Compute bounding box for an ellipse.

ellipse_bounding_box.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "from matplotlib.patches import Ellipse\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import ipywidgets as widgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_ellipse_bb(x, y, major, minor, angle_deg):\n",
    "    \"\"\"\n",
    "    Compute tight ellipse bounding box.\n",
    "    \n",
    "    see https://stackoverflow.com/questions/87734/how-do-you-calculate-the-axis-aligned-bounding-box-of-an-ellipse#88020\n",
    "    \"\"\"\n",
    "    t = np.arctan(-minor / 2 * np.tan(np.radians(angle_deg)) / (major / 2))\n",
    "    [max_x, min_x] = [x + major / 2 * np.cos(t) * np.cos(np.radians(angle_deg)) -\n",
    "                      minor / 2 * np.sin(t) * np.sin(np.radians(angle_deg)) for t in (t, t + np.pi)]\n",
    "    t = np.arctan(minor / 2 * 1. / np.tan(np.radians(angle_deg)) / (major / 2))\n",
    "    [max_y, min_y] = [y + minor / 2 * np.sin(t) * np.cos(np.radians(angle_deg)) +\n",
    "                      major / 2 * np.cos(t) * np.sin(np.radians(angle_deg)) for t in (t, t + np.pi)]\n",
    "    return min_x, min_y, max_x, max_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_ellipse(x=50, y=50, major=30, minor=10, angle_deg=45):\n",
    "    plt.figure(2)\n",
    "    plt.clf()\n",
    "    ax = plt.gca()\n",
    "    ax.add_patch(Ellipse((x, y), major, minor, -angle_deg, \n",
    "                             edgecolor='r',\n",
    "                             facecolor='none'))\n",
    "    min_x, min_y, max_x, max_y = get_ellipse_bb(x, y, major, minor, angle_deg)\n",
    "    plt.vlines([max_x, min_x], 0, 100)\n",
    "    plt.hlines([max_y, min_y], 0, 100)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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   "source": [
    "plot_ellipse()"
   ]
  },
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   "cell_type": "code",
   "execution_count": 9,
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   "outputs": [
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    "interactive_plot = interactive(plot_ellipse, \n",
    "                               x=fixed(50), \n",
    "                               y=fixed(50),\n",
    "                               major=(0, 40),\n",
    "                               minor=(0, 40),\n",
    "                               angle_deg=(-180, 180),\n",
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