affine.ipynb

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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import numpy as np \n",
    "import matplotlib.pyplot as plt \n",
    "\n",
    "plt.axis([-10, 10, -10, 10])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[[0 0 2 2 1]\n [0 2 0 2 3]\n [1 1 1 1 1]]\n"
    },
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# Θα θεωρήσω ένα μικρό αριθμό από σημεία.\n",
    "# N = 5, και θα τα τοποθετήσω σε έναν πίνακα 3xN : Κάθε στήλη αντιστοιχεί σε ένα σημείο.\n",
    "X = np.array([  [0, 0, 2, 2, 1],\n",
    "                [0, 2, 0, 2, 3],\n",
    "                [1, 1, 1, 1, 1] ])\n",
    "print(X)\n",
    "plt.scatter(X[0,:], X[1,:])\n",
    "plt.axis([-10, 10, -10, 10])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[[3.  3.  4.  4.  3.5]\n [2.  3.  2.  3.  3.5]\n [1.  1.  1.  1.  1. ]]\n"
    },
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "T = np.array([ [0.5, 0,   3],\n",
    "               [0,   0.5, 2],\n",
    "               [0,   0,   1] ])\n",
    "Xout = T @ X  # @ = πολλαπλασιασμός πινάκων\n",
    "print(Xout)\n",
    "plt.scatter(X[0,:], X[1,:])\n",
    "plt.scatter(Xout[0,:], Xout[1,:], c='r')\n",
    "plt.axis([-10, 10, -10, 10])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "points_input = np.zeros([3, 100])\n",
    "points_input[2, :] = 1\n",
    "for i in range(10):\n",
    "    for j in range(10):\n",
    "        pos = i*10 + j\n",
    "        points_input[0, pos] = i\n",
    "        points_input[1, pos] = j\n",
    "plt.scatter(points_input[0, :], points_input[1, :])\n",
    "plt.axis([-12, 12, -12, 12])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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ZNwb5DFGtxqRUckk3jVZk0iU4evq8aLZ0YVCrN2n9HYpQWQV5AG8D6AXwhtOGKAb54vkdzLz+kvczoGgYHHe+3q/++OFX1KPPdao/fvgVtfP1/sJ1l3AUka5vwcYXPqmvQB9nlvn2n29W5y+qdNVuy7pcKKpPfKhP93JpOgX5sC68NimlrlJK1YdUXzzoeHETAOrq3F+oNXy45+gdd2L/d3/oOfHn7Gzrib7sHk+zTcRZ1Gg7oim3zB27dyQXGcmqOH9Ekx/JQiiynM5JTUyGIn/oPH58+nT3wdHw4Z4TPxrBPXufznrMTWLMls+vy5su+OzEKdjy+XX2hdrb8YfXfQ59f30D9j92