxZPDw88PHxwdPTU6tEssYWxc3NrZstyujRo9m6dSu5ubnExMSwd+9eXF1dmT9//oAnbkaMGMHmzZtJS0vj3LlzZGdns3z5csaNG0d0dDRVVVW8/fbbvbZXU1jB0dGR8PBwvvjiC9auXftE9jHDkWcWnERRJDY2ltjYWMaPH8+qVau0+jE4OzszY8YMYmJiKCgoIDs7Gy8vL5YsWTKoIUR1dTWRkZHcvXsXBweHbmP6R9HYqRw4cICioqI+fXjKysokQWZrayvOzs4sWbKEiRMnapUPsba2xtzcnJycnCcOTtOnT+fgwYM0Njair69PfX09ycnJtLe3U11dTXR0tGTVq3lo9EsahXhLSwvQKS0wMjJCoVA8ZtGrUYcbGRmRm5uLQqGQ6v6Zm5sP6eRBTk4ONjY2fQ7ZjIyM8PPzw8/Pj6amJsnx8uDBg1oLL3NycigrK+vVoXTMmDG4urqSlZVFVFQU//rXv5g4cSLz588fUO9FEAQmT57M2LFjOXXqFPv378fd3Z379++zYMECrXzY7e3t+cEPfsDhw4fZu3cv8+fPJyQk5KVZ+vJMEuLt7e0cO3aMO3fuMGfOHGbOnDmgE3j//n327duHKIosX76cyZMnD/gLaG1tJTY2lsTERMzMzJg3b55Wa5g0diojR47klVde6fZcR0cHGRkZJCUlUVxcLAky/fz8esyR9cfx48cpKSl5rOZbY2Oj5FPu5+fH//t//485c+ZgZWWFi4sLv/rVr6iurubdd9+lpqaGiooKrl69yogRIx67+yoUCszMzDAyMpKEmF1FmDdv3pQC2bFjxzh58iRGRkaSCFOpVD5m0dvc3ExDQwOPXktGRkaMGDECS0tLyZ7XxsaGkSNHDmj4J4oiH3/8MePHjycsLGzA5/VR4aWLiwtBQUE91if8+uuvaWtr08oWRa1Wk5aWRkxMDM3NzYSEhDBz5swBB2VRFElMTOTs2bPo6uqyZcsWXFxctH69Wq0mOjqa+Ph4fH19WbZs2ZPKDYZFdHvqwam+vp59+/ZRXV3N6tWrmTBhgtavValUxMTEEB8fj5OTE2VlZUyePJlly5ZpfQxRFLlx4wZRUVF0dHQwc+ZMpk6dOqAkYkpKCidPnpRmohoaGkhMTCQ5OZmWlhbGjh1LYGAgnp6eTzS9fevWLY4cOcLPfvazbvmoixcvSuWrLC0tcXR0xMHBQeoFaBb0aqx6NYExOjqamzdvolAomDVrFr6+vigUCl599dV+2zJQP6ddu3ZhYWHBnDlzutnzagSYmiU1GjQl1u3s7CTxpYWFRY8Bobq6mk8++YRNmzYNSpSrQaVSkZmZSVJSEnl5eZiYmBAUFERgYCAmJiYUFxfzr3/9a8Dpgvb2duLi4rh69SqGhoYsXLhwwIt3Dx8+zL1797C2tqasrIzZs2czY8aMAV1PN2/e5MSJEzg4OLBx48YncWQYFsHpqQ7rSktL2bdvHwqFgrfeeksrA3kNtbW1HDp0iNLSUubNmycJIyMiIvD09NTqIi0tLSUiIoKioiImTZrEggULBjWT4+PjI/nvGBgYkJ6ejq6uLpMnT2bKlClDZnei0fvk5OTg4+ODUqmkqKgIHR0d9u7dS1FRkTTcMjc3l3y3bW1tJZV41zvmo0OTkydPUlpaOiRtfZTm5mapYnFv56Ojo0NSh5eXl1NRUUFaWhpxcXEAksPAqFGjcHFxwdHREV1dXXJyclAoFH1qu7RBR0dHSpRXVlZy7do14uLiuHz5Mj4+PtTV1WFlZTWgGyh0Jqnnzp2Lv78/58+f58iRI6SkpLBkyRKt9Ei3bt0iPT2d1atX4+3tzcWLF4mJiSEnJ4e1a9dqfc36+PhgbW3N/v372bVrF5s3b36h9VBPred07949Dh06xMiRI9m0adOAgsLdu3c5duwYhoaGrF27ttvs2b59+6ShT285p/b2di5evEhCQgIjR45kyZIlT2TmVVBQwMmTJ6mqqsLMzIyQkBD8/PyGfGZKrVbzySefSOWWioqKUKlUGBgYSGppJycnHB0dB5Vvi46OJi0tjZ/85Cf97jvQntOf/vQnZs6c2evi2L5oaGigtLSU4uJiioqKKCoqor29HV1dXZydnWloaEBHR4cf/OAHQ+542dLSQnJyMlevXqW5uRl7e3uWL18+aK0cdKYhzpw5Q21tLTNmzGDmzJm9DrPq6urYsWMHHh4erF27Vtqel5fHkSNHUKlUrF27tte8aE/U1tby3Xff0dDQwIYNGwbjTzYsek5PJTilpKRw6tQpPD09WbNmjdZjcLVazYULF7hy5Qrjxo1j5cqVjyWTGxsb2bFjB87Ozj2qx7Ozszl58iRNTU1SJdjB2qDm5eVx6dIlcnNzGTlyJLW1tfj7+7N48eJBHa8nmpqaJM1Odna2JIQcN24crq6uuLq6YmtrOyQ/ymvXrhEZGcmvf/3rfoccAwlOSqWS3//+96xatWpI1n+p1WrKysrIz88nNzeXrKwsoDOHNXbsWEl4OZTGbMeOHSMzMxMTExNqampwd3cnNDR0QHKKriiVSi5fvkxcXByWlpYsX778sZ6fKIp88803VFVV8d577z12rTc1NXHkyBFycnKYNWsWs2bN0nqo2NraysGDB8nLy5N6ZANgWASnIR3WiaLIpUuXuHjxIoGBgSxevFjrH1VTUxOHDx8mLy+PBQsW9DrrYGpqyvLlywkPDyc1NVVSj7e2tnLu3Dlu3LjBmDFj2Lp166CS0tCp5o2OjiYvLw97e3s2bNjA+PHjiY6OJjExkdmzZz+RIrm2trabIBM611FNnToVQ0NDzp07x7x584a8S25qaopKpaKtra3XXt9gnDCHWoCpUCgke15nZ2eysrJYsmQJDQ0NZGVlkZ6eLpUG1wgvn6RYQENDA+np6cyePZtp06aRkZHB5cuX2b17N+7u7syZM2fAPSldXV3mzJmDt7c3J0+e5KuvvpIWEGtu1gkJCeTm5rJly5YerycTExNeffVVLl++zMWLFyktLWX16tVa9dgNDQ3ZvHkzJ06c4PDhwzQ2Ng5ojeBwYMiCkyiKREREkJSUNOAZuZKSEg4cOIBSqZT8u/viUfV4TU0NJ06coL29neXLl+Pn5zeo6dSKigqioqLIysrC1taWjRs3dluyEBwczNWrV7l+/TqhoaEDOnZDQ4MkyNTkkcaOHcuKFSvw8PCQkpcdHR1ERUVJU+dDiSZ4NDU19XqBD2bh79NSh0Nn/s3AwICAgAAUCgVz586loaGBu3fvkpmZyfnz5zl79iwuLi5SPmmg7UhISEBXV1daJD5p0iS8vb0lr/KdO3cyYcIE5s2bN+D8oo2NDW+88QaJiYlcuHCBrKwsVq1ahaGhYY8q8EfRTGY4Ojpy5MgRdu7cycaNG/v1oYLOHNuqVaswMzPj3LlzNDY2Mm/evBdGajAkwUmlUnH8+HHS09P7XQv3KOnp6Rw/flwKBtreAcPCwsjNzWX37t00NTUxduxYli9fPih73fr6emJiYkhLS8PS0pK1a9f2WADR1NQUPz8/rl27RkhISL8zfh0dHWRmZnLz5k2ys7NRKBS4u7uzZs0aPD09e9R56enp4ezsTE5ODsHBwQP+LH3RNTgNpWf50w5Orq6u3XrgZmZmkvCytbVVEl6eO3eOc+fO4e7ujq+vr1bCy9bWVpKSkggMDOwWsAVBwNvbGy8vL27evMnFixf59NNPCQgIYPbs2QP6rIIgEBwcjIeHB8ePH+err77C2NgYKyurHlXgPeHh4cH27dsJDw9n165drF27VqtJIUEQmD9/Pqamppw7d47W1laWLFnyVMvEDxVPHJyUSiUHDx7k/v370o9aG0RR5OLFi1y6dIlJkyaxfPnyAU3vV1dXo1araWpqwsPDg02bNg34jtDR0cGVK1eIj49HT0+PsLAwAgIC+sxRdbVT6epb1JXy8nKSk5O7CTKXLl2Kl5eXVsNBNzc34uLiUKlUQ1o2SPODamhooKmpSRJitre3097eLmmYutr0pqSkYGZmho6OjiTC7GrRa2RkJFUHHurg1N7eTmFhYZ+WyYaGhpLZX3Nzs+R4efDgQYyNjSXhZW+90OvXr/dpi6JQKJg8eTLe3t4kJiZy+fJlbt68SWhoKMHBwQPSE1lZWbFt2za+/vprCgoKMDQ05MGDB1r3kK2srHjrrbc4cuQI+/btY968eUyfPl2r637q1KkYGBhw8uRJ2traWLVq1XAsSdWNJwpOHR0d7N+/n4KCAjZt2oS7u7tWr1MqlRw7doyMjIwBnWDoDGoJCQlERUVhZ2eHp6cnycnJlJSUaL2MQBRFaS2WZiw+c+ZMrcbylpaWeHl5cfXq1W5eUSqVitu3b3P9+nUKCwsxNTUlICAAPz+/AfdS3NzciI6Opri4GBcXFy5dusRf/vIXkpOTKS0t7dOVoKtVb01NDbdu3eLo0aM4OjpKN45Dhw712waNZOH8+fNaL2v5/PPPMTMzk+x5R4wYIYkvB7O0JT8/H7VarfVMlbGxseQhXllZSUpKCjdv3iQhIQFXV1eCgoIYP3689J0plUquXbuGr69vv7PJGguUyZMnExsby4ULF0hOTiYsLGxA2qv8/HwKCgqYOnUq2dnZfPHFFyxatIiAgACtzo++vj4bN24kJiaGCxcuUF1dzbJly7QKNH5+fhgYGHD48GGUSiXr1q0b1gFq0LN1ra2thIeHU1xczKZNm7SermxqaiI8PJzS0lLWrFkzIE1Jc3Mzx44dIysri5CQEObOnYsgCOzevZvW1lbeeeedfmcGq6qqOHPmDDk5OXh6erJo0aIBJ85LS0ul9Uxubm4kJSVx/fp1GhsbGTNmDIGBgYwbN27QX7xareYvf/mLZK1x5swZ4uPj8ff3Z+3atVJwam5upqysjLKysm6WvV09wpubm1GpVNTX17N69Wpu3LiBq6srfn5+GBkZYWhoiIGBAXp6epJKXKFQPDZbp1KpJJteTU9Low5PSkqitLSUSZMmdRNgdq32YmBgIFnzasSX9vb2ffYkz549y507d3j//fcHnSdRKpXcuXOHpKQkCgoKpCII/v7+ZGRkcPr06UH5t1dWVnL27FnpOgoLC+vXgLC1tZUdO3ZgZWXF1q1bUSqVnDt3juTkZLy8vFixYsWA1jempaVx4sQJRo8ezYYNG7SWtty7d48DBw7g5ubGunXrevrNDIuk1KCCU2trKx999BFKpZItW7ZoLY578OAB3377LW1tbWzatGlACyaLioo4ePAgHR0drF69utv6s+rqaj7//HN8fHx6VY8rlUri4uKIi4vD3Nx8wHe8R/nyyy+prKyko6MD6BTATZ06dciS2AcOHKCxsZE333wT6OyZlZWVsW7dOklCUVtbC/yPza2tra3kz21lZcWPf/xj3N3d0dHR4dixY9y4cYPPPvtMGmb2xUCkBEeOHKGuro433nij2/aOjg5JHa7xOa+oqKCiokKaDbSyssLR0ZFRo0bh7OyMvb291LPZsWMHjo6OrFy5cjCn8DHKysq4du0at27dQkdHB0EQcHFxGbTlb9ceeHNzM7Nnz2bq1Km93pQOHz5MVlYW7733Xrfc6O3btzlx4gQmJiasX79eq3V1GvLy8ggPD8fc3JxXX31V65xtVlYW+/fvx9DQkJ/85CePDk+HRXAa1LBOX18fe3t78vPzKS4u1io4lZaWsnfvXgwMDHjrrbe0trkVRZGkpCTOnj2Lo6Mj69ateyzpbW1tzcKFCzl9+nSP6vHCwkJOnDhBTU0N06ZNIzQ0dNAeOFVVVVy+fJnCwkJEUcTHx4dFixYNeTHEMWPGEBERQUxMDEVFRRQUFKBUKpk3bx5KpZJJkyZJy1isrKweS3B++eWX3L9/n2+++Ybf/e530nYTE5MePZ16MpvTlt5KQunp6UlBsytqtZrq6mpKS0spKSmhuLiYO3fuoFKp0NfXx8XFBXt7eyoqKpgxY4bW7egPe3t7Vq5cybx58zh9+jSZmZlkZ2dz4sQJZs6cOWDrZUEQ8PLywt3dXRpm3bp1ixUrVjwmPdCowNesWfPY9evl5YW9vT0HDx5k165dLFu2TGu9mMZR49tvv2XXrl289tpr/d4gRVGkqKhIssIerra/gx7WiaJITEwMly9fZsGCBUybNq3XF+bm5rJ//35GjhzJ5s2btU6cdnR0EBERwY0bN5gyZQoLFy7s9a7Uk3q8vb2d6Ohorl27hpOTEytWrNBqCrYnqqqqiI2NJT09HTMzM6ZPn86NGzcwNDRk27Ztgzrmo/QkyNTV1ZVWwru4uODq6sqhQ4f6dMLMyspixowZXL58GU9PTz744AOp53T06FFqa2sf6+V88MEHPZrNadNz0rY31hdKpZKSkhIKCgrIy8sjLy8PlUr1VISXoiiyc+dO9PX18fT05MqVKzQ3N+Pj48OsWbMG7Q9fUlLCyZMnKS8vZ/r06cyaNQtdXd1eVeCPolQqOX36NDdu3CAoKIhFixZpnRqor69n79691NfX8+qrr/bqoNF1ImrevHm9Bf8Xt+cEnXcNzWLUyMhIgB4D1N27dzl48CCjR49m48aNWqvF6+vrCQ8Pp6KiQivlsSAIrFixgh07dnDixAmmT5/O8ePHqa+vZ8GCBUydOnVQ06e1tbXExsaSlpaGmZkZS5cuZfLkyejq6mJmZsbBgwf7tVPpiwcPHkiCzMLCQuB/BJnJycmMHz++24++P3GkSqVi8+bN/Pa3v+1x2GpsbExxcfFj25/EbG4oimnq6uri4uKCi4sLM2bM4MiRIxQVFeHt7c39+/cl4aWLi4tUanywVZlzcnIoLS2V7HKCgoJISUkhLi6OW7du4efnx6xZswa8DtPR0ZG3336b+Ph4YmNjuXv3LqtWrSIyMhIDAwOWLFnS7zlYsWIFTk5OnDlzhoqKCtavX6/VuTU3N+eNN97gu+++Y8+ePT3mgbUMTMOGJ16+0lcPSjNTNH78eNasWaN197G4uJj9+/ejUCjYuHHjgNS5GRkZ0myUk5MTq1evHpSmp6WlhcuXL5OYmIihoSEzZ84kICCg22dQq9X885//xMbGho0bN2p9bI0iOSMjg+LiYkmQOX78+G6CzJMnT1JQUMCPfvQj6bX9eYjX1tZiaWnZ7Y6rVqsRRREdHR127dpFaWkp//7v/95nG7XNOYmiyH/913+xePHiIbEY1hzzww8/xNvbm4ULFwKd5+zevXtkZmaSk5ODWq3G2dmZiRMn4u3tPaDguGfPHlpbWx+zReno6OD69evExcXR0dFBSEgI06dPH5QJX3l5OUePHqWiogJRFHnttdcGZAZXWFhIeHg4enp6vPLKK1ovmu/o6CA8PJy8vDzWr1/PuHHjgAEHphe756Shtx7UjRs3OH78OL6+vqxYsULrXsvt27c5evQo9vb2A7Z9qKmp4cqVK0CnPmXVqlUDDkwqlYrr168TGxuLWq1m5syZhISE9Njj09iuahYF92Xsr5k1SktLk1bZa7r5np6ePR7fzc2NlJQU6urqtO4lmJubc+vWrW7b/vnPfxIdHc2hQ4doamqShkxDMY3c0tKCKIpPYs/xGJWVlTQ0NHSTEJiZmREQEEBAQACtra3cu3eP9PR0zp8/LwkvJ0+e3O8saUlJCbm5uaxbt+6xGUA9PT2mTZuGv78/8fHxXL16leTkZObMmYO/v/+Aet52dnasWLGCf/3rXwBcunSJkSNHav09Ojs7s337dvbt28fu3btZt26dViaEmmB25MgRDhw4wNq1a5kwYcIL1WPSMCSZsEcDVFFREXfu3MHf359ly5ZpNQ0siiJXrlwhKioKb29vVq5cOaBE3c2bNzl9+jQmJiZs27aNEydOcOzYMd58802tL6rs7GzOnDlDTU0Nfn5+zJkzp98fnY+PDzExMVy5coUVK1Y89nxlZSVJSUncvHmT1tZWXFxcWLZsGV5eXv1O/Wq65Xfu3Om2b25uLjdu3OhmNldcXMyePXtQKBSPLfK0tbXF0NAQb29vaRFtU1NTjz2iga6t08gFhlKAmZOTg46OTq8TLYaGhvj4+ODj4yN5o2scL42NjfH19SUgIKDHG1N8fHy/tiiGhobMmzePoKAgoqOjOX36NElJSYSFhWntbqFUKjl+/Dg2NjYsWrSI48eP89lnn7FixQqt5TMWFha8+eabHD58mH379mndO9XV1WXdunUcPXqUQ4cOMW7cODIzM1+owARDuLZOE6AaGhq4ceMGo0aN0jowaaraJiUlMXPmTObMmaO1rqWjo4MzZ86QmpqKj48PS5YswcDAgDVr1rB7924uX77cY1nxrtTV1XHu3Dnu3LnD6NGjWbdundbTubq6ukydOpXo6Ghmz56Nubk5arWazMxMrl+/LpmaDUaQaWxsjIODA6mpqfzwhz+UtmtyQ9u2beOrr76itLRUWkD8KJphu4WFBZmZmRQVFQFw7tw5BEGgtbVVmqnT2PS+8cYbtLS08Jvf/IaPPvoIIyMjSSGup6cnKcSNjIwkKUVubi4tLS1YWFhgYWGBoaHhoLVJubm5uLi4aDWjamxsTFBQEEFBQVRUVJCamsqNGze4evUqbm5uTJkyBU9PTwRBoLq6mtu3b7Ns2TKtbljm5uasWrWKoKAgzp49y9dff42Pjw8LFizo96alEUhu374dOzs73n33XU6ePMmBAwcIDg5mwYIFWvVcNaLLc+fOERERQW1tLfPnz+/33CoUClavXk1lZSWZmZlMnTr1hQpM8BQsU9RqNUeOHCEjI6PfWTzovMMcOXKEzMxMli1bNqB1eTU1NRw4cIDq6mqWLFnymH2vJhf25ptv9piwVqvVXLt2jZiYGAwMDAblYAid0/AffvghPj4+WFpacu3aNerq6vq0g9WWqKgobty4wc9+9rM+26VSqSQdkUaMWVNTw4MHD7qJMgVBQBRFRowYwYgRI3q06tXR0aG5uZmwsDDOnj2LsbFxN4ve9vZ22traaGlp4cGDB9TV1UnH1WBgYCDZ82rElxodVl+BQaVS8ec//1nyQRoMSqWSjIwMrl+/TnFxMVZWVgQHB1NaWkpWVhbvv//+gKfPuzqqqlQq5s+f36uqOzc3lz179jx2/WvseM+fP4+DgwPr168fUFJfU8vO19eX5cuX93tNXbx4kdjYWHx9ffuc3e2BYZFzeip+TtrKDNra2ti3bx/FxcWsW7dOSt5pQ1ZWFkeOHMHY2JgNGzb0mDBUqVS9qsfLyso4ceIEpaWlTJkyhblz5w66+khTUxP79++nqKhIGlZNnTq1W/WOwaK50N99913pM4qiSGVlJYWFhZSUlFBSUkJFRQVqtRroXKBsY2ODlZUVlpaWWFpaSj0afX19/vjHP7Jy5UomT57c6/tqmxDXeET96le/orm5mfr6empra6mtrZWW0FRWVkraKh0dnW7WvM7Ozt0KiGqKc27fvv2JDN80FBUVkZCQwO3btxFFkTFjxrB+/fpBW960tLQQGRlJamoqzs7OrFixoluusaWlhc8++0xSgfcUvIqLiyVB8fr16wdkhJiens7Ro0dxc3Njw4YNvfYuNYFpkEO5lzc4Qf8Bqrm5mW+//ZYHDx6wefNmraetRVHk8uXLxMTEMG7cOMl+ojceVY+rVCouX77M5cuXGTlyJMuXLx+0DKCxsZErV66QlJQEdN6xQ0JCWLBgwaCO1xNKpZI//elPBAQEYG5uLq3NamtrQxAEbGxsJDGmZllIf7ksbVwrtQ1O2rprtrS0UF5eTnl5uSS+rKysBDpzPBoNV1VVFRkZGfziF78Y0pXzmgq+CoUChULBlClTCAkJGbRuKj8/nxMnTlBXVyf5QCkUil5V4I/S3NzMoUOHyMvLY+HChQQHB2vdY8/JyWH//v04ODiwadOmbt/3EMkFhkVwemrS0L50UA0NDezZs4eWlha2bdumdX6no6OD48ePk5GRobUzYFf1uK2tLampqZLyODQ0dFDDrebmZuLj40lMTERHR4eQkBCCg4OlH+rs2bOfuAqrpuJKVlaWNBzQ2KlMmzYNZ2dnnJycBlV+qTeVOAw8Id7U1KTVTJ2RkZHk7Kmhra2N4uJiCgoKKCgoIDo6GqVSiY6ODkePHh0y4WVrayvp6elMnTqVkJAQrl69yrVr10hMTJS2DdRyefTo0bz77rvExMQQHR3N3bt38fLy6lUF/ijGxsa89tprREVFce7cOSoqKliyZIlWw003Nze2bt3K3r172bNnD6+99hrGxsYvnI6pP5569ZVHe1ATJ05kz549krGctgnihoYG9u/fT2VlJatWrcLLy0vrNqjVanbs2EFVVRXW1tasXbt2UEOujo4Orl69Snx8PNBpPjdt2jTpwq6pqeGTTz4ZtOanpqZGEmRqEteaAFRQUMDPf/7zJyp8qWH37t1YWlqyevXqXvfRtue0f/9+1Gr1oNendaWxsZG//e1vjB07lubmZkpLSxEEAWdnZ8nxcjCVbePi4rh48SL/9m//Jgkru95gdHV1mTlzJlOmTBnUUo7CwkKOHDlCbW2tJMQcSN4yLS2NkydP4uTkxMaNG7UOxuXl5ezZswdTU1O2bNnC9evXhyowvdw9Jw2P9qDi4uLQ19fn9ddf13qZQHl5Od999x2iKPLGG28MKLA0NjZy7Ngxqqqq0NXVxcrKakALK6EzwKalpREdHU1TUxNBQUHMnDnzselzKysryU5F49zYH/X19aSnp5Oenk5paSm6urpSWXQPDw9MTEwoKyvj888/p6SkZDBm9Y9hamraa89poDQ1NfWp7xoImoC8dOlSLC0tJVvezMxMLly4wPnz5xk1apQkvNSmx6axRfHx8emm+DY2NpZWDsTGxhIVFUViYiLz58/v0WiwL0aNGoW5uTlNTU2Sq+vy5cu1DjK+vr5YWVl1q5qizU3bzs6O119/nT179rBjxw6am5tfih6Thmey4k8ToIqKisjNzSUgIEDrwJSTk0N4eDiWlpZs3rx5QF7R2dnZHD16FIDXXnsNpVLJ/v37SUlJISAgQKtjFBYWcubMGUpLS5k4cSLz5s3rs+3Tp0/niy++4Pbt272aymsEmTdu3JA0PZ6enkyfPh0PD4/Hhmp2dnYYGxuTk5MzJMHJ2NiYmpqaJz4OdAb/Jy3ZpCEnJ0cqwgmdwkt/f3/8/f1pa2uThJeRkZGcP39eK+FlWloajY2NvebXzMzMWLZsGVOnTiUqKorDhw+TmJhIWFiY1gn5q1evUlBQwNatW2lra+PEiRN89tlnrFu3TuvimM7Ozrz99tt899137Nq1i02bNmmVhx05ciTjx48nKSmJ8ePHvzSBCZ5hOXJBEKQxdlxcHEZGRv3KDDQzE5oZFm2HNGq1mtjYWC5dusTYsWNZvXq11Mvx8/Pj3LlzuLq69nl3ampqkqbxHRwceOONN7S60BwcHHBzcyM+Pv6xO3BVVRVJSUmkpaVJgszly5f3K8jUuCDk5eUxf/78PpevQKeFyY4dO7hx4wZtbW1MnDiRDz74QHKUHMqcU3Nz85AJMHNycno1ljMwMGDSpElMmjSpR+Hl5MmTCQwM7HbjUKvVXLlyhQkTJvTbE9FUdM7JyeHcuXPs3LmTwMBA5s6d2+fMXnl5OdHR0YSEhEg3DkdHRw4fPsxXX30l1VzUpidmaWnJm2++SXh4OHv27Ol3BluTY0pKSiI0NFQaobwsPFOvBIVCwYIFC9DV1e1zsTBAYmIiZ86cwcfHhxUrVmiduG5ububw4cPk5ub2WGghLCyMvLw8jh492qN6XBRFUlNTpfYtXbp0wEsXpk+fzjfffEN2djZjx44lKyuLa9eukZOTg7GxMf7+/vj5+Wk9HGpqasLCwgJdXV2tEreXLl1iwYIF/OEPf2DEiBF8+eWXLF++nGvXruHn5ycFp8rKym4izPb2dsmIrbGxkYULF3Lt2rVuNr0aAaahoSF6enq0t7cPiVNAXV0d1dXVzJ07t999HxVepqSkkJKSwpUrV/Dw8CA4OBg3Nzfu3LlDTU0Na9as0bodbm5uvPPOOyQmJhITE8Pt27cJCwvrUf+m0ehZW1t3a7e5uTnbtm0jJiaGqKgoioqKWLVqlVY3VyMjI1577TWOHDlCeHg4K1as6FHy8bIlv3viqSfEezxQHzKDrlIBzbS8tuP/srIywsPDaWtrY926db3ehQsLC/nyyy8JDQ1l9uzZ0vbq6mpOnjxJfn4+vr6+LFiwYFC9AlEU+eKLLyT1dHV1NY6OjgQHB+Pl5TWopGtdXR0fffQR4eHh/OEPf+hXVNfc3ExVVRXV1dXU1NSwd+9eRo8ejbm5OQ0NDfT2vSsUCnR0dGhra+P//t//y3/+539iYGCASqWSdFQ9vcbMzEzSUmnsea2trRk5cqRWmqLU1FROnDjBL37xi0FpkDo6OkhPT+fatWuUl5dja2tLW1sblpaWg7a0aWho4Ny5c2RkZDB27FiWLVvWLSF/7tw5rl+/LqnAe+LevXscOXIEU1NTNm7cqLUZoVqt5vTp06SkpLBo0aJuHufPIDANi4T4cwlO0HOAEkWRqKgorly5MuDyUrdv3+bYsWOMHDmSDRs29Dur01U97ujoyLVr14iOjpZyEAOpsNqV9vZ2kpOTuXTpEq2trbi6ujJ37lxGjRr1xCV5PvnkE86dO8dbb70lBSdRFKmtrZXEmOXl5ZSVlXUbtpmbm3P37l1Gjx7NlClT6Ojo4Nq1a6xatQoHBwcMDQ0RRRFRFKUeosYypetsnVqtltThra2tFBQUEBERIXnAawSYDx48kAokQGdeR6PB0tSjs7Cw6HY+Dh8+TE1NDdu3b3+icySKIvn5+URFRVFcXIyxsTGzZs3C399/0KZq9+7d4/Tp07S2tjJ//nwCAwPJzc3lm2++YeHChYSEhPT5+urqasLDw6mvr2ft2rVaLeDVfJauv4fQ0NBn1WMaFsHpuVngPTqLJ4oiDQ0NXLt2jbCwMK3LInUt5Ont7c2KFSu00hiFhoaSnZ3NoUOHMDc3p7CwkODgYObOnTso7ZDGbiM+Pp7W1lZ8fHzIzc3FyMho0FVjH2XMmDG4ubnR3NwsJWELCwulQGRhYYG9vT0BAQHSUhErKys++ugjDh48yJ07d7C1taWqqopr165hYWEhme/1ZjbXFYVCgaGhIYaGhlhYWEg2wVOnTn1s5qyjo4Pq6mppSU15eTk3b96UZBhmZmY4Ozvj4uLC6NGjyc7OHtDSpd4QBAFXV1cMDAywtrbG0dGRs2fPEhcXx4wZMwYVpDw9PXFxcSEyMpKIiAhu375NZWUlrq6uWhWqtLa27lY1RTNL2N/NSlPWycDAgJiYGJRKJdCZg3xZh3Jdea7+nJoApblDQGeOJzAwUKvXK5VKTp48yc2bNwfc01IoFIwfP54LFy5IYtCBLCPQoFKpSElJ4dKlSzQ3NzN58mRmzpzJiBEjSE5O5tSpU1RXVz9RnbjGxkaysrIoLy/HysqKrKwscnJycHZ2xt/fn1GjRuHk5NTjEHTfvn188MEHUm1AQAokXXtXgzGb07y+p5yTnp4e9vb2j8k2GhoaKCkpobCwkMLCQiIjI6Xke0lJCTdv3nxi4WVJSQk5OTmsXbsWb29vZs2axeXLlzl79izx8fHMnj0bX1/fAeURDQ0NWb58OePHj5cKwM6ePVvr683AwICNGzcSHR3N+fPnqamp0aoitiAIhIaGolAouHDhAsD3IjDBcw5O8D8BKj8/n8LCwm6LVPtCU/2lsLBQugi1pa2tjdOnT3Pr1i2cnJwoLi7u5p+tDaIocvfuXaKioqiurpYsXrtWcvH19eXixYvEx8f3aKfSF9XV1ZIgU+Nc6eDggCiK2Nra8oMf/KDfHkB4eDhvvfUWBw8eZP78+dJ2AwMDFApFt+CkqUM3EJqamjAyMhrQj9zMzIxx48ZJs1AdHR2cO3eOlJQUWlpaJOlHV+HlQG1zr1y5IpXwgs6ey6pVq5gxYwYxMTGcOHGChIQEFixYoHU5Mw0tLS0olUqcnJw4ffo0JSUlhIWFadXbVigUzJ8/HysrK06dOkVdXV1v1U8eQ5O/HDt27PciMMEwCE7Q+aW98cYbxMTE9DuLB939krdu3aq1lgQ6Cy0cPHiQpqYm1qxZg7e3N/v37+fEiRO89957Wgn7ysvLOXv2LHl5eYwdO7ZXixVdXV2Cg4O5ePEic+bM6df2tb6+XjLCLysrQ1dXFw8PD4KCgnB3d8fExIS3336bESNG9BuY9u3bx5tvvsm+ffse8/YWBKFPOYG2NDY2PrHJnJ6eHrW1tbi5ufHaa69Jwsu7d+8SHR1NZGQkTk5OTJw4kUmTJvX7fjU1Ndy+fbvHqrYjR45k/fr1FBcXExkZyd69e3F3d2fRokVazZzW1dURERGBt7c3a9asITU1lbNnz1JUVMT69eu1Tnb7+/tjYWHBgQMH+Prrr/v11X/ZZ+V6Y1gEJ9Dek7y6uppvvvkGURR58803B1SKKSUlhYiICGxtbXnttdekXs7y5cvZsWMHJ0+e5JVXXum1q97a2kpMTAzXr1/HysqKzZs395vcDAwMJC4uTrpTP4pSqSQzM5PU1FRycnLQ1dXF09OTmTNn4uHhgZ6enjSsg04tkIuLC6mpqVhbWz9mNgedgWnr1q18/PHHTJ06lbKyMqBzmlqz5qs3lfhAdE5DoXFSKpXk5+dL3/2jwsusrCzS09O5cOECkZGRuLu74+fnh6enZ4/ykvj4eMlwrjecnJzYtm0bmZmZnD9/nh07dhASEkJoaGivvRhRFDl27BgGBgYsXboUQRDw9/fH2dmZgwcPsnPnTpYvX86kSZO0+txjx47l9ddfZ+/evXz55Zds2bLlsfV43we5QF8Mm+AE/QeosrIyvv32W4yMjNiyZYvWanGlUklERASpqakEBAQQFhbWredhamrKihUrelWPi6JIRkYGZ8+epb29nXnz5vVZn6wrhoaGBAYGcv369W5VhWtqakhKSuLGjRu0tLTg4uIiuSQ+qmVKSkqSzouLiwuzZs1i6dKlLFy4sEezuc8//xylUsmPfvSjbv7jGnM66F2IqXmNZm1dXwxFYYPCwkKUSmWPs6MGBgZ4e3vj7e1NS0sLGRkZ3LhxgwMHDmBiYoKfnx8BAQHSzGxjYyNpaWnMmjWr30kRQRCYMGECHh4exMfHS8UNlixZ0qPw8erVq+Tl5bF169Zu34+NjQ1vv/02p0+f5siRIxQXF2ttJOfg4MCbb77JN998w+7du9myZYvUg/u+ByYYZsEJeg9QxcXFfPvtt1haWkqrsLWhoaGBAwcOUFpayooVK/Dz8+txv3HjxuHv7/+Yery+vp5Tp06RlZXF+PHjWbx48YCW0EDnAuGEhAQSExNxdnYmISGBe/fuYWhoyOTJkwkICOhzWDF79mxJl6RSqfjv//5vDhw4IF2wmoCj4eLFi/22ycTE5ImXsDQ2Nj5xEVGNMLU/A38jIyMCAwMJDAykvLyc5ORkaXZ0/PjxTJ06lXv37qGjozOgRde6urrMmjULHx8fIiIi2L9/P15eXixevFgaQvakAu+Kvr4+q1atwsnJiXPnzlFeXs769eu1ukatrKykAPXll1+ydetW7OzsvveBCZ6jzqnfN+uigwoKCuLmzZvY2tqyefNmre0tSkpK2L9/PwAbN27st8Jwe3s7n3/+OUZGRrzxxhukpaVx/vx59PT0WLp0KePHjx/UZ1Gr1Xz77bfk5+ejVquxtbUlODiYSZMmDcpa5bvvvpNcHbRBFEWampok18q6ujoyMjKorq7G2dmZlpYWSSHe0dGBSqWiubmZ3//+9/z617/G2NgYXV3dbgpxIyMj8vLycHR0lMo0WVhYYGlpibGxsdazWDt37sTKyqrPem690d7eTlpaGteuXaO6uhpBEPD09JQqIg8UURRJT0/n7NmziKLI4sWLGT9+vFSkYPv27f3m+vLz8zlw4AD6+vps2rRJ6zqJzc3NfPPNN9TV1eHl5UVycvLzDEzDQuc0bIMTdF4sZ86c4fr164wYMYL33ntPaw1SZmYmR44cwcbGhldeeUXrGmRFRUXs2rULKysrampqmDx5MgsXLhyUalmtVpOens6lS5eorq4GYMqUKYSFhT2RIDMhIYGoqCh++ctfPhbcNFYjGmO3yspKqquru82C6uvro6urS0tLC+PHj5e0SxqrXo1N77x587hw4QLGxsaSv7hmqUtzczN3796VipdqZpOgczimKYtuZ2eHvb29JPbsSktLC3/+85/77NFqgyiKHD9+nLS0NKCzoENoaCheXl6DOs9NTU2cOXOGjIwMrKysqK2t5Qc/+IHW5Zlqa2vZt28fdXV1bNiwQWtBb0tLCzt27KChoYGZM2dqtZTnKTEsgtOwG9Z1RRAEwsLCqK2tJSsri6SkpH4XC0OndezZs2eZMGECq1evHlDvpLm5GT09PWpqapg/f36fbpG9IYoit2/f5uLFi1RVVeHp6cnq1au5cuUKWVlZLFq06ImCk5ubGyqVivz8fMkdU6Mb0ggjNaXA7ezsmDhxItbW1pJdr6GhIWlpaRw7duyx8/NoQjwwMLDHYWxjYyN3795l2bJljBs3jra2NkkdrhFfVlZWkpGRIYkHraysGDVqFM7Ozri6ulJeXi59nidBpVKRnZ2Nn58fvr6+XLp0iUOHDmFnZ8ecOXOkAgfaYmJiwrp167CysuLy5csYGBjQ3Nys9etHjBjBm2++yaFDh9i7dy/Lli3rN/iKokhCQgINDQ14eXk9z8A0bBjWwQk6ZQabNm3SSmYgiiIXLlwgPj5+wOvyVCoVkZGRXLt2DXd3dxobG0lJSSEoKGhAivG8vDwiIyMpKSlh7NixUi4COhcE79y5kzt37jBx4kStj9mVxsZGiouL0dXVJTw8HKVSiUKhwMHBgXHjxuHk5ISjoyNWVlZ9fnZNIrupqanbUh9tE+KaZLqJiQmCIGBoaNij6FKtVlNdXU1paSnFxcUUFRVx69YtRFGUhon5+flPJLy8efMmjY2NTJs2jZEjR7JlyxbJWXP//v24uLgwf/78ASn1W1papCpCurq67NmzhxkzZjBnzhytdF0GBgZs2rSJiIgITpw4QWNjIzNmzOj1O5FzTI8z7IMTaCczUKvVnDx5khs3bmi13qkrtbW1HDp0iNLSUhYtWkRwcDA1NTV8/vnnnDt3juXLl/d7jJqaGiIjI8nMzMTR0bFHxbmjoyNubm7ExcUNaMhRVVUlCTJLSkoAJPGjxvdnoLmr3oKTtmiCU3+6I4VCgY2NDTY2Nvj4+ACduaKCggIOHTokWfJCp2mbRnjZVczaF2q1mvj4eCZMmNBtUsHFxYVt27aRnZ1NVFQUu3fvxtvbm/nz5/c7CymKIqdPn6ajo4N169ZhZmZGfHw8MTExkuhXmzSBQqFg6dKlmJmZER0dTWNjY49Dejkw9cwLEZyg7wDVtbzU6tWrpR+BNty/f5/Dhw9jaGjIW2+9JRmMdfUe9/T07NVXp6Ojg8uXL3PlyhVMTEwkYWdvgUdjp5KTk9Nneer6+npu3rxJeno65eXl6Onp4eHhwZQpU3B3d+f+/fscO3YMOzu7QSXVe1rCMhC69pwGir6+PtbW1rS1tUkTFffv3+fu3btcvHiRqKgoHB0d8fb27ld4mZmZ2astiiAIuLu74+bmJjmZfvLJJ8ycOZNp06b1mtzWlIpfu3atFMhmzpzJ6NGjOXToEJ9//jnr16/XymRPEARmzZqFiYkJp0+fpq2tTaqALcsF+uaFCU7Qc4AKCgriwIED5ObmsnHjRq3LS4miSFxcHNHR0bi7u7NmzZrHkt4BAQFkZWX1qh7PysoiIiKChoYGpk+fzowZM/oNFGPGjMHBwYH4+PjHglNPgsxx48ZhY2PD119/zSeffEJpaSlHjx5l3rx5QGfpqJ6W7sTGxvLTn/6UjIwMHB0d+cUvfsG7774rPa8ZQj0anLQVYTY1NUkFNgdDTk6OtEjX0NAQPz8//Pz8aG9vJysri4yMDEl4OXbsWPz9/R8TXoqiSHx8PK6urn3OxCoUCvz8/PDy8uLSpUvExsZy8+ZNli1b9ljvtq6ujtOnTzNp0qTHzquLiwvvvPMOhw4d4uuvv2bRokVMmTJFqx5wYGAgBgYGHDt2jI6ODlavXs3ly5flwNQHL1RwgscDVHJyMvX19WzevFnrxGpHRwcnTpwgPT29zwrDgiD0qB5vbm7mzJkzpKen4+bmxpYtW7QehgiCwPTp0zl06BAlJSU4OjpSV1fH9evXSU1Npbm5WRJkenl5YWBgIJnuvf7669KUu5mZGTY2NuTk5Dz2I8rNzWXJkiVs376db7/9lvj4eH74wx9iY2MjvV5HRwdDQ0OpnLgGbXNOjY2NTyTAzMnJwcnJ6bEZPH19fSZOnMjEiRMfE16ampri7+9PYGAgZmZm5OXlUVJSwquvvqrVexoYGLBgwQImT57MqVOn+Prrr/Hz82PhwoUYGhqiVqslFfiSJUt6PIaJiQlbtmwhMjKSs2fPSlVTtBFdTpo0CX19fQ4cOMBnn31GdXW1HJj64IULTvA/AaqsrIysrCwCAgK0DkyNjY3s37+f8vJy1q1b129i+lH1uJGREadPn0YURVatWoWPj8+AZ940i1mjoqIwNjbm9u3b6OvrS4LMR4WNixcvZvHixY8dx83NjczMTERR7NaGzz77DBcXFz766CPp/ZKSkvjrX//aTU/0JIUOnkQdrlarycnJYcqUKX3u96jwMikpiYSEBOLi4vD29qa6uho7O7s+h8c9YWNjw+uvv05ycjKRkZHcv3+f5cuXU1FRQV5eHtu2betTS6dQKFi0aBG2tracOnWKmpoaNmzYoJXcxNPTUyohNWnSJDkw9cELGZygM0C98sornD17Vlrr1p/MoKqqir1796JUKnnjjTe0NrAfN24cvr6+UlAaP348S5cuHdSiV40ZmkKhIDc3FwsLC8LCwpg8efKAh0hubm5cu3aNmpqabpYsV69eZeHChd32XbRoEbt27aKjowM9PT2USiUGBgZUVVWRlZVFQ0MDTU1NKJVKVCqVZBYXFxeHmZkZurq66OnpSRa91dXV6Ovro1QqB+yPVFZWRmtr64AkBHZ2dixdupR58+aRmprKlStXaGxsxM7OjqKiogF7ZgmCQGBgIB4eHpw8eZLvvvsOQRCYMmWK1tY5fn5+WFlZER4ezu7du9m8eXOfDgqaHFN6ejrTpk0b0uKrLyMvbHCCzjvY4sWLMTQ07FdmUFRUxHfffYepqSnbtm0b0AyVpriAKIpYWlqybt26QRXjzMvLIyYmhoKCAuzt7TEwMMDNza3fHkRvuLq6olAoyM7O7hacysrKsLOzQ6VSUVlZSUVFBQ0NDaxatYqdO3fS1NTUTbeTnZ0NdPZoOjo6UCqVtLS0AJ32uXp6eqhUqh7tbH7/+99jYmKChYUFVlZWWFlZMXLkSMnsrqfzlJ2djb6+/qAqLRsaGhISEkJRURF5eXmo1Wp2797NmDFjJMfRgWBhYcHGjRv5xz/+QUNDA9nZ2ZSWlmpdfmz06NG89dZb7N27l927d/Pqq6/26FAhJ78HzgsdnEA7mcH9+/cJDw/H0dGRV155RWu1tybhGh0djZOTE4sWLeLgwYNcvny5m/d4f5SVlREVFUV2drZUQlqz4FRbO5We0PzAc3NzCQoKoqamhsLCQqZMmYJSqeQPf/iD5PttYGCAiYkJ1tbWeHt7Y25ujiiKGBsb4+DggCAIqNVqaXhYX1/PJ598wv/+3/9bEmGKokhHRwetra0UFxfT2toq7asRYObm5kpDRR0dHcmad9SoUbi4uDBixAhycnIYPXr0oAI8/E/x0cWLFxMYGMidO3eIjY1l165djBs3jnnz5g1ozV90dDTNzc288sorXLx4kV27drFw4UKCgoK0GrJrnC737t3LV199xaZNm7rN5MmBaXAM6+UrA6G3ogkZGRkcOXIEd3d31q1bp/W0e0tLC8eOHePevXvdxHeai+zNN9/s9y7d0NBAdHQ0N27ckCp0TJgwQbrgW1tb+eijjwgICNC6iy8IglQaqqGhgdOnT5OVlYWxsbGU3G5sbERPT4/Vq1djZ2eHra0tZ86cYcOGDZICvj+0rfjbEy0tLVRUVFBWViaJL6uqqoDORH5jYyPe3t4sWrRoUHmrU6dOcefOHd5//33ps6jVajIyMoiOjqaurg5/f3/mzJnT7/FzcnK6eYErlUoiIyNJTExk4sSJLF++XGsTvra2NskAccOGDXh4eLyogWlYLF95aYITPB6gTE1NOXbsGN7e3qxcuVLrO3V5eTnh4eG0tLSwZs2abp5NKpWKL7/8kpaWFt55550e80QqlYqEhARiY2PR09Nj9uzZvVYA1sw4vv/++1otaLaxseF3v/sdCoVCEmTq6enh6+uLp6cnzs7O/OY3v+HkyZPcvn1bet17773HjRs3uHr1qlbn4EmCU0+0tLRQUFBAZmYm6enp0pKWUaNGMW7cOK1qy0Fn4P3oo48IDQ0lNDT0seeVSqVUllsURebMmUNQUFCP516zlk2jKu/aS7p9+zbHjx/H3NycjRs3al3GS6lUcujQIbKysli3bh1lZWUvWmACOTg9HboGKIDJkyezfPlyra1k79y5w9GjR7GysmLjxo09Jjirq6v5/PPPmTRp0mPq8YKCAk6ePEl1dTVTpkxh9uzZfQadhoYGPv74Y2bPnt3rxVtSUkJcXBzFxcXU19cDnWrzsWPHEhwczO9+97tuZnMa7dM777zD9u3buXr1Ku+++y779u3rd/V/V53TvXv3hiw4PYrGQO/evXvcv38fpVKJg4ODJLzsbZh74cIFEhMTef/99/scnjc3NxMdHU1ycjL29vYsW7asmxZKFEUOHz5MdnY27733Xo+fsaqqivDwcBoaGli3bp3Wlr4qlYojR45w584dRFF80QITyMHp6SGKIl9++SWFhYVaL97tKsr08vJi5cqVfc6eaYoXvPLKK9LCV00vaNSoUSxbtkzrVewnTpzg3r17vP/++9LMl0qlIjMzk5SUFHJycujo6JB6HdnZ2SiVSsk87vXXXycvL6+bj1NsbCw/+clPJBHmL3/5y24izP4Y6p5TX3R0dEiOl/fu3UOtVuPu7i4JLzU3lra2Nj788EP8/f0fm43sjeLiYk6dOkV5eblUXUdPT4+bN29y9OjRfv3nW1tbOXLkCPfv35eWNvVH1xuku7u71jqsYYQcnJ4marWamJgY4uLiHivc+SgqlYrTp0+TmpoqFdrsLxEqiiL79++nqKiIJUuWEBkZSUtLC/PmzdM6kaqhurqaTz75RFrhf/36dVJSUmhsbMTZ2VlSNw+0AMGT8CyDU1daW1tJT08nNTWVkpISzM3NCQgIIDAwkNTUVKKjo/m3f/u3AbVJrVaTkJBATEwM5ubmzJ8/n+PHj+Pp6alVNWC1Wk1kZCQJCQkEBwezcOHCXnviXXNMc+fOZebMmVq3cxghB6enTV+VhTW0t7dz8OBBcnJyWLFiRZ/e049SV1fHJ598glKpxNXVlZUrVw5qES3AN998Q1FRESqVCoVCga+vL0FBQVqblQ01zys4daW0tJTr169z69YtaZuHhwcbNmwY1PGqq6s5duwYRUVF6Ovr8+Mf/3hACfnr169z5swZyYrnUX3XC5r87gk5OD0L+gpQLS0t7N27l8rKSjZs2DAgpXFlZSWHDx+msrIStVo9oHp7XamoqODSpUtkZGQgCAIhISHMmDFjUOZ2Q8lwCE4ampubuXjxIklJSUDnMpDQ0NBB1QKMi4vjwoULCIKAg4MDa9eu1XrpEXQuND58+DCjRo3ilVdekXqzL1FgAjk4PTt6ClCNjY188803NDQ08Nprr2mtFodO/6BTp05hYWHBunXrSExM5NatW7zzzjta/2AePHhATEwMt27dwsLCghkzZuDj4zPohbRDxbNKiA+G1tZW0tLSiI+Pp7GxEV9fX2bPnt2vBYqGsrIydu7cSXBwMBMnTuTw4cM0NzezcuVKJkyYoHU78vPz2bdvH9bW1rz66qsYGxsTExPzsgQmkIPTs6VrgJo5cya3b9+mvb2dLVu2aC3YU6lUnD17lqSkJHx9fVmyZAn6+vqPeY/3JVloaWkhNjaW69evY2JiQmhoKH5+foMWJD4thlPP6VGUSiVJSUlcvnyZ9vZ2goODmTlzZp85OaVSyRdffIFCoeDtt99GV1eX1tZWSXIREhLC/PnztZ7VLS0t5dtvv8XMzIwxY8aQkJDwsgQmkIPTs0cURSIjI7l69SqGhoZs375d6y59Y2MjBw4coKSkhMWLFz9WPqqoqIjdu3dLCfVHUavVpKSkEB0djUqlYvr06YSEhAzKi+lZMJyDk4a2tjauXLnClStXMDAwYP78+fj6+vY4GaG5qfzgBz/olsfT2ONGRkbi6urK+vXrtR5Sl5eXS+sVZ8+ezaxZs4bssz1n5OD0PNBUQsnNze13Fk9DWVkZ+/btQ61Ws3Hjxl6V4b2px0tLSzl16hQlJSVMnjyZefPmPXGl3KfNixCcNNTV1REVFUV6ejrOzs4sW7asWwDKzs7m22+/7dMhNS8vjwMHDmBkZMSmTZv6FV12zTF5enqyadOmIf1Mz5lhEZy0L3L/kqBQKNiyZQszZ84kMjKSK1eu9Ll/VlYWX375JcbGxmzfvr3PJSuhoaE4Ojpy5MgRqSJJZGQkO3fuRKlU8uabb7Jy5cpBB6Z//vOfjBkzBkNDQwICAiShaW/s3bsXX19faf3cG2+8IVWB6Y1PP/0ULy+vAdV+e95YWFiwdu1atm7dSnNzM59//jkXL15EpVLR0tLC8ePHGTNmDFOnTu31GK6urmzfvh2FQsGuXbvIy8vrdd9Hk98vWWAaNnzvek4atJEZpKamcvLkSTw8PFi7dq1WyWqNetzNzY2qqipqa2uZNWsW06ZNe6K8Unh4OFu2bOGf//wn06dP5/PPP+df//oXt2/fxsXF5bH94+LimDVrFh9++CHLly+nuLiYd999Fw8PD8mzuy9epJ5TV5RKJZcvXyYuLg4bGxtMTU0pLi7uVQX+KK2trRw4cICCggJWr179mN/XSzYr1xvDouf0vQ1O0HeAio+PJyoqCn9/f5YuXap1olStVhMeHs69e/ewtrZm48aNT1wVFzqrBvv7+7Njxw5p24QJE1i1ahV//OMfH9v/r3/9Kzt27JDsUAD+8Y9/8Oc//5nCwsJ+3+9FDU4aSktLCQ8Pp66ujkmTJrF69eoBVeI5fvy4VJ5c04v8ngQmGCbB6Xs3rOuKxm6l6xBPU14qKiqK0NBQli1bpnVgamhoYM+ePWRlZTFu3DjeeeedIQlM7e3tJCcnP7ZkY+HChb0OS6dNm0ZRURERERGIokh5eTmHDh1i6dKlPe7f1tZGfX19t8eLjIODg9RTvHXrFnv37tXa9VNHR4fVq1cTHBxMREQEcXFx36fANGx44f2cnpRH/aDu3r1LQUGB1slyDTk5ORw+fBgdHR22bdumVWUObamqqkKlUj22Vs/Ozo6ysrIeXzNt2jT27t3Lxo0baW1tRalUsmLFCv7xj3/0uP8f//hHfvvb3w5Zm4cDhoaGbN68mfv373P06FGpaoo2rpmCILBo0SIMDAy4cOEC9+/fJz8/Xw5Mz5Dvdc9JgyZATZw4kYKCAsaNG6d1YNIY0n377bfY29vzzjvvDGlgerSdj753b0OV27dv8+Mf/5j//M//JDk5mbNnz5Kbm9vr4t9f/epX1NXVSQ9thn4vCu7u7rz77rtYWlry1Vdfcf36da1eJwgCs2fPxtXVlfz8fAICAuTA9Az53vecNAiCwJo1a9DV1SUtLY0rV670G6CUSiUnT57k5s2bTJ8+nblz52o9BBwIGrvbR3tJFRUVvTof/PGPf2T69On8/Oc/B8DHxwcTExNmzpzJ7373u8dsaA0MDJ7pwuJnjZmZGVu3buXcuXNERERQUVFBWFhYn5MUmqFcXl4egYGBvQ6JZZ4OcnDqgkKhYOXKlZibm/frSd7c3Ex4eDjFxcWsWbOGSZMmPbV26evrExAQQGRkJKtXr5a2R0ZGsnLlyl7b9+jCVM0PcQCTIC8VOjo6LFmyBDs7OyIiInjw4AHr1q3r0W9LzjE9f+Tg9AjaeJLX1tby7bff0tLSwrZt2wZc+WMw/PSnP2XLli0EBgYSEhLCF198QUFBgTRM+9WvftXNcG758uVs376dHTt2sGjRIkpLS3n//feZMmXKgNYRvowEBARIVVO++uorXn311W7mdnJgGiaIoqjt43uFWq0WL1y4IH7wwQdifHy8tL28vFz861//Kn788cdidXX1M23Tp59+Ko4ePVrU19cX/f39xdjYWOm5bdu2ibNmzeq2/9///nfRy8tLNDIyEh0cHMRXX31VLCoq6vM9PvnkE3HChAmip6enCIh1dXVP46MMC8rLy8W//e1v4ocffih9l2q1WoyOjhY/+OAD8fLly8+5hc+NgcSFp/b4Xuuc+kN8RAfl6urKt99+i7m5Oa+99tqwX4LyJLzoOidtqaur45tvvqGtrY3XXnuN27dvyz2mYaJzkoNTP3QNULq6utjZ2fHqq68+d7+lp833JThBZ/Xib775hpqaGjo6Or7vgQmGSXCSpQT9oMlBjR49GoVCwebNm1/6wPR9w8TEhE2bNiGKIp6ent/3wDRskHtOWqJWq2lvb9eqfNOLzHA2m3vatLa2vvTfr5YMi57TQIKTzPcIQRDMgTrAQhTFF3sti8wLiRycZHpE6JSemwENonyRyDwH5OAkIyMzLJET4jIyMsMSOTjJyMgMS+TlKzIyMkOCIAiWwG/ojCvuwAHgO+AvdM4AWgK/F0XxtjbHk4OTjIzMEyMIgj7wT+BnoiiWCIIwGsgFVgLvAx7AaeAB8L+0OaY8rJORkRkK3gW+FEWx5OHfrXT2lvJEUcwFdIAsYJ+2B5R7TjIyMkPBA1EUz3f5O/Dhv2cBRFE8A5wZyAHlnpOMjMwTI4riN49smgOogLjBHlPWOcnIyAw5giCkAB2iKAYP9hhyz0lGRmZIeThr5wtcfGT72wM5jhycZGRknghBEGwEQUgUBOE3DzeF0RlbErvuA2hfzggtE+Jd1lnJyMh8PxjImspZQBAQIQiCEbARKAFMAQRBMAH+DvxyIA3QKufUZYW6jIzM9wOt3SgEQTADPgTa6QxIfwTMgT8A+YA+8GdRFG8OpAHaBqe+ek6JwJR+DtHfPk96DDOgCBgFNDzHdmjzvDZtfZnOqTb7DJe2yt////Dc3Si0GtY9bGSPUVQQBHV/Eba/fZ70GF0KSzY8yfs8i8+iTVtfpnP6IrVV/v6HF0OREP90CPYZimNow7Nox7No51C1Q27r0Lfj+3ZOnxovhc7pRXJtfFHa+qK0E+S2vqy8LFKCNuC3D/8d7rwobX1R2glyW19KXoqek4yMzMvHy9JzkpGRecmQg5OMjMywRA5OMjIywxI5OMnIyAxLXtjgJAjCrwVBuCIIQrMgCLVavkYQBOEDQRBKBEFoEQThoiAIE59yOy0FQfhGEIS6h49vBEEY0c9rvhIEQXzkkfAU2vZDQRByBUFoFQQhWRCEmf3sP+vhfq2CIOQIgvDuULdpKNoqCMLsHs6fKAjC+KfcxlBBEE4+vL5EQRBWafGa53ZOhzsvbHCic73OQWDHAF7zC+CndHoYBwFlQOTDtUFPi++AyXSu1A57+P9Hjbl64izg0OWxZCgbJQjCRuAj4PeAH3AZOCMIgksv+48BIh7u50fnuqm/C4KwdijbNRRt7cI4up/DrKfYTAATIA0tPbKf5zl9IRBF8YV+AK8DtVrsJwClwC+7bDMAaoF3nlLbJgAiENxl29SH28b18bqvgGNP+bxdA3Y8su0O8Mde9v9v4M4j2z4Drj6D73igbZ398ByPeNpt66PNIrCqn32e2zl9ER4vcs9poIwB7AHJ51gUxTYglgH6zAyAEKBOFMVrXd4zgU6FcH/vOVsQhApBEO4JgrBTEATboWrUw0oZAXQ5Fw8530e7QnrY/xwQKAiC3lC17VEG2VYNqYIglAqCcEEQhDlPpYFPxnM5py8K36fgZP/w3/JHtpd3ee5pvGdFD9sr+nnPM8CrwFzgZ3QOQaMFQTAYonaNpLMaxkDOhX0v++s+PN7TYjBtLQV+AKwF1gB3gQuCIIQ+rUYOkud1Tl8IhlX1FUEQPqCzKF9fBImimPQEb/OoJF7oYVufaNvOXt6v3/cURTG8y5/pgiAk0emLsxQ4on1L+2Wg56Kn/Xva/jTQuq2iKN6lMyBpuCoIgjPw/wMuPZ3mDZrneU6HNcMqOAGfAPv72SdvkMcue/ivPZ13Vg22PH736g9t2+kD2PXwnM1A3lMUxVJBEPLpLEw4FFTRWRnj0Z5HX+eirJf9lUD1ELWrJwbT1p5IAF4bqkYNEc/rnL4QDKvgJIpiFZ0X49Mgl86LYQGQClI+YxYDtA/Vtp2CIFwFLARBmCKKYuLDbcGABXBF2/cTBMEacKZ7UB00oii2C4KQTOe5ONrlqQXA8V5edhVY/si2hUCSKIodQ9GunhhkW3vCjyE6f0PIczmnLwzPOyM/2AfgQue0/H/S6Sg4+eHDtMs+mcDqLn//ks7ZudWAN53T/CWA2VNs5xk6p5enPnzcBE4+so/UTjptTv9KZ7LUlc6Zpyt0uicOWTvp9HluB96kc1bxQ6ARGP3w+T8Ce7rsPwZoAv7fw/3ffPj6tc/gux5oW98HVtHZ05z48HkRWPOU22na5ToUgZ88/L/LcDunL8LjuTfgCS6Erx5eAI8+ZnfZRwRe7/K3AHxA5x20lc6ZOu+n3E4r4Fs6nUTrH/5/xCP7SO0EjOicsal4eKHmP/yszk+hbT+kc/jZBiQDoY+c34uP7D8LSHm4fy7w7jP8vrVuK516tvtAC1BDp45oyTNo4+xersmvhuM5He4P2TJFRkZmWPJ9khLIyMi8QMjBSUZGZlgiBycZGZlhiRycZGRkhiVycJKRkRmWyMFJRkZmWCIHJxkZmWGJHJxkZGSGJXJwkpGRGZbIwUlGRmZYIgcnGRmZYYkcnGRkZIYl/x9PUVh3isDm0QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "Graphics object consisting of 20 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = polar.plot(cartesian,ranges={r: (1,2), ph: (pi/4,3*pi/4)},\n",
    "               number_values=10, color='grey')    # plot coord.lines r,ph \n",
    "p.show(figsize=3)         # in the subset r0<r<r1, ph0<ph<ph1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "### 3-dimensional case\n",
    "\n",
    "<br>\n",
    "\n",
    "**Example 2.4**\n",
    "\n",
    "Now consider the 3-dimensional case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "E.<x,y,z> = EuclideanSpace()  # number of variables determines the dimension\n",
    "cartesian.<x,y,z> = E.cartesian_coordinates()  # Cartesian coordinates in E^3\n",
    "spherical.<r,th,ph> = E.spherical_coordinates()  # polar coordinates in E^3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the domains and variables ranges."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Euclidean space E^3, Euclidean space E^3)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cartesian.domain(), spherical.domain()  # domains of Cart. and polar coord. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x: (-oo, +oo); y: (-oo, +oo); z: (-oo, +oo)\n",
      "r: (0, +oo); th: (0, pi); ph: [0, 2*pi] (periodic)\n"
     ]
    }
   ],
   "source": [
    "print(cartesian.coord_range())         # ranges of Cartesian coordinates  \n",
    "print(spherical.coord_range())         # ranges of spherical coordinates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the spherical coordinates don't define a homeomorphism on the entire $E^3$\n",
    "(appropriate restrictions will be given below)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The transition from\n",
    "the spherical coordinate system to the Cartesian coordinate system is given by the functions \n",
    "\n",
    "$x = r\\cos\\phi\\sin\\theta,\\quad\n",
    "y = r\\sin\\phi\\sin\\theta,\\quad\n",
    "z = r\\cos\\theta$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x = r*cos(ph)*sin(th)\n",
       "y = r*sin(ph)*sin(th)\n",
       "z = r*cos(th)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sph_to_cart = E.coord_change(spherical, cartesian) # transition \n",
    "sph_to_cart.disp()                                 # spher-> Cartesian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<iframe srcdoc=\"<!DOCTYPE html>\n",
       "<html>\n",
       "<head>\n",
       "<title></title>\n",
       "<meta charset=&quot;utf-8&quot;>\n",
       "<meta name=viewport content=&quot;width=device-width, user-scalable=no, minimum-scale=1.0, maximum-scale=1.0&quot;>\n",
       "<style>\n",
       "\n",
       "    body { margin: 0px; overflow: hidden; }\n",
       "\n",
       "    #menu-container { position: absolute; bottom: 30px; right: 40px; cursor: default; }\n",
       "\n",
       "    #menu-message { position: absolute; bottom: 0px; right: 0px; white-space: nowrap;\n",
       "                    display: none; background-color: #F5F5F5; padding: 10px; }\n",
       "\n",
       "    #menu-content { position: absolute; bottom: 0px; right: 0px;\n",
       "                    display: none; background-color: #F5F5F5; border-bottom: 1px solid black;\n",
       "                    border-right: 1px solid black; border-left: 1px solid black; }\n",
       "\n",
       "    #menu-content div { border-top: 1px solid black; padding: 10px; white-space: nowrap; }\n",
       "\n",
       "    #menu-content div:hover { background-color: #FEFEFE; }\n",
       "\n",
       "    .dark-theme #menu-container { color: white; }\n",
       "\n",
       "    .dark-theme #menu-message { background-color: #181818; }\n",
       "\n",
       "    .dark-theme #menu-content { background-color: #181818; border-color: white; }\n",
       "\n",
       "    .dark-theme #menu-content div { border-color: white; }\n",
       "\n",
       "    .dark-theme #menu-content div:hover { background-color: #303030; }\n",
       "\n",
       "</style>\n",
       "\n",
       "</head>\n",
       "\n",
       "<body>\n",
       "\n",
       "<script src=&quot;/nbextensions/threejs-sage/r122/three.min.js&quot;></script>\n",
       "<script>\n",
       "  if ( !window.THREE ) document.write(' \\\n",
       "<script src=&quot;https://cdn.jsdelivr.net/gh/sagemath/threejs-sage@r122/build/three.min.js&quot;><\\/script> \\\n",
       "            ');\n",
       "</script>\n",
       "        <script>// fat_lines.js\n",
       "\n",
       "var _fatLines = [];\n",
       "\n",
       "function _createFatLine( lineStrip, geometry, materialOptions ) {\n",
       "\n",
       "    var vertexCount = geometry.vertices.length;\n",
       "    var positions = [];\n",
       "    for ( var i=0 ; i < vertexCount ; i++ ) {\n",
       "        var v = geometry.vertices[i];\n",
       "        positions.push( v.x, v.y, v.z );\n",
       "        // For a line strip, duplicate all but the first and last vertices.\n",
       "        if ( lineStrip && i > 0 && i < vertexCount - 1 ) {\n",
       "            positions.push( v.x, v.y, v.z );\n",
       "        }\n",
       "    }\n",
       "\n",
       "    geometry = new THREE.LineSegmentsGeometry();\n",
       "    geometry.setPositions( positions );\n",
       "\n",
       "    var material = new THREE.LineMaterial( materialOptions );\n",
       "    material.resolution = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "\n",
       "    var line = new THREE.LineSegments2( geometry, material );\n",
       "    line.computeLineDistances();\n",
       "    line.scale.set( 1, 1, 1 );\n",
       "\n",
       "    _fatLines.push( line );\n",
       "\n",
       "    return line;\n",
       "\n",
       "}\n",
       "\n",
       "function createFatLineStrip( geometry, materialOptions ) {\n",
       "    return _createFatLine( true, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function createFatLineSegments( geometry, materialOptions ) {\n",
       "    return _createFatLine( false, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function rescaleFatLines() {\n",
       "    var res = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "    var n = _fatLines.length;\n",
       "    for ( var i=0 ; i < n ; i++ ) {\n",
       "        _fatLines[i].material.resolution = res;\n",
       "    }\n",
       "}\n",
       "</script>\n",
       "<script>\n",
       "\n",
       "    var options = {&quot;animate&quot;: false, &quot;animationControls&quot;: true, &quot;aspectRatio&quot;: [1.0, 1.0, 1.0], &quot;autoScaling&quot;: [false, false, false], &quot;autoPlay&quot;: true, &quot;axes&quot;: false, &quot;axesLabels&quot;: false, &quot;axesLabelsStyle&quot;: null, &quot;decimals&quot;: 2, &quot;delay&quot;: 20, &quot;frame&quot;: false, &quot;loop&quot;: true, &quot;projection&quot;: &quot;perspective&quot;, &quot;theme&quot;: &quot;light&quot;, &quot;viewpoint&quot;: false};\n",
       "    var animate = options.animate;\n",
       "\n",
       "    if ( options.theme === 'dark' )\n",
       "        document.body.className = 'dark-theme';\n",
       "\n",
       "    var scene = new THREE.Scene();\n",
       "\n",
       "    var renderer = new THREE.WebGLRenderer( { antialias: true, preserveDrawingBuffer: true } );\n",
       "    renderer.setPixelRatio( window.devicePixelRatio );\n",
       "    renderer.setSize( window.innerWidth, window.innerHeight );\n",
       "    renderer.setClearColor( options.theme === 'dark' ? 0 : 0xffffff, 1 );\n",
       "    document.body.appendChild( renderer.domElement );\n",
       "\n",
       "    var b = [{&quot;x&quot;:-1.3032567512679742, &quot;y&quot;:-1.3045727724329577, &quot;z&quot;:0.0}, {&quot;x&quot;:1.3062526079130183, &quot;y&quot;:1.3058136968862606, &quot;z&quot;:1.25}]; // 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 rxRange = Math.sqrt( Math.pow( b[1].z - b[0].z, 2 )\n",
       "                            + Math.pow( b[1].y - b[0].y, 2 ) );\n",
       "    var ryRange = Math.sqrt( Math.pow( b[1].x - b[0].x, 2 )\n",
       "                            + Math.pow( b[1].z - b[0].z, 2 ) );\n",
       "    var rzRange = Math.sqrt( Math.pow( b[1].x - b[0].x, 2 )\n",
       "                            + Math.pow( b[1].y - b[0].y, 2 ) );\n",
       "    var xRange = b[1].x - b[0].x;\n",
       "    var yRange = b[1].y - b[0].y;\n",
       "    var zRange = b[1].z - b[0].z;\n",
       "\n",
       "    var ar = options.aspectRatio;\n",
       "    var a = [ ar[0], ar[1], ar[2] ]; // aspect multipliers\n",
       "\n",
       "    var autoScaling = options.autoScaling;\n",
       "    var autoAspect = 2.5;\n",
       "    if ( xRange > autoAspect * rxRange && autoScaling[0] ) a[0] = autoAspect * rxRange / xRange;\n",
       "    if ( yRange > autoAspect * ryRange && autoScaling[1] ) a[1] = autoAspect * ryRange / yRange;\n",
       "    if ( zRange > autoAspect * rzRange && autoScaling[2] ) a[2] = autoAspect * rzRange / zRange;\n",
       "\n",
       "    // Distance from (xMid,yMid,zMid) to any corner of the bounding box, after applying aspectRatio\n",
       "    var midToCorner = Math.sqrt( a[0]*a[0]*xRange*xRange + a[1]*a[1]*yRange*yRange + a[2]*a[2]*zRange*zRange ) / 2;\n",
       "\n",
       "    var xMid = ( b[0].x + b[1].x ) / 2;\n",
       "    var yMid = ( b[0].y + b[1].y ) / 2;\n",
       "    var zMid = ( b[0].z + b[1].z ) / 2;\n",
       "\n",
       "    var box = new THREE.Geometry();\n",
       "    box.vertices.push( new THREE.Vector3( a[0]*b[0].x, a[1]*b[0].y, a[2]*b[0].z ) );\n",
       "    box.vertices.push( new THREE.Vector3( a[0]*b[1].x, a[1]*b[1].y, a[2]*b[1].z ) );\n",
       "    var boxMesh = new THREE.Line( box );\n",
       "    var boxColor = options.theme === 'dark' ? 'white' : 'black';\n",
       "    if ( options.frame ) scene.add( new THREE.BoxHelper( boxMesh, boxColor ) );\n",
       "\n",
       "    if ( options.axesLabels ) {\n",
       "\n",
       "        var d = options.decimals; // decimals\n",
       "        var offsetRatio = 0.1;\n",
       "        var al = options.axesLabels;\n",
       "        var als = options.axesLabelsStyle || [{}, {}, {}];\n",
       "\n",
       "        var offset = offsetRatio * a[1]*( b[1].y - b[0].y );\n",
       "        var xm = xMid.toFixed(d);\n",
       "        if ( /^-0.?0*$/.test(xm) ) xm = xm.substr(1);\n",
       "        addLabel( al[0] + '=' + xm, a[0]*xMid, a[1]*b[1].y+offset, a[2]*b[0].z, als[0] );\n",
       "        addLabel( ( b[0].x ).toFixed(d), a[0]*b[0].x, a[1]*b[1].y+offset, a[2]*b[0].z, als[0] );\n",
       "        addLabel( ( b[1].x ).toFixed(d), a[0]*b[1].x, a[1]*b[1].y+offset, a[2]*b[0].z, als[0] );\n",
       "\n",
       "        var offset = offsetRatio * a[0]*( b[1].x - b[0].x );\n",
       "        var ym = yMid.toFixed(d);\n",
       "        if ( /^-0.?0*$/.test(ym) ) ym = ym.substr(1);\n",
       "        addLabel( al[1] + '=' + ym, a[0]*b[1].x+offset, a[1]*yMid, a[2]*b[0].z, als[1] );\n",
       "        addLabel( ( b[0].y ).toFixed(d), a[0]*b[1].x+offset, a[1]*b[0].y, a[2]*b[0].z, als[1] );\n",
       "        addLabel( ( b[1].y ).toFixed(d), a[0]*b[1].x+offset, a[1]*b[1].y, a[2]*b[0].z, als[1] );\n",
       "\n",
       "        var offset = offsetRatio * a[1]*( b[1].y - b[0].y );\n",
       "        var zm = zMid.toFixed(d);\n",
       "        if ( /^-0.?0*$/.test(zm) ) zm = zm.substr(1);\n",
       "        addLabel( al[2] + '=' + zm, a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*zMid, als[2] );\n",
       "        addLabel( ( b[0].z ).toFixed(d), a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*b[0].z, als[2] );\n",
       "        addLabel( ( b[1].z ).toFixed(d), a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*b[1].z, als[2] );\n",
       "\n",
       "    }\n",
       "\n",
       "    function addLabel( text, x, y, z, style ) {\n",
       "\n",
       "        var color = style.color || 'black';\n",
       "        var fontSize = style.fontSize || 14;\n",
       "        var fontFamily = style.fontFamily || 'monospace';\n",
       "        var fontStyle = style.fontStyle || 'normal';\n",
