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@jlaura
Last active January 17, 2023 15:29
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Plane Fitting LTSQ
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"worksheets": [
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"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import numpy as np\n",
"import scipy.optimize\n",
"import matplotlib.pylab as plt\n",
"from mpl_toolkits.mplot3d import axes3d"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def fitPlaneLTSQ(XYZ):\n",
" # Fits a plane to a point cloud, \n",
" # Where Z = aX + bY + c \n",
" # Rearanging Eqn1: aX + bY -Z +c =0\n",
" # Gives normal (a,b,-1)\n",
" # Normal = (a,b,-1)\n",
" [rows,cols] = XYZ.shape\n",
" G = np.ones((rows,3))\n",
" G[:,0] = XYZ[:,0] #X\n",
" G[:,1] = XYZ[:,1] #Y\n",
" Z = XYZ[:,2]\n",
" (a,b,c),resid,rank,s = np.linalg.lstsq(G,Z) \n",
" normal = (a,b,-1)\n",
" nn = np.linalg.norm(normal)\n",
" normal = normal / nn\n",
" return normal"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 21
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.repeat(np.arange(10), 10)\n",
"y = np.tile(np.arange(10), 10)\n",
"z = np.random.random(100)\n",
"xyz = np.column_stack((x,y, z))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 27
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure()\n",
"ax = fig.gca(projection='3d')\n",
"ax.plot(xyz[:,0],xyz[:,1],xyz[:,2],'o')\n",
"fig.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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BAyVKumrygpqXv5hRBoIgKIZTsZ+zW3Gqj6BEaFbmqyVzAOpNL9ledLx04mJD\nr+NHniQwZ864AgegkWiJbmK8T/zMLmI0I33Y5ek3M0Z+Aav+4k83AoFNus5HvwlbjzadTiORSMDt\ndkueMT1JHvyOz/nfJpFIlEzlvJIkXQJLNCzZKnn5ixllAKhZWd2f05jhcBgAvz6CVajJBlOmjBDn\noBQW5vEkRCdZZWWl5tx6si6AllU1Y8YY5HI5PPTQLV84ADOYN28Cpk4diUwmI3mReVv9YmrCpZa2\nzA/3a8SCBZNNj0lk7PV6RSNDnvqstKtZtYrX8Tn/29DYpYCSJF3W0s1ms7pDqopJuoIgoKEh36dL\nqYkkW/nL5/NploI0O18t2YCwaNHUgqaXgwYtxoIFkxAKhcQGlVrn7W3IrapLLpmMKVNGqMalbtu2\nD7feugft7dKtfiAQ5Z7DDmLsrbRls4uiPPkk3wJpsu0xunqTPJR+g08+iaGysnSSa0uSdIFux1Mm\nk4HH49EVv2rGejVS26G2dhy3ieSMGWPErhLBYBCZTEZ3QRozepyabMCivn7CF/GYTYjFXAgGs7ju\nuun4t3+rtqQn93a4HTsPeasVepEfemgX2tvvk/xbW9syHHPMldyxzBAjWWoEM4ki8jF6GmzyiVoL\npGJAvqsJBvn+m3ff/X9IJvfim9/8Js477zx8+9vfxuWXXy45RqshJQDs2LEDP/rRj5BKpXDcccdh\nx44dtl8TUKKkm8vl0NnZKf4Yeh8EowkPRkBEU18/QdROKSY4HA5LykHqrb9rZA4s0allk9FxuVwO\n8XgcY8d+E5MmDbfUSLKUQC9yMsmPQf3qVytQVdWI9vbubezgwYsxZ051gTxhFL3Vxr0YyQhWxjF7\n/5QWrZ///CdYuxZ44IEH8NprrxXwQSaTwQ9/+ENJQ8pLLrlE0hvt6NGjuO6667B582acfPLJ+OQT\nfricHShJ0hUEAVVVVaJ33cj3zGawGRlbqT6C0XmYlRd4sgHJHGTpdXR0FIR/mUFfsWqNQmmrP3Dg\nCViwYCJWr25ELOZGMJjFvHkTMXXqSCQSCYnTRx6Tquc56a20ZbuTEczCCumyi1Ys5kIgkMbChZMx\nbNgZ+MMfjsEFF1yACy64oOB7ehpS/vd//zeuuOIKMZX4uOOOMzVHPShJ0gXyYUWZTH7LZ4YY9cAo\n6WUyGUQiEduz3Yw+qGRpy2WOadNGIRqNIpvNorKyUrXLaV8h02LFtapt9Wtrx4mON7lHnHYJSl0g\nWCK2y8KSh6k7AAAgAElEQVTsC7p5X3gWgO5Fi+LZvV4v3n33XdUC5noaUr777rtIpVKYPHkywuEw\nbrzxRvzHf/xHUa6hZEkXKH5NXb3HUw2CZDKJQCBguT4Ce34jx7JzZWUOcuDFYjH4/X4kk0nb20oX\nA7wQob17F2Lw4D/ixBOPs0TAWlt9pWdKyekjT+4gMqa/m4lJtQu9GXZWrLmw42jF6Oo5XyqVwt/+\n9jds3boV0WgUY8aMwejRo3HGGWdYnqscff/NU4BarK7ad+wkXdJFKRWWqpTZOQ8ji4ocVOCcHHhU\nH8GIJKN3fsUAL3wrFluNt966DW+9dbfl+Fk7t/q8mOJoNAqPxyP6EpQKjxMR9wWLVgl9xeImsM+c\nVi1dPQ0pTznlFBx33HEIBoMIBoOorq7Gq6++WhTSLXnPSW+QLtUgOHr0KDKZDCorKw21xykGUck1\nZbbAeVVVleEC52buldnvKkEprjWfHUUxmi/oGqu5eTdmzrwHdXXLe6xrMJHr1q37cNVVv8IVV/wW\n//7vD+DFF/8mxmbTwsgWHk+lUmIqtB3oK9IAYC950zhaKcBsQ8pkMoknn3wSl1xyieSYSy+9FLt2\n7UImk0E0GsVLL72Er3/967bMU46StXQJPUG6bHaX15vANdeMQV3deFRUVIjbdDM6rd1zzuW6y0Aq\nacp9RatVA81RydmVT0fNQ0/8bG+l3wLU9mhXwbkFwSU5t1L9AgK1GO+tql59IXpBaRwtS1dPQ8qz\nzz4btbW1OO+88+ByuTBv3jyHdOWwIi8Y0YCbm3dhyZKdkkiA9vYlKC8vL6ge1lsdgSmlWKk2sBn0\nBXLmObvyBVdqxb/piZ/tzcpj+bZH/Cwq9txKmXbRaFR0yrFOO6OFgOxAX5MXWEv3pJNOUj1eqyEl\nANx88824+eab7Z0oByVLugSjpGsUq1fvQGurNIieV8SmmBa3EihBhIrleL1ezZhlu8m0mOTMOrs+\n+iiC9vYjiMWuA9UC0FtTobfSb/O/j/lzk0VLtYkJcqedViEgO6zLYlioVsZgUUoVxoASJl3W0jVa\nyFzrhyerIplM6ipiYxRGrWL5Q0bzIyvIaBlIs+AV0Zk+fbQ4p2KQL+vsam7ejTVrNiEef95QYkFv\ndg3mtTcycm7es2q0EBD7u5iVJ/oi9