m+sEpdzkHbfDPeOSZBSXcrqS5C/9ACsQ+Q2ADwAoAD9WSj2e8/x6AOsBoKamZmlHR0eg25NpeHgYU6dODa2+LL29wLlz+Y9PngwsWeLtvQYHkzuJsbFPHquoSAZnu8nGBgeBRCK5DZMnJ3+9p17rqV8OH7Z/bulSlw3I2S4vbXFoh2cObemd/WnUVALvZfxAXlJ3qf3rE6dRPfIhZg//OyZdGMX5CRNxcurvYajyEutyFu0eE0Fi2qzxeezt6utNnM66//un3sakC6P5L8z5bOWWy1SobWle+6TU+nQulyns2NLU1HTY7kxJGEG+TimVEJFZAF4C8F+VUvusXltfX68OHToU6PZk6unpQWNjY2j1ZamoSP6CzyWSHeDcam93P0QyfRSR+au1qmr817qnflmwwHqI5Pz5yV/OxXDblgLt8MymLf3TZmLZXU/hm0tG8b3e5KjjuupKHNh0ne1bNbTtHT+dkcm2XIG6nerLrWtVXzfadm/PXuHJol88b6NFuUD7JGblMoUdW0TENsgHfrpGKZVI/TsAYCeAa4KuMxY0Oy2hVRaqRitLjV5UiR9c95Wsx8YTYxza4TmhxiETtVAiTm5dXYub8MCNX8fZOXWOp9vikmQUl3K6CjTIi8jFInJJ+m8AfwrgzSDrjA1moZZ+LSKElaUm7ngCyx64O38VpKM9ju3wvLqQzc59oHpmwVWJrOpa9sDdqDrR77ij9GPlJBRZTucVnrgylLfhk58C8C+pWx+AFqfXl90QSk3HjwfaL34OkQx5NaasfgkiQcnL/29I4+ALifw7pCmdhlAGGuS93souyHsR4vhxy37RMQs15CShrH7xewlGL9vmc/JbKWL1HQqRTkGec9fEhd+nWIDiL9TqMpdNSO3oPJLA1j3HsGbeh2hp25ucx8RFO9LlXM9/kprPZrxc7whq0/VllrO5FnGy+Rv4o95qT3OteN7GnHJZfRJCfbqX0xHHyccFL9RaX4sIuB12iT8H79zg2A6rhJr93/1hckUph2sqrhJxbHbss4ZOhZ4shCLL6ZzUxGQoika5LhQd8YVau8SYeyYscmxHbrlVfd347guPJleUcmiHq0ScAtMFW5bx0DaWMysZikE+LrwER7+nGjDlKKKIdtQf2IX9j92GXz/yBfz+qbfHs1BPDI04tiN3FaH79j2bPW7dph2uViWy2OGfnTgFW65dZ1+m0HuyXMnldMUgHycajR+P5VFEEe1o27N9fF3XSRdGx9dD9bq6kNupBlytSpSzwz9ZPQubVjaja3GTq/fyVBfLuS6nKwZ5E4UwfjyWRxFeTxW1tOStyFQ1+jE2vvoTzwk1bleWcp2Ik7HDf23v63jpquWFyxTYRpYrrZyuGORN5PfpFcCcowgvp4pss1BPeU6o2bHyDoxelPNL0KIdmeVu6uvGaz/+Ko623oDVNzfY7iijTBZCyPXpXE5bdmMro7hxnLxPShw/3v3oo3qMg7fYtlDHj+fkJowvphLGikwajYV3Yux3qEQ6jZOPPLBn3hjkfVRCQOnetk2b1Zgirdtrv+i6eEqAjP4OlUCnIM/TNaYyZRy8FwFdizg7pw5jEJyfMBEP3nh3cgGPXDYLjjz4pW9h4aYX0dC21/U4684jCYy9460tnUcSaGjbW1RdpZTrTZwOtT7dy+mIGa/EbFoHnYsasfn2HRg5fwHfnDmKpxd+GpXP9wJAwSzUiR+N4I7dO/D0XQ3jCTV55XLrSyXi1E+bgblnTrlqS7pMemy317pKKjcv5Po0Lqcr/pInc8bBB3AU4ToxxmGqYMdyOdL1bbk2f2Upu7bEJVnI9HK6YpAnc06xBJBN6zoxxkUWqtP75T7ftbgJm1Y2o3/aTIxB0D9tpm1b4pIsZHo5XTHIU35wnDw5vKkGND+KcJ0Y4zILNaucxY4y8/muxU1YdtdT+NTGf8SXNnfYtiUuyUKml9MVgzwlZQbHJUtifYrFNRdHEZ6SkzJ2lGfn1OGBG7+elYWaVc5mR/mDC0c9J+LEJVnI9HK64oVX8q6MLtSmL7Qlz8d+iDqnaWdTUwUDQBWAZUcS+IXddLU2O8qrn9iGh3ce8DTNbeY2epka149