       "        var fontWeight = style.fontWeight || 'normal';\n",
       "        var opacity = style.opacity || 1;\n",
       "\n",
       "        if ( options.theme === 'dark' )\n",
       "            if ( color === 'black' || color === '#000000' )\n",
       "                color = 'white';\n",
       "\n",
       "        if ( Array.isArray( fontStyle ) ) {\n",
       "            fontFamily = fontFamily.map( function( f ) {\n",
       "                // Need to put quotes around fonts that have whitespace in their names.\n",
       "                return /\\s/.test( f ) ? '&quot;' + f + '&quot;' : f;\n",
       "            }).join(', ');\n",
       "        }\n",
       "\n",
       "        var canvas = document.createElement( 'canvas' );\n",
       "        var context = canvas.getContext( '2d' );\n",
       "        var pixelRatio = Math.round( window.devicePixelRatio );\n",
       "\n",
       "        // For example: italic bold 20px &quot;Times New Roman&quot;, Georgia, serif\n",
       "        var font = [fontStyle, fontWeight, fontSize + 'px', fontFamily].join(' ');\n",
       "\n",
       "        context.font = font;\n",
       "        var width = context.measureText( text ).width;\n",
       "        var height = fontSize;\n",
       "\n",
       "        // The dimensions of the canvas's underlying image data need to be powers\n",
       "        // of two in order for the resulting texture to support mipmapping.\n",
       "        canvas.width = THREE.MathUtils.ceilPowerOfTwo( width * pixelRatio );\n",
       "        canvas.height = THREE.MathUtils.ceilPowerOfTwo( height * pixelRatio );\n",
       "\n",
       "        // Re-compute the unscaled dimensions after the power of two conversion.\n",
       "        width = canvas.width / pixelRatio;\n",
       "        height = canvas.height / pixelRatio;\n",
       "\n",
       "        canvas.style.width = width + 'px';\n",
       "        canvas.style.height = height + 'px';\n",
       "\n",
       "        context.scale( pixelRatio, pixelRatio );\n",
       "        context.fillStyle = color;\n",
       "        context.font = font; // Must be set again after measureText.\n",
       "        context.textAlign = 'center';\n",
       "        context.textBaseline = 'middle';\n",
       "        context.fillText( text, width/2, height/2 );\n",
       "\n",
       "        var texture = new THREE.Texture( canvas );\n",
       "        texture.needsUpdate = true;\n",
       "\n",
       "        var materialOptions = { map: texture, sizeAttenuation: false, depthWrite: false };\n",
       "        if ( opacity < 1 ) {\n",
       "            // Setting opacity=1 would cause the texture's alpha component to be\n",
       "            // discarded, giving the text a black background instead of the\n",
       "            // background being transparent.\n",
       "            materialOptions.opacity = opacity;\n",
       "        }\n",
       "        var sprite = new THREE.Sprite( new THREE.SpriteMaterial( materialOptions ) );\n",
       "        sprite.position.set( x, y, z );\n",
       "\n",
       "        // Scaling factor, chosen somewhat arbitrarily so that the size of the text\n",
       "        // is consistent with previously generated plots.\n",
       "        var scale = 1/625;\n",
       "        if ( options.projection === 'orthographic' ) {\n",
       "            scale = midToCorner/256; // Needs to scale along with the plot itself.\n",
       "        }\n",
       "        sprite.scale.set( scale * width, scale * height, 1 );\n",
       "\n",
       "        scene.add( sprite );\n",
       "\n",
       "        return sprite;\n",
       "\n",
       "    }\n",
       "\n",
       "    if ( options.axes ) scene.add( new THREE.AxesHelper( Math.min( a[0]*b[1].x, a[1]*b[1].y, a[2]*b[1].z ) ) );\n",
       "\n",
       "    var camera = createCamera();\n",
       "    camera.up.set( 0, 0, 1 );\n",
       "    camera.position.set( a[0]*xMid, a[1]*yMid, a[2]*zMid );\n",
       "\n",
       "    var offset = new THREE.Vector3( a[0]*xRange, a[1]*yRange, a[2]*zRange );\n",
       "\n",
       "    if ( options.viewpoint ) {\n",
       "\n",
       "        var aa = options.viewpoint;\n",
       "        var axis = new THREE.Vector3( aa[0][0], aa[0][1], aa[0][2] ).normalize();\n",
       "        var angle = aa[1] * Math.PI / 180;\n",
       "        var q = new THREE.Quaternion().setFromAxisAngle( axis, angle ).inverse();\n",
       "\n",
       "        offset.set( 0, 0, offset.length() );\n",
       "        offset.applyQuaternion( q );\n",
       "\n",
       "    }\n",
       "\n",
       "    camera.position.add( offset );\n",
       "\n",
       "    function createCamera() {\n",
       "\n",
       "        var aspect = window.innerWidth / window.innerHeight;\n",
       "\n",
       "        // Scale the near and far clipping planes along with the overall plot size.\n",
       "        var nearClip = 0.01 * midToCorner;\n",
       "        var farClip = 100 * midToCorner;\n",
       "\n",
       "        if ( options.projection === 'orthographic' ) {\n",
       "            var camera = new THREE.OrthographicCamera( -1, 1, 1, -1, -farClip, farClip );\n",
       "            updateCameraAspect( camera, aspect );\n",
       "            return camera;\n",
       "        }\n",
       "\n",
       "        return new THREE.PerspectiveCamera( 45, aspect, nearClip, farClip );\n",
       "\n",
       "    }\n",
       "\n",
       "    function updateCameraAspect( camera, aspect ) {\n",
       "\n",
       "        if ( camera.isPerspectiveCamera ) {\n",
       "            camera.aspect = aspect;\n",
       "        } else if ( camera.isOrthographicCamera ) {\n",
       "            // Fit the camera frustum to the bounding box's diagonal so that the entire plot fits\n",
       "            // within at the default zoom level and camera position.\n",
       "            if ( aspect > 1 ) { // Wide window\n",
       "                camera.top = midToCorner;\n",
       "                camera.right = midToCorner * aspect;\n",
       "            } else { // Tall or square window\n",
       "                camera.top = midToCorner / aspect;\n",
       "                camera.right = midToCorner;\n",
       "            }\n",
       "            camera.bottom = -camera.top;\n",
       "            camera.left = -camera.right;\n",
       "        }\n",
       "\n",
       "        camera.updateProjectionMatrix();\n",
       "\n",
       "    }\n",
       "\n",
       "    var lights = [{&quot;x&quot;:-5, &quot;y&quot;:3, &quot;z&quot;:0, &quot;color&quot;:&quot;#7f7f7f&quot;, &quot;parent&quot;:&quot;camera&quot;}];\n",
       "    for ( var i=0 ; i < lights.length ; i++ ) {\n",
       "        var light = new THREE.DirectionalLight( lights[i].color, 1 );\n",
       "        light.position.set( a[0]*lights[i].x, a[1]*lights[i].y, a[2]*lights[i].z );\n",
       "        if ( lights[i].parent === 'camera' ) {\n",
       "            light.target.position.set( a[0]*xMid, a[1]*yMid, a[2]*zMid );\n",
       "            scene.add( light.target );\n",
       "            camera.add( light );\n",
       "        } else scene.add( light );\n",
       "    }\n",
       "    scene.add( camera );\n",
       "\n",
       "    var ambient = {&quot;color&quot;:&quot;#7f7f7f&quot;};\n",
       "    scene.add( new THREE.AmbientLight( ambient.color, 1 ) );\n",
       "\n",
       "    var controls = new THREE.OrbitControls( camera, renderer.domElement );\n",
       "    controls.target.set( a[0]*xMid, a[1]*yMid, a[2]*zMid );\n",
       "    controls.addEventListener( 'change', function() { if ( !animate ) render(); } );\n",
       "\n",
       "    window.addEventListener( 'resize', function() {\n",
       "\n",
       "        renderer.setSize( window.innerWidth, window.innerHeight );\n",
       "        updateCameraAspect( camera, window.innerWidth / window.innerHeight );\n",
       "        if ( window.rescaleFatLines ) rescaleFatLines();\n",
       "        if ( !animate ) render();\n",
       "\n",
       "    } );\n",
       "\n",
       "    var texts = [{&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;x&quot;, &quot;x&quot;: 1.1548494156391085, &quot;y&quot;: 0.47835429045636224, &quot;z&quot;: 0.0}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;y&quot;, &quot;x&quot;: -0.47835429045636224, &quot;y&quot;: 1.1548494156391085, &quot;z&quot;: 0.0}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;z&quot;, &quot;x&quot;: 0.0, &quot;y&quot;: 0.0, &quot;z&quot;: 1.25}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;(x,y,z)&quot;, &quot;x&quot;: 0.24818097361470023, &quot;y&quot;: 0.9687136854280833, &quot;z&quot;: 0.7}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;\\u03c6&quot;, &quot;x&quot;: 0.5319106430483738, &quot;y&quot;: 0.5450422624089488, &quot;z&quot;: 0.0}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;\\u03b8&quot;, &quot;x&quot;: -0.07653668647301796, &quot;y&quot;: 0.18477590650225736, &quot;z&quot;: 0.5}];\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;: [0.46193976625564337, 0.1913417161825449, 0.0], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;point&quot;: [0.44052969425835165, 0.23650282974341605, 0.0], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;point&quot;: [0.4147179951757867, 0.2793008852069325, 0.0], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;point&quot;: [0.38476257097296834, 0.31930825855005923, 0.0], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;point&quot;: [0.3509627263465844, 0.3561252093230308, 0.0], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;point&quot;: [0.31365617817139835, 0.38938387472378977, 0.0], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;point&quot;: [0.2732156811448715, 0.4187519451615048, 0.0], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;point&quot;: [0.2300453033454419, 0.4439359845841556, 0.0], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;point&quot;: [0.1913417161825449, 0.46193976625564337, 0.3535533905932738], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;point&quot;: [0.1712835073195068, 0.4135149663815847, 0.3870835392384732], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;point&quot;: [0.14951389027013218, 0.3609584616533158, 0.41674607711240824], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;point&quot;: [0.12625037985189952, 0.30479537929321077, 0.4422446259417738], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;point&quot;: [0.10172541737101383, 0.24558688225516523, 0.4633244126553665], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;point&quot;: [0.0761840481457092, 0.183924562269856, 0.4797748149923952], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;point&quot;: [0.0498814730944308, 0.12042452885572347, 0.4914314659704884], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}, {&quot;point&quot;: [0.02308049885261569, 0.05572125335632147, 0.4981778961862494], &quot;size&quot;: 7.0, &quot;color&quot;: &quot;#000000&quot;, &quot;opacity&quot;: 1.0}];\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], [1.0624614623879796, 0.4400859472198532, 0.0]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 5.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [-0.4400859472198532, 1.0624614623879796, 0.0]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 5.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [0.0, 0.0, 1.15]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 5.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [0.31930569908625617, 0.770872149277062, 0.0], [0.31930569908625617, 0.770872149277062, 0.59], [0.0, 0.0, 0.0]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 5.0}];\n",
       "    for ( var i=0 ; i < lines.length ; i++ ) addLine( lines[i] );\n",
       "\n",
       "    function addLine( json ) {\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "        for ( var i=0 ; i < json.points.length ; i++ ) {\n",
       "            var v = json.points[i];\n",
       "            geometry.vertices.push( new THREE.Vector3( a[0]*v[0], a[1]*v[1], a[2]*v[2] ) );\n",
       "        }\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var transparent = json.opacity < 1 ? true : false;\n",
       "        var materialOptions = { color: json.color, linewidth: json.linewidth,\n",
       "                                transparent: transparent, opacity: json.opacity };\n",
       "\n",
       "        var mesh;\n",
       "        if ( json.linewidth > 1 && window.createFatLineStrip ) {\n",
       "            mesh = createFatLineStrip( geometry, materialOptions );\n",
       "        } else {\n",
       "            var material = new THREE.LineBasicMaterial( materialOptions );\n",
       "            mesh = new THREE.Line( geometry, material );\n",
       "        }\n",
       "\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "    }\n",
       "\n",
       "    var surfaces = [{&quot;vertices&quot;: [{&quot;x&quot;: 0.9238795325112867, &quot;y&quot;: 0.3826834323650898, &quot;z&quot;: 0.0}, {&quot;x&quot;: 0.9231302645211706, &quot;y&quot;: 0.38237307540173165, &quot;z&quot;: 0.04026594010941514}, {&quot;x&quot;: 0.8498390152539148, &quot;y&quot;: 0.5255019526313497, &quot;z&quot;: 0.04026594010941514}, {&quot;x&quot;: 0.8505287956623296, &quot;y&quot;: 0.525928481591544, &quot;z&quot;: 0.0}, {&quot;x&quot;: 0.9208836758662425, &quot;y&quot;: 0.3814425079117869, &quot;z&quot;: 0.08046656871672588}, {&quot;x&quot;: 0.8477707928550152, &quot;y&quot;: 0.5242230575822999, &quot;z&quot;: 0.08046656871672588}, {&quot;x&quot;: 0.9171434105215159, &quot;y&quot;: 0.37989323927912705, &quot;z&quot;: 0.12053668025532305}, {&quot;x&quot;: 0.844327483129925, &quot;y&quot;: 0.5220938708168408, &quot;z&quot;: 0.12053668025532305}, {&quot;x&quot;: 0.9119155352110577, &quot;y&quot;: 0.3777277824231398, &quot;z&quot;: 0.16041128085776024}, 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1135, 1134], [1095, 1096, 1136, 1135], [1096, 1097, 1137, 1136], [1097, 1098, 1138, 1137], [1098, 1099, 1139, 1138], [1099, 1100, 1140, 1139], [1100, 1101, 1141, 1140], [1101, 1102, 1142, 1141], [1102, 1103, 1143, 1142], [1103, 1104, 1144, 1143], [1104, 1105, 1145, 1144], [1105, 1106, 1146, 1145], [1106, 1107, 1147, 1146], [1107, 1108, 1148, 1147], [1108, 1109, 1149, 1148], [1109, 1110, 1150, 1149], [1110, 1111, 1151, 1150], [1111, 1112, 1152, 1151], [1112, 1113, 1153, 1152], [1113, 1114, 1154, 1153], [1114, 1115, 1155, 1154], [1115, 1116, 1156, 1155], [1116, 1117, 1157, 1156], [1117, 1118, 1158, 1157], [1118, 1119, 1159, 1158], [1121, 1120, 1160, 1161], [1120, 1122, 1162, 1160], [1122, 1123, 1163, 1162], [1123, 1124, 1164, 1163], [1124, 1125, 1165, 1164], [1125, 1126, 1166, 1165], [1126, 1127, 1167, 1166], [1127, 1128, 1168, 1167], [1128, 1129, 1169, 1168], [1129, 1130, 1170, 1169], [1130, 1131, 1171, 1170], [1131, 1132, 1172, 1171], [1132, 1133, 1173, 1172], [1133, 1134, 1174, 1173], 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1214, 1213], [1174, 1175, 1215, 1214], [1175, 1176, 1216, 1215], [1176, 1177, 1217, 1216], [1177, 1178, 1218, 1217], [1178, 1179, 1219, 1218], [1179, 1180, 1220, 1219], [1180, 1181, 1221, 1220], [1181, 1182, 1222, 1221], [1182, 1183, 1223, 1222], [1183, 1184, 1224, 1223], [1184, 1185, 1225, 1224], [1185, 1186, 1226, 1225], [1186, 1187, 1227, 1226], [1187, 1188, 1228, 1227], [1188, 1189, 1229, 1228], [1189, 1190, 1230, 1229], [1190, 1191, 1231, 1230], [1191, 1192, 1232, 1231], [1192, 1193, 1233, 1232], [1193, 1194, 1234, 1233], [1194, 1195, 1235, 1234], [1195, 1196, 1236, 1235], [1196, 1197, 1237, 1236], [1197, 1198, 1238, 1237], [1198, 1199, 1239, 1238], [1201, 1200, 1240, 1241], [1200, 1202, 1242, 1240], [1202, 1203, 1243, 1242], [1203, 1204, 1244, 1243], [1204, 1205, 1245, 1244], [1205, 1206, 1246, 1245], [1206, 1207, 1247, 1246], [1207, 1208, 1248, 1247], [1208, 1209, 1249, 1248], [1209, 1210, 1250, 1249], [1210, 1211, 1251, 1250], [1211, 1212, 1252, 1251], [1212, 1213, 1253, 1252], [1213, 1214, 1254, 1253], [1214, 1215, 1255, 1254], [1215, 1216, 1256, 1255], [1216, 1217, 1257, 1256], [1217, 1218, 1258, 1257], [1218, 1219, 1259, 1258], [1219, 1220, 1260, 1259], [1220, 1221, 1261, 1260], [1221, 1222, 1262, 1261], [1222, 1223, 1263, 1262], [1223, 1224, 1264, 1263], [1224, 1225, 1265, 1264], [1225, 1226, 1266, 1265], [1226, 1227, 1267, 1266], [1227, 1228, 1268, 1267], [1228, 1229, 1269, 1268], [1229, 1230, 1270, 1269], [1230, 1231, 1271, 1270], [1231, 1232, 1272, 1271], [1232, 1233, 1273, 1272], [1233, 1234, 1274, 1273], [1234, 1235, 1275, 1274], [1235, 1236, 1276, 1275], [1236, 1237, 1277, 1276], [1237, 1238, 1278, 1277], [1238, 1239, 1279, 1278], [1241, 1240, 1280, 1281], [1240, 1242, 1282, 1280], [1242, 1243, 1283, 1282], [1243, 1244, 1284, 1283], [1244, 1245, 1285, 1284], [1245, 1246, 1286, 1285], [1246, 1247, 1287, 1286], [1247, 1248, 1288, 1287], [1248, 1249, 1289, 1288], [1249, 1250, 1290, 1289], [1250, 1251, 1291, 1290], [1251, 1252, 1292, 1291], [1252, 1253, 1293, 1292], [1253, 1254, 1294, 1293], [1254, 1255, 1295, 1294], [1255, 1256, 1296, 1295], [1256, 1257, 1297, 1296], [1257, 1258, 1298, 1297], [1258, 1259, 1299, 1298], [1259, 1260, 1300, 1299], [1260, 1261, 1301, 1300], [1261, 1262, 1302, 1301], [1262, 1263, 1303, 1302], [1263, 1264, 1304, 1303], [1264, 1265, 1305, 1304], [1265, 1266, 1306, 1305], [1266, 1267, 1307, 1306], [1267, 1268, 1308, 1307], [1268, 1269, 1309, 1308], [1269, 1270, 1310, 1309], [1270, 1271, 1311, 1310], [1271, 1272, 1312, 1311], [1272, 1273, 1313, 1312], [1273, 1274, 1314, 1313], [1274, 1275, 1315, 1314], [1275, 1276, 1316, 1315], [1276, 1277, 1317, 1316], [1277, 1278, 1318, 1317], [1278, 1279, 1319, 1318], [1281, 1280, 1320, 1321], [1280, 1282, 1322, 1320], [1282, 1283, 1323, 1322], [1283, 1284, 1324, 1323], [1284, 1285, 1325, 1324], [1285, 1286, 1326, 1325], [1286, 1287, 1327, 1326], [1287, 1288, 1328, 1327], [1288, 1289, 1329, 1328], [1289, 1290, 1330, 1329], [1290, 1291, 1331, 1330], [1291, 1292, 1332, 1331], [1292, 1293, 1333, 1332], [1293, 1294, 1334, 1333], [1294, 1295, 1335, 1334], [1295, 1296, 1336, 1335], [1296, 1297, 1337, 1336], [1297, 1298, 1338, 1337], [1298, 1299, 1339, 1338], [1299, 1300, 1340, 1339], [1300, 1301, 1341, 1340], [1301, 1302, 1342, 1341], [1302, 1303, 1343, 1342], [1303, 1304, 1344, 1343], [1304, 1305, 1345, 1344], [1305, 1306, 1346, 1345], [1306, 1307, 1347, 1346], [1307, 1308, 1348, 1347], [1308, 1309, 1349, 1348], [1309, 1310, 1350, 1349], [1310, 1311, 1351, 1350], [1311, 1312, 1352, 1351], [1312, 1313, 1353, 1352], [1313, 1314, 1354, 1353], [1314, 1315, 1355, 1354], [1315, 1316, 1356, 1355], [1316, 1317, 1357, 1356], [1317, 1318, 1358, 1357], [1318, 1319, 1359, 1358], [1321, 1320, 1360, 1361], [1320, 1322, 1362, 1360], [1322, 1323, 1363, 1362], [1323, 1324, 1364, 1363], [1324, 1325, 1365, 1364], [1325, 1326, 1366, 1365], [1326, 1327, 1367, 1366], [1327, 1328, 1368, 1367], [1328, 1329, 1369, 1368], [1329, 1330, 1370, 1369], [1330, 1331, 1371, 1370], [1331, 1332, 1372, 1371], [1332, 1333, 1373, 1372], [1333, 1334, 1374, 1373], [1334, 1335, 1375, 1374], [1335, 1336, 1376, 1375], [1336, 1337, 1377, 1376], [1337, 1338, 1378, 1377], [1338, 1339, 1379, 1378], [1339, 1340, 1380, 1379], [1340, 1341, 1381, 1380], [1341, 1342, 1382, 1381], [1342, 1343, 1383, 1382], [1343, 1344, 1384, 1383], [1344, 1345, 1385, 1384], [1345, 1346, 1386, 1385], [1346, 1347, 1387, 1386], [1347, 1348, 1388, 1387], [1348, 1349, 1389, 1388], [1349, 1350, 1390, 1389], [1350, 1351, 1391, 1390], [1351, 1352, 1392, 1391], [1352, 1353, 1393, 