MoLfQ0lS7oEo/GQWpYZhVdls1l4vV6Vl0b6eTEtPnZcIlsg\nXxuYHDJk7RgdTwny61EqorN8eRoTJlyIcDgs6o4EqxlccpiNNih2nzY1zJ8/sUfOrSRPkNMXgGpM\nsdbv1NcsXXYMx9LtIVixdKmBIgteeFUikcC8edU4eFC5iA07bjHkBbpO3vzkEQNGxjMKpSI6K1cu\nxrhx5yMUConXRN53NoOLp0H2VEFvM+m3di2gNTVj4XK5ejz1F+iWJwRBgM/nkzSqpOQOrQaVWr4B\no79hMeSFUqqlC5Qw6RKshoFRiEg6nZbUR6BjZ8wYg0AgUJDdJa9NW0xNNx6Pi2TLzs/KmHoffjpO\nqYhOIuGFy+WCz+dDKpWSLIKBQKBg20uEvGXLS7j99r2SGgdtbU0AgGnTRum+DjWw16fHSi5Wu3Er\n8cDFiI8lnVh+Ht7vRGFvNA8i57yTWV9UiLzw+KJFU1BXN97yNRC6uroceaEnYZZ05fUReGRGx7LZ\nXXbMQ8+xVB84lUrB6/ViwIABpl4+ng47evQ3dM2RHePNN9/mHhcKZVXnpbTtfeQRKeECQFvbvVi5\ncjEmThwmyeQyet1mrFQegVhtN97b0R8EPcStJk+wGnEsFhPliZUrC7sFyyMz+IXHmyAIgm0LEVUa\nLBWUzkxlMBMyRkgkEohGo5rhVb0RNsVmufl8Pvh8PjGrSQ28uSrpsHfcEcZ3vlMnH4KLTZt24eab\nt+Kzz34Ieb+s005rEgtab9q0Cw8+uAWJhBc+XxJz547Ht77FL3atZjknk90F3akam96mh1bACyuz\no914KTusyKKl9klU66CbiPmV2mKx/PEulwurV/MKj1u7ryzp9pWFzQhKlnQBae0FLVDb8FQqVZT6\nu2aP5SVe1NdPEKt/RaNR0w+Wkg67fv1ifPvbtboIYcWKv6K1lX1p8v2yvvKVt/CrX81DTc1Y/OlP\nf8XPftYiOa6trRFer0/xxVKKKAgG8+3bc7kcgsGgYtKAXH+0WtOgL3Z1sEIoxdjSE+jeK0Vg+P1p\n8XeKRvnvmN33tZQWt5ImXUCb7IhsqbMEpcPqSR4oNunyLFFe4oXZ8yvrsNo/ezqdJ8VYjH05uvtl\nff3rt6O+fgIymQweemgXWlul28z29uWq1ozeiAKlba9anzT6bVn9UQtWw8p4DqUJEwrLDBobJ4Vr\nrhmNmTOnaX9RNkaxt/SA8m/Y0DAZwWAQQF5+4sHrTZpuTim3dEuJcIESJ116oXjRC+w23ev1ipYj\nhYPpHd9olIFe/SyXy+HBB7egtVW6pZUnXliROJSKmfv9acUxqf1RKpX/bijEP44NmUsmlTpVKFsz\nahEFRPhK0NIfqeQn6Y88i1gPgQwerK8fmJJD6c4747jkEv39xHjjtLY2IhAIGiJLfgaedalEDj1R\nIQsXTub2WVu4cBLcbrepQkDsO9bT3SzsQEmTLlBIdmyWlsfjKSjSzdbh1TO2GSedFumm0+kvUjzJ\n2n4RwPPI/xxpfPjhvyRj6lkkeHNVKmY+Z07hi0fxnH/5ywvYsGEv0mk/XK4Yxo4dqNr3LR+OpNSp\novA+FytMjNUf3W43UqkUysrKJBYxld/k6cQ1NWMBdBOIz5fCvHkTdM1NKc14/fpbcOmlU3RfA19X\nVt8x8FAMqUTpudaKzJAXHvf7U2homFLwHXbR1Pqt5HUX1Grp9kX0C9IlYqJYVrfbLSlGIz/eqOVo\npFaD2thsxAQAlJXlkCfczWAdVG1tC7Fx407DEoN8rkrFzMeNO0+cJ7tIbd++H3fc8ZJEm/3ggyWY\nNetrePll5ZC5OXPG4YMPpMQ8ePBiLFggJRwjhWfscpDIY03zpL9d4vCbOnUUstksqqsvxKRJw8WF\nWW/9ikKSyy+iBw4cwWWX3YOFC/U1c7SLLHszA48HIuZ0Oq/1kvTAgl00Wahp+r/73e/Q1taGRCKB\nw4cPY+DAgdz3VE9/NAB4+eWXMWbMGDz11FMFPdbsREmTLkty4XAYLpcLZWVlYmtnre/oGV+v9aoG\ntj081dw9evQoFi2ait27VyAWe0pyfCy2WpQY9M5XaX68cLeOjg7kcvlWR2wq8fr1u7mOt5dfXopn\nn/2Z4rmnTx+N8vJyPPhgE+LxvAV77bXjC4hGb+GZYml03aTfvai0ty+B1+tDTc3YgpoGmUxG9MKr\nteaRklz3IhoOA9u26ato1ty8G3//+/8CuANAGsAMkH5ulCyLkYHXW/UbeFIS1Sk+9dRT8dprr+GN\nN97A8OHDkU6n8cQTT2D69OnisXr6o9FxjY2NqK2tLXpEREmTbjKZRFdXl+jp1lMz1moyhZFj5eFf\n8oiJurrxGDLkWfz974VjsbUd7H4I8tJGYSqx3i7CQHfURTzugdsdx4031uBPf1oKQRBEi0aO3o4Q\n0CJ99uWmba3H45G05mETBujPggXVaGtr+mLs58HuWuTn4IEWg88/ZxffWwEAgwb9pWDHoIXC1ulJ\nLFpUuKXvadjp9HK5XJgxYwYymQyGDh2KW2+9FR9//HGBvqunPxoA/Pa3v8W3v/1tvPzyy7bMTw0l\nTboAEAwGRUnBDgnAyvF0LLtlZ514vGNPOinEJV1yVBl5SLWscpI3stks/H4/QqGQzGJT7iLMghd1\n8cEHS7BsWUo1LKk3t73Nzbtx4EAbeJakEunLoyEAvvZYXT0Md96ZwPr1i3HgwMcIhwvHUltYeIsB\ncA+OPfZK/Pzn3zdFlrSlp12WVWeTWcJkNfy8nDMB3/rWJEtzAaQFzCkb7Wtf+1rBcXr6o3344Yd4\n+umnsW3bNrz88stFj4YoadL1+/1Ip9NIJBJFS8EFjFmayWQSkUhEVVdm56HWuVfPfNk4X5crhuuv\nn16QusqGzfn9fjHIXf5w8eaSDwGShiwpxf+uXduEurrxinPurcIzZEl2dDzJfHrrF/+tNkT6Strj\npZdOxcUXT8IVVyzD9u2F3/P7U4oZdko7gHPOOVOs4mYWvRlSxdfwm+D1ei1Z3XJHGo9sCXqu/aab\nbsK9994rMZqKiZImXUKx4mnpeD2grWc2m9XUldl5KDm7WB1Wab5KFqfL5UJ9/YQCi5vkjTDPFEOh\n483jiWPRoikFmrARGYKFmcIzdkDJkgRuw5AhG20hfUHI1zNoaJiC9vbC0LM5c8YpFgBSC+0zAl5k\niFXSBszLW8XK8mNJt7OzE2eeeabisXr6ox04cACzZs0CAHzyySfYtGkTvF5vQUsfu1DSpGslFdiu\niIR0Oi22NScLUotw5VCr7aA2RyWL8667GrBixZYvQnTSuO66qdwtHa8uAzuXzs5OrqdZrwzBg5ni\nL1bDzJQsyQEDDmL58u8VKXa1CZGIgLIyYMGC7ugFXmGZa64ZjdbWRkktiiFDGjFvXrXuRV8pMiSb\nzWDy5BG2XJtRi7lYoWsstCqMsf3RTjrpJDz55JN4/PHHJce0traK/z979mx861vfKhrhAiVOugS9\nsax0rJGIBCXSZcO/yIkXjUZ1P5hGohKUjlOyON96qwuJxCrx74cOLYHb7ZYkXGzatAtLlrxYUJcB\ngGZihpIMMX++9YpcctjR30zJYhw+fGDRSknW1IxFJBJBeXm55N943vhLL50Kv9+PNWuaEI+74fen\nMHv2WEycOEwskalV91bJSbh2bZNl0jUrURRTw2ctXTXS1dMfradR0qRLN95IwgN9z6wcIQ//Kisr\nM2VxW8k0IyhZnInEYMnfee2F1qzZIaupwD+OB7kM4XbHcP31MxRLMlqxVO3ob9abRcz1QBAE1NVN\nQF2d9L5T3ztBELhteViJQsmqPHDgQ/z1ry2GMuPsgpUsPyXIFwA9Bcz19EcjbNiwwfTc9KKkSZfQ\nUxEJsVhMrOFgtdOuHZYuz+IMBBYgHv9+wbGs3mo0PIwHVob47LPPMGDAAG6YmFVL1Y4tam9oyXY4\nsGhX5vN1V/NSShbwePitmjo6BuOnP90Nn0+5+