benjaminrose/sep.mask_ellipse vs matplotlib ellipse.ipynb

## sep.mask_ellipse vs matplotlib ellipse.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# mask_ellipse vs patches\n",
    "\n",
    "At first study, it looks like `sep`'s `mask_ellipse` does not produce an object the same size as `matplotlib`'s `patches`. \n",
    "\n",
    "I am going to test them both with a \"standard\" ($r = 1$) ellipse then I will use the scaling as is done in the data analsysis using `sep` and its parent `Source Extractor`.\n",
    "\n",
    "## A Standard Ellipse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Ellipse\n",
    "%matplotlib inline\n",
    "\n",
    "from sep import mask_ellipse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = 11\n",
    "y = 8\n",
    "a = 5\n",
    "b = 7\n",
    "theta = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mask = np.zeros((20,20), dtype=np.bool)\n",
    "mask_ellipse(mask, x, y, a, b, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.Ellipse at 0x109d8a278>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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a8o+4CAk/J6aF36bPIFnn9RbAjwrCBBzhclF47l+/iOUwYDCEkStH5ZzL4gArlmEtLBJ+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\n4QtRQyR8IWrI/wOxDyGkJT5UlQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109d7d780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure('testing mask')\n",
    "plt.imshow(mask, origin='lower')\n",
    "\n",
    "e = Ellipse((x,y), a, b, theta*180/3.1415)\n",
    "e.set_facecolor([1,.733333333,0])\n",
    "e.set_alpha(0.25)\n",
    "plt.gca().add_patch(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see that `patches` is smaller then `sep`. When looking at the documentation of `sep` and `Source Extractor` it is seen that $(a,b)$ are radii, where as with `patches` it expects a [diameter.](http://matplotlib.org/api/patches_api.html?highlight=ellipse#matplotlib.patches.Ellipse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.Ellipse at 0x109d7d550>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WbpRPxTzZBpHwy52I7b3XMCyN/k6LsvHmZVDhl4zJET97Lh3ZHAKGeLj4hNjU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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109db2a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure('testing mask - 2x patch')\n",
    "plt.imshow(mask, origin='lower')\n",
    "\n",
    "e = Ellipse((x,y), 2*a, 2*b, theta*180/3.1415)\n",
    "e.set_facecolor([1,.733333333,0])\n",
    "e.set_alpha(0.25)\n",
    "plt.gca().add_patch(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It works when we understand the APIs. But what about if we need a scalled ellipse, aka $r \\neq 1$?\n",
    "\n",
    "## A Scalled Ellipse\n",
    "\n",
    "Looking at a standard (skip rotatoin here) ellipse, it is defined as:\n",
    "$$\\dfrac{x^2}{a^2} + \\dfrac{y^2}{b^2} = 1^2 $$\n",
    "then scalling it, you get:\n",
    "$$\\dfrac{x^2}{a_s^2} + \\dfrac{y^2}{b_s^2} = r^2 ~ ~ ~.$$\n",
    "You can relate $a$ to $a_s$ by deviding both sides by $r^2$ and now \n",
    "$$ a = a_s \\times r ~ ~ ~. $$\n",
    "\n",
    "Lets also change our box a bit to increase understanding. Lets make a quarter ellipse 3 units wide and 6 units tall. But scalled by 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = 0\n",
    "y = 0\n",
    "a = 1\n",
    "b = 2\n",
    "theta = 0\n",
    "r = 3\n",
    "\n",
    "mask2 = np.zeros((10,7), dtype=np.bool)\n",
    "mask_ellipse(mask2, x, y, a, b, theta, r=r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# convert a, b to what matplotlib wants\n",
    "e_a = 2*r*a\n",
    "e_b = 2*r*b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.Ellipse at 0x10c6b2518>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c6c67f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure('scale test')\n",
    "plt.imshow(mask2, origin='lower')\n",
    "\n",
    "e = Ellipse((x,y), e_a, e_b, theta*180/3.1415)\n",
    "e.set_facecolor([1,.733333333,0])\n",
    "e.set_alpha(0.25)\n",
    "plt.gca().add_patch(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It all worked! The conversion to what `matplotlib` expects is the most \"challenging\" part and that is not hard but rather shows that you understand what the APIs expect."
   ]
  }
 ],
 "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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}