{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Implementation of Spiral Architecture" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Spiral architecture has been introduced by Sheridan in \n", "\n", "- [_Spiral Architecture for Machine Vision_](https://opus.lib.uts.edu.au/research/handle/2100/280), PhD thesis\n", "- [_Pseudo-invariant image transformations on a hexagonal lattice_](http://www.sciencedirect.com/science/article/pii/S0262885600000366), P. Sheridan, T. Hintz, and D. Alexander, Image Vis. Comput. 18, 907 (2000).\n", "\n", "The implementation with hyperpels that we use in the following is presented in \n", "\n", "- [_A New Simulation of Spiral Architecture_](http://ww1.ucmss.com/books/LFS/CSREA2006/IPC8173.pdf), X. He, T. Hintz, Q. Wu, H. Wang, and W. Jia, Proceedings of International Conference on Image Processing, Computer Vision, and Pattern Recognition (2006).\n", "- [_Hexagonal structure for intelligent vision_](http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=1598543&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F10652%2F33619%2F01598543), X. He and W. Jia, in Proc. 1st Int. Conf. Inf. Commun. Technol. ICICT 2005 (2005), pp. 52–64." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Inizializations and auxiliary functions" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "from numpy import fft\n", "from numpy import linalg as LA\n", "from scipy import ndimage\n", "# from scipy import linalg \n", "from scipy import signal\n", "import matplotlib.pyplot as plt\n", "import matplotlib.cm as cm\n", "\n", "import os" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# ALPHABET = \"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ\"\n", "ALPHABET = \"0123456\"\n", "\n", "def base7_encode(num, alphabet=ALPHABET):\n", " \"\"\"Encode a number in Base X\n", "\n", " `num`: The number to encode\n", " `alphabet`: The alphabet to use for encoding\n", " \"\"\"\n", " if (num == 0):\n", " return alphabet[0]\n", " arr = []\n", " base = len(alphabet)\n", " while num:\n", " rem = num % base\n", " num = num // base\n", " arr.append(alphabet[rem])\n", " arr.reverse()\n", " return int(''.join(arr))\n", "\n", "def base7_decode(string, alphabet=ALPHABET):\n", " \"\"\"Decode a Base X encoded string into the number\n", "\n", " Arguments:\n", " - `string`: The encoded string\n", " - `alphabet`: The alphabet to use for encoding\n", " \"\"\"\n", " base = len(alphabet)\n", " strlen = len(string)\n", " num = 0\n", "\n", " idx = 0\n", " for char in string:\n", " power = (strlen - (idx + 1))\n", " num += alphabet.index(char) * (base ** power)\n", " idx += 1\n", "\n", " return num" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def rgb2gray(rgb):\n", " r, g, b = rgb[:,:,0], rgb[:,:,1], rgb[:,:,2]\n", " gray = 0.2989 * r + 0.5870 * g + 0.1140 * b\n", " return gray" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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KpYJms4lYLIbR0VEMDAygUChgdHRUclSyr7u7u/H7v//7mJ+fx5/8yZ+0PY87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\n7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pS0oupQd3cjr8HIg+Bx0+k0Ll++DLfbjb6+vorj6Q2E+rd6U6enp7Gzs4MzZ84IYGe1\nWuH3+9He3o6BgQF0dnZiZGQEzc3NSKVSwkXguZjNZpw6dQrNzc344Q9/iGQyKbtCoVCA3++XeNnl\ncklq0u/34+DgADdv3pTzjcVi8Pl8OH36NAYGBtDV1YVgMCgU7Hg8jtXVVZhMJgQCgQq3mtdLpR03\nNjaira0Nfr9fduBcLgez2YxcLoeZmRns7u7C5XJJlSYVrRiTezweASnZCZzpzuXlZcEpiLMA90Iv\n3hPunuQY0Jiurq4il8vB4/HAZDKho6MDFy5cwLlz5zA8PIyOjg7JoNAw7+7uYn5+HvF4HCaTqUIK\njgVbzKTQc1hfX5eq0ZGRETzzzDPwer2YmZnBr3/9a9y6dasio9LU1AS32w2bzSahmRrCqfRuo0XP\n763HGVityTBFX2/B97/++uvHDiseqHHguJ/l0xsIo9hL/a0aimrhi/446rGbmprwwQcfwOl0Ymho\n6NjZDvV3Op1GNBpFf38/HA5HRYhD7yIYDCIcDsPlciGZTCKVSlVoIpZKh63oFhYW8OGHH6KmpgYu\nl0vox1x4DAXYj5GTNZfLIRqNYn9/X1SmWRrs8/nQ2dmJUCgkGZGlpSVMT08LrqHSjnldmU2gp2Cx\nWNDe3i5kq/X1dQCHgOry8jKKxSLsdrtoL/Jak5bd1taGUCgkRobS9qxevXv3LhYWFiTzQAOsHou7\nrapMNTMzI1kEp9OJM2fO4LHHHkM4HBYspK2tDSdOnJCKSqYzs9kspqenkUgkUF9fLypVaoPdnZ0d\nLC8vSzm2x+PBI488gqeffhotLS24cuWKlF3zuBaLBV6vF52dnQCA1dVVMQ4UeSEP46ihGgfVKPCn\nGt6gaRp+97vfffaNw7e//W0AR2MNatzEv/XAjDr0OV8+Vu34+tiOP/v7+7h16xZKpRLOnDlTEbuq\nxzIaPAb5/tQR1IchahrKZrOhpaUFt2/flkwDvZFSqYTr169LOXR7e7u4w2azGT6fDwBkx1Xd05aW\nFiwvL4tXQjn37u5uWfTBYBCdnZ2w2WwibDo5OVnRhJd5d6beVLSd2QSv14twOAxNO6xo5GtZBs2Y\nXBXQAe71CqWRYLk4CT4AkM1mJWXJNoI0Egz3eEwyS2/fvo3V1VVo2iGvYmBgAJYuJZMAACAASURB\nVH19fUJbJhM2HA4jFAqho6MDfr8fZrNZpPQZym1tbUklKus79vf3BfylbsXw8DC8Xi82Nzfxzjvv\nSG9VsiODwSDa29tFWzSXy8lC93q9wnGoFkJwPqseEin3qmFQhWg4uHbeeuutPy7jUG0Hr+Y1VGN6\nVSODcFTzUIwwCFKez58/X0EcUof+MS5oTTtEzNl63ePxfMJoqe8zmUxwuVyIRqOIRqNiHMrlQyER\nElna2trgdrsrOj6HQiGYzWbJm/M3KzNLpZLsoPv7+0gkEohEImhvb8fBwWFDX4Y7oVAILS0tSCaT\nmJmZkfoIZkeI5PNecELy2lksFvj9fimYIliZTqclvcgOVwSQ+f2bm5ths9kQDAYRDAZFz5FisuVy\nWbwbLliqUKviM6urq0gkEpicnEQulxMdBoYSrMJkaTkZluxBEgwGpaiOWRg1u7OzsyMLkmxIis6c\nPHkSADA+Po4PP/wQsVhM2JcOhwOnTp2C0+lEJpOR1DQrRm02m1w3fdirn+NqKKEaBpUjYpTtKJfL\nePvttz/72Qp9poC/9Tu6ERLL1+qzCPqLarR4q+346mtMJhP8fj/GxsaQyWRE+kzv7qngqPp53K0A\nVKQq1e+qH/X19Th79iwuX74srjJTd8y9Mx1JWuzm5iZyuRxcLpeoXrPCkwIoZ8+exZ07d0RFKp1O\n49e//jVcLheGhoYkRedwODAyMoL29nb09vbiX//1XzE7O4tcLifVnqFQCDabTeTtGB5wgrLv44UL\nF0TnIBqNCqbw7rvvYnt7W9q9MTzhAjWZTMLU9Hq9GBgYwPz8PMbHxxGLxSTkKBaLiEajYlD6+voQ\nCARgMpmwvLyMhYUFJJOHSoZcmF6vt8IgqdwO4hWapsHj8YhHlkqlMDs7i/n5eeRyOcEYYrGY0Ml5\nL/b397GwsACXy1XBU2CWhS3/2A5xd3cXZrMZzz33HDo7O6XxDT0jDn3mTY8z8G81jFANgt6D+DTj\nM9Erk/+rjxthD/d7Dy8GfwPVU6XqbyMOQyAQkIwA27Crxz3qewGQm0bSjOpKG90sk8mEgYEBDA8P\nY3R0FLW192Tb9vf3RY+AYQcXVjabld1JJcFomiZZgp6eHty5cweZTAb7+/u4du0aGhsb8b3vfQ8A\npO6CYNmZM2ekyOzatWt47bXXsLi4iAsXLuCRRx6ReJ8CurW192TkgcMKxoceegh2ux3vvvuuZA4Y\nixeLRXzpS1+C1+sFcBgKcNIDECCQOEUgEBDq+cLCghi0XC4njXxdLpdod6bTaZGPt1gsgsWQ/ciq\nSXpaxBFYDEW+AkloPT09WFhYwOLiItbX1+We8t4w1JqYmBCOh4qxMHzc2dnBysoKMpkM6uvr