JAWzF4LL3TN7kL1pVbAHHBIVxdSqVRBDQelcY10\nsdADpbnmcjlMmTICd9zRhUceaUQy6YPXm8Snnybx2mvVBcfL9VY1XZa03mjUhUAgjR/+cLqm9ZtM\nJsVtMN2HXC5n2VK1a4tqVEvuC4VU2Dmo7RZyuRwaGibj0KEm2b3Od05ub6/G6tVNmDFjTEFiR7HB\n3ncqp2oF8t8lFoshFApZGrOnUdKka9aRpud4ythKJBIQBEE1/MvIuGaOpfnQd6hPmtvtxuWXT8eV\nV+a3TuFwGNu370dTk3p7IUEQMH/+RLS3Fx43YsSJ3MpnALjES8Vp4vG4eH9I6olEIojFrJX266vS\nQE+1GqJzqe0WBEFAff0EuFwuzJ9/FY4ePQdABvlW9fkFOBZzGSoAxMKuBahYWW1607X7CkqadAFj\nNXXZ7ygdT6RGzfz8fv8X2zd7b5WZ9F62KSUvLE0QBNTUjIXH49FsL1RTMxY+n6/gOKWICLnWK69G\nVlZWJmqOVD0qEAgoWqQ+X16v1CpK3lthZmqww7lnBHp3C7W14zBs2A5s23ZHwRihUM5QAaBiFIq3\nm3SLHU9bLJQ86QL2Wbps+Belx6ZSKd2tzc1Yr3rR1dWl2JRSfn6t9kJqx91//4vc75DWy6Y2U+eN\njo4OxONxcU5ExJlMBvPnV6O9XbrtHTy4EfPmTShwDtELL783VnqMFQN6SNAOQiCCMaJrazmv1Nq3\ny3ViOpYtjmSWNItJkL0tAxlFyZOuHZYuL/yr2BEJeo6lSAkAcLvdik0p7YSa1ksFcijbjrzqwWAQ\n6XQa6XRa1LTdbjdyudwXOiKwdm3TF5ZqGvPmVYv6Imut00ufyWTE+hDFtr7MQC8J2jVXI7q2fGeg\np0QlL4yNjScmEo5EImI2nloBIDXYaelSC6FSQ8mTLiCNMDASe6sW/iU/1sg89B6r5HSTF8oRBMH2\nYj5GIiKGDGnCNdeMFZ0WJB/QGPRier1ecZ4sgU6adBGqq4dxyZO9B5TV5Xa7xZRlJeurN4m4p2tI\nGNW12Z0B+SSMgiVierd8Ph9yuZxmASA9OrFZyFOAS6kLMKHfkC5gbPtDsoFWc0oaVwlsVpfPl88u\n+s53anXNWT4uOe+ogA9FSvBCsaxA7R6xMbiRiCAG6v/bv02Ez+cTrR8gb5lSy5WysjKJ1eHxeCQ6\nOL2s7B8iUbmswLZyJyJm50xbYTkR29ErjfDXv7bg4Yd3I5n0FjjKesq5R8+zFV2bpBs7QESqVQCI\nJxkVg4DZYjelhJInXTZBQk9EAtUicLlcquFf8vF54NU+eP/9RrGiEy/FVglqTjI7YnrlUDuurm48\nJk++SFIQnkiTzhGPx0Vnmd5uxVpETB01yMpiIzbY+eZyOUUiZiUOsz24mpt346c/3S1Jy2UdZb3h\n3OtNXVvNmOERMX2HFlb6fQGIkpFZQmYXEcfS7WVoRSSwFiRpkHr0ILVxeZ7+9vbluOuuBnR2DtCV\nYpvJZBCNRlWdZHZkr8nH40F+nygoP51Oi3NIJBJIpVLw+/2KDj0j8yASTiaTcLvdYhwnS8Rya1aL\niGlR4PXg0tNBePXqHRLCBQodZVokWKqedSNQC5tjf1uge1dE0UDsbyv/XXjOPoJcXii1xAigH5Cu\nmsOLDf8SBEG0ICm9Uu/4SnqxUlZXe3sER4+uknwmD7vK5XJIp9Po7OxEIBCwxUmmphNrgSI3crmc\nqNsmk/mOrclkUrwPtGjpsW61QJo6LTjsmHKLWN7NgcokynVdsq4IbrdbHIu0ZtIjKeJCb0qt0UIt\ndjiNrEoDdoVpyedhNGyOlRuoMBR9Li8AJNeJWYuYfccdeaGXIf9BeOFfZiMSlKDk6ReEJPfzeNwj\ncZIB0NSTjc5XD9jx2HhbsrTpBaB7RouW1+uVSAv0AtEfvVtFspiTySR8Pl9BMXXefJW863IiJrCk\nLV+IqCMEjS13DCml1PZWj7G+CDtqYgDKvy37+5J2T89sKpXC1q1bcfDgQRxzzDH2XFAPorRSOVTA\nbtfD4TDC4bDoJJNvg+2K6120aCpOO22J5LNBgxbj1FMLyyECgM+XREdHB9LpNEKhkOo2Ss/5zR4H\ndLfs6ejogMvlQlVVFbxer0hc9O/xeBzBYBDl5eUIBoMIhUKoqKhAZWUlAoEAXC6XuMB1dnaiq6tL\njAih0C/2nMlkEuFwGNlsFuXl5QgEApa86z6fD4FAQHxp6e80r3g8LpIpzYWNXqHrdblc8Pl8CAaD\nWLRoMgYPljYv9PsX4MiRj/DsszvEbbHavX7++T246qpfoq5uOWbOvAfNzbt1XVdz827MnHkP6uqW\n48or78Pzz+81fG9YFCsLzOhuwMg8yMr1eDzw+/0IBoMoKysTfSUulwvPPPMM1q5di5tuugkjRozA\n/Pnz0dnZWTBWc3Mzzj77bJxxxhlYvnx5wb8/9thjOP/883Heeedh3LhxeO2113TN0QpK3tJlf8hE\nIoFoNKq5XbeLdHkFyH/wg3EIBoNYvLiwO+7s2eNFiUNOSD0FkjWo4SIbb0sgolLTbbUcY9TRgyxi\nIkEg32LJaM1hpWth62JUVFRoBv6TRczqiOQMIgtr6tRRuOuuBH71qwV4550YEolBSCS+jzfeqMat\ntzZ9ccxIUW6Ra8SbN+/BkiU70db2S3EeeptTyrfsBw82we1296nkEMB42Jwd5E/f9/l8ePDBB3HP\nPfdgzJgxOP744/HKK68UtCTS05TytNNOw4svvoiqqio0Nzdj/vz5aGlpsTRPLZQ86dL2OJlMwuPx\nFGW7rna8PKvr6NGjKC8vh8vlwsqVSxGNCvD5Uli0aAq+9a1J2LRpV0FDR61iMnZZuhQhQfpaMBgs\n2LYlEgl4vV7xGoyAR8Rs4glFJFCChRlpgkBWLJBvrqnWFkmvNEHkm81mMWPGWGzYsBeJxBrJeO3t\n92L9+iZcfPFEyTaYDZV68MGtEsIF9G29+Vt2650WrIJHmL1RE0P+bIfDYZx44okYOXIkxo4dW3C8\nnqaUY8aMEf9/1KhROHz4cHEmz6DkSRfI/xjk9TZCFEaTKfSAXtqJE4dhzJhzJRluSu11AH4xGflc\nzc5TnnHncrm+KEYTg8fjETVWcjbakeVDUgKROJt4omYRaxFxNpsVIygCgQC315sWeEScTqfF7L9u\n7Vp5Cy2v30w7grz17eN+LxZzqdabKFanhWLEyBoNm7NzHjSOliNNT1NKFg8//DDq6+ttmaMaSp50\n3W43ysrKxBdRD9jtpJ2kS5ZPV1cXAoFAgdWtt5gM7/xmkMt11wAmfZsILxAIiFosnYMkANo2mz0v\nbfl5SRN0LiPSBBEwhX/5fD5RFrEKcgzySDwU4keC+HwpMeSQtY4JaqnUasXIlb/Xuw48pffESOxw\nMbTljo4OVUeakfNt374d69evx+7d+rR3K+h3jrRiHK91LFmKR48eFUOuyFHGwmzhcKPyAjufbDaL\nyspKMaWW4iKJ3AKBACoqKkStmToHd3Z2IhwOIxqNIpFIiGSsBsrPj8fjCAQCYuiZHhARU2t41lmX\nv0f50DWgO+aT56zTC9apl8vlUF5eXqBfNzRMKXCUDhnShOuumyJJd04mk+Jcstks5swZX+CIyxf5\nqYbH40EwGBR3QNT1JJFI4JprRnO/t2CB+TZIxbJ0zcDueWhZunqaUgLAa6+9hnnz5uGZZ57pkWiI\nkrd0zYSBGT1e7VjSSQUhX3OXrbYlh5WGjkaiEsiLS7osa4WRbuvxeAp0WzXdkyIA2FhLdotuJARM\nL4gY0+m0xPlmVpogkNxCC6SSHlxXNx4AsHr1UnELvXDhFPFz1hlIVngymcTUqSORzWaxfv0tSCS8\nCATy1dZqasaKFj2BFhuXy4VvfWsyfD4/1q5tRCyW75V27bVjUV19obhzKGZarRKKFQFhdYx0Oq3q\nkNXTlPLQoUO4/PLL8fvf/x5Dhw61ND+9KHnSBeyvqcuD/FilOGC1cZWKybAFxpXmqgUiErYFPMXb\nkkXGJonoSX/WckBRphcd7/P5bKk7zOrBPCnBqDRBfwRBMJxRV1c3XiRZJdDugF0crrhiBi67bJok\nzTmRSBREPLBJHQAwffpoTJ8+Wpyrz+cTF06lLC4lIlZ6Du+5Zx3Wrm1BJhOE2x3D/Pmjceut81Sv\nsS+AJV02/E8JeppS3nXXXfj888/R0NAAIL+Q7tu3r6jXIeR6I27JZpA1FA6HdacFUhwv23+KIG9N\nPnfueNTUjBO9/Wwygbz6VyQSgdvtFrfFvLFXrdomRi/88IfTcPHF6ttHIgp5Z1lAqtv6fD4kk0lU\nVlaKLyYRAi/rywpYkudVFuNZxHrOSw4tl8slib81CpaI5XUdiLStWo3yxUFPJTgiT3bxYsPqaOdB\nERXswkCLOjsWOx5LxPQnGo1Knpt77lmH//N//hfp9GrxM49nIX7ykzO5xJvL5RCJRLgV+IyAWvVY\ncdKmUilxYcvlcqivr8euXbtMj9dbcCxdGfhFbJqQy+W7LWhVJtOaBxti1tHRURBbqBf0wkejUbF3\nG2m54XBYLABEL65dW37WqlOKHmDDqFiLWI2I5daix+NBc/NurFq1Xcztb2iYrGl1EohcBUEQa0cE\ng0GJnm1GmiDQogPAUMSHUhFxuYxDx9JCwd4nFkppzuwuhGppuFwurF3bgnT6KckY6fRqrFt3laq1\na4c0YAfklm4pol+QLmC+pq4cvAiDfKzkLZg+fbRmZTI7HXRKx7E6sly3LS8vF3VbesFpJ2DG8iTI\nQ8DUogeUpAnW8mSJGICYdkzXs2nTLixevF3yW1CCgR7ipQUomUwWSAlmpAk2918p2kEJmzbtUl08\nKHKE7gnpzLxSmHJpgp559nqIiGmuHo9HTHNOp/k7MKXPixHqZRbsXChTshTRr0jX6PE8wlOKMEgk\nvNztPW/cYnUEllckU9Nty8vLRdJTIjy9Fp5WCJjea5BrsVRQh/6NUrjdbjcefHALWlvvk4zR2roM\nq1cvVSVdyrijGGStJA8j4Wv0O1BiiR6pRmvx4GXVsYuD0ZrErEbMluIkIvZ44tx5ut0xUdYphrPO\nbkfa0aNHS7LYDdBPSJfVvIhM9HyHR7pWYyWLYenSy0YVycrKysTP6NpZMpaTgZm4WNbxlMvldNfN\n1QMK+cpmswUpwTQvpcUvFnOJmrF8Luy4alEJWpDfL1a/pu4JdB4t7XrVqu3c2OzVq5dixowxeOaZ\n7Vi3bifSaT8CgYyqhKL1O7JETGAt8Ww2i7lzR+L++xfKNN35mDdvlJievnHjTqxbt1O0zOfMGYuL\nL54kSZk2gmJIAaVaYQzoJ6RL0FPInMCzSDOZDK69dhzee69RUk91yJAmzJ2rLwi8GPG/pB1WVlYC\nAJ577oUv6ph64fUmvujsUG1It1V7gVkSBvK6IZs0YdYKUtvyy+cVDConJlDUCGuhkx4aCAQs1/nV\nO181yYTmppRNFo0K+J//2Yqf/ayFW6PBqHbNZhayUQ/yUpi33HI1crlHsX79lUilAvB645gzZyQa\nG2cjl8thy5aXcNtteyRzOniwES6XW7XehF5JzwpolwHkLd1SrKUL9BPSZS1dM4THRgDU1o5DIBCQ\nFLGZP38yqqsvLNr8eWB121AohGg0inQ6jeef34PFi6VFUdrblyAUCul+UdVAThiPxyM6+cgpRttg\ndrvKWndKji+jW34AaGiYjLa2wvC6666bKulkQRIFe9/khGzmZWejKJTmq8fyVCoT6fen8OijLQW1\nFvRIKFrz1Sr809Q0G7fc8gORiFmH3dq1L6KtTVqNq719uVhvgnXWKbXmkYfD2WXpsvKCY+n2ERgl\nXazB3ccAACAASURBVPKYx2IxeL1eMSJBXsSGtMZizEF+LE+3pZcjEolgxQp+MRUzL6r8vGRRy7fm\nbP1ZoDvsiUgvk8ngr39twe237y1ocZPNZjFp0nDDW36txASy6tg4aaNOMR54MbdGICfi66+fjg8+\nkC4egwYtxuzZY7Bq1cvcMYzUWtDr2NMTd50nbv5iKK83QXHZZOWyYXByImbJ14q1y74rpdqqB/iS\nki5ZXlRqsKKiQpUMiqHTyo+llz2RSHB1W7J2lYqiRKMCnn12O9aufRHJpE93iJWeEDA5yJJhCenR\nR1sKWty0ti7DypW3YNKk4WLKqxHwEhPYLb88FM6sdk3EQFEfarUdtCIR5KitHYd0Oo3VqxcjmfQi\nFMpi4cJpqK0dh0ce4ZcQ9HrzUSJaUSbUFYV2D5s37zE0Nx4Rl5Xxn12frzsjkQ3RlEt0Xq9X1L2B\nbocekI9hl9ebMLoToWM7Ojrwla98Rff3+hL6BekakRfYTDLailG5RaUmksUkXdba9vl8om7LWhUs\nySi9FF1dH6GpaaeE+N5/vwnpdAr19dUFD7eREDA9KHR8vQjgeRw4cARXXfVLzJ07HpMnj5C86Kzl\nqQdsFIXe0pM8ImY717KSCZAnDQrBk98zo2Fs1I5o0qThqKsbX7CwL1o0Fe3tcgmlEQsWVKvGN5OD\nk7XGrYbYAflnYs6c8Xj//UKfxqJFU8Rdl1JNYpIpeLHEuVx3JUA2Jlne/05tJ8JayuFwGEOGDNF1\nXX0N/YJ0CWqER9tnyiTzeDzo6urCpk27CpIh5E0kCXq2R0ZIlx48t9vNrZPw3HMvYtWq7UilfAgG\nM2homIKGhilcrVMQ/Ghvl+qD7e33Ys2aRkyadJHEugMglhi0q5SjtKj1iwA2A7gH4TCwfTtw8OAS\nLF/uR03NWElarJ7sNXkvNasF0NkXnLL1qNsE/Sasdk1/Vq7chtZWbQ2WXdDU0o35EsrUgrF4qcS0\nmNDisWqVvrkpgTTh6dNHw+v1YM0avqzDzksuTdCzK5cVUqlUgeOa6k2wOz12HB4Rs++fVoWxvox+\nQbpqli5v204PQC6X01Vu0S5NikC6LSUslJeXF8TbPvvsji/agEs92/fdNxn33Te5QOt84IGd3HOl\nUj7R8UTbZ3lcr9FsLDnyFtI4xkJ6HsA9kmNaW5dhzZr8PVXTFeWFdUgKsruQDhGr3LEnL2LDzktN\n7yToccCx0KrtQORKZTcFQZpZRxZxJMK/L1r6MKsJ04JWX1+N+vpq1e8pacRsBAxZskC3tctaxOxu\nDuATMdVPpnGi0SjWrVuHTz/91NY44p5EvyBdAruasuFWPp+vIG2XCFpvuUUjoVhKmXFksSWTSTHu\nlSpT0cMbi8WQTqexfv1urka6evVSPP30Twte1FWrtnPnEwhkCnRQqhFAhMZadwC4VqfSdo++N2PG\nGNFC2rfvQ3DaVXEJQOnlZedjV1YdYCyWV65dh0L8HYzHk0BXV5e4gJB1a1TD5oG1muULDzt3JdnJ\n40kUdOpgLVDShO2oT8xqvSQ/UNsseSwxgIJ6EwAKiFieXZdKpfDBBx9g7969+OMf/4gTTjgB06dP\nF4vYEJqbm3HTTTchk8lg7ty5aGyUlswEgBtuuAGbNm1CKBTCI488ggsv7JkIpX5FuvRyUk0Ct9ut\n6CSjB0xvuUW9soESObELAOm21KeMSICuwe/3qywGfMtFKcRq7txqhMNhbqiWIOQ7/CpZdxSZABQS\nMe0ggO7aA2QhXXLJ3di6tXCOehJMeDUYWKcNWVFyvVOrgI2eGGEtKN3jhQsnida5fCHVs3gpwUh9\nByXZqaFhMtxud4FGTIaB3XHNSrIKu3ixFjGrEQOQ/IZsUgf9e1lZGZYvX44rr7wSu3fvxqeffooP\nP/yw4L5p9UbbuHEj3nvvPbz77rt46aWX0NDQUPTeaIR+Qbrsj0PbOypvqPW9hoYpBeUWTzutsNyi\nGWeaIAjiAkBOO9Yap5c0nU7D4/FIwp6U24Dza+/K9UG/P4XZs8di8uSLRKtaD+TWnXzLSDosHUtz\nZi17ZXKaonheuUUnt7xYi5gqw+mNTCAiN+KA46FQg01j9uyxmDRpuLhAyO+Z1uLFmwu7QOiNKNEK\nsaNxybqlc7POSSu7CHaB0JN6TTKD0oJPf+i5yuVy2L9/P0444QS89tprePPNN+H3+3HWWWfhrLPO\nkoyvpzfaM888g6uvvhpAvjfa0aNHceTIEXz1q1/Vfc1m0S9IN5fLt8ghwb6yslLXAyMIAmprx0EQ\nBEkyREPDtAInmlHSZQmKtrFy3VatseL110/HoUPSxn+DBi3GD34wViwfKX9x6+rGo6ZmrOEQMK1r\noT9UNIXCguglIWcUvbhTpozAsmUZrFu35It7ynfGEGihFAQBO3f+P6xZ84KusCetEDEiGKB7MSGJ\nwmzSRF3deNTWjlMt6cgjFb1ETIRrZoFQ04dJ2qJ6y/J7prdgvfye2bGDIMgX/HQ6LYaZeTwe/PnP\nf8bmzZvxr3/9CyNGjMDtt9+O22+/vcChpqc3Gu+Yw4cPO6SrF4IgwO/3IxAIoKury7D+Kk+GUDtW\nC+Sgi0QiCAaD3DoJpNuqkSLfcpkm8f6TzklWINBdTd+uHmI0plYBdPmLO3HiMEyYcIHkxZXXTJDH\nCG/Z8hKaml6wFPZE94LmQUTAShNWSjrquRdK81IjYhqX3TGwEoVZ65zVx5WckUq6uhYRU+ia1R0E\nb86k35JB8txzz+H111/Hhg0bMHz4cLzyyis4cOAAQqFQwff1Pvfy97mnHHP9gnQBwO/36+rjxcLO\n+FtWtwW6NTileFs9pKhkuchfXLK66N/oBbHqdDKSOKH04irVJiBrny3nuHr1DsXiMHpJV0kHVcuq\nY0PE2NRmVofVm/llBOz3aQchj2Wl3ZKZ+Ga5dWskNFCNiFlNnRCPxy09awRafMgf09nZicWLF8Pl\ncuH5558Xrdpp06Zh2jR+xxU9vdHkxxw+fBgDBw40NWej6DekC0gjB7QSHtjjjYwtB1kSrOMuEomI\nSQcU+8kLT7IK1hOvx+mk17LT0lf1grf9py0/ERylWLvdbl0hWUowSoq8rDolJyJJK263u0AKMpqh\nxoIlRV7qNbuwsnPTImK1iAcrYKMeKMab7o0ZaYKFPHTN4/Fgx44duOOOO7B06VLMnDlT9zXo6Y12\nySWXYMWKFZg1axZaWlowYMCAHpEWgH5IugB0JzxYJV1en7RMJt+pgd0uAt21UZXCyYxAS0cz63Qi\npx5tGe1KnADUrWZ6aZUiSfz+7swl3r1Qirk1CjkRk9VMBdZzuZzYst7tdmPr1n1YunSnpGiNHjnE\nKCnq2f6zREzPl1WNVT5nJeeeGWmCJWJ5bHMsFkNjYyM+/fRTbNy4Eccff7yhuerpjVZfX4+NGzdi\n6NChKCsrw4YNGyzfI73oFz3SgO6eUp9//jn+4z9+jS1blhUcM336Ujz77M/Ev2v1M2PBdo9l422D\nwaCYa84WuiaCoZoDrOXJ28bqIQo5wVAWlVnIvcVUi4K24mwYllmwc/Z6vQgEAookwEtlHTy4Effc\nMw5TpowEgIIXlhYPNnrAKuSkyDrKWB32ssvuwfbt9xV8f+rUJjz99G3c62Tlj2AwaNuiRqRIOyw2\nNtaOyASKwAkGg6aeBzkR0x96X9566y1R4rnzzjtx44034nvf+16P6aw9iX5l6QJ5q0Ce2EDgJTwY\nsXTphSGnhFadBKVtuVosrLxcIiGdTqtGO5gBq62S04m6UfAcdUpzU4KROFNAPS1WzenEaudW9EQ9\nc2YdYqmUnztGNOpCZ2enhOwocsJIJ2Ijc2bDEllStCsywaqOLbfWM5mMGJng9XrxxhtvYN26dXj7\n7bcxePBgbNq0CWeddRYuuugi8zemj6LfkC49DPltlb0JD/SyJ5NJSWQA60ggUtSzxeXFwiq9GGQl\nZ7NZWwPZAeUCMm63W9fclF5aK04nJechG7ZGYV+0Q7GqJ5qds7TeRDfKyiB2ZKZ5sbsIepasOp30\nkKKVyARyjtkdmSCf86uvvorHH38c119/Pa6++mq8/fbbOHDggK72WKWIfkO6BJfLhQULJhUE5ysl\nPMgrIsnB6rb0AGYy3S2vyZlF0oMZC5T3YlDOeTKZFMmXSMFomJMcrAOOHnwjc1PLDqN7QkXQi6EJ\ny4veqBGKnsw1eYlEvQSjlgRC1jDtZEj+kMcRm10kjNZ4YGEkMoHuux2RCfIEikwmg3vvvRctLS14\n7LHHcNpppwEAzj//fJx//vmmzlEK6DeaLgXud3V1wev1YuvWfVi1ahuT8DClIHohkUgglUpxV1S5\nbisIAmKxGPx+v0isdiYhsGAt0EAgIL4c8hAso/qwnYHscrBbfvKg8xx1ZLHqBauvamnCamPItUTW\nMZfL5Uzfj02bdmH16h2MHDIJdXXjJUSupr2zZCefG/u70iJRjNA1gly7lUcmmNWIeenBb7/9Nn70\nox/hsssuww033GDb4vzrX/8aDz30EHK5HObNm4cbb7zRlnHtRL8jXSPOMXoQKioqxM/ooY7H4/D7\n/ZK4SbJaSD90uVzw+XyWLQCC3ALV0wiS91IAKLDqyMqwwwHHgiUBOXHlcjkJmbBz07NI9ITTiX43\nknCsLhJkGbLWrZn5KS0SNEda/IsdmcA7llfSUYmIs9msGPFBLdMffPBBbNq0CatXr5ak5lrFG2+8\nge9+97t4+eWX4fV6UVtbi9WrV+P000+37Rx2oN/JC2bDwHjxtqz8QFsy2t5TKBa7heWRiZ6XwooF\nqqUPs1tFImGSRqyGrWmFagmCdkEdnqPO5XKJu5BiWHPsFlcu6bBbf6Wqa1qha5TwYcXpxMY353I5\nsRY03UtanM0+c+z9IOtWj0xhJAmG3q8PPvgAkUgEVVVVuPnmmzFlyhRs2bLFcl1kOd5++22MGjVK\nNLgmTpyIP/3pT7jllltsPY9V9BvSZR1pRkmXdFtWl2XrJJDUoKbbyuNg9bywdsaYstfEWre0dWYL\nXltdJIi4zOjYRhcJuq9WdxJ6rDkjCRNyi450fTt1bKBbb/Z6vQU1RXjPXC4nLbyuZK3bHZnALhJk\n3eZyOfh8Przxxhu477778P7772Po0KE4dOgQWlpaMGGCeuq9UZx77rm49dZb8dlnnyEQCOC5557D\nyJEjbT2HHeg3pEvQ4xwj0EMbDocl8bYUPwjoq5NA5+W1heFZdfQikEfbrhAwuiY1IldKllBKg5Uv\nEkpSglnQIgHkCQbI3w9aNOxYJOh+mPHE8xYJVjYhi5Oug21Vb+XesDKF0vOh9cwpWesAxFRbuyMT\n2DoPfr8fH330Ef7whz/gsssuQ2NjI95++23s379f9ztqBGeffTYaGxsxY8YMlJWV4cILL7Tt2uxE\nv9F0AYg6nZJzjMDqtrlcDgMGDBAtLgLVRDXrvFE6L72obGC4ktPEKNits5FyjgQ1fVgQ8o0bPR6P\n6QB5HvRKK0o6p5pVpxbxYBW0LRcEQXw+rDqc6Dr1JpPoBf2uGzfulFRwmz9/Amprx2tq63rPwaY0\nC4KAJ554AuvWrcP999+PsWPHWroGM1i6dClOPfVULFy4sMfPrYYvlaVLXlR2lQ+Hw2JYFpsA4Xa7\nbd0qyr3wlLeulp4rJ2IlUHiZVQ2UZ9WRFUzOEiq3Z5RMeDAS9sSz6thkCXmnCdpJ2F1xTS16QG9Y\nndICq1aLwQpcLhc2bdqFpUt3Sto/HTrUBJfLjalTRxp2crIgCYRSmv/1r3/hxz/+MU4++WRs376d\nWwnMLJYtW4bf//73cLlc+OY3v4kNGzaIzm4A+Oc//4kTTjgBhw4dwp///OeCko59Af3K0k0mk2IE\nQ1VVleTfWN2WvMqsJcQSNWVmmbU45VAKAVOCnogEdktOVpGRNudahVqULFA5mfAsTi1rvZgWKFsx\njLz9gHq2n16wFbDMRICoWetA3nom69buncTlly/DCy/8suDfp03Lt3+SZ/zR/NSyEeWRGm63G888\n8wz+8z//E/feey+mTJli22IHAO3t7ZgyZQreeust+P1+XHXVVaivrxeLkQNAdXU1Pv30U3i9Xtx/\n//2YPHmybee3C/3S0mXXERL1qTYn250hn73mF4mEiIU0WMDcyk8wkoTAQktHpKB6ul6fz2fIulVr\n111bO04kF6UWP3QvjOrDgiDY2vadxcaNO7Fy5VaxaPqiRfm4bCtpsAS7FgmetU4yBd2vdDotVl1j\nyc5MtAkbmZDJ8EMoqYIbja83U5Lek46ODlRVVSEcDuOWW275oi7ylgKjxw5UVlbC6/WKEUbRaLSg\nHOOLL75o+3ntRr8iXXpwiKTYeNuqqiqRHAgsAfC6TfCqOOnNWbfT4UTXRcW4ybqgQiz0cumNM121\nartC3dolqK6+0PD2Vq8TkUCLhF34y19eQGPjDrS3dxefOXhwCQRBQF1dt2ZJUMtak1t0tIgUQ6ZQ\n6iemJ2JCzQDgRSYopSyr9a3jhYeRBEItpv74xz/iF7/4BQKBAC644AJceuml+Oc//1kU0j322GPx\nk5/8BKeeeiqCwSBqamoUa+r2ZfQr0iXkcjl0dHRIupyyZEsWqFb5QrXwJiWvOumrbHFuu65Ja5FQ\n0jjlRJxI8H/2SCRPnnZEJdC983g84jxI/mCdiVYqYNECtHLlNolWCagXP9eKNWWtdUAa32yH5MQ6\nPHnPn9nQNZojTyc307dODpLoPB4PKisr0dXVhfb2dlx66aWYN28eWltbsX//fgwaNAhnnHGG6fuj\nhPfffx8PPPAA2tvbUVVVhe985zt47LHH8P3vf9/2cxUT/Yp0aWsGQDPe1sh2n6C2tSYHHYFIkrU4\nrVyXnhYxvKB6logTCWrHHed+v6wsJ3FKWAHJIWyLb/kCRIvYxo07sXr1DiQSHvh8KcybNwG1teMU\n9WG5h19r66wHzc27RY3b601i9uwxqK+fIBZaN5osoXRP7EyCYSUntmEoS8C009HTuFJt3vIC47t3\n78ZPf/pT/PjHP8ZVV10FQRAwZcoUzJ07V9f1mMH+/fsxduxYfOUrXwEAXH755dizZ49Dur0JiqeN\nRCKidUsPtd3xpQQiV1bv4xEda9F5PB5dFpNcSzRK3ko63XXXTcWhQ02S4tuDBy/GtddWiwuFFYuO\n1bLVZApBEPD883uxdOlOtLZ2SwOHDjXB43Fj6tRRBfow6cLsAmRm68yCp3G3ty9BKBRCXd14QxYn\nO0/5PTGS+aUFVnJKp9Ni5TXyUfB2E1OmjMD06aMN7Sbk7XPi8Thuv/12HDx4EE8//TROPPFES9dB\neOeddzBr1izx762trbj77rtxww03iJ+dffbZuPvuuxGLxUTtuC8mP2ih30UvUEhTOp2WCP7k3S9W\nCJhaPKVSURMl/ZUdm9dt1uq8E4kEnnvuRTzyyF4kkz4EAmnMm1eN6dNHi3MEjFt0Ziy5Sy65G1u3\nFhacJ686AEkmHetApPv217+2YMmSFwu2zr/8pT5L7pJL7sLWrfcWfM7OQe2a1YrCUAQFWYl2pjTr\nySpTijbRig2XW7derxcHDhzALbfcgvnz5+Oaa64pWuJBNpvFwIEDsW/fPknHXgC477778Oijj8Ll\ncmHYsGF46KGHbE8nLjb6laW7cOFC/OMf/8CwYcNQXl6O119/HcuWLUMoFBJ1TjMdG+RgQ8D0xPKq\naYi8GFPaFtoZqwlI42Ivu2warrhiRsExJC+oZdPx9FezpQaV9GVWGiCd3OVySWpi0PwmTRqOO+6I\nY/36xUgmvQgEMliwYCJqa8fpuifRqPnebEq/bTablTQMzV9rQkxptrqb0Hu/9USbyFs30W6Cxk6n\n07j77rvxt7/9DU888QQGDx5sas56sWXLFpx++ukFhAsAixcvxuLFi4t6/mKjX5Huww8/jD179uD6\n66/H4cOHUV1djVmzZuGMM87AiBEjMHr0aLHiEC8aQWvbbzYEjAe5/krOFXr4c7mcWFmf3baaeVHN\nhDxp1Uhgw4foHGaKrKtJA2ryipzoLr98BmbOnCax6Do7OxXjh6WWHF+G0CtP8EAx4+zCqUZ0eonY\njpoJSokmNC+S5RYtWoSPPvoI//znP1FdXY1Vq1Zh0KBB5m6IATzxxBP43ve+V/Tz9Bb6FekKgoCu\nri5cc801aGhoEBtFvvPOO9i7dy/Wrl2Lv//97/D7/Rg2bBhGjBiBkSNHYsCAAZLQIZ4+V0xNmG3x\nI+/HRVtr3ouq1cNMLlNYCXmSW3Q0byqP6PF4kEwmxRoHerPplLzqc+dWi7WR9czbSPwwWyKxrKwM\nixZNRXu7Nc8+gfXwyy1QvRl1SrKOlcLlWqAFjnYT2WwW5513HlKpFEaMGIH29naMHz8ejz76KKZP\nn27beeVIJpN49tlnsXz58qKdo7fRrzRdPcjlcujq6sL+/fuxd+9evPTSSzhy5AhOPfVUXHTRRRg1\nahS+8Y1viCmv1G6anBZKjhIz82CdFGr1DKTZYynMn1+NadNGq2arkeWsNwvOCNiQJ3mdW73ZdOz9\nYwuB+/1pXHvtGEydOsrWZpM0N4pnZiuYAcC2bfvw8MN7kEh4EAxmsHCh/lbqQHf5RasJFEr3j85B\nNZ6LqQu/9957uOmmm1BTU4Obb765YKGwM8tMjqeffhqrVq1Cc3Nz0c7R2/jSkS4P2WwWBw8exN69\ne9HS0oJXX30VnZ2diEQiOOWUU7Bq1Socf/zxkhfCSpEaVqbQIhaeZ/2005bgvvsmiw0beUWlgW7L\nSm+0hBbU6g6ofUfN0SSPSihGVwte9Sv5bkJpfnrih9nyi3YVR5KPTXIPzdVKfDOBXTypPsJDDz2E\nP/7xj1i5ciXOO+88267j6NGjmDt3Lt58800IgoD169dj9OjRBcfNmjULdXV1ktTe/gaHdDlYsmQJ\nHnnkEcybNw9VVVXYt28fDh48iOOOOw4jRozAqFGjcMEFF4gZYpRtxYtGYFEs7z6NzUZTUIyyPFpC\n77ZfPm825tZqbQB5DQIqhwhALHpOJGJnIoLe7hN660sA3b4Bu61yXvQAb37sQqvXEOBlwx0+fBjX\nX389Ro4cidtvv12UaOzC1VdfjYkTJ+Laa68VI4zkWWuRSASDBg1CW1ubpJtLf4NDuhy88sorOP30\n08UW60D+QT1y5AhaWlrQ0tKC/fv3IxaL4eyzzxZliSFDhkgC1llrhAjXaEGTmppl2LXr7oLPx4+/\nDZs35+slsMkTSsQit+a0ohHY75GDr5jEwmaryWUJtYVMbWw7+8HJ9eFMJiNutWmRMxsNI4eZwjp6\nSl/Sc8EuQoIg4LHHHsMjjzyCBx54AKNGjbI8fzk6Ojpw4YUXorW11faxSxH9ypFmFy688MKCzwRB\nwNe+9jXMnDkTM2fOBJB/Od58803s3bsXv/nNb/C///u/KCsrw/DhwzFy5EhcdNFF6OzsRCwWw8kn\nnwygO/xJ70uq17uvtd03Eo1AcgR9bnfrd3lGGesok2dcqSWZKC0UxXA40QJFWj8tcIC0fx5gvqKZ\nmnWrd35ajjr63e+//36ceeaZ+L//9//i61//OrZt2yZej91oa2vD8ccfj9mzZ+PVV1/F8OHD8etf\n/9rWko+lBMfStRFU82Hfvn3Ytm0bnnjiCXz22We4+OKLRVnirLPOEhM26CVVszZ5mu6QIU1YtmwC\nJk4cXpQi66lUSqyyxpufXcWujVrOerb9RDDFSERQ0oV58zOqD1stG6kGNv3d7/cjHA7jtttuQ0tL\nCz766CNUVFRgzJgxeOqpp4riJNu/fz/GjBmDPXv2YMSIEbjppptQWVmJu+66y/ZzlQIc0i0S6urq\ncMopp+Duu+9GZ2en6KR7/fXX4Xa7cf7554tEfNxxx0leVvkLunnzHqxZ88IX3v0UZs8ei+nTR9va\nIRfgpx3zttVmOyIUI8uOrX1B7X4A+xcKtqOtkXuutVCwOwoqPWoXeAvF559/jp/85CeoqqrCr371\nK1RUVKCtrQ1vv/026uvrbTs3i48//hhjxoxBW1sbAGDXrl2499578Ze//KUo5+vrcEi