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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"pycharm": {
"name": "#%% md\n"
},
"id": "H2WXTBUBAS92"
},
"source": [
"# Quadric Projection Theory\n",
"\n",
"From Hartley & Zisserman’s Multiple View Geometry In Computer Vision, 2004, p.201\n",
"\n",
"### Action of a projective camera on quadrics\n",
"[..]\n",
"Result 8.9: Under the camera matrix P the outline of the quadric Q is the conic C given\n",
"by:\n",
"\n",
"$$C^{*} = PQ^{*}P^{T}$$\n",
"\n",
"$$C = (PQ^{-1}P^{T})^{-1}$$\n",
"\n",
"Where the asterisk $C^{*}$/$Q^{*}$ denotes the dual form. In 3d the dual form of a quadric describes the quadric by all planes tangent to its surface. If Q is invertible, $Q^{*}$ is simply given by $Q^{−1}$. [Wong et al. 2010 Section II](https://ieeexplore.ieee.org/document/5535178)."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"id": "n0Xj4qKyAS97"
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"pycharm": {
"name": "#%%\n"
},
"id": "vDd4QmMfAS99"
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"np.set_printoptions(suppress=True, precision=4)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "xUbUC6wcAS9_"
},
"source": [
"### Construct projection matrices \n",
"\n",
"The $3 \\times 4$ matrices used to describe a projective mapping are constructed from geometrical parameters. A x-ray source is positioned at $-622mm$ on the z-Axis pointing into positive z-direction. The emerging ray of beams has a focal length of $1164mm$. This imaging setup is able to project a volume of shape $160mm\\times160mm\\times160mm$ onto the detector.\n",
"\n",
"We want to use volume indices; therefore we convert these units in mm to voxel by dividing with the voxel-side length. Furthermore we define the center of the resulting volume with side-lenght 512 as the centroid. To adapt the projection matrices, we add the transform _iso_from_ijk_ .\n",
"\n",
"A detector is positioned at the focal length, with a resolution of $976\\times976$. The coordinate system it describes is denoted $u, v$. The central ray hits the center of this detector at $p_u, p_v = 488, 488$.\n",
"\n",
"The projective transform $P$ is contructed like so:\n",
"\n",
"$$\n",
"P=\n",
"\\begin{bmatrix}\n",
"f & 0 & p_{x} \\\\\n",
"0 & f & p_{y} \\\\\n",
"0 & 0 & 1\n",
"\\end{bmatrix}\n",
"\\times\n",
"\\begin{bmatrix}\n",
"1 & 0 & 0 & 0 \\\\\n",
"0 & 1 & 0 & 0\\\\\n",
"0 & 0 & 1 & 0\n",
"\\end{bmatrix}\n",
"\\times\n",
"\\begin{bmatrix}\n",
"\\mathtt R_{c}^T & -R_{c}^TC \\\\\n",
"\\mathtt 0 & 1\n",
"\\end{bmatrix}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "1xPeBlwrAS-B",
"outputId": "e4e9202d-a13b-4c91-d3ec-64c9b07d5cfe"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[[ 2.1475 0. 0.2818 -60.6833]\n",
" [ 0. 2.1475 0.2818 -60.6833]\n",
" [ 0. 0. 0.0006 1. ]]\n",
"[488. 488. 1.]\n"
]
}
],
"source": [
"# construct standard projection parameters\n",
"sid_mm = 622 # source isocenter distance\n",
"sdd_mm = 1164 # focal length is source detector distance (~ 2*sid)\n",
"v_mm = 0.313 # voxel side length\n",
"pu, pv = 488, 488 # center of detector with resolution of 976x976\n",
"c = 255.5 # center of volume of interest (512 / 2) - 0.5\n",
"iso_from_ijk = np.array([[1, 0, 0, -c],\n",
" [0, 1, 0, -c],\n",
" [0, 0, 1, -c],\n",
" [0, 0, 0, 1]])\n",
"K = np.array([[sdd_mm / v_mm, 0, pu],\n",
" [0, sdd_mm / v_mm, pv],\n",
" [0, 0, 1]])\n",
"R_c = np.eye(3) # dont rotate for now\n",
"c = np.array([0, 0, -sid_mm / v_mm]) # camera sits on z-axis at z = -622mm\n",
"t = -R_c.T @ c\n",
"Rt = np.column_stack([R_c.T, t]) # shape (3, 4)\n",
"P = K @ Rt @ iso_from_ijk\n",
"\n",
"P /= P[2, 3]\n",
"print(P)\n",
"\n",
"isocenter = np.array([255.5, 255.5, 255.5, 1])\n",
"detector_center = P @ isocenter\n",
"\n",
"print(detector_center / detector_center[2])\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "rZLJqIWhAS-D"
},
"source": [
"### Construct Ellipsoid in quadric representation\n",
"\n",
"The Covariance $\\Sigma$ and the mean point $\\mu$ define an ellipsoid-shaped 3d Gaussian distribution, which yields an ellipsoid when thresholded at a certain $\\sigma$.\n",
"\n",
"We can define the $\\sigma$-surface of this ellipsoid:\n",
"\n",
"$$(x-\\mu)^\\top\\Sigma^{-1}(x-\\mu)-\\sigma=0$$\n",
"\n",
"which multiplies out to\n",
"\n",
"$$x^{\\top}\\Sigma^{-1}x+2\\mu^{\\top}x+\\mu^{\\top}\\Sigma^{-1}\\mu-c=0$$\n",
"\n",
"It can be compared to the general quadric equation:\n",
"\n",
"$$x^{\\top}Ax+2b^{\\top}x+c=0$$\n",
"\n",
"By comparing the two equations, the following correspondances between the parameters can be established:\n",
"\n",
"$$A=\\Sigma^{-1}, b=-A\\mu ,\\; c=\\mu^⊤\\Sigma^{-1}\\mu-\\sigma$$\n",
"\n",
"The $4\\times4$ symmetric homogenous matrix $Q$ can be seen as an affine mapping comprising a translation and a non-isotropic scaling along principle axis and represents the general quadric polynomial in homogenous coordinates:\n",
"\n",
"$$Q = \\begin{bmatrix}A & b \\\\ b^⊤ & c\\end{bmatrix}, $$\n",
"$$ \\hat{x}^{\\top}Q\\hat{x}=0, \\hat{x}=[x^{\\top},1]^{\\top}$$"
]
},
{
"cell_type": "code",
"source": [
"def as_quadric(_Sigma, _mu, _stddev=1, verbose=False):\n",
" # converts the ellipsoid of the gaussian (Sigma, mu) at stddev to a quadric\n",
" A = np.linalg.inv(_Sigma)\n",
" assert np.all(A == A.T), f\"Covariance must be symmetric\"\n",
" b = -A @ _mu\n",
" c = _mu @ A @ _mu - _stddev\n",
" Q = np.zeros((4, 4))\n",
" Q[:3, :3] = A\n",
" Q[3, :3] = b\n",
" Q[:3, 3] = b\n",
" Q[3, 3] = c\n",
" if verbose:\n",
" print(f\"Sigma\\n{_Sigma}\\nmu\\n{_mu}\\n--> Q\\n{Q}\")\n",
" return Q"
],
"metadata": {
"id": "QHMddnEYXOd8"
},
"execution_count": 4,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"\n",
"Lets draw some samples $\\hat{x}$ on the surface of the ellipsoid to test the equation."