0dfX\nh+985zvw+XwYHR3FnTt3KuYD5xLnnBpO8BrpPQbgXs+RP9QocHxmjIP6mOodVHuPPg1q9GOUqVCH\nUajAx4nYr6ysiLuoPq8/pv5YvHl0/6udt3oD7XY7vvjFL2J6elokxPhddnZ2EI/HUSqV4PP5UFdX\nh2QyiWw2K/gDd0AAwgPw+XwYGRlBKpXCW2+9JamzDz/8EKdPn8ZTTz0Fm80mi4LdqMPhMP7iL/4C\nfX19+OUvf4nR0VGsrKygrq4OQ0NDsNlsgtxzkahS9vX19eju7kZLSwt6e3vx3nvvIR6PyyLa2trC\n2bNn0dbWhoaGhoru3OQVUJaPknaBQABjY2MiokN59729PcRiMXkvjaOmHaZA2WOT9Q/0BPk5zFrk\ncrkKhmZjY6PUgPT19WF1dRXvv/8+otGoGBnyNDRNQyqVwvLysihENTY2CheCxo4Uc6a5g8GgcEbU\n2gduRvybJCcaBhZ2kTRF42DkZevn7XHHZyKs4NAbBjWsMBp690v/5fUGQnUrqx2Dr21paYHT6RRE\nWaVRGx1XXegMQViRqC4a9bvpz6O2thYnTpzA008/jfHxcUn/eTwehMNhWK1WJBIJmEyHkuzs9zAz\nM4ORkRGYTKaK/gmkgVPVeG5uDnfv3oXJdCjI+k//9E/weDw4c+aMLCQqJ3EXam1thaZp+NWvfoXl\n5WX8+Mc/xle+8hV88YtfhN1ul3JkKkIXi0VpPQ8ALpcLLpcLdXV1eO+996RP5vz8PObn5zE0NISL\nFy+KRgSvoSpDR40LhjVutxtjY2MCUnKhsJKTBhm416CHnktdXZ1wE3hcGlgaBr2uBfEPktGi0Sgu\nX76MtbU1yejQm6DqN+nT5Mqwj6aq1H3y5El4PB6sra3hxo0bFfJvvIf8rWYmVMNAT1FNWdJzUDcl\nzsdPMx64EhSHkZcAfLKoikOP+h819O+73+AOGgqFRGEpFAp9wghU+2zuFFarVSTR1PCIC0eNFXlc\nm82GF154AV/5ylcknuWiJWZQLBYxMTGBxcVFka/v6OgQN50pQZV6TPYelYzq6+uxsLCAX/3qVzCZ\nTBgaGpIdVGXxeb1ePP/887Db7XjppZcwOTmJl19+GbFYDE899RTC4bCAfACkLoG7OEOewcFBWCwW\nfPTRRxIaAIfg3cHBAc6dO4fe3t4KHUl+F4KfAOBwOPDQQw+ho6NDiEvr6+tSKEVOBA3F+vo63n77\nbZTLZTzyyCPweDxSBFYqVbbyI62dalZNTU1oamqC3++XHhKRSASadtjb49q1a5iampL7Rv7D+Pi4\nvEe93wSJKZ7La5DNZoWopZ9XRpkJVduThoNrRJ1jekm5P1rjoB/VFqLelVdTgkd9+WrHMsIi1BTj\n3NwcFhYWEAgEKtSKjvJUAIhKM9WfeMMoILu7uwu/3y+xMiv4ONHU7whAuPdNTU0olUoSdnCXm5ub\nE4CO+ggcnOSnTp3C/v4+rl69KvTimzdvCn9gcHBQPAFVnMRsNuOxxx6D3W7Hm2++icuXL+PatWvI\nZrO4ePEihoeHpbnMxsZGhYGgt1ZfX4+uri54vV6Mjo7io48+QjabRUNDAyYnJ6W/RzgclmIw4hn6\n8FDFR7xeL+LxOMbGxjA3NyeZB1aYlkqHUvNXrlxBU1MTzp49K5qY9B5oEOiWqx4EAWX+TXzCbDaj\nra0Nq6ur0iuDYRAJYeq8ZFNldc6wb8Xdu3eF5KXeb5UhS6NAr0EVrgXu4Qz8TUYu56RapXnc8Zkx\nDkYnzptF9F6POaiGQT1Otd1c/a33RNTnGO8NDg5ifHxc2rjRQle7yOpn1NUdNr2NRqPI5/OwWCxY\nXl7G2NiYpL/a29sRCoXQ1NSEgYEBSfHpv4f6m7FnOBxGc3OztFNLJBKidqyXLmd8TaAwn8+LHkJN\nTQ3u3LkjOoY9PT2yMLmbsXSZ0nPt7e146623sLS0hNdeew2FQgEjIyOw2+0ol8uSNlVrFNRdrKur\nC9vb27hx4way2SxKpRLm5+flOKdPn4bVapXrTUOjov80YoFAAFarVWjoc3NzItSq9njY2NjAlStX\n4HQ6BahUqxoBVLThIxlpe3sbq6urMJvN0riGHAiSm3iOhUIBZrO5InPAcLRUKmF1dRVNTU2i+zA2\nNoa+vj68/vrrFcpXalaCYYT6o5a2cy7TGKheA72u/7+9d49tLDvvBH+XEiWRIkXqRb0f9ZBUerTq\n2Y+qdnfb7XanbXectoNsvMHAxiTZLDKLySCbYJMMEKyzCwSDATYYzD8DTMabZGYT7zjjJI4dd9vV\n7kf1q7repVJJVarSkyVRpCSSIimJevHuH9Tvq4+nLlVVGaerGqsDEKJI3nvPPfec3/m+3/ci0Hxq\nwKGYpcApbl4vfk4wc8Hov04qRzGeYDdpI5fLobGxET09PQXMs3lup79MbrqxsSEM9+joKKLRqOz2\nnFDz8/Noa2uTAKLduBT2meHAGxsb6OzsxPj4OKanpxEIBFBTUyO1HVjX0bZtyeFAZyQgvzsuLi7i\n7Nmz8Hq9Eh4NQKpQEWj0zh4IBPD666/j1q1b+P73v4+FhQWcOnUKzc3NcLvdEvLOHZmWHgaoPfXU\nUwgEArhw4QJmZmakbgfTtvf19aGzs1MmNuMXOG7a1Ov3+6VAscfjweXLl6U6OIO/tre3MTMzg9On\nT2Nubg6nTp0SAOG4Ly8vC8lIcb2qqqoAFFisaHZ2VqJtubCpiulK6drUGY/HAUD69uMf/1j8J/Sz\n1hwDSUz+pelYE5DadKr5BjO5y6cGHHbjAfSC1n/5nbm7avGtGA9hqin364Nt27h16xba29tl8gAQ\nDiCXy4lPQVVVVUFgEADxUOzo6ACQDwMnX6BJJQaOcRI53ZvTfZDFB4AXXngBKysrmJ2dFfs/xeZs\nNivxARxHOvswS/TGxobkq2xtbcWxY8fg8/lkTKkjk1sIBAI4fvw4/H4/fvjDH+LChQt46623EA6H\n8cUvfhF9fX2yQzKjMtOrUWSvqKjAiRMn4PV6cfbsWYyNjQk5eO7cOSwuLqKsrAzt7e0FKdP0eFDS\nYtVxAlk2m8XFixfFzEgPxrKyMkxNTUklskOHDqGlpUXGi8Qq75MqBcGOO3UsFsP09LSkhtOZrNra\n2pDJZLC4uCgRnVQL6JzGhTs9PS3PwwkYtIWDqiHvg/ORUgKfL8+tVTvOK21Of5D2yHNImhKE0yLW\n4ED1wklycBLJnc65GyiwbW1t4ebNm/ja175WIDWQmQ6Hw5LpqK2tDa2trQUJPV0uF+rr69He3o5Y\nLIZIJCLA4PP54PP5YFmWxBFot2Kn/pvjVVlZiX379uHKlStob29HTU0NpqenMTExIS7SJAQ58anD\nMvHt0NCQ1HLc3NzE1NQUzpw5I26+7AdrT1LMzeVyCAQC6O3tlUV77tw5DA8PS0Rle3u7gAqfoc6o\nzFwQhw8fxr59+/D+++9LKjwAmJiYwD/8wz/g85//PPbv318w9gxzd7vdEqOxubkJj8eDlpYW9Pf3\nY2xsTHZ8ADLOfr8fyWRSiMwXXngB1dXVwmPw2du2XVBnw+/3Y35+HslkUhLwrq6uAsirOJ2dnTh4\n8KDk95yfn8fly5clOxWtQZon2NraktgPLnjNMxAgeI8ej6dAbdGqGsfUVCm0qvypAgfAeaE6idLF\npIv7HW/yFPq3u0ksN27cQDKZRDwex8WLF9HT0yN6J0ut0e4/Pz+PmpoaBAIBOS8ZbeqsXBQky+gU\nA0AmOYB7gM5JDeJ4kAdhgBCQF1nHxsbg9/sRCoUKxHlOmJKSfEbtw4cPw+PxSExHLpfDlStX4Pf7\n8dWvfhVtbW3C/jN8W6c+Ky8vx+DgoESC/vjHP8b169exsrKCz33uczh69KiI+hSdubNT5KeD1/PP\nP4/W1lacO3cO4+PjKC0txfj4OJaXl3Hq1CnJVcF7JmfARCzkNzweDzo7O/HUU0/hpz/9aQHRR+sE\nczKQ/+nv70d3dzd8Ph88Ho/k3GBuh8XFRUnWsri4iMnJSSSTSQQCAYlNGRwcFPdyAi5VOVbRohSn\nK36xngkXvSYgtcTA91QpbNuW+BNKDKalwomfe5j2yOtWOOnvTgu/2Dnu9x64NxfDbuHdbJcuXZLk\nIVNTU4hEItjY2IDH48HCwgIWFxfFfs5cjKaEwp1BO9/wIbOgCgBRKUzCczcJoqSkBC0tLcjlcpic\nnJQdx+VyIRqNYmRkBB6PR3JTMGeAHu/GxkZJC0/XXQbnbG1t4Td+4zckaIx6M6M/6SNQUVGBnp4e\n+Hw+lJeXi3rx5ptvYnNzEydOnBDfBBac1TyGx+ORvAuHDh1CJpNBOp1GNBoV5p/OW4cOHUJ9fb1I\nJHRH1mQegbavrw8TExMYHx+X+yUwk3AtKytDOBxGMpnExMQE+vr60NLSUrAAaWlixart7W0J0+7s\n7MQ3vvENDAwMoKurC0NDQ3j77bclkxgBhf3Su73mIli8yMkDUqsWVMuoilIqM60Umm/Q0uan2pT5\nIEQfWzFC06npGAgeW0xqAPKDPT4+jv7+frEEUCynaOj1eqW+Ah+o2VKplAROEZS4gDc2NiT+guKp\n0/0XU7GYw8HlcmF2dhY1NTXw+XziAbm8vIyJiQl0d3fL9el1yF3Lsiwp3MMSfXQSGxoawocffohn\nnnmmYDFZliWBRjqGIxgM4sknn4TX68WPf/xjzM3N4a233kI8HsfJkyfR3NwMn89XYOok0UinKY/H\ng8HBQVRVVeH8+fO4desWNjc3kc1m8dFHHyEej+OJJ55AR0fHPSQncLfEPc25AwMDiEajooq0tLSg\npqYGLS0tiMfj4ifCHXxhYQFdXV3o6upCTU3NPYBDC4921KNJmibTyclJjI6OSrQmo1Zra2vF5Zvl\nCLWjl1PoNa9rWin0HNZRy+RYdNKghwUE3R65tcJsxQhHp989zLmL+SY4nYd26kOHDknyUk5eThpK\nIwx40hGGQH7hZDIZZDIZmcTUGan/aq9AntPsk364Jm9CB6O5uTk0NzeLR142m5UycLdu3UJvby/c\nbrfkLqT0QvBpamrCwMCAEHaMNjx9+jTKysrQ3d0Nr9crocpMIUfViCDT2NgIj8eDra0tvPfee5ie\nnsb777+PjY0NPPvss9i3b5+cg/4CnNyUampra0XH9vv9uHnzJpaXl7G+vi7SjdvtRlNTk0guFKUp\nxgP5Kll9fX2YmprC6OgoSktLUV9fLy7buVwO4+PjuH79OiKRCJLJJObn57GysoJYLIaOjg50dHSI\nqzWQd0mn/0JlZaVIZNvb+UI1b731Fm7cuIFEIiGcSkVFBaqrq9HZ2VlQMIc7uxllqV9aeiAwEOh5\nv5qENKUHPt/d0hzs1h6L1PSAs/+BEzjoY/S5zGOdnJucSEndD342MTEB27YlsQoA0V1ZmZk+/aur\nq4hGo5ifnxfnHZ4/l8uJ2MtdgrZzEl0k+NgIOk6qj2m9oTidyWRkwjIfQTabxXPPPYc33ngDk5OT\n6OnpkV1HL0jbtiU4ixaKa9euwbIsRCIRnDlzRtLP8XqsHMXdisflcjl4vV6cOnVKUvPfuHED7733\nHtLpNF555RV0dnYWeCSSpGSSW0plrBpeW1srNT/cbjcmJiawvr6OY8eOoaenp8BkyHuj8xRNnJOT\nk+J3wrqjlHroyHTt2jXJibmxsYFYLIb5+Xl0d3ejrq5OcjpwsQF56S2ZTGJ0dBS3bt3CxYsXJQu1\n1+tFRUUFOjo6JIgrHA6LpMl57ff7hWzkfTgBghmKzXvVpkstNWiiUv/uYdojzyGpfcLZnMR+3ThA\nWhpwMnsWAxEOmpYA9DmnpqYkz0Emk5FoPx0CSxGbZs1oNIrGxkYEAgEAd4uXEsEpjlJf1g5ejIrc\nTY0yG4m8trY2LC4u4tChQ1hdXZV0ayxOe+LECQwPD+PWrVvo7OwUklRzB/SCDIVC6OnpwfT0NOLx\nOCzLwvDwMEpK8olem5ubC4KNSAhaliVOVMyKdPjwYdGxx8bGcP78eayuruLVV19FKBRCMBiUxLtM\nL8ex4oKnP0RTUxPee+89CU6anJzEwsICkskkDhw4gOrqatTW1gKAeIdyXlE6CQQCCIVC8Pv9ch1m\ny66vr0dzczN6e3vxzjvvYHFxEclkEmtra0gmk+js7ERlZaXUDyE4+P1+eDweLC4uSu7LVCqFsrIy\nNDU1Sdat1dVVxGIxCZvXUZbkhZgD05QgqDbpTdL0hjQlB77ITWiPyYdpj7xuhbmAnRa6uZPutuh5\nzmIgYf7W5COY3oyZeRYWFgqQnqQkRUfqgqzF0NnZiYqKCqytrSEajRY403B30z4ZmhXXY8C+FgMI\nBmm98sor+NGPfoQDBw4glUphampKEtZeunQJ+/fvx+c//3lcvnwZExMT6OjokP7lcjnZsThxmpub\n8cwzz+Cjjz4Sffz69evw+Xz43Oc+J6npeS90PQZQUPOhvLwcnZ2deOmll+B2uzE0NCT1JF999VUc\nPHgQfr9fVIxIJCKJVwGIeVLr636/H0NDQyKx/eQnP0FNTQ2OHz+OgYEB1NTUiEs01b2ZmRmR+oLB\nYEG9TIrn+rtQKISRkREMDw8jEomIVOh2u6XStp5fPJ6JXSgJbW9vo7m5GU1NTXj33XfFtZvPnjxC\nXV0dOjs7CxL4UnowMzoRADjGOsW/Bgi+gLtA8qmqsq1FI+7gpsqgd+piOpMTUDiBg/5f6/amesMs\nS9XV1ZJZiGnDCATZbBZ1dXWwbVs8EVm9amVlBZ2dnchkMpidnS0IjCGoEAiYTo1Sidl2s7pw4lRW\nVmJlZQUlJSU4efIkKisr8e677+LChQs4ffo0ent78Tu/8zvw+/14++23sbS0hFAoJCZK4K4nJL0J\n9+3bh83NTdy6dUucec6fPw+v14uTJ0/C7/dLIlS6asfjcZEcWKk8m82ira0Nr7zyCoB8kNXt27fx\n+uuv47Of/SwOHDggpelY4m57e1tMilTFcrkcurq6hJy7ePEistmsZK366KOPMDc3hyNHjqC6uhpr\na2uIRCKYmpoqiLcIBAIFMSw0sZIDyOVyqKurw9GjR1FXV4ePP/4YU1NTkoIvEokUbCZMAMPCuACk\nvCD9RiYmJjA7OyuA2dfXh8HBQSSTScRiMezfvx9+v7+AJKYEob0gueBt2xYLByU3U53QXIRl3a0T\n8qkBBzYNEpQQnNylgftbJpwkDiepQbtgc/cmQDBd+LFjx3Dz5k0JeXa73Ugmk+LdmM1mEQwG4XK5\nJH0YcwBGIhGk02msr69L/D6JJABi56ZeubCwgKWlJcmfaHInpjSlpZ+WlhYpDNPf34/nnnsO9fX1\nWFpaws2bN3Hz5k3cuXMHR48ehcfjwU9/+lMkEgnU1NSIisOJRVXJ5/Ohv78fXq8XFy5ckOQp77//\nPvx+P/r7+yU+wbIsMU/S4Yph1PX19WLDf/nll2Xnv3Xrltj1GxoapHbD5uamxHuQrAXuhk53duYL\n9wQCAZw9exbLy8soLS1FJpPBzZs3sbS0BL/fj3g8LvUrSVJS/dvc3ERdXZ2ETwOQGAlaYnK5HJqb\nm/Hss8/C7XaL9ybHi3ENq6urmJubkzSAbMwh4ff7xYeEWbl+//d/H83NzXjjjTcQj8cLAsQ0qa2T\nt2g+gdIOrThaiuA5NC/C78xgvAdpj1xycPqMD0rv8CYxWUzk3k2lcPpMm4TW1tZw8+ZNVFRUoKam\nBktLS1hYWJAHsrGxgfn5eSlhzypWlG6Y3JTiem1tLZLJpOiNOsqRx5C0jMfjEg5sSlAa1MzGHAUk\nBtfW1rB//37s378fU1NTWFlZwU9/+lMcO3YMzz33HEpKSvCDH/wAkUhECuuyD7ZtSwJWt9uN1tZW\nxONxSey6uLiI9957TxYq1arS0lKRPhi96PF4pD4Ficznn38etm3jwoULuHHjBgDg6aefRnt7u+jV\nzDq9vb0tujhFd7fbjcbGRpw8eRIejwcXLlzA9PS0qEWRSASxWEx2S84FZrluaGgQfkirFjq6leI3\n+SJGzdJngRmlGGAWDodRV1cnUo920qJDFEnI1157DXV1dUilUvD5fAX8ABexBn7NMTC8m2oFndJ4\nfi018K/+Pcf2Ydqu4GBZVhuA/wwgBMAG8B9t2/73lmXVAPivADoATAH4H2zbTu4c8wcAfhXANoDf\nsm37J07n1ru3XgjUy8wd1OmvyRcAxcHABBOn/yORCO7cuVNAKvJh0yzFB8Nzcleji6yemM3NzQVp\n4ijeJZPJAgKJ4rMJjsVUJv2d1+tFbW0tEolEQaBRY2OjqBxXr17FtWvX8Eu/9Ev4whe+ALfbjT/7\nsz/D9vY22traxBxI8o6SgMfjwYEDB2RnzuVymJ2dxVtvvYWXXnoJ+/fvB4B7djj2k96IdXV1WF5e\nhtfrxTPPPIPNzU0MDQ3h2rVrAgJ+vx8VFRUiDq+srBT4CXAB2LZd4JlpWRYmJiZE6tHWIVpQmLBF\nW3N03Uru0jT1ptNpyZPJv/p5ESBKSkqQSCRw9epVxGIxeTYEy6WlJTGBt7a24sknn4TL5cL8/LxI\nSyY4mHyB/p8Ln1IDAcLJI9JcZ9pR7EHb/SSHTQC/bdv2FcuyfAAuWpZ1GsA/B3Datu1/a1nW7wH4\nfQC/b1lWH4BfBtAHoAXAm5Zlddu2fc+WZy4E83PepP5OWxaKmSSdrqH/17+nRGDvmPVY8drlyqeH\nY/wDveR4fboi87dUTbRDDicldwq32410Ol3AGJM3IAA5qVAaCDKZDKampkT0Z4h2VVWVcAMUo48f\nP45Lly4hmUxiYWEBb775Jj7zmc+gu7sbr732GsbHx/HDH/4Qa2treOKJJ6TS89raGtbX16V2ZlVV\nFdra2hCNRhGNRlFWVoY7d+7g7NmzAICOjg4JbyYwsQ7o1taWOB2l02ncuXMHwWAQL7zwAra2tjA0\nNITR0VE0NDRIIBf5GC5WEpW0Zti2LepLV1cXLCsfBTk3NyemP73QCN7MtcD0b5ubmxJRSS5Jm/9W\nV1cxPz+PmZkZsTTRXKznUjabxfT0tEiQJBQBCNgwnoWLmuop5wn7y3ml1QPes7ZEmOBg8g3mnH9Y\nE6bMz92+tG17HsD8zvuMZVmjyC/6rwB4YednfwHgHeQB4hcAfMe27U0AU5Zl3QbwFICzDucueK8X\nNjkA4F6vSPO3fG/qU7vtvpr9nZ6eFjVgZmZGdhzqoysrK8La23beI46+CTTxcSJSAuCuUVtbi8bG\nRpSUlMhupXc0itJ6UjqpT2zZbBbj4+MSGRmJRCQ1fSaTkZ0fuBt5yck9MzODqakpURW+9rWvIRgM\n4q/+6q8wNjaGgwcPIhAIyATVxWNDoRCOHz+O0dFRjI+Pw+PxSEWrY8eOobW1FVVVVdje3pZitvTE\nTKfTYu9nX2pra6WmJYFmY2MDJ0+ehNfrFYctgnEsFpOkrdTH6YTV1NSE5557Du+88w7m5+eFC6E1\nhmNNF3bLyvsW0FWc0tzq6qoEP5WUlEihXe7yBD6qftlsVpyzuNDZt42NDUSjUUkOY9s2Zmdn8frr\nr6Orq0ukRT5fclI6VkTv9OwnvyMhSRXIlBzMufOPBYgH5hwsy+oEcBTAJPLBDAAAIABJREFUxwAa\nbNuO7nwVBdCw874ZhUBwB3kwcTpfgRhU7Mb4PXBX5zYlB00qmrqakxrCc29tbUk1pY2NDYyOjspO\nTKKL6M/BZ/AOUVznG2SSUi1RMH0Yf0cSkhWXCTBacigGED6fD6FQCENDQ1KzcWxsDAAKEtnSetDX\n14dbt24hl8shlUrh0qVL8Hq96O/vR0dHBwKBAN58802MjIxgY2MDhw8flgzMuoANrQe85sLCAvx+\nv5TYa2trEzdqjrOOGUgmk2hsbMShQ4dw6dIl2LaNffv24ctf/jK+//3vIxKJ4OOPP4bH4xHilA5a\nlLQSiYSkn9fqBRPxdHd3S4HbdDot4dy2bUtKeYr8JOf8fr8QxxsbG1heXgYA4YVYrbyiokIK7hw8\neFDiRM6fPy/FgBn/wIVKN3FKc8lkEtPT02htbS2wmHDumJY5vZi1KVK/mC9DSxp6zfBcJg/xoO2B\nwGFHpfgegH9l23bamLi2ZVm7XdXxu+985zsyOAMDA+jr63MUpXeucQ+Y8C+JSz0QeuDNAeNvOPHm\n5uYKRLTm5mZ4vV6UlZVJDL9O9U6Aols0Yw68Xi/S6TQymYxMklgshs3NTTQ1NWFhYQHxeFzUD52J\nmLkDzOAocyyYOGZiYgIulwvd3d1obGzEwsIC5ufnxePStvMh083NzQiHw/jhD3+ISCSCv/zLvwQA\nHDp0CADQ0tKCr3zlK2JSvXLlCvr6+iRxLNl57n4MBXe58uXzPB4Prl27JtmrWTHK6/VKf6mScRyC\nwaDUAhkcHMT6+jq++93vYmVlBR9//DG8Xm9Bujqtqi0uLopYz+AtIO+M1NPTI1XHCeBMlEuSM5VK\nSeAWM0PTckTpj3E0uuhMXV0d2tra8JnPfAZA3iQ9NzeHqqqqgjqbtm0Lf8O+83lsbW1JODqfKzcE\nbZng/1qq5Byh1KCjZItxDpQAE4kEEonELsuzeLsvOFiW5UYeGP6Lbdt/t/Nx1LKsRtu25y3LagIQ\n2/l8FkCbOrx157N72te//vWiSKZZeRMQTJLS5CQ0AOjfOEki2WxWMhZR/6Ttnpl7LMuSB7yysiJS\nBiUB7vaMabBtWyQFSgRk9FdWViTKkZGZdHihCO2kUnGCxGIxyTgN5E2is7P54XW73VLghseWlJTg\nySefxNDQEMLhMObm5vC9730PTz31FE6dOoXKykq89NJLGBkZwdWrVxGPx3H+/Hl0dHSgtbW1IIU7\nr9fb24uGhga8//774uNx8eJFIRRZlKasrAzBYFCsF0Dee7G9vR1LS0uIx+Pw+/04duwYZmZmcObM\nGUn0wrBrcjJa0stkMpLqjTsqPR1bW1sxOTkpwJ1KpQTobt++jYsXLyIYDKK2tlbAjmQx+YOtrXwh\nnkQiAZfLhY6ODnzxi1/EiRMnEA6Hsb2dryB27do1AVXtT0B1VC92zkE60+lnq1O98ffmBqE5Bw0G\nOnGMk3TgcuUL+gSDQfmcCWYepO1q+LTyvfs2gBHbtv+d+urvAXxz5/03Afyd+vzrlmWVWZa1D0AX\ngHMP2hm9q5svJ1ON+dcEBT2x1D3Ji7orB5w+7iwbTxMfLQ5kqIPBoOwWuVxOqiYRSPhbmhjX1tbE\n00+TX3p3KS8vd7xPiozT09MYHh