3SIjH49w2\n8LlcDtFoFAcOHEBLSwv27duHDz/8EF/72tfEuOHzzjtPLLRC1jCRRiaTKcp232hKs9yJoxbkz273\n7Q5f4yV+yOdnx0JhZ0RFT+8oqOfc5s2bsWzZMtx5552oq6uz7fkZPHgwKisr4Xa74fV6sW/fvoJj\nqqur8dBDD+HMM8/EHXfcgVgs1q9jcdVQ8qTb3NyMm266CZlMBnPnzkVjY2NvT8kwcrkcDh8+LDrp\n/va3vyGZTOLcc8/FsGHDEIlEkEwmMXv2bFGasCNTDTDn3efNX05yAEQHYrEWCr29xMx4++24L2pz\nl2u3ZuKblcC2zyE5YcmSJUilUvjNb36DY4891rZrAYAhQ4bgwIEDquO++uqrmDt3LpLJJE4//XRs\n2LChKDV3SwElTbqZTAZnnXUWtmzZgoEDB2LEiBF4/PHHcc455/T21CwjmUziD3/4A376058inU7j\n3HPPBQAMHz4co0aNwvDhwxEMBk2HhJmJudULshApw0m+UFiJLQXsiahQ8/YD+WfL7kQEQL92a0Yf\n5rXP2blzJ2677TYsXrwY3/72t4ui2Q4ZMgT79+8XSy46UEdJRy/s27cPQ4cOFQtwzJo1C08//XS/\nIF2fz4d33nkHt956K6699loIgoBPP/0UL730Evbu3YsVK1ags7NTrCsxatQoDB06FAAknnT5lhWA\nJObWqHdfq7caS4hlZWWS2r5aBeCVOl0Q5LrwCy/8TazDy5uLGnjefkrhBfIWJiVr/P/2zjWoqWsN\nw+8mAYlB0GmhlIRRRikQRRQCigdM6g056vE6U8UK5SLazjjipfVYO+OFcVBBWkbH++ioVewfrVbU\nsVRFvARE8VLbSgVjAwgIqBCCEJKcH5y9TSCBJCSQ4Hr+Bdlrr2yZb639re97X3OrETrO3ZTKPf4i\nGQAAEHRJREFUBFr2UvtZL18uRlTUBL3PkKIo5mdDhgxBa2srNm3ahMrKSpw/fx4fffSRyXM2Foqi\nMGXKFLBYLCxbtgxLly612r36A3YddCsqKnSUiPh8vk26f5pLx9PdDz/8EDNmzMCMGTMAQEdX4uDB\ngwZ1JWjFq47mm6a+7nfnraYdEGkbbpqutBEMaQ9od6tpv+5zuVxcvnwb69Zd0zsXU9p36XnoE5Hp\nqqzOlNSO9u7W2EXO0LOmqHZBcvoZ0od8tJ7uzp07cezYMaZ0MT4+3moSjDQ3b97Exx9/jJcvX2Lq\n1Knw9/dHZGSkVe9pz9h10LXEq1JCQgJycnLg4eGBR48eWWBWvQeLxYJAIIBAIEBiYmInXYmTJ0+i\nuroaXl5eYLPZuHfvHq5cuQIulwuVSgW5XM6M0zHI6cOQt9revesRERGkIyxuDB13mx1rc+lXZToA\nOjo6wsnJCQ4ODl34vOm36DFEVzW9XUlyatcPGxJJAmB23a0x309bXIfL5TKLhkgkwpw5cyCVSnHg\nwAHU19cjMTHR6HubCi1k7u7ujrlz56KwsJAE3S6w66DL4/Egk8mYzzKZjGlCMJb4+HisWLECsbGx\nlp5er0NRFAYNGoRPP/2UsZ6WSCT4/PPP4ebmhujoaCxZsgQajQajR49GSEgIxo8fD09PT518oKGd\nnCHtW4WCYmzrjV0IDaUpKOqd0wUdVOiApp26UCj038dYix5zGxG6kkXs2CRBK5o5OzubnHfuSmdY\n39wfPnyI1atXY/Hixdi2bZvVd7c0CoUCKpUKgwYNQlNTEy5fvoyNGzf2yr3tFbsOukKhEH///Tek\nUim8vLzw008/ITs726QxIiMjIZVKrTNBG4DD4SAjIwOzZ89mdowtLS0oLi6GRCLBpk2bdHQlwsLC\nMHbsWKbRQHsn5+jYovceXK7GpF79rtIUtIhPV4pdGo3GoAauk1Mr86ptaAHoSn7RHOhWYNqqqbm5\nGUqlknkmtH+e9iFYbm4B9u+/hpYWR735aEOdiAMGKCGXy8FitdvntLW1IT09HdevX8fRo0ctbgip\nUqkgFArB5/Pxyy+/dPr36upqzJ07F0D7c128eDGmTessjk94h10HXTabjd27dyMqKgoqlQqJiYl9\ncogmk8kQGxuLmpoaUBSF5ORkHW+nviQoKAhBQUHMZ4qi4OzsjPDwcISHhwPQ1ZXIy8vDzp07oVAo\n4O/vzxzS+fj4IDlZhLKyb/D8+Ts/s2HD1mHpUrFJkn9dWcBPmTKOUewypKPbLrDdWQN32LB1SEqK\nNLhjp3WReyq/aIiOfmLawVw7P3zhQj42bLgBqfRdnWpZ2X+hVqvx739HgqIovTrDw4atQ1xcOJN3\nfvLkCVJSUjBz5kxcvnzZomVtNFlZWRAIBIzha0d8fHxw//59i9+3P2PXJWOWQiqVYtasWWbndKuq\nqlBVVYUxY8ZALpcjJCQEP//8s11XUWjrSkgkEjx58gQNDQ14/rwePN5kDBnCB5cLJCVFYNKkUJMq\nEQyJ+ISHf4szZ1YaXQamrcPb7m4rZnaLhpTMrCFQY2qqwpBynFj8DbKzV2vthiU4eDAfzc0sODq2\nYunSCPznP5Og0Wiwf/9+RnuWLie0NOXl5fjiiy+wYcMGZGZm6t3pEkzHrne6toKnpyc8PT0BAC4u\nLggICEBlZaVdB102m83skuPi4iAWi+Hm5oasrNUoLy9HQUEB6uvrce7cc7x4UYJx48bB398fDg4O\n3VYiGHp15nBUcHFxMXrHHB0dYfDQTFughj6Ms7RADaCbqjDWmcNQvratbQBcXFyYhUIsFiIysl18\n6eXLl8jJyUFOTjP27dsHkUiEK1euWNWUcdWqVUhPT0dDQ4PV7vE+QoKuhZFKpSguLraKRF5fweFw\nsH37dkycOFFnZ6hWq1FaWorbt2/jxIkTenUl3N3doVLp2oEnJExAWZmuBbyPz3/x1VeTrdaxph3M\njVVa09eppj2+uZUJXSnH0Wpw9OLFYrXbqqtUKhQWFmL37t2or6+HXC6HSqVCamrnNwZLcP78eXh4\neGDs2LG4du2aVe7xvvLepxcWLVqEvLw81NXVwcPDA1u2bEF8fLxZY8nlcojFYnz33XeM/KOxvH37\nFiKRiKkXnT17NtLSOr+C2jIddSUKCgpQWVkJT09PCIVChIWFISgo6P8arudw9uxfePu23R4nOVmE\n6OgIi7zy91TJTF+nmnYQBsA0l9CatKZgSDkuPX0Spk//V6ea4aqqKqxcuRIBAQFITU2FWq1GcXEx\nampqmEMsS/Ptt9/i+PHjYLPZePv2LRoaGjB//nwcO3bMKvd7n3jvg66lUCqVmDlzJqKjo5GSkmLW\nGAqFgrGLj4iIQEZGBiIiTCv0tzU66kpcvXoVMpkMvr6+SEpKQkhICIYOHco4cPSkXdgY+UVz0O6k\nUyqVTG64OwH4rtCXj542LVzHPoeiKMY6h/5bsMT3MXWBz8vLQ0ZGBsnpWgiSXrAAGo0GiYmJEAgE\nZgdc4J1PFZ1vtLQwSV9AURS8vb3h7e0NFouF7OxsRkC7sLAQ6enpKC0thZubG7MbFgqFcHJyYnKv\nxhzSdexYs+RJPu1NplQqGbsi7R2xvjl216mmnY+m25ubmpqYTsG6ujqsXr0aHh4eyM3Ntah9jbOz\nM65evaqzwN+4caPLBd6aZpTvG2SnawFu3LiBiRMnYvTo0cwfZ1paGqZPn27SOGq1GsHBwSgtLcWX\nX36JHTt2dH+RHSGXy9Ha2tppMdFoNDq6Enfu3GF0JWgrpE8++UQn0AHvDunooGVpJTN6bsbkbvVV\nS2jP0ZAIUUetXgcHB+Tk5CA9PR1bt27F1KlTrRrwFAoFRCIRjh49CoFAYLX7EN5Bgq4N8ubNG0RF\nRWHbtm0Qi8UmX99dQbs9oK0rIZFI9OpKyOVyvHr1imkI6IlDsz5oiURzc7fd6frSjSr0YtHQ0MBI\nk2ZlZWHIkCFmz92YufXnBd6WIUHXRklNTQWHw8HatWtNvjYzMxN3795FY2Mjzp07Z4XZ9T4ajQaN\njY0oKirCzZs3cfLkSchkMsycORPBwcEICwvDqFGjmFQAXZdrjjB4dx1xPfkO9NxaWloYrYyYmBiM\nGDECBQUFWLt2LZYvX95rbbw9XeAJptM7/7OEbqmtrcXr168BtJ+M//rrr3oNMrujvLwcFy5cQFJS\nEvrTekpRFFxdXTFp0iTU1NTAx8cHjx8/RlpaGvh8Pk6fPo358+djzpw52LhxIy5evIhXr14xAbOl\npQWNjY1obGyEQqFgrNM7PiOlUsl0Xw0aNMjidbAqlYpRYnN1dcXAgQMxZswY1NXVISAgAFu3boWX\nlxdaWvS3XFsaNzc3zJgxA0VFRb1yPwI5SLMZXrx4gbi4OKjVaqjVaixZsgSTJ082eZz3oaA9LS0N\nXC6Xed338fFBTExMJ12JzZs36+hKhIaGIjg4GCwWS+8BGJ0KsLRXGdBZZ9jBwQESiQTr16/HypUr\nERMTw3yf6upqDBgwwKL316a2thZsNhuDBw9mFngiUtN7kKBrIwQGBuLevXs9GsNSBe3GeF71JS4u\nLnp/bkhXoqqqChKJBNevX0dmZqaOrkRYWBjq6+uhVCoRHBwMiqLQ3NyM1tbWHguX02jb5wwcOBAt\nLS3YunUrSkpKcObMGfB4PJ3f74nguDE6IJZa4AnmQXK6/QhLFbQb43llz9C6EleuXMHevXtRW1sL\nsVgMX19fhIWFITQ0FK6urp1sckw9pOton8Nms3H//n2sWbMG8fHxSEpKsnjutj/qgPQ3SNDtp/Sk\noP198byKi4sDh8PBjh07oFarUVhYiNu3bzO6Ej4+PsxuOCAggNFxMKYcjN7d0qaZbW1tyMjIgEQi\nwb59+zB8+PBe+Y5z5szBihUryE7WhiDphX6Mua/E74vn1aFDh3Ryt9OmTWO0YNVqNZ4+fco4cDx8\n+BAsFgtjxozR0ZVQq9XMoRxdDka3Djs5OYHD4eDPP/9ESkoK5s2bh0uXLllFglEf/VEHpD9AdrqE\nTrx48ULH82rXrl1m2a+8fv0aSUlJePz4MSiKwuHDhzF+/HgrzNj66NOVqKiogKenJ3NIp1KpUF1d\njenTp+P169cQCoXw9fVFbW0tvv76ayxYsABeXl69Mt+e6IAQrAsJuoQu2bx5M1xcXLBmzRqTr42L\ni4NIJEJCQgLa2trQ1NQENzc3K8yyb6B1Ja5du4bMzEyUlpZi4sSJ4PF4GDp0KHJzcyEQCODu7o47\nd+7g7t27KCsrYyQmrYUldEAI1oOkFwg6WMrz6s2bN8jPz8fRo0cBtOvz9qeAC7zTlXj69CkCAwMZ\n088HDx7g+PHjWLVqFWbNmsX8vinuGuZiKR0QgvUgO12CDs+ePevkebV+/XqTx7l//z6WLVsGgUCA\nBw8eICQkBFlZWYyoT39CpVJZPU9rrGu1pXRACNaDBF2CVSgqKkJ4eDhu3bqF0NBQpKSkwNXVFVu2\nbDFpnCdPnmDhwoXM57KyMqSmptqMB11vkZ+fDxcXF8TGxpptK0WwDUgbMMEq8Pl88Pl8hIaGAgAW\nLFhgVvOHn58fiouLUVxcjLt372LgwIFWE+62ZSIjI60qgEPoPUjQJVgFT09PeHt7o6SkBACQm5uL\nkSNH9mjM3NxcDB8+HN7e3paYIoHQJ5CDNILV2LVrFxYvXozW1lYMHz4cR44c6dF4p06dQkxMjIVm\nRyD0DSSnS7ALWltbwePx8Mcff8Dd3d3k69PS0vDjjz/CwcEBgYGBOHLkiFVFZayBVCrFrFmzSE7X\nziHpBYJdcPHiRYSEhJgVcKVSKQ4ePIh79+7h0aNHUKlUOHXqlBVmSSB0Dwm6BLsgOzsbixYtMuta\nV1dXODo6QqFQoK2tDQqFopOyV19y6dIl+Pv7w9fXF9u3b9f7O4sWLcKECRNQUlICb2/vHqdqCH0H\nSS8QbJ6mpiYMHToUz549M9ug8cCBA1izZg04HA6ioqJw/PhxC8/SPFQqFfz8/JCbmwsej4fQ0FBk\nZ2cTVbB+DNnpEmweLpeL2tpaswNuaWkpfvjhB0ilUlRWVkIul+PEiRNmzycrKwuBgYEYNWoUsrKy\nzB4HAAoLCzFixAgMGzYMjo6OWLhwIc6ePdujMQm2DQm6hH5PUVERJkyYgA8++ABsNhvz5s3DrVu3\nzBrr999/x6FDh3Dnzh08ePAA58+fR2lpqdlzq6io0CmB4/P5qKioMHs8gu1Dgi6h3+Pv7w+JRILm\n5mZoNBpGiMYc/vrrL4wbNw7Ozs5gsVgQiUQ4ffq02XOzthYDwfYgQZfQ7wkKCkJsbCyEQiFGjx4N\nAEhOTjZrrFGjRiE/Px/19fVQKBTIyclBeXm52XPj8XiQyWTMZ5lMBj6fb/Z4BNuHHKQRCCZy+PBh\n7NmzB1wuFyNHjsSAAQPw/fffmzVWW1sb/Pz88Ntvv8HLywthYWHkIK2fQ3a6BIKJJCQkoKioCHl5\neRg8eDD8/PzMHovNZmP37t2IioqCQCDAZ599RgJuP4fsdAkEE6mpqYGHhwf++ecfREVFoaCgAK6u\nrn09LYKdQLQXCAQTWbBgAerq6uDo6Ig9e/aQgEswCbLTJRAIhF6E5HQJBAKhFyFBl0AgEHqR/wFy\nH8SlmTUx3wAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x1063c1690>"
]
}
],
"prompt_number": 28
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"normal = np.array(fitPlaneLTSQ(xyz))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 29
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Need a point with the normal vector to compute the plane\n",
"pt = np.array([5, 5, np.mean(xyz[:,-1])]) #Middle of the point cloud.\n",
"d = -pt.dot(normal)\n",
"#Compute the plane\n",
"xx, yy = np.meshgrid(range(10), range(10))\n",
"z = (-normal[0] * xx - normal[1] * yy - d) * 1. /normal[2]\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.gca(projection='3d')\n",
"ax.plot(xyz[:,0],xyz[:,1],xyz[:,2],'o')\n",
"ax.plot_surface(xx, yy, z, alpha=0.5)\n",
"fig.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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akkUhXX+3XM93yZIrcPJkNx5//Nvo73fB53Phkkumo75+ukKqkiQpcalECiBz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\nd2Dx4ovx9a9/FSzLKlmR2lhWsluiv1+zRKy1bq2E2qUiYpL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slrypxdaXEpDgyuT7uAId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"text": [
"<matplotlib.figure.Figure at 0x106074410>"
]
}
],
"prompt_number": 30
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 30
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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