],
"metadata": {
"id": "TGB6mo9qaY1q"
}
},
{
"cell_type": "code",
"source": [
"# sample points on the ellipsoid by transforming the unit-sphere\n",
"def draw_samples3d(_S, _m):\n",
" theta = np.linspace(0, 2 * np.pi, 20)\n",
" phi = np.linspace(0, np.pi, 20)\n",
" x = np.outer(np.cos(theta), np.sin(phi))\n",
" y = np.outer(np.sin(theta), np.sin(phi))\n",
" z = np.outer(np.ones_like(theta), np.cos(phi))\n",
" unit_sphere_ijk = np.array([x.flatten(), y.flatten(), z.flatten()])\n",
"\n",
" # transform them to the ellipsoid (cholesky resembles the sqrt for matrices)\n",
" L = np.linalg.cholesky(_S) # decomposes to (L @ L.T); only returns L\n",
" return (L @ unit_sphere_ijk) + _m[:, np.newaxis]\n",
"\n",
"def plot_points3d(_points):\n",
" # scatter plot with equally spaced axis to prevent distortions\n",
" fig = plt.figure()\n",
" ax = fig.add_subplot(projection='3d')\n",
" ax.scatter(*_points, label=\"$(\\Sigma \\hatx)+\\mu$\")\n",
" mi, ma = int(np.min(ellipsoid_ijk) - .5), int(np.max(ellipsoid_ijk) + .5)\n",
" ax.set_xlim((mi, ma))\n",
" ax.set_ylim((mi, ma))\n",
" ax.set_zlim((mi, ma))\n",
" ax.set_xlabel('x [px]')\n",
" ax.set_ylabel('y [px]')\n",
" ax.set_zlabel('z [px]')\n",
" ax.legend()\n",
" plt.show()"
],
"metadata": {
"id": "ClriLXudVIsU"
},
"execution_count": 5,
"outputs": []
},
{
"cell_type": "code",
"source": [
"mu = np.array([1, 1, 1])\n",
"Sigma = np.array([[1, -.5, 0],\n",
" [-.5, 1, 0],\n",
" [0, 0, 1]])\n",
"\n",
"ellipsoid_ijk = draw_samples3d(Sigma, mu)\n",
"\n",
"plot_points3d(ellipsoid_ijk)"
],
"metadata": {
"id": "hTGJT-mraYEH",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 248
},
"outputId": "bbca7c68-d5e0-4883-b766-18b3207d45c1"
},
"execution_count": 6,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"source": [
"def on_ellipsoid(x, _S, m, debug=False):\n",
" maha_dist=(x-m)@np.linalg.inv(_S)@(x-m)\n",
" if debug: print(f\"X:{x}, S:{np.diag(np.linalg.inv(_S))}, mu:{m}: {maha_dist}\")\n",
" return np.isclose(maha_dist, 1)\n",
"\n",
"def on_quadric(_x, _Q, debug=False):\n",
" xh = np.ones((4))\n",
" xh[:3] = _x\n",
" _dist = xh.T@_Q@xh\n",
" if debug: print(f\"X:{xh}: {_dist}\")\n",
" return np.isclose(_dist, 0)\n",
"\n",
"# create quadric\n",
"Q = as_quadric(Sigma, mu)\n",
"print(Q)\n",
"\n",
"for t in ellipsoid_ijk.T:\n",
" assert on_ellipsoid(t, Sigma, mu, debug=0)\n",
"\n",
"for t in ellipsoid_ijk.T:\n",
" assert on_quadric(t, Q, debug=0)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "vvmiwzZnqJSt",
"outputId": "c59b12de-b681-4cee-d8e1-cfba8aab97f9"
},
"execution_count": 7,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[[ 1.3333 0.6667 0. -2. ]\n",
" [ 0.6667 1.3333 0. -2. ]\n",
" [ 0. 0. 1. -1. ]\n",
" [-2. -2. -1. 4. ]]\n"
]
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Z0nwdIYaAS-I"
},
"source": [
"## Real world example\n",
"\n",
"### project using spin geometry\n",
"Verify the projection setup by forward projection of volume points onto detector. We should see a elliptical shape emerge."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 546
},
"id": "BmzUMnkVAS-M",
"outputId": "d64cf21d-09f6-47b5-ccca-e496be1b1d66"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Center of mass Ellipsoid: [263.2086 255.5 255.5 ]\n",
"Center of mass Ellipse: [502.4378 488. ]\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"# centered in VOI aligned with the x-axis\n",
"mu = np.array([255.5, 255.5, 255.5])\n",
"Sigma = np.array([[255.5**2, 0, 0],\n",
" [0, 100**2, 0],\n",
" [0, 0, 100**2]])\n",
"\n",
"# verify the projection matrices map the isocenter to the detector center\n",
"test = P @ np.array([255.5, 255.5, 255.5, 1])\n",
"assert np.allclose([488, 488, 1], test/test[-1])\n",
"\n",
"# make homogenous\n",
"ellipsoid_ijk = draw_samples3d(Sigma, mu)\n",
"plot_points3d(ellipsoid_ijk)\n",
"ellipsoid_homog_ijk = np.pad(ellipsoid_ijk, ((0, 1), (0 ,0)), constant_values=1)\n",
"print(f\"Center of mass Ellipsoid: {np.mean(ellipsoid_ijk, axis=1)}\")\n",
"\n",
"# project points onto detector\n",
"ellipsoid_uvw = P @ ellipsoid_homog_ijk\n",
"ellipsoid_uv = ellipsoid_uvw[:2] / ellipsoid_uvw[2]\n",
"print(f\"Center of mass Ellipse: {np.mean(ellipsoid_uv, axis=1)}\")\n",
"\n",
"# plot\n",
"plt.figure()\n",
"plt.scatter(*ellipsoid_uv, label=\"$P(\\Sigma\\hatx+\\mu)$\")\n",
"plt.plot([0, 0, 976, 976, 0], [0, 976, 976, 0, 0], label=\"detector area\")\n",
"plt.xlabel('u [px]')\n",
"plt.ylabel('v [px]')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Qwi6_ELTAS-P"
},
"source": [
"### Project quadric and visualize\n",
"\n",
"Finally, lets project the quadric $Q$ along the geometry $P$ to obtain the conic $C$. Then, transform the unit-sphere to verify the new shape. It should draw a perfect outline around the projected points from 3d on the outline of the Ellipsoid."
]
},
{
"cell_type": "code",
"source": [
"# define a quadric\n",
"Q = as_quadric(Sigma, mu, verbose=True)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "KNgJXEzrTY0c",
"outputId": "5f395058-8373-4630-b390-a93b6a1fcd14"
},
"execution_count": 9,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Sigma\n",
"[[65280.25 0. 0. ]\n",
" [ 0. 10000. 0. ]\n",
" [ 0. 0. 10000. ]]\n",
"mu\n",
"[255.5 255.5 255.5]\n",
"--> Q\n",
"[[ 0. 0. 0. -0.0039]\n",
" [ 0. 0.0001 0. -0.0255]\n",
" [ 0. 0. 0.0001 -0.0255]\n",
" [-0.0039 -0.0255 -0.0255 13.056 ]]\n"
]
}
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"id": "vo9nteeVAS-Q"
},
"outputs": [],
"source": [
"def is_elliptical(_C):\n",
" # discriminant of polynomial is negative for ellipses \n",
" a, b, c = C[0, 0], 2 * C[0, 1], C[1, 1]\n",
" return (b**2-4*a*c) < 0\n",
"\n",
"# Use the inverse as dual quadric Q* \n",
"C = np.linalg.inv(P @ np.linalg.inv(Q) @ P.T)\n",
"assert is_elliptical(C), \"no valid ellipse\""
]
},
{
"cell_type": "markdown",
"source": [
"To visualize the conic, we have remember what it represents\n",
"\n",
"$$x^{\\top}Cx=0$$\n",
"\n",
"$$C=\\begin{bmatrix}a&b/2&d/2\\\\b/2&c&e/2\\\\d/2&e/2&f\\end{bmatrix} = \\begin{bmatrix}A&b'\\\\b'^{\\top} & f\\end{bmatrix}$$\n",
"\n",
"$$x^{\\top}Ax+2b'^{\\top}x+f=0$$\n",
"\n",
"$$ax_1^2+bx_1x_2+cx_2^2+dx_1+ex_2+f=0$$\n",
"\n",
"An Ellipse must fulfill:\n",
"\n",
"$$b^2<4ac$$\n",
"\n",
"To plot it, we derive its covariance $\\Sigma$ and mean $\\mu$ analogously to the quadric derivation above:\n",
"\n",
"$$(x-\\mu)^\\top\\Sigma^{-1}(x-\\mu)-\\sigma=0$$\n",
"\n",
"which multiplies out to\n",
"\n",
"$$x^{\\top}\\Sigma^{-1}x+2\\mu^{\\top}x+\\mu^{\\top}\\Sigma^{-1}\\mu-\\sigma=0$$\n",
"\n",
"It can be compared to the general quadric equation:\n",
"\n",
"$$x^{\\top}Ax+2b'^{\\top}x+f=0$$\n",
"\n",
"$$\\Sigma=A^{-1}, \\mu =-\\Sigma b', f=\\mu^{\\top} \\Sigma^{-1} \\mu - \\sigma$$\n",
"\n",
"To obtain the scale-corrected Covariance $\\Sigma'$ we first calculate the $\\sigma$ by\n",
"\n",
"$$\\sigma = \\mu^{\\top} \\Sigma^{-1} \\mu - f$$\n",
"$$\\Sigma'=\\Sigma\\sigma$$\n",
"\n",
"I am not sure about that last part, but if I dont normalize $\\Sigma$ by $\\sigma$, it appears to big."