6GbdtobW3F/v37hU1naHg8Hr9n3Pbt24fXXnsNfX19KC8vRzgc\nxunTpyXfwL59+/DVr34VVVVVaGxsxGc/+1n4fD6cPXsWc3NzBbkYmd2qvr5ealdsbGwgHo/jypUr\nkuaNBB5fLpdLFg7T2NF5qKKiAl/60pcwODgoLspXr15FJBIR8pc7LMec6d6pehC8dIYkPmuqhblc\nDtevX8f58+cxOzsrnINOuUbHsFQqJancWltb8eyzz6K1tRUA8Pbbb+ONN97AyMiI5H0oKcmXASBo\nUWXUKqnH40FbW5sQruY85Yt94UZnqgZaktDzw1S5i70ept1PcngWwD8DMGRZ1uWdz/4AwL8B8F3L\nsn4NO6bMnRsesSzruwBGAGwB+Bd2EfGgmNRgqhO7/ZZil3YxLUZEmtewbVvMdczuk81mJSMyJ6a2\nLuiCLVQzSJIROHQoLu3Ktm0XFKkh2lO1yOVyIt6a90GA+vDDD2UiBgIBqROxtrYm9zAzM4N9+/YV\nLBCa/ZaXl3Hnzh1EIhH84Ac/QGdnJ775zW9K8NHg4CC2trbwpS99SZKxXrp0CQcOHEBLSwsCgYCE\nbrvdbuzbtw8lJSUYHh5GKpXC7du3Ydu2JHrltbnoyGPQ/yGRSCAej0vClF/8xV/E6dOnceHCBUxM\nTMDj8UjlaT0mHPdEIoHq6mp4PB7hN0zpkPEiXKQrKyu4dOkSUqmUEKk0mzIQjinttre34ff70dLS\nIs/TsvJmU0bpEhSqqqpE0rlw4UIB72LbNnw+H5qbm9HS4ki/3SNNaJAoBhDmq9haoYT1sMAA3N9a\n8T6KSxcvFTnmjwH88f0ubFod+NnDHKeBgAPH//VfNlOPtywL9fX14sy0ubmJZDIpOjRDq4nSOiyY\ntRJpKrNtW3YSBiMBEPAgq82EI/Sw4+7NEGDzXqkHR6NRIf22trbE2Yq7ZjAYRCQSEbDg8STuGhoa\nEAqFEI/HMTMzgz/90z/FsWPH0NfXh9LSUvz8z/88PvzwQ3z729/GwYMH0d7ejqmpKQwPDyOTyaC/\nvx+BQKBgsrEY7+joKDKZjKSIZ/p8zddQmmAC26qqKnFaCgaDksSXrtrXrl1DIBDA4OCgjC+JOy68\nVCqFmpoaVFRUiLmY1qCysjIcOHAAvb292NjYEMtDNBoVSe/48eMS18JntLy8jGQyKfky/H6/gPOZ\nM2eEcM7l8nkoBgcHcejQIZSUlOD8+fOyUXBHd7vdch80jevm9L9+aYDQz9SUmM3147RGPlUekk4A\nwe/M393vWEoQ+niT2NMDlkqlEA6HhbghOMTjcTQ3N4skQUDQTjg6fyAZeb0AAEhkIVlz7ehCCYSB\nRz6f7x7dU9/r/Py8XIMmLi6QXO6ux9/CwgJisRja29sLjrcsC4FAAA0NDZifn0c2m8XY2JhYCg4e\nPIhDhw5heHhY6lr29/cjm83i9u3bGB4extraGrq6utDQ0CD3V15eLjkaGBB18+ZNVFZW4oknnpDE\nreRnqKLV1NSgra1N4gvcbjd6e3vR0tKCZ599FtFoFOPj4xgaGkIwGJTM3DrAiAswkUhI7gqd5Leu\nrg7Hjx9HV1cXSkpKMD8/L5WvV1ZWMDExgXQ6jZ6eHrE+TE1NSYWzQCCAxsZGlJWVIZVK4caNG7h0\n6ZJITuXl5WKlYeXv6elpUVdJTno8HjzxxBM4ePDgPZm49PN2Un8JDKaq5AQQ9wOKfwq14p+s6Zsw\nxSpz4LSa4LR4OIDaUYmNi1WrHkA+G/SVK1fEVEcx37IspNPpAvLIPN62bZEadG0HBhsBkFBcBmrp\nRB3hcBgHDhwQKwkToTpJUltbW5iamhKzKhOVMAaAmZ9oertx4waampoK6kVSQuru7paQ7nQ6je9+\n97viYdnW1oaXX34Z586dw+XLl4WsjMViklY/HA7j+eefR1tbm3AnQN4RKpPJYGRkBLlcDmNjY+Kg\nVV5eXpBMlzU86+vrUVNTI0RpMBhEKBTCgQMHcPLkSanM9eGHH+Lzn/88KioqRCLQcQTU7S3LEnK5\nrKxMwIYJdnw+H4LBIM6ePYvr169LIZpEIoG2tjZxkab0BwD19fUIBAJIpVJCOK+urqK6uhqnTp1C\nT08Pzp49i9u3b4tVh2QzA9kaGhrw5JNPSs6LYpuhlgIfhDNw2kDNNWKurU8NOGiLxP06bhKNWoVw\nQmD9W/M8bC6XSwqs3rlzB5lMRsjEeDwutRu0DZnEGrkFqh/cyWjl8Pv9Ahy0YKTTaTQ1NQnpyZqX\nAKQKFvMl6IfNuhbaEkP3XiY05Xi43W6Ew2HE43HU1dUV3LvH48GRI0ewtraGlZUVTE5OIhqN4m//\n9m9x8OBBMUF+85vfxPT0ND744APYto3f/u3fxtDQEP7mb/4GuVwOFy9eRDKZRE1NDUKhkOS9oITA\nVHP0WyBI6ujCcDiM6upqNDQ0IJlMSqg5xXjmfyQxee7cOZSUlEhmZ4bIU2rb2NiQgkGseRkIBCRy\nlL+tqanB008/jcrKSnz88ceiIjAQLRKJSM0KAEJWZ7NZSRLMTWBubg4rKyuIRCJCXtbV1SEYDCKb\nzaKqqgrd3d144oknJLt1sR28mKSsjzFJSic1w5SyTQn6YbNPl3zrW996qAN+Fu2P/uiPvvW1r33N\nURoodqP8zjTXOEkeTiIVf2dyAWtra1I5SsfHayac59PIrgOFgLsPUkfZaU7C5cqnifP5fEilUrLj\n0U9iY2NDUrDrduPGDUxMTIjeXV9fL34UyWRSzLFk9CORCKqrq6VKuB4j7vTkDEjAbW5uiujOPAu3\nb98W86kOKHO5XJiZmZGIQor76XRa7oO5LnK5nFSusqy7lhySh/TspK8A/UX8fj8CgQBmZ2cLysgx\nhRwA8VJldOXMzAxu374t+RYoPQAQ5ygWpEkmk7CsvHOWDrkHIL4D5eXl6O7ulkxRo6OjSCaTKCsr\nQ1dXFzweDyYmJoT3OHz4MH73d39XXL2/8IUvSHYtTS7qqGMnwlFLEVRD+TL9Gky3aacXr0n+Z2xs\nDN/61rf+6EHW6SOTHLQHmBOi6gVfjI01gYG7u959Tc8zsv937tzB0tISlpaWZOFqV1ROFp5H25I1\nAPD6DBBaXV2V/Ao0i5JVLy8vlwzMACQHJACJgWBiE9u2C/z2LSufni2bzQq7zpRmtp1n8Jnf8urV\nq+jq6pIEtLwPl8uF9vZ2rKysoLq6GnV1dfjoo4/wwQcfwOVy4ctf/rI4J/36r/86YrEYfvSjHyEU\nCiEUCmF8fByrq6vCdXz00UdYX19HS0uL+DcsLy9LiPfExARKS0sxODiI5ubmAu6Fi6q2tlYW7tLS\nEurq6lBZWYmWlhacOHECiURCMi1VVFRgYGBAfDlsO+95ePv2bam3SWBgQluC8Pr6OjKZDCYnJzE5\nOVmw2DKZjMReMIaDhX5YwIaVuSsrK9Hc3Cx5P3K5HI4dO4bf/M3fRF1dnWSBMq0NmkMA7lVzddNz\nWoOJeQ6z6c3TVCcIDg/THltw0CSMky6lv6OK4eTXoLkIIL+LhMNhxGIxiY5kWDaJJl2ujiiuk4IS\nHCjKsw+0s+tFsL2dL3lXVlaGtbU18UtYXV1FNpsVq4dlWbhz5w5yuZzkB1hcXEQ8Hpcdl2nk6e7L\nvlmWJcFSDQ0NuHLlCiYnJxEMBu/RU8nik2NZWFjAyMgIfvKTn0j689LSUnR0dODEiRPIZDI4c+YM\n1tbWUF9fXxCCns1mceHCBcRiMRw6dEgko2AwiMXFRaRSKYyOjgp5SWccPpNkMinXZPLWlZUVBAIB\n1NbWYnBwEIuLi3j//fexvr4unAZdv7PZLCYnJ3H27FkpxEvugg5c2puQ5t5YLFYgIZLHYFwGQ7Kj\n0SguX74sLtIcM3InQF5de/bZZ9HU1IRoNCpp5JzIcBMknCRdvSb0e/MYEyCcTJpamqU69DDtsQMH\nPWDF+AQnXoEShtareA49+FxwFEez2WxBIhYWCjHJIR1BCdyN+6e4zwejQ7oJSvRopB8/E8wyQpBS\nyMrKisRKVFdXIxqNFjxw5rKkuMnFTsnG5XLh0KFDmJ+fx/Xr1x2L8wL5GI2uri6MjY2hr68PiUQC\nMzMzePPNNzE5OQmv14vDhw/jG9/4Br7+9a9ja2sLr7/+uqhITHHGWIsbN25gcXERTU1NOHDggOj0\n5Eamp6dRX18vC5EOX6urqygtLUUwGBTCLxKJCJHr8/lw5MgRLCws4MaNG1hbW8PIyAjS6TR8Ph8W\nFxcxNzcnCXarqqrQ1dWF7u5uAQ86oS0vLyOdTmN5eVmKy9BxqaWlBZZlYXx8XDxbbdvGwsIC0um0\nAEx5ebnUP52bm8PW1hYGBwdx8OBBJBIJ3Lx5U+JlTLGe/2v1wgQAJxBx+v1u3IVJbPNYBo49THts\nwAG4t9qTEzo68RH6eP2dNlPyWDLPvBYtE5p41M5KGnD0Q+Li5/dcsLp4LHVyndQ1m80WpHOnPr65\nma/cHI/HUVpaiqqqKkxMTIhUQK/CZDIp/dTHcuJVVVWhvr4et2/fxsrKisQ5mFIZK2Ktra3hwIED\nYlYk+clSeb/2a7+GV199FW63Gx988AGWlpYAQKIiyTlEIhEsLS2htLQUX/rSl1BTU4N33nkH8Xgc\nyWQS165dw+rqqsRNcHwzmYwkrKH1IJ1Ow+/3o6ysDPX19Th69ChisZhk3JqZmZFcCvSnqKqqQk9P\nD9ra2iRDVyKREL+HVCqF6elpkeIOHz6MiooKtLa2IhAICIcyPT0tGaQYIEdJksF4MzMzIkHZti0R\nr/SXoeTBa+v5yWfhJCmbUrApaWhPyt14Ns2vUZ0oVltlt/ZIwUGjKQfHHDhN1gCFAAE4u6Hqxt9y\nIfn9fmH86f/PcF46JXFiUISkyEnSD7ibi2F9fb1Al9MEpU5Uwu/YFwIQE6twAi8sLAi/wInJ39Kc\nCdzNFcD+lpaWFqR+q6yslOsV43IaGxuxurqK5uZmpNNpSYu3vr6OWCyGP//zP8edO3fw4osvor29\nHaurqzhz5ozUCKVjGJ9lNpvFjRs3xLnK5/PhrbfeQjQahW3bWFpakrBxqi/kA+iFmM1mkU6nUVtb\ni1wuX6R4//79ePrpp/H222+LtUUvovr6ejQ0NKC+vh61tbXCabCkHBPS0rPx2LFjOHXqlOSZoBs8\neRwdas04EV5veXlZSMHy8nIsLi7i3LlzaGhoECcsJxGfkq3ps6CbEwDo/52+M0FC/+Wc53z71EkO\nmjjkDQP3EjbaYsDfm43inG70V+AOU1dXJ2XVWU+AoiDNceQKuMC1BELTmO4THzrBhd9pvVqrO1pF\nYa6A1dVVSbSysrIiu08ul5PcDeQdOJE3NzclqSuLypSXl+Oll15CJpMpcD3WjZ+Vl5ejpaUFmUxG\nXI3Hx8cRDoclVoOl6E6cOIEjR44gkUjgnXfeKchhqBdCNpvFj370I7zwwgs4evQo9u/fj3fffRfD\nw8NSei4Wi6G3t1fG3+Vyoa6uTojWxcVFVFVViQmwoaEBfX19yGQyuHbtGhKJhBCj3Dz279+PpqYm\nsYYw+/f6+jpaW1tFImxtbcWLL76Il19+GRsbGzh37hwikYjwF4uLi/JM+QypSpn6PADhosgl8aWj\nRjnmnN/aTd5Jeihm2dAv8gicozyX5jsIClQpPjXgwMVt6mXAvdICf8e/OtDEPMYU3UxrRUVFBY4c\nOYLNzU0sLS3B5/PJLsWJrglFvcuT/KMoz3RhNOXxWAKSTv+mg2TYZ53Qgw+dxVcYxs2is7wnfQ6a\nDre2thAKhSTrs9vtluxMxfRT9svn86Gzs1PAmg5LzDiVy+Vw48YNVFZWSvbp8+fPy27Mc3EBlZSU\nIJ1OY2JiAgMDA6irq8Nrr72Gnp4evPPOO1hZWUEikcDU1JQk5aWzEk2W9EDlxC4vL0dNTQ0aGhow\nMzMj4EwJgmDL+A0Wp2VGayatqaioQHt7O9ra2oTwJSF7584dyZPAc3JekgCmW7i5GzMuQ5PQ+jnp\nOerEKzhxbQQAzgkNClQT9NzU/BqlU7OS1qcGHMwd3hS9nNyhi9l0gcIoTPM3JntMn/hbt26JOaqu\nrg4ul0syKnGS5HI5AQGK9Rog6ApNZySN/OwXpR06LlmWJROKwUlkymkx4e5I4pKTmxwEiUxGkw4O\nDhZICsW4GxMkGEPAEngrKyuSLp2mwNnZWUSjUcm0PDAwgDNnzhTsbvRRIJDt27dPdH+Xy4XBwUEc\nOHAAN2/exPT0NCoqKsS/hP3u6uoS1SaVSgmpyJDvjo4OccTiM6avBssAxONxRCIRcdOura3Fvn37\nEIvFRPIbGxvD0NAQVlZWcPPmTUxMTEiVLJ/PBwCyqJgLguHRfAbMkNXY2AgAMo+cAMKUcp0AQs9h\nneeBAKEXO/tm8nZ6fZi//1SZMk1rg/kdUbDYsU7EJEHACSDMVltbC5/Ph7m5OYTDYdi2jVAoJAVh\nqHcy1FhncCJwcYFz8PV1ifbA3cSrnJx0kKKzDXA34pN6ty7SyzGitMLdiirHsWPH0Nvbe49N3Omv\n05iXlJSgpqYGNTU1yGQyqKysRG1tLUpLS4WAXFpawszMjFyDu6jeqXhun88nIc76+2AwiKeffhpP\nPvmkgGs4HIbL5ZJq2NlsFh6PR47TIjuQL7pD70Q9hxgzEY/HJc1/T08P+vv7JaYkGo1KrgaSw7FY\nDCUlJWhqakJtba1kkl5cXBQVhWDAZ+52u1FdXY2amhrhTdhfrVqQt3DyBi4GDk48g17kBAZTddHg\nwP+dAOJh2iOtW1FMHzZFLf2dfhVTO/jXCRj08Uwq4na7cfnyZSEsKYKlUinZ+akCaJ2RMQ40Z7K/\nmvvgA7MsS4hH2t05cQgCJEC1Ls9jKZ3QwrG1lc9q/NnPfhbd3d0FTLTT2Onx1n/Zz4qKCkmlz3Bl\nWjtaWlpQUlIieRE3NzcLMnSz/7adz7F56NAhVFdXF/Rf90t7THZ3dwu5NzIygnA4LF6GzNTU3NyM\nWCyGRCJxTyFbSlL0glxfX0dtbS26u7vR2dkpJQRYkMYEfpfLJaXrWI6Az5WBdNxxaYFgaT06THG+\nmZ6NxfgxEwC0lGyCBqUHLnRdO0NLquTFtNqqQcGJrL9fe2Tg4ISgJgnjBA5AoanG/F8f46S6mMe6\n3W40NDSgsbERw8PD2N7elp2TPvyavXa57laWprXB3AF4LcZcmLs2JxEA0Yf50LUlQPMllDp0/wcH\nB9HV1VWQ4PRBx12PG3f2UCiEZDIJIF/mjunFSkruFp9h4hufzyf+HAw2q66uBgCJZuTC0KZkAoNu\nbrdbckYEg0FcunQJ0WgUa2treO655wo8WckrABDpheNId236W1RVVUmezevXr4szkx4Hn8+HyspK\ncZCiWkkQY5+5AH0+n3hCap5Km7T50mptMXLSlBz4V0sNGhyYPs+Jx+D1+Z1WSx5kbpjtkYGDaZXQ\nJho9cEAh58DG35mfmWaeYi9em7r+0aNHkcvlcPXq1QLrhd/vL9CdNzfzNTFTqZTsltw5NedBNQG4\nSzxyl6OYTPE8GAxia+tunQOtmlCtoTTDaEiXK+/wRJLJSZrS46J/oz/XEg9L4QEQcpAVqCj50GS6\nvb0tvhd0W2YiVloHNOOvAcKUXChdVFZW4siRI2hpacE777wjLtO6QnUulxPnJgAFuR642HXkZjQa\nxe3btxGLxQrmWy6XEwsEA65yuRxCoRB+4Rd+Af39/RgdHcWZM2ewsLAg5fQqKirEXMm5yedOAtuJ\nlDTnvrmTEwRMgOCiJxiZZlI+U84VbmLmhukkwdyvPVJwMBcx0Vl/rxsHxeVyFSCz9mYsZgfm96ZI\nx+/9fj9OnjyJ6upqjI+PIx6PS2IVy7KEsHK5XBKMw51TE0P6gep74oPTvy0vL5fITu0NqdGfoiwl\nFKZQf+aZZxAKhRxVhfs1ExSAuwDs9XpRU1MDIF83dGtrC1VVVfB6vaI2cDFVVVVJgWCqIh0dHaiq\nqhLpSFuKtJrBz8wd1eXK+y383M/9HD744AMMDQ0hlUphcHBQUr6nUqmCcWc+Tor/yWQSY2NjsG1b\nVBFapViXcnx8XFQ73n8oFMIf/uEfSozKrVu34Ha7UV9fL5YYrTJqYNN8l75XPW/1PWqg1uNjAgQd\n9La3t2Wc9XU55zg/KF1p7kHPq4dpjwwcdOILvaCK7fgcOO5CfM/P2czFDxRWtTYfihbrKEEMDAxg\nYmICZ86cgW0XhkizRFtLS4sslpWVFVE9SFox/TkLwm5ubiKRSIh1ghYQAJITkQ+ZY6Odi7grra2t\nob29HY2Njfewz06SAz8zVR4NEPyrC8LQ45HVpXmcx+PB6upqAYjrvIi3b99GZ2enBJARILSnqmnN\n4bF6t/P5fHjxxRcRj8fx5ptv4uOPP4bL5RIzL3dInqO8vFx8DnSkp2XleSRaT2ZnZyW/A30atMqQ\nyWTQ1NSEc+fO4dy5c3Ju9pOqovbLoYTA/7U0UYxzMKU4EtM8Vi9uzT1QauHv9Riax2sQYaDZw7TH\nAhxMYHDa+bW/ur7xYrZkbRcuJqWYkobuG7MsX7t2DZcuXRLU5UKlyYsThxWtaL2gRYJ5Elwul7g/\n68mo090TGLQDFr/jfdi2LR6dehICzin0zOYk1mtQYfzC4uKiWAhs+249SfIwvDZzLpaWlsLr9Uqw\nVU9PjwChFodN6cHsG/tFjqWurg5f+cpX8O677+LDDz+Uat762TOAigBIqYV9pBNaPB7H3NycjDUr\nXxEA6urqsLq6ir/+67/GzZs3BezNpglEk3B1Ao1inIN575QSOSd5DOeLDvLThLteDzpS2JRCH0Sq\n1O2xAAdzoTotZsA5f54TOACFSTr53gQDJylCt/r6ejz99NOora2VfAabm5uYmJhAPB4HcBccuNjZ\nJ4IInWeampqwubmJhYWFgmhPLk69q3IHpM8Dg7x47nQ6jaWlJcm25NT33e6r2KLc3t7GyMgILl++\nLLsM80Zw5yGQcDzpZARAisKUlZVhbm5OzKFaP9cv8zMnVYOc0PPPP49QKIQrV65gdHRUgt7MBWNy\nULaddzunL0N5ebnkfEylUhKIx76+8cYbkqBH9908pxMg63HVlggn3sFsehy02ZHn56ZBLoxzSKsd\n5lpx2kQfpj1yzsEJHJyAA3A2U+qbLiY9mKDjdF0nUQ+A5DfgA1hbW0NLSwtGRkbEA487PR2BGCUI\nQHwhVldX0djYKI5G2g+fuwUDtEhwcgJwUTJkOJfLZ1NiujanZk5Yc+KYKsj29jYmJiZw9uxZ8Xzk\n5NPSCs9VVVVVAMTc6Xgd5migydHpOZnvzf7rPvt8Phw9ehQdHR0IouEMAAAYRUlEQVTo7u7GlStX\npLgvQZQLSpueS0pKxIsUgFRIX1lZkfia5uZm1NbWylzgGGtS0Rw3U2Lg95QouGtrEd8EPj0GWqoi\n8av5Go6zNm2agKDPx+tr9eRTAw7aaeZ+UsNuA6AfHJs5ac1r8L2+vn6ZurgGLbfbjb6+PtTV1eHC\nhQuYn58XvkFLAHpB0MsvGAzC7/fLDsY4CersmnjipKbEwPvhrpJIJMQrk/ehF6f+zNTxzUli27YU\ntCExqsdbl/Ijx0P1QvNAVK8IJsvLy/ekqzOvrcfLaez1gnO5XAiFQqiurkZPT4/wAsxWpW36NG1a\nliVBXky4wwzTuVwOtbW1wo/o2pNUVbRqwMXotEnp/8157gQM5jGm2qUB4n7zWj8rDUTa1KrVlAdt\nj9TPQb93EvFNycHpeCfdT5+Dv3HiGMydlO/18ZqF1n0KhUJoaGjAxsZGQe6AdDoti5i7FT+nXp7J\nZIT9z+VyEtmpSSwWyeFEJ3dBSQIA5ufnEQqFBFw04LE5kX/6e9vO51VgghhyK1qcZpo7HkvRlt6C\nHBdORDrf6B272HM3wc38rQkUQN7s19LSgldffRXPPPMMTp8+jatXrxYQblrnLysrw7Fjx/C5z30O\nTU1NCIfDBYl3dB1KgoS2LmnLC8fG3JicAIJjYt5bMemBfwkQlCi5kWopoNimCRQmKdLWjU8NOADO\nN2lOHjYnBOXNmhYL89zFOAan67CZ4pi589LENTQ0JPUUmY3JsvImR8u6W3GJvvcMUKK1ghmFLMuS\nHAkM9GG/qU6wH3TSCYfDaG9vlxJ7+l70wnJq/HxrK1/+7fr16+LMxIVlWVZB2rO1tTVUVFSgpqZG\nrC/kVUjeEVABCPnX29t7jwenuZOagGWOvdNiKCkpQUtLC37lV34Fhw8fxuzsLBobGzE7O4vJyUnp\nb29vL1588UX4fD7E43FUVVVJ2nh6pGo3Y1OC0BKSliTYP036Of3lPHCSNMx71tIDLSOajC620E1u\nQfdT9/Vh2iPlHPQC1M0kqfiZk3Rh27YjMDhNKlN1cGKizeY0gfm3sbERnZ2dGB8fx8bGBiorKyVO\noaKiAul0WjwKc7mcqAjM8aB1RvIQACQakfEXFId5HoZ2l5SU4PLlyzh16hT8fr/jAioGqpxM0WgU\nV65cETGbi1uPfSqVktBwJmnN5fLeiJWVlRJurVPYcWHNz8+jublZMlA7ATbg7OBmgnIxCaikpATH\njx/HsWPH5Diak+lVSPDVgW6miZC/Zxg9JQjtVKVL3GlVg++d5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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "example = 1 - rgb2gray(plt.imread('./test-images/butterfly.png'))\n", "plt.imshow(example,cmap=cm.binary)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Oversampling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We start with a $M\\times M$ image, and transform it to a $7M \\times 7M$ one" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def oversampling(image, factor = 7):\n", " old_shape = image.shape\n", " new_shape = (factor*old_shape[0], factor*old_shape[1])\n", " new_image = np.zeros(new_shape)\n", " for i in range(old_shape[0]):\n", " for j in range(old_shape[1]):\n", " new_image[factor*i:factor*i+factor,factor*j:factor*j+factor] = image[i,j]*np.ones((factor,factor))\n", " return new_image" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ykEgkUCgUkE6nMTMzA4/Hg9bWVpnzwcFBFItFpNNpeL1edHd347rrrsMVV1yB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\nBcDFlZOTI+ze9fX1GeNjJ5DtBLadgLAKQIaD77vvPnz88ceoqqpCZ2cnh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "oversampled_example = oversampling(example)\n", "plt.imshow(oversampled_example,cmap = cm.binary)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Rows/Columns hexagonal grid" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The grid where we place the hyperpel is centered in the center of the central hyperpel." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Distance between centers of adjacent hexagons\n", "# with the hyperpel\n", "# \n", "# o o x x x x x o o\n", "# o x x x x x x x o\n", "# o x x x x x x x o\n", "# x x x x x x x x x\n", "# x x x x x x x x x \n", "# o x x x x x x x o\n", "# o x x x x x x x o\n", "# o o x x x x x o o\n", "\n", "dist = np.sqrt(65)\n", "\n", "# The centered hyperpel\n", "hyperpel = np.array([\\\n", " [-1,4],[0,4],[1,4],[2,4],[3,4],\\\n", " [-2,3],[-1,3], [0,3], [1,3], [2,3], [3,3], [4,3],\\\n", " [-2,2],[-1,2], [0,2], [1,2], [2,2], [3,2], [4,2],\\\n", " [-3,1],[-2,1],[-1,1], [0,1], [1,1], [2,1], [3,1], [4,1],[5,1],\\\n", " [-3,0],[-2,0],[-1,0], [0,0], [1,0], [2,0], [3,0], [4,0],[5,0],\\\n", " [-2,-1],[-1,-1], [0,-1], [1,-1], [2,-1], [3,-1], [4,-1],\\\n", " [-2,-2],[-1,-2], [0,-2], [1,-2], [2,-2], [3,-2], [4,-2],\\\n", " [-1,-3], [0,-3], [1,-3], [2,-3], [3,-3]])\n", "\n", "for i in range(56):\n", " hyperpel[i] = [hyperpel[i,1],hyperpel[i,0]]" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# This function returns the coordinates of an hexagon, given\n", "# its position with row/column, for the above hyperpel\n", "# and assuming an oversampled image by a factor of 7\n", "\n", "# Here the hex of position [0,1] is right UP w.r.t. the central hexagon\n", "\n", "def hex2cartesian(row, column):\n", " x = 7 * column\n", " # even column\n", " if column % 2 == 0:\n", " y = 8*row\n", " # odd row\n", " else:\n", " y = 4 + 8*row\n", " \n", " return x,y" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# This function returns the coordinates of the points of \n", "# the hyperpel corresponding to the hexagon of given\n", "# row/column positions\n", "\n", "# Here, we assume the center of the [0,0] hyperpel to be at the \n", "# intersection of the 2 rightmost pixels of the central 4,\n", "# while the \"center of the image\" will be as in picture:\n", "# o o x x x x x o o\n", "# o x x x x x x x o\n", "# o x x x x x x x o\n", "# x x x x x x x x x\n", "# x x x C x x x x x \n", "# o x x x x x x x o\n", "# o x x x x x x x o\n", "# o o x x x x x o o\n", "\n", "def center_hyperpel(image,column,row):\n", " # The center of the image are 4 pixels, we denote as center\n", " # the one left-down:\n", " #\n", " # O O\n", " # C O\n", " cent_y = int(np.floor(float(image.shape[0])/2))\n", " cent_x = int(np.floor(float(image.shape[1])/2))\n", " \n", " h_x,h_y = hex2cartesian(row,column)\n", " \n", " # We return the translated one\n", " return hyperpel + [cent_y,cent_x] + [h_y,h_x]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following shows that indeed the hyperpels are generated correctly" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ciao = np.ones((40,40))\n", "hp = center_hyperpel(ciao,0,0)\n", "for i in range(56):\n", " ciao[hp[i,0],hp[i,1]] =0\n", "hp = center_hyperpel(ciao,1,0)\n", "for i in range(56):\n", " ciao[hp[i,0],hp[i,1]] =0\n", "hp = center_hyperpel(ciao,2,0)\n", "for i in range(56):\n", " ciao[hp[i,0],hp[i,1]] =0\n", "plt.imshow(ciao,cmap=cm.binary)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# This function returns the value of the hexagonal pixel,\n", "# depending on the values of the oversampled image\n", "# given its row/column position, for the above hyperpel\n", "\n", "def hex_value(oversampled_image,row,column):\n", " hp = center_hyperpel(oversampled_image,row,column)\n", " val = 0.\n", " for i in range(56):\n", " val += oversampled_image[hp[i,0],hp[i,1]]\n", " \n", " return val/56" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# This function returns the grid for the hex row/column representation\n", "# given the ORIGINAL size of the image\n", "\n", "def hex_grid(image_size = 256):\n", " up_rows = down_rows = int(np.floor((7*image_size/2-4)/8))\n", " left_columns = int(np.floor((7*image_size/2-4)/9))\n", " right_columns = int(np.floor((7*image_size/2-5)/9))\n", " \n", " # My computations suggested +1, but up to\n", " # +22 works without catching any exception\n", " return np.zeros((up_rows+down_rows+25, left_columns+right_columns+25))" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# This function, given an image, fills the corresponding hex grid\n", "\n", "def image2hex(image):\n", " original_size = image.shape[0]\n", " oversampled_image = oversampling(image)\n", " grid = hex_grid(original_size)\n", " \n", " hex_center = [(grid.shape[0]-1)/2,(grid.shape[1]-1)/2]\n", " \n", " for i in range(grid.shape[0]):\n", " for j in range(grid.shape[1]):\n", " try:\n", " grid[i,j] = hex_value(oversampled_image,i-hex_center[0], j-hex_center[1])\n", " except IndexError:\n", " continue\n", "\n", " return grid" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def hex2image(grid, image_size=256):\n", " image = np.zeros((image_size*7,image_size*7))\n", " hex_center = [(grid.shape[0]-1)/2,(grid.shape[1]-1)/2]\n", " for i in range(grid.shape[0]):\n", " for j in range(grid.shape[1]):\n", " hp = center_hyperpel(image,i-hex_center[0],j-hex_center[1])\n", " for k in range(56):\n", " try:\n", " image[hp[k,0],hp[k,1]] = grid[i,j]\n", " except IndexError:\n", "# print(\"[{},{}]\").format(hp[k,0],hp[k,1])\n", " continue\n", " return image" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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BopHwa1WKx5xcbE6fVPX1pxZmnqNXU6BemDWPQNNA2+Om1gDcmoKP33k/3guA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\nbm5OUt9tbm7C6/WKlra6uopUKoVIJIL5+Xk0Nzejp6cHR44cw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "example_hex = hex2image(image2hex(example))\n", "# plt.imsave(\"tryout.png\", example_hex, cmap=cm.binary)\n", "plt.imshow(example_hex, cmap=cm.binary)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spiral Architecture Hexagonal grid" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Algorithm inspired from \"A New Simulation of Spiral Architecture\"" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# They use a different hyperpel!\n", "\n", "# The centered hyperpel\n", "hyperpel = np.array([\\\n", " [-1,4],[0,4],[1,4],[2,4],[3,4],\\\n", " [-2,3],[-1,3], [0,3], [1,3], [2,3], [3,3], [4,3],\\\n", " [-2,2],[-1,2], [0,2], [1,2], [2,2], [3,2], [4,2],\\\n", " [-3,1],[-2,1],[-1,1], [0,1], [1,1], [2,1], [3,1], [4,1],[5,1],\\\n", " [-3,0],[-2,0],[-1,0], [0,0], [1,0], [2,0], [3,0], [4,0],[5,0],\\\n", " [-2,-1],[-1,-1], [0,-1], [1,-1], [2,-1], [3,-1], [4,-1],\\\n", " [-2,-2],[-1,-2], [0,-2], [1,-2], [2,-2], [3,-2], [4,-2],\\\n", " [-1,-3], [0,-3], [1,-3], [2,-3], [3,-3]])\n", "\n", "hyperpel_sa = hyperpel - np.array([1,1])" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Here, given a spiral address, we return the corresponding hexagon \n", "# in the form row/column\n", "\n", "def sa2hex(spiral_address):\n", " # Split the number in basic unit and call the auxiliary function\n", " # Here we reverse the order, so that the index corresponds to the \n", " # decimal position\n", " digits = str(spiral_address)[::-1] \n", " \n", " hex_address = np.array([0,0])\n", " \n", " for i in range(len(digits)):\n", " if int(digits[i])<0 or int(digits[i])>6:\n", " print(\"Invalid spiral address!\")\n", " return \n", " elif digits[i]!= '0':\n", " hex_address += sa2hex_aux(int(digits[i]),i)\n", " return hex_address\n", " \n", "# This computes the row/column positions of the base cases,\n", "# that is, in the form a*10^(zeros).\n", "def sa2hex_aux(a, zeros):\n", " # Base cases\n", " if zeros == 0:\n", " if a == 0:\n", " return np.array([0,0])\n", " elif a == 1:\n", " return np.array([0,8])\n", " elif a == 2:\n", " return np.array([-7,4])\n", " elif a == 3:\n", " return np.array([-7,-4])\n", " elif a == 4:\n", " return np.array([0,-8])\n", " elif a == 5:\n", " return np.array([7,-4])\n", " elif a == 6:\n", " return np.array([7,4])\n", " \n", " return sa2hex_aux(a,zeros-1)+ 2*sa2hex_aux(a%6 +1,zeros-1)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Computes the value of the hyperpel corresponding to the given\n", "# spiral coordinate.\n", "\n", "def sa_value(oversampled_image,spiral_address):\n", " # WORKS ONLY FOR IMAGES WITH EVEN PIXELS\n", " center = [(oversampled_image.shape[0])/2,(oversampled_image.shape[1])/2]\n", " \n", " # The center of the hyperpel for them is the point [1,1] for us\n", " hp = hyperpel_sa + sa2hex(spiral_address) + center\n", " val = 0.\n", " for i in range(56):\n", " val += oversampled_image[hp[i,0],hp[i,1]]\n", " \n", " return val/56" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Assigns the given value to the hyperpel corresponding to the given\n", "# spiral coordinate\n", "\n", "def sa_put_value(spiral_address, value, oversampled_image):\n", " # WORKS ONLY FOR IMAGES WITH EVEN PIXELS\n", " center = [(oversampled_image.shape[0])/2,(oversampled_image.shape[1])/2]\n", "\n", " hp = hyperpel_sa + sa2hex(spiral_address) + center\n", " for i in range(56):\n", " oversampled_image[hp[i,0],hp[i,1]] = value\n", " \n", " return oversampled_image\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Spiral addition" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [], "source": [ "addition_table = [\n", " [0,1,2,3,4,5,6],\n", " [1,63,15,2,0,6,64],\n", " [2,15,14,26,3,0,1],\n", " [3,2,26,25,31,4,0],\n", " [4,0,3,31,36,42,5],\n", " [5,6,0,4,42,41,53],\n", " [6,64,1,0,5,53,52]\n", "]" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Auxiliary function to recover a vector with the\n", "# digits of a given integer (in inverse order)\n", "\n", "def int2intvec(a):\n", " digit = a%10\n", " vec = np.array([digit],dtype=int)\n", " a = (a-digit)/10\n", " while a!=0:\n", " digit = a%10\n", " vec = np.append(vec,int(digit))\n", " a = (a-digit)/10\n", " return vec" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def spiral_add(a,b,mod=0):\n", " dig_a = int2intvec(a)\n", " dig_b = int2intvec(b) \n", " \n", " if (dig_a<0).any() or (dig_a>7).any() \\\n", " or (dig_b<0).any() or (dig_b>7).any():\n", " print(\"Invalid spiral address!\")\n", " return\n", " \n", " if len(dig_a) == 1 and len(dig_b)==1:\n", " return addition_table[a][b]\n", " \n", " if len(dig_a) < len(dig_b):\n", " dig_a.resize(len(dig_b))\n", " elif len(dig_b) < len(dig_a):\n", " dig_b.resize(len(dig_a))\n", " \n", " res = 0\n", " \n", " for i in range(len(dig_a)):\n", " \n", " if i == len(dig_a)-1:\n", " res += spiral_add(dig_a[i],dig_b[i])*(10**i)\n", " else:\n", " temp = spiral_add(dig_a[i],dig_b[i])\n", " res += (temp%10)*(10**i)\n", " \n", " carry_on = spiral_add(dig_a[i+1],(temp - temp%10)/10)\n", " dig_a[i+1] = str(carry_on)\n", " \n", " if mod!