yBftEk+0Mo5y27MZWRnHjOHk9FOyXYsZw+zWGPMTFU3J1d3fruXhKhPgdssZx8hRvxUw1oOO6rl4v1A4O6nstgsgGT9eQd15PsTidw496LHzGKRY76VWCHrzouKd2OK4u1NqafdoJGN9RFrMqUVQrJ3FlKP3xlzwVx4eJvkKZLhgo6UJt5ipBky6MWr/Ioh0FVxeyOYroXNToeVWiKFdOQsj16VxOVwzyFLwopwsu8VRRZmLM+Qk2B74W7XCVUGOxoywmEScuyUKml9MVgzwFL8rpgksc7pmZAHNy6u+5zkJNl1vV1z2+stT+x25D/YFdrutz83ixZVjO/3K6YpCn4EW56EiJp4oyE2CGKi/JykJ1akdtdSVW9XWjbfcnK0vNPXMKbXu2O7almEScuCQLmV5OVwzyFI6oFh0p8VRRbmJM1+ImXP/1Z9H1+nHHdty74kpsfPUneeu6Vp7/2LEtxSTixCVZyPRyumKQJ734PV1wiaeKVh/tKXoVpFqrWSQBx7YUsyoRV4bSo5y27AbQR3FjMpQeIu2XIBbL8GllKc/9EpOFP0rB75A1JkMR2QliiGRc1qclCgCToUgvUc5lY3MaRf32t1jWttd74s+iRrxx4924Y/cO1J55Hx/NqUXV1kdcJ18xGSp+5XTEIE/6cZGFOi6EbNoT02YmE3+sVkFqb7fcIY2vLrSwAU/f1QAgefHu4UVLsNphE4pZlYgrQ+lRTlc8XUPxFnA27cikKXjk81/OfiydGOMw3DPMRJy4JAuZXk5XDPIUbwFn025a0Zw1J3zaiaERx6OIMBNx4pIsZHo5XTHIU7z5faE25yLtoYYbLN+itrrS8SgizEScuCQLmV5OVwzyFG8Bz2XjmBjjcBQRZiJOXJKFTC+nK154pfgL8EKt4ypIDtMFh7kqEVeG0qOctuwG0EdxYzKUHozulxJWZLLsF79Wioopoz8rJdApGYq/5Km8RLDoCFGUAj8nLyIrReSYiLwlIpuCro/IUREXag+2bsfJy2qAw4dx8rIaHGzd7qqqziMJNLTtxcJNL6Khba/rRSeKKRdmXZnlehOnQ61P93I6CvSXvIhMAPAjANcD6AdwUES6lFJHg6yXyJbHjNqDrdvxme9sQOX5j/FLALOHBnDpdzbgIICrW5ptqwkzEYfJUHqU01XQv+SvAfCWUurXSqlzADoA3BRwnUTOPCw6Mm/bQ8npgTNUnv8Y87Y95FgFk6HKr5yuJHnOPqA3F/kigJVKqTtS978M4A+UUs0Zr1kPYD0A1NTULO3o6Ahse3INDw9j6tSpodUXF+yXDIcPj/85PHcupvb3f/Lc0qW2xXoTp22fW1J3qa/lwqwrt1xNJfBeRo5Q0PXpXC5T2N+hpqamw0qpeqvnIg/ymerr69WhQ4cC255cPT09aGxsDK2+uGC/fOLkZTWYPTQAAOjZtg2NGzYkH6+ehdkfvGdbrqFt7/hC15nqqitxYNN1vpYLs67cct9cMorv9U4MrT6dy2UK+zskIrZBPujTNQkA8zLuz009RhQLxzfcj5FJ2eu6jkyaguMb7ncsx2So8iunq6CHUB4EcIWILEQyuK8B8JcB10nkm6tbmnEQGD8Hf7J6Fo5vuN/xoisQbiIOk6H0KKerQE/XAICI3ADgBwAmAHhSKWU7Vo2na/TAfrHGfsnHPrGm0+mawJOhlFK7AOwKuh4iIsrHCcqIiAzGIE9EZDAGeSIigzHIExEZjEGeiMhgDPJERAZjkCciMhiDPBGRwRjkiYgMxiBPRGQwBnkiIoMxyBMRGYxBnojIYAzyREQGY5AnIjIYgzwRkcEY5ImIDMYgT0RkMAZ5IiKDMcgTERmMQZ6IyGAM8kREBmOQJyIyGIM8EZHBGOSJiAzGIE9EZDAGeSIigzHIExEZjEGeiMhgDPJERAZjkCciMhiDPBGRwRjkiYgMxiBPRGQwBnkiIoMxyBMRGSywIC8iD4pIQkTeSN1uCKouIiKyNjHg9/8bpdS2gOsgIiIbPF1DRGQwUUoF88YiDwL4CoAzAA4B+KZS6gOL160HsB4AampqlnZ0dASyPVaGh4cxderU0OqLC/aLNfZLPvaJtbD