],
"metadata": {
"id": "6wpJt1K4THLf"
}
},
{
"cell_type": "code",
"source": [
"def gaussian_from_conic(_C):\n",
" Sigma2d = np.linalg.inv(_C[:2, :2])\n",
" mu2d = - Sigma2d @ _C[:2, 2]\n",
" sigma = mu2d.T @ C[:2, :2] @ mu2d - _C[-1, -1] \n",
" print(sigma)\n",
" print(f\"C\\n{_C}\\n--> sqrt(Sigma)\\n{np.linalg.cholesky(Sigma2d * sigma)}\\n-->mu\\n{mu2d}\\n\\n\")\n",
" return Sigma2d * sigma, mu2d\n",
"\n",
"S2d, m2d = gaussian_from_conic(C)\n",
"print(f\"rightmost point: \\n projected points: {np.max(ellipsoid_uv[0])}\\n calculated conic: {488 + np.linalg.cholesky(S2d)[0, 0]}\")\n",
"print(f\"leftmost point: \\n projected points: {np.min(ellipsoid_uv[0])}\\n calculated conic: {488 - np.linalg.cholesky(S2d)[0, 0]}\")"
],
"metadata": {
"id": "R_dDDRuwTGwT",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "e3643ae5-f0c1-4f86-9e6f-027278c6f5ae"
},
"execution_count": 39,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.7613154017695472\n",
"C\n",
"[[ 0. -0. -0.0016]\n",
" [ 0. 0. -0.0106]\n",
" [-0.0016 -0.0106 5.1936]]\n",
"--> sqrt(Sigma)\n",
"[[478.7448 0. ]\n",
" [ -0. 187.3757]]\n",
"-->mu\n",
"[488. 488.]\n",
"\n",
"\n",
"rightmost point: \n",
" projected points: 966.4935687333856\n",
" calculated conic: 966.7448004969974\n",
"leftmost point: \n",
" projected points: 16.032459874317908\n",
" calculated conic: 9.255199503002586\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"It seems like the inverse produces more consistanve projections, whereas the adjunct does not. So we will continue to use the inverse.\n",
"\n",
"### Visual proof of Conic C\n",
"\n",
"We draw samples on the conic at $\\sigma=1$ by multiplying with the Cholesky factor of the Covariance $\\Sigma = LL^{⊤}$. Points on the ellipse can be obtained by transforming points on the unit-sphere $\\hat{x}$:\n",
"$$x=L\\hat{x} + \\mu$$"
],
"metadata": {
"id": "Na5xhXGKQKMr"
}
},
{
"cell_type": "code",
"source": [
"def draw_samples2d(_S, _m):\n",
" theta = np.linspace(0, 2 * np.pi, 100)\n",
" u, v = np.cos(theta), np.sin(theta)\n",
" unit_circle = np.array([u, v])\n",
"\n",
" # transform them to the ellipsoid (cholesky resembles the sqrt for matrices)\n",
" L = np.linalg.cholesky(_S) # decomposes to (L @ L.T); only returns L\n",
" return (L @ unit_circle) + _m[:, np.newaxis]"
],
"metadata": {
"id": "Rdv-kCTxUh5-"
},
"execution_count": 12,
"outputs": []
},
{
"cell_type": "code",
"source": [
"# transform unit-circle to conic outline\n",
"ellipse_uv = draw_samples2d(S2d, m2d)\n",
"\n",
"# plot\n",
"plt.figure()\n",
"plt.scatter(*ellipsoid_uv, label=\"$P(\\Sigma_{Q}\\hatx+\\mu_{Q})$\")\n",
"plt.plot([0, 0, 976, 976, 0], [0, 976, 976, 0, 0], label=\"detector area\")\n",
"plt.plot(*ellipse_uv, label=\"$\\Sigma_{C}\\hatu + \\mu_{C}$\")\n",
"plt.xlabel('u [px]')\n",
"plt.ylabel('v [px]')\n",
"plt.legend()\n",
"plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 279
},
"id": "itoH19e1TBhQ",
"outputId": "7e4381e6-5e6f-4b1e-a78a-4371fe7081a1"
},
"execution_count": 18,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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BNW14nqW1pEidG8uJ2KbD8gi/d9GKR8rK3LorDLnaWKBOUHb+G3Ysg81vGes7nQlnnM9yhvHb1W346kjdEDqmySrNnHRZII8D72qtr1ZKZQItgd8AH2itH1JKzQZmA78GLgL6BZaxwJOB1+aN1rBnjSEYW96pszI6nAFjZsLp5xmmdmbLBrsG/8Avff511D7lcMItlHQEr4PncmKNgFHOPrPfTpngzbl8ELctLGrwW2uSn87r1N2XSssjXosjnS7JWkIEpWB1Ca+++wFnnVjBuXvXMnrfn5mganhTZ7PMM5x3fGP42D+USp1Vm7xyqohIymMgSqm2QBHQV4ecXCm1BZiktS5TSnUDPtJaD1BKPRV4/0r4dlbnaLIxEK3hm2JY/zqsX2z03FUu6DnOyJIacJHR5yIKos9wiUzwwU7HkBLR+tBT1YLtPftty+++eihBgyuG4fS3SKXlEUuMw+NStMrKSKvbNEj4UCnnntmJ11eV1ruebE4y3rWRC1yrmOIupIM6RqXO5GN/Pu/4RvORHsnaB69OS/lPhRhIH2A/8FelVD6wCvgl0CVEFL4BugTe5wG7Q/YvCayrJyBKqZnATIBevRwMx9CYOLAd1r9mCMeBrUZq7ennwqTZ0P9CyOkQ86GDbqAgoQ9IbksPx0/W4PVHJytBSyR0QqU7FxdTuOsQH27en1RRCbdGIoliqrK13BYtbXcSU0QjxTsgua14s3GpnJQJjN/Fr3WjEozw56G0vNLUiq8ki2X+ESzzj+Cumh8yxrWZC11fMNVdyIXulZzUHnjtHci/zniOm1AQPlrSISAZwAjgv7XWK5RSj2O4q2rRWmulwseYtkdr/TTwNBgWSKIKmzS8lbBxiZFS+PWngILTJsDYn8LAaXGJhh12ghKeUmmFW6kGlUSl11fvYUumuyv0GkLLb1fqZLvfrNw0Pq2TFgfZE8Gdl+gsMLv/Snijwo50ZYFFsi7M0scjVSQ+3HzmH8Rn/kHMqZnBcLWdKzOW873t/zIaha26GinFw26Azmcl4arSSzoEpAQo0VqvCHx+DUNA9iqluoW4sPYFvi8FQlMfegTWNXrM3Ef91W5ubPERV3uWk+k9agwNMvkeGDod2qanL0M0Fkq2x21ZSTRoqYUEtJM1impo+e1SasPLk2jseqUnWriCv6Vd5ZbtcTNrqs1AhzGcM1QgzGIulV6frSWWCovD6n9mNg1xImKEoWhcrNb9GTjyfLi0v5H0svbv8PmT8OkfjAbimJlw5iXNZpiVlAuI1vobpdRupdQArfUWYDKwMbDMAB4KvL4R2GUJ8Aul1N8xgudH7OIfjYX6f1jNBNd6ZrrfYqK7mCqdwbsnR/OK7zw2Hx4KH7oof7uI7rnpH6LDTlBC3RROU1T3lFeaPrzJsAZmTR0QsRUcLE+ixczu3IkSLqcB83YtPQkfeNKpa8qndYNGRqosDrv/mVn5nYqHlZs0fH2DLKyBVxjLiQNQ9BKsfAYWzTDmSBn9QxhxI7TqFMUVNj7S0pFQKTUMI403E/gS+AFGp9JXgV7ALow03kOBNN4/AhdipPH+QGttGyFvDEH0CQ8tY2/5MS5xfc7MjLcZ5NrFPp3LgpqpvOI7l8O0Md0v2+Pm2yPzkh5LiAezQKnVQ5aXa0yEZCY47Vp6aJmZkdDrjJTOmpvtoarG36AyScSwHgVrSm0HWIwnmO4kOB1vvMNOWPvMfttRhZuqBItoGjZ5udkRXZxWhD6PpeWV8fVH8ftg61L44in48iNjAq6RP4AJvzQm30oAqQ6iS0/0MBIiIH4/t9z1v9yesYjerr1s8+fxtO8S3vBNoJrIpmt4ZWwnKumaYMdRtkqg5WmW4mpGIluqZhVutsdNlsdlOVRKIs5/+p3/tHTh7Hjw4piPG8k9p4CdCRao0N8j0vnDt48Xu/+1VVmtxFUB3S1cjOHPWspGZti/BZb/Hta+Aq4MGDkDJtwatxv7VMjCar5oDds/gA/m8PvMYjb5e/Gj6jv4wD8cjfNpPM1iCWYB6sJdh+pV2uGuoWSKS7irC2DUae1Nz+fU5WXm6on1GkKztUL3vc3GQkiEq8kumB4PkQLm3XNjm/LWzmIL/T3MXHSJSL81u7+ArcvTzB1lF38JHtdMdNJm7XcaANOegIn/A588CoXPGQk1434GE2dBi9bJL0MCEAFJFAd3wNu3G6Zp7mkUjnyE73/Rk4ooU2StMBOV4HDt4evnLd0CWD+E0LBiTXRAOxQnsYkgoRWllU/babqwWXkiiVmkijoSVsF0t1JxZWNZtaAh9oC5E7dY8PewEuR4XX5m9zfL4zIViKCYWd0jq/hLaDkb3XS47fvA5X8wROPDB2H540bg/fw5MPTaRj9/vAhIvPi8RobFxw8bQ4tc+DCM+iGjMjJ5oEf0nfii6exn1ardU15p2Uqb++YGTnr9lq27ZGD28J6oqjENBoe2pK2uIZ504UhiFjx/rJaP1fF9Wkc9/Wp4RpzHpRr02YknYO4kMB56P6waCHbltvvtrO6vVZmCwmElppHiL07Lnw4KdrqZt+UaOlWdyb38jaEFP2PN4t8xq+YnbPcbZU5GckS8iIDEw96NsPjHxsx9Z10GF82rFwyz+sOG59MrRa0bwCyWYCUqdia7VSvNzP9v5bqxS4mMtnI1y+4ycymEtqStrsEuXTgSwW3Mho0Pnt+sZXzrwiLmLNkQMdAe/O72V4sINz69Pu14+tW7CorrCeXhCi8etyI32+PYPx/pPkWytpxYNpFiYXYCH621FxQzK3dU8PrSWcFaueTsnqPQBmYpZ3DFyXu40vUJd3le5C3Pb3ig5npe8E3hcIW30c0BbykgSqkRDvb3aq2LI2/WDFn3Krz5S8NXOf0lOOtSx7tG+pOHxxKsAtTfHplnuj7aVFto+DDbuY+cVhB2OHEp2LltIpU/0rnthHDCQ8tMW8Hllc6m1Z023HqeECdznRSsKTXto+D1aXJaZNjO42E1dI3ZfbL7fZ1kGTntW2El8FbnN8uUCxWzxuCOchq7mfXaWtDU691u9hyF/mYaF4v9E/lP1RAe8TzNvZ7nmexaw+3en3HQ17bRTJcM9hbIx8BKjAawFX0wRs89dfB54d07YeVfjI5BV/8VWneJvF8URBOgtloPmLbSWmS4IrqOwNq9YBd3sfpTW1XUkYTUrKVpZY1ZBZHD3UBaU68Fb9ZT206MUjHar10nQbuyhVfokSpyq5a800yqaPpWmJXb6vzBCaLsBCIRlkakTC+nWWB2sRuzUR2snqNw9tOOH3h/xXf9/+KujBf5R+bd3Oj9NTvLu8d13YnETkBWaq1tx0FQSi1LcHkaNzVVsOgHsOVt+K9bjB7kKZq9zOqBsVsPDR9CMBeWcFeFXaDSDKvt7Tp3mZUvvJII38bKGjNztYSfO7T1b2c5RbJ8nFg7udkeU6HOzY6cxm13fLtsKycxjdBjh/++QYG9zeHYYdFYfWbljmRJJKM/S+g2dv/LWLLAohlA0nlWnuJF3wWs9/fhmcz5LM68h9+2mB15txRhWftFEg+n2zQbvCfh1e8bE81cPL9uIppGjF0rLdIDZlWJ2sVdrM4TTzA/GmvMybnDy2FmTTgNtNsx5/JBzFq0tl7Q2+NSddOv2mDXZ8EuJuGkQg8te3gs7nhVw7GtwLoid9q3wi6WEqslEc2QJWbXYfW/DGYwxpIFFg1Wz5EVRfoMrqyey4LMefy+5v/B12OMuYDSTMTms1LqJq31syGf3cBdWuu5SS1ZI6FgTSlzl6zn/pr5XOz+gju9N/Huu6dxyZ7i2lTS8EB4ujv5RcLJQ2uXN+/UAgDrSi2aYL5Z+aFOBOct3WKa2uvkQTfbxkmgPYidey5YxmAl6/Vr7nh1LYW7DtUOdxE+PEm7lh4uGdrNNJHihnG9bH+bSJZTaNmdjm1ldz+i7VuRqKSMaIcsMbsOq/+G3X8mUhaYWezG41b1YiChv5FVskxuoD45XOFFKaN7GcDx7B5smbKI01fOgJenw03vGf1J0ogT/8tkpdS3gZuA9sACjPhIs6dgTSmzXlvL9/gnF3u+4D7vDbzimwwV3tqJY6D+wxcp2GzXhyHSg5RKQbJzLzi1ACC6QDg4a0WbVSCh9yP4W7e1cCOFl8+M0EB7aAWf5anLyzcrx20Li2oFYtrwPAp3HapXNp/WtZ9Hnda+gZVyuMLLwpW7mT66Z+3wGcFK5MXPv+btdWWWqZx2MaPwoLjTsa3s7kc0wexEJmXYiYRTYbD6Xwb/D3bfRRu7MVsX7XNUj/6vwbNT4MWr4WefGFNZpwlHQ5kopaYDTwAngOu11suTXbB4SNRQJhMeWkaHI+t5PXMOy/zD+Yn3NuxzCuqwMlHNzPsHrzJao3YBzUhDTUQjLrEGD2PBqtxWwXwnQ5A7GVYDjNZ8qJssHCcBY6vOdsFYhtVUto9NH8a04Xm2Q5t0bZsVMQsqXGAA3C5F6xYZlFd6G4zNBM4qdKdjW4WWxemxzbC6Z1bPid3/wKrsdkOWhB/P7nkC+2cxuH9avQslhfDsBcZYWpc+Wru60Q1lopTqhzHh0+vAWcD3lFJrtNYVMZWwCbGnvJLfZb7MYVozyzsTp+IB1kEyq8yY4Huz7+wCd5F6nScyeGhFpIcpNDslOGhh+LnAeY9qpz7o8govj00fZpuFZdX3JXTgPNNj21g2oVPZ2g1tEsldMm/pFtPJvnz+ummGg8cP3qsHrxriaA6QaCzD0vJKZi1aC4qoYiTh12NGtEkZYG892PURCcWJ9ZTsLLC46DHKmDvo8ych/1roOSYtxXDiwnoT+IXW+l+BkXFvx0jvjRwNbOJc0noH47ybmOv9HkdpFdW+0QTJnPhd7Uxzp35fiC94aEY0ggRQVeMHond/hG5nCJLftDyhdM/NjupBD7+WeMavCt4vu/kx7CwQu86gVlR6jdkXb11YFLEfh93YVmbxKTMhiyalOVFJGVZlj2XIErv/RtoFwgnn/taYxfTf8+CGRWkpghMBGaO1PgrGTIHA75RSbya3WI2DOzv+h/172vKyb3JU+0UKkoXjxO9q1+qKJiAYT/DQjHgEyclDaiZQTohmfKhIQ8DHQvC+XTe2Z70YSJDrxvY0jYGAEXiNpTNoKJEsBLuKNhr3llORS1RSRqSyB79v9JV/ImjRypjpcPnjcOwbaN015UVwIiDVSqnbgW9h1H+fAE8mtVSNAb+fvPJCdvU6l5alOVSFtMqCmTKRsrCc9ih30j/DrtVlVdGYteLiCR6akWhBCsdpsDcn001uy8yofdJOBhSMdN6Kap9l2mow2yq849iLn3/Ni59/zf9NH9YgCys0SG4mME4JWiShWV+hWFW00bi3NMYQ9vUmUjLBrNLv3SG7we+SF1h/x6truXVhUcNJmmzKfldBce3xwvez+y6ceI4Ty75m64F66/p2asmX+ytqf6tgY7Sv6s6yFj7ueegBXvBNpVPrFvTpmBPhriUOJwLyAnAM+EPg8/XA34BrklWoRsGBLVB5iNNGTGHNTdZDR9gRSx+GSJ2qoul1btaKi+QjjjYukWhBCsep2FRU+9hwb/TdkpwKlBnZHjf3Xzmk9jhW9/S+aUNMrRCAWxcWWU40FTxGqMDkZLqprvFHJSrBc9tV8KFEM3oy1M8siyQiwWu6q6DY9Ddpmeli+Y5DUR87/Hih+wGW34UfM57jxLLvii8Psm3fCct9gutCt4E6T8aXujtHdEv6qj1oYN+xKlJJxCwspdRGrfXASOsaEwnJwprqgwWXwIw3oc/ERBYvKaQrCyvebJZIOM24cpK9ZUbv2W872i7euSPszhPtTIWxuNyindAq2eewyk6L9dh22W5gHs8yO2Y8x4ll30TwVdb1APQ++XLduhgnF0vGhFKrlVLjtNafB04wFoitdhaSRjR+30QGD4N9HULN7W+PrDuG3XdOOPfMTpat9/DtYsFpssO3R+Y5bsEnGyct+XCirbyC53AqsNGeI9ryRNo+lom8zL6L5zjJmkysMeNEQEYCnyqlgv/SXsAWpVQxRlx9aNJKl04yA37EEwfSW44kkGgL5PVVpfUeotdXlTLqtPYAlt85FZEPN+9P6HbhOH24X19VWnuedI8sEKt1EMs5oiGacxcaoUIAACAASURBVEQ7lEekY9tlu4G15ZDI48SybyI4oNvwns+x0ZBQnAjIhUkvRWOky2DIbAW7PoXBVyXssPFU3omo+BPdDyTRacHhOI2BxDo+kdUMguFUen2mvd0huXMzOJl73gnBwKzTc8aSWBDNOayy0/p1zmng73dybLtsN8D2u0QdJ5Z9ra7XKZ05TEd1lF26bkTwzq1bxHy8aIkoIFrrXakoSKPD7YFe4zix4V0mFk7mYGVdvwOnWVjRTLYD9pV3oir+RFf4yc7CcpoRlOVxMeGhZVFbB9EGjEOp9PqYs2RDvTGzgh0lw4XfSqj+b/owhs19zzQLK9KQLU757rheUbnfok0siJTVFCT8eZhwens+//JwvZZ5RbW/3nqnxw7PdjPbz0kWVjzHiXXfeLKwrnL/B4Cl/lEoSHkWlmUQXSm1WmttO6mUk23SQaKGMvni7ecYs/I2bqn+OUv8ExwfI9p+IHk2GUvB4LBVMNnJvqHYDQOBRfkUsNMiKJeoclkRa2s4mmB9ovuBeFyKedfk14qA2ai8867JB8zTdD1uxbyr8+MuU6TfwMpqjaYfiN1/I/xc0fQDcTLETGMcqDSl+LzwxFjI6QQ3LQUa11AmZyml1tmdC0jfKF4p4PZ1vXjG35NfZizmneqxeB3OAGw1YUwskwQ56Ykead9QEp12G09asJNKwCx9ubyimhPV9oISjassdODEePqEBPH6de255yzZ0EAgvH7NnCUbyGmRYZqO6/Vp24EBnRCpJ7qZdTNr0VrmvrnBsXiA85TsRE9QFslaPyXE5fM/waEdcMG9aSuCXY14poP943vSGjmlR6p42HUtf82cx28yXmJuzQzH+0YTMIu3J3qkfUNJdD8QJ0NHmI1m63TehuDn0HV9HGYGhVfAkSqW0GuJNBaW03NbjZlVXunliM14WsEyRmOBxDuboNevLafc9bhUvbGwgudz2ts/kWNhJXJcuFQNKppwDu2EDx+EAZdENZ12orGbUOrUjH2E0D03mw/Lh/NszUXclPEOX/jP5B3/WEf7RjMab7w90SPtG0q8g8iZESn1Nzj+FRjDld+5uJgWGQ2n/3RqNTitWLvnZkc1R7jZtdiNxhucs8Hq3E7KZzcW1qypA7htYZGpRRD8f5mNxuskFhSNdZOI0XgTORZWIsaFizemmFaBqTwMr1wL7ky4+JHUnNOC1MzH2kSZNXUAs15by0M11zHctY1HPU9y1NuS5X77gJ6dbzdSZ7RYe6JH+i6UePuBRPPwWD3QVm4iJxWbk8B3tsfNuWd2imqOcCvMRhOujW+8trbBvNcel6qtcNu19JiKTLuWHsvh2j1uxblndmLeUvO50a0sDav5ScwGV3QqwgrqxauiacWHksixsBIxLlw8ySTRTtNsti5msfGehFeuh0Nfwndfh7Y9YjtOghABsSF4k+e+uYEfVfwPL2U+wHOe+dzumkW7/IujHgsr0h8nUuWdyA6ATjCrHCC6VN9o/fhOWu5mYnrumZ0aCLOTbCKr8hWsKTWdkTDUmgr9f5hlYRWsKcXMQ+Nxq3rjXTmdkdBsYqhQzK7XyuJymn1mdz/sJomyaiQlYmKlRIwLF09M0Up85izZUG9GwtLySma9trbejIRWYhM61UBbixkJe2ZX83rHp+i8/zP49rONYoQMJ/OB3A4s1FqXpqA8jY56FXPFVHjhCp7YPx96dYdp33O+byPCSavRqnKI1vVk1Vo0m+zJqU/daav3toVFEY9lVkHaBdPDr9XqHptlX0HDwRLN9p/w0DJTIcjN9thmr0US6/CRkKGuAmub7eFEdU1UMQ6rivSlz7+2FC6z3yqW0Q9Cyx7LuHDxxBStfmezeFe4dQrmYhPaUAk9TlA88tjPM755tNtXxuoR9zNiyNWmZUg1TiyQ1sB7SqlDwEJgkdZ6b3KL1Uhp2R5mLIFFP4Alv4DdK+DieeBxPjhgKonHgkiU68mqtXjPZebTf0Zykdj1pQnfN5KbxqqCjGS5OLGqzLKvwKgQIlWWdhVUwZpSy/2duKVCj20W74nGErAqZzSuwlhjCXZiBJH/V/HEFKNNbjAj0lTLofyXaz3/5/kTWVQxw/trdm0ayPIr4jp9wnDSkXAuMFcpNRSYDnyslCrRWp+f9NI1RrLbGb7Hjx40JnIpWwtX/hm6pGd+LasHMF4LIlGup0gPdKRc//BrCG3d2pUfopsjPJRI1+7EzWaXfRUJuwrKLmbjxC0VXvZ4gsHRVKRmv2m0sQSn5XJi0cQTU7QSnyyPyzKpIhZaUM2sjIX8KOMddvi7cYP3N2zTPVAJ6q+UCKKJgewDvgEOAp2TU5wmgssN590FeaPgjZvhqYkw4VaYOAs8WXEf3spyiMaaiNeCSKTrKVZXnp1PPxyzCipSJVGwptQ0Y8muYowmdTVWZk0dwK0W7jc7cQtPQ7bL+IPogu5W5bQS6HDMRDeaWEIyho2JNaZo9b+ChpaLx63qxUDAmdgMU9t52PM0A1wlPF9zAQ/WXM9JjCFKopkOIdk4iYHcDHwH6AQsAn6std6Y7II1CQZcCL8ohKW/hf/Mhw3/gEvmw+n2vaxDBSI8AG/morGaj9rOmojXgojX9eSESK3faIc8McOsIjALkIdWUlYtebNhSqyuy6XAbMqOdi09Ea9l2vA80wA+gEsp+sx+27bjpdNU02iC7lblDB7H6aRpoUQTSwi3MtPdT8NOYGJp/AXpxGF+7VnI1e5/s1fnMqP613zsz6/9PjhbZWPBiQXSE7hVax05IhkFSik3xrDwpVrrS5VSfYC/Ax2AVcD3tNbVSqkWGJNajcSwfqZrrb9KZFniomV7uPJJGPodeOtW+NuV0HcSnD+Hgr2dLVuDQUIfFisXjdV81HbWRLwWRDyuJzNiiWVYXUOklnWkckQKkAcD1bFUUMHjm4lHMPvKCfdcNsi0nME+E6Xlldy6sIi5b26oF5QPJZLlF03Q3QqzczjNqoo2lhAsb7JcX4kgUmwmnGBZu2b7ma7f4Uf6dTJVDX/lCuZXXU6FqmsYhSdgNAYiTiiVtBMb2V2jgDYBAXkVWKy1/rtS6s/AWq31kwELaKjW+qdKqWuBK7XW0+2OnaixsKLGexIKnzNiI5WHeMc/jvneb7NDp/aGB90PdhM9pfIhM6u07cYFC1bgduMnxTqseqQJqpyO7RTt8d1K8bvv5Ef1O4eKrsumV3y0k3RFKmsoob9Holv9VvfXyr0TaVy43GxPPddX8HjB3ybdVosp1SeMOmP57+HEPhhwMUy5DzqcHtPhGtNYWElDKdUDuAS4H7hdKaWA8zCmywV4HpiDMff6FYH3AK8Bf1RKKZ0u5bPDkwXjb4bh3+W5eXcwXb/B1MwVvO8fyVM1l7Ja90/o6eysiURbEE6wekBjjWU4zaiJhkQEyO2wqpB9Wkdd7tDWrN3wLdGM+xVKNEF3u7Gzwvs/OSWaWEKolRmL6yv8mE76rCSVqmOw8hn49A9QcdDwWkxcAL0nJP/cCSRdHQn/D/gVRoowGG6rcq11TeBzCRC8i3nAbgCtdY1S6khg+3ozPSmlZgIzAXr16pXUwkckqw3/78Q0nuBcZmQs5XvufzG1RSGr/P14uuZS3vePxI/Lcvfw1rnVOESR4hHJ7IcSjUsqnlhGPNdgJmjJDpBHmlQoViK5e2IZeDGaoHuksbNiDXRHE0uI5Nq0wm6Ik/A+K7NeW8ucJRs4UhmbKEbkwDb44mkoegWqj8Hpk+GcX0MvZ0MkNTZSLiBKqUuBfVrrVUqpSYk6rtb6aeBpMFxYiTpurBh/cni05js8WXM533F/zI/c/+SpzMco1R14tWYSr/omUUaHevtZuWggtdaEHdGm1yYjlmFXNruxr8yGzgDnAfJI507WtKaRrAWN4ZKKxQpwEph2IlCxWkKRyhVOtGm0dkOcNIg3+nStJRNupYQOsOkkS60Wvw+2vWcIx45l4PIYk9SN/QnkjYy8fyMmHRbIBOBypdTFQBbQBngcyFVKZQSskB5AsOd7KUYgv0QplYExhPzB1Bc7OkL/5JVk8bxvKi/6zucC1yqud3/AbZ7XuSVjMZ+qYSxW5/NW5RA657aOOIZVqjGrVKJ1ST02fVjCYxlWZY009tWHm/fz4FVDEu4LD57birw4XWPB8oUOexJOvOmudpW201b/nvLKpMcaYnF9WQ1xEolwKyU0iSGY8hykwQRS+zbB2ldg3atwrAxad4Nz74KRM6BV8+gJkbYgOkDAAvmfQBB9EfB6SBB9ndb6T0qpnwNDQoLoV2mtv2N33LQF0cOwag23a+nh4fPaMqXqPVjzIhz/BrLbw8ArYPC34bT/MvqapIHQhz+3pYfjJ2sa5LBHGj8plGDgMxUBzGiDwqk6d6xBbisiTYAVS8DeyTmdjJ1lFpfzuBStsjJijpVEW04nHWvBOpEjHtpzlHtP38yl/o+grAiUG/pdAMOuNwLk7shp3PFwSgTRLfg18Hel1H3AGuDZwPpngb8ppbYDh4Br01S+qInsvx8Lk+6E7e9D8SJYtxBW/dVoqQy6EgZdZZi4Lut4SbyE90kJHQ/JzB1Q6fXFNFR9suIxoeV3UhkkqxOWnXAlUjyg7re0mjnQp3XCO96Ft/qtxs7SuuFItomIlURTTrs02kh9VmKhM4eZ6l7JRa4vGOvahLtUQ9ehMPVBGHINtOoU1/EbM2m1QJJFY7FAoqb6BGx5B9YvNkTFVw2tukD/C43WS99z4h53K5KF4ZRwSyQZLqlIRDuDYKItgVBOv/OflsHzHQ9enPDzgTOLKypffZSYtfat5i8Jx60Ufq3Tnk4b6XmwslJ6qb1McRVykfsLRrq2AbDNn8c7/tG87RvH0gd/lpoLCONUtkCEzBwYcrWxVJbD1nfrBGX185CRDaefawjK6edBbs+Ih7Ryo4H1ZEiRyAuJhaQjpz6aOcydjH2VCJIVPLfDSRpuMlv8Zq19p/clNJYQbzpwPIRfg1V2ofZWMM61kUmutZzjWksflzGe7Hp/b+Z5v8O7/tG1/b3izbhrSoiANFaycyH/WmOpqYZdnxhisuUd2PJPY5sOZxj5430nQe+zjX0C3FVQ3CAzKhFVWWg/k1S2Gu2E0AwFKauMCtaU2naMTBbB67rj1bW2QlXp9XHHq2vr7ZMsnM4zEkoqXVyRqP1f+/2wdz189W/+u+vb5O7/ghZ4qdSZfOofxALvhXzgH06JbhgMv25s5IZdc0EEpCmQkWlYHKefBxc9YmR3fPmRsRS9YnRIUi7oPhx6n80Le7qzZFMumlZxn9rjVuRkZiQvL94BkbKrwgntzZ4K5izZYFomBUkftyh4LyJV2smIi9iVxy5WEolKr49bFxYxb+mW1P3fagXjE2PZtRxOlgPQpWN/GDcTzphM9mkTmOzJ4tiaUv61dAuEWFsNsrBOAURAmhpKQZeBxjL+ZsM6KS00xGTHh/DZH/m+v4bvZ8Fmf08K/f1Z6R9AoX8ApUQO5qUyYyYS0biqgqRitNxQCtaUWqbValLTig7vEGhFqiwRO7eQ3ZAs4YSmysbU/8KOqmNQuhpKVhrL15/XCgbt+sBZlxlWfe8JptPGptoCb6xIED2MtAbRE0F1BdfOeYJRagujXVsY4dpGa2VUKnt1Luv8p7PW35d1ui/r/H054W6TdgsjnII1pbb9HaxIdpzDDLtAdqotIXCWWJDMZIJIRJv4YEVUAwv6fUYP8NJVUPIFlBTCvo2gA9MTd+wPPcdA74mWgtFUkCC6EB+ZLVmpB/G5fyD4wIWfM9XXjHJtYZhrB/lqBxd4VtVufqJlT3L6jDbcX10HQ5fk5qlHIpYKJp0Vol2LPx3DbjuJiwTn3EhXjAHic3GBkQBy68IiFhV+zUs/Dqksa6oMF+8364zJ3srWGa4pb4XxfYu20GMknHkp9BhtvM9ul6jLO+UQAWmGXDe2Jy9+/jUAflxs1L3Z6OvN33yGW6V/Wz93j6zmWy2/Jidoxm9YXHeAnM7GDItdBkHXIcZrx/6Q0SIp5Y3FVZWq7KqI5VB181aH4lLpCQKDs7hIeaWXYXPfi3v4lliwcnFFd//95KmDZO5cw9KnCpjaqRz2bYB9m8EfsFwzW0O3oTBiBnTLNxpJHfsntV/VqYYISDMkGMR7ZcVufFo7C+6dOGg8gN+sh70bjFbbF38BX5XxvXJDu97GA9ixH3QaUPc+jhacWbZYJNItGkEK1pSaigeYTyaVSpxYIuWVXm5bWEThrkNpDfwGBcXM+syghp5qP31UGX1VGf1VCf1dJfRTJeSowH+zDDjeHTqfCf91vtGJr1u+EcsQsUgqIiDNlPumDYmuUsjpAH0mGksQXw0c2gHfFMP+LXBgq7Hs+MDo5Fi7b2cjpbh9H+OhDX3Nbmc000244S+fsXzHIcdFTKeryozf/iN5Y18lguDvZDU9LhhWXNBaTZuI+LxwpIRpbXbSZ/h6tmxYQ8fqEvqoMnqq/WQof+2m+3Vbtvp78Kp/Elt1D7b6e7BN92DdHNvRjYQkIQIiWOPOMCyNTmG+fL8PDn9lBCYPbIUDW+DgDmOk0WNl9bdt0cawXNr3gbY9jQBl2x78ac1JNu/wYoylGbnjVWObja1gTSknqq3jNI1l2tFpw62nxw0lqSLiPWn8L47shvKv65bDu4zXY3tqA9r5QL4nB/L6UuIazot7W7GusiM76cZOf1fKa2eAqONU6rjX2BABEaLH5TZmTOtwujEvfCjVFVC+Cw7thMM76173boCt70GN4ee+Gbg5C6q0hz26PXt0R76hHft1O/bp3NrloGrHrVeezWWjEzsZV7zMfXOD7feNRejAenrccF78/GtGndbeedl9NcZkSCf2GwOCHt0DR8sMQQh9XxE2eLZyQZs8yO0Ffc42XnN7Qe5phiXbuisoRQ/gxpDdrCzWU6njXmNDBERILJktofNZxhKO1lBxCI7s5sd/fIPu6iDd1QG6q4PkqQOMVZvpzGEyVVhF9zbwfitjXLCcTpDT0ZiLvmWHwNIx5H17w23Wok1S/d92Lfrc7PRmsoUTFAR7S0TTkir++I8PmdZ1KFQerluCInFiPxzfBycOGNOvVhzCtFtnTidjQNC2edBzNLTuDm26GRZobi9DPDIyo76Ol348nrsKiqOL7QlJRQRESB1KGbGWnA4s03vwmUaaNbkcZ3CbSn42shUTutQYrdtje43XEwcMq6ZkpVGx+WtMjgGgDBHJagtZwdeQpUVr8LSEzFaG6GXmgCfHeM0MrPe0NDLPMlqAu4UxFLdSFKwptTinwZzLB8X9U0XE74eak8birTDcRN6KwOdKY6k+bnSYqzrGtKpjTBtznFVbd1G2/wCtqaSVqqQNFeSq47TleJ1wP2VyvszWxqiyOZ0Ny/O08QExDyytukCb7ob