{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Spinning Circles Fourier Visualization in Python/Matplotlib\n", "### By Alex Miller ([@alexpmil](https://twitter.com/alexpmil))\n", "\n", "This notebook goes through the process of how to construct an a Fourier approximation of a simple image and then animate the approximation using matplotlib." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Main imports/Initialization\n", "%matplotlib inline\n", "import matplotlib\n", "from matplotlib import animation, rc\n", "import matplotlib.pyplot as plt\n", "from matplotlib.pyplot import imshow\n", "from IPython.display import HTML\n", "import numpy as np\n", "from PIL import Image, ImageEnhance\n", "import requests\n", "from io import BytesIO\n", "from copy import deepcopy\n", "from scipy.spatial import distance\n", "from scipy.interpolate import UnivariateSpline\n", "from copy import deepcopy\n", "\n", "# Default figure size in notebook\n", "matplotlib.rcParams['figure.figsize'] = (6,6)\n", "matplotlib.rcParams['image.aspect'] = 'equal'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 1: Image Manipulation\n", "The `ImageObject` class below provides functions for extracting a path of coordinates from a simplistic monochrome image. This path forms the basis of the parametric functions that I will be approximating using Fourier series." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class ImageObject:\n", " def __init__(self, url):\n", " self.url = url\n", " response = requests.get(url)\n", " self.img = Image.open(BytesIO(response.content))\n", " self.og_size = self.img.size\n", " \n", " def show(self):\n", " imshow(np.asarray(self.img))\n", "\n", " def monochrome(self, scale=3, threshold=200):\n", " \n", " # convert image to monochrome\n", " image = self.img.convert('L')\n", " image_array = np.array(image)\n", " \n", " # Binarize a numpy array using threshold as cutoff\n", " for i in range(len(image_array)):\n", " for j in range(len(image_array[0])):\n", " if image_array[i][j] > threshold:\n", " image_array[i][j] = 255\n", " else:\n", " image_array[i][j] = 0\n", " \n", " image = Image.fromarray(image_array)\n", " \n", " # scale image down to reduce number of non-zero pixels\n", " img_sm = image.resize(tuple([int(v/scale) for v in image.size]),Image.ANTIALIAS)\n", " \n", " # convert image to black and white\n", " img_bw = img_sm.convert(mode='1', dither=2) \n", " self.bw_img = img_bw\n", " self.pixels = (1 - np.asarray(img_bw).astype(int))\n", " self.pixels_flat = np.reshape(self.pixels, self.pixels.size)\n", " \n", " def show_bw(self):\n", " print(\"Dimensions: {}\".format(self.bw_img.size))\n", " print(\"Num. pixels: {}\".format(self.pixels.sum()))\n", " imshow(np.asarray(self.bw_img))\n", " \n", " def get_tour(self, starting_point=\"random\", plot=True):\n", " # Get greedy tour through pixels\n", " \n", " absolute_index = np.where(self.pixels_flat > 0)[0] # positions of non-zero pixels\n", " relative_index = np.array(range(1, len(absolute_index)+1 ))\n", " \n", " # Replace each non-zero pixel in the array with its number\n", " # i.e., the 10th non-zero pixel will have 10 in its place\n", " flat_img_mod = deepcopy(self.pixels_flat)\n", " for rel, pix in enumerate(absolute_index):\n", " flat_img_mod[pix] = rel+1\n", " \n", " # Get coordiantes for each non-zero pixel\n", " img_idx = np.reshape(flat_img_mod, self.pixels.shape)\n", " self.coord_list = []\n", " for p1 in relative_index:\n", " p1_coords = tuple([int(c) for c in np.where(img_idx==p1)])\n", " self.coord_list.append(list(p1_coords))\n", " \n", " # Calcualte distance between each pair of coords\n", " dist_mat = distance.cdist(self.coord_list, self.coord_list, 'euclidean')\n", "\n", " # Initialize search space with nearest neighbor tour\n", " cities = self.coord_list\n", " num_cities = len(cities)\n", " if starting_point==\"random\":\n", " start = int(np.random.choice(range(num_cities),size=1))\n", " else:\n", " assert starting_point < num_cities\n", " start = starting_point\n", " tour = [start]\n", " active_city = start\n", " for step in range(0, num_cities):\n", " dist_row = deepcopy(dist_mat[active_city,:])\n", " for done in tour:\n", " dist_row[done] = np.inf\n", " nearest_neighbor = np.argmin(dist_row)\n", " if nearest_neighbor not in tour:\n", " tour.append(nearest_neighbor)\n", " active_city = nearest_neighbor\n", "\n", " y_tour = -np.array([cities[tour[i % num_cities]] for i in range(num_cities+1) ])[:,0]\n", " y_tour = y_tour - y_tour[0]#- min(y_tour)\n", " x_tour = np.array([cities[tour[i % num_cities]] for i in range(num_cities+1) ])[:,1] \n", " x_tour = x_tour - x_tour[0]#- min(x_tour)\n", "\n", " # Circle tour back to beginning\n", " np.append(x_tour, x_tour[0])\n", " np.append(y_tour, y_tour[0])\n", " num_cities = num_cities + 1\n", " \n", " self.x_tour = x_tour\n", " self.y_tour = y_tour\n", " self.num_pixels = num_cities\n", " \n", " if plot:\n", " plt.plot(self.x_tour, self.y_tour)\n", " \n", " def get_splines(self, degree=1, plot=True):\n", " # Convert tours into parametric spline curves\n", " \n", " x_spl = UnivariateSpline(list(range(0,self.num_pixels)), self.x_tour, k=degree)\n", " y_spl = UnivariateSpline(list(range(0,self.num_pixels)), self.y_tour, k=degree)\n", " \n", " self.x_spl = x_spl\n", " self.y_spl = y_spl\n", " \n", " if plot:\n", " p = plt.plot(*zip(*[(x_spl(v), y_spl(v)) for v in np.linspace(0, self.num_pixels-1, 1000)]))\n", "\n", " \n", " def plot_parametric(self, num_points=1000):\n", " # num_points = number of points at which to sample the curves\n", " t_vals, x_vals = zip(*[\n", " (v, self.x_spl(v)) for v in np.linspace(0, self.num_pixels, num_points)\n", " ])\n", " x_vals = np.array(x_vals)\n", " y_vals = np.array([self.y_spl(v) for v in np.linspace(0, self.num_pixels, num_points)])\n", " t_vals = np.array(t_vals)\n", "\n", " plt.plot(t_vals, x_vals)\n", " plt.plot(t_vals, y_vals)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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4zUv4TY9HOBzGn//8ZwwaNAiff/45otEorrnmGtTXd4OqqujZcz+oqpI1J8en\nRxk6f+oZ9dvnO//BCzk3sHGBvLwFfoVrkP29bGIBuSFXzBeKUkrJjkRH+9srCA70xCzqDsgXfHuX\nsl3pmQC9ehW+TzOX5Sj6XSjTMk0TqVQKn376KVQ1E/P/8ccfx+7du/Gn2bNhWQDl325uSMpL+Lah\nrp5ctPHWKQ+/QtiP9cuvQnR7rliUpQDgJTiV6n47XDF5UvCNzZt/xYD3CXuZijxNwmse5PjZLehV\nt/lcZzWtIJmZiD43puLVjn4VCFbD4pmFV11RTZJPz+3ZYmnP1R9FrgW6RJFYFjZuaMB//dd/uaab\nqxx+21R08paoDHSFEPWls/nTVTSWZWHy5EPw2WefoaUlhZaWJgCAaaSht+bDB8Zjy0KtH7cwD37h\n1lZuQoLyMdO2WucmLMDKnhBnxypd5GFZVuZAGHod2W6zYlE2LiA3BMV0c8HL/8pORhUagpVNm54t\nCog7kp/GFfmY9zRE5xnngle9+30vn/TdPiwok8hXiy+EpiDg18XCLsFsaWlBLBbD73//+0BoKBSs\nr5syedHB9GwZn376aVRVVYEQgmg06hweT98V1QWbhkijLqULkc87nU63o9HLJSS6DnRQNNA9jSCl\nXRAIguEGZU2UE/OnyNd/XWoU4lOnbZKPz7rQdvR7BoVfeJWXWmayLOOee+7Beeedl7Vmfk/Bj5+b\n/d+jRw988cUX0HUdF1xwATRNw+7du524QFSQuLWPV1vlUgwK6d+03mm8In6CWpSXl7JJ8w+iz3QK\nAQCU3gLwmsTiY4IXm77XhFM+E3rsdzmgEM3Eq96DADvBzufllm+pNUI2X79RJIMAZUS6ruMf//gH\nTjnllLzCQZcCbF14CV62TXRdR+/evfHxxx/jwQcfxLfffovq6mpEIhEAcA6t9yugS9n/KO1A9qZR\n9jf7jOg9r/SKha9QEKWG10Ywkd87aAQxSSVKz82H6zcPLz9jIXXi5WMu5Dl6jzfR/abrlWY+KFX7\n5ZueqL1FbZWrHf1aIDzNufpFKpWComTi5YdCIaRSKecam3d2+Vl3TAAMh+TeaOXVf2zbdtb4W5aF\n+m5dsXvXLliWjeaW5naH24gOUfJDC/sMSx97nT1Anp2nbKdACvz2hBBIIMJFLiJrwO1/dXX1HgkF\nUTJ4Se1SamZBmPNsA5aK9j0psEXMhWqxfphVoczUz7NB9otc4T+CQJDp+y1/JBKBoijYsmUL0um0\nE3DNCx2J/qRRAAAgAElEQVShHdOP1zm4LEzTRGNjIwgh2LBhA6qqq3H/A/e3mzvIhwY/ZWStNf7j\nBd66YctciDs4SKux7AQAj1Kb4xRBuVSCdFnxQimXtpJven5cIH4Ghx+N2S/tQZq3haLQ/sZbQbk0\n8nzmGNyu50NnIpEAIQRnnXUWIpEIQqGQ8FhFr7xKPR79zIcYhoGamho0NzfDtm3cf//9uPSSS5wD\nbjqCX+QD6o4SCbhcY8/NNRRUGctOAPC+WTf/rVfHzNdFwjPDfKSyW4MFqTHxZSpmHoL97bcjuQmN\nXC4ft7z9MJV8OreXllpIXflZduyXJkDMsL383Hwa/LNufZWQ9rtRWUQiERx00EF47733sH37dsdX\nzo+37LRl58NrvbnqnacNgBOmIZlMOi4fVVWdw+DZMrDvsd+KoiCdTkPTNIRUDadOOwWXXnIpDh43\nHldeeSUIyawOAjJtmU6n2/Ut9j87aew17tkJe8MwXPusBTvrk7U6zsos26ZxvUT9ge87hYw3vyg7\nASCCXwbjNjDyyYP/LpXp21nREVrgnkApy8QKFK/wD4X2XRZeSoJhGNiyZQtmzpzpuINY/38ueLW9\n1z2WJkmSUFtb6zBoy7IQj8cRDoezxlyuvKhWnUqlEIvFcN9992G//fbD888/j02bNmH37t3QNA2p\nVArhcNizntiQGqzwcQsFwQvLoCBSEtg8glwtRlH2AoBtbBZ+LYJ88mGZv18BUOyALRSFaO8VuMOv\nO6yQ+vQKBx10//FK65FHHoFlWfi///u/rFUy+abtxyphwY7hb775BvF43Dn/t6WlBYcddlhW5M5c\nihwhxNHaa2pqnOsfffQRnnrqKUyYMAF1dXWOpZJKpdq1Hb9SiKabT12wafmF3/7ECiK2/wSNshAA\nuToiu2zSrRL4zlKMpHRzAZWKkebDBEQCjwcfe4R++HNMvcxdr/zpO3wwsnzSyFfb5Z/jtWY3BN1e\nXkoHn6+bZu+lKfuxZN3ui5iIaZrO+vhrrrkGq1atyhoj+VgAfuuF7yP0GETDMBANRxAJhdHw3UZA\nIlixYgXWrVuHwYMHQzcz5wITWXLo8mpbQgjS6bTzkSQJRx55JKZOnQpN0zB//nwnIqiqqs4YoBPf\njluGoRVocwnR66J2ZOu6HY2WDdu0YBkmLMPMit/PWg9U6LkpuHz+IgupWJSFAPDDAPZW1wNQmJbu\nxTz9Mla/ebrV/Z50j4m0aRH21j7Dwq1slNlJkoSlS5eiqakJXbp0KXi1TDFgmVdzczNuuukmaKqG\nXr16Qdd1NDQ0IBaNZblkeAbt5yNJEp588klccsklOPnkk3HttdciHA47ZY5EIs5z9JvSRTeRUWZf\naJ9h0+IFLKuAURro816KAf97r1sF5FbhQUq7fQX5CAD6vF+4abV7UhiUEqUoY9DpubUjIcTR/p99\n9llH0wzajywCa4WyzPmdd94BAKxevRonTjkRffr0QW1tLQYMGICDJxwM27ZzrkzyAj2R7He/+x2u\nvfZaPPLIIwiFQlAUBaZpIplMOs+KrB+W1/D9nIVXv2BP8uOFLTsfxAoh287sEKYfv9ZgsSgbAZAL\nXo3R2VFIuYLSbP3k69v07UD4ZWR7a58RgS8j1UBN08Rdd92FcDgMwzAKilRaKHhm2tDQgFgshgcf\nfLA1oFsLzj33XEQiEaxZswbNzc2IRWNCDV304S0Aeh5wOBzGb37zG8ydOxe9e/dGdXW1o2nTQ+T5\nswdYhl2MlaQobWGpvQQH/U+D0+UTFiSoCeGyEgBug5Q19/NheH6fdXOjiK7x1zvCxSDKl12K5zah\nxF/z6zv20jj4eOuFaCdu9OZ6h18eSMteyDyEF138Nbff5eKW5M+ldsaKaSEZT+CE43+IkKrh/PPP\nh6ZpAuZktfvYtonsXcDudQG0TVTyE6v0wHZ678NFC2HaFn76Hz/BEYcdjh//5AyMPmgMli9fgb59\n+2LatGloibdkMX9eCND8bbttVzAdD6ZpOlaArus45JBD0NDQgGEjhmPgoAPwX5dfhpSezqo307Yy\n0TdlCZBIZueuLLWLpOvlemLrhN9IyI4PlnGzbi6vcWTBztAitUUMDUqpKftQEIUgXy1V5H7y6wNk\nO7oX8yiksbx8gW7PeMGLBjYd3rfolUdHWgSFuKyKTZ8KOdFvHvx7outu74qec3vH6zlWUSIgeGfB\nAkybNg3Lly9Hz969XI5JbK9Jtj2THZdeVBfs82x4BCf11rkI27Zx4IEHIpFIYOXKlbBtGzW11bAs\nABbBp0s+wWGHHYaWlhYY6eyjKkXMn6eXFRpAxgKim99iVVW45Xe34O6778bOHTsw6/pZuPnmmxGP\nxzMTzy5jiz2H2619c4F9TyQcaHpu7doupLvV1k9jsdjeFQqis0HkGtnTKNZ3WKhmW2oG3ZngVe+l\ndEvRVT+EEDz37LOYMmUK5s2bhz59+kBRFGfDVakg6jOyLCOZTEJRFGzbtg19+vRx9gHMmTMHNTU1\nIJKEUaNGYdy4cfjggw98910vqzcejzuxj+KJOK677jrcdtttCEcimD17Ni699FJUV1dnCcVC24Qy\ncD916+XpyGV1s/+DaMeytgBEBzdQeDVYKRgR62rxo6mVYnC7nY6Wj+vF7VnWDHUrQ66y8/Sw6ZRD\nPys1/GrptB7dDi5hQe+L3F+0XqnLg270uuGGG/DMM8/ghBNOwHPPPedslvLbHqw7iV2F4zXW6Nig\nz7OaOB3Hu3fvxv4DBzi0EUJgpHWYpumsVkomk+jRowcaGxsRj8cRiUScZaS0Hui337oD2nz61FUk\naxoGHjAQ27dvh22a2LRpE0KhECRknykg2rjn5j51EwJuFqBonHhZmBQW2vhQVbRiAewzCEJzdAt0\nVtHaOxZ+hSmrdNAPdTdS5qTrOmRZxtq1azF69Gi88sorePnll/HSSy85q0r4HaW58mS/3cDvnqUu\nGD59yryfeuopJJNJHH/88Vl+/VAoBCAzKatpGmKxGM4//3xEIhFnFRMFZbD51B3PpC3LQiqZwLfr\nvsavf/UrqKqKo48+2pmnICSzespr17bfzX2s4sjPjRSKoOa8gE4gAIplen7dGYW6S4JOo5Tw8jeW\noyuLRbnXLZD/bmI/cPN3A20bvVRVxTHHHINRo0Zh2rRp2LFjB4499ljnsJdIJJIVKI2nyS3ffMAe\ncqJpWlb6uq5D0zRs3rwZkUgEmqohkUhk/O/MChhCMnGB/vKXv2DOnDnYsmWL8HAXmk8+bk7ejaIp\nKpqbmjDruuvxzjvvYMWKFRg4cCAikYgTPoI/U4DPt5C68qKTtmdHLNOlKMszgSm8KsKvBuBltuab\nVq5neU0jaATB+HKtpvLKI19XU5CM2k998vlmTHh2TXn7g7Zz05jPYPSnT3nlyZ4aRVfPAEDa0KGp\nGmzYSMRT2Lp1K+6//3689957WL7sCxx33HGwbdtxBQFtTNmyLEfL5hmXSAjQc4PpM6w7hPYffrKX\n5sm7jKg2nUql0KdPH+cdSZIygsJq04gJIdB1HaeeeiquvOoyjBo9HBvWb3KWVVL6vQQXpZPVtFl3\nG83fMAyoqopUKoUDh49AoiWO8ePHgxCCRYsWYfjw4Y5bSlRfblo/X3ZC2h9xSZ/hv9n6zOJ9Unba\nMglOby/rOYBSgR/8foRER9DjRks+7xeaRtDwKyiDhKhd3Q40CUIAtK938fr6fMtLmZyu6wiFQvjs\ns88w95/P44MPPsA7CxYgFFaQThsIhVRUVVXhpv/vd7jkkkug63reroVctGXXZduz/OEtoj5ImSWd\nlH7qqadw/gXnQ291r+i6DlVuv1NWlmWAGFDVCGzLbueO8VK0qEXB++P5sc5r9PF4HLW1taiqqnIC\n1LW0tGTtmfBy4fBj2EtYiN7jn8uqa3Crr5giV1VVFTUHUNYWQGfDnmB65QovoVSswOvscCs/ZRym\naWLRokU4+uijIUkSqqurMWTwAKxZswafLl6E8Qcf7LyTTCSghWJ5M/9ck6huzIudk/DSxGn6dL5C\nVVVEIhGomgZZkqHreoapy9lpAxnrIhRSUF9f46TlF27WZ67JVUVRkEqlsH37dgwYMACEEOzYscM5\nZpJNwy8Nzj4DxgIot76/VwoAv5VcLo1RbN7l0JFyoaMEIO8CKmW2Qdc7db3Isoy//vWvIIRg4cKF\nGDduHGS5lTkaBiwjwzUNw4CqxGCaJjRNaxdCwavOvSygXPd4d4XI1cpOVNPJ3BUrVmT74TUNYEjM\n0uzhHhLCq1y8YBO5PN3cLXQuYtq0aZgzZw7q6uqyQkcA7iuoRPM+1BLxK5hdFQPB/6BQdpPAXhNl\n+UyeeUE0eVTIBJ1f2kXacKETmm4mdy6a+P/55FtsvfDwW3a3iT639/jB6bWdP4g5Cj991Y1ZiPod\nnfC84IIL8NJLL+GBBx7AqFGjsHXrVhgGYBiADQWmbcCCCUkhgGQ7fnaadi6w2qnfcrJuFd61Qv+z\nvykzZePc0JO8dEN3DlXhD05x5gIM4JRTz8DHnyyGpMhZdNB8ROEWWFqANqbOtoXIraUoCgjJhJl+\n4IEHIEkSnnnmGecwGX4JNmtRsOmzebDB5dhxx+/cptfcjnqUQDJuH8t2NoEFhb3SAnBzN/D39hQ6\n0h3Ed1TWLOUHTjnAq+38ItfeET4fLwTRf3KlQRlDMpnE9u3b8eKLL2L9+vXYunWr44Lg49b4gSif\nfOGm8bLp0W++3mk/owJg0KBB2LlzJ1RFFT7PMkjTsnDKKafgsccew+jRo50duSyDF9FF77ET1jy9\ntF7Y9f4UlmUhkUhgxowZuPXWW3HGGWcIT/+itPtVZPK5LnrOyyorBmVnAVRQOrArOzoyIFg+KNba\nKFeh5mW90Gtr167FsGHDsHjxYkiShEGDBgEAFi5cWFC9FGrVFvoev8eE9jPa1w4//HBomoYt32+B\nruvtLDRWa5dlGQcccADWrFmTtXuZCggRnSI3D2+x0HuikBUAHK39F7/4BZYsWYKtW7c61gpfRyzd\nQVvJPAr1GORC2QkAr8HCm14UXhXvx3VQqkYLukPwGlc+afODgF9V4fXJhz4/7ZCLzmI7enY/Ic4n\nO+CZO3iTPZsmyfnw/dFvncXjcQCZNjAsE7KiQNVUjBs3Dv/4xz+w//77o0uXLgCA7777DpMnT856\n3y3SJE3TjQY3Td0maOeKAUQCNBMkjn7zrg/+bF26IkfXdRBCMHjwYIQ1FZ99shhaOApFCzvn48pE\nykqvJZHA2HHj8dm//41oVRVkWYamac7eBp4+vt+wrhfRs6I6ZOusX79+0DQN0398BmwCyGq2s4S3\nrHMJeJHrR9Q+ztgmbe1iWCZM23KCwbGfYlF2AsALpZay+dAB5KdhlkqCFwOvzhg0/LZdubSxH7gx\nmFyorq6GbWeWeYa1EH41a5ZzGMqkSZNw/PHHIxQK4bzzzkOPHj1c8xV9ckWIFYHtl6zPnGfwdDkm\nZfD0eZYuEWggOFmWoaoq3nzzTSQSCSQSiazysGkqkgTYFnbv3AnbNKHruhPm2S8KjZlD91Kk02l8\nyMQlYuFHscwXtM5FrjRRmwaBTiUAgkYxlVmMprynIOq0Ig22HFHogAu6XEG0u2maUBQFH374IWqq\nqnHv7Huw9N+fY/v27di6dSvWr18P27Zx7733wrIsNDc3e6bHuzpYZppPOURlMU3T+YgOeaFpUb+7\nW96EEKRSKQwcOBBPPPEE0uk0YrFYFj3ss7BspJMpqLKC55+b66RJhYYfuIU9yfWOJElty2pJ5tjJ\noHbnevVh1nLi32GfYdMpFjkFACGkHyHkbULIckLIMkLIla3X6wkh/yKErG79rmu9Tgghswkhawgh\nSwkh4/MhyEu7YStPtIqhUA0z34rkGWiuxugIH2EusIMUaB9Yzu/HC7wm6aYd03pgl+zR/170F1KH\n2fTLzEfsTuRhmnbWR5Rem1uoPb0AnElE2g9kScaPp5+Bc846G41NTdi9ezdeeOEF9OjRA4sWLcLq\n1avxy1/+MrNMEkA4HPYcF3y+9Nut/fjxQ7V7+o5pW0gbOhRNzRp7umnBAoGihaCb3HnTrTH0aUx9\nnjbq71+wYAEGDhyIFV9+DltPOvH304buxL2XFBmhUAiyLOOjjz7C5ZdfjkgkglAohOrq6nZtRN09\ndAUNW3a+LwDtl4pS15Wqqk4fpMHzDpkwERJI5oxfRvCxgtAvcr3Hzm1QtxixAcswYZsWJBCosuKs\nCiIBsBI/FoAB4H9s2z4QwGQAlxFCDgRwPYD5tm0PATC/9T8ATAUwpPVzEYD/y4cgvwxnTzPUckC+\ngotdlhfEeaJe8Ao+Ru+xgcNEmk+p4afveC3Py9VX2XuKojj+8PNmzsT8+fNx9NFHAwB27NiB66+/\nHl999RVUVUVtbS1uuukm17S84Pc5ujqHPkcDxtHAcqqqZnbqqqpzqpimaZBl2TmEXQRRndL+RgXN\n/PnzceyxxzoxgwzDcEJV0Hg41A0zcuRIjBkzBn/84x+dk7xUVXUOfqFlYcNesLuBRTS5uXOolSPL\nMk488URIkoQ77rgj64QvNr1CNXC390SWHJ2U5gMABoWcI8627U22bX/W+rsJwFcA+gA4FcCjrY89\nCuC01t+nAnjMzmARgFpCSK9AqS4ChbgRygWFaOVeKKUQ5TVO0X3+26/AD4Jer/SC7iNUs7zjjjsQ\njUaxcOFCrFq1Cn//+9/xw+OPx+DBg5FKp9G3b1/MnDkTO3fuRDKZ9IzcWiyNbHhl9jSvUCiEVCrl\naMnNyQSShg4oGaFAY+iw7htKE61LykhFtFNtffbs2ZAkGc3NzYhGo+0ErW3biEQi0HUdb775Ju6+\n+27U19fj/fffz1hRsizc50EZOW91814EHnT555///GdomoY333wThmFg7NixQsZfaBvkUhhE4SDY\n/NkyBDEO8lK5CCEDAIwD8BGAHrZtb2q9tRkAna3qA2AD81pD6zVf8DvQOzMj31OgmhHrCioVWA1G\npNnTtmUHfGez5nL1VXr9mWeeQZcuXfCrX/0K0WgUX61Yge777Yc5c+Zg8eLFWLBgAZKJBP7+9787\nmix7wlw+zMavkBRZAIQQZ8UOPVv3oosuwn/+53/iiCOOwH//93+jsbHRsQjc8mfhuIha+x09oOWC\nCy7AxRdfhO7dujkRTNlJZkmSEI/Hoes6UqkUvvzyS4wePRpTp07F2LFj8eqrrzpWAysMWAvAiy4W\ndF6htrYWv/nNbxCLxTBgwAA0NjY6ZaAWHFtnxcDLYgSy3UF8P3B7vyA6/A46QkgVgHcA/M627bmE\nkF22bdcy93fatl1HCJkH4A+2bb/fen0+gOts2/6ES+8iZFxE6N+//8Fff/21MF+WPr7QbMXwvk+P\ncoive1RDruVWQXUKmhYPt87i1nb5aAciZuHnSMhiLY98tRiRNlRoGmw6FG6H7fBLRtmAb24uBiCz\nsxQAmpub0btXD/Tr1w9LliyBFgoBtoQpJ56If/3rX1j79Tr07NkToVAIY8eORXV1Nd5++23PPpXL\nUvICdSOwaVg2cVw+lmVhyZIleOedd/DrG24AkHk2FAohmWxz+xxx5JGYcuKJOOnkkzFm7BjAzlgS\nLS0tqK6uhkQkJJKJjEuFtF8yS7Xdxx9/HLfcchM2NHyLdNpGWk9nmK1htmsvVVWxePFinH766Whu\nbkZjYyMSqaTD/CPhCJLMJDFbRr6/0PODQ6EQdN2EpqkYMmQoNjQ0YPDgwVi1ahU2bdqESFhz9jK4\nCT03viT6z85ReLmSvPoWy49ikWjpD4QhhKgAngPwpG3bc1svb6Gundbv71uvbwTQj3m9b+u1LNi2\n/YBt2xNs257QvXt3r7yFmg+79rYj42fzYP2bQYAtL7uMLYgyijRWNh8/Gma+NPFmLb1WbJl4s5zC\nrwXp5hooRrDxPlxd1zF27FgcPGECvly2DHrrZqL6ujpnt+uAAQMgyzI2b96MZcuW4YknnnCERz7w\nU5+sVcYLzu+//x7Tp09HVSyGKVOm4C9/+QtOnDIFZ511FjZu3IhFixahpqYG3bt3h6qq+GjRIjz3\n3HOYOnUqQuEIFFnG448/jsbGRhBC0NTcBNvOBIETuVCAjBVy7rnnYsWKFbjttttw5VVXOv5/3o1E\n5wbGjh2LVatWYdeuXVi8eDHCoRDWrVsHVVWR1tOu8zV8O8uy3CrUkpAkCZFIFJs2bUJjYyOWLl0K\ny7Jw5JFHOnMgup59RjFPm8jdxFvBrAXuZTF2pCXsZxUQAfAggK9s276LufUigBmtv2cAeIG5fi7J\nYDKA3YyrKDCwboNc4VZLWbGseRsEWFq9Th0KAvxEmZ86ypcmL8ZUTHu4CYA9Cb4ObdvGzp078eK8\nlxBPJhCNxXDbHbejvr4eTz/9NAAglUrBtm288cYbiEajGDBggHMyViF55wLrQqDvbNu2DQMGDMBr\nr70GAEgmk1i//htcffXV+Oabb9CvXz+MHTsWMpGwc/sOHH7oYRh8wCAsWbIE4XAYr7zyCrrvtx+u\nuOIK7N+/PyKRCKqrqkFIJsyyyGqj/9PpDNO++qqrcc/s2e3cLSzd9GhI+n7//v0hKwqmT5/uTF7z\nZeU/tMypVArxeByWZTmnkLW0NEGWZfTt2xeSJGHXrl1Ci4mv91xgl88WorB6CZdi4YerHA7gHADH\nEkL+3fo5CcAfAPyQELIawPGt/wHgFQDrAKwB8FcA/5UPQV6FFGmvfMPw0tWtA/AfuguS32lnEzhL\nrkRLr9gDMIKASBPlmUqu/NzuiQYEfZ69xnZYt00pxcJNgOSinUK0zFT0LlsOfukwK2iz3YiZ3a65\ndgzzu0lpQLFMuSwMGzYEK1d+hVikCpoSAoGEWdf9CmvWrYUa0mBaphMk7d5770XXrl3buQdEEPVf\nUX3yyxb5e0DGfz7z5z+HIsuIRiJQFAVDhw2GJBGccuqP8Omnn+KII47AzTffjPMumIGBg/rj30s/\nxcjRw/HWu+8hHA7jtCnHY9LEyXh3wXt4a/4C1Nd2hUwIvlq2HJFwDJAIUnoaaUPP6suSlFkyalg2\nDIugd59emDFjBpKJtLPyhS0vpZvOT1RVVcE2LWdppG22j89Dy862lWVZUNUQqqqq0L17Zupy69at\nSCRSWP/tt9ixfTuikQguveSSdv2DfmhbO+VgkIvniFxGfHuz/ZsNkkcIgQTSFiCuSOS0Ne2ML99t\nxB8neN4GcFmRdBUFXsthwQuHYsGfVBQkgrIqis23I+nwajs3eD3HM3z+Hh2QrHbmt7j0oBP6oTFr\nfvazn+HVV1/G559/Dk3LHH8Yi8WgKAqSySQMw3CWFlqWhWg0io0bN2LChAk5y5MP2LLzbUj77UEH\nHYRVq1ZB0zSkUmkcddRR2N3UCK31IJpBAw9wnk8m4/jjH/8IWZZRU1OD559/AQ8++CDOOeccfPXV\nVxg1ahRGjBiBtWtX49bf34LDDjsMW77fhmgsjKqqqkw8HS6apaIozuRvPB7H6NGjMy4wu32cIMqM\n6Uqka6+9FuPHj8fixYudsM28q4cinU47TJsQAlXN7OGgcx/JZBLRaBijRo0CADQ1NeHqq68W1hnQ\nFkiOziV4WcOFjB+6Wkq00zrI8Vh2O4FFGmq+KLUvTWSh5MorCB9zOSAIc9QrDb/16aYFe/Uft+eA\n9stS/YB/VlVVvPHGG3j77bexbt06DBkyBDU1NQiFQrjlllvw+uuvO0HQJElyAow1NzdDURRMnTrV\n2ZAV1LyWW9s0Nzdj5MiR2Lx5Mz777BNYloFJkybilVfmIRKJgBCCoUOHOtpuKpWCqqpIJpPQdR2N\njY34wVFH4IYbbsCq1WvRv39frFmzCtFoGLFYDL1798bxxx+PutpabN68GfF43FnHz9NH6zEWi2HF\nihWuRyjScoRCIWzfvh0PPPAA3nrrLceNxLchyzCj0ajDsBVFwezZ90JRFGzduhWpVAqNjY1YuPAj\nWJaFdDqN1atX+wqYWEw7+Rk/ufp0sehUR0L61d6pv1D0nOg9UR34fc4tfzfXlJubIt/GLUTrte22\nCUDKhPykw9JXaH9xo4mdy+HTLuXGMP/1xzOjNppkWXYYOiEEEyZMwKpVq5BKpdDc3IxIJALTNLFu\n3TqMHTsWLS0tTv23tLSAEIJIJARCCKqrq7Fq1Rr06NEDhGTCD8iyLFzs4Mbo2N+8K8m2befQGF3X\n8dxzz+HnP/85li9fjgMOGADLshAOh7FixQqMnzARF198MW666SaosuLaLy3LgmXq6F5fh1599seK\nVathmDbCYQUHjx+LJUs+R319LfRW18yuXbuQTqedjVv0Qzd9hbXMEZcff/wxBg8ZgXQ67Ww+M420\n0x/oterqamzevDmrHmgf590ttP4Mw8D555+P5//5ItLpJLZv34lQKISWlhb06tkTQMYSMU3TiWHk\nB+w8gZviwS/tpdYD7UvsHIcb/+LbORrtgFVAnQ2FMNRSIx+G7SYoirVsqFnJ7pwUpe2mhZeCJl6o\ndyZLie6UDYfDkGUZX375JZ577jlnc5Ou69A0DTNmzMD//M//OOUyTROxWCzruEFN09CzZ09ntzA9\nEJ717fupF5HGyOZrGAY2bNiAGTNmYPny5RgwYIDDbBobG3HmmWcimUzizjvvFCox7EfTNMiKgqef\nfhobGr7Ffffdi3i8GbpuY+HChXjhhecdjVqSJNx9993OTttUKgVFVhxma9uZCeHXX38dp5xyihMv\niQoH2m8ty0IymYSiKBg4cGA7N5fbnhLK0Kurq/HMM89gzJgx+P77bYhGo5BlGSeccAJkRcGCBQug\nqqqzIc4vvCxIQohwGalhGI5/n7oTg7T+/GCvtADYkAc8eGYr0qLc0vdjKbj56fxoz7loKHb+gi8v\nryHy8JNHPlaZ6J188ioW+Vhwbe+4WwDscwMGDMCsWbNw8cUXQ5IkJBIJqKqKhoYGDBw40GFw7733\nHoDKQ4UAACAASURBVL744gtcfvnlrVp+Zo19t27dsG3bDqRSKWdugDJ+ti+L6pu/5ia4DcNwdt0C\nmRVIGc3YcP7X1NSCyJlNWKqqQk+ls9aus9BNAyFVQSoZx8aNmzBq9EFo+G4jqmI1MPQUFEXBxo0b\ncfrpp2PlypUZlxcBFn/yCYYNGwZN05zJTkVRkEokEYlE0LVrV/To2RsrVnwFw8gILYK21WeRSASR\nSAR//OMfcUnrRC1bHyyjZWk2DAN33303br75ZmzesrV19U8EW7ZsRa+ePSHJMnbvypwDnEqlnG8/\nyOWf58ebm6DghVfFAigA1HTOh+F6xXzxC1ZDcxuEuZiflwZcrHbMxhPxWrnA0+pWJi+a/Pg3+TTL\nUev3KgftY7/85S/x3Xff4dJLL3UmMwnJLGccPXo0li1b5rzbq1cvzJo1C6lUCtFoFKFQCMuXL0dt\nbW0mDDKzkoi2FRuoLRcoTaLvaDQKTdPQu3dvJy86GU03RQGZuYympiY0NTVlabbt6kKSYFgmFE3F\n/vv3w3HHHYNevXpAVghCoQgACQMGHIAP3/8ALU3NuHf2PQCAyZMno6a6Gv369cOiRYvw/vvvY+XK\nlTjqqKMRjVbhpZdexupVqyBLctZKNLoy6IknnoBpmqipqcnSlukKIVGgSOr7nzdvHgzDwB/+8AcM\nHz4cEpExcOBAXHnVVdi1a5cjfKkl5hdelhfN388+DZpWR6FsBADfuUQDzi8DZP1nfDps2nzcDbd8\nRVLZjemx90Xg/ZVsLJZCNX4/kQnZjiiyjrzyFgkCUR2JDtlg74v8smyahZu+9IASw7Md3ehxa+/M\ndSnrw5rtQIYpPf7447jmmmuQSCRASEajD4fDGD9+PLZt24YDDzwQAJxNRbZtY+7cuY57pKamBrfe\nemu7pa3UdUA3hrFzAF59j9JOXX2GYSAcDmP06NGwLAsNDQ1Ip9NOjH2aT2Z1kgSJKHjv3Q+gKiHX\nNieEQAEBLALYCtK6jRdffBEENvr17QnD0mFYOnQzDUmRoYVDuOyKy5FKJjBi2FCoioytW77Hcccc\ng5OnTsG4g8bgq6+WQdMU/OAHR2Z2TAMIhVTEYpGsPrN48WIQScHulmSWkGPLD2Qvn6RlePbZZ9Gt\nWzfcfttt2NjQkLluGbjrzttRXZWZKKartPg5F9rHvfq5uA+1vcum5+Xy5K+xvCJIlI0ACBJeGmuh\n6RWrffMdwstnyL/HfnvRB7TflVgIfXRyjk/T6z3eTeFVZ7wwKLZugfYxhXIpEH4tPp6+UCgEy7Iy\nPuxW7Xnq1Km49dZbneiWdFPSMcccA03TnJg2hBBMmzYNt956K5544glHK33yySfRs2dPIe0iwZhL\nyKmq6tSJbdsYMWIEQqEQVqxYgZaWFifGDQUNPBeNRmEYFqZMmYIzpk9HIpFw/PM0PVp3fFvRQHHr\n1q1FS0sLopGo426KxWJIJBIOY/3444+RSCTQ0tIEyzKde/F4HM3NzejRowcURUFLPA5dNxGPJ7P6\n4qmnnoqamhp07do1y2rl+xN7jc4L9ujRA9988w2uu/56KKqK444/Hrt27UJLS4sjwGkd8y4lmk4x\nTJhd3pmvlVyMd8INe6UAANw3Gu0piBhdEMyfTScogcfTwDJNUd50YLhZcSINm377HQS54Eer8kuf\nF6g7JhwO4+yzz8aNN96Ixx57DPF43Lk3b948WJaF22+/HYQQhyHbto3169cjHA7jyy+/dMIQzJ07\nF4MGDRLS7oc+thy6riMejyMcDuOss86CpmnYuXMnZs2a5eTHn6pFJ0KTySS6dKnGsmXLQCQJTz31\nVE7XIEtrJBJB/379MXHiRMx/a77jwkkkEtA0zUmD/mYnedPptCMojzzySCSTSUQioaz5PPo54ogj\nkEgk8MorrzgTw5IkZR0DydcbTYNO8N53330YOnQo/vWv11s3hqnOrmy+XkVlzweiOnRzFflJI0iU\nD4d0AfXribQgVkKLtEqg/S46Po1CNFE3bdsvM+FNafrN5+vH1GTTczMlvZiwSCum7/Bb4EX5sO/S\n+9RX66ZhizTIXGBpaj8wJWS6h7g7ewlIcf22nR1M+xZlMIRkNnwdddRRmDt3Lm688UbYdiZ0cTIZ\nB2DhyiuvQE1NTevmqSRUVYWmaXjttdeQTCZx//3348Ybb2yNqmlj9eq16N27r7AfiRgF1UhZlwL1\n6c+fPx/XXnstunXrhldeeQUzZsxAU1OTM+9A/f20bTO+aTibqyZMHI/1m1ajb8+B+O2vr8P5518G\nGxJaEo2Zc3sN0zmsxCaAaVswbQspPY14MgXdBJ6b+yL+44wfo6m5CaTVmqSaMz1YxzAsp90kSYFt\nZyZ3DcPAz372M2iqjCefeAKyBIS0tg1c1CUWCWt4/pk5WfXCH9zOzqPQshuGAVmWUVffBSedPAWG\n2bb6JhQKufID+kwuwSy6xoaBoO3lZq2yeYj6r9dYLwRlswroo48+cr3PM3UgO565yNR3AytI2Ofy\nqUw3plpIWoC40YsBr8Xw64/ptxv9vK+Z7aSiyWMKuh7eTdjmohVwX/vP1hEbfoO3TNyYPDuw2ed4\nzay1Btp+WdmhkpcuXYqJEyfi7LPPxuOPP+5ojZmJ093o06cPnn/+eZxwwhTE43FEo1Gk02kYhoEx\nY8agS5cuWLJkibNKSJIkJygZz8DcQIVqPB5HLBZDc3MzBgwYgObmZqTTaZx99tn4/e9/jx49emRp\n33R5qSzLmclbRcnskJVUGEZmLqClpQk9evaEnrKR1lswZOgAfL9lJyxLwvuLPsDECRORTGVcMgoz\nBtnNbZIkYeD+A6CbBjZs3AgFRNhWfPvS+RHTNPGHP/wBd9xxBxKJhLMkkzLzHTt2YNmyZZgyZQqa\nmprQ2NiISCQiDFvCuk9okLlt27bhgEEHYHdjI0zTRCQUzqKDviuiMdfeGR6s4BB9i/KgAp1tbzdE\nIpHOvwool/Ysaozm5manU3S0EHPTzgoFz2TzNfv52D0sTVT7ovnkQxPNh/73axn5oZ19x28dshYA\nAF87NXPRl6uuqcZMCMHatWtx+OGHo2/fvnjooYcAZNbvh8NhLFmyBHV1XTFv3jyccMIJADJHOdJg\nY9FoFF9//TUuvPBCDBkyxFlxs23bNgBwPWFLhHg87mySGjNmDLp27QpZlvGLX/wCyWQSjzzyCGpr\nax1moqoqEomEw7wkSYIWCkOSFSiahpCmIhLJHPDSvXt3nP2fZ+LAkUNAZAXfrPsWs/90N/r17Ymj\nDjscCiE466dnwtYNxyqiZwbbto2qWBW2bNmCgQMHYtfOnUKlwatcdD5g1qxZaGpqwsMPP4xVq1Y5\nlkE0GkWXLl1w+OGHw7IsrFq1qh3DFIEK16qqKjzzzDNQNQ3VVdVZezEAfws48rXIab/l60E05r0U\ns1KgLASAFwNwYyrRaNQJNcu6StwkN9sIpZhMYctRzLuFCBTe3cJ3KpHLhdYnq027Pe/FJN3caG5u\nJ1F7eVkNvHnM1hdvFYgFi41MTHvbNV9BjUKWVUiSAlOSYRIFX37xOSaNH4Mbb7wR69evb33OQm1t\nDWpra9DYuAuGkYmlQxkiW7/093nnnYeJEyc6Gv8Df/srrpt1feYsXZ8IhTKrc26++WasWbMG55xz\nDtauXYvf/va37ZZ00t2/dAko3d2qyQQRTUFddRXCEQ3V1RFUVcWwZs0a3PfXR7CzKY5IrBrHHHcS\nLrjocixfsQbpVByff/oxutVWo/d+XRHSFIRDMiZPOhj7deuOmqpqSITglB9NQ3NzM/r17Yd5/3zB\nUUS8BDYhmQn2UCgEVVWdoyfPPPNMdOvWDclkEk8++SRef/11pA0dLS0tWPbFl5g4cSIikYhzbjLf\nB+mYoH5+AHjssccycxPJRNZ44YPG0TZj//N9nQWvaNE+ya+8Y60SEX9jr4n4VJACoiwEgBdymY77\nKoKwPGg6+aQn0lhyMW/6HJ2kK5ROfnDT635daH72hgAZbTGZTCKVSkEmwN8ffwyjx4zFsOEjcNVV\nV6GxsREPP/wwNE3D7bffjs2bN+PYY491TY/63Hv16oXNmzc7jFiSJHz44YdYunRpXu1Iy7t+/Xok\nk0n86U9/clwgNC9RPB26rl1RFAwZMgR33nknGhsb0dTUhC1btmDy5Ek4/PDD0a1LFM07v0d1WMb7\n77+Pgw8+GKFQJjz1iBEj8LeHH8bu5ma8/vqrmDZtGgDgkksuwcaNG2HbNr788kssW7YMX331FX7y\nk5+0Uza8ykU/bHC3VCqF3r17o76+HoceeqjDzPv37494PI5du3YhmUwKw0Gz9ZVOp2FZFpYtW4bp\n06dnhV+g1gwPdv4iF+25VqHROqACScT0+X0PbsdeBoX8T57YQyjGNHJjEkFWZC540c5r236e85t2\nLpr8MFC/9Hmlzfvg/UDUXiIzOR8B4EfIsWvne/XcD1u37cCOHTtQW1cHAuDXv/417rjjDtx22204\n66yzHM3SDYZhoKmpCTNnzoQkSU68HwB499138be//S0TVkL2NxwJyUwEf/TRRyAkM3nKa6Vu7UQ3\nlg0bNsxhMHRT2ocffoiPP/4Yny1ehDfeeAMLFixAJKzh63Vr8OwzT+Mn/3EGZC0EXc+s2jn6B8fi\nB0cd05ounGBx9Axk9mAbP+3P0qxpmkNbly5dkE6n8cILL7Sla2U09lgshksuuQRPPPGEsJ4oKHNe\ns2YNFEXBFVdc4bj2csXxoQpoLiHg1c9ZgcCeWczmyVoIbByoXHVVDMpCAHi5GLx2r/pBIcyrM8Cr\nLCLNwg0id41fYeBFB7/phf726tRe4F1B9FxaqknRidpc/nzal7xoyKxnX4dx48bhi88+xtADR6Il\nYaC2W0/Ed2/HI488gqamJihKW+Auus6/raxt6SmKgj/96U+YPn06+vbtiwMPPNAJHd3U2Jg5VSsU\ngmWIjxwUwTRNrF69GqNGjXL8++FwOOusX74u2Dq67rrr8PTTTzvaNH3vkEMOweDhI/Hzi6+Aruuo\nCikgkoRUMgnDtAEQqFoYkqw6E7SGYTgraNidy2wUUdr2PNwmO2mb0sNx/v3vf2PYsGHOih5NUWEa\nJmbNmoVZs2Z58geWIc+bNw+EEFxxxRVYuHBhRnMn7VeytbUjcaWdf44NsEjfo0KWda+K+iHrsmLL\n7wYvnpkPysKv4uYPFklJilymFv+cKI1S0E7zFK1IyNdl45Y273rhP37nOViGzNcnuztZRDv/PK+R\nuz3H5y8CT4fIXGb9rXSgZOjNfNqWcrI7eZFVP1llIplJTT1tIyQrOGLyoTj6iCMx9MCDcNrpP0GX\nmiqcceoJSCQSOPPMM1tpA0zTBiEyZFl18rHt7GW0hpHGP/85F6NHj0QqlcDzc59Fc3MzQuEwhg8b\njqpoDKbefgUQLQvhTv4wTR2yTLDfft3Q3NyIaCwGmwAWTGEdsxu4aL2OHj0ajz32BCKRGAzLBpEV\nKGoILYkkqiNhyLaFsCIjrZtIpw1IcsbKobuXTdN0Ti1jhTF7UAoN6Mb2CfZbtLSbFWCWZWHWrFnQ\ndR0jDjwQNgEMy4SmtFpcEsHMmTOhKAp2797dWtdGu/0ANG1ZlvHFF18gFArhvPPOyyxl1c2sfNll\nxiydfL2K+jzPxIG2fSO0Ldg64Jdcs+m6jUk/u/7zQVkIgM4MNwZXqLDhhV9nslq8hJybEPASEH7K\nn0/9eOZlZZhGKCzjyB/8AKdNn45XX38dPz3zZ5g370VceOGFeOjBRxwNl807lwIiSRIaGhqcTUgv\nvfRS6+lfwJAhQ6DrunCC2o1WVVUdt9P27dsBwNnI5aUUsYyoujqGZDKOhx56yGHadE08C5EFzTM0\nUXuz5WE1cB58n6HMkx5Q/+yzz2LSpEmwbCsrcihlmF27dsWMGTMwZcoU2LbtHMDDKz/UCrn99tuR\nTqexdu1a2Lbt1COrDLkpoV7wUrpo+fk5Ar9gl7x7LbUuBGUnANw0zlKgkMbweo/VmvMJL5ArbfZa