1392], [1353, 1354, 1394, 1393], [1354, 1355, 1395, 1394], [1355, 1356, 1396, 1395], [1356, 1357, 1397, 1396], [1357, 1358, 1398, 1397], [1358, 1359, 1399, 1398], [1361, 1360, 1400, 1401], [1360, 1362, 1402, 1400], [1362, 1363, 1403, 1402], [1363, 1364, 1404, 1403], [1364, 1365, 1405, 1404], [1365, 1366, 1406, 1405], [1366, 1367, 1407, 1406], [1367, 1368, 1408, 1407], [1368, 1369, 1409, 1408], [1369, 1370, 1410, 1409], [1370, 1371, 1411, 1410], [1371, 1372, 1412, 1411], [1372, 1373, 1413, 1412], [1373, 1374, 1414, 1413], [1374, 1375, 1415, 1414], [1375, 1376, 1416, 1415], [1376, 1377, 1417, 1416], [1377, 1378, 1418, 1417], [1378, 1379, 1419, 1418], [1379, 1380, 1420, 1419], [1380, 1381, 1421, 1420], [1381, 1382, 1422, 1421], [1382, 1383, 1423, 1422], [1383, 1384, 1424, 1423], [1384, 1385, 1425, 1424], [1385, 1386, 1426, 1425], [1386, 1387, 1427, 1426], [1387, 1388, 1428, 1427], [1388, 1389, 1429, 1428], [1389, 1390, 1430, 1429], [1390, 1391, 1431, 1430], [1391, 1392, 1432, 1431], [1392, 1393, 1433, 1432], [1393, 1394, 1434, 1433], [1394, 1395, 1435, 1434], [1395, 1396, 1436, 1435], [1396, 1397, 1437, 1436], [1397, 1398, 1438, 1437], [1398, 1399, 1439, 1438], [1401, 1400, 1440, 1441], [1400, 1402, 1442, 1440], [1402, 1403, 1443, 1442], [1403, 1404, 1444, 1443], [1404, 1405, 1445, 1444], [1405, 1406, 1446, 1445], [1406, 1407, 1447, 1446], [1407, 1408, 1448, 1447], [1408, 1409, 1449, 1448], [1409, 1410, 1450, 1449], [1410, 1411, 1451, 1450], [1411, 1412, 1452, 1451], [1412, 1413, 1453, 1452], [1413, 1414, 1454, 1453], [1414, 1415, 1455, 1454], [1415, 1416, 1456, 1455], [1416, 1417, 1457, 1456], [1417, 1418, 1458, 1457], [1418, 1419, 1459, 1458], [1419, 1420, 1460, 1459], [1420, 1421, 1461, 1460], [1421, 1422, 1462, 1461], [1422, 1423, 1463, 1462], [1423, 1424, 1464, 1463], [1424, 1425, 1465, 1464], [1425, 1426, 1466, 1465], [1426, 1427, 1467, 1466], [1427, 1428, 1468, 1467], [1428, 1429, 1469, 1468], [1429, 1430, 1470, 1469], [1430, 1431, 1471, 1470], [1431, 1432, 1472, 1471], [1432, 1433, 1473, 1472], [1433, 1434, 1474, 1473], [1434, 1435, 1475, 1474], [1435, 1436, 1476, 1475], [1436, 1437, 1477, 1476], [1437, 1438, 1478, 1477], [1438, 1439, 1479, 1478], [1441, 1440, 1480, 1481], [1440, 1442, 1482, 1480], [1442, 1443, 1483, 1482], [1443, 1444, 1484, 1483], [1444, 1445, 1485, 1484], [1445, 1446, 1486, 1485], [1446, 1447, 1487, 1486], [1447, 1448, 1488, 1487], [1448, 1449, 1489, 1488], [1449, 1450, 1490, 1489], [1450, 1451, 1491, 1490], [1451, 1452, 1492, 1491], [1452, 1453, 1493, 1492], [1453, 1454, 1494, 1493], [1454, 1455, 1495, 1494], [1455, 1456, 1496, 1495], [1456, 1457, 1497, 1496], [1457, 1458, 1498, 1497], [1458, 1459, 1499, 1498], [1459, 1460, 1500, 1499], [1460, 1461, 1501, 1500], [1461, 1462, 1502, 1501], [1462, 1463, 1503, 1502], [1463, 1464, 1504, 1503], [1464, 1465, 1505, 1504], [1465, 1466, 1506, 1505], [1466, 1467, 1507, 1506], [1467, 1468, 1508, 1507], [1468, 1469, 1509, 1508], [1469, 1470, 1510, 1509], [1470, 1471, 1511, 1510], [1471, 1472, 1512, 1511], [1472, 1473, 1513, 1512], [1473, 1474, 1514, 1513], [1474, 1475, 1515, 1514], [1475, 1476, 1516, 1515], [1476, 1477, 1517, 1516], [1477, 1478, 1518, 1517], [1478, 1479, 1519, 1518], [1481, 1480, 1520, 1521], [1480, 1482, 1522, 1520], [1482, 1483, 1523, 1522], [1483, 1484, 1524, 1523], [1484, 1485, 1525, 1524], [1485, 1486, 1526, 1525], [1486, 1487, 1527, 1526], [1487, 1488, 1528, 1527], [1488, 1489, 1529, 1528], [1489, 1490, 1530, 1529], [1490, 1491, 1531, 1530], [1491, 1492, 1532, 1531], [1492, 1493, 1533, 1532], [1493, 1494, 1534, 1533], [1494, 1495, 1535, 1534], [1495, 1496, 1536, 1535], [1496, 1497, 1537, 1536], [1497, 1498, 1538, 1537], [1498, 1499, 1539, 1538], [1499, 1500, 1540, 1539], [1500, 1501, 1541, 1540], [1501, 1502, 1542, 1541], [1502, 1503, 1543, 1542], [1503, 1504, 1544, 1543], [1504, 1505, 1545, 1544], [1505, 1506, 1546, 1545], [1506, 1507, 1547, 1546], [1507, 1508, 1548, 1547], [1508, 1509, 1549, 1548], [1509, 1510, 1550, 1549], [1510, 1511, 1551, 1550], [1511, 1512, 1552, 1551], [1512, 1513, 1553, 1552], [1513, 1514, 1554, 1553], [1514, 1515, 1555, 1554], [1515, 1516, 1556, 1555], [1516, 1517, 1557, 1556], [1517, 1518, 1558, 1557], [1518, 1519, 1559, 1558], [1521, 1520, 1560, 1561], [1520, 1522, 1562, 1560], [1522, 1523, 1563, 1562], [1523, 1524, 1564, 1563], [1524, 1525, 1565, 1564], [1525, 1526, 1566, 1565], [1526, 1527, 1567, 1566], [1527, 1528, 1568, 1567], [1528, 1529, 1569, 1568], [1529, 1530, 1570, 1569], [1530, 1531, 1571, 1570], [1531, 1532, 1572, 1571], [1532, 1533, 1573, 1572], [1533, 1534, 1574, 1573], [1534, 1535, 1575, 1574], [1535, 1536, 1576, 1575], [1536, 1537, 1577, 1576], [1537, 1538, 1578, 1577], [1538, 1539, 1579, 1578], [1539, 1540, 1580, 1579], [1540, 1541, 1581, 1580], [1541, 1542, 1582, 1581], [1542, 1543, 1583, 1582], [1543, 1544, 1584, 1583], [1544, 1545, 1585, 1584], [1545, 1546, 1586, 1585], [1546, 1547, 1587, 1586], [1547, 1548, 1588, 1587], [1548, 1549, 1589, 1588], [1549, 1550, 1590, 1589], [1550, 1551, 1591, 1590], [1551, 1552, 1592, 1591], [1552, 1553, 1593, 1592], [1553, 1554, 1594, 1593], [1554, 1555, 1595, 1594], [1555, 1556, 1596, 1595], [1556, 1557, 1597, 1596], [1557, 1558, 1598, 1597], [1558, 1559, 1599, 1598]], &quot;color&quot;: &quot;#d3d3d3&quot;, &quot;opacity&quot;: 0.9}];\n",
       "    for ( var i=0 ; i < surfaces.length ; i++ ) addSurface( surfaces[i] );\n",
       "\n",
       "    function addSurface( json ) {\n",
       "\n",
       "        var useFaceColors = 'faceColors' in json ? true : false;\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "        for ( var i=0 ; i < json.vertices.length ; i++ ) {\n",
       "            var v = json.vertices[i];\n",
       "            geometry.vertices.push( new THREE.Vector3( a[0]*v.x, a[1]*v.y, a[2]*v.z ) );\n",
       "        }\n",
       "        for ( var i=0 ; i < json.faces.length ; i++ ) {\n",
       "            var f = json.faces[i];\n",
       "            for ( var j=0 ; j < f.length - 2 ; j++ ) {\n",
       "                var face = new THREE.Face3( f[0], f[j+1], f[j+2] );\n",
       "                if ( useFaceColors ) face.color.set( json.faceColors[i] );\n",
       "                geometry.faces.push( face );\n",
       "            }\n",
       "        }\n",
       "        geometry.computeVertexNormals();\n",
       "\n",
       "        var side = json.singleSide ? THREE.FrontSide : THREE.DoubleSide;\n",
       "        var transparent = json.opacity < 1 ? true : false;\n",
       "        var depthWrite = 'depthWrite' in json ? json.depthWrite : !transparent;\n",
       "        var flatShading = json.useFlatShading ? json.useFlatShading : false;\n",
       "\n",
       "        var material = new THREE.MeshPhongMaterial( { side: side,\n",
       "                                     color: useFaceColors ? 'white' : json.color,\n",
       "                                     vertexColors: useFaceColors ? THREE.FaceColors : THREE.NoColors,\n",
       "                                     transparent: transparent, opacity: json.opacity,\n",
       "                                     shininess: 20, flatShading: flatShading,\n",
       "                                     depthWrite: depthWrite } );\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var mesh = new THREE.Mesh( geometry, material );\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        if ( transparent && json.renderOrder ) mesh.renderOrder = json.renderOrder;\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "        if ( json.showMeshGrid ) addSurfaceMeshGrid( json );\n",
       "\n",
       "    }\n",
       "\n",
       "    function addSurfaceMeshGrid( json ) {\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "\n",
       "        for ( var i=0 ; i < json.faces.length ; i++ ) {\n",
       "            var f = json.faces[i];\n",
       "            for ( var j=0 ; j < f.length ; j++ ) {\n",
       "                var k = j === f.length-1 ? 0 : j+1;\n",
       "                var v1 = json.vertices[f[j]];\n",
       "                var v2 = json.vertices[f[k]];\n",
       "                // vertices in opposite directions on neighboring faces\n",
       "                var nudge = f[j] < f[k] ? .0005*zRange : -.0005*zRange;\n",
       "                geometry.vertices.push( new THREE.Vector3( a[0]*v1.x, a[1]*v1.y, a[2]*(v1.z+nudge) ) );\n",
       "                geometry.vertices.push( new THREE.Vector3( a[0]*v2.x, a[1]*v2.y, a[2]*(v2.z+nudge) ) );\n",
       "            }\n",
       "        }\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var gridColor = options.theme === 'dark' ? 'white' : 'black';\n",
       "        var linewidth = json.linewidth || 1;\n",
       "        var materialOptions = { color: gridColor, linewidth: linewidth };\n",
       "\n",
       "        var mesh;\n",
       "        if ( linewidth > 1 && window.createFatLineSegments ) {\n",
       "            mesh = createFatLineSegments( geometry, materialOptions );\n",
       "        } else {\n",
       "            var material = new THREE.LineBasicMaterial( materialOptions );\n",
       "            mesh = new THREE.LineSegments( geometry, material );\n",
       "        }\n",
       "\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "    }\n",
       "\n",
       "    function render() {\n",
       "\n",
       "        if ( window.updateAnimation ) animate = updateAnimation();\n",
       "        if ( animate ) requestAnimationFrame( render );\n",
       "\n",
       "        renderer.render( scene, camera );\n",
       "\n",
       "    }\n",
       "\n",
       "    render();\n",
       "    controls.update();\n",
       "    if ( !animate ) render();\n",
       "\n",
       "\n",
       "    // menu functions\n",
       "\n",
       "    function toggleMenu() {\n",
       "\n",
       "        var m = document.getElementById( 'menu-content' );\n",
       "        if ( m.style.display === 'block' ) m.style.display = 'none'\n",
       "        else m.style.display = 'block';\n",
       "\n",
       "    }\n",
       "\n",
       "\n",
       "    function saveAsPNG() {\n",
       "\n",
       "        var a = document.body.appendChild( document.createElement( 'a' ) );\n",
       "        a.href = renderer.domElement.toDataURL( 'image/png' );\n",
       "        a.download = 'screenshot';\n",
       "        a.click();\n",
       "\n",
       "    }\n",
       "\n",
       "    function saveAsHTML() {\n",
       "\n",
       "        toggleMenu(); // otherwise visible in output\n",
       "        event.stopPropagation();\n",
       "\n",
       "        var blob = new Blob( [ '<!DOCTYPE html>\\n' + document.documentElement.outerHTML ] );\n",
       "        var a = document.body.appendChild( document.createElement( 'a' ) );\n",
       "        a.href = window.URL.createObjectURL( blob );\n",
       "        a.download = suggestFilename();\n",
       "        a.click();\n",
       "\n",
       "        function suggestFilename() {\n",
       "            if ( !document.title ) {\n",
       "                return 'graphic.html';\n",
       "            } else if ( /\\.html?$/i.test( document.title ) ) {\n",
       "                return document.title; // already ends in .htm or .html\n",
       "            } else {\n",
       "                return document.title + '.html';\n",
       "            }\n",
       "        }\n",
       "\n",
       "    }\n",
       "\n",
       "    function getViewpoint() {\n",
       "\n",
       "        function roundTo( x, n ) { return +x.toFixed(n); }\n",
       "\n",
       "        var v = camera.quaternion.inverse();\n",
       "        var r = Math.sqrt( v.x*v.x + v.y*v.y + v.z*v.z );\n",
       "        var axis = [ roundTo( v.x / r, 4 ), roundTo( v.y / r, 4 ), roundTo( v.z / r, 4 ) ];\n",
       "        var angle = roundTo( 2 * Math.atan2( r, v.w ) * 180 / Math.PI, 2 );\n",
       "\n",
       "        var textArea = document.createElement( 'textarea' );\n",
       "        textArea.textContent = JSON.stringify( axis ) + ',' + angle;\n",
       "        textArea.style.csstext = 'position: absolute; top: -100%';\n",
       "        document.body.append( textArea );\n",
       "        textArea.select();\n",
       "        document.execCommand( 'copy' );\n",
       "\n",
       "        var m = document.getElementById( 'menu-message' );\n",
       "        m.innerHTML = 'Viewpoint copied to clipboard';\n",
       "        m.style.display = 'block';\n",
       "        setTimeout( function() { m.style.display = 'none'; }, 2000 );\n",
       "\n",
       "    }\n",
       "\n",
       "    function getCamera() {\n",
       "\n",
       "        function roundTo( x, n ) { return +x.toFixed(n); }\n",
       "\n",
       "        var pos = camera.position;\n",
       "        var pos_r = [ roundTo( pos.x, 4 ), roundTo( pos.y, 4 ), roundTo( pos.z, 4 ) ];\n",
       "   //     var up = camera.up; // up is always (0,0,1)\n",
       "        var textArea = document.createElement('textarea');\n",
       "        var cam_position = JSON.stringify(pos_r);\n",
       "        textArea.textContent = ',camera_position=' + cam_position;\n",
       "        textArea.style.csstext = 'position: absolute; top: -100%';\n",
       "        document.body.append( textArea );\n",
       "        textArea.select();\n",
       "        document.execCommand( 'copy' );\n",
       "\n",
       "        var m = document.getElementById( 'menu-message' );\n",
       "        m.innerHTML = 'Camera position '+ cam_position+' copied to clipboard';\n",
       "        m.style.display = 'block';\n",
       "        setTimeout( function() { m.style.display = 'none'; }, 2000 );\n",
       "\n",
       "    }\n",
       "                                       \n",
       "</script>\n",
       "\n",
       "<div id=&quot;menu-container&quot; onclick=&quot;toggleMenu()&quot;>&#x24d8;\n",
       "<div id=&quot;menu-message&quot;></div>\n",
       "<div id=&quot;menu-content&quot;>\n",
       "<div onclick=&quot;saveAsPNG()&quot;>Save as PNG</div>\n",
       "<div onclick=&quot;saveAsHTML()&quot;>Save as HTML</div>\n",
       "<div onclick=&quot;getCamera()&quot;>Get camera</div>\n",
       "<div onclick=&quot;getViewpoint()&quot;>Get viewpoint</div>\n",
       "<div>Close Menu</div>\n",
       "</div></div>\n",
       "\n",
       "\n",
       "</body>\n",
       "</html>\n",
       "\"\n",
       "        width=\"100%\"\n",
       "        height=\"400\"\n",
       "        style=\"border: 0;\">\n",
       "</iframe>\n"
      ],
      "text/plain": [
       "Graphics3d Object"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "var('u v t')                                   # symb.var.\n",
    "\n",
    "po1 = {'thickness': 5, 'color': 'darkblue'}         # param.\n",
    "po2 = {'fontsize': 20, 'color': 'black'}\n",
    "po3 = {'size': 7, 'color': 'black'}\n",
    "\n",
    "ax = line3d([(0,0,0), (1+0.15,0,0)], **po1)     # axes\n",
    "ax += line3d([(0,0,0), (0,1+0.15,0)], **po1)\n",
    "ax += line3d([(0,0,0), (0,0,1+0.15)], **po1)\n",
    "ax += text3d(\"x\", (1.25,0,0), **po2)\n",
    "ax += text3d(\"y\", (0,1.25,0), **po2)\n",
    "ax += text3d(\"z\", (0.,0.,1.25), **po2)\n",
    "                                               # hemisphere:\n",
    "s = parametric_plot3d((cos(u)*cos(v), sin(u)*cos(v), sin(v)),\n",
    "                      (u,0,2*pi), (v,0,pi/2), opacity=0.9, color='lightgrey')\n",
    "\n",
    "a = 0.59                                         # triangle\n",
    "tr = line3d([(0,0,0), (a,a,0), (a,a,a), (0,0,0)], **po1)\n",
    "\n",
    "dots = point3d([(0.5*cos(t), 0.5*sin(t), 0)        # dots\n",
    "                for t in srange(0,pi/4,0.1)], **po3)\n",
    "dots+=point3d([(0.5*cos(t), 0.5*cos(t), 0.5*sin(t))\n",
    "               for t in srange(pi/4,pi/2,0.1)], **po3)\n",
    "                                               \n",
    "t = text3d(\"(x,y,z)\", (0.6,0.8,0.7),**po2)        # variables\n",
    "t += text3d(\"φ\", (0.7,0.3,0.0), **po2)\n",
    "t += text3d(\"θ\", (0.,0.2,0.5), **po2)\n",
    "                                               # combine plots\n",
    "(ax+s+tr+dots+t).rotateZ(-pi/8).show(frame=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The spherical coordinates defined on the entire $E^3$ are not homeomorphic. They do not define a one-to-one mapping of $E^3$ onto an open subset of $R^3$, since for example, points of the form (𝑟,𝜃,𝜑) \n",
    "and (𝑟,𝜃,𝜑+2𝜋) pass to the same point. \n",
    "\n",
    "To obtain homeomorphic charts on an open set\n",
    " and smooth invertible transitions, we can restrict ourselves \n",
    " to the  open subset of $E^3$ with  half plane {y=0, x>=0} excluded.\n",
    "\n",
    "With this restriction in mind the inverse transition is well defined. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "r = sqrt(x^2 + y^2 + z^2)\n",
       "th = arctan2(sqrt(x^2 + y^2), z)\n",
       "ph = arctan2(y, x)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cart_to_sph = E.coord_change(cartesian, spherical); # transition\n",
    "cart_to_sph.display()                 # Cartesian -> spherical"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://en.wikipedia.org/wiki/Atan2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us check the determinants of Jacobians of the transition maps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "r^2*sin(th)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sph_to_cart.jacobian_det()           # det(Jacobian(spher->cart))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1/(sqrt(x^2 + y^2 + z^2)*sqrt(x^2 + y^2))"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cart_to_sph.jacobian_det()           # det(Jacobian(cart->spher))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "**Example 2.5**\n",
    "\n",
    "As we have observed, to obtain well defined transitions, we can restrict ourselves\n",
    " to the open subset of $E^3$ <br>\n",
    " with  half plane {y=0, x>=0} excluded.\n",
    " \n",
    " Below, we show how to make  appropriate restriction.\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# continuation                      # define open subset U\n",
    "U = E.open_subset('U', coord_def={cartesian: (y!=0, x<0)})\n",
    "spherU.<r,th,ph> = U.chart(r'r:(0,+oo) th:(0,pi):\\theta ph:(0,2*pi)')\n",
    "cartU = cartesian.restrict(U)         # restrict Cart. coord to U"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make a plot with some neighborhood of the half plane {y=0, x>=0} excluded\n",
    "it is sufficient to use appropriate ranges of parameters.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot coord. lines using the values 0, 5.7 of r;\n",
    "#                      values 0.3, 2pi-0.3 of ph;\n",
    "#          and 20 values of th from [0.3,pi-0.3];\n",
    "\n",
    "p1 = spherical.plot(cartesian,        \n",
    "                    ranges={r: (0.5,7), th: (0.3,pi-0.3), ph: (0.3,2*pi-0.3)},\n",
    "                    number_values={r: 2, ph: 2, th: 20},\n",
    "                    color={r: 'red', ph: 'grey', th: 'red'},\n",
    "                    thickness=1, label_axes=False)    # plot coord. lines r,th,ph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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",
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       "    body { margin: 0px; overflow: hidden; }\n",
       "\n",
       "    #menu-container { position: absolute; bottom: 30px; right: 40px; cursor: default; }\n",
       "\n",