1kKRsPYghtickFREQIS2EphqHMuH0Drz040udHURrqDpqCEnFIUNcKg7AySMhy9G69+W7oWp93fpYRgdzt+B8n5uVLTKoxkO1zqCGDHy48OPCh2LIyvawym1krrnchsvG5Q7k++q6vN96nwOv2mckKPhqjHRUn9cQSV91/fc1J6MsuILMVoxs0Zp9LTPZU+nmuM7iG9pxxN+KclpRrnMopxWPfPccw4rLbgdZuYZVF+co0ELzRARESAsxpRqHo1SdRdG+b3QF0NqohKsrjJZ69QmjBV99PLDuBHhPGEPF1Jw00plrqsFXxaKPN5NJDZl4yVQ1ZFCDG40bPy78RoXr9xli4PcblX5NVSAbTTV8DbralAJXhjHlqdtjvHd76j6HvvdkG0tGdsj7LMNq8mQZ61u0hhatAtZWTu15OgNjZr9t/pMCj5yV+Am3hOaJCIiQNtLqjlCqruLN6RB5+xCeWWU9fElutoei705JRAmTynfH9TK1AG8Y1ysNpRGaKtLLRhCiZNbUAXjcDVNHXaQo/pEA7ps2hO+O61WbAutWiu+O6yXxBSEqxAIRhCgxy2rKzfakZViQeJCAtBAvIiBCo8fr9VJSUsLJk9EGjpPHgCx4+Zrw/gdH2bTpaFrKkw6ysrLo0aMHHk/jSlsWUocIiNDoKSkpoXXr1vTu3RslvY4bBVprDh48SElJCX369El3cYQ0ITEQodFz8uRJOnToIOLRiFBK0aFDh0ZlFQqpRwREaBKIeDQ+5J4IIiCCIAhCTIiACEKUzJkzh/nz59tuU1BQwMaNG2M6fnl5OX/6059i2lcQUokIiCAkgVQLSE2N1Zhg9vh88c1NLpzaiIAIggPuv/9++vfvz7e+9S22bNlSu37Hjh1ceOGFjBw5krPPPpvNmzfz6aefsmTJEmbNmsWwYcPYsWOH6XYAe/fu5corryQ/P5/8/Hw+/fRTZs+ezY4dOxg2bBizZs1Ca82sWbMYPHgwQ4YMYeHChQB89NFHnH322Vx++eUMHDiwQZl/9rOfMWrUKAYNGsQ999xTu7537978+te/ZsSIESxatIj33nuP8ePHM2LECK655hqOHz8OwL333svo0aMZPHgwM2fORFtNvyicskgar9CkmPvmBjbuSWxfi4Hd23DPZdY9yFetWsXf//53ioqKqKmpYcSIEYwcORKAmTNn8uc//5l+/fqxYsUKbr75ZpYtW8bll1/OpZdeytVXXw3A5MmTTbe75ZZbOOecc/jHP/6Bz+fj+PHjPPTQQ6xfv56iImMmwddff52ioiLWrl3LgQMHGD16NBMnGjNHrl69mvXr15um0t5///20b98en8/H5MmTWbduHUOHDgWgQ4cOrF69mgMHDnDVVVfxr3/9i5ycHB5++GEeffRR7r77bn7xi19w9913A/C9732Pt956i8suuyxxP7zQ5BEBEYQI/Oc//+HKK6+kZcuWAFx++eUAHD9+nE8//ZRrrrmmdtuqqqoG+9ttt2zZMl544QUA3G43bdu25fDhw/X2/+STT7juuutwu9106dKFc845h5UrV9KmTRvGjBlj2Q/j1Vdf5emnn6ampoaysjI2btxYKyDTp08H4PPPP2fjxo1MmDABgOrqasaPHw/Ahx9+yCOPPEJFRQWHDh1i0KBBIiBCPURAhCaFnaWQavx+P7m5ubWWQrzbxUJOTo7p+p07dzJ//nxWrlxJu3btuPHGG+v12Qjup7Xmggsu4JVXXqm3/8mTJ7n55pspLCykZ8+ezJkzR/p8CA2QGIggRGDixIkUFBRQWVnJsWPHePPNNwFo06YNffr0YdGiRYBRGa9duxaA1q1bc+zYsYjbTZ48mSeffBIwAtpHjhypty/A2WefzcKFC/H5fOzfv59///vfjBkzxrbMR48eJScnh7Zt27J3717eeecd0+3GjRvH8uXL2b59OwAnTpxg69attWLRsWNHjh8/zmuvvRb9Dyc0e0RABCECI0aMYPr06eTn53PRRRcxevTo2u9eeuklnn32WfLz8xk0aBBvvPEGANdeey3z5s1j+PDh7Nixw3K7xx9/nA8//JAhQ4YwcuRINm7cSIcOHZgwYQKDBw9m1qxZXHnllQwdOpT8/HzOO+88HnnkEbp27Wpb5vz8fIYPH86ZZ57J9ddfX+uiCqdTp04sWLCA6667jqFDhzJ+/Hg2b95Mbm4uP/7xjxk8eDBTp06td82CEESlOrNCKdUTeAHogjEl3NNa68eVUu2BhUBv4CvgO1rrw8ro7vo4cDFQAdyotV5td45Ro0bpwsLCmMo3/anPAFj4k/Ex7S8knk2bNnHWWSZzrAtpR+5N4yLe+ksptUprPcrp9umwQGqAO7TWA4FxwM+VUgOB2cAHWut+wAeBzwAXAf0Cy0zgydQXWRAEQQgn5QKitS4LWhBa62PAJiAPuAJ4PrDZ88C0wPsrgBe0wedArlKqW4qLLQiCIISR1hiIUqo3MBxYAXTRWpcFvvoGw8UFhrjsDtmtJLAu/FgzlVKFSqnC/fv3J63MgiAIgkHaBEQp1Qp4HbhVa12vZ5g2AjNRBWe01k9rrUdprUd16tQpgSUVBEEQzEiLgCilPBji8ZLWenFg9d6gayrwui+wvhQInfqtR2CdIAiCkEZSLiCBrKpngU1a60dDvloCzAi8nwG8EbL++8pgHHAkxNUlCIIgpIl09ESfAHwPKFZKBbvm/gZ4CHhVKXUTsAv4TuC7f2Kk8G7HSOP9QWqLKwiCIJiRcgHRWn8CWE1lNtlkew38PKmFEoQkUFxczAUXXMD777/PkCFD0l0cQUg40hNdEJLEAw88wKeffsoDDzyQ7qIIQlKQwRQFwSEZGRn07du3dlTeq666qna4czOCAxSGD1QoCM0FERBBcMjDDz/M8uXLef311zFyQeLno48+YsGCBSxYsCAhxxOEVCIuLEFwyB133EF2djb33XdfxG3Hjx/Pzp07ASgtLa2dgCoWJk2aVDuD4cGDBxk8eHDMxxKERCICIghR8Mwzz/C3v/2N//znP5bb+P1+du3aRe/evQHqzQQYC9u3b6d///61x5KAvNBYEBeW0LR4ZzZ8U5zYY3YdAhc95GjTTZs24fP5yM/Pt9xmx44d9OnTp9bNZVbpjx07lqqqKo4fP86hQ4cYNmwYYLjJpk6dWrvdrl27yMvLw+Vy1R4rHjEShEQiAiIIDqmqquLGG2/kySefpE2bNrXr//rXv7J69Wq01uTk5DB27Nh6glFYWMjMmTPrHWvFihVA5BjI2rVr6wnGqlWraqejDT/vww8/nKhLFQRHiIAITQuHlkIyuPvuuxk3bhxTpkypXffZZ59RXFzMH/7wB8CYU/yFF14gNzcXMCyWt99+mz/+8Y8xnbOoqKh2dsBt27bxxhtvcN9995meVxBSjQiIIDhk/vz5nHHGGbXupokTJ1JVVcVvf/vb2m0yMzOZOnUqf/zjH9m9ezcDBgygQ4cOdOnSxeqwtqxdu5asrCzy8/MZOnQoAwcO5Pnnn6ekpKTBeQUh1YiACIJDfD5fg3UzZswgIyOj3jY9Eqpe3wAADNpJREFUe/akqKiodp1dX5FJkyYxadIky+/XrVvH6tWrad26dcTzut1uJ5chCAlDBEQQ4uBXv/oVd9xxB506deLYsWM89thjte6reDl27BhKqQbikezzCoJTREAEIQ4GDRqUtJ7mrVu3ZuvWrSk/ryA4RfqBCIIgCDEhAiIIgiDEhAiIIAiCEBMiIIIgCEJMiIAIgiAIMSECIgiCIMSECIggCIIQEyIggiAIQkyIgAiCIAgxIQIiCI2A4uJiunbtSnFxguc6EYQkIgIiCI2ABx54gE8//ZQHHngg3UURBMeIgAiCQ5566im6du3KsGHD6Nu3b+0kUJWVlZxzzjn4fD4yMjLo378/w4YNY9iwYdx7772Ojv3KK6/Qt2/flI5vVV1dzcSJE6mpqUnZOYXmhQiIIDikuLiYOXPmUFRUxGuvvcYdd9wBwHPPPcdVV12F2+3m4YcfZvDgwaxZs4aioiLbodyj5aOPPuLGG29M2PEyMzOZPHkyCxcuTNgxhVMLERCh2VGwppQJDy2jz+y3mfDQMgrWlCbkuOvWrePMM88EoEePHrXzg7z00ktcccUVANxxxx1kZ2dz3333