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@leggitta
Created February 8, 2017 19:12
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Generates a two dimensional polynomial, centered in the image space"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# define the width and height of our space\n",
"w, h = 64, 64"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# generate a grid of x and y coordinates\n",
"x = np.repeat(np.arange(w), h)\n",
"y = np.tile(np.arange(h), w)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# define the linear coefficients for a 2D polynomial,\n",
"# centered in the image\n",
"beta = [(w / 2) * (h / 2), -2 * (w / 2), -2 * (h / 2), 0, 1, 1]\n",
"\n",
"# generate the image\n",
"z = beta[0] + beta[1] * x + beta[1] * y + beta[3] * x * y + beta[4] * x**2 + beta[5] * y**2\n",
"z = z.reshape((w, h))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x10e7bf828>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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J5XtFJKJYzlPLQFhUv4APH9NrY2ROwGXglyEbAo7plVcxwLsEvkesdLkd54cMVHLjvYJf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\nHYB/sIPdhvZ/bFOxvE/cY6gAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1037b7668>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# show the image\n",
"plt.imshow(z)"
]
}
],
"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": "3.5.2"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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