=0:\n", " return res%mod\n", " \n", " return res" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10000 loops, best of 3: 134 µs per loop\n" ] } ], "source": [ "%%timeit\n", "spiral_add(23,15,100)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10000000 loops, best of 3: 22.6 ns per loop\n" ] } ], "source": [ "%%timeit\n", "(23 + 15)%100" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Spiral multiplication" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [], "source": [ "multiplication_table = [\n", " [0,0,0,0,0,0,0],\n", " [0,1,2,3,4,5,6],\n", " [0,2,3,4,5,6,1],\n", " [0,3,4,5,6,1,2],\n", " [0,4,5,6,1,2,3],\n", " [0,5,6,1,2,3,4],\n", " [0,6,1,2,3,4,5],\n", "]" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def spiral_mult(a,b, mod=0):\n", " dig_a = int2intvec(a)\n", " dig_b = int2intvec(b) \n", " \n", " if (dig_a<0).any() or (dig_a>7).any() \\\n", " or (dig_b<0).any() or (dig_b>7).any():\n", " print(\"Invalid spiral address!\")\n", " return\n", " \n", " sa_mult = int(0)\n", " \n", " for i in range(len(dig_b)):\n", " for j in range(len(dig_a)):\n", " temp = multiplication_table[dig_a[j]][dig_b[i]]*(10**(i+j))\n", " sa_mult=spiral_add(sa_mult,temp)\n", " \n", " if mod!=0:\n", " return sa_mult%mod\n", " \n", " return sa_mult" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Tests" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Spiral multiplication is roughly three order slower than normal multiplication" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "100 loops, best of 3: 2.02 ms per loop\n" ] } ], "source": [ "%%timeit\n", "spiral_mult(435,316,100)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10000000 loops, best of 3: 21.5 ns per loop\n" ] } ], "source": [ "%%timeit\n", "435*316 & 100" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1000 loops, best of 3: 463 µs per loop\n" ] } ], "source": [ "%%timeit\n", "spiral_mult(15,10,100)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10000000 loops, best of 3: 23.7 ns per loop\n" ] } ], "source": [ "%%timeit\n", "15*10 & 100" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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JxcVF7ty5Qz6fb7vuxMTEuW3z8vIyhUKBQqEQBl49vJy6oIdvDfvg4CAbGxvUajUSiQQj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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "test = np.ones((40,40))\n", "test = sa_put_value(0,0,ciao)\n", "test = sa_put_value(1,0,ciao)\n", "test = sa_put_value(2,0,ciao)\n", "# plt.imshow(np.fft.fftshift(test),cmap=cm.binary)\n", "plt.imshow(test,cmap=cm.binary)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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/aYz53lHMwRhTBH4M/MYUl/0h4DMichP4a+DXROSbU1w+xpg7g69p4Lv0d2+m\ntfxNYNMYc2Vw/Tv0XwS2p/ncj2OSoX8FOC8iZ0XEA/w28P0JLu9evg98bvD95+jvZ0+EiAjwNeC6\nMear05yDiCwMjwyLiB/4NPD6NJYNYIz5Y2PMGWPMo8DvAH9rjPndaS1fRAIiEh58HwR+HXhtWss3\nxmwDt0XkwmDoU8A14AfTWP57MskDBvQ3s94E3gK+POkDFPTXMEmgRf94wueBGP2DSzeAF4DoBJf/\nT+jvz14FXh1cnp/GHIBfBf4e+Dn9f/b/MBif2uPfNZePAd+f5vLp71NfHVx+Mfx/m/Lz/z7gyuA5\n+F/0D+5N/e//oIt+DFcpm9FP5CllMxp6pWxGQ6+UzWjolbIZDb1SNqOhV8pmNPRK2YyGXimb+f9J\nypCLPNkVbwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "test = sa_put_value(10,0,np.ones((70,70)))\n", "for i in range(2,7):\n", " test = sa_put_value(spiral_mult(10,i),0.5,test)\n", "plt.imshow(test,cmap=cm.binary)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Time to extract the values of an orbit:*" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1000 loops, best of 3: 1.58 ms per loop\n" ] } ], "source": [ "%%timeit\n", "for i in range(1,7):\n", " sa_value(oversampled_example,spiral_mult(10,i))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Time to put the values of an orbit*" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1000 loops, best of 3: 1.54 ms per loop\n" ] } ], "source": [ "%%timeit\n", "test = np.ones((60,60))\n", "for i in range(1,7):\n", " sa_put_value(spiral_mult(10,i),1,test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*$7^5=16.807$ seems to be the biggest power of $7$ contained in a 256x256 image* (recall that in total the pixels are $256^2=65.536$)\n", "\n", "It corresponds to spiral addresses of at most 5 digits" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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dEBFPRsSPIuKJiHjtzPIPN21xMSLu7m7LlxcRn4mIqxFxYWbe0vsaEXdGxIXmuY+1vR/L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\nVGSQkFRkkJBUZJCQVGSQkFRkkJBU9P/aEVyOHD2HnAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "test = np.ones((7*256,7*256))\n", "for i in range(7**5):\n", " sa_put_value(base7_encode(i),0,test)\n", "plt.imshow(test, cmap=cm.binary)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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WvIylpSWYzWaEw+FNS1oeOnQIhw4delbPPS8joWmaC4BZ1/W8pmluAL8N4BYAPwTwxwA+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\n2zQObCJDT4JeBTM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uh9vtltCI/Ae7WNHb8Pl8LVxGu6EgD6Oma4lCodBi5Mxm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\n7dqlEqMrV65UDXYWwq9//WsA3n77bd577z21JZmdnU1fXx9NTU1MTEw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "test = np.zeros((7*256,7*256))\n", "for i in range(7**5):\n", " sa_index = base7_encode(i)\n", " sa_put_value(sa_index,sa_value(oversampled_example,sa_index) ,test)\n", "plt.imshow(test, cmap=cm.binary)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Videos" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "img = np.ones((256,256))\n", "for i in range(7**3):\n", " sa_put_value(base7_encode(i),0,img)\n", "# plt.imshow(img, cmap=cm.binary)\n", " plt.imsave('_tmp%05d.png'%i, img,cmap = cm.binary) \n", "\n", "FPS = 10\n", "\n", "os.system(\"rm movie.mp4\")\n", "\n", "os.system(\"ffmpeg -r \"+str(FPS)+\" -b 1800 -i _tmp%05d.png movie.mp4\")\n", "os.system(\"rm _tmp*.png\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.9" } }, "nbformat": 4, "nbformat_minor": 0 }