OT7uueeey/vvvw/AXXfdxX//93/HVL5JkyaxefNmAA4ePMjgwYMj7jNt2jReeumlmM4nCDKcu9CsKFhTyp2Li6n0GpV7aXkldy42AtPThufFdezi4mLOOusstNb8/ve/59JLL6W6upovv/yS3r171273zDPPkJ+fz6RJkzj77LMjHnfu3Lncfffd7Nu3jzVr1rBkyZKYyrd9+3b69+8PGGIXOi+7FYMHD2blypUxnU8QRECEZsW8pVtqxSNIpdfHvKVb4hKQ3bt3c/z4caZOnYrH42HMmDE88cQTHDhwoMFETps2bcLn85Gfn+/o2BMnTkRrzaOPPspHH33UYGbBsWPHUlVVxfHjxzl06FDtlLoPP/wwU6dOBWDXrl3k5eXhchlOhXXr1jF06NCI53a73WRmZnLs2DHTiasEwQ4REKFZsae8Mqr1TikuLmby5Mm8++679db7/X5OnjxZ+7mqqoobb7yRJ598kjZt2tTb9vnnn+eTTz4hMzOT3Nxc7r///tpjl5WV0aFDB9NKfMWKFYARA1mwYEFt8D6UtWvX1hOMVatWMX369IjnDpY5Kysril9DEAwkBiI0K7rnZke13inr1q0ztSjatWuHz+erFZG7776bcePGMWXKlHrbLV++nI0bN/KXv/yFJ554goMHD7JlyxbKysq44YYbeOONN2jVqlUDgXJKUVFRbRm2bdvGG2+8UevCsjo3GLGSjh074vF4YjqvcGojAiI0K2ZNHUC2p74LKNvjZtbUAXEdt7i42NIlNGXKFD755BMA5s+fz8cff1ybxnvLLbcA8OyzzzYIjp88eZKrrrqK3/3ud5x11ln87//+L3Pnzo2pfGvXrsXv95Ofn8+9997LwIEDef755y3PHXR1ffjhh1xyySUxnVMQxIUlNCuCcY55S7ewp7yS7rnZzJo6IO4Aul2m0s9//nMee+wxzj///NrMrHC8Xi9KKQB27txJWVkZ+fn5fPbZZ7XbTJw4sd7ncCZNmsSkSZNMv1u3bh2rV682dYGZnbtfv34AvPzyyzz00EOW5xQEO5qMgCilLgQeB9zAM1pr+dcLpkwbnhe3YETDiBEjOPfcc/H5fA0C4EFmz57NrFmzaNOmDdXV1fzlL39J2PmPHTuGUsoyCG517urqaqZNm1abuSUI0dIkXFhKKTfwBHARMBC4Tik1ML2lEoQ6fvjDH1qKB8CgQYN4+eWX+elPf0qrVq3o3Llzws7dunVrtm7dGvW5MzMz+f73v5+wcginHkprne4yREQpNR6Yo7WeGvh8J4DW+kGz7UeNGqULCwtjOlfv2W8DMLZP+5j2FxLPz4dnk9fnjHQXQzChdOd2nlgTX4abkDg2lh1lYLc2LPzJ+Jj2V0qt0lqPcrp9k7BAgDxgd8jnksC6WpRSM5VShUqpwv3796e0cIIgCI2Bgd3acMWw1Llvm0wMJBJa66eBp8GwQGI9zlcPSUZKY2PTpk2c3qlVuoshmFB9oAULfzIs3cUQ0kRTsUBKgZ4hn3sE1gmCIAhpoqkIyEqgn1Kqj1IqE7gWiG3AIKFJ0hRidacack+EJiEgWusa4BfAUmAT8KrWekN6SyWkiqysLA4ePCgVViNCa83BgwdlCJRTnCYTA9Fa/xP4Z7rLIaSeHj16UFJSgiRHNC6ysrLo0aNHuoshpJEmIyDCqYvH46FPnz7pLoYgCGE0CReWIAiC0PgQAREEQRBiQgREEARBiIkmMZRJtCil9gO74jhER+BAgorTlJDrPvU4Va9drtuc07TWnZwerFkKSLwopQqjGQ+muSDXfepxql67XHdiEBeWIAiCEBMiIIIgCEJMiICY83S6C5Am5LpPPU7Va5frTgASAxEEQRBiQiwQQRAEISZEQARBEISYEAEJQSl1oVJqi1Jqu1JqdrrLk0iUUj2VUh8qpTYqpTYopX4ZWN9eKfW+Umpb4LVdYL1SSv0+8FusU0qNSO8VxIdSyq2UWqOUeivwuY9SakXg+hYGpglAKdUi8Hl74Pve6Sx3vCilcpVSrymlNiulNimlxp8K91wpdVvgf75eKfWKUiqrud5zpdRzSql9Sqn1IeuivsdKqRmB7bcppWY4ObcISACllBt4ArgIGAhcp5QamN5SJZQa4A6t9UBgHPDzwPXNBj7QWvcDPgh8BuN36BdYZgJPpr7ICeWXGFMBBHkYeExrfQZwGLgpsP4m4HBg/WOB7ZoyjwPvaq3PBPIxfoNmfc+VUnnALcAorfVgwI0xh1BzvecLgAvD1kV1j5VS7YF7gLHAGOCeoOjYorWWxUgkGA8sDfl8J3BnusuVxOt9A7gA2AJ0C6zrBmwJvH8KuC5k+9rtmtqCMYPlB8B5wFuAwuiNmxF+7zHmnBkfeJ8R2E6l+xpivO62wM7w8jf3ew7kAbuB9oF7+BYwtTnfc6A3sD7WewxcBzwVsr7edlaLWCB1BP90QUoC65odARN9OLAC6KK1Lgt89Q3QJfC+Of0e/wf8CvAHPncAyrUxURnUv7ba6w58fySwfVOkD7Af+GvAffeMUiqHZn7PtdalwHzga6AM4x6u4tS450Givccx3XsRkFMMpVQr4HXgVq310dDvtNH0aFZ53UqpS4F9WutV6S5LGsgARgBPaq2HAyeoc2UAzfaetwOuwBDQ7kAODV08pwzJvMciIHWUAj1DPvcIrGs2KKU8GOLxktZ6cWD1XqVUt8D33YB9gfXN5feYAFyulPoK+DuGG+txIFcpFZxQLfTaaq878H1b4GAqC5xASoASrfWKwOfXMASlud/z84GdWuv9WmsvsBjjf3Aq3PMg0d7jmO69CEgdK4F+gUyNTIyg25I0lylhKKUU8CywSWv9aMhXS4BgxsUMjNhIcP33A1kb44AjISZxk0FrfafWuofWujfGPV2mtb4B+BC4OrBZ+HUHf4+rA9s3yRa61vobYLdSakBg1WRgI838nmO4rsYppVoG/vfB62729zyEaO/xUmCKUqpdwIKbElhnT7qDP41pAS4GtgI7gN+muzwJvrZvYZix64CiwHIxhq/3A2Ab8C+gfWB7hZGVtgMoxshoSft1xPkbTALeCrzvC3wBbAcWAS0C67MCn7cHvu+b7nLHec3DgMLAfS8A2p0K9xyYC2wG1gN/A1o013sOvIIR6/FiWJ03xXKPgR8GfoPtwA+cnFuGMhEEQRBiQlxYgiAIQkyIgAiCIAgxIQIiCIIgxIQIiCAIghATIiCCIAhCTIiACEISUUotUErtVEr9NMb9pwdGTn0r0WUThHgRARGE5DNLa/3nWHbUWi8EfpTg8ghCQhABEYQYUEr1Dpt/4X+UUnMc7LdAKfVnpVShUmprYKyu4PwVzwXeDwnMY9EyaRcgCAlABEQQUk9vjDkX/n97d5CSVRSGcfz/SJAjHQhtIIVW0QZ0EtQ8bFDrqB0ISbPmrUEQAxdhQYPCQU0iiAgKHwe3IB2o31H7HPx/o3vhvod3cnk4F85714FXSRaZ5nOtJnkAvAaetv0xvxal8xkg0v/3pu1R2/fAB+Be2yPgMdPYjb22+/NsULoIA0Qa85uT78/iDLWn5wf9vV8DvjONIJduPANEGvMZuJNkJcltYGOG2kdJFpLcZRrwd5BkGdgC7gMrSR6euYJ0A9w6/xFJp7X9leQ50/TWQ6bJrxf18U/dEvCs7c8k28DLtu+SPAF2k7xt++XMlaQ5MkCkQW23mHYNs9ppe+JcSNvNf64/AauXbE+6dn7Ckq7XN+DFZQ4SAtvA1yvtSroC/g9EkjTEHYgkaYgBIkkaYoBIkoYYIJKkIQaIJGnIMZsn2pnon2LnAAAAAElFTkSuQmCC\n"
},
"metadata": {
"needs_background": "light"
}
}
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.13"
},
"colab": {
"name": "quadric_projection.ipynb",
"provenance": [],
"collapsed_sections": [
"xUbUC6wcAS9_"
]
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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