       "    #menu-message { position: absolute; bottom: 0px; right: 0px; white-space: nowrap;\n",
       "                    display: none; background-color: #F5F5F5; padding: 10px; }\n",
       "\n",
       "    #menu-content { position: absolute; bottom: 0px; right: 0px;\n",
       "                    display: none; background-color: #F5F5F5; border-bottom: 1px solid black;\n",
       "                    border-right: 1px solid black; border-left: 1px solid black; }\n",
       "\n",
       "    #menu-content div { border-top: 1px solid black; padding: 10px; white-space: nowrap; }\n",
       "\n",
       "    #menu-content div:hover { background-color: #FEFEFE; }\n",
       "\n",
       "    .dark-theme #menu-container { color: white; }\n",
       "\n",
       "    .dark-theme #menu-message { background-color: #181818; }\n",
       "\n",
       "    .dark-theme #menu-content { background-color: #181818; border-color: white; }\n",
       "\n",
       "    .dark-theme #menu-content div { border-color: white; }\n",
       "\n",
       "    .dark-theme #menu-content div:hover { background-color: #303030; }\n",
       "\n",
       "</style>\n",
       "\n",
       "</head>\n",
       "\n",
       "<body>\n",
       "\n",
       "<script src=&quot;/nbextensions/threejs-sage/r122/three.min.js&quot;></script>\n",
       "<script>\n",
       "  if ( !window.THREE ) document.write(' \\\n",
       "<script src=&quot;https://cdn.jsdelivr.net/gh/sagemath/threejs-sage@r122/build/three.min.js&quot;><\\/script> \\\n",
       "            ');\n",
       "</script>\n",
       "        <script>// fat_lines.js\n",
       "\n",
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       "    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",
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       "\n",
       "    _fatLines.push( line );\n",
       "\n",
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       "\n",
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       "\n",
       "function createFatLineStrip( geometry, materialOptions ) {\n",
       "    return _createFatLine( true, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function createFatLineSegments( geometry, materialOptions ) {\n",
       "    return _createFatLine( false, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function rescaleFatLines() {\n",
       "    var res = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "    var n = _fatLines.length;\n",
       "    for ( var i=0 ; i < n ; i++ ) {\n",
       "        _fatLines[i].material.resolution = res;\n",
       "    }\n",
       "}\n",
       "</script>\n",
       "<script>\n",
       "\n",
       "    var options = {&quot;animate&quot;: false, &quot;animationControls&quot;: true, &quot;aspectRatio&quot;: [1.0, 1.0, 1.0], &quot;autoScaling&quot;: [false, false, false], &quot;autoPlay&quot;: true, &quot;axes&quot;: false, &quot;axesLabels&quot;: false, &quot;axesLabelsStyle&quot;: null, &quot;decimals&quot;: 2, &quot;delay&quot;: 20, &quot;frame&quot;: false, &quot;loop&quot;: true, &quot;projection&quot;: &quot;perspective&quot;, &quot;theme&quot;: &quot;light&quot;, &quot;viewpoint&quot;: false};\n",
       "    var animate = options.animate;\n",
       "\n",
       "    if ( options.theme === 'dark' )\n",
       "        document.body.className = 'dark-theme';\n",
       "\n",
       "    var scene = new THREE.Scene();\n",
       "\n",
       "    var renderer = new THREE.WebGLRenderer( { antialias: true, preserveDrawingBuffer: true } );\n",
       "    renderer.setPixelRatio( window.devicePixelRatio );\n",
       "    renderer.setSize( window.innerWidth, window.innerHeight );\n",
       "    renderer.setClearColor( options.theme === 'dark' ? 0 : 0xffffff, 1 );\n",
       "    document.body.appendChild( renderer.domElement );\n",
       "\n",
       "    var b = [{&quot;x&quot;:-9.874370415290343, &quot;y&quot;:-9.874370415290343, &quot;z&quot;:-6.68735542387924}, {&quot;x&quot;:9.899494936611665, &quot;y&quot;:16.97056274847714, &quot;z&quot;:9.0}]; // bounds\n",
       "\n",
       "    if ( b[0].x === b[1].x ) {\n",
       "        b[0].x -= 1;\n",
       "        b[1].x += 1;\n",
       "    }\n",
       "    if ( b[0].y === b[1].y ) {\n",
       "        b[0].y -= 1;\n",
       "        b[1].y += 1;\n",
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       "    if ( b[0].z === b[1].z ) {\n",
       "        b[0].z -= 1;\n",
       "        b[1].z += 1;\n",
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       "\n",
       "    var rxRange = Math.sqrt( Math.pow( b[1].z - b[0].z, 2 )\n",
       "                            + Math.pow( b[1].y - b[0].y, 2 ) );\n",
       "    var ryRange = Math.sqrt( Math.pow( b[1].x - b[0].x, 2 )\n",
       "                            + Math.pow( b[1].z - b[0].z, 2 ) );\n",
       "    var rzRange = Math.sqrt( Math.pow( b[1].x - b[0].x, 2 )\n",
       "                            + Math.pow( b[1].y - b[0].y, 2 ) );\n",
       "    var xRange = b[1].x - b[0].x;\n",
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       "\n",
       "    var autoScaling = options.autoScaling;\n",
       "    var autoAspect = 2.5;\n",
       "    if ( xRange > autoAspect * rxRange && autoScaling[0] ) a[0] = autoAspect * rxRange / xRange;\n",
       "    if ( yRange > autoAspect * ryRange && autoScaling[1] ) a[1] = autoAspect * ryRange / yRange;\n",
       "    if ( zRange > autoAspect * rzRange && autoScaling[2] ) a[2] = autoAspect * rzRange / zRange;\n",
       "\n",
       "    // Distance from (xMid,yMid,zMid) to any corner of the bounding box, after applying aspectRatio\n",
       "    var midToCorner = Math.sqrt( a[0]*a[0]*xRange*xRange + a[1]*a[1]*yRange*yRange + a[2]*a[2]*zRange*zRange ) / 2;\n",
       "\n",
       "    var xMid = ( b[0].x + b[1].x ) / 2;\n",
       "    var yMid = ( b[0].y + b[1].y ) / 2;\n",
       "    var zMid = ( b[0].z + b[1].z ) / 2;\n",
       "\n",
       "    var box = new THREE.Geometry();\n",
       "    box.vertices.push( new THREE.Vector3( a[0]*b[0].x, a[1]*b[0].y, a[2]*b[0].z ) );\n",
       "    box.vertices.push( new THREE.Vector3( a[0]*b[1].x, a[1]*b[1].y, a[2]*b[1].z ) );\n",
       "    var boxMesh = new THREE.Line( box );\n",
       "    var boxColor = options.theme === 'dark' ? 'white' : 'black';\n",
       "    if ( options.frame ) scene.add( new THREE.BoxHelper( boxMesh, boxColor ) );\n",
       "\n",
       "    if ( options.axesLabels ) {\n",
       "\n",
       "        var d = options.decimals; // decimals\n",
       "        var offsetRatio = 0.1;\n",
       "        var al = options.axesLabels;\n",
       "        var als = options.axesLabelsStyle || [{}, {}, {}];\n",
       "\n",
       "        var offset = offsetRatio * a[1]*( b[1].y - b[0].y );\n",
       "        var xm = xMid.toFixed(d);\n",
       "        if ( /^-0.?0*$/.test(xm) ) xm = xm.substr(1);\n",
       "        addLabel( al[0] + '=' + xm, a[0]*xMid, a[1]*b[1].y+offset, a[2]*b[0].z, als[0] );\n",
       "        addLabel( ( b[0].x ).toFixed(d), a[0]*b[0].x, a[1]*b[1].y+offset, a[2]*b[0].z, als[0] );\n",
       "        addLabel( ( b[1].x ).toFixed(d), a[0]*b[1].x, a[1]*b[1].y+offset, a[2]*b[0].z, als[0] );\n",
       "\n",
       "        var offset = offsetRatio * a[0]*( b[1].x - b[0].x );\n",
       "        var ym = yMid.toFixed(d);\n",
       "        if ( /^-0.?0*$/.test(ym) ) ym = ym.substr(1);\n",
       "        addLabel( al[1] + '=' + ym, a[0]*b[1].x+offset, a[1]*yMid, a[2]*b[0].z, als[1] );\n",
       "        addLabel( ( b[0].y ).toFixed(d), a[0]*b[1].x+offset, a[1]*b[0].y, a[2]*b[0].z, als[1] );\n",
       "        addLabel( ( b[1].y ).toFixed(d), a[0]*b[1].x+offset, a[1]*b[1].y, a[2]*b[0].z, als[1] );\n",
       "\n",
       "        var offset = offsetRatio * a[1]*( b[1].y - b[0].y );\n",
       "        var zm = zMid.toFixed(d);\n",
       "        if ( /^-0.?0*$/.test(zm) ) zm = zm.substr(1);\n",
       "        addLabel( al[2] + '=' + zm, a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*zMid, als[2] );\n",
       "        addLabel( ( b[0].z ).toFixed(d), a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*b[0].z, als[2] );\n",
       "        addLabel( ( b[1].z ).toFixed(d), a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*b[1].z, als[2] );\n",
       "\n",
       "    }\n",
       "\n",
       "    function addLabel( text, x, y, z, style ) {\n",
       "\n",
       "        var color = style.color || 'black';\n",
       "        var fontSize = style.fontSize || 14;\n",
       "        var fontFamily = style.fontFamily || 'monospace';\n",
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       "        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",
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       "        }\n",
       "\n",
       "        var canvas = document.createElement( 'canvas' );\n",
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       "        var font = [fontStyle, fontWeight, fontSize + 'px', fontFamily].join(' ');\n",
       "\n",
       "        context.font = font;\n",
       "        var width = context.measureText( text ).width;\n",
       "        var height = fontSize;\n",
       "\n",
       "        // The dimensions of the canvas's underlying image data need to be powers\n",
       "        // of two in order for the resulting texture to support mipmapping.\n",
       "        canvas.width = THREE.MathUtils.ceilPowerOfTwo( width * pixelRatio );\n",
       "        canvas.height = THREE.MathUtils.ceilPowerOfTwo( height * pixelRatio );\n",
       "\n",
       "        // Re-compute the unscaled dimensions after the power of two conversion.\n",
       "        width = canvas.width / pixelRatio;\n",
       "        height = canvas.height / pixelRatio;\n",
       "\n",
       "        canvas.style.width = width + 'px';\n",
       "        canvas.style.height = height + 'px';\n",
       "\n",
       "        context.scale( pixelRatio, pixelRatio );\n",
       "        context.fillStyle = color;\n",
       "        context.font = font; // Must be set again after measureText.\n",
       "        context.textAlign = 'center';\n",
       "        context.textBaseline = 'middle';\n",
       "        context.fillText( text, width/2, height/2 );\n",
       "\n",
       "        var texture = new THREE.Texture( canvas );\n",
       "        texture.needsUpdate = true;\n",
       "\n",
       "        var materialOptions = { map: texture, sizeAttenuation: false, depthWrite: false };\n",
       "        if ( opacity < 1 ) {\n",
       "            // Setting opacity=1 would cause the texture's alpha component to be\n",
       "            // discarded, giving the text a black background instead of the\n",
       "            // background being transparent.\n",
       "            materialOptions.opacity = opacity;\n",
       "        }\n",
       "        var sprite = new THREE.Sprite( new THREE.SpriteMaterial( materialOptions ) );\n",
       "        sprite.position.set( x, y, z );\n",
       "\n",
       "        // Scaling factor, chosen somewhat arbitrarily so that the size of the text\n",
       "        // is consistent with previously generated plots.\n",
       "        var scale = 1/625;\n",
       "        if ( options.projection === 'orthographic' ) {\n",
       "            scale = midToCorner/256; // Needs to scale along with the plot itself.\n",
       "        }\n",
       "        sprite.scale.set( scale * width, scale * height, 1 );\n",
       "\n",
       "        scene.add( sprite );\n",
       "\n",
       "        return sprite;\n",
       "\n",
       "    }\n",
       "\n",
       "    if ( options.axes ) scene.add( new THREE.AxesHelper( Math.min( a[0]*b[1].x, a[1]*b[1].y, a[2]*b[1].z ) ) );\n",
       "\n",
       "    var camera = createCamera();\n",
       "    camera.up.set( 0, 0, 1 );\n",
       "    camera.position.set( a[0]*xMid, a[1]*yMid, a[2]*zMid );\n",
       "\n",
       "    var offset = new THREE.Vector3( a[0]*xRange, a[1]*yRange, a[2]*zRange );\n",
       "\n",
       "    if ( options.viewpoint ) {\n",
       "\n",
       "        var aa = options.viewpoint;\n",
       "        var axis = new THREE.Vector3( aa[0][0], aa[0][1], aa[0][2] ).normalize();\n",
       "        var angle = aa[1] * Math.PI / 180;\n",
       "        var q = new THREE.Quaternion().setFromAxisAngle( axis, angle ).inverse();\n",
       "\n",
       "        offset.set( 0, 0, offset.length() );\n",
       "        offset.applyQuaternion( q );\n",
       "\n",
       "    }\n",
       "\n",
       "    camera.position.add( offset );\n",
       "\n",
       "    function createCamera() {\n",
       "\n",
       "        var aspect = window.innerWidth / window.innerHeight;\n",
       "\n",
       "        // Scale the near and far clipping planes along with the overall plot size.\n",
       "        var nearClip = 0.01 * midToCorner;\n",
       "        var farClip = 100 * midToCorner;\n",
       "\n",
       "        if ( options.projection === 'orthographic' ) {\n",
       "            var camera = new THREE.OrthographicCamera( -1, 1, 1, -1, -farClip, farClip );\n",
       "            updateCameraAspect( camera, aspect );\n",
       "            return camera;\n",
       "        }\n",
       "\n",
       "        return new THREE.PerspectiveCamera( 45, aspect, nearClip, farClip );\n",
       "\n",
       "    }\n",
       "\n",
       "    function updateCameraAspect( camera, aspect ) {\n",
       "\n",
       "        if ( camera.isPerspectiveCamera ) {\n",
       "            camera.aspect = aspect;\n",
       "        } else if ( camera.isOrthographicCamera ) {\n",
       "            // Fit the camera frustum to the bounding box's diagonal so that the entire plot fits\n",
       "            // within at the default zoom level and camera position.\n",
       "            if ( aspect > 1 ) { // Wide window\n",
       "                camera.top = midToCorner;\n",
       "                camera.right = midToCorner * aspect;\n",
       "            } else { // Tall or square window\n",
       "                camera.top = midToCorner / aspect;\n",
       "                camera.right = midToCorner;\n",
       "            }\n",
       "            camera.bottom = -camera.top;\n",
       "            camera.left = -camera.right;\n",
       "        }\n",
       "\n",
       "        camera.updateProjectionMatrix();\n",
       "\n",
       "    }\n",
       "\n",
       "    var lights = [{&quot;x&quot;:-5, &quot;y&quot;:3, &quot;z&quot;:0, &quot;color&quot;:&quot;#7f7f7f&quot;, &quot;parent&quot;:&quot;camera&quot;}];\n",
       "    for ( var i=0 ; i < lights.length ; i++ ) {\n",
       "        var light = new THREE.DirectionalLight( lights[i].color, 1 );\n",
       "        light.position.set( a[0]*lights[i].x, a[1]*lights[i].y, a[2]*lights[i].z );\n",
       "        if ( lights[i].parent === 'camera' ) {\n",
       "            light.target.position.set( a[0]*xMid, a[1]*yMid, a[2]*zMid );\n",
       "            scene.add( light.target );\n",
       "            camera.add( light );\n",
       "        } else scene.add( light );\n",
       "    }\n",
       "    scene.add( camera );\n",
       "\n",
       "    var ambient = {&quot;color&quot;:&quot;#7f7f7f&quot;};\n",
       "    scene.add( new THREE.AmbientLight( ambient.color, 1 ) );\n",
       "\n",
       "    var controls = new THREE.OrbitControls( camera, renderer.domElement );\n",
       "    controls.target.set( a[0]*xMid, a[1]*yMid, a[2]*zMid );\n",
       "    controls.addEventListener( 'change', function() { if ( !animate ) render(); } );\n",
       "\n",
       "    window.addEventListener( 'resize', function() {\n",
       "\n",
       "        renderer.setSize( window.innerWidth, window.innerHeight );\n",
       "        updateCameraAspect( camera, window.innerWidth / window.innerHeight );\n",
       "        if ( window.rescaleFatLines ) rescaleFatLines();\n",
       "        if ( !animate ) render();\n",
       "\n",
       "    } );\n",
       "\n",
       "    var texts = [{&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;x&quot;, &quot;x&quot;: 9.899494936611665, &quot;y&quot;: 9.899494936611664, &quot;z&quot;: 0.0}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;y&quot;, &quot;x&quot;: -7.071067811865475, &quot;y&quot;: 7.0710678118654755, &quot;z&quot;: 0.0}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;z&quot;, &quot;x&quot;: 0.0, &quot;y&quot;: 0.0, &quot;z&quot;: 9.0}];\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;: [[0.06893903768860732, 0.13069222325317978, 0.477668244562803], [0.08104994971498428, 0.15365166787873838, 0.5615829361751873], [0.09316086174136123, 0.176611112504297, 0.6454976277875716], [0.1052717737677382, 0.1995705571298556, 0.7294123193999559], [0.11738268579411515, 0.2225300017554142, 0.8133270110123402], [0.1294935978204921, 0.2454894463809728, 0.8972417026247245], [0.14160450984686906, 0.2684488910065314, 0.9811563942371088], [0.15371542187324605, 0.29140833563209007, 1.0650710858494932], [0.16582633389962298, 0.31436778025764867, 1.1489857774618777], [0.17793724592600005, 0.3373272248832074, 1.232900469074262], [0.190048157952377, 0.360286669508766, 1.3168151606866465], [0.2021590699787539, 0.3832461141343246, 1.4007298522990308], [0.21426998200513092, 0.40620555875988323, 1.4846445439114153], [0.2263808940315079, 0.42916500338544183, 1.5685592355237996], [0.2384918060578849, 0.45212444801100055, 1.6524739271361841], [0.25060271808426193, 0.47508389263655926, 1.7363886187485684], [0.26271363011063886, 0.4980433372621178, 1.820303310360953], [0.2748245421370158, 0.5210027818876765, 1.9042180019733372], [0.2869354541633927, 0.543962226513235, 1.9881326935857215], [0.29904636618976976, 0.5669216711387937, 2.072047385198106], [0.31115727821614664, 0.5898811157643522, 2.1559620768104897], [0.3232681902425236, 0.6128405603899107, 2.239876768422874], [0.3353791022689005, 0.6358000050154693, 2.3237914600352583], [0.34749001429527737, 0.6587594496410278, 2.4077061516476426], [0.3596009263216544, 0.6817188942665865, 2.4916208432600264], [0.37171183834803134, 0.704678338892145, 2.5755355348724107], [0.3838227503744083, 0.7276377835177036, 2.659450226484795], [0.3959336624007852, 0.7505972281432622, 2.7433649180971793], [0.40804457442716224, 0.7735566727688208, 2.8272796097095636], [0.4201554864535392, 0.7965161173943793, 2.9111943013219475], [0.4322663984799161, 0.819475562019938, 2.9951089929343317], [0.44437731050629303, 0.8424350066454964, 3.079023684546716], [0.4564882225326701, 0.8653944512710552, 3.1629383761591003], [0.4685991345590469, 0.8883538958966137, 3.246853067771484], [0.48071004658542377, 0.9113133405221722, 3.3307677593838685], [0.4928209586118009, 0.9342727851477309, 3.414682450996253], [0.5049318706381778, 0.9572322297732895, 3.498597142608637], [0.5170427826645547, 0.980191674398848, 3.5825118342210214], [0.5291536946909317, 1.0031511190244067, 3.6664265258334052], [0.5412646067173086, 1.0261105636499652, 3.7503412174457895], [0.5533755187436855, 1.0490700082755238, 3.8342559090581743], [0.5654864307700624, 1.0720294529010825, 3.9181706006705586], [0.5775973427964395, 1.094988897526641, 4.002085292282943], [0.5897082548228165, 1.1179483421521996, 4.085999983895327], [0.6018191668491933, 1.1409077867777582, 4.1699146755077106], [0.6139300788755704, 1.1638672314033167, 4.253829367120095], [0.6260409909019472, 1.1868266760288753, 4.337744058732479], [0.6381519029283242, 1.2097861206544338, 4.421658750344863], [0.650262814954701, 1.2327455652799926, 