\nvvXit4yFro5yW33Egy0vrSfRgBOlzVs1LHPJh1434SpJEjY2bEHfvn2hhWRcc921eOiRh9Ftv+5Y\nuOgdpFIJ3HPPPYCdCd1AGTCvKYpAmQw7iK+//nqMGjUK7777Hk477TRomuZrApGC7py98cYb0dzc\nDMuCE37CjYGxaRJCkNZTeONfr+Hiiy9EVVUVNFXFlVdeiUg4IrQA2XKyGqlIk6d50PLSZ1iNl01b\nJADos926dcPSpUuRTCYRi8WyVvLReD1/+9vfsH79euy///7YtWtXuzkR+jFNE7W1tZg2bRoeeOAB\n5xql160/FrJxka8LUX/3Al/PAJxNcIXyLRHKTgDwg8CtwoIQFF7M1ut5t8HltqzLLy1uGghbRr5+\n8smHdnKqRdBrorpw035YxstvMMvFlEVpicxclla2ztl6cqurbDcMgW2boIHiqJ/esiwYVgqQbIDI\nmD79bAwbPgiXXHIJDN3GCVN+iNNPPxXJRAvWrvkWlpXJVzf0djvT6caq999/H7t373ZWmmS3K7Bj\nxy6Hrv+98UbU1XXB1CnH49hjj3U2KLH+X7YsQDYDkhQVNpEwfNgQKHJmfwJlDixtbDvxfZZAwWGH\nHoElS5Zg8MB+6FIdwaMPPYDuXWswc+alUEMabGJAUVUYlgmbtA9Ux9JE6xVAu37B9gf6n+4WZ9uX\nnTeSJAmqqmLOnDlQFAUD+u+P+to6/P2JJ2FagGkBSqsQbmlpwZtvvoldu3bhzDPPdJg625+pa8iy\nLDz11FOwzYwgUTQ1S+iw80p8X2XblC0v32dF8OJTbLvwK7hEY8SP5ekXZScASg034VKohh0k8sm3\nEE2CMn635WWid/x2snwFkds77D2+ffhnRMvz+DAHPI2U+WhyDA/99XH02K8bZvz8NDQ1NeGaa66B\nYRg46qij8M9/voiVK1e2EzCUodLQCQAwfPhwnH322ejWrZsTYpmCMjlVVR3hoKoq3n77bWcHL53D\nYIWaV/tIkgRN0/CDo49GOm3hwgsvRDgUzixbZRgrrQ92TwK/YXDYsGFYvmIFNn//PZpaWvDWggWI\nxkzIRMFBoyZl3jOBVEr37BesUpHP0kVanyIfvGVZGD58OL7//nts3boVH3zw/8g77zCpqvPxf26b\nugVYiiBIFSuIBRULKvaGvYMlxp4YW8QWG7EFjEajMSj5aiwIWDDWKIKKXQTFAirSBAQpu7DTZ+69\nvz/unrtnzt6ZnQU0JL/3ee6zszPnnvqet533fc97TJ48mQ4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C77hkclkee/yf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\nVwG4CgB69+7N79d6R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1aiWh4xcc4AAZ/5O46DM844Qx6usnbtWpn61/P8fRvZbBZdu3bF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\nZEH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L9+pNDUxVXlaOLtHLDU7vXa7tjHsKL84XSlShGTq42VO6o/rIAzvQjWlSYrqaKmD2\nKI+G9gHT1SUOTWKMzbLbxrJzljY39ToeZpeQVNxjSWG8MDvH0myCxDT8w8qhsHFWh3HKOo6mq1NC\nmK5oCQDCYMp3hpfHL33Go4013VXLZfPYT3lcBULLI2SwlVLeLWcNvqEO7QHNx8OnqizMKCdbKqq4\nN3tH6kKLokAo2/uduI3HCwujAOYFFQhslXjENfDCLF0Dqc97tuj6uMdqoXdZrymcPAZPWfbesjiv\nzL51dz336slZR1qOzruklHKuH+fxqgx0A1dLkRZpvrHBmbvej/Ol2j8juDus7a56Uu+YNhbmKMvq\nxE6rnxVTqn8B52gFsCeaXirNCqgvX+k+AKYNH26YsqYBtJe6OsZaH+Vq6W0Xc64/vSMrvPHnRgOI\nXyrFnDaG5oX7rAIA2u6XKoKuQbYX9XrMDPSzzBQ39Sq6IOehpOrqEgh9hCTTV/FtWdtEH14m2rd9\nZR2j5v853Ll+D1/7rXly5Wm9tn4+1U9meHTNr3TxZmoiuA9/5ZSgKS/bCey10zwADW0pjdmLYF5o\nxqQttxwMWstbc5sbPdxT7TGvw87j1/QzQlQgN2fHC0RyaRiXcjJ75AfjZF5LozCEtz1DqWlHAo95\njJoULNxhcPOAChQWdqkYmcYgWYmktD+n6xIifSyIEKbHTSjO87bdE4yKg9Whbe9r7XiQy+cpHVVY\nOeHHbVNvbl7LZzcegDuRK8JQecLedd32xLj09cCUT3YDqbrMWk6VnVr1xeUq3qwk+EpSAM31jXxd\nKZC+jIe/DexqRT3I0fDVPkv1Fdej/NzFL3y9ZB+D05aFGqTw4Pf2jNtkdfG4OB5YGA/AE7oKao1p\nWi+mZmWzoLd3KYKrtcqrjngw8k1VLLi8tnhuq80DpJaYelaMWma6Pl2FhVrfShP77eGgtPLmG7gc\nbg+30d6p16D9MaOIAz2vl8zlJretr7T/lT+8AcX04RgyGxO2K3NQDIAoB3YBrR2b7KZbSCXUcfHC\nlhCW09mIALQubAFAS1XR7Bi2uHOVpxaysY2vx9eN1RkjYt2OFM0iHQ5nfRljbARYc4ppRHOBiXlG\nTftt6Wvhe+gNbrFo2l9N0nTPBQHTuRevLzVtjNXRD+3OmlVirAwNJpFOAQAdPWK7dmsaxOEACNXq\nqpm7GyJQ1DxsOMcYp4frGR3RHueG23iyM/UKY/+9GH1gYRSAgcbu1NpIgbd+V92qPuBpZu/mKU6v\nF5R41rnuaOY4826sOm+we/il2mQ4WTk5JaTPvLqsDJ7U5n7UdppCSVmTIUx3q/I7tbgYN1Y4XC4L\nOJ2M47Qp5eKl7QKmeR9LT58DyC5VZVqoIk4BL5RQwdnVli7vlPfW5MbfzHg+fhmWhFy7UjzOK6Vi\njDMT2I0Frvsj5oBmL1JsTzKnsO0rA3cDC6cAchOEucaz4GWrznNPu+r1mFatbH2fEk4pXLXOeaEP\nc3eV20dRdpWhXoXda2vvvL5IxchnBCNbcLR1PzWRqHWlvrku9WR4qaK2YZ4QnSqu4zFKvLIVf603\nlY/bm4J5xx7Xq2vn59lvstfQZbxwOjXaGjoBM7wDzHriOeDxHugOBOVFJPoxZSTtBSyMAtAGe1q3\njyb0iNPH0tHBzQPXs1Q1DTAbYvCUz4wLjPbgSeHdaUll3hmOnuJSvFOC2cJgngDl8jxa5yxgfsa0\nNgXQCGYKD2jYi8vMhYdyeHlKU5WWQYOjtKElPJwDxlL80LRL6eRMOKug1XJbyxuDtCdWnyLU3pnt\ngA3TssuyxLCY3SCm/JMar6qcGH8dE9VvWvJapr1abSsLbU3TnMQayZAo0jyYGnchVOEXxSmE0HLP\nGl6tQ2sWGmxwttNawzRMWFVc14PZfvTolaLJ8cDCKACgu8G7ccVzcG8QNyW01bLUQXI8kMufs1RY\nsXnWMUPq6kpePmiTYikvSfH1LNmWQJSwgq3P9gZ/Cjhdn9UdXrtTCtRrY+NFBLofNxPM6esZaJvt\nP88BaHlR8hdEB68/rDx9l7oE3sCWvfKErxf+7BLsuT7ldvVdbp1Lk3quY4KVWCsP/ewav1ZmLpSc\ng3vTg1ooBdAFeyH0703IeRp9vJDdQmq5oP2edxDMA55ATln49q2WoZaneQxXDaXM24bhcNichtkX\nPIu2C2as0kyWHC361JGjdR/8gOnch61saSacRTlruTxZHklRezzXxf9qgPRRhl66lseRJkG27Fb5\ngwQ/zlEmGyCLJsMW4kKYEMLdAL56svHoAT8M4LsnG4kesMRzb2GJ597BfQFH4L6D5yNjjPt3m3lR\nPICvxuO41eZEQQjhb5Z47h0s8dxbuC/geV/AEbhv4Xk8+e/TG8GWsIQlLGEJu4elAljCEpawhPsp\nLIoCePvJRqAnLPHcW1jiubdwX8DzvoAjcD/BcyEmgZewhCUsYQknHhbFA1jCEpawhCWcYDjpCiCE\ncHEI4ashhJtDCK85ybi8K4RwRwjhRnp2Rgjhz0IIB+rvB9TPQwjhrTXefx9CuPAE4XhuCOGTIYQv\nhxC+FEJ4xYLiuRZC+OsQwhdqPH+zfv6wEMINNT7vCyGs1M9X6/831+/POxF4Er6DEMLfhRA+uqh4\nhhAOhhC+GEL4vK3+WLR+r+s+PYRwbQjhKyGEm0IIT1g0PEMIj6zpaJ/DIYRXLiCer6rHz40hhD+q\nx9Xe8SbvcjzRHwADAF8DcD6AFQBfAHDBScTnyQAuBHAjPXszgNfUv18D4E3176cB+BiqPSGPB3DD\nCcLxbAAX1r/3A/gHABcsIJ4BwCn17xGAG+r63w/gV+vnvwvgxfXvywD8bv37VwG87wT3/X8C8IcA\nPlr/Xzg8ARwE8MPybKH6va77agAvqH+vADh9EfEkfAcAvgXgoYuEJ4AHAbgFwDrx5H/YS948oYR2\nGvgEAH9K/18L4LUnGafz0FYAXwVwdv37bFR7FgDgfwB4jpfuBON7HYB/vch4AtgH4G8BPA7V5pqh\n9j+APwXwhPr3sE4XThB+DwbwCQBPAfDRepAvIp4HMasAFqrfAZxWC62wyHgKbv8GwKcXDU9UCuBW\nAGfUvPZRAP92L3nzZIeArIEGt9XPFgnOijHeXv/+FoCz6t8nHffaxfspVNb1wuFZh1U+D+AOAH+G\nytu7K8ZoF7oyLg2e9ftDAH7oROAJ4C0AXg3AztT4oQXFMwL4PyGEz4UQXlg/W7R+fxiA7wB4dx1S\n+70QwsYC4snwqwD+qP69MHjGGP8RwH8D8E0At6Pitc9hD3nzZCuA+xTESrUuxLKpEMIpAD4I4JUx\nxsP8blHwjDFOYoyPQWVhPxbAj59klGYghPDzAO6IMX7uZOPSA346xnghgJ8D8JIQwpP55YL0+xBV\nGPV3Yow/BeAeVKGUBhYETwBAHT//RQAf0HcnG896/uHpqJTqOQA2AFy8l3WcbAXwjwDOpf8Prp8t\nEnw7hHA2ANTfd9TPTxruIYQRKuH/3hjjhxYVT4MY410APonKXT09hGBHkDAuDZ71+9MA3HkC0HsS\ngF8MIRwE8D9RhYF+ewHxNIsQMcY7APwxKqW6aP1+G4DbYow31P+vRaUQFg1Pg58D8Lcxxm/X/xcJ\nz6cCuCXG+J0Y4xjAh1Dx657x5slWAJ8F8Ih6VnsFlSv2kZOMk8JHADyv/v08VDF3e/7cenXA4wEc\nItfxXoMQQgDwTgA3xRh/a4Hx/JEQwun173VU8xQ3oVIEz0rgafg/C8Cf1xbYvQoxxtfGGB8cYzwP\nFf/9eYzxkkXDM4SwEULYb79Rxa1vxIL1e4zxWwBuDSE8sn70swC+vGh4EjwH0/CP4bMoeH4TwOND\nCPvqcW+03DvePJGTLYmJjqehWsnyNQD/+STj8keoYm1jVJbMpahiaJ8AcADAxwGcUacNAN5W4/1F\nABedIBx/GpVb+vcAPl9/nraAeP5zAH9X43kjgP9SPz8fwF8DuBmV271aP1+r/99cvz//JPT/v8R0\nFdBC4Vnj84X68yUbK4vW73XdjwHwN3XffxjAAxYUzw1UFvJp9Gyh8ATwmwC+Uo+hawCs7iVvLncC\nL2EJS1jC/RROdghoCUtYwhKWcJJgqQCWsIQlLOF+CksFsIQlLGEJ91NYKoAlLGEJS7ifwlIBLGEJ\nS1jC/RSWCmAJS1jCEu6nsFQAS1jCEpZwP4WlAljCEpawhPsp/H/PRxmzwrr4KwAAAABJRU5ErkJg\ngg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Initialize an ImageObject instance and view the Image\n", "# Obviously, it helps to have a simple image with only 2 colors and \n", "# close to a single path\n", "url = \"http://thevirtualinstructor.com/images/continuouslinedrawinghorse.jpg\"\n", "horse = ImageObject(url)\n", "horse.show()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Dimensions: (266, 231)\n", "Num. pixels: 2981\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Scale the image down by a factor of 3 \n", "# and binarize the pixels using a threshold of\n", "# 200 (out of the 0-255 scale) as my cutoff\n", "horse.monochrome(scale=3, threshold=200)\n", "horse.show_bw()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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GNHu8hZmCBWP8qFNr9IVtotKLOZpSxFubYnloWr9OZ2E9klzI5pgcPBys6Ots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\n6egpol8XC3Y+OZRflgyhj1PLhdkawsJInw0LfCV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lcn4NSGLr+STp/1SiyEwfzfTA3YK+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mCenbT3+BkGPb/MlnzQnklrLu3WmqX/dzE3D27PkYJzrDxQMWX1W7+k2cYpOlYz88wTmnUgEMKT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\nogmRKwIh6mnjoTwWp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Get a tour through the coordinate space of pixels\n", "# Experiment with various starting points until the\n", "# final result looks reasonably simple without too\n", "# many jumps\n", "horse.get_tour(starting_point=1300)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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UWj2PfXuUA2mlLJ4awfo4Q27iuen96ONq12M/t6f1zgUtQbjMVNSqeXzVMfan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\nk/rbsyU4o03HtXqVmuDUkmZth1eCp6f78NfFPF7YGcXu1eN0Eg00N9Q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czbmYXcFjW8LZ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op/3zmdSSMG8dWBHIxa8/DF0ay5dxa+7k7c/sGFtYO80mque2MnO9OLef7a8Tx8UdR5QXLyCB/u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\nEkKIAU4CgRBCDHASC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Get parametric spline functions of the tour\n", "horse.get_splines()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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HKlMOBizzGLc7USktGGtLcjEwTQLp8XB87lcncHzAqlhUADhXF50BTMMg8uoQ\nA0sfUNIQ23uUrQVmx8AXLPjh6z3YVGPCpY0BxMXSCwBoadsMl4fjv/Z14c72GnzmZlpxtZYXoGt8\nNnUK0Lz+9BR0FdkGyCKQi5pkEYhGDOp3UTbS2Kn4XV8qYB+inltlcRIDxpb30wqSXcSlAPHetWS1\nefPl5ZnIaVR41j81jz+eHsX9uxuQlxV7M+faklycHrZj0e1BZSH9fzSY87yWgd2xhJ8fGcB7v3PI\nJ2bAvEVn0vOYryR8VocYWPtiD65JQeSTx4/iwtgsHrisCSxQAZsUn2ho3YhLGopx6+YqfP2edm9m\nwpqKAswtujFiS5EvSn4ZrSr7U0AMpnuACVVxn3WA4gUyhbIYhFlwpqZuJ20HM8xVJPfMKouw51Yo\nZCvD28k0sIC6pUl5ebl0s1tmGaS4GFjmFvHzI/2wO5bwo0O90OsYHghk7UdBXXEuOiV3sOxKbjDn\nwTq/BLtjCQtSvcGi2wOXx6+FtSqbSEvLIPPnGXBO7oa2m2J7H0kMjh59A+b83bizPcjqVLIMWEkj\nnvnrkmXpaa3lBQCA7ok51BTnxnZN8aJ+D3D+OSmTIYkjOh/bRtsvSlXatn66NhmTFDeIRgyKG6hp\n3cARYNfDsV1nKiEnNUTagDEUshhUtwMzYzQUKgBLi04YAOTk5ELH1DGD1K8zWHR5cOu3DmDU7sDE\njBMdfRbsbDKj0rQ8BhgNdSXKd1t+TznLaGB63qf5ndsnmcijtKMA8Bf6l3HS0wwgyNyOOJL5lsHs\nGK1QYrUMihvBdUY4R87h3p31wTsZWpT4RKA85dbyfAAplFEEUBB5YTq5HUz95zF73NR6olhlGVS3\nU7FZpP2lAKn4bGfmZRSNnaZMN/8Z0LEgv1dRA7UsCeJacy064eYMudlZMOh0imVQVAvojED/ofhd\nU5zpn57HqFQQdqhrCl3js2irKIjb+9f6iAEF1BtUYrCwqFQiuz0eJWDNVcNtAHzR+BSeyQ4wyS8B\nZL4YWGJMK5XRGzCZXYdW3UjAdFLlfL0Unwiywi4vzEZhtgHdqSQG9btpm8y4gbq6e3Gect09Ll83\n0fYHgL87TX2VoqFuF/19ZsdjutSUweMGLr5IzfjiadG13wdc/wXg8k+QGEycCxh4dy05sQgjcrP0\n0OuYYhnkltAEupO/pOdzU0B3hPOV48S5UTu+82oXrPO+i40eaaDMhmoTDnVPYdbpwpp4ikGx0uCu\notDXMuhgp83BAAAgAElEQVSfnse8SgzOjczAIIuBx6PqTaQtmS8G1hjTSiUGLfM4Nl+OrTljod07\nK8QnGGNoKc/3zkEIxGMvX8St3zqgXZC5tI2+wANvaHO+QKiH2NiHlEE2asuAseUdMiMh04rP+l4n\ny3fTu+L7vjkm4MpPUvFY5WayrAN0MnU757EIA/KyDDDomU9WDGovpX5JDhvw5C3AU3dqXpHcOT6D\n2x97DV9+/hx+eth32l2PNJTq9i1V3n2tCbIMsgx0my3KNaIo14iB6QXMLyri6vJwb20Z83MTaUnS\nxIAxdgtj7DxjrJMx9tmEnchrGcSWTfSlZ8+gi9eiwjXiO5xdjccjZS41hXyv1vKCkJbBv710AWdH\n7N4AVMLR6cg6SGYQWT3ExjagPC+KMQtMTfU2cl9kgqto5ATw/D8Axjxg7c2JO488GTCQq2jBAgsv\nRF6WHgYd8+m+6a0FsQ0pcY2Z0cRdZwD+fG4cbg9HQbYBr130bUXSMzkHc34W9rSUevfF0zKoDlB/\nBFBBWr+fmwigQDIAxU20WiwDxpgewH8AuBXARgD3McY2JuRk1l7yMRujD9a+cn4cfzw9hjUbt4N5\nXNK82QDMjgFu54ouqZbyfAzbHD6rA5mJGWX1dLBTw1469bupeClUL5pEorYMbEPKUJtIC8xCYcyh\n2c/pXnzGOfDf99Nq/bp/ArLyE3eu8nVUva0Sg//c14njA1ZgYRoWFMKUY4ReHTMAVGKg6tI7MwL8\n+J3AT96duOtVcWbYjipTDv5idwOO9ll8vm/dE3NoLsv39gwCgPKCOFRwS+QY9fjUTWvxzEf3+uxv\nMOdhYHoeDleQjq5yNtEqsgx2AejknHdzzhcB/DeAuxJxItvwRSwW1q98YBAcS2588Xen0VKWj6sv\nu4x2BhuUImUSoaQ55HuqM4r8OTFo9T5+rVPDG7McN0jWqtk6QGNCwegGYh2gQGZWZMNFVqRuFxXY\nBbPu0gG7JJY3fQnY+zeJPZchmzLppIwiy9wivvrCeTz8VAf43CQsvABFuUbJMgggBrKbFiAx6Poz\n0PmnxF6zxJkROzbVmHBlWxkW3R4c7lHGTvZMkhgUZBtw7bpy/K/r1gROFY+Bj13XhksbzT776s15\nGLQswLFElsDHr/OrD+EcbuhwuEcp9JvgJmhBssSgFoBqKYhBaV9csc4vYna0G0eshb4f1Aj43v5u\n9E3N44t3bkJWpZS+Nxl4HnK48YkWSQwCZRQdH7RBx4C7t9XgcPcUXG6NZg3UbpcyQJIUN7D1U5fX\nwiqaWWDzqzGIF/W7qE1CJLN+Uw15tR2PxnThULGBxmEC3ur58RknXPYxTHETivKM0OuYr2VQUEkW\nhbojrk2VJJDg+IFjyY2uiTlsrDFhZ5MZWQad11U063RhfMaJ5jKyqJ78q1345E1xTM0NQYM5D4tu\nj7d76T07/D7j3I2+6QW8KPUjWuJ6PO/ercm1pXQAmTH2YcZYB2OsY2Ii8jkAxTl6lGU5cWymCN95\ntSvinx+Ynse/v9KJ27ZU4aq15UB2IRU+BUvBtPQCYCvexBpL86BjwS2DtopC3LCxEjNOF05oNRnN\nmEupm1pmFNlHlJYFcoGZqVaxDIoTJAZAehefeUd/xn39FJjSNXROlxMXx0gMvnL3elTCgkFejsJs\nCiD7LLh0eqoUl3scAb4tT4K5WuPEudEZuD0cG6tNyDHqsbvZjAMX6R7SI33vWsoS6F4Lgty9tGuc\nrsGU45sQwbgbSx4Grio6U9csJJJkicEQAPU3vU7a5wPn/HHO+Q7O+Y7y8ijyqHV6ZH2uDxc3/C3+\n7aUL3rmkKzFud2D/hQl86dkz0DGGf7xdFc4oawvhJuqj9gnG0IUrOUY91lYW4n+ODmJqVlkhcc5x\nYtCGrXVFuKy1DADwupZxg4Y91LpYi6wPjwf4t/XArx6ix/YhuvkX1ZEQJMoyKKojQU/njCI5DbdI\nIzEwtwLcA1h6cXF8BrlGPd67hkHHOFymOuh0bLllANDfb0YaU5pbAnS/orw2ldialjcll9Al0oD6\nK9aU4cLYLMbsDrx4hgLZW+uLE3oNgWgsJTG4MEadjLMMOvzj7RvwaaldDbgH0Om9dcc6cBTmxJBB\nFwHJEoM3AbQxxpoZY1kA7gXwu0SciOl0+NK7LkGVKQd/94u3sRSG2+Xvnn4bH/zBEbx4Zgz/6/o2\n31TS8nVkGQRK+7T0hm26f/U9WzE568RHf/qW95oGLQuYnlvE1vpimPOzsLHahIOaxg12UQA8VKfK\neDEn5fqf/b0UeF+km0dRHTDdRemMMWaABSXdi89sQ0BWIZAT3SSuiJFnK093o3N8FmsqCqCzU4D/\n0/fcCADLs4kARcybrgRargHmVZ/lBFsGb3RPobks39sK4oo2Wlz979+ewr+/0olbN1ehNgkdAOpK\n8pCl16FbqnMw6hkeurIFe1qk2AL3gDMdPNKtWce06wqQFDHgnLsAfAzAHwGcBfA05zxwzXscKMo1\n4ot3bkLf1DxePB26N7jL7cGbvWRB3NFegwev8AsGl62lUZGzAd4ngtGaW+uK8ZV3b8WRnmn839+T\nP1Yeot1eR1/yy9eU4mifZVkaWsKQWz9oUW+gzjKRM4mKG4AGVfZFIiwDgILI1n7NUx3jhm1QO6sA\n8E7sw1QXLo5JlbreOhASbINOh0WX3wIpT0rbXHcbULVV2W/IDVi3EJCZUWB+euXjVLjcHhzpmVZu\nsAA2VJlQVpCFP54ew64mM77xvm0RvWe80OuYN1ahY9ThFIASvJZSS5PRxjJpMQPO+XOc87Wc81bO\n+SOJPt916ytQb87Fjw71hjyua2IOiy4Pvvm+bfj2fZd4C0a8lLXR1t9V5HJS+4QIgnp3X1KLj1zV\ngh+/0YefHe7HiUErsvQ6rK+i7IHL18hZEBpZB4WVdP1auFBkMdAZlRtLUT2w9hblmIoNiTl3uhef\n2foTZzUFIs8M5BRjceIiRu0OrKmUxIDpvXGLHKMOTv90ycs+Dux8GLj0AV8xqNwUnhh4PMB3rwL+\nY1dEl3tmxI4Zp8unhkCnY7hnRz0uay3FEw/sCN5ORgNaK0gMjJIQoOcAcmZpQSQXnXGfOoMMtgyS\ngV7H8IE9jTjSM42zI8HHTh6XUju31AUxweURmBN+GUXWAQA84gyPz9yyHlevLccXfncKT7zWgw3V\nhV4B2t1cipI8I374em9E7xkTVVto6HyikcVAn6WyDOqp1cTd36GWCObQKbpRU91O501XV5F1QFsx\nAIDSVsyPkJ9/bUUhiYGp1tsaJMeoh2PJTwxM1cDtX6M6CLkDKkCWRjhuorGTZIHPTQAL1pWPlzjU\nRYunvSoxAOi79rOH92jmgw/GGimb0Ov9+dE7sPHpK+mxR7YMVAKQyW6iZHHPjnrkGHV46lBv0GNO\nDtpQkG1Ac2mQTIPCaiCrYHlGkVxjEGEPJL2O4bF7L0FdSR7cHo6tdUpQKzdLj4eubMG+8xNU5KMF\nZeto1ebfOC7eyEFQ9yLd3HKKKVsLALbdB7zzO4k7tyFbypxKw4wihw1wWBPnQguGuRWY7kKWXoc9\nraUkBipBIjEIEY8rrAR2fRj44G9JDGwDKycqdKkCztPhZwO+0T2FlvJ8VMSpA2m8kdteBPr/YtwD\nD0uO1bKqxKA4Lwt3b6vFr48NLWtcJfNm7zQ215oCdhwFII3ADJBRZO2lbRS530V5RjzxwA7cva0G\nD13puxr+4N5GFOUa8e0/a9RRtHw9+S0j+PJFhWwZeJaoujURaaShqN9NqY6JFr14Y1XFVzSEm5th\nWhzDta0mFGQbAoiBbrll4M9tj1Ig2dwCgCutYoKh7no6FV6MQY75+VsFqYRcdAqALAE13AMPhGWg\nCR/c2wTHkge/7Bhc9lrXxCzOjc7gxo1VAX5ShWoeshdLL6DPjq69MugD8s17L0Gjn0VSmGPEQ1c0\n409nx3FKi5qDctkNdi6x51EHkAcOx7cHUTjU7aTMqXQrPpvqpK1WBWcSg6wGOnC8s3mJBNQ+7CMG\n2QZ98BYL/sgB6VBxA4+HPhdb7gHAlN97BU4N2zHrFy9INZrV9Q1LvjORGXfDzSFiBlqwscaEXU1m\nPPVG77Kq5GePj4Ax4PYt1UF+WqJsLVXJOlUVxJZeyiTSxf+/9IHLm1CYY9DGOihtA8CWx0TijX2I\num3qs+i55paBXHyWZnGDgcOUjVO5WdPT7pskF97lZjt99sEDWAZhVsuHIwZzEzR7uW4nfTbCtFTl\neEEqi0F+tgEfu3YNvnXvNmrXroZ74OKrLJsomXzwskYMTC94KxIBKvj6/Ylh7Gwye3OTgyIHkdWr\nFUtf7DMTgmDKMeJDlzfjj6fHQga/40JWHn3JEykGLicFBsvXKVkmWvvATTWAqS79Mor6XgfqdgCG\nLE1P+0wffScK5/qWpZUCkmWwkptIJs9MA6AsIYLIHql3lCGb4hVhWgb7L0ygraIA5YXxazqXCD51\n8zrcta2W5ler0LsdmOdGYRloxY0bK1GQbcBLZ5RagfNjM+gcn8UdW1ewCgBFDNSuojBaV8fChy5v\nRkG2RtZB+fr4iMHinK87SMYuVaUW1dEISkMu9b/XmvqdK7el+NcG4Kfv1eZ6VsI5A4ye8K3F0ICe\nyTm8PQE4jEXAVFdAMZCzif50ZgxPdwwEeScJxihTLKSbSBIWnZ7aYUx1BS70VPFG9xQOdU8FH0mb\nivhZBnrXHCyubHhEzEAbsg16tNcX4aTKB//s8RHoGHDrSi4igD7ITK80rFuwAE5bzAN0QlGUZ8Rf\nXtaE506O4vzoTMLOA4BW7FOdAadbRcQ3twKPXbJ8v5xJZKoF2u8FPj8CNGp7gwNAxWe2AUWcAuG0\n0TSxVGDgCLUr0Pj/6s/nqFqcSRlF/jUGAFCSZ8SSm+Ohpzrwmf8Jo4J9JTHgkhgwPVVAO+3AXPDW\nLI4lNz73q5OoN+fiwSsTlJKcCFwO70M93DC65jC5mOVnGWjDqhQDANhYbcK50Rm43B54PBy/Oz6M\ny1rLUBZOT3NDNlkBckaRt3V1U4KulnjwimbkZ+kTbx2Ur6PgqnWFbI9QuF3A/CSljvrniMvdK2XX\nUBJ6twNQxQ06knP+SOk/RDfHusiKsGJl3/lxrKkoQHZlG9UH+NUYAFjZteqPuYXeJ9SgKECxDICQ\nrqLHXr6Insk5/Os7tyIvK8qxqMnAoyy4SkAxyIklfxegsAwSysYaExZdHnRPzuFg1yT6p+fx7ksj\nKPFXZxTJKXIJFoOS/Cy8a3sdXjwzltiRmOXraRuLq8iucg/5B//kIjNTks35qi1S8Vma1Bv0HaLh\nPNnxm8i1EnNOFw53T+PadeVSfcAgLYL8UluriyLs82NuoRuhLYhLyWsZ6FQB58BB5DPDdnx3fzfe\nc2mdtwdR2qASAzOjeKDVnS1SS7VkgzTh6Fi/BV969gwqCrNx6+YwXEQyZW20UvG4oy44i4bW8nws\nujyYnktgfrzcciOW9FL5/wQgf68a+xCQa47/4JpIkYvP0sEycDmBoQ6g4TJNT3uwcxKLbg+uXV9B\ngVxwqs9YJgZRWAZAcFeRRyUGxY00GyGAZeBye/DZX51ASZ4Rn78tQe1LEolKDEolMZjlueBcEQCt\n7OZVKwat5QXI0uvwz384iwtjs3j0ve2R9SspXydVz/bRv1wzDRJPMFXSCmzE5ljhyBjIKZLmNgRp\n1R0O6nYD/jUZtqH4jrOMhdod6TH5bPht8i9rHC945fwECrIN2NFoBmouoZsyoNSjSFSYIsze8YpB\nkIwirnIT6Q1kdfsvKgA8ebAXJwZt+MIdm1CSn6AMq96DwNfWAc9/VnFfxQuVGJSBYpizyPVJLeXC\nMkgsRr0Oa6sKMONw4UOXN+PqtRHOS1BnFE1cUNr8JhjZNzuaSDEA6Mseq2WgM9IK0n9FZxtMHTGo\n20GTz6RJXkFJpFsuHPpfp62GmUScc+w7P44r28qoX1bZGuDDrwK3fQ3Y/dc+x2Yb9CgriOBmXFAJ\nGPOCWwbqADKgZBSp6J+ax9dfOo8bNlTgHeFkAQZjsCNw1pvMyaeB2VHg8H/5zIKOC6oKZDOjxJBZ\nnitSS7XmuvWVuLSxBJ+5JYqRd3JQa+AwMPyWb1fGBCKb4yP2RIvBehK5aFdCll4SgrJ1y8XAPqjd\nlK6VqNtJ25XiBovLp9JpSt8hWoDka+cTPzc6gxGbA9euq1B2Vm2mdGDj8hhBWMkXMoxJDetWcBPp\nJDEwt9Kxqs/jN1++AB1j+NLdm6OfX8w58MT1wDc2BT9m/JziFhuKs0tRbRkwtWUgsok05ZM3rsUz\nH70suna2eWYa2P7aN6mkvP2++F9gAMoKsqHXMYwl3DJYRwUxP74beOM7kU8/s/SQae+fI+6coWZr\nqWIZFDcA+RUrxw2cCS72C4XHQzMmNK4vkFNKr1kXntXsbckcLqHSS2U3kWwZVG0mC26ERmfOOl14\n/uQo7tpWG3nwWo1cMwEET6W29AKNV1CygToWFg9UYlAOyrqbRY5fnUF8TxmMVS0GMVO2lszZ7CLN\niqb0OobKwuzExgwAahWx92M0XOSFfwAOfJ3y3F99NDyXiaWXvuylrSQq8iAZb1ppiogBY2QdrGQZ\nOJIoBuNnSEAbtQ0e7zs/js21prC7f37xThoPW5gdZmqnuYU+J/7N2gCVZSDdotbeQt+z5z4DuJfw\n3MkRLCy58Z5Lw/wcvf5t4OKflu9X96YKlEq9OE8uotIWWjjEXQyU372CSWLAc+GrANrcpoUYxIKc\ndWNuSkhPomBUFeVg1L6Q2JPkFgM3PwJ87AjQfBVw+jfA928EXvnnlVNOFyx085ItA0BxFckpp6ni\nJgIobjDVuXyiltpFlkzLQO7eGaVl4PZwXPf1ffjGSxdwdsSOc6Mr/y7W+UUc7bPgOrWLaAUubTTj\n4Sub4Q43vmJuoSSMQEV//jGDPDNwxzfJTbPvy/jt20NoLsvH9oYw5hhzDrz4j8BP3+1rCQC+MYBA\nCRPy8SXN9C+BYtDERuGGDrPI8+1NJALIaYAcRDZoO0u1qign8ZaBmnW3KdXWANC9L/Tx6iI8fzGQ\nA3WpYhkAStxg6Kjvfq5asYY7pjER9L1O4hll2+pTQzZ0T8zhWy9fxK3fOoBbvnlgxZ/Zf3ESHg5c\nsz58MQAAvU63rAFkUEKll/rHDABg87uAbe8HP/B1ZA0cwuVrSsOLFThU3X6f+4zva6MnyU0IBF7k\nqD/LJU3AdG98kwlUbqIW3SgGs1qxBINPzECklqYD8pdTwyIgAKg05SQ+ZqCm7SblsTEf6H4l8HFz\nk8Cv/1rxv5c0003MkKsSgyHKHS+MIfsj3tRcQtd0/nnf/aovKgYOa3tNMpyTZdCwN+oV4oBlfuWD\n/Hjl3DjM+Vlorwtj5a3CoGPhi0GJ1DYikBh4YwZ+t6hbvwJXcTMewWNoLw3zPDMjtM02Le9SO3mR\nKtELqgJbBv5i4LSR5RsvPL5xikm9JExJqMoXYhALLdcAW98H3PEtTU9bacrB3KIbs84YeweFS2kr\nsOFOYN3tQPv7gN7XAuflH/g34PjPgZe+QM/llt6lqq6T9iH64ulTqGVAdgFw6V8CHd8HTvyS9p19\nFnhENdci0S29g2HpBWZGMGCKfoD7oGW5S3HGEbyuwu3hePXCBK5eWw59sCFPQdDpGFzhioGplmaA\nBBQDPzeRTHYBOnY8ijLYcEPnI+Gt0mU3VOPlwPyUb/xnZoSs1PK1wS2DrAIgr1QZwxqq22qk+ImB\nDTTrQK9yO2uVWSTEIBayC4F3Pa65y0NOL+2b0jDd8Z6ngPt+BrRcCyzOBs6+kd1HS3NAXpkyxlIt\nBtb+1HIRydz6VaB6G/DaN+h5x/d9X0/0sJ9gSPGCz3VEb31eGJ1BYY6v+I7Zg2eHnRi0YnpuMews\nIjUGSTw84QiCTie5Xropy2xuSnlN3ZvIjyOORnzdfQ9K+l4Ajv1k5fPIloEcgJdv5s5ZigUVVlEK\n9OSF5eJi6aVrZExpNxPPuIGfGFg8VJWvU4lB1GmzESLEIA3Z21IKHQP+c19XYnsUqZE/kM1Xkunu\n7yoaPwuMn1aeqzu4lq6hL5B7iTI2NJ7SFRZ6IwXK5RYjRlWrjJJmWlGG6JqZKKbPvwY7z8OhmTIs\nuSOv+XC5PXi9awp7Wkrxiw/vwbfvoy6y4zPB3YyvnBuHjiHyQkzAa0mEbR2YW6gK+VvtwKMtyv5g\nlgGAc6N2vGh6L40u3f/Vla0Du58YyJaInOFWWEPxP6ddEQ4ZWQwApd2MLAZ2v2OjwS+TatpN8cdK\nVXsPrcodhRikIRWmHPz9TevwhxMjeOzl8IZ+xI3cEvKx+weRz/2Btjd8kbbquoTSNbQCmuqkAHIq\nigGgdGu19AIGVTplpVSQlARX0Wzf2zjDG+Hmuqiqzjv6LBi1O3D3tlrsbin19uQaD2EZHOicRHt9\nMYrzIm/vIItBREHk6S4SWzX+qaUquifm0FppArbeQ5bmSt11Z4apXUy5VFwqt8CYkdxHpmqgRnLD\nqZMIOPcVg+wCCjZP9wAjJ4B/Ww+89VR4v2cw/CyDaTd97mrUtRPCMhCE4m+uacW7ttfiG3+6gBdO\njWp78pZryE2kztIYOU5f7I130/PcEuU1OaOoex8FBlNVDMqkm8XkBd8KW68YaOsq4h43yuY70W8g\nX/WwNfJ04lfOj8OgY7hqLVUuV0o9hIJZBnbHEk4M2nDFmugqnWU3Ufjppc0+Pf29o2SDWAYeD0fv\n1ByaSvOB+j20s/+N0OewD1N8IruQCkVlN5G8si+spoaF+izfyXez41Topv68ljSRQMgpp6eeCe/3\nDAb3tQxmluiWzFTuMSZiBoJQMMbwr+/agtbyfDxxQOO0x5Zr6UPce1DZN3qSWkKbm4G7v0OxFBlZ\nDC6+RNuUFQO5W+t5XzdRcSM9D9AoLZH0d51BHpzIb6RV67AtcjHYd24CO5vMKMwxAgAKsg3Iy9IH\njRkc7p6G28NxWWt0YuC1DNwRppfKyG6aQKmloDYsTpcHzeX5QMUGKkST6zCCYR+m1b98Pq9lIItB\nlaqDrar4MFA34pImalkvtyeJtRhRtgwkS3SR0y1ZHUAWFciCFck26PGOrTU42m/B5GyE7SJioX4X\n3RzluIHDTqutqi30fNt9vrMK8sxkKXS9TM9TVQxyi6mB2uQFJfgNUDwhgjm88WLgLN2Y1rVTsdlQ\ngKygUAxbF3B+bAbXrld8/4wxVBRmY3wm8OflYOckcow6bG+MLKVURokZhBnf8BcD+zBw9IfAi/8k\nXbDvLap3km7CzaX5JBT1u1a2DGZGlFTmkmZfMcgqVP7Wdbt8O9h6C85UYmBupsJJeVpfrMiiJy0+\nXJzEj/lkcQnLQBAGN26sBOfAn8+Oa3dSQzblvffsp+djUuA4VLM+eWCOPju1agz8KZNSDNUr0pJm\n34wojZgfOA43GFo37kBpfhaGrJHFDPadnwAA30ZzoJjTWJBGh693TWJnkxnZhij6dUERA4crTDEo\nqqe22HLhl30I+P0nAJt0I/ZzE/VIYtBURimYaNhD7jv/6nEZ1yIwN6EsTszNdI4lB4mBSfVZLF9H\nLis5FdXaq1yjTEkTuTrl2EKsrc9ly0ByS7pAv2+kKb3xQIhBmrOpxoTa4ly8eGZM2xM37lW+hHJ/\nF9kyCEQF9a1BcYOmrTsiplxKMXSrhgfV7/TNiNKIvOmzGDfWg2XloaY4N+KYwSvnx1FbnIs1Fb5p\nqZWmHEwEsAzGZxy4MDYbtYsIUFbu39sfputSb6Aalj0fpefDx3xf1y0XgxyjDlVyvyS5RUewosAZ\nVVwAkCwRTkFn+4jvwqRIapHiFYN+EqksP5chAAy9Rdu5iZV/x1C4l0gM9RSsl8VAp/69RQBZEA6M\nMdy4sRIHLk5gflGjIjRACd4NvgmMnqC6glArfjkIq1miXJRUt1OK4Zg03+ATx2lbuobiJJYVMlfi\nxOSsEw1L3ZgroaB2bXEuhiIQA6fLjYOdk7hmXfmyPPXqohwMWRZwcWzGZ/+hLsrouXxNadTXfY1k\nhWQZIri1vPdJ4MpPkv9fjivJBHATNZXmQyevnGu309yMYHEDOY1Udkd5q557fN1HgNIvS3YBWfqW\ntwCRXUZyJtLsaGxxA5eDXETS7+kVAybcRIIouH5DBZwuD97onlr54HhReymtaPoPKcHjUCsYeQXX\ndrM21xctjZfTtu8gtS+Q4xvy8CKNXEXHLg6gQTeB3Lp2APBaBuHWlXT0WjC/6F7mIgKAD+xpRHGe\nEe///mEMTCutKl67OAlTjgGbaoqivu5LGymLrCSKtFSYapZX9/pbBnImkYwxl1Kd+4NYBvLfS/77\nyVXE091UZ2AKIAZy/yxrv2+8ACDxKJAr06XP+8jx0L9XKJbmKXjsLwbqorPo3z0ihBhkADubzMg1\n6vHq+RhN1kjIyqNVdO9rVHAWykUEAJUbgY+/BVz7OW2uL1rMLRREXpxVRjwCSkZUkKHs8Wb4PAWP\nK9p2AABqS3Ixv+jGVJizr1/rnIRRz3BZgFV+vTkPP35wNxxLHnzg+4cxOesE5xyvd03hstaymPzV\nSp1BFEORTAEsS1XMwOX2oH9qnjKJ1DTspgFTSwHiIFNdtPKWLYC8UhL5nlcBz5JvMkOOiV6zD1Fg\n1za43DLQ6YH7nwZu/zrwkVfpMyInRkTD0gIJ2jIxUP4GYuylIGxyjHrsbS3Fqxc0FAOAVvuDb1Kh\nVjiT3kpbfbN0UhHGlEpVvVHZL2dEaWQZOAZPAACMNSSym2uoWOz4gDWsn+8cn0VTaT7ysgL3gFpX\nVYgn/2onhq0OPPrCefRNzWPIuhCTiwhQ6gyWwk0tVVMoBXnVXYBVlsGQdQEuD6dMIjUNeynG4x9v\nAEi8S1sVq1VuK3HhBXpeudn3eFMtNVOcGSGxCNQptrod2PkQbRv2AhdejOz3VLO0EMRNpLYMxDwD\nQZ+3ragAACAASURBVARcvbYcvVPz3gCeJjTsUR6vZBmkEw2SGOiMvvtL12giBo4lN4ps57GgN3ld\nF1vqiqDXMbzVH17HzJ7JObT4r6D92N5QgvfvacT/vDWIn7xBsZDLoiw2k2GMwaBj4aeWqpEtg7Xq\nLrlK8FbOJFpmGdTvpm2guMFUJ6UFq5FdRXml1I9KTVEtpY56W62v0Da87UZqwxJqhnIo/C0DHiiA\nHN1bR4oQgwxB7iOjqXUgfwkBxY2SCXgtA79VtblVk8Kz4wNWrGV9cJjXe1e0eVkGbKguxFt9K1sG\nbg9H39QcmstWbm73N9e2ItugwxOv9aCmKActZaEFJBz0kXQuVbP+HcD2B3w/V1nK9XjTSv0tg/wy\nSgn2rzdwL1EQ2P+zKaeKtl63/G9sqqVsonDnbsjt3f0D3+ESzDIQqaWCaGkqy0djaZ62YlBQAWx5\nL3Dt51OrJXWsVGwEcooCWwb2IaX6NEF09E5hHRtAbn27z/7tDSU4PmiFa4WGdYOWeSy5eVg39rKC\nbPzs4T24f3cDvvqe9rh0yDTqdXBF4yaq2Qbc+ZhvKxDVCrl3cg4F2QaUFQQITjfsoTnRaovE0kcZ\nYKV+lsGmd9F2x4PL36eojtJF5SykohUm8pWvJ+shWjFwLQDGHK/oe+sM1POkRcxAECnXrC3H612T\n+OnhPnzp2TNR9bKJmHc/AVz9mZWPSyd0Olo15vt17ZRvKgmeejbQdQb5zImcuuViML/oxnm/lFB/\nuoO5U4Kwrb4Yj7xzC65oi81FJGPQsxUFKyT67IC7e6bm0VyWH1iwGvZSryx1/yjZpefvJqq7FPin\nKaqV8UfOKBo4DOQUrxzjYoxcRd37fJszhsvinGQZ0O8kzy7Q+aTUCjEQRMi16yvgWPLg878+he+/\n1oNfvDmQ7EtKX+78NnDvT333edNLE+cq8ng4FoekVEVvbQaxvYHSNt/qD+0q6pmQxCAOLp9oMOh0\nWIrGTSSjD5yW2jM5q1Qe+yPHrwZUrqKpi7SVe075nCOIJVssuZA6/+RbeRyKtptohkffwZWP9WfB\nSlaodPPXgUTUpzeREANBpFy9thw/f3gP9n/6WmyoNuFYmJknggBkF1IGkRo5s8SWOJHtnJhFo6sH\nHDpqxKai3pyLsoIsHFshiNwzOYfCHANK86PI9Y8DBh0Lv1FdIAIMtFl0eTBkWUBzaV6AHwAVk+VX\n+MYNJi9S62r/v2Mo6ncrFmG4Q5iaryRrJhpXkcNKPbG8YkD/b+qYgVYTMIUYZBCMMextLUVDaR7W\nVRaga3w22ZeUWeQUU2Mza+LE4M3eaWxg/VgqafX1nYP+vpc0lODYSpbB5Bxaygs0m5Dlj0HPsBRN\nNpHMutuAvR8DPvAb767+6Xl4eAjXF2NkHagziqY6A1sFoTBkK7GExTC/P1n5QNMVwMUIU0yXHFSB\nnKOIAfOKgbAMBHGitbwAQ9YFbVtUZDqMkXUgd7NMAB29FmzSD3jrC/zZ3lCCnsk5TIcoPuuZnItL\nVlC0RB1A9r5BDnDzI0Drtd5dQTOJ1DTspb+NTWonMXkRKI1QDABg90dou/ld4f9M200kPpG4EB2S\nqOcWA2tvAQCMcXIF+rawFmIgiIFWqTlZ94SGdQergeL6hLqJzvQMoBbjYFWbA75+SQO1lg7mKlpY\ndGPIupC0eAEgp5bGYBkEoGuCVukhfy913MBhA+bGgbIoUp7zzBRg3vGh8H+m7UbaRuIqkgPcRQ3A\nFZ8EPnURQyAXldoySPuxl4yxLzLGhhhjb0v/blO99jnGWCdj7DxjLMWb1aQnreUkBvKXSBAnihsS\n5iYasS2g0HaBnvhXxkpsXaH4rHcqucFjgGIGMVkGAXi734oGc17oUZxVWwFjPsUNJqUbbdna6E4Y\naap0aStlIqnHZq7E+FnaVm6iDLYCpY+UT28ijSyDRCeHf4Nz/jX1DsbYRgD3AtgEoAbAnxhjazn3\nm/8miInG0jzoGNAlLIP4UlQPOG2UBZIb3QCYYHT0WrBBJ7mggoiBXHx2tC+wGHirdJPtJoolmygA\nxwYs2NOyQqsMvQGo20FiUHsp7YvGTRQtpWsi613llFKEAwS4feoMNCIZbqK7APw359zJOe8B0Alg\nVxKuI6PJMepRb84TlkG8kVMPE+AqOtpnwRbDAHhuie+kOD92NplxrN8KxxKtn04O2vDwUx0Yn3Gk\nhBgY9Ay9k3M4PWxb+eAwGLEtYMzuxCX1YYhvw15g7BTN6GZ6bafqlUZYob4k1QFJIy/V+AaQM6M3\n0ccYYycYYz9gjMkT0msBqL9Jg9I+QZxZUy4yiuKOnF4aZ1fRktuDP54exfbsIbDKzSGDhpe3lsHp\n8niziv50dgwvnRnD3z99HF0Ts6gy5SA/O3kV4TdtrMKQdQH3Pv5G2C23Q9HRS1bQJQ0lKxwJ6mDK\nPcCb3wPqdgIGDdNrza0UFA42dc2fpXmfgjM1+iS4iWISA8bYnxhjpwL8uwvAfwFoBbANwAiAr0fx\n/h9mjHUwxjomJjTuyJkBtFYUoHtyDu44m+yrGrlxWZwzip47OYJR2zya3X1BXUQyu1rM0DEaUQkA\n1nnKLDpwcRK/emsoqVYBAHz0mlb8wy3rMeNwwTIf+2S4fecnUJRrxCapc2tI6nYqjzfdHfO5IyLS\nokS5SV0A9EmYBhjTGTnnN3DONwf491vO+Rjn3M059wD4HhRX0BAAdWlfnbQv0Ps/zjnfwTnfUV5e\nHugQQQhay/O9xTqCOJFfRi2W4+gm4pzj+6/14HLzDPTuhWWVx/6YcozYWleMg50kBmN2J1rK8rG1\njobSNJUFKczSkJpiusnF2hLF4+HYd34c16wrhyEcP3p2oTKacsMdMZ07YiKdeSE3qQuAT6O6dC86\nY4ypJ1W8E8Ap6fHvANzLGMtmjDUDaANwJFHXsZoRGUUJgDGKG8TRMujos+DEoA0Pr5WC/UHSStVc\n1lqK44M2zDpdGJ9xoLo4B4++px27m824b9cKbZc1oK6ExGAwxoXI8UErpuYWcd365RPbgvLgi8CD\nL4VfQRwvihupeCzcNudL80EtA4NPFXYauIlW4KuMsZOMsRMArgXwdwDAOT8N4GkAZwC8AOBvRSZR\nYhBikCCK4isGTxzoRnGeEXtN0tjSsnUr/szla8rg9nAc6ZnCmN2JisIcrKsqxC8+shdb6+Kb5RQN\n8bIMXjk/AR1TWrSHRWEVUJ+EnBRDFo3E3P8ocPhxJUAcjBBuIp92FOkuBpzzD3DOt3DOt3LO7+Sc\nj6hee4Rz3so5X8c5fz5R17DaKcnPgjk/S4hBvCluiJubqG9qDi+eGcP9uxuQZe+n8YxZK7t5Lm0s\nQZZBh4OdU5iYcaLCFLjTZ7IoyTMi16iPWQwujM6guSw/dH1BKlG7nbbPfxr4z71AZ5CRmG4X4LQH\ndRPpDYplIMZeCuJCa3k+usZFrUFcKa4H5qfiMtfgyYO9MOgYPri3CbD0UsO1MMgx6nFpQwmePzmC\nRbcHFYXL0xOTCWMMNcU5GIpRDPqn59EYqgVFqnHnt4FPHAc++DtquPeTdwGnf7P8uMevpj5KQS2D\nNAsgC1KfNRUFwjKIN3KAMsb0UtvCEp7uGMAdW2tQacoBpnsiyou/fE0phm00BL4yxSwDgFxFsVgG\nnHP0T8+jwZz8gHjY5Jnpb9hyNfDXBym76bcfI6GXcTmpFgIIahnkq2ZXp0VqqSD1aS0vwNTcIiwh\nGptlCj8/0o/XpQybhFIUoPBsuht49auAwx722/z3kX7ML7rxoSuaqYPlzLAynzcM9rYqw2hSzTIA\nKIgci2UwPbeIWacrvcRAjTEHePf3KengmYfJNQT4pp4GsQwKctRT9oQYCOLAagoif+5XJ/EXTxxO\n/InkwrOeV5V9+78GvPJI2G2Ml9we/PD1XuxtKcXm2iLASgPpI7EM2qVUUkDJ3kklaopyMTm76K2U\njpT+6XkASF8xAICSRuAd3wAGjwCvf4v2yVYBELD6GKABQV6EZSCIB6tFDGxxKG4KG1M1sOUe4PVv\nA289Rfvsw9KFDIb1Fq+cG8eIzYEHr5AsAdmNEGbMAAAMeh2ypNz76qLUswxqJYGSW2REiiwGjcEG\n2qQLW95DMxoOPkaWo7qZHQt8C2aZVGcgSA1qS3KRZdBlfMO67klF7DxaVFzf/Z9A/R7g1UdpCPu8\n5J6SRWEF9l2YQH6WHlfJKZPTPbSNsJfOvk9fg2c/fkXSBtmE4oo1ZdDrGH5zLGBN6Yr0TZEY1Kez\nZSBz1aepVUXH933FgAdu9c1UIqHVX1aIQYaj1zG0lOVnfI+ik0NKU7QZhwYDffRGYNfDgK0f6D0A\nWCQ3j33lGx/nHPsvTGBvaxmyDNJX0NILZBVQhXME1BTnkpspBakw5eCGDRX45dFBOF2Ru4r6p+dR\nacpGjnH5GMy0o3Y7sOYG4PV/B0ZO0HQzIKhl4CsBmdGoTpACtGZ4RtGozYFvvHTB+3x6XqNg+frb\ngewichc5pcBxGG6i3ql5DFoWcPVa1Y3fImUSpeAKPxbu29WA6blF/PH0WMQ/m3aZRCtx1afJgnQ7\ngas+BVRsBDbeFfhY1ecgvmOCgiPEYBXQWl6A/un5qFZn6cB3Xu3CnNON//2OjQCA6TmnNic25gJb\n3g10StOt8ivCsgz2X6Cmi1e2qapqLb3atlvWiKvaylFXkoufH468YnvM7kB1UeoFxqOmYQ/QdCU9\n3ngX8DeHgDXXBz5WZTFo1WdSiMEqoLU8Hx4O9E7OJ/tS4s6c04Vnjg7iti1VXv+77GvWhG33K4+b\nLgfmJiiPPAQHLk6gwZyHJrm7qMeTsWKg0zHct6sBh7qn0B2Bdco5x7jdifLC1KufiInbHgWu+ycl\nPTkoKstAiIEgXmRyRtGvjw1hxunCB/Y2orE0DwYdQ6eW8RF5ohagrPpCBJEXXR4c6prCVWoX0ewo\n4HJEVGOQTrx3Rx0MOoanDvWF/TNzi24sLLlRkWliULGBXEQruQOZEANBAmgppxVopgWR950fx1ee\nP4dt9cXY3lACo16HxlKNp7sxBnz0deChPwPmFtoXwlV0tM+CuUU3rvJ3EQEZaRkAVBD37u11+Onh\nPvSGmWY6MUPWVcZZBmGjFgNt1ECIwSogL8uA2uLcjLIMrPOL+PjPjqG2JBf/cf92b2pla3mB9mm0\nlZuAukuVlsm24GJw4OIEDDqGva2qeb7etNLMtAwA4O9vWgujXocvP39u2Wunh22YnPV1ra16MVBZ\nBm4uis4EcaSlPD+jag2eONCDGacL37x3G2qLlSBja0UB+qbmsOTWKgdDhTy32B48o6ijz4KtdUUo\nVLcbsPRSwHBFP3L6UmHKwUevbsULp0dxpEcZC3l8wIrbH3sN//zsGZ/jV70YqNDIMBBisFqQG9bF\nYyZtspmeW8STB3tw+9ZqrK/yHYXYWl6AJTfHwHQSguVZ+ZQ/HiJmMGRZUALHMpYesiq0nNebBB66\nsgXVRTn45z+c8RYGPvEaWUXHB20+x07MUAO+8oLVJQafumktxUl8UkuFm0gQR1rLCzC/6Mao3ZHs\nS4mZ777ahfklN/7uhrZlr7XK8ZFkWUFFdUHdRC63B6N2h48lAyBjM4n8yc3S49M3r8OJQRue7hjA\nqM2B50/SmJPJGafPQmVi1gm9jqEkXeYYxImPXdeGI5+/ASKbSJAw5IwiTTNtEsDA9DyePNiLd15S\nizUVhcteb0l25pSpNqibaNTugNvDl4vBdE9GxwvU3L2tFntbSvHPfziLLz9/Fh7O8aHLmzHjdGFy\nVikWnJhxoqwgy3cW8GrCJ5tIxAwEcaS1IjMyir78wjnodQyfuXl9wNeLco0oL8xOnuiZaoJaBkPS\nPOBadYdR5wxVpa4CywCguoOvvmcrZp0u/ObtYdy4sRJXr6PMKnUdwsRMBtYYRIKq6MytkWkgxGCV\nUF6QDVOOARfSWAw6eqfxhxMj+MjVLagK0aWztTw/eZZBUS2wMB1w/u2wjfbVqC0DOa00Q2sMAlFv\nzsNX370V+Vl6fPy6NrRIMZRuVdrpxKxz1cULfGBKPybhJhLEFcYYNtaYcHo4/OErqYTHw/GlP5xF\npSkbH76qJeSxayoK0DWepGC5SUovDRBE9loGgcRglVgGMvfsrMdb//tGbK4tQk0xddY9O2LHuBTT\nWvWWgU6ZdCbEQBB3ttQW4eyIPTlplzHy2+NDOD5gxWduXo881UjAQLSWF8Du8PVBa0ZRLW0DNKwb\nsi6grCDLtwvnKqgxCEa2NPRdr2PINujw1KE+XPXoK5ie+3/t3WlwXNd14PH/6UY3lsa+klhIECRA\nLdROybK8KHYcm/ISSV5m5IzjJVOjkpfKLJVJpHI846kppxJn7A+usSMriRNnRrGskSJLKS+K7LEt\nj20tlEVLoEmQ4I6FIHaA2Lv7zod3X6MBYukFveGdXxWKjdcP3fexGzh97zn33kVGLi9qMLB0oTq1\n5Q60VLEYjhZcEvknPZd48MnXuaGtmntvatn0/Jwuv1Fp27fGLOT+ifmVQ0Tg9AxKqqG0OvNty2Nv\nv6oRgPmlKN95tZ9I1LC7NrTJT21jvuUPDNn67KbBwEOubXbWve/un9zkzPzyuae7aa8L8fcfvzWh\n6pK9jZkPBi+dGeOT//uVK5N77sSzNZLI/eOza5SVnvFUvmA9f3bvdfzyobcT9Pt49EVnDSN3GRVP\niusZZGuwU4OBh3TUhwgF/QWVNxi9vMCFsTk+dLCVmlBiNec7K0soDfg5dSlzcw3+1dd/yfe7L145\nbyNQCmV1V/QMjDH0T8x5do7BZkLFReysKuXGtmpODc8QCvrzdtOerNCcgcokn89JIr9eQD2DnqFp\nAPbvuHJOwXp8PrHLb2R+mGhw4sqqIWeuwcpgMD67xPxSdGVZaSQME+c9mS9Yz217agF421WN22OH\ns1T5l5credeBHVl5Sg0GHnNtcxW/GZjKWu1yunou2mDQlHgwACdvkKncyOTsUuz2q+cnODqwKrjW\ntMPoqRWH3EqiFTmDqX6IhrVnEOcOu4Dfe67bmeOW5FjcPINQMLDBiVtHg4HHXNdSxdxSJKmNRnLp\n2OAUNWWBpCtL9jaU0z8xx9xieru7/ejYEG//0k9WBJavP7/8h/4L3zvGe77y/2Jr7QBQ3+UM/8Rt\nctM/4ayVtLKs1FYSac4g5o1763jyk3dwKEufhvNW/H4HWdoKVYOBx7jjsN2rP83mqdf7pzjQUhVb\nojpR7ozr0yPpBb0vfPcYp4dneMeXf8rLZ8fo7p/k68+f5oO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the x/y splines as parametric functions\n", "# of a separate varaible, t\n", "horse.plot_parametric()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Step 2: Calculate Fourier Approximations" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class FourierTransform:\n", " \"\"\"Calculate the complex Fourier coefficients for a given function\n", " \"\"\"\n", " def __init__(self,\n", " fxn, # Function to be transformed (as Python function object)\n", " # Note: y is parameterized by its own index\n", " # 13th value in array = value of function at t=12\n", " rnge, # (.,.) tuple of range at which to evaluate fxn\n", " N=500, # Number of coefficients to calculate\n", " period=None, # If different than full length of function\n", " num_points=1000, # Number of points at which to evalute function\n", " num_circles=50 # This is needed to calculate proper offsets\n", " ):\n", " \n", " self.num_circles = num_circles\n", " \n", " t_vals, y = zip(*[(v, fxn(v)) for v in np.linspace(rnge[0], rnge[1]-1, num_points)])\n", " t_vals = np.array(t_vals) \n", " self.t_vals = t_vals\n", " \n", " \n", " # Save the original coords when plotting\n", " y = np.array(y)\n", " y = y - y[0]\n", " self.fxn_vals = np.array(deepcopy(y))\n", " \n", " # Spline function doesn't make endpoints exactly equal\n", " # This sets the first and last points to their average\n", " endpoint = np.mean([y[0], y[-1]])\n", " y[0] = endpoint\n", " y[-1] = endpoint\n", " \n", " # Transform works best around edges when function starts at zero\n", " # (Can't figure out how to avoid Gibbs-type phenomenon when \n", " # intercept !=0 )\n", " y = y - y[0]\n", " \n", " self.N = N\n", " if period==None:\n", " period = rnge[1]\n", " self.period = period\n", " \n", " def cn(n):\n", " c = y*np.exp(-1j*2*n*np.pi*t_vals/period)\n", " return(c.sum()/c.size)\n", "\n", " coefs = [cn(i) for i in range(1,N+1)]\n", " self.coefs = coefs\n", " self.real_coefs = [c.real for c in self.coefs]\n", " self.imag_coefs = [c.imag for c in self.coefs]\n", " \n", " self.amplitudes = np.absolute(self.coefs)\n", " self.phases = np.angle(self.coefs)\n", " \n", " \n", " def f(x, degree=N):\n", " # Evaluate the function y at time t using Fourier approximiation of degree N\n", " f = np.array([2*coefs[i-1]*np.exp(1j*2*i*np.pi*x/period) for i in range(1,degree+1)])\n", " return(f.sum())\n", " \n", " # Evaluate function at all specified points in t domain\n", " fourier_approximation = np.array([f(t, degree=N).real for t in t_vals])\n", " circles_approximation = np.array([f(t, degree=self.num_circles).real for t in t_vals])\n", " \n", " # Set intercept to same as original function\n", " #fourier_approximation = fourier_approximation - fourier_approximation[0] + self.original_offset \n", " \n", " # Adjust intercept to minimize distance between entire function, \n", " # rather than just the intercepts. Gibbs-type phenomenon causes\n", " # perturbations near endpoints of interval\n", " fourier_approximation = fourier_approximation - (fourier_approximation - self.fxn_vals).mean()\n", " \n", " circles_approximation = circles_approximation - (circles_approximation - self.fxn_vals).mean()\n", " self.circles_approximation = circles_approximation\n", " \n", " # Origin offset\n", " self.origin_offset = fourier_approximation[0] - self.fxn_vals[0]\n", " \n", " # Circles offset\n", " self.circles_approximation_offset = circles_approximation[0] - self.fxn_vals[0]\n", " \n", " # Set intercept to same as original function\n", " self.fourier_approximation = fourier_approximation\n", " \n", " \n", " " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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9QcrzH+C+YzGxjz2K70O3oLnMbwJCiNZHAr8FOLJ7J5n7kug8aOhF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\n6G7t0JX7pBI+cPbaWRaEL2Bg3YEMrj/4lvORB/Zg5+REt9F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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Calculate Fourier approximations; initialize NC equal to the\n", "# number of circles the final animation will have to get an \n", "# accurate view of how well the image will be approximated\n", "NC = 50\n", "xFT = FourierTransform(horse.x_spl, (0, horse.num_pixels), num_circles=NC)\n", "yFT = FourierTransform(horse.y_spl, (0, horse.num_pixels), num_circles=NC)\n", "\n", "# Plot the full approximation and the NC-degree \n", "# approximation for t from 1-R\n", "R = 50\n", "plt.plot(xFT.t_vals[0:R], xFT.fxn_vals[0:R])\n", "plt.plot(xFT.t_vals[0:R], xFT.fourier_approximation[0:R], \"--\")\n", "plt.plot(xFT.t_vals[0:R], xFT.circles_approximation[0:R], \".-\")\n", "\n", "plt.plot(yFT.t_vals[0:R], yFT.fxn_vals[0:R])\n", "plt.plot(yFT.t_vals[0:R], yFT.fourier_approximation[0:R], \"--\")\n", "plt.plot(yFT.t_vals[0:R], yFT.circles_approximation[0:R], \".-\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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AD8MZhyCMRKVH0ih7aSbzGr8n1eN8RhkLO/c135uDX+RUi/uqrm/k15dvZsGB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\noRY0NCscmVi5trP8s72kI6J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446Ts+pnmVycTX7mGJI+LUf/fAcIX3U5ORjJpz85hRspj\n1Kq8KV2ynrg73sPGoe8JUGUlBUQdeoZsdSQt8/4HQFX2vh7b2takUWQVgGYQBddM7a0E6PNpdD1x\n0QTH6EXm+A6bb2801FYRVb2BFJcFeHhaNp7+mLAbV5KnHsPE/Q9TnpUwoLh1KmdsjY0DOtZSUv5O\nXm19jEbZlsxzvwKXIPN2ScJP0065wa7Hq5qGn/5BMzaEX/5k57aQRcs5qhjFqOT/gaF9WOM+lUQi\nEM4YDc0tbHtzOdGbrkWPiszzvyX+7tXISjU73/kbgV8tIEh/hAOx/2T0o78TENX7al9/JJtMlHx6\nJxracVjyLj4dY/q1ZVk9tvdpzaHKIWJQ76UkMwGVZMTK/8RjYMaERWCUJRrKjgCQ8vMKbKU2POfd\n0+9zKqxtsV36FU3YovvmdoyG/t8u0Vs7Y29q6vdx/bLtv6gNTRwmhB/Tu66r7G7VQoNBRWGttsv2\n3MRfidXuISXoRlw9jidIhVLFkbF342MsI//g1uGN+xQSiUA4IyTs3EjFS9M5q/ozDnldhPuD+4ic\nfDb7N35B44uTmFX+EYdd58Nd+5lw6QNIFsyUPWbvj+8R17qbtPC78Rk9Djc3d+qxx1Tb/dZQTUUh\nntRi8Ox9QXVL1GXvAcAr8sTJSqPRUGvljrG2gDa9nlFHviBHPZagGMuS3J/5+gdTMOnvBBny2L7G\n8nINxxitXbBBB4buxeiGzKUrYfKtzFAc5uHcG9B/cgXk7zI/JwmZywxFGhmH9h9vL8vIvz5JJS6M\nu/yRbt1NPvtSTLLEkf0bhi/mU0wkAuG0VltVxu5XriV+yxJcaSR/wftMWP4RNTU1JD6/mMl77sCg\nsCbn3C+YcO/XOHp0n3h1IpWlhUQc+Dc5qggmLHkCMN+CKFONwrGxe9nj0gzzLRWHIMsWpe9V6QEq\nZReCgsP6bFpjP4YQbQp7Nn1LIKUYJ908qFNPXnwr+dYRxGa8QmZWZr+OlTsWj5G1Ax991CfnUXD+\ni+Reu4+X9ZdjKtwLq8+HjB9xXvQorZIGvwPHy2pnbv+CsPZ0MsPvxsGh+9oRTq4elNqE4VS+p8c1\nD04HIhEIpyXZZCL5x3eQ3prMlPr1JPldi+ODBwmacQUpezZivWou0doEEkffg++jiYRNOa/vTv98\nDlmm4NO7sJNbsVvyDoo/PLStdYwkUH8ETF0nh7UUmIdyBkRaVkuoN24NaeRbh6O06vufcGvIOfhJ\nVYTte4w6yZnws68b1LklhQKXa97DRmpH+dVV6FoaLD5WYWdeU7m1YRhmF/9JZGgQqaoYMOrBNQQC\n4pHs3NnmsoSYpp1Ql49s1GO/67/k40f8pb3fLrOKupA4KZNdW38a9rhPBZEIhNNOZUUZiS9dwsSk\nR6hQ+lG0ZCOTbn0bla0jO796iYgNV9OmsKXmmo3EXfcflOqBrUWb8PMqJmt3kBK2HN+wrstEmjzG\nYouOurK8LtuV1YcpwwMnV48Bvz+Tth4/YzFNbpZV13ePM09885NqKAtdgqQa/Nq7ToGxHJ3zBsHG\nfHI/sPwKQ2lnLjzXUl856Bj6IuVt5x3+S5XkDsvWQ8dMYyefEAAqGnWk//Iu/sYiiiY+hMa6e5mO\nY3wW3U+Nwo3gpGeQTZbN/B5JRCIQThuyLLN9wzfIK6YzvnknCSF3M/qRXQRHxaPT6dj9+o3Mynia\nHNsJOP1tF/7hA789U1tZQljiU+Qow5hw1T+77bf3M5d+rjjadVaqR3M25bZ93845kbJM8/MB1SjL\nhp/6+wV0vnaLnH2Clv0Tc9YV7PC5kejaTaT8btn9c7XjsSuCqiGLo0c5m+HzK6nR+LNMfqqz5hBA\nmIN59E9SqQ7PpJc5rAhn6nk3nLg/tR25MQ8QYczhyNbVwxf3KSISgXBaqKutZucr1zJ37y0YrGyp\nWPIT8Tc8g1Klory0iJwX5zOzbi2JftcT+cBG7J3dB3W+/E/uwl5uQXXpCqyU3UsUe4eYv603lR4f\nOdTS3Ii/qYQ2t7GDOnd9jnlYqndkzzOK/0ySJNplc60cST20Sy5Ovf5pqiVXlJsep6FZ12f7zgqk\nTcN8ayjpQzC2oXUKo1arp67l+NBPLxfzcwDVhofwkGuom/E4KmXftYRiz7uNo/iiT/5i2MI+VUQi\nEEa8tO1raH99MjMa1pMScD0+Dyfg3zH0My1pF/LKuYTpM0md8iJxt77Z5V7+QKRs/oSJTdtIDLyV\noLGTe2zj7TOKFlmDsSqnc1thZhJWkowmYHyPx1hKUXaAAtmLkICAvht3+H/2zjs6qqrrw8+dkknv\nvfdGEhIIvYMoRRQU7B1FsSv2/trba1dUUBBpCgJSpfce0jvpvfcyyWTmfn8MJARSJoXi++VZi7Uy\n955zz7khc/c9++z921WC9uGnEjp3f/QGAyMTGia8RaCYRtQvT3Tb3thcawjUdZdxsxjg5u9h5BN4\nlvMGSQEAACAASURBVOzhgOJ5ag98o90rACRhd6FGwlThFCflwxg9qWPRvosxUMgptRmFa30spVV1\nl3P2V5wBQzDAvxZRFDn6+38IOjCfBokx2XP+JmT+d0gU2oShQxt/wmvzHKSCSOm8vwme/kifx6yr\nqcDhyFukSzwIv/vdTtsJEgmFMicMa9v2CKoyIwGw8+1bRrFNTTzZ+v46bRSfx0TUPrj0Dfu/9q7r\nxAeJdryDiZXridnUdXU2MxNTGkQFmobLJDx3HgNzmPYhxXfvJUrjjevp92DxGMg4AAoTNOcefXo+\nk5FIdJf1cA27DiOhiYMHdl2miV8dBgzBAP9KlM0q9n33OGPSvyDKeDz2L5zAM3QCAE3NzRz44QnG\nx7xErr4P+k8cxiVoTL+MG//7i1iJlahmfoleF5uLAJXG3jgoL9gsLoqnDgPsXX17Pb6mpghrTRkN\n1j3LQzAQtK4RmV7HYnl9JejB74jUG4p/9AdUl+R22s7cUE4VRnC5FEgvws5zMI/yKlvcXoWyFFh7\nD8qSDORok+EM6d6ddSH2odNoEAyxj/0etab3mkvXGgOGYIB/HaXF+cR/Po0p5auJc7iV0Oc2YmBo\npD1XWkL85zOYVLqKaLs5eL2wH1PrnuUGdEZixH6Gl/xFhO2t+A+d1G37ZusAbKiktrIYALPqZPL0\nPPukbV+UfAwAPbeOXVIdcWJnm09boujfPYLzyORyTG/5EpnYQsz6jzttpy+XUo0JUmUlkfs2UFt1\nefcKJBKBaRaFjMlbAnJDuOkbsja0SUik1fbQTWhoSc6gJxiriSDmwIZ+nu3VY8AQDPCvIi1yH+Li\nsYQ0RZMQ9jbBC35pzQJOiD1Nw/cTCGmKJC70HUIXLkcq7x+fuFqtQbLjJSoEcwbd85lOffSdtG/t\nRalnUKvVuKoyqTHrm7REbdpJWkQJTgHdl7JsrK/l+DcPMPJ4W30DmaL/XUPn8fYfTJLFZMKK/yI5\nM6fTdnUSU3yrjjDk0IM0fDWMQwd2XrY5Eb2az2pfRqmRwPxd1Jn54FO0hUgD7UZ7WnnPM5y9Zi0i\nDztsj797SZ7Iv5UBQzDAv4aTO1fj9PftqAQ5eXO3MOjm51sVQQ9v/R3Xv2ZhSh35N60lePZz/Tr2\n6e3L8Fenkhe2CCOzSwu4dISNlza3oDYnltyMJIyFRiQOfZOWkBZFkYYzXo5dF1zMjj9K2X9HMKpi\nI6cc7uKEy8Pa/v0cNXQxbnPewlBQUrjp0pDa8zRKtWJ7BYIdSGT47F9ISXFh/05Eo4YdL8OmhRSZ\nhjKz8V3qLQIo2vAa9aI+hrd8S43CgYl126mu75mYnFxhQIL3ApxVWRT2UnzvWmPAEAxwzaPRiOxc\n8QlDjz1BgdwN/cf24XlOK0fV0sLen15gzOmnKNNzQnj0IO5Dr+/X8ZVKJU6Rn5EtdSNk5kKd+zk6\nuVEnGqApPUvp2QgALD37IC0hitjVJpJn0PlGsajREPHnRzium4WeppG4KSsY/uhiBEQ0ooCsn1ZI\nnWHiFkqc/a2Mr9pEdmLH6qvBqlgAskOeQzP3N6yoovj3+e1qJvSZojg4+SMAKrvBGAuN5CSfwbvy\nEAes78Lfx4fSoc8yWJJB1rE/e3z5sIlzAIg/fhlXM1eQAUMwwDVNfW01J764jRsyPiTDeCguz+3F\nys4ZgPKKciI/v4kphUtIsLoel0UHMT+XNdqfRPz1BS5iIQ3j3+xR6KlMJqVQ5oiiJovm/BjUooCz\nX3cVcztHU56JiVhLg03H4ae1NVWc+XIu4YkfE2cwDMnjxwgepy1/KVUraUQPSQ8ijXqL29wPqcaY\npq2vXHpSFLEQtBFModMfwiFwNMc8niK47ijJB3v+QO4Ux1C4Yw343IDH2V85rHiOgI3aFwQD77EA\nOE14kEzRHovYpT2+vK2zF2Uye+Q5h1Gq/v3uoQFDMMA1S0FWCmVfjmFk7W6iPBfg8/w/6Blp4+FT\nk2Ko/nYC4Y3HiBv0IsFP/YFMv//931WV5QSeXUySYjAB4+f2uH+NoSuWTbkYVCSRL3VGz8Co13Mp\nSdFmFBu4X7pRnJwQSemX4wir2ccJ9ycIfXF7u3oDErWSJrqvRtYfWFjbEeVyH74NkeSntS8CU5we\n1fqzgagt5znijtcoxAbV4a9QqTuu6tYr/GfA3X+ieiqWL1rmtR6eevJB2Pse+goFNQoHGho7Lyva\nFU0+NzJePMPRI/9+eeoBQzDANUncmaPIl9+AhaaC+MnLCLvvs9ZN4WM7/8Bu7XSsxEqyZ6wkeN4b\nPSrx2KN5rHsPS2owmPl+r8ZQmXtirynBuTGZMhO/Ps2lLuMkSlGOi3/bqkLUaDj459c4/zkDS7GS\ntBt+Y+QDHyKRto9MkqqVKK+QIQAYPONRWkQJqTt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ERnZcNexyk3l0vdYtNFp3t9CF+I6Y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\nDH3zMGpR+38tfGCPpqWl1+NdiGXmdgqkTlh69r3anFoj8v7fUVjsepJ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Hi7IWtbIOsen8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\nxIZL7oHtRAD2QVP63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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Visualize