7pamp6bBSqt7quZKCvIi8DGC2xVMtAF4D8D4ABeAhAHOUUl91er/6+np16NChorfHq56eHjQ2NoZWX1ywX6yxX/KxT6yF3S8iYhvkSzonr5Ra7nIDngDwQil1ERGRd0GOrpmTcfdmAG8GVRcREVkLcnTNFhG5CsnTNW8D+FqAdRERkYXAgrxS6stBvTcREbnDIZRERAZjkCciMhiDPBGRwRjkiYgMxiBPRGQwBnkiIoMxyBMRGYxBnojIYAzyREQGY5AnIjIYgzwRkcEY5ImIDMYgT0RkMAZ5IiKDMcgTERmMQZ6IyGAM8kREBmOQJyIyGIM8EZHBGOSJiAzGIE9EZDAGeSIigzHIExEZjEGeiMhgDPJERAZjkCciMhiDPBGRwRjkiYgMxiBPRGQwBnkiIoMxyBMRGYxBnojIYAzyREQGY5AnIjIYgzwRkcEY5ImIDMY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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "theta = 1\n",
    "Trot = np.array([ [np.cos(theta), -np.sin(theta), 0],\n",
    "                  [np.sin(theta),  np.cos(theta), 0],\n",
    "                  [0,             0,              1]\n",
    "                ])\n",
    "points_out = Trot @ points_input\n",
    "plt.scatter(points_input[0,:], points_input[1,:])\n",
    "plt.scatter(points_out[0,:], points_out[1,:], c='r')\n",
    "plt.axis([-12, 12, -12, 12])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "tranX = 3\n",
    "tranY = 4\n",
    "Ttranslate = np.array([ [1,  0,  tranX],\n",
    "                        [0, 1,  tranY],\n",
    "                        [0, 0,   1] ])\n",
    "Tsynthesis = Trot @ Ttranslate\n",
    "Tsynthesis2 = Ttranslate @ Trot\n",
    "\n",
    "\n",
    "points_out2 = Tsynthesis2 @ points_input\n",
    "plt.scatter(points_input[0,:], points_input[1,:])\n",
    "plt.scatter(points_out2[0,:], points_out2[1,:], c='r')\n",
    "plt.axis([-12, 12, -12, 12])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "tranX = -5\n",
    "tranY = -5\n",
    "Ttranslate = np.array([ [1,  0,  tranX],\n",
    "                        [0, 1,  tranY],\n",
    "                        [0, 0,   1] ])\n",
    "Tsynthesis3 = np.linalg.inv(Ttranslate) @ Trot @ Ttranslate\n",
    "points_out2 = Tsynthesis3 @ points_input\n",
    "plt.scatter(points_input[0,:], points_input[1,:])\n",
    "plt.scatter(points_out2[0,:], points_out2[1,:], c='r')\n",
    "plt.axis([-12, 12, -12, 12])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  }
 ]
}