4.505573441957248], [0.6623737269810781, 1.255705009905551, 4.589488133569632], [0.6744846390074548, 1.2786644545311094, 4.673402825182016], [0.686595551033832, 1.3016238991566684, 4.757317516794401], [0.6987064630602091, 1.3245833437822268, 4.841232208406785], [0.7108173750865858, 1.3475427884077853, 4.925146900019168], [0.7229282871129629, 1.370502233033344, 5.009061591631553], [0.7350391991393397, 1.3934616776589024, 5.092976283243937], [0.7471501111657167, 1.4164211222844612, 5.176890974856321], [0.7592610231920935, 1.4393805669100195, 5.2608056664687055], [0.7713719352184706, 1.4623400115355782, 5.34472035808109], [0.7834828472448476, 1.4852994561611368, 5.428635049693474], [0.7955937592712246, 1.5082589007866956, 5.512549741305858], [0.8077046712976015, 1.5312183454122539, 5.596464432918242], [0.8198155833239784, 1.5541777900378126, 5.680379124530626], [0.8319264953503553, 1.577137234663371, 5.76429381614301], [0.8440374073767323, 1.6000966792889297, 5.848208507755395], [0.8561483194031091, 1.6230561239144883, 5.932123199367779], [0.8682592314294861, 1.6460155685400468, 6.016037890980163], [0.8803701434558632, 1.6689750131656056, 6.099952582592548], [0.8924810554822402, 1.6919344577911641, 6.183867274204932], [0.904591967508617, 1.7148939024167227, 6.267781965817316], [0.9167028795349941, 1.7378533470422814, 6.3516966574297], [0.9288137915613708, 1.7608127916678398, 6.435611349042084], [0.9409247035877479, 1.7837722362933985, 6.519526040654468], [0.9530356156141246, 1.8067316809189569, 6.6034407322668525], [0.9651465276405018, 1.8296911255445156, 6.687355423879237]], &quot;color&quot;: &quot;#ff0000&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 1.0}, {&quot;points&quot;: [[0.1306922232531798, 0.06893903768860729, 0.477668244562803], [0.1536516678787384, 0.08104994971498423, 0.5615829361751873], [0.176611112504297, 0.0931608617413612, 0.6454976277875716], [0.19957055712985564, 0.10527177376773815, 0.7294123193999559], [0.22253000175541424, 0.1173826857941151, 0.8133270110123402], [0.24548944638097286, 0.12949359782049205, 0.8972417026247245], [0.26844889100653146, 0.141604509846869, 0.9811563942371088], [0.2914083356320901, 0.153715421873246, 1.0650710858494932], [0.3143677802576487, 0.16582633389962292, 1.1489857774618777], [0.33732722488320743, 0.17793724592599997, 1.232900469074262], [0.3602866695087661, 0.1900481579523769, 1.3168151606866465], [0.38324611413432463, 0.20215906997875382, 1.4007298522990308], [0.4062055587598833, 0.2142699820051308, 1.4846445439114153], [0.42916500338544195, 0.2263808940315078, 1.5685592355237996], [0.4521244480110006, 0.23849180605788478, 1.6524739271361841], [0.4750838926365593, 0.2506027180842618, 1.7363886187485684], [0.49804333726211786, 0.2627136301106387, 1.820303310360953], [0.5210027818876766, 0.2748245421370157, 1.9042180019733372], [0.5439622265132351, 0.2869354541633926, 1.9881326935857215], [0.5669216711387937, 0.29904636618976965, 2.072047385198106], [0.5898811157643523, 0.3111572782161465, 2.1559620768104897], [0.6128405603899109, 0.32326819024252346, 2.239876768422874], [0.6358000050154694, 0.3353791022689004, 2.3237914600352583], [0.658759449641028, 0.34749001429527726, 2.4077061516476426], [0.6817188942665866, 0.35960092632165425, 2.4916208432600264], [0.7046783388921452, 0.3717118383480312, 2.5755355348724107], [0.7276377835177037, 0.38382275037440805, 2.659450226484795], [0.7505972281432622, 0.3959336624007851, 2.7433649180971793], [0.773556672768821, 0.408044574427162, 2.8272796097095636], [0.7965161173943796, 0.42015548645353895, 2.9111943013219475], [0.8194755620199381, 0.4322663984799159, 2.9951089929343317], [0.8424350066454966, 0.4443773105062928, 3.079023684546716], [0.8653944512710553, 0.45648822253266985, 3.1629383761591003], [0.8883538958966138, 0.4685991345590468, 3.246853067771484], [0.9113133405221723, 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-6.351719619631155], [1.2621745606999295, -2.6575502350688653, -6.351719619631155], [1.462352857700061, -2.552877198999025, -6.351719619631155], [1.6539101298130678, -2.4331541578975973, -6.351719619631155], [1.8357170873456312, -2.2990869163256775, -6.351719619631155], [2.006701921741228, -2.1514658423671764, -6.351719619631155], [2.1658566242249004, -1.9911612081631567, -6.351719619631155], [2.312242928328476, -1.8191180593869092, -6.351719619631155], [2.4449978412632016, -1.6363506439057995, -6.351719619631155], [2.563338731530616, -1.4439364324746622, -6.351719619631155], [2.666567942778638, -1.2430097667106024, -6.351719619631155], [2.7540769067027284, -1.0347551717963892, -6.351719619631155], [2.8253497307453124, -0.8204003733361132, -6.351719619631155], [2.8799662394428474, -0.6012090595309287, -6.351719619631155], [2.917604451490857, -0.37847343134410316, -6.351719619631155], [2.938042477923852, -0.1535065845744621, -6.351719619631155], [2.941159830219794, 0.07236523125171401, -6.351719619631155], [2.9269381306174056, 0.2978104315341108, -6.351719619631155], [2.8954612204587815, 0.5214999467037245, -6.351719619631155], [2.846914665918611, 0.7421150575013062, -6.351719619631155], [2.781584664033862, 0.9583551692375177, -6.351719619631155], [2.6998563554832407, 1.1689454792031129, -6.351719619631155], [2.6022115540631163, 1.3726444920273657, -6.351719619631155]], &quot;color&quot;: &quot;#808080&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 1.0}, {&quot;points&quot;: [[0.9651465276405053, 1.8296911255445223, -6.68735542387924], [0.8219197882676943, 1.8983480440548548, -6.68735542387924], [0.6738475761264162, 1.9558136104602246, -6.68735542387924], [0.5218028229576253, 2.00174904737491, -6.68735542387924], [0.3666818798670909, 2.035883551112401, -6.68735542387924], [0.20939923305686503, 2.058015888157354, -6.68735542387924], [0.05088211264471565, 2.068015581499742, -6.68735542387924], [-0.10793497364578486, 2.065823679837413, -6.68735542387924], [-0.2661157496989226, 2.051453105112346, -6.68735542387924], [-0.42272769064572446, 2.024988576331787, -6.68735542387924], [-0.5768475203880769, 1.9865861101233524, -6.68735542387924], [-0.7275666545984608, 1.9364721009684875, -6.68735542387924], [-0.8739965571071338, 1.8749419865365917, -6.68735542387924], [-1.015273978099183, 1.8023585059880747, -6.68735542387924], [-1.150566043240655, 1.7191495615141945, -6.68735542387924], [-1.2790751637317794, 1.625805695720564, -6.68735542387924], [-1.4000437383409905, 1.5228771997259298, -6.68735542387924], [-1.5127586196998024, 1.4109708690248899, -6.68735542387924], [-1.616555318528336, 1.2907464262397377, -6.68735542387924], [-1.710821921006277, 1.162912631850431, -6.68735542387924], [-1.7950026961951533, 1.0282231058311393, -6.68735542387924], [-1.8686013722450492, 0.8874718848261189, -6.68735542387924], [-1.9311840620715, 0.7414887410567512, -6.68735542387924], [-1.9823818212547946, 0.5911342905562387, -6.68735542387924], [-2.0218928230820716, 0.437294919570439, -6.68735542387924], [-2.0494841379096567, 0.28087755903527734, -6.68735542387924], [-2.064993106355758, 0.12280433793682766, -6.68735542387924], [-2.0683282982281037, -0.03599285292584575, -6.68735542387924], [-2.0594700515333635, -0.19457785472676248, -6.68735542387924], [-2.0384705883907137, -0.35201575956045283, -6.68735542387924], [-2.0054537071662017, -0.507378422014815, -6.68735542387924], [-1.960614052642879, -0.659749930876973, -6.68735542387924], [-1.9042159685292703, -0.8082320087147239, -6.68735542387924], [-1.8365919390710004, -0.9519493075013652, -6.68735542387924], [-1.7581406289527632, -1.090054569064543, -6.68735542387924], [-1.6693245330460238, -1.2217336199366786, -6.68735542387924], [-1.5706672498579113, -1.3462101711607635, -6.68735542387924], [-1.4627503947551836, -1.4627503947551883, -6.68735542387924], [-1.3462101711607584, -1.5706672498579155, -6.68735542387924], [-1.2217336199366733, -1.6693245330460273, -6.68735542387924], [-1.0900545690645376, -1.758140628952767, -6.68735542387924], [-0.9519493075013591, -1.8365919390710033, -6.68735542387924], [-0.808232008714718, -1.904215968529273, -6.68735542387924], [-0.6597499308769668, -1.9606140526428812, -6.68735542387924], [-0.5073784220148086, -2.0054537071662035, -6.68735542387924], [-0.3520157595604464, -2.038470588390715, -6.68735542387924], [-0.19457785472675604, -2.0594700515333644, -6.68735542387924], [-0.03599285292583909, -2.0683282982281037, -6.68735542387924], [0.12280433793683398, -2.0649931063557574, -6.68735542387924], [0.2808775590352838, -2.049484137909656, -6.68735542387924], [0.43729491957044553, -2.0218928230820703, -6.68735542387924], [0.5911342905562451, -1.9823818212547928, -6.68735542387924], [0.7414887410567573, -1.9311840620714977, -6.68735542387924], [0.8874718848261247, -1.8686013722450463, -6.68735542387924], [1.028223105831145, -1.7950026961951502, -6.68735542387924], [1.1629126318504368, -1.7108219210062736, -6.68735542387924], [1.2907464262397428, -1.6165553185283321, -6.68735542387924], [1.410970869024895, -1.5127586196997982, -6.68735542387924], [1.5228771997259343, -1.4000437383409856, -6.68735542387924], [1.6258056957205675, -1.2790751637317739, -6.68735542387924], [1.719149561514198, -1.1505660432406495, -6.68735542387924], [1.802358505988078, -1.0152739780991773, -6.68735542387924], [1.8749419865365948, -0.873996557107128, -6.68735542387924], [1.9364721009684902, -0.7275666545984549, -6.68735542387924], [1.9865861101233544, -0.5768475203880707, -6.68735542387924], [2.024988576331788, -0.42272769064571813, -6.68735542387924], [2.051453105112347, -0.26611574969891616, -6.68735542387924], [2.065823679837413, -0.10793497364577842, -6.68735542387924], [2.0680155814997416, 0.05088211264472209, -6.68735542387924], [2.058015888157353, 0.20939923305687136, -6.68735542387924], [2.0358835511124003, 0.36668187986709744, -6.68735542387924], [2.001749047374908, 0.5218028229576317, -6.68735542387924], [1.9558136104602222, 0.6738475761264225, -6.68735542387924], [1.8983480440548524, 0.8219197882677006, -6.68735542387924], [1.8296911255445192, 0.9651465276405113, -6.68735542387924]], &quot;color&quot;: &quot;#808080&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 1.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [9.19238815542512, 9.192388155425117, 0.0]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 3.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [-6.363961030678928, 6.3639610306789285, 0.0]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 3.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [0.0, 0.0, 8.0]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 3.0}];\n",
       "    for ( var i=0 ; i < lines.length ; i++ ) addLine( lines[i] );\n",
       "\n",
       "    function addLine( json ) {\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "        for ( var i=0 ; i < json.points.length ; i++ ) {\n",
       "            var v = json.points[i];\n",
       "            geometry.vertices.push( new THREE.Vector3( a[0]*v[0], a[1]*v[1], a[2]*v[2] ) );\n",
       "        }\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var transparent = json.opacity < 1 ? true : false;\n",
       "        var materialOptions = { color: json.color, linewidth: json.linewidth,\n",
       "                                transparent: transparent, opacity: json.opacity };\n",
       "\n",
       "        var mesh;\n",
       "        if ( json.linewidth > 1 && window.createFatLineStrip ) {\n",
       "            mesh = createFatLineStrip( geometry, materialOptions );\n",
       "        } else {\n",
       "            var material = new THREE.LineBasicMaterial( materialOptions );\n",
       "            mesh = new THREE.Line( geometry, material );\n",
       "        }\n",
       "\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "    }\n",
       "\n",
       "    var surfaces = [];\n",
       "    for ( var i=0 ; i < surfaces.length ; i++ ) addSurface( surfaces[i] );\n",
       "\n",
       "    function addSurface( json ) {\n",
       "\n",
       "        var useFaceColors = 'faceColors' in json ? true : false;\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "        for ( var i=0 ; i < json.vertices.length ; i++ ) {\n",
       "            var v = json.vertices[i];\n",
       "            geometry.vertices.push( new THREE.Vector3( a[0]*v.x, a[1]*v.y, a[2]*v.z ) );\n",
       "        }\n",
       "        for ( var i=0 ; i < json.faces.length ; i++ ) {\n",
       "            var f = json.faces[i];\n",
       "            for ( var j=0 ; j < f.length - 2 ; j++ ) {\n",
       "                var face = new THREE.Face3( f[0], f[j+1], f[j+2] );\n",
       "                if ( useFaceColors ) face.color.set( json.faceColors[i] );\n",
       "                geometry.faces.push( face );\n",
       "            }\n",
       "        }\n",
       "        geometry.computeVertexNormals();\n",
       "\n",
       "        var side = json.singleSide ? THREE.FrontSide : THREE.DoubleSide;\n",
       "        var transparent = json.opacity < 1 ? true : false;\n",
       "        var depthWrite = 'depthWrite' in json ? json.depthWrite : !transparent;\n",
       "        var flatShading = json.useFlatShading ? json.useFlatShading : false;\n",
       "\n",
       "        var material = new THREE.MeshPhongMaterial( { side: side,\n",
       "                                     color: useFaceColors ? 'white' : json.color,\n",
       "                                     vertexColors: useFaceColors ? THREE.FaceColors : THREE.NoColors,\n",
       "                                     transparent: transparent, opacity: json.opacity,\n",
       "                                     shininess: 20, flatShading: flatShading,\n",
       "                                     depthWrite: depthWrite } );\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var mesh = new THREE.Mesh( geometry, material );\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        if ( transparent && json.renderOrder ) mesh.renderOrder = json.renderOrder;\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "        if ( json.showMeshGrid ) addSurfaceMeshGrid( json );\n",
       "\n",
       "    }\n",
       "\n",
       "    function addSurfaceMeshGrid( json ) {\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "\n",
       "        for ( var i=0 ; i < json.faces.length ; i++ ) {\n",
       "            var f = json.faces[i];\n",
       "            for ( var j=0 ; j < f.length ; j++ ) {\n",
       "                var k = j === f.length-1 ? 0 : j+1;\n",
       "                var v1 = json.vertices[f[j]];\n",
       "                var v2 = json.vertices[f[k]];\n",
       "                // vertices in opposite directions on neighboring faces\n",
       "                var nudge = f[j] < f[k] ? .0005*zRange : -.0005*zRange;\n",
       "                geometry.vertices.push( new THREE.Vector3( a[0]*v1.x, a[1]*v1.y, a[2]*(v1.z+nudge) ) );\n",
       "                geometry.vertices.push( new THREE.Vector3( a[0]*v2.x, a[1]*v2.y, a[2]*(v2.z+nudge) ) );\n",
       "            }\n",
       "        }\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var gridColor = options.theme === 'dark' ? 'white' : 'black';\n",
       "        var linewidth = json.linewidth || 1;\n",
       "        var materialOptions = { color: gridColor, linewidth: linewidth };\n",
       "\n",
       "        var mesh;\n",
       "        if ( linewidth > 1 && window.createFatLineSegments ) {\n",
       "            mesh = createFatLineSegments( geometry, materialOptions );\n",
       "        } else {\n",
       "            var material = new THREE.LineBasicMaterial( materialOptions );\n",
       "            mesh = new THREE.LineSegments( geometry, material );\n",
       "        }\n",
       "\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "    }\n",
       "\n",
       "    function render() {\n",
       "\n",
       "        if ( window.updateAnimation ) animate = updateAnimation();\n",
       "        if ( animate ) requestAnimationFrame( render );\n",
       "\n",
       "        renderer.render( scene, camera );\n",
       "\n",
       "    }\n",
       "\n",
       "    render();\n",
       "    controls.update();\n",
       "    if ( !animate ) render();\n",
       "\n",
       "\n",
       "    // menu functions\n",
       "\n",
       "    function toggleMenu() {\n",
       "\n",
       "        var m = document.getElementById( 'menu-content' );\n",
       "        if ( m.style.display === 'block' ) m.style.display = 'none'\n",
       "        else m.style.display = 'block';\n",
       "\n",
       "    }\n",
       "\n",
       "\n",
       "    function saveAsPNG() {\n",
       "\n",
       "        var a = document.body.appendChild( document.createElement( 'a' ) );\n",
       "        a.href = renderer.domElement.toDataURL( 'image/png' );\n",
       "        a.download = 'screenshot';\n",
       "        a.click();\n",
       "\n",
       "    }\n",
       "\n",
       "    function saveAsHTML() {\n",
       "\n",
       "        toggleMenu(); // otherwise visible in output\n",
       "        event.stopPropagation();\n",
       "\n",
       "        var blob = new Blob( [ '<!DOCTYPE html>\\n' + document.documentElement.outerHTML ] );\n",
       "        var a = document.body.appendChild( document.createElement( 'a' ) );\n",
       "        a.href = window.URL.createObjectURL( blob );\n",
       "        a.download = suggestFilename();\n",
       "        a.click();\n",
       "\n",
       "        function suggestFilename() {\n",
       "            if ( !document.title ) {\n",
       "                return 'graphic.html';\n",
       "            } else if ( /\\.html?$/i.test( document.title ) ) {\n",
       "                return document.title; // already ends in .htm or .html\n",
       "            } else {\n",
       "                return document.title + '.html';\n",
       "            }\n",
       "        }\n",
       "\n",
       "    }\n",
       "\n",
       "    function getViewpoint() {\n",
       "\n",
       "        function roundTo( x, n ) { return +x.toFixed(n); }\n",
       "\n",
       "        var v = camera.quaternion.inverse();\n",
       "        var r = Math.sqrt( v.x*v.x + v.y*v.y + v.z*v.z );\n",
       "        var axis = [ roundTo( v.x / r, 4 ), roundTo( v.y / r, 4 ), roundTo( v.z / r, 4 ) ];\n",
       "        var angle = roundTo( 2 * Math.atan2( r, v.w ) * 180 / Math.PI, 2 );\n",
       "\n",
       "        var textArea = document.createElement( 'textarea' );\n",
       "        textArea.textContent = JSON.stringify( axis ) + ',' + angle;\n",
       "        textArea.style.csstext = 'position: absolute; top: -100%';\n",
       "        document.body.append( textArea );\n",
       "        textArea.select();\n",
       "        document.execCommand( 'copy' );\n",
       "\n",
       "        var m = document.getElementById( 'menu-message' );\n",
       "        m.innerHTML = 'Viewpoint copied to clipboard';\n",
       "        m.style.display = 'block';\n",
       "        setTimeout( function() { m.style.display = 'none'; }, 2000 );\n",
       "\n",
       "    }\n",
       "\n",
       "    function getCamera() {\n",
       "\n",
       "        function roundTo( x, n ) { return +x.toFixed(n); }\n",
       "\n",
       "        var pos = camera.position;\n",
       "        var pos_r = [ roundTo( pos.x, 4 ), roundTo( pos.y, 4 ), roundTo( pos.z, 4 ) ];\n",
       "   //     var up = camera.up; // up is always (0,0,1)\n",
       "        var textArea = document.createElement('textarea');\n",
       "        var cam_position = JSON.stringify(pos_r);\n",