the approximation as 2D image\n", "plt.plot(xFT.fxn_vals, yFT.fxn_vals)\n", "plt.plot(xFT.fourier_approximation, yFT.fourier_approximation)\n", "plt.plot(xFT.fourier_approximation[0], yFT.fourier_approximation[0], 'o', color='red')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Step 3: Calculate positions of each circle throughout cycle" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class ComplexCircles:\n", " \"\"\"Complex Circles Class:\n", " Tracks radii and centers of circles implied by \n", " Fourier decomposition of given FourierTransform object\n", " \"\"\"\n", " def __init__(self,\n", " FT, # FourierTransform object\n", " num_circles=20, # Number of circles to keep track of\n", " t_init=0, # Initial time state of object\n", " origin=(0, 0) # Center of the first circle\n", " ):\n", " self.FT = FT\n", " self.t_init = t_init\n", " if num_circles > FT.N:\n", " raise Exception(\"num_circles exceeds the degree of the given Fourier series.\")\n", " self.num_circles = num_circles\n", " self.origin = origin\n", " self.origin_x = origin[0]\n", " self.origin_y = origin[1]\n", " self.t_elapsed = 0\n", " self.steps_elapsed = 0\n", " self.t_current = self.t_init\n", " self.t_index_current = 0\n", " self.true_fxn_val_current = self.FT.fxn_vals[t_init]\n", " self.fourier_approx_val_current = self.FT.fourier_approximation[t_init]\n", " \n", " self.Xs = [] # Track the coords of the center of the last circle\n", " self.Ys = [] # for each value of t \n", " \n", " self.As = FT.amplitudes[0:num_circles] # Amplitude of each frequency/circle\n", " self.Zs = FT.phases[0:num_circles] # Phase of each frequency/cirlce\n", " \n", " def circle_positions(self, transpose=False):\n", " \"\"\"compute the current radii and centers of each circle at the current value of t\"\"\"\n", " \n", " num_circles = self.num_circles\n", " t = self.t_current\n", " \n", " running_x_offset = deepcopy(self.origin_x)\n", " running_y_offset = deepcopy(self.origin_y)\n", "\n", " # There will be 1 more center than radius;\n", " # Use this to plot the last point on the last circle\n", " # Stored in final_x, final_y below\n", " radii = []\n", " x_centers = [deepcopy(self.origin_x)]\n", " y_centers = [deepcopy(self.origin_y)]\n", " \n", " for i in range(0,num_circles):\n", " freq = i+1 # Corresponding frequency for given circle/coefficient\n", " a = self.As[i] # Magnitude (i.e., amplitude) of complex coefficient\n", " z = self.Zs[i] # Argument (i.e., phase) of complex coefficient\n", "\n", " radius = 2*a\n", " radii.append(radius)\n", " \n", " running_x_offset += 2*a*np.cos(t*2*np.pi*freq/self.FT.period + z)\n", " running_y_offset += 2*a*np.sin(t*2*np.pi*freq/self.FT.period + z)\n", " \n", " if i < num_circles-1:\n", " x_centers.append(running_x_offset)\n", " y_centers.append(running_y_offset)\n", " \n", " if t==0:\n", " self.circles_offset = running_x_offset\n", " radii = np.array(radii)\n", " x_centers = np.array(x_centers) - self.circles_offset + self.FT.origin_offset\n", " y_centers = np.array(y_centers)\n", " \n", " x_final = running_x_offset - self.circles_offset + self.FT.origin_offset\n", " y_final = running_y_offset\n", " \n", " self.Xs.append(x_final)\n", " self.Ys.append(y_final)\n", " \n", " if transpose:\n", " return(radii, -y_centers, x_centers, -y_final, x_final)\n", " return(radii, x_centers, y_centers, x_final, y_final)\n", " \n", " \n", " def get_circles(self, transpose=False):\n", " return(self.circle_positions(transpose=transpose))\n", " \n", " def step(self, dt=1):\n", " # dt = how many times to increment t_vals array for each step\n", " self.steps_elapsed += 1\n", " next_index = dt*self.steps_elapsed \n", " if next_index > len(self.FT.t_vals)-1:\n", " print(\"Max t-value reached\")\n", " self.steps_elapsed -= 1\n", " else:\n", " self.t_current = self.FT.t_vals[next_index]\n", " self.t_elapsed = self.t_current - self.t_init\n", " self.t_index_current = next_index\n", " self.true_fxn_val_current = self.FT.fxn_vals[next_index]\n", " self.fourier_approx_val_current = self.FT.fourier_approximation[next_index]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 4: Animate the circles!" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x_spl = horse.x_spl\n", "y_spl = horse.y_spl\n", "num_pixels = horse.num_pixels\n", "\n", "# Number of circles to draw in animation\n", "num_circles = 100\n", "\n", "anim_length = 20 # in seconds\n", "fps = 24 # frames per second\n", "num_frames = anim_length*fps\n", "interval = (1./fps)*1000\n", "\n", "# Ensure that the approximation has at least 2000\n", "# points to ensure smoothness\n", "dt = (int(2000. / num_frames) + 1)\n", "num_points = dt* num_frames\n", "xFT = FourierTransform(x_spl, (0, num_pixels), num_points=num_points, N=num_circles)\n", "yFT = FourierTransform(y_spl, (0, num_pixels), num_points=num_points, N=num_circles)\n", "\n", "# Distance between circles and image\n", "X_circles_spacing = 200\n", "Y_circles_spacing = 300\n", "\n", "# Origin calculation: Offset the circles so they line up with \n", "# the plotted image\n", "x_main_offset = xFT.origin_offset\n", "y_main_offset = yFT.origin_offset\n", "x_origin = (0, X_circles_spacing)\n", "#y_origin = (circles_spacing, y_main_offset)\n", "y_origin = (0, Y_circles_spacing)\n", "#y_origin = (0,0)\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# These calculations set transparency based on how close the \n", "# approximation is to the original function (prevents the big \n", "# swoops across the drawing to dominate the image)\n", "approx_coords = np.array(list(zip(xFT.fourier_approximation, yFT.fourier_approximation)))\n", "og_coords = np.array(list(zip(horse.x_tour, horse.y_tour)))\n", "approx_dist = distance.cdist(approx_coords, og_coords, 'euclidean')\n", "closest_points = approx_dist.min(1)\n", "def alpha_fxn(d):\n", " # Takes distance between approx. and true value\n", " # and returns transparency level\n", " return(np.exp(-(1/10)*d))\n", " #hist = plt.hist(closest_points)\n", " heights = hist[0]\n", " scaled_h = heights/heights[0]\n", " breaks = hist[1]\n", " for i, b in enumerate(breaks[1:]):\n", " if d < b:\n", " return(scaled_h[i])\n", " \n", "cutoff = int(len(closest_points)*.95)\n", "alpha_vals = [ alpha_fxn(p) if i < cutoff else 0.33 for i, p in enumerate(closest_points) ]" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### Note: The rendering will take several (5-10) minutes!\n", "Adjust the `num_cirlces`, `fps`, and `anim_length` parameters above to reduce render time. Particularly when just getting started, making all of these numbers smaller will significantly speed up the animation process." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Max t-value reached\n", "Max t-value reached\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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9fVFg46r2TAesCDzSxJcxZGiOSUSGgt2AOYGbGzz+KmKt01W1bxSZjSWqQjyV\nUs93IxbM1vZ+PgamSX9/AXi+pj0vAv9rsD1DinpMIjIUfAL8pafeUpWrgK8Xma2Ygg8ARWbDibmh\n/xIZdfcCOwMbEFXKa+9ZCUxjgHfSNUYR9fS2b6I9Q4p6TCIyFCxIbNzXqOeAR4EzgFmLzG4j1iKN\nAZYmKpA/T6xF2j8vfUKR2YJFZsOrFu0uDnyeGBacBXg7vf4D4Ma89Mr8lNRQYBKRoWA14M5GD85L\nnwCsCVBkNg+wBbEm6TbgYOCJOr2dT4BpgUpgOgf4SpHZb4HRwLgisy8BhwBLtv6lDH4KTCIyFExP\nBIem5aW/BJxWZPZ/wKt56U92cWhl6O6D9O/jiNp52xD7My0JHATsnpf+fN0rCKA5JhEZGo4hsuBa\nknpNI+l+OLB6Tqmyt9M5wHlEavmJwA5pTybphgKTiAwFNwFfLDKbpdkTqxIe/pOG+LryMTGUV+1k\noirEjcTC3ruavf9QpMAkIoNe2h9pNFGzrllLAq+n9U3dmazHlO7rqajrK/RcSUISBSYRGSouoptq\nDvUUmc1EVGx4qIHDq9ct1XqDqAwhDVBgEpGh4imiAkMzlgcezUv/qIFjK1l59cwOfLnJew9ZCkwi\nMlS8SYOb/wEUmc1LBJpG1z9NMZRXfTlglSIzBacGKDCJyFCxOo0NyVUSHpYlEh4arc7Q5VBeXvpN\nRBHZ04rMvtrg9YYsBSYRGfSKzMYQgeEHDZ6yFPBaXnqzCQsHFJnNVu+NvPR7gV8DfyoyOywVcpU6\nFJhEZCj4HnBVWizbrZTwMD+N965mLDI7htgkcD2ibFFdeeknEPs4LQv8p8gsb+QeQ40Ck4gMaqkM\n0E+BPzV4ygrAI3npH/d0YBryOw3YjqgwflM3lSGAqCSRl/5V4P8BJxaZfaPBdg0ZCkwiMigVmVmR\n2Z5E4sG2jRRNLTKbDxgBPNPAsRlwEvEcXRyYGXig0fblpZ8JfAH4mXpOk1NgEpFBJ83fnA7sDqyT\nl351A+eMAJYB7usp4SEFpROILdhzYAYiFf2xZtqZl/4YkUa+T5HZr5s5dzBTYBKRQWMYUGS2DTE/\ntDKwbl76sw2e3lDCQ5HZNMApRGHW3dIap7HAOrTwTM1Lf45IzNi+yOzbzZ4/GCkwiciAV2Q2TZHZ\noQdEXYcdiZ7SKnnp7zV4/szAfDSW8PBdIsnhm1Vbq48FxhEJEE1LW7KvAuxdZLZZK9cYTLTthYgM\nWGlIbWM4KnhRAAAgAElEQVTg+8BCVzgcaHythZ1hVwAe7inhId1vXWC7vPQP02szER/yZyFKD7Uk\nL/35IrMdgQuKzD7KS/9Hq9ca6NRjEpEBqchsYeBZogdzBLDU40Th1CavMz+QpWv1ZD9gLeCwIrOz\nisx+BswDvAqMIm2f3qq89IeIPZsuKzLbvDfXGsjMteW8iAwwRWZbAT8jEhzOqAQjM3N3b7hQa0p4\n2Bi4PS/97QaOz4CFiErlSwNfBa4EbibWSS3c7NfSxX1WILbMuB44smq79iFBQ3kiMmCkxIMbiGfX\nTnnpj/TykpsC7zYSlGDi5n+VdUp3F5k9BBwFPAE0dI0G73NfmmsqgOeLzFbPS3+hXdfvdBrKE5EB\nocjsc8BVxNYVX2lDUILYcr0313kfuAQ4BJg9lT5qi7z0ccDXgT8Dd6RhwyFBgUlEOl6R2XLAvUTW\n27p56a+14ZojgI+IquOtGgtcBnyQ2veTIrMZetu2irz0Mi/9YGLeaa8is6b2kxqoFJhEpKMVmR0J\nXEssZn2lh+3NmzEGGNdCBl+lXSOJbdPfAJ4DziZ6Xz9KQa+dHPhHq20daDTH1MGancgVGUyKzKYF\njgR2JbaUeARYFfhtm24xC73LohtLCpRFZqOBd4EriBp4txeZXUXMRz0JvJSX/kov7vUdYr+nIUE9\nJhHpOEVmCxBJDosT5X6+RzyvzmvjbcbQu4SFscB/099HE72vCUQwPYFIIV+JKCD7cJHZPq3cpMhs\nI6IO39d60dYBRT0mEekoRWaHE72kk4DtgQOAx4GZgGvaeKsxNLi1Ra3UmxsNVOa6RhOVH0gZfn+t\nOX4u4DdFZs/mpV/ZxH1mI/ZwylMyxJCgHpOIdIQis+mKzE4kekcHEsN2N+elnwZ8Bbi0XfNLqcjr\ncGB8kdmoIrMvF5lt3cQl5ibq6pXp3zOTAlM9aRjvKOCsIrMZG2yjEVt1nJ+XfnsTbRvw1GMapMzM\niInZ0cAEYsjiI9eKaulARWbrAccATwOLERUWRgGHpkO2BfZu4y3HAB8SWX6LAi8AsxWZfYvo7Zzf\nQxAcCzyf2j4stfV/PdxzceCveenv99S4IrOFgE2A1RhCQ3gVCkyDgJnNSnyi3BBYkSiRUnfbZjP7\ngMgguhu4DrjcfWIhSpGprshsRSJp4BTgYCIA7Q8smJf+aZHZusAcwF1tvO3qxBDZjcAX89I/TIt3\ntyWGEL9bZPZ1IpX8QuCUvPQbU3tHEBmCd6ZrjQYmVPWeurJJutYUUobfKkS5ozWBDYj1WjektjxK\nVKdoqCjtQKfANEClHlFlyGN+Yh3F88AdRMC5wn3yH2IzmwPYhvihX4sYv5/GzP4POMzdL5t6X4EI\npHpwpwLb56VfVWS2NjGntE5eemV90VeBh9oxjJfmbA4k9lC6FfhWJaDkpX8C/LXI7CKip/YQ8BRR\ngmgt4HPpMnMCb1SVCVoImKaH+85MJEJ8L/17GLHFeiUQrUBkHd5CBOefE3s7PUAMaf6ISJn/Vq++\nAQOEAtMAY2ZzAccTPaRhxCfNddz9+Z7OdffXiNpip1ddbyUivfUiM3uPGNP+ibt/0P7Wi0xSZPZ5\nogexWwpKSxJVDnbOS/9POsaIfZW+18t7jSV6Q/sS6dv7AwsATxWZ7ZmXfm3l2Lz0T4HDi8zeAL4I\nnAj8vyIzS+uI5mFSNh7EkPnfemjCD4DXgf3T17kY8B4RiM4C9qwM8RWZ/YRIZT80L/2zIrN/ET28\nlrL6BiIFpgHEzH4J/JhIQz0EOKm3c0bufi+wvpmNJCo058CeZraHu/+pl00WqStlqV1ABKGL0sP6\nUuCgvPSbqw5dhnhO3dfifb4NLElsAngV0UMZR+ynlAP3AzsWmV1Xu3g1L/0UYnixssh31iKzd4ie\n071Vh85HzFFV33dWYHmiJ7QCsAUxz/s20Qs6KC/9pTrtNaJ3tHVVj2xX4MJG5qYGCwWmAcDMFgL+\nTnxS+4G7n9Lue6R5pgPN7EfEGozCzL4DbOru77b7fjJ0FZnNTgSJM1JQmoMYpvpXXvr5NYdvQ2Tj\nNbuVxWjgcGArYljskLTTLEVm8xBD318ggsrZxAe+o7u55GiiCvnrRLDcpsjsXWIOal3g3SKz04EF\ngZFEj+d+4MF0zozAennp90556cksBTxVNZ81E/E92KLxr37gU7p4hzOznxOVi8cBc/VFUKrmYT9g\nWeKX9jUz27kv7ylDR1r/czHwGXBS6jldBvyG6BlUHzuMeChf0uQ9NiS2ixgHLJ2X/qdKUErGALMC\nL+elvwGcA+yb5oFqr5UVmR0IzE4MoR9PDC1OT9TZe49INHoeeJHI8suJ358LgZ2JAPgesEYDzd+W\nSUkVEEVcb8pLf7Wxr35wUI+p8x1KH/WSuuPuD5vZvMT4+p/MbD53P3JqtkEGl5TNdiaRUPBtIuX6\nEuCsNGxWCVx75aX/iggA7+WlP9rg9Rf8bhTwOgzYOy+9qyy+WYB1SFXF89LPKTL7ItGz2rfqeisT\n5Y9GEIHuy8DmwA1VW6pTZLYxcFJeeiV9fE1iu4rpiUSORYgEhz2KzH6Xkiy6sjkp+zB9v3YhNkIc\nUhSYOpSZVSZT13X3W/ujDWn+al8zexg43cxGu/uB/dEWGdjSBnunETvF7kH0Ii4EjshL/33VoYcD\ne6dFqOsDDQWl5KBZ47+bVLY9r9MOI4bllmDy9PNDgfuLzM4GniHmW7cg5nLHErX6ZicCZXVQmomY\nS9o3VRVfn3iuHgKcl+ronQT8g0iY2A84tpuv4VgiGEEEwmcaDcyDiQJTBzKzi4gfcPorKFVz9zPM\nbBxwnpmNU89JmpF6Qf8ihrxWAz5PpIifWx2Uisy2IHoMqwG3E3MzP27wHrMAW57u8NaE+kEpGUU8\n95YCtqu8mJf+dpHZCcROtO8C5wPLEb2eu4gU8+raeBUTiF7f7cRw3V3AZXnpb1UdszUxfHk3PRdi\nvRE4Jw0rHkFkDw45Ckwdxsx+Rfwgrw3c1s/NmcjdLzSz0UTP6QV3P7u/2ySdL2WnnQu8BOxJDKEd\nB+xXmeCv8nsiRfr/isxuIbLpGl1Uuw9w2dtxj+6MIXprE6qDR+qh7UMEFyO2sliBmFP6A3A58CUi\ncEyUMuW+390N89KfKDI7lUgqqk3uqD32nSKz54mvYzrgnz18PYOSkh86iJktR4xx7+LeebWx3P0M\nYsz9DLMpJ4pFqhWZLUE8WO8iJvEPJurF7VwblNJQX6WnApGS/Xoji2rTffYmAl5PxhBJPUdUnT8b\nEXiuA+Yl5rY2IHo5e+elH0Fk1Y3Py5bX971CrHX6bZHZTUVmO3Rz7EPEuq2d2rj31ICiwNQhUiWH\na4Fb3P3c/m5PN/YjUmTbWeVZBpEiM0s15+4jyvv8ksi624Gokv1gndPGAu9UPfhHEdmojZib6OVM\nsS6ojs8BWwJXp7bOl/5+A/C9vPRP89L/S/SOVstLv6OqfbXDeA1J81prEcNySxMp5N0tGJ4LeDov\n/e5W7jcYKDB1jlOISdnN+rsh3UkJERsDq5nZN/u5OdJhUvHRy4CdgE2JDzB/I2rLLZKXfn8Xpy5C\nZOtVLEmD5XdS7+sRIvOtu7YNI/Z2egkYlxb1XgX8IS/9mOq1UnnpE/LSn6w6veXARMypvZ+X/lyq\nKnEMMGO9bdJT1YcViSSRIUuBqQOY2dJESmg+EEoBufvDxJDe6WY2Q3+3R/pfkdn0RWZnEUkA1wIb\nEUNmjxCLw3fooXLBIkSpIADy0r2q8kEjLibWAHVnJmA8URB2Z6LSxOF56Wd0d1KR2RigzEvvqXp4\nV9YFbqr8Iy/9ZWId13xV97Aisz2IrMTHgIb3bBqMFJg6wynAIx0+hFdrP+KX/Ih6b5rZAma2n5ld\nYWbPmdl4M/vUzEoz+8zMPjGzd8zsHjM7xcw2M7MRU/dLkN4qMhtWZPZVoiDqcKLSwvlEPcafAsfk\npR/dwFzJ7sSi11ZdC+w2svtjZgHeImrTnQz8Li+9kcW7vRnGG01kAN5Z89bMxHbplazFU4AfAiVw\nEbF4d8hSYOpnqUbdmsBvzOwgM/ubmT1oZo+l9x8ys7+b2eFmtkz/tnaSNKRXALtVXjOzac3saDN7\ng1gL8lNi/P9qYEeiEOXSRBruBkRQe5lYr3EJMN7MbjWzbodkpDOkCfxbiCG376Y/GxD/T8cBK+Sl\nH1dzzi+LzM4uMnsqFVateIaojN+StNbnvA27P2wMUal7I2Lu6/Aisy80cPneDOOtCdxdvfYp+RQ4\nt8hsTmKocwwwLfG7MpxYNzVkKTD1IzP7ClH8MSNSZQ8mJmefAP6dDnuUGBffG3gg9TaeNrNvp4SJ\n/vRTYKbUluuB94mH0znAKHefxd1Xdvfvu/sl7n6Puz/m7g+7+y3ufqK7b+nuC7r7tMQDYwTwLzN7\n2cz2678vTbpSZDZzkdlRRIWF64BvEj+fjxK9g23y0n9YO3RXZLY6sbj2BeIhPH3V2yOJ3kxvHLCU\nTazYUE+e7r91XvqBxLKMPxaZbdXVBdMC2iwv/Z1mG5PmkNalJuW7yGx6IvtvFLFu6jqiRzWC6DmN\npYv91IYKBaapzMxGmNmv04LVC4mEh0uA4e4+2t1XcvevuvsuAO7+dXdf3d1nJQLYesD/ET/AH5jZ\nn/srdTsVfn2RCKrzAF9LwWi/VubK3P1Gd1+VCM5XAceY2RNmtkAbmy0tSvMgWxJzRk7UfvsvsXh2\neWDjvPSd8tKn2AKiyGwBYohvp7z0Q4n06eo9jGYk1hC1LC/93XsifeGqOvffhdjXadO89MfT8f8E\nvgH8qsisq3mm3vSWliKGu5+reX1JIrP1PGJI/CwiY+9Togc6hpgHG7IUmKYiM9uUKHu/G3AGkbU0\njFi31NPul5UCq7e4+1bEJ8wjiF0xXzezvO9aPqU0h/Q48YvrwErt2mjQ3d9y9+8Qwe4D4EkzO6wd\n15bWFJmtQtSL+z7RK/6E6AlsAnw9L33ZvPRHujh3ZiJT75iqfY8+YfI5pVFEj7tX0hDCxTX3r2z0\nt3de+ovV7+WlP0yksW9QZDZvnUv2JjDtDvynOtuvyGw48Xs7M1E66Woi4eEB4OpUR+8CYq5pyFJg\nmgpSL+kqYvz4amBMqjm3BfByi72L0t2PcffPERO5vzezu6ZG78nMtiQyqD4kfnE/IdaG9OaaS5jZ\nn8zs6tSjnNXd33D3FYhPlT8xs7vNbEin0U5tqZe0PdHbeY3odXwz/TkpL/1reekPdXc+sZ7psbz0\nU6vemotIo66YkTYEpsUiMt1Sdf9RRDC9mqqsv2p56f8mtlk/rjqFO9W+a2mIMW3TnlE1jFdktjCx\nsedqwD/y0h9Lc1zrEL3Hy9OhTxNZikOWAlMfS9uZv0rshLmOu29X1TtanVjl3SvufgCxR8zcwCsp\n/bxPpC0wLgFOSUFjOSL19fdm9j8z+8DMxpnZo2Z2nln3k8tmlpnZ34nhyS8Qv6BbA6+a2elmNoO7\nn0w8xJYmtuHY08ym7auvUUKqiHAWMS+zOfAr4kE7Alg2L/3MBi6zFVHRYbea1+8gEh4qwWuhNrR3\nwZQdVLluRixkvZNIyHi7m9NPJbZM36bqtbHAf5vdCypZHLgzL31cassSRCr9eOAvwIOpfccR39el\nmBTEngKWqLfOaahQYOpDaduIp4i6W59z91tqDlmYNtXCcvdHiHURdwD3mXU5AdyylKxxJrGS/yEz\ne5XIKPqUCE57EKVn9iY+tS4N3G5mL6RzK9cxM5srlWD6O1GTbCl3X4r4RH4D0Qv7LvCemX1KTKxP\nQwz/nMqk+bUh+8vbl4rM9iTmjp4kqiBsR6zFOSovfc+89B7ng1LiwNHEtuG1WWkfM2mCfw5ifulF\nWpTude45EUIqFRO2JYqsXkzM23SZwJAWvv4YODuleEPvhvGWBh5ObfsSsdB4/7z0bYkemAE/S/co\nia00Kini44nf5d1bvPeAp8DUR8xsVqIX8CywpLt/WvN+RiQ+XNque6Y5qA2IuYDbzGyJdl07papf\nQKxP2ZjYwuAiYm3IT4Bp3P1cd7/a3c929++4+zLEQ+dm4Hwz+4eZ/ZH4BP0S8QBZl3hA/czMniLS\njHckMhT3J+avxhO/yEZMGjsxTLIzkWLeUIUA6VmR2bRFZscRNe32JT6E7Ef0mDZpcN1PxU+IB27t\nGh6IdTqVwLQ8cG9e9jzP2kWbhxNztjffRizOTZl5qxI/rxkxJNftAtm0f9O/gbWKzEYS815vtNCe\naYmdbB9LAf5UYoHxX9IhHxAZiWOJn/MtiSG+Sjs+I4b7flhktn6z9x8MFJj6zr+JT0YrpDU/tdYA\nSnd/qs57veLumxM7ad5pZqN6O+xVVcfvTqJHNBewhLvv5e7vEUN7M3bRlrfcfSdin5n1iWDyC6L3\ncyqRsXQQ8el24XTatOnvI4mf0buILK5hRGmbSi/JiTUfvzOzPXrzNcrEJIG/EUNaCxAfKM4mknQ2\nqaob18i1ViSG8X7WxSGzMWn4bnliG/JW/T/i5+DQdO+5id1wT049uzHAuAaH5M4meu1zA6+0WER1\nCSIl/rjUjg1qgvOcxO//4sTC5JWJUYKJ8tKfSucWRWabt9CGAU2BqQ+Y2S+JdQqrdpNtNycxBNZX\n1iWCxf+Aj8zs17241slE725B4hPkou7+TNX7r0IssK13spl9mwg+BxN77FSyEGcD3kxzSNXfCyPm\nrg4ihggXpP7EuBGfhj8l1lRJi4rMdiV6+H8lHoifEpPxawGb56W/3sS1jEg2OKWb9T+vE3OsEA/p\nlgJTkdn+xPqkPC/9s7SPz97AhXnpz6bDZqGbYbwalxPr6RamahivyGy2IrMHisxuLTJ7vMi6zYL9\nAjEMPRewYV76CzXvX0JknI4HNgT+VW9jwxTMzgJOLDJbvMH2DwoKTG1mZguRhqHcvbthgJmIh25f\nWZPJC0Hu00rJHzPbkUl73MxNTNJ+Ymaeygu9Tnyyhlh/VHv+GGLN1cHufgywLLCImR1OpMhWekm1\ncxDLE9+j4cQn60W7aeZ0xO6i0qQ0dHcmsVh221Q3bj5iOPgVYNEeatzVsy5R7+3kbo75MbBYkdn3\niYdzK5lvywI/AtbMSx9XZJatE289kZd+c9WhY+g+8WGitEfT60RgeS3dZy1iqO1qYsPAK4j1hPXa\ntACRDn4LsH0X37s7iSH+4cRQY72hzkp7DieGUs8eSsFJgan9/gY8mHoB3RlGDEX1lXpp49PUeW0K\nKTnhQDP7L1HF4SNiWO0Yoqc3nOiNfYGYa6rsyvlMKqm0WNXlfgm87u7HQwztAT8gtp7+EzC9me1F\nTIZfRXyafLOm/T0lOBgxbi9NSENe1xKBYbW89L8Vma1HDEO/QfRCetpxtfaaRmy4d3x3w2Bpe4t7\niKG+VfLSb+jq2C7uM5qY89y/ahuN764Q/63dxLLbxIc6TiN67IsWmV1O/A7sn5d+SBrOPBJYt8hs\n/jrnvgr8KC/90G7mzFYkkj0OIeZUv5YyIOvKS7+KGP6+schstSa+jgFLgamNUoLAojS2puc9+nYH\n4cuZfH+ahxtZL5Uy5f5L/CLcRmQ13Z7OP9jdX0trqD5w93vd/Wcp4QIii2hB4NG0FsmIxYun1dzm\nDGKo6Bli+OgEosezIPGp9FmmVC84fcikmmJn9fS1ySRFZgcS/3//RswnDS8y+yOxnme7vPRtWpxf\n+SKRNHBtTwcSyS0rp0WuDSsyG0HUabw+L6PwcVo3tN55TEweqBw7HTC8yV7fQ8Tc561E8Fy7eo4o\npYC/SfSeJpOX/lFe9ri789ZEr+tLRCLRP4En0geFuvLSryQ+MPQ6rX4g0Nbq7XUC8Ji7N5L2+jZ9\n+P13dzez+YgJ6EOJh0W3zOxYosLxLcS+UH8igsSadLM3TtWi3j+7+1lprdPviYSGmZlyZ9FTmFQn\nbSWi52hEim1R78thysDk6Rqe/miOqQEp2+xwYh7pIODPRMbdqcT/6y92lwqe1t5cCdyRl/6LmveM\nyOY7qZEMu7z011r8Mn4KrE3M01RsCTxVZ6fApnpLKejNRgxfl3k52VxqtX3pOrGju+tPT/RQjyeS\nKx4GHi4y24SeRwYuJ0YpBtIuBC1Rj6lN0sT/esDPGzzlFmCEmc3VV21K6eOXEav0FzOrO/QAgJmd\nDRxAJCasSwzfbUH8EgwnJsW7snU6fnozW4kYYvkc0Ss0oidUuc9cTLlvTiNDdfVem0AM4b1FDBlK\nN4rMliY+nc9BZI79i6jXdhjRS1q7h6C0KFFaaEUm39SvYkNiznCKWnVtNgMxVPhxatdIYmPCP9Q5\nttlhvDmBN/PSn+wmKEH8/s5dZNZshYYvEaMEKxPD1hXP0vO2H3cSaeSDngJT+xwAjHf38xs5OBVA\nfR/4Sk/H9lba2O8lYmx8Cmb2O2IB5XruE9da7ET0RD4G3qhNeU/zULua2S3Aienld4mhj/8RazSW\nT6/fmxbULkM80NqVqDCMSO09iyjGKXUUmWVFZucQKcm/Jqow7EAsWr6XSB64rYdrDCPW3BnR27+n\n5n0jhua+3+y8VAu2IyojnFlk9m2iksL4vPSn6xw7Cw0mPiQNLapNPcIHiVGSZmxD/J78KyVaVLxN\ntLU7TwDzFpkt1+Q9BxwFpvbZkObLCz1HrO2ZGm4hhgEmY2abEXNDW9RUptiYqNk1HzUZU2ke6k3g\nd0RPKSMSKypZgNMAv3f3j9O5HxOf1K8gkiiaWUjpdL1p2gR3v46Y7J5dVSCmVLU2aVFiDdrlxLDd\nN4lU5uMqPY8e5MSc4E5ED/i5mvc3ItafXUHfO5MIqssRVUPWADYsMluhzrEN95jSMOUcRDZiI44C\nFi4y26jB689DlNb6kKh4Um1J4neuS2nO7wMieA5qCkztsxSRJNCMu5nUq+hr1xNrqyZKw4/nAee6\ne+1k9YrAf2ovYmZjiSGFO4EZ3P1LxFBfbbpvJUicTQSiRYlJdqPxuTUnhjg+Ij5R1gaovQDc/YF0\n7OoIMLH46u5EGaErie/NKGL4DmDdnnpJVddaiEhZ3peoyfhcKuFTeX84Ue/tmBYTJrr7Go4uMpus\nh52X/pMUUFckehG/IuZAb1hr8vNnALxOOaSuzEEsxG1ok7689PuIBeONrjPaivg5vrD6+5c8T53f\ntzr+R/3koEFFgal9ZifG35txFTDvVKqYfQkwXVpXVHEO0ZvZpc7x8xIbmL3A5GPfpwAvuftm7l6a\n2XeIJIQjiABUGfI7N63p+gYx39TTz9pnTJ4+XwJHu/vC7j7G3Wd195HExPQ2wNzuXp3t9zq9rHA+\nWKS1NM8B3yZ6Rb8l5ibOB65Kte6mWNDZxbUy4DfEnM4zRILKlTWHHUn0hP/RjvZXOYXo2d1ZZPZE\nkdnONW2bnUi5vjhlrf3hi5P3mRtev5Q0XRsvL/0/RNbp3UVmXc4RVSWGPED9kZXpiZ/hnoxkyjV/\ng44CUxuY2SLE97KhT6BVLiUeyJPt1JrmY65Jf2/LduqpdNBHRHkZ0mLbrYD96swfjSJ+UdYmxvPn\nTFXDx6dzZk917+4ghvMg5i42IYZV/kkMD95BrH7vzgRiHdR44hf3MyIbcBV3P7TO1/GWu1/m7rXD\nLY8yRCaGu1JkNrzIbF/i+38BsE5e+hOpiOhfiZ1bG03OqdiT+Ln5U/r3SkwqkkqR2WbEPN9qrda6\nq7rWmikrrhJ0vg2sQgxz/Z7YCv2YlAIOkVn466okhZ/OxMSdcqG5YbxhxM9q00Vb89JPJuY5L0p1\n8uqZiejtXNdFaaTRxJqmnoyk66HtQUOBqT3mJOreNbVgNh1/MVWBKc2TPEUKIESl8HbtsfQx0eOA\nWHn/sfukNRdmNoOZncik9U9fIuYVPiPmJb6eXv8tMSS3atW1hwHfd/c7iU/Oi1bdqysTiE+0E4j5\nqQOBb7n7bu5+X5Nf26vEL/eQlB7GLxNznevnpR+Yl/5RkdnPiCD1jbz0G5u85mbE8oH9qoboViUS\nJir7C/2OKFDadLHTmnttSSRn3J0m99cFnsxLfykv/ZO89OOJILUw8EqR2Q+Jn8c1isx+ClEh/Nr4\nDfxxumwziQ+zA+83MexX6wdEpYg/pCBXa2uiGsZMXZzfY2BKva4ZiTmqQU2BqT1mJB6urfghMFfV\nvkVzM2mND8QDe8NetK1aWXXt3Ynq4ACY2U+JT5c7EcN+n7n7Qmm33GuJidlKGvDJ7r4+U1Zr3tTM\nNmRSdlFPP1+VoqyfEZ+IZ6sOlE0az6Rq1UNGkdmsRWZHEWn9pwNb5KU/m+Znfkj0eHftosJ3d9cd\nRqSRX17Z9TVVOlgceLPIbCUiM+8PqSp3b61GLK5+Ov33DGKB60R56W8TQ8PfIRJ5piXmvFaqHJMm\neTcsMvsG8bBvNFW8N1tcVBITdiNGDCZbi5dSyhcm5mXnqz03fa+XauA2RqTKD/qf8yEbmFKtt7b8\nIbKeRrR47qvED9xd6d911ghyUZvaOQtwdPr7fMA3q947gtgAbjZiXH941XubEw+ASvB9Nb1e6clN\nIMbOLyWC2J7EkENPViW2yxjl7vul4cZWVdY1DRkpC+0JItPrC3nph6UtH2YjJtK3BdbLS+8yU67I\nbLu0DqjWrsQHj4m9+bz054ELiSD4JyIZotmhwa4sDvw57Ve0PHBQXvp3ag/KS5+Ql34h0YMfQwwf\nz5k24qsUnzyMCF6fNJK6nnoic9OLwJTaNp5ImZ84UpCCzteI343nqElASudNIOapuh2KTsddzRDY\n3XbIBiZ3t3b9IR4M3ovzv0Q8VL+Y/r0BqYAkseC1Xe38kEj7XZxINFiFGK9+EJiz6rgliVTs6nP/\nQgyL/JCYEzqS6IHN7e6Zuy/v7tsThTtHUj/zrnqo8353/7f7FNlJrRrJpPJEg1qR2bAis72IZIY9\n89K3zEt/I80x7UHMAT1GzCm92s11FgP+CIyrmpehyOxzRHWFfetk2d1GDHutnZd+VoNbSfT09WTE\n0Phf9bwAACAASURBVPW9AHnpb+al/66b41clEnd2zkt/hJg/q07gOYkYMlu2wSbMCnzcQrHaeq4B\nFqoqL7QWsdD8fmIjxCkCU3IxUW2lJ4/SWO9qQBuyganNHgGwFrc0d/e/E+ncV5iZufuN7j5neq/V\noa3JpGSH6Yn5ny8Ti3tvA65z9+XcJysP8yIwzGyyLKNdiYB0NLFO6VBi/untdP35zewiIoW73sPq\nQ+IT4QfEfFy9NSe9MZYWKlQPNEVmSxFrhTYn9vm5IL2+K/B4ev3LeenbN1DyZwvig8QfiQ9XFUcB\n59SrYZeXflpe+qrdbGfRigWAt/LSG+2xbAmcmpdeSX2/ANinklaekjBOBb6dUsZ70qthvGopDfw6\nYLMis1FEj+6iFMBfoM5QXnI3sEgKut15BAUmaURKYniHKUvtNGNrYsy8r4qRbgp86u7PE8kaMwJ/\nd/etaw/0KPb6QWpT5bWS+IRevXXGosCHZvYREaSWS8fUW+h6EfFA/Yi+SXddguazIgeUInZlvZ74\nULF5XvqLRWaLFJldSHxQuICYY3q0gWsZUa3kCiLpYIf0+gbEB4hj+uarqGspYjPIHhWZVYLIsZXX\n8tJfSeevlI4xovf8GT3UlUvHbk57P9TcQdQh3Ar4d1Wv9VVgyXqZe6lnehdwapHZ5qld9bwL7Nxg\nwB2wFJja50kivbolqUrCjsCOZrZG21o1yWZMWtG+PTF02N3OmM8RQ4rdmUAMB24KzOPui9J1KuvO\nxJDhj7t4v2Upk3E2ml9HNmAUme1CLFb+Vl76dsS8ynHEAto7gGXz0g9uYmhtLuKD0G1EzsDKaSHt\nZcRC2amZ+bUMjVdNWQu4vU5q+uXEkDjpezAN0cufu8jse91cb1bgnl4UlK3nJmIx8xLE/HPF+0TG\n7V9TNfTJ5KXvRzwDdie2uKiX1foPokd2feqRDUoKTO1zK9FjaJm7X0GMUd9gZl2NRbdqLeBBM9uB\nGOd+v4f09v8Q1R+qXVfz74+ITKOjgYPMbFu6Htcf7+4bEZlS7d65d1Vi+LA323N3pCKzaYrMTiDW\n9Gyel359ERvXPUwElxXy0k/IS292bctywK156Z4+0d9B/P89Li/9nHZ+DQ1YlZg76VYq6TOa+IBT\n6wZSYEquJpIjtgX2KzL7UReXnY8pyyv11ltEYLyh+v9L2o5jNWJu9qxUMWMyeemPEZmH0xI92lrT\nEHNqo4Dju+lZDWgKTO1zLDBrG3o7WxKfqpqtu9clM6tUkz6SWAh7KTCqh9pylwMLVapSpPp4lxPD\nRVsCS7r7DMRwxavEfMX5RNXkeioPntWJOax22gV4rdl1ZJ0uree5ingYbwo8V2R2ADG5v3Ve+s69\nWD9UW3LqNeC22q0sppJ1iSGqnlR6S/WyLx8DsjnSP9L35SNiWPlQ4NA0DzdRypibh/b/PK5BDO2/\nWftGmoPaiUj7viMlftQe8zHx+7RNkdmaVe2dndjB4HHi52EXonc16CgwtYnHNuoPMOXeQ81ex4mH\nxpsAbeo5HU88eMakP7vQc225S4iezX5mtiYxOft3d/+Gu1/p7o+l9v4tzVNdz+RbuVdMIPb8WTYl\nYCxHVeWANtmBKOw5aBSZrUL0YJ4kMinnJ+bpVgE2yUv/ZzfnWpHZOj3cYuJCWYAU5L7Z23a36E16\n6DEVmc1HLE/4v3rvp+G7G2qyAh4hMkwvJL5vBxWZnVPVy5gLeLedw5Zp7mczIngs2kVbPyaG05eh\ni2UVqfL4T4ErU3X4hYne1r/z0p9KiSI/A3YfjL0mBab2OhhYPZX0aVlKNKgUhXwsBYaWpF7RV4lP\n2b8Abk7JDa8TvxxdtcGJX+iDiTHzy9z9y93cql6duv8BC7j7rkRW3v9v78zj5Zrv//98O0FEFkXU\nHv0p1bSKItaIpYi1amk0qiKnllJfS/Wri6W2tipftZVUHW3xra9d04XaGpoitFIllhBrUFsQREhO\nPr8/Xp/JnUxm7p1778zcc5P38/GYx03mzpxzZu7M5/V57ycj10nD5vWY2QFo99kTO/2mEHvCXQF8\nLc3D0ShR5X9RZ4CD6rCStgDuyhL7bI3jL4O6gVermesJ+qFkm/YYjlyP7dWqTdyybIlO8/A6sprW\nSvMwDWWjjkButOXQZ/HFblx3NfZCgt8XuV9r8TmU5bppO4+ZhFy2G6MC3b/G11Ti5yh1f3R3LriI\nuDA1kKAO3TNRjUV3j1UK7t4N3GNmV3VxrMPPkDtjHPqAlwoir6WdD3QU18+gotxrQghfrfXYSGWW\n0DvACqFtmu8twFEoU+r3nXkBHXAqcFdMHunVZIktHRMaDgO+nObhrzEOcR6ylsZ21I8uZnxdiDYe\ntZJbdkYW7iMNu/jusTztCFPsOLE8sSyjHSavqMeXNxl/HGXCWZqH55EV8zF6/ZvTQHGOVt2GKL61\nJ0pQ2avs95YltnGW2OXI9X8SGpdei77IoloWuLuyziq6BR9APQSXyhL7fpbYNo16PT2JC1PjGQXs\nZVbfjJaOCCHshbpp7wO82ZkYlpmtjyrRj6MtKeHe+PNkYFCcx1T5vIPQwrYO+mJ/vvIxdfBURczn\nDygD6oZGxYLiezGU6kHiXkWW2IZoRs9gVIf0bIw/3IpcWD+pM+PuRmQlzKb6mHpQm6JrG1Ec212i\n8Pah/eLo4Sj+1W5njzQPr47XKzonS2yFeN/rSIjWjP+fg4T/FZS0s3PVg3WS6E47APhDmocP0zx8\nABwJ/CZL7LYssYdQVuwk9B3cJdaEVS2diNc/HL0v98fEicrHLI1clTcA2wJHABdnia3aiNfUk7gw\nNZgQwt0oPnNDjKk04pgTUDr0ZOBvZnavmdXTSfsOYEoIYTxR2EqiEN15E1EhIgBmto+ZPYZiQleg\nNi17AJ83s2PNbJ12rLbK/l2VO/sByHI7t47r7pB4Hb8Hbg1h0ULQ3kLMujsBpQG/CaRpHt4vs3w+\nRFNhO+zcnSX2CTQ472Lg9dhbrvIxKwHb0JqBfvUwGGWaVf2uZIkdgBbojqwlQI32UGbrWWWxlwVW\nEyyIR12CUrMvzBK7KEus36JH6xSlwtgF9VhpHh5C1u75qFxiPeATaR6uTPMwN1o5i3yfYvbhcCSe\nA9vZQOyL3OW3oDZid6Hv2KU1Ht9rqHdgm9M5RqGU0VtpUAPW6KraPTZJPRe4z8z+g7LsxpW5/gAw\ns/EouFsaRLgpKoIt5wDU9+4fqP9Wf7SbG1W22D9vZteiL9f5wHtmtm5M9iid63jkbihnTtnvB6Av\ny1w6V7PSHr9FC1p3ipqbRpbYQJRtNhhlfc1HCSdDkNtqLnIl7YMC/1uleZge3T07IXH5C7B/Pf3e\nIkejRWoYtZuX7gfcnubd6ktYk+gyq9sSS/PwapbY/UhQFyqyjdbUf6MuD52x7s5FLvALssRuQeng\nfZA4vYk+6yuh92oi6pb/bJbYkWkeOl0LF0Vtb+DSyutM83B2O089H9g9S+zLaR6mRpEaij4jf0OD\nC6uOW49xwlPQ5uVxFDP8Snytj2SJDY3tmnolLkxNIGiA3k7AA2Z2dQjh6w089p3AJjEF/FyUmXOW\nmb2EYgZ3odHXhwH7hbCgdUx/YJZpdtR+aNHcEO1UN0UL/bdCqOpaGFn27wFo0RwFC7IGq3UJKK+4\nL8Xe+qKswG4RXXgHAXsXIbYU3XAHI/FZH8XmBiBxmI2EyZCHYn20E34RLUCXpHm4KEtscJbY8SgD\nbz5y+ZxUryhFa+kIVOT9ExTnqHxMAvwIjWjoyusstbXqG38uV3brhz5jB2aJXQlM7ETvuUnIQqjs\n/nAIcn/9pjPXmebhoyyxc5BFMRqVSgxDPeveRYv9o+jv8ec0DwfH2N7PMo1JPzXNwyKp3u2wB/Dv\nUhf2WmSJTQDOS/MwMd51N8qMnZQldjeaxFuKJ83JEvsQSCrFPm56bkYejctRw9o/RguNLLGz0VTd\nkUVw13YFF6YmEUL4p5ntCtxuZsvUkTzQ2eO/BnzDzA5BO6U90A58d2RJ5MA1ZjYPLYrLxZ/TUGLC\ndBSPuAkFYUehHmnTqpyuMg28/HMzMZ6vnHdDCBmAmf1fvK5N0FjvbqW2mtkGSHxvCCEssvi2ilh1\nvyUa6b0NEp+rkft0GmqbsxIwKM3DM1Web2jnvn2W2NNIsCegReb+Liwop8Xnv4Y2HEdUecwRKI35\n5hqvaTD6W20Xj1UpPPORa7HyVsp+mw1MQe/HGVliDwJ31ZFFOAltpMaVXcsnUJeQfbqyuMaO6gvc\nlbFmqVQDNBR9P3ZGKeTPo/f9TFTz9FCW2K3IhdruuWOLpE1QjWB7j/ssigN9IUvsWpTt+jbaGB6J\nMuw+Ah4oxdKiwM5Fgv9ePM566O/3DCqUT+K1jyk73S9R3PU0tBHpddhiVpNYOMxsOFpIpwJfCiHU\n3ZNL/VxDXQu5mS2LvohfQrvuGWixG4i+hP+FPsRfrOL2MyQamwM7hRDuq/j9GBRzKl3LdSGEUWa2\nBm3WAMhVNQ+J3ASU8PAlYMcQwiQzm4WGCXapMW209qYAD4cQOqrTaSpZYvegerN/IetkeVQIOxy9\nHyvE29w0DyvH56yDLNURaJGcj6bNvo7cQF1KXY4xiSfRQjsAGJPmYXTFY9ZFsZdd0jy8EN1PG8XX\nsFn8ORC9v6+gGMxsJDyzgTkxC6zeaxoUX+twZKX8M83Dn2s89pPIzbx6mod3430/BZZJ83BCveeE\n9r8zWWKrIctpLnBrqhEh6wPHoBjRFchzMAxZ/BcB59QSp7i5OBZ4KM1DzT6N8XFXIivtBtRl4wgk\nLnfGcx6E+hxOqXjuS8iSmoSazY5HSS2nxOs/E3V6H1HxvMNR4tNGsW6qV+HC1ALignoH+mAdG0Ko\nKzhZrzCZ2T6ozuVDYM8QFh0KZ2Y/QSM01mjnODcg6+tKNEk2lP1uLZSdlyArawJyHZ7OwlbQ3ii+\nNgG5JXYIIfwjJoJ8BAwpSyGvGzPbBPV0exjYtqe7PMTkhBFoh30L2v2+jcRoGlrkf4cWnnkoljQT\nWZil27Pt7chjosLHHcWDssSuBh5J83BulthNwL1pHs4v+/3S6PM3He28N0V1MU+gYX8Po9qbZzvK\nfOss8X06B1gpzcPB7TzuemBymodxWWKfQWK/ZSddah1+Z7LEDgOmpxXTfGNK+vHI83AfSsM+DhU4\nn0rbhuI+4J40Dw/EIugdgHHtvW9ZYp+Kx1kxzcOsLLH9gQPSPIzKEvsCiiXeCbyS5uGkiudegVyO\nn0aCmaZ528YuS+xe4Ko0D7+qct6r0Ibg/MrfFR0XphYSxeG/0YJwXIwXtff4dr9kZrYpCn5uhdxI\nh9RasGNc5p4QQruZgma2N1pQP0IxrHOrWFjDkIVVmYkX0Bd3K5T4sV8pBhTT0m8MIXRq+ma05sah\nnemtMX2+cESXzkjkXhmG3Hx9UUeKycAbwG11uIYMueJK7WY+QG2g7kLteGZWPH435K7ZDr3/LyL3\nYh/aLKGt0eL2f0iA/glMbdVOOu7eN2jP+onv359Qq52LgTvTvL4NXDkdWEyG2gHNSvNQtZYu0+Tb\nz6Di2z1QAsKDSFj6IkF/BRWtn4wm+D7f3jVFS/n2NA/rx/8vjaymscga3Skeqw+wRqXIRet2O+Dl\nNA+Plt2/EZr8vHW1rM1MTXlvj79/vfL3RcZjTC0khPB9M8uQiNxuZjORP/iMeoP4caE+HpnpqyMX\n4dbVrKQK7kczljYNIfyz1oNCCBPiHKZLUdbPGWZ2L3I53RxCeDyE8GC8b2cWtpYM1dzsFkK4veLQ\ne6MvdN3EeNLtKLPtmyGE33Tm+c0kLi6boh3zDijO8DayNn8OrIISG47uxDFXQhlWpRqk0syqXVFM\nYmiW2BnI5fQeiln8Clkk30YLaf94/n8iS+gO5KLdKs1DZVZmq/iYGungJdI8vBxjUn9FKdCXN+E6\nViZ22M8SWz3NwyKfxzQP18bffxa972ulZXOissRWRHGqo4EnOhKlyADKegHGVPHLkAvxOhQz+hTa\ntF6I/pal8y2PRGl67F5RzjeQtVS1lCDWwv0ZxZKHV3tMUXFhajEhhGeALc1sEMqeOgb4QYy/PIt2\nZ/9GLfIxs2+hrKKtkDn/CRRovhn4Tgjh1UVOUv28wcyeQK639sZdlFLTx5pZChyKAtPHA2fGMqb5\naAdeuTOdAOxbaWFF9qXOjhhx4OI4JHyTgQ1DCPU0+WwqMYC+IxLt5dDf668oaeSBtKyTdEzn/XGW\n2JBUI8k7OvaayCX4v8CJFbvm8cD4uFieCpyF3IOGXKsjkRB9hALe58X4w1qo/dOve1CUQJ+XRWYQ\nVeEi9HnbozPxrE4wBFmUH6AEiKobpZh48WvUHXyhAYJpHmZmiT2OsjDrXewHIbEt5xokQpORdfi9\naP3ukSWWAz9Af9/tgGmVCTSZukyMpUY/vjJupEFFxK3EhamHiAvtUcBRZjYEpXDviBaZA2n72/wU\nidRUFAS9sdRAtQucCVxlZkvXM9I8ugWviLeStbYecm/cjLLOAvoCzUcuidlm9mfgpBC0wzOz3ZCg\nnlzrXDEGdTjKJhqCLIf9Q+h8XUmjibvkg5FrbRZq53RZe8kKaR4+zhJ7C7nZDu3g+OshUfplmocL\ny+7vj6ydLeJtM7TjfxrVuYwHnkrzMC8uptPRuPGQqfr/OuCCNA9XdOmFN47NkXVXk/ge/yL+txEj\nziuPn9DmYZiDrM/V0nzhjV20UH6HShxOr3IcQ4kIo5FlWw8bInFaQJqH97LE/gKsWube/RAlRZwI\nPIcy7Z6ssan4JPBSHTG4UueLXoULUwGIU2XPi7cFRH/5oOrP6tJ5rjWzX6Id90kdPb7K8wMwzcz2\npa0eyZA4vYEKeg9Fab5PmtlctCtdEXgB2N/M3kdunYGoTdIWyG+/Alow/gCM6EqCRKOJQfirUdLK\nH9EO9R/1pC9Hi+mTdNBtPktsH+T+OxqYmKnTQUmI1kUJJg8gl29arZtDZCfk7nkzugSvBX5XAFEC\nuTVPq/aLLLEt0YbsIPR6ty7V4zSY1YB3Si2AssSeQFbTAmHKEuuLshLvBk6v8XfeBLlR56GN5UV1\nnPs1KkouolA+hmKRJQbF60mR633VWpmM6LPV4QwrJJ5Vi3SLjAvTksepwP+Y2SVRELvCEBZuZ2XA\nteUWVrSAdgG+i3ru5ehL3AdZV/NQPdWjyK1xSwg96m5aQJbYKigjaw/kVt0rbRuPXS/fAp5Ja4w5\njzGqs5CbdCpy3ZyKXDsPIGF5pBNdH3YELo/pz38BfpXmoZ5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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xCircles = ComplexCircles(xFT, num_circles=num_circles, origin=x_origin)\n", "yCircles = ComplexCircles(yFT, num_circles=num_circles, origin=y_origin)\n", "\n", "#------------------------------------------------------------\n", "# set up figure and styling\n", "fig = plt.figure()\n", "plt.axis([-400,75,-150,350])\n", "\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", "ax.set_facecolor('#f9f9f9')\n", "\n", "# Suppress axes\n", "ax.set_yticklabels([])\n", "#ax.set_xticklabels([])\n", "plt.tight_layout(pad=0)\n", "plt.axis('off')\n", "\n", "circle_color = 'black'\n", "drawing_color = '#9c0200'\n", "\n", "\n", "#------------------------------------------------------------\n", "# Set up animation elements\n", "\n", "\n", "# INITIALIZE CIRLCE PLOTS\n", "alphas = np.linspace(1, 0.25, num_circles) #np.repeat(1, num_circles)\n", "X_circle_objs = []\n", "X_center_objs = []\n", "Y_circle_objs = []\n", "Y_center_objs = []\n", "\n", "X_radii, X_x_centers, X_y_centers, X_x_final, X_y_final = xCircles.get_circles()\n", "Y_radii, Y_x_centers, Y_y_centers, Y_x_final, Y_y_final = yCircles.get_circles(transpose=True)\n", "\n", "\n", "for c in range(0,num_circles):\n", " # X Outer Circles\n", " Xcirc = plt.Circle((X_x_centers[c], X_y_centers[c]), radius=X_radii[c],\n", " edgecolor=circle_color, facecolor='None', alpha=alphas[c])\n", " X_circle_objs.append(Xcirc)\n", " # X Center Point Circles\n", " Xcenter = plt.Circle((X_x_centers[c], X_y_centers[c]), radius=2,\n", " edgecolor=circle_color, facecolor=circle_color, alpha=alphas[c])\n", " X_center_objs.append(Xcenter)\n", " \n", " \n", " # Y Outer Circles\n", " Ycirc = plt.Circle((Y_x_centers[c], Y_y_centers[c]), radius=Y_radii[c],\n", " edgecolor=circle_color, facecolor='None', alpha=alphas[c])\n", " Y_circle_objs.append(Ycirc)\n", " # Y Center Point Circles\n", " Ycenter = plt.Circle((Y_x_centers[c], Y_y_centers[c]), radius=2,\n", " edgecolor=circle_color, facecolor=circle_color, alpha=alphas[c])\n", " Y_center_objs.append(Ycenter)\n", "\n", " \n", "# Connectors between end of circles and actual drawing\n", "X_connector_line, = ax.plot([], [], '-', lw=1, color='black')\n", "Y_connector_line, = ax.plot([], [], '-', lw=1, color='black') \n", "\n", "# Point on plot at current time t\n", "trace_point, = ax.plot([], [], 'o', markersize=8, color=drawing_color)\n", "\n", "# Trace of full drawing\n", "drawing_segments = []\n", "for idx in range(len(xFT.t_vals)):\n", " segment, = ax.plot([-1000, -1001], [-1000,-1001], '-', lw=1, color=drawing_color, alpha=alpha_vals[idx])\n", " drawing_segments.append(segment)\n", "# Add one more for line segment\n", "segment, = ax.plot([-1000,-1001], [-1000,-1001], '-', lw=1, color=drawing_color, alpha=alpha_vals[0])\n", "drawing_segments.append(segment)\n", "\n", "\n", "# Plot axes of cirlces\n", "x_main_offset = X_x_centers[0]\n", "y_main_offset = Y_y_centers[0]\n", "\n", "axis_length = 50\n", "axis_style = {\n", " \"linestyle\": \"solid\",\n", " \"linewidth\": 1,\n", " \"color\": \"black\"\n", "}\n", "x_x_axis = ax.plot(\n", " [x_main_offset-axis_length, x_main_offset+axis_length], \n", " [X_circles_spacing,X_circles_spacing],\n", " **axis_style\n", ")\n", "x_y_axis = ax.plot(\n", " [x_main_offset, x_main_offset], \n", " [X_circles_spacing-axis_length,X_circles_spacing+axis_length],\n", " **axis_style\n", ")\n", "y_x_axis = ax.plot(\n", " [-Y_circles_spacing-axis_length, -Y_circles_spacing+axis_length],\n", " [y_main_offset, y_main_offset], \n", " **axis_style\n", ")\n", "y_y_axis = ax.plot(\n", " [-Y_circles_spacing, -Y_circles_spacing],\n", " [y_main_offset-axis_length, y_main_offset+axis_length], \n", " **axis_style\n", ")\n", "\n", "\n", "def init():\n", " \"\"\"initialize animation\"\"\"\n", " for idx in range(len(xFT.t_vals)):\n", " drawing_segments[idx].set_data([],[])\n", " \n", " X_connector_line.set_data([], [])\n", " Y_connector_line.set_data([], [])\n", " trace_point.set_data([], [])\n", " #centers.set_data([], [])\n", " for c in range(num_circles):\n", " ax.add_patch(X_circle_objs[c])\n", " ax.add_patch(X_center_objs[c])\n", " ax.add_patch(Y_circle_objs[c])\n", " ax.add_patch(Y_center_objs[c])\n", " return([])\n", "\n", "def animate(i):\n", " \"\"\"perform animation step\"\"\"\n", " \n", " X_radii, X_x_centers, X_y_centers, X_x_final, X_y_final = xCircles.get_circles()\n", " Y_radii, Y_x_centers, Y_y_centers, Y_x_final, Y_y_final = yCircles.get_circles(transpose=True)\n", " #Y_x_centers = [x - circles_spacing for x in Y_x_centers]\n", " #Y_x_final = Y_x_final - circles_spacing\n", "\n", " \n", " for c in range(0,num_circles):\n", " # X Outer Circles\n", " X_circle_objs[c].center = (X_x_centers[c], X_y_centers[c])\n", " # X Center Point Circles\n", " X_center_objs[c].center = (X_x_centers[c], X_y_centers[c])\n", "\n", " # Y Outer Circles\n", " Y_circle_objs[c].center = (Y_x_centers[c], Y_y_centers[c])\n", " # Y Center Point Circles\n", " Y_center_objs[c].center = (Y_x_centers[c], Y_y_centers[c])\n", " \n", " \n", " #idx_current = max(int(np.round(xCircles.t_current)),len(xFT.fourier_approximation)-1)\n", " idx_current = xCircles.t_index_current\n", " x_true_current = deepcopy(xCircles.fourier_approx_val_current)\n", " y_true_current = deepcopy(yCircles.fourier_approx_val_current)\n", " X_connector_line.set_data(\n", " [x_true_current, x_true_current], \n", " [y_true_current, X_y_final]\n", " )\n", " Y_connector_line.set_data(\n", " [Y_x_final, x_true_current], [y_true_current, y_true_current]\n", " )\n", " trace_point.set_data([x_true_current], [y_true_current])\n", " \n", " # Iterate circles to next step\n", " xCircles.step(dt=dt)\n", " yCircles.step(dt=dt)\n", "\n", " drawing_segments[idx_current].set_data(\n", " [x_true_current, xCircles.fourier_approx_val_current], \n", " [y_true_current, yCircles.fourier_approx_val_current]\n", " )\n", "\n", " \n", " return([])\n", "\n", "\n", " \n", "\n", "\n", "ani = animation.FuncAnimation(fig, animate, frames=num_frames,\n", " interval=interval, blit=True, init_func=init)\n", "\n", "HTML(ani.to_html5_video())", "\n", "\n", "# If you get the \"KeyError: 'ffmpeg'\" error (as you will if you run this on Binder),\n", "# then your system does not have the ffmpeg video library installed.\n", "# You can get around this by using an alternative image library.\n", "# COMMENT OUT the line \"HTML(ani.to_html5_video())\" above, and UNCOMMENT the following lines:\n", "\n", "#from IPython.display import Image as DisplayImage\n", "#ani.save('./animation.gif', writer='imagemagick')\n", "#DisplayImage(url='./animation.gif')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Fun miscellaneous function to draw a single frame of the \n", "# circles animation; understanding this step and getting the\n", "# phase/amplitude of the circles correct is 90% of the work\n", "# for understanding how the full animation works\n", "def draw_circles(FT, t, num_circles=200):\n", " \n", " period = FT.period\n", " As = FT.amplitudes[0:num_circles]\n", " Zs = FT.phases[0:num_circles]\n", "\n", " t_vals = np.linspace(0,3000, 500)\n", " Xs = []\n", " Ys = []\n", " \n", " fig = plt.figure()\n", " ax = fig.add_subplot(1, 1, 1)\n", " \n", " x_offset = 0\n", " y_offset = 0\n", "\n", " col=\"#004785\"\n", " \n", " for i in range(0,num_circles):\n", " Hz = i+1\n", " a = As[i] # Magnitude (i.e., amplitude) of complex coefficient\n", " z = Zs[i] # Argument (i.e., phase) of complex coefficient\n", "\n", " plt.plot([x_offset], [y_offset], marker='o', markersize=10, color=col)\n", " circ = plt.Circle((x_offset, y_offset), radius=2*a, edgecolor='black',\n", " linewidth=2, facecolor='None')\n", " ax.add_patch(circ)\n", "\n", " x_offset += 2*a*np.cos(t*2*np.pi*Hz/period + z)\n", " y_offset += 2*a*np.sin(t*2*np.pi*Hz/period + z)\n", "\n", " Xs.append(x_offset)\n", " Ys.append(y_offset)\n", " plt.axis('equal')\n", " plt.show()\n", " return(fig)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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d3p+2AXo+o/zKcm3aI+EbPp1C2ldhmFph2bJl4ujoKIAMHz5cUlJScrW8KlWq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\nKCMog69QKBRlhP8H8VxwEhWgN5gAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f = draw_circles(xFT, 1400, num_circles=20)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.2" } }, "nbformat": 4, "nbformat_minor": 2 }