       "        textArea.textContent = ',camera_position=' + cam_position;\n",
       "        textArea.style.csstext = 'position: absolute; top: -100%';\n",
       "        document.body.append( textArea );\n",
       "        textArea.select();\n",
       "        document.execCommand( 'copy' );\n",
       "\n",
       "        var m = document.getElementById( 'menu-message' );\n",
       "        m.innerHTML = 'Camera position '+ cam_position+' copied to clipboard';\n",
       "        m.style.display = 'block';\n",
       "        setTimeout( function() { m.style.display = 'none'; }, 2000 );\n",
       "\n",
       "    }\n",
       "                                       \n",
       "</script>\n",
       "\n",
       "<div id=&quot;menu-container&quot; onclick=&quot;toggleMenu()&quot;>&#x24d8;\n",
       "<div id=&quot;menu-message&quot;></div>\n",
       "<div id=&quot;menu-content&quot;>\n",
       "<div onclick=&quot;saveAsPNG()&quot;>Save as PNG</div>\n",
       "<div onclick=&quot;saveAsHTML()&quot;>Save as HTML</div>\n",
       "<div onclick=&quot;getCamera()&quot;>Get camera</div>\n",
       "<div onclick=&quot;getViewpoint()&quot;>Get viewpoint</div>\n",
       "<div>Close Menu</div>\n",
       "</div></div>\n",
       "\n",
       "\n",
       "</body>\n",
       "</html>\n",
       "\"\n",
       "        width=\"100%\"\n",
       "        height=\"400\"\n",
       "        style=\"border: 0;\">\n",
       "</iframe>\n"
      ],
      "text/plain": [
       "Graphics3d Object"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "po1 = {'thickness': 3, 'color': 'darkblue'}         # param.\n",
    "po2 = {'fontsize': 20, 'color': 'black'}\n",
    "\n",
    "ax = line3d([(0,0,0), (13,0,0)], **po1)         # axes\n",
    "ax += line3d([(0,0,0), (0,9,0)], **po1)\n",
    "ax += line3d([(0,0,0), (0,0,8)], **po1)\n",
    "ax += text3d(\"x\", (14,0,0), **po2)\n",
    "ax += text3d(\"y\", (0,10,0), **po2)\n",
    "ax += text3d(\"z\", (0.,0.,9), **po2)\n",
    "                                              # show plot:\n",
    "(p1+ax).rotateZ(-pi/4).show(frame=False, label_axes=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "**Example 2.6**\n",
    "\n",
    "Below we show the part of the sphere, which is excluded from the domain of the restricted spherical coordinates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<iframe srcdoc=\"<!DOCTYPE html>\n",
       "<html>\n",
       "<head>\n",
       "<title></title>\n",
       "<meta charset=&quot;utf-8&quot;>\n",
       "<meta name=viewport content=&quot;width=device-width, user-scalable=no, minimum-scale=1.0, maximum-scale=1.0&quot;>\n",
       "<style>\n",
       "\n",
       "    body { margin: 0px; overflow: hidden; }\n",
       "\n",
       "    #menu-container { position: absolute; bottom: 30px; right: 40px; cursor: default; }\n",
       "\n",
       "    #menu-message { position: absolute; bottom: 0px; right: 0px; white-space: nowrap;\n",
       "                    display: none; background-color: #F5F5F5; padding: 10px; }\n",
       "\n",
       "    #menu-content { position: absolute; bottom: 0px; right: 0px;\n",
       "                    display: none; background-color: #F5F5F5; border-bottom: 1px solid black;\n",
       "                    border-right: 1px solid black; border-left: 1px solid black; }\n",
       "\n",
       "    #menu-content div { border-top: 1px solid black; padding: 10px; white-space: nowrap; }\n",
       "\n",
       "    #menu-content div:hover { background-color: #FEFEFE; }\n",
       "\n",
       "    .dark-theme #menu-container { color: white; }\n",
       "\n",
       "    .dark-theme #menu-message { background-color: #181818; }\n",
       "\n",
       "    .dark-theme #menu-content { background-color: #181818; border-color: white; }\n",
       "\n",
       "    .dark-theme #menu-content div { border-color: white; }\n",
       "\n",
       "    .dark-theme #menu-content div:hover { background-color: #303030; }\n",
       "\n",
       "</style>\n",
       "\n",
       "</head>\n",
       "\n",
       "<body>\n",
       "\n",
       "<script src=&quot;/nbextensions/threejs-sage/r122/three.min.js&quot;></script>\n",
       "<script>\n",
       "  if ( !window.THREE ) document.write(' \\\n",
       "<script src=&quot;https://cdn.jsdelivr.net/gh/sagemath/threejs-sage@r122/build/three.min.js&quot;><\\/script> \\\n",
       "            ');\n",
       "</script>\n",
       "        <script>// fat_lines.js\n",
       "\n",
       "var _fatLines = [];\n",
       "\n",
       "function _createFatLine( lineStrip, geometry, materialOptions ) {\n",
       "\n",
       "    var vertexCount = geometry.vertices.length;\n",
       "    var positions = [];\n",
       "    for ( var i=0 ; i < vertexCount ; i++ ) {\n",
       "        var v = geometry.vertices[i];\n",
       "        positions.push( v.x, v.y, v.z );\n",
       "        // For a line strip, duplicate all but the first and last vertices.\n",
       "        if ( lineStrip && i > 0 && i < vertexCount - 1 ) {\n",
       "            positions.push( v.x, v.y, v.z );\n",
       "        }\n",
       "    }\n",
       "\n",
       "    geometry = new THREE.LineSegmentsGeometry();\n",
       "    geometry.setPositions( positions );\n",
       "\n",
       "    var material = new THREE.LineMaterial( materialOptions );\n",
       "    material.resolution = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "\n",
       "    var line = new THREE.LineSegments2( geometry, material );\n",
       "    line.computeLineDistances();\n",
       "    line.scale.set( 1, 1, 1 );\n",
       "\n",
       "    _fatLines.push( line );\n",
       "\n",
       "    return line;\n",
       "\n",
       "}\n",
       "\n",
       "function createFatLineStrip( geometry, materialOptions ) {\n",
       "    return _createFatLine( true, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function createFatLineSegments( geometry, materialOptions ) {\n",
       "    return _createFatLine( false, geometry, materialOptions );\n",
       "}\n",
       "\n",
       "function rescaleFatLines() {\n",
       "    var res = new THREE.Vector2( window.innerWidth, window.innerHeight );\n",
       "    var n = _fatLines.length;\n",
       "    for ( var i=0 ; i < n ; i++ ) {\n",
       "        _fatLines[i].material.resolution = res;\n",
       "    }\n",
       "}\n",
       "</script>\n",
       "<script>\n",
       "\n",
       "    var options = {&quot;animate&quot;: false, &quot;animationControls&quot;: true, &quot;aspectRatio&quot;: [1.0, 1.0, 1.0], &quot;autoScaling&quot;: [false, false, false], &quot;autoPlay&quot;: true, &quot;axes&quot;: false, &quot;axesLabels&quot;: false, &quot;axesLabelsStyle&quot;: null, &quot;decimals&quot;: 2, &quot;delay&quot;: 20, &quot;frame&quot;: false, &quot;loop&quot;: true, &quot;projection&quot;: &quot;perspective&quot;, &quot;theme&quot;: &quot;light&quot;, &quot;viewpoint&quot;: false};\n",
       "    var animate = options.animate;\n",
       "\n",
       "    if ( options.theme === 'dark' )\n",
       "        document.body.className = 'dark-theme';\n",
       "\n",
       "    var scene = new THREE.Scene();\n",
       "\n",
       "    var renderer = new THREE.WebGLRenderer( { antialias: true, preserveDrawingBuffer: true } );\n",
       "    renderer.setPixelRatio( window.devicePixelRatio );\n",
       "    renderer.setSize( window.innerWidth, window.innerHeight );\n",
       "    renderer.setClearColor( options.theme === 'dark' ? 0 : 0xffffff, 1 );\n",
       "    document.body.appendChild( renderer.domElement );\n",
       "\n",
       "    var b = [{&quot;x&quot;:-8.851426966064658, &quot;y&quot;:-8.851426966064658, &quot;z&quot;:-6.283185307179595}, {&quot;x&quot;:9.899494936611665, &quot;y&quot;:16.97056274847714, &quot;z&quot;:9.0}]; // bounds\n",
       "\n",
       "    if ( b[0].x === b[1].x ) {\n",
       "        b[0].x -= 1;\n",
       "        b[1].x += 1;\n",
       "    }\n",
       "    if ( b[0].y === b[1].y ) {\n",
       "        b[0].y -= 1;\n",
       "        b[1].y += 1;\n",
       "    }\n",
       "    if ( b[0].z === b[1].z ) {\n",
       "        b[0].z -= 1;\n",
       "        b[1].z += 1;\n",
       "    }\n",
       "\n",
       "    var rxRange = Math.sqrt( Math.pow( b[1].z - b[0].z, 2 )\n",
       "                            + Math.pow( b[1].y - b[0].y, 2 ) );\n",
       "    var ryRange = Math.sqrt( Math.pow( b[1].x - b[0].x, 2 )\n",
       "                            + Math.pow( b[1].z - b[0].z, 2 ) );\n",
       "    var rzRange = Math.sqrt( Math.pow( b[1].x - b[0].x, 2 )\n",
       "                            + Math.pow( b[1].y - b[0].y, 2 ) );\n",
       "    var xRange = b[1].x - b[0].x;\n",
       "    var yRange = b[1].y - b[0].y;\n",
       "    var zRange = b[1].z - b[0].z;\n",
       "\n",
       "    var ar = options.aspectRatio;\n",
       "    var a = [ ar[0], ar[1], ar[2] ]; // aspect multipliers\n",
       "\n",
       "    var autoScaling = options.autoScaling;\n",
       "    var autoAspect = 2.5;\n",
       "    if ( xRange > autoAspect * rxRange && autoScaling[0] ) a[0] = autoAspect * rxRange / xRange;\n",
       "    if ( yRange > autoAspect * ryRange && autoScaling[1] ) a[1] = autoAspect * ryRange / yRange;\n",
       "    if ( zRange > autoAspect * rzRange && autoScaling[2] ) a[2] = autoAspect * rzRange / zRange;\n",
       "\n",
       "    // Distance from (xMid,yMid,zMid) to any corner of the bounding box, after applying aspectRatio\n",
       "    var midToCorner = Math.sqrt( a[0]*a[0]*xRange*xRange + a[1]*a[1]*yRange*yRange + a[2]*a[2]*zRange*zRange ) / 2;\n",
       "\n",
       "    var xMid = ( b[0].x + b[1].x ) / 2;\n",
       "    var yMid = ( b[0].y + b[1].y ) / 2;\n",
       "    var zMid = ( b[0].z + b[1].z ) / 2;\n",
       "\n",
       "    var box = new THREE.Geometry();\n",
       "    box.vertices.push( new THREE.Vector3( a[0]*b[0].x, a[1]*b[0].y, a[2]*b[0].z ) );\n",
       "    box.vertices.push( new THREE.Vector3( a[0]*b[1].x, a[1]*b[1].y, a[2]*b[1].z ) );\n",
       "    var boxMesh = new THREE.Line( box );\n",
       "    var boxColor = options.theme === 'dark' ? 'white' : 'black';\n",
       "    if ( options.frame ) scene.add( new THREE.BoxHelper( boxMesh, boxColor ) );\n",
       "\n",
       "    if ( options.axesLabels ) {\n",
       "\n",
       "        var d = options.decimals; // decimals\n",
       "        var offsetRatio = 0.1;\n",
       "        var al = options.axesLabels;\n",
       "        var als = options.axesLabelsStyle || [{}, {}, {}];\n",
       "\n",
       "        var offset = offsetRatio * a[1]*( b[1].y - b[0].y );\n",
       "        var xm = xMid.toFixed(d);\n",
       "        if ( /^-0.?0*$/.test(xm) ) xm = xm.substr(1);\n",
       "        addLabel( al[0] + '=' + xm, a[0]*xMid, a[1]*b[1].y+offset, a[2]*b[0].z, als[0] );\n",
       "        addLabel( ( b[0].x ).toFixed(d), a[0]*b[0].x, a[1]*b[1].y+offset, a[2]*b[0].z, als[0] );\n",
       "        addLabel( ( b[1].x ).toFixed(d), a[0]*b[1].x, a[1]*b[1].y+offset, a[2]*b[0].z, als[0] );\n",
       "\n",
       "        var offset = offsetRatio * a[0]*( b[1].x - b[0].x );\n",
       "        var ym = yMid.toFixed(d);\n",
       "        if ( /^-0.?0*$/.test(ym) ) ym = ym.substr(1);\n",
       "        addLabel( al[1] + '=' + ym, a[0]*b[1].x+offset, a[1]*yMid, a[2]*b[0].z, als[1] );\n",
       "        addLabel( ( b[0].y ).toFixed(d), a[0]*b[1].x+offset, a[1]*b[0].y, a[2]*b[0].z, als[1] );\n",
       "        addLabel( ( b[1].y ).toFixed(d), a[0]*b[1].x+offset, a[1]*b[1].y, a[2]*b[0].z, als[1] );\n",
       "\n",
       "        var offset = offsetRatio * a[1]*( b[1].y - b[0].y );\n",
       "        var zm = zMid.toFixed(d);\n",
       "        if ( /^-0.?0*$/.test(zm) ) zm = zm.substr(1);\n",
       "        addLabel( al[2] + '=' + zm, a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*zMid, als[2] );\n",
       "        addLabel( ( b[0].z ).toFixed(d), a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*b[0].z, als[2] );\n",
       "        addLabel( ( b[1].z ).toFixed(d), a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*b[1].z, als[2] );\n",
       "\n",
       "    }\n",
       "\n",
       "    function addLabel( text, x, y, z, style ) {\n",
       "\n",
       "        var color = style.color || 'black';\n",
       "        var fontSize = style.fontSize || 14;\n",
       "        var fontFamily = style.fontFamily || 'monospace';\n",
       "        var fontStyle = style.fontStyle || 'normal';\n",
       "        var fontWeight = style.fontWeight || 'normal';\n",
       "        var opacity = style.opacity || 1;\n",
       "\n",
       "        if ( options.theme === 'dark' )\n",
       "            if ( color === 'black' || color === '#000000' )\n",
       "                color = 'white';\n",
       "\n",
       "        if ( Array.isArray( fontStyle ) ) {\n",
       "            fontFamily = fontFamily.map( function( f ) {\n",
       "                // Need to put quotes around fonts that have whitespace in their names.\n",
       "                return /\\s/.test( f ) ? '&quot;' + f + '&quot;' : f;\n",
       "            }).join(', ');\n",
       "        }\n",
       "\n",
       "        var canvas = document.createElement( 'canvas' );\n",
       "        var context = canvas.getContext( '2d' );\n",
       "        var pixelRatio = Math.round( window.devicePixelRatio );\n",
       "\n",
       "        // For example: italic bold 20px &quot;Times New Roman&quot;, Georgia, serif\n",
       "        var font = [fontStyle, fontWeight, fontSize + 'px', fontFamily].join(' ');\n",
       "\n",
       "        context.font = font;\n",
       "        var width = context.measureText( text ).width;\n",
       "        var height = fontSize;\n",
       "\n",
       "        // The dimensions of the canvas's underlying image data need to be powers\n",
       "        // of two in order for the resulting texture to support mipmapping.\n",
       "        canvas.width = THREE.MathUtils.ceilPowerOfTwo( width * pixelRatio );\n",
       "        canvas.height = THREE.MathUtils.ceilPowerOfTwo( height * pixelRatio );\n",
       "\n",
       "        // Re-compute the unscaled dimensions after the power of two conversion.\n",
       "        width = canvas.width / pixelRatio;\n",
       "        height = canvas.height / pixelRatio;\n",
       "\n",
       "        canvas.style.width = width + 'px';\n",
       "        canvas.style.height = height + 'px';\n",
       "\n",
       "        context.scale( pixelRatio, pixelRatio );\n",
       "        context.fillStyle = color;\n",
       "        context.font = font; // Must be set again after measureText.\n",
       "        context.textAlign = 'center';\n",
       "        context.textBaseline = 'middle';\n",
       "        context.fillText( text, width/2, height/2 );\n",
       "\n",
       "        var texture = new THREE.Texture( canvas );\n",
       "        texture.needsUpdate = true;\n",
       "\n",
       "        var materialOptions = { map: texture, sizeAttenuation: false, depthWrite: false };\n",
       "        if ( opacity < 1 ) {\n",
       "            // Setting opacity=1 would cause the texture's alpha component to be\n",
       "            // discarded, giving the text a black background instead of the\n",
       "            // background being transparent.\n",
       "            materialOptions.opacity = opacity;\n",
       "        }\n",
       "        var sprite = new THREE.Sprite( new THREE.SpriteMaterial( materialOptions ) );\n",
       "        sprite.position.set( x, y, z );\n",
       "\n",
       "        // Scaling factor, chosen somewhat arbitrarily so that the size of the text\n",
       "        // is consistent with previously generated plots.\n",
       "        var scale = 1/625;\n",
       "        if ( options.projection === 'orthographic' ) {\n",
       "            scale = midToCorner/256; // Needs to scale along with the plot itself.\n",
       "        }\n",
       "        sprite.scale.set( scale * width, scale * height, 1 );\n",
       "\n",
       "        scene.add( sprite );\n",
       "\n",
       "        return sprite;\n",
       "\n",
       "    }\n",
       "\n",
       "    if ( options.axes ) scene.add( new THREE.AxesHelper( Math.min( a[0]*b[1].x, a[1]*b[1].y, a[2]*b[1].z ) ) );\n",
       "\n",
       "    var camera = createCamera();\n",
       "    camera.up.set( 0, 0, 1 );\n",
       "    camera.position.set( a[0]*xMid, a[1]*yMid, a[2]*zMid );\n",
       "\n",
       "    var offset = new THREE.Vector3( a[0]*xRange, a[1]*yRange, a[2]*zRange );\n",
       "\n",
       "    if ( options.viewpoint ) {\n",
       "\n",
       "        var aa = options.viewpoint;\n",
       "        var axis = new THREE.Vector3( aa[0][0], aa[0][1], aa[0][2] ).normalize();\n",
       "        var angle = aa[1] * Math.PI / 180;\n",
       "        var q = new THREE.Quaternion().setFromAxisAngle( axis, angle ).inverse();\n",
       "\n",
       "        offset.set( 0, 0, offset.length() );\n",
       "        offset.applyQuaternion( q );\n",
       "\n",
       "    }\n",
       "\n",
       "    camera.position.add( offset );\n",
       "\n",
       "    function createCamera() {\n",
       "\n",
       "        var aspect = window.innerWidth / window.innerHeight;\n",
       "\n",
       "        // Scale the near and far clipping planes along with the overall plot size.\n",
       "        var nearClip = 0.01 * midToCorner;\n",
       "        var farClip = 100 * midToCorner;\n",
       "\n",
       "        if ( options.projection === 'orthographic' ) {\n",
       "            var camera = new THREE.OrthographicCamera( -1, 1, 1, -1, -farClip, farClip );\n",
       "            updateCameraAspect( camera, aspect );\n",
       "            return camera;\n",
       "        }\n",
       "\n",
       "        return new THREE.PerspectiveCamera( 45, aspect, nearClip, farClip );\n",
       "\n",
       "    }\n",
       "\n",
       "    function updateCameraAspect( camera, aspect ) {\n",
       "\n",
       "        if ( camera.isPerspectiveCamera ) {\n",
       "            camera.aspect = aspect;\n",
       "        } else if ( camera.isOrthographicCamera ) {\n",
       "            // Fit the camera frustum to the bounding box's diagonal so that the entire plot fits\n",
       "            // within at the default zoom level and camera position.\n",
       "            if ( aspect > 1 ) { // Wide window\n",
       "                camera.top = midToCorner;\n",
       "                camera.right = midToCorner * aspect;\n",
       "            } else { // Tall or square window\n",
       "                camera.top = midToCorner / aspect;\n",
       "                camera.right = midToCorner;\n",
       "            }\n",
       "            camera.bottom = -camera.top;\n",
       "            camera.left = -camera.right;\n",
       "        }\n",
       "\n",
       "        camera.updateProjectionMatrix();\n",
       "\n",
       "    }\n",
       "\n",
       "    var lights = [{&quot;x&quot;:-5, &quot;y&quot;:3, &quot;z&quot;:0, &quot;color&quot;:&quot;#7f7f7f&quot;, &quot;parent&quot;:&quot;camera&quot;}];\n",
       "    for ( var i=0 ; i < lights.length ; i++ ) {\n",
       "        var light = new THREE.DirectionalLight( lights[i].color, 1 );\n",
       "        light.position.set( a[0]*lights[i].x, a[1]*lights[i].y, a[2]*lights[i].z );\n",
       "        if ( lights[i].parent === 'camera' ) {\n",
       "            light.target.position.set( a[0]*xMid, a[1]*yMid, a[2]*zMid );\n",
       "            scene.add( light.target );\n",
       "            camera.add( light );\n",
       "        } else scene.add( light );\n",
       "    }\n",
       "    scene.add( camera );\n",
       "\n",
       "    var ambient = {&quot;color&quot;:&quot;#7f7f7f&quot;};\n",
       "    scene.add( new THREE.AmbientLight( ambient.color, 1 ) );\n",
       "\n",
       "    var controls = new THREE.OrbitControls( camera, renderer.domElement );\n",
       "    controls.target.set( a[0]*xMid, a[1]*yMid, a[2]*zMid );\n",
       "    controls.addEventListener( 'change', function() { if ( !animate ) render(); } );\n",
       "\n",
       "    window.addEventListener( 'resize', function() {\n",
       "\n",
       "        renderer.setSize( window.innerWidth, window.innerHeight );\n",
       "        updateCameraAspect( camera, window.innerWidth / window.innerHeight );\n",
       "        if ( window.rescaleFatLines ) rescaleFatLines();\n",
       "        if ( !animate ) render();\n",
       "\n",
       "    } );\n",
       "\n",
       "    var texts = [{&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;x&quot;, &quot;x&quot;: 9.899494936611665, &quot;y&quot;: 9.899494936611664, &quot;z&quot;: 0.0}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;y&quot;, &quot;x&quot;: -7.071067811865475, &quot;y&quot;: 7.0710678118654755, &quot;z&quot;: 0.0}, {&quot;color&quot;: &quot;#000000&quot;, &quot;fontSize&quot;: 20.0, &quot;fontFamily&quot;: [&quot;monospace&quot;], &quot;fontStyle&quot;: &quot;normal&quot;, &quot;fontWeight&quot;: &quot;normal&quot;, &quot;opacity&quot;: 1.0, &quot;text&quot;: &quot;z&quot;, &quot;x&quot;: 0.0, &quot;y&quot;: 0.0, &quot;z&quot;: 9.0}];\n",
       "    for ( var i=0 ; i < texts.length ; i++ ) addText( texts[i] );\n",
       "\n",
       "    function addText( json ) {\n",
       "        var sprite = addLabel( json.text, a[0]*json.x, a[1]*json.y, a[2]*json.z, json );\n",
       "        sprite.userData = json;\n",
       "    }\n",
       "\n",
       "    var points = [];\n",
       "    for ( var i=0 ; i < points.length ; i++ ) addPoint( points[i] );\n",
       "\n",
       "    function addPoint( json ) {\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "        var v = json.point;\n",
       "        geometry.vertices.push( new THREE.Vector3( a[0]*v[0], a[1]*v[1], a[2]*v[2] ) );\n",
       "\n",
       "        var canvas = document.createElement( 'canvas' );\n",
       "        canvas.width = 128;\n",
       "        canvas.height = 128;\n",
       "\n",
       "        var context = canvas.getContext( '2d' );\n",
       "        context.arc( 64, 64, 64, 0, 2 * Math.PI );\n",
       "        context.fillStyle = json.color;\n",
       "        context.fill();\n",
       "\n",
       "        var texture = new THREE.Texture( canvas );\n",
       "        texture.needsUpdate = true;\n",
       "\n",
       "        var transparent = json.opacity < 1 ? true : false;\n",
       "        var size = camera.isOrthographicCamera ? json.size : json.size/100;\n",
       "        var material = new THREE.PointsMaterial( { size: size, map: texture,\n",
       "                                                   transparent: transparent, opacity: json.opacity,\n",
       "                                                   alphaTest: .1 } );\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var mesh = new THREE.Points( geometry, material );\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "    }\n",
       "\n",
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3.0199112155999157e-16, -6.283185307179586], [-7.307917626706027e-16, 2.408834358652442e-16, -6.283185307179586], [-7.485874194419435e-16, 1.7804017949525652e-16, -6.283185307179586], [-7.609894867023644e-16, 1.1391413955222436e-16, -6.283185307179586], [-7.679086072730607e-16, 4.896734562338192e-17, -6.283185307179586], [-7.692949287317696e-16, -1.6332259152761266e-17, -6.283185307179586], [-7.651384626006136e-16, -8.151418962745585e-17, -6.283185307179586], [-7.554691563133129e-16, -1.4610880849799127e-16, -6.283185307179586], [-7.403566774432391e-16, -2.09650710055223e-16, -6.283185307179586], [-7.199099117469525e-16, -2.71682073442372e-16, -6.283185307179586], [-6.942761786398318e-16, -3.317559612647884e-16, -6.283185307179586], [-6.636401697563093e-16, -3.894395397841217e-16, -6.283185307179586], [-6.282226182424132e-16, -4.44317197495324e-16, -6.283185307179586], [-5.882787083683924e-16, -4.959935396170673e-16, -6.283185307179586], [-5.440962369202019e-16, -5.440962369202042e-16, -6.283185307179586], [-4.95993539617065e-16, -5.882787083683944e-16, -6.283185307179586], [-4.443171974953215e-16, -6.282226182424149e-16, -6.283185307179586], [-3.89439539784119e-16, -6.636401697563108e-16, -6.283185307179586], [-3.317559612647856e-16, -6.942761786398332e-16, -6.283185307179586], [-2.7168207344236918e-16, -7.199099117469537e-16, -6.283185307179586], [-2.0965071005522005e-16, -7.4035667744323995e-16, -6.283185307179586], [-1.4610880849798822e-16, -7.554691563133136e-16, -6.283185307179586], [-8.151418962745265e-17, -7.65138462600614e-16, -6.283185307179586], [-1.633225915275816e-17, -7.692949287317698e-16, -6.283185307179586], [4.8967345623384925e-17, -7.679086072730605e-16, -6.283185307179586], [1.1391413955222712e-16, -7.609894867023639e-16, -6.283185307179586], [1.7804017949525923e-16, -7.485874194419429e-16, -6.283185307179586], [2.408834358652469e-16, -7.307917626706018e-16, -6.283185307179586], [3.019911215599941e-16, -7.077307345031643e-16, -6.283185307179586], [3.609229543037911e-16, -6.795704901760193e-16, -6.283185307179586], [4.1725432889129883e-16, -6.465139248948342e-16, -6.283185307179586], [4.705793764777839e-16, -6.087992119699496e-16, -6.283185307179586], [5.205138888734451e-16, -5.666980867722197e-16, -6.283185307179586], [5.66698086772225e-16, -5.205138888734394e-16, -6.283185307179586], [6.087992119699544e-16, -4.705793764777778e-16, -6.283185307179586], [6.465139248948384e-16, -4.172543288912923e-16, -6.283185307179586], [6.795704901760228e-16, -3.609229543037841e-16, -6.283185307179586], [7.077307345031673e-16, -3.0199112155998693e-16, -6.283185307179586], [7.307917626706043e-16, -2.4088343586523936e-16, -6.283185307179586], [7.485874194419448e-16, -1.7804017949525173e-16, -6.283185307179586], [7.60989486702365e-16, -1.1391413955221933e-16, -6.283185307179586], [7.67908607273061e-16, -4.896734562337684e-17, -6.283185307179586], [7.692949287317696e-16, 1.6332259152766295e-17, -6.283185307179586], [7.651384626006132e-16, 8.151418962746078e-17, -6.283185307179586], [7.554691563133119e-16, 1.461088084979961e-16, -6.283185307179586], [7.403566774432376e-16, 2.0965071005522784e-16, -6.283185307179586], [7.199099117469508e-16, 2.716820734423768e-16, -6.283185307179586], [6.942761786398298e-16, 3.3175596126479294e-16, -6.283185307179586], [6.636401697563067e-16, 3.8943953978412605e-16, -6.283185307179586], [6.282226182424103e-16, 4.443171974953281e-16, -6.283185307179586], [5.882787083683891e-16, 4.959935396170712e-16, -6.283185307179586], [5.440962369201984e-16, 5.440962369202077e-16, -6.283185307179586]], &quot;color&quot;: &quot;#808080&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 1.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [9.19238815542512, 9.192388155425117, 0.0]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 3.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [-6.363961030678928, 6.3639610306789285, 0.0]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 3.0}, {&quot;points&quot;: [[0.0, 0.0, 0.0], [0.0, 0.0, 8.0]], &quot;color&quot;: &quot;#00008b&quot;, &quot;opacity&quot;: 1.0, &quot;linewidth&quot;: 3.0}];\n",
       "    for ( var i=0 ; i < lines.length ; i++ ) addLine( lines[i] );\n",
       "\n",
       "    function addLine( json ) {\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "        for ( var i=0 ; i < json.points.length ; i++ ) {\n",
       "            var v = json.points[i];\n",
       "            geometry.vertices.push( new THREE.Vector3( a[0]*v[0], a[1]*v[1], a[2]*v[2] ) );\n",
       "        }\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var transparent = json.opacity < 1 ? true : false;\n",
       "        var materialOptions = { color: json.color, linewidth: json.linewidth,\n",
       "                                transparent: transparent, opacity: json.opacity };\n",
       "\n",
       "        var mesh;\n",
       "        if ( json.linewidth > 1 && window.createFatLineStrip ) {\n",
       "            mesh = createFatLineStrip( geometry, materialOptions );\n",
       "        } else {\n",
       "            var material = new THREE.LineBasicMaterial( materialOptions );\n",
       "            mesh = new THREE.Line( geometry, material );\n",
       "        }\n",
       "\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "    }\n",
       "\n",
       "    var surfaces = [];\n",
       "    for ( var i=0 ; i < surfaces.length ; i++ ) addSurface( surfaces[i] );\n",
       "\n",
       "    function addSurface( json ) {\n",
       "\n",
       "        var useFaceColors = 'faceColors' in json ? true : false;\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "        for ( var i=0 ; i < json.vertices.length ; i++ ) {\n",
       "            var v = json.vertices[i];\n",
       "            geometry.vertices.push( new THREE.Vector3( a[0]*v.x, a[1]*v.y, a[2]*v.z ) );\n",
       "        }\n",
       "        for ( var i=0 ; i < json.faces.length ; i++ ) {\n",
       "            var f = json.faces[i];\n",
       "            for ( var j=0 ; j < f.length - 2 ; j++ ) {\n",
       "                var face = new THREE.Face3( f[0], f[j+1], f[j+2] );\n",
       "                if ( useFaceColors ) face.color.set( json.faceColors[i] );\n",
       "                geometry.faces.push( face );\n",
       "            }\n",
       "        }\n",
       "        geometry.computeVertexNormals();\n",
       "\n",
       "        var side = json.singleSide ? THREE.FrontSide : THREE.DoubleSide;\n",
       "        var transparent = json.opacity < 1 ? true : false;\n",
       "        var depthWrite = 'depthWrite' in json ? json.depthWrite : !transparent;\n",
       "        var flatShading = json.useFlatShading ? json.useFlatShading : false;\n",
       "\n",
       "        var material = new THREE.MeshPhongMaterial( { side: side,\n",
       "                                     color: useFaceColors ? 'white' : json.color,\n",
       "                                     vertexColors: useFaceColors ? THREE.FaceColors : THREE.NoColors,\n",
       "                                     transparent: transparent, opacity: json.opacity,\n",
       "                                     shininess: 20, flatShading: flatShading,\n",
       "                                     depthWrite: depthWrite } );\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var mesh = new THREE.Mesh( geometry, material );\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        if ( transparent && json.renderOrder ) mesh.renderOrder = json.renderOrder;\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "        if ( json.showMeshGrid ) addSurfaceMeshGrid( json );\n",
       "\n",
       "    }\n",
       "\n",
       "    function addSurfaceMeshGrid( json ) {\n",
       "\n",
       "        var geometry = new THREE.Geometry();\n",
       "\n",
       "        for ( var i=0 ; i < json.faces.length ; i++ ) {\n",
       "            var f = json.faces[i];\n",
       "            for ( var j=0 ; j < f.length ; j++ ) {\n",
       "                var k = j === f.length-1 ? 0 : j+1;\n",
       "                var v1 = json.vertices[f[j]];\n",
       "                var v2 = json.vertices[f[k]];\n",
       "                // vertices in opposite directions on neighboring faces\n",
       "                var nudge = f[j] < f[k] ? .0005*zRange : -.0005*zRange;\n",
       "                geometry.vertices.push( new THREE.Vector3( a[0]*v1.x, a[1]*v1.y, a[2]*(v1.z+nudge) ) );\n",
       "                geometry.vertices.push( new THREE.Vector3( a[0]*v2.x, a[1]*v2.y, a[2]*(v2.z+nudge) ) );\n",
       "            }\n",
       "        }\n",
       "\n",
       "        var c = new THREE.Vector3();\n",
       "        geometry.computeBoundingBox();\n",
       "        geometry.boundingBox.getCenter( c );\n",
       "        geometry.translate( -c.x, -c.y, -c.z );\n",
       "\n",
       "        var gridColor = options.theme === 'dark' ? 'white' : 'black';\n",
       "        var linewidth = json.linewidth || 1;\n",
       "        var materialOptions = { color: gridColor, linewidth: linewidth };\n",
       "\n",
       "        var mesh;\n",
       "        if ( linewidth > 1 && window.createFatLineSegments ) {\n",
       "            mesh = createFatLineSegments( geometry, materialOptions );\n",
       "        } else {\n",
       "            var material = new THREE.LineBasicMaterial( materialOptions );\n",
       "            mesh = new THREE.LineSegments( geometry, material );\n",
       "        }\n",
       "\n",
       "        mesh.position.set( c.x, c.y, c.z );\n",
       "        mesh.userData = json;\n",
       "        scene.add( mesh );\n",
       "\n",
       "    }\n",
       "\n",
       "    function render() {\n",
       "\n",
       "        if ( window.updateAnimation ) animate = updateAnimation();\n",
       "        if ( animate ) requestAnimationFrame( render );\n",
       "\n",
       "        renderer.render( scene, camera );\n",
       "\n",
       "    }\n",
       "\n",
       "    render();\n",
       "    controls.update();\n",
       "    if ( !animate ) render();\n",
       "\n",
       "\n",
       "    // menu functions\n",
       "\n",
       "    function toggleMenu() {\n",
       "\n",
       "        var m = document.getElementById( 'menu-content' );\n",
       "        if ( m.style.display === 'block' ) m.style.display = 'none'\n",
       "        else m.style.display = 'block';\n",
       "\n",
       "    }\n",
       "\n",
       "\n",
       "    function saveAsPNG() {\n",
       "\n",
       "        var a = document.body.appendChild( document.createElement( 'a' ) );\n",
       "        a.href = renderer.domElement.toDataURL( 'image/png' );\n",
       "        a.download = 'screenshot';\n",
       "        a.click();\n",
       "\n",
       "    }\n",
       "\n",
       "    function saveAsHTML() {\n",
       "\n",
       "        toggleMenu(); // otherwise visible in output\n",
       "        event.stopPropagation();\n",
       "\n",
       "        var blob = new Blob( [ '<!DOCTYPE html>\\n' + document.documentElement.outerHTML ] );\n",
       "        var a = document.body.appendChild( document.createElement( 'a' ) );\n",
       "        a.href = window.URL.createObjectURL( blob );\n",
       "        a.download = suggestFilename();\n",
       "        a.click();\n",
       "\n",
       "        function suggestFilename() {\n",
       "            if ( !document.title ) {\n",
       "                return 'graphic.html';\n",
       "            } else if ( /\\.html?$/i.test( document.title ) ) {\n",
       "                return document.title; // already ends in .htm or .html\n",
       "            } else {\n",
       "                return document.title + '.html';\n",
       "            }\n",
       "        }\n",
       "\n",
       "    }\n",
       "\n",
       "    function getViewpoint() {\n",
       "\n",
       "        function roundTo( x, n ) { return +x.toFixed(n); }\n",
       "\n",
       "        var v = camera.quaternion.inverse();\n",
       "        var r = Math.sqrt( v.x*v.x + v.y*v.y + v.z*v.z );\n",
       "        var axis = [ roundTo( v.x / r, 4 ), roundTo( v.y / r, 4 ), roundTo( v.z / r, 4 ) ];\n",
       "        var angle = roundTo( 2 * Math.atan2( r, v.w ) * 180 / Math.PI, 2 );\n",
       "\n",
       "        var textArea = document.createElement( 'textarea' );\n",
       "        textArea.textContent = JSON.stringify( axis ) + ',' + angle;\n",
       "        textArea.style.csstext = 'position: absolute; top: -100%';\n",
       "        document.body.append( textArea );\n",
       "        textArea.select();\n",
       "        document.execCommand( 'copy' );\n",
       "\n",
       "        var m = document.getElementById( 'menu-message' );\n",
       "        m.innerHTML = 'Viewpoint copied to clipboard';\n",
       "        m.style.display = 'block';\n",
       "        setTimeout( function() { m.style.display = 'none'; }, 2000 );\n",
       "\n",
       "    }\n",
       "\n",
       "    function getCamera() {\n",
       "\n",
       "        function roundTo( x, n ) { return +x.toFixed(n); }\n",
       "\n",
       "        var pos = camera.position;\n",
       "        var pos_r = [ roundTo( pos.x, 4 ), roundTo( pos.y, 4 ), roundTo( pos.z, 4 ) ];\n",
       "   //     var up = camera.up; // up is always (0,0,1)\n",
       "        var textArea = document.createElement('textarea');\n",
       "        var cam_position = JSON.stringify(pos_r);\n",
       "        textArea.textContent = ',camera_position=' + cam_position;\n",
       "        textArea.style.csstext = 'position: absolute; top: -100%';\n",
       "        document.body.append( textArea );\n",
       "        textArea.select();\n",
       "        document.execCommand( 'copy' );\n",
       "\n",
       "        var m = document.getElementById( 'menu-message' );\n",
       "        m.innerHTML = 'Camera position '+ cam_position+' copied to clipboard';\n",
       "        m.style.display = 'block';\n",
       "        setTimeout( function() { m.style.display = 'none'; }, 2000 );\n",
       "\n",
       "    }\n",
       "                                       \n",
       "</script>\n",
       "\n",
       "<div id=&quot;menu-container&quot; onclick=&quot;toggleMenu()&quot;>&#x24d8;\n",
       "<div id=&quot;menu-message&quot;></div>\n",
       "<div id=&quot;menu-content&quot;>\n",
       "<div onclick=&quot;saveAsPNG()&quot;>Save as PNG</div>\n",
       "<div onclick=&quot;saveAsHTML()&quot;>Save as HTML</div>\n",
       "<div onclick=&quot;getCamera()&quot;>Get camera</div>\n",
       "<div onclick=&quot;getViewpoint()&quot;>Get viewpoint</div>\n",
       "<div>Close Menu</div>\n",
       "</div></div>\n",
       "\n",
       "\n",
       "</body>\n",
       "</html>\n",
       "\"\n",
       "        width=\"100%\"\n",
       "        height=\"400\"\n",
       "        style=\"border: 0;\">\n",
       "</iframe>\n"
      ],
      "text/plain": [
       "Graphics3d Object"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# continuation ; \n",
    "# plot coord. lines using the values 0, 2pi of r;\n",
    "#                             values 0, pi of ph;\n",
    "#                and 20 values of th from [0,pi];\n",
    "p1 = spherical.plot(cartesian,\n",
    "                    ranges={r: (0,2*pi), th: (0,pi), ph: (0,2*pi)},\n",
    "                    number_values={r: 2, ph: 2, th: 20},\n",
    "                    color={r: 'red', ph: 'grey', th: 'red'},\n",
    "                    thickness={r: 2, ph: 1, th: 2}, label_axes=False)\n",
    "(p1+ax).rotateZ(-pi/4).show(frame=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What's next?\n",
    "\n",
    "Take a look at the notebook [Function graph as a manifold](https://nbviewer.org/github/sagemanifolds/IntroToManifolds/blob/main/03Manifold_Graph.ipynb)."
   ]
  }
 ],
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