Unit_Circle.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "afd5bc26",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.patches as mpatches\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "#import seaborn as sns\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56b06fe2",
   "metadata": {},
   "source": [
    "The definition for the circle on a phase plot is $ x^2 + y^2 = 1 $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f8b7f6a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8574984e80>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create a figure and axes\n",
    "x_limits = (-1.1, 1.1)\n",
    "y_limits = (-1.1, 1.1)\n",
    "\n",
    "fig = plt.figure(figsize=(10,10))\n",
    "ax1 = plt.subplot(1,1,1)\n",
    "ax1.set_xlim(x_limits)\n",
    "ax1.set_ylim(y_limits)\n",
    "ax1.set_xlabel('Cosine')\n",
    "ax1.set_ylabel('Sine')\n",
    "\n",
    "circle_origin = (0,0)\n",
    "circle_radius = 1\n",
    "\n",
    "circle = plt.Circle( circle_origin, circle_radius, fill = False, color = \"gray\" )\n",
    "ax1.set_aspect( 1 ) # force circle despite plot size\n",
    "ax1.add_artist( circle )\n",
    "\n",
    "arc = mpatches.Arc([0, 0], 0.5, 0.5, 0, theta1=0, theta2=180, lw=3, edgecolor=\"grey\")\n",
    "plt.gca().add_patch(arc)\n",
    "\n",
    "# These are to be updated\n",
    "txt_title = ax1.set_title('')\n",
    "cos_line, = ax1.plot([], [], label='x', color=\"red\", lw=3)\n",
    "sin_line, = ax1.plot([], [], label='y', color=\"blue\", lw=3)\n",
    "radius_line, = ax1.plot([], [], label='r', color=\"green\", lw=3)\n",
    "_, = ax1.plot([],[], color=\"grey\", lw=3) #This needs to be defined so the arc has a legend\n",
    "point, = ax1.plot([], [], 'g.', ms=2)\n",
    "\n",
    "ax1.legend(['x','y', 'radius', 'theta']);\n",
    "\n",
    "ax1.plot([x_limits[0],x_limits[1]], [0,0], color=\"grey\", lw=1)\n",
    "ax1.plot([0,0], [y_limits[0],y_limits[1]], color=\"grey\", lw=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0ec39b3",
   "metadata": {},
   "source": [
    "$ \\sin \\theta = \\frac{y}{r} $"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92c705d5",
   "metadata": {},
   "source": [
    "$ \\cos \\theta = \\frac{x}{r} $\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "395e7ed8",
   "metadata": {},
   "source": [
    "It seems there's no nice way to do find the inverse sine and cosine methods.\n",
    "https://math.stackexchange.com/questions/1160996/how-to-find-the-inverse-cosine-without-a-calculator?rq=1\n",
    "\n",
    "This will need to use the numpy definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5ee8ef8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def drawframe(n, *fargs):\n",
    "    theta = n\n",
    "    radians = np.deg2rad(theta)\n",
    "    pt_x = np.cos(radians)\n",
    "    pt_y = np.sin(radians)\n",
    "    \n",
    "    sin_line.set_data([pt_x, pt_x], [0, pt_y])\n",
    "    cos_line.set_data([pt_x, 0], [pt_y, pt_y])\n",
    "    radius_line.set_data([0, pt_x], [0, pt_y])\n",
    "    \n",
    "    arc.theta2 = theta\n",
    "    \n",
    "    point.set_data(pt_x,pt_y)\n",
    "    txt_title.set_text('radius = {0} \\n x = {1:.3f} \\n y = {2:.3f} \\n theta = {3} \\n radians = {4:.3f}'.format(1,pt_x,pt_y,theta, radians))\n",
    "    return (cos_line, sin_line)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8d7b47bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "# blit=True re-draws only the parts that have changed.\n",
    "anim = animation.FuncAnimation(fig, drawframe, frames=360, interval=100, blit=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "69c99bbb",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ffmpeg version 4.2.4-1ubuntu0.1 Copyright (c) 2000-2020 the FFmpeg developers\n",
      "  built with gcc 9 (Ubuntu 9.3.0-10ubuntu2)\n",
      "  configuration: --prefix=/usr --extra-version=1ubuntu0.1 --toolchain=hardened --libdir=/usr/lib/x86_64-linux-gnu --incdir=/usr/include/x86_64-linux-gnu --arch=amd64 --enable-gpl --disable-stripping --enable-avresample --disable-filter=resample --enable-avisynth --enable-gnutls --enable-ladspa --enable-libaom --enable-libass --enable-libbluray --enable-libbs2b --enable-libcaca --enable-libcdio --enable-libcodec2 --enable-libflite --enable-libfontconfig --enable-libfreetype --enable-libfribidi --enable-libgme --enable-libgsm --enable-libjack --enable-libmp3lame --enable-libmysofa --enable-libopenjpeg --enable-libopenmpt --enable-libopus --enable-libpulse --enable-librsvg --enable-librubberband --enable-libshine --enable-libsnappy --enable-libsoxr --enable-libspeex --enable-libssh --enable-libtheora --enable-libtwolame --enable-libvidstab --enable-libvorbis --enable-libvpx --enable-libwavpack --enable-libwebp --enable-libx265 --enable-libxml2 --enable-libxvid --enable-libzmq --enable-libzvbi --enable-lv2 --enable-omx --enable-openal --enable-opencl --enable-opengl --enable-sdl2 --enable-libdc1394 --enable-libdrm --enable-libiec61883 --enable-nvenc --enable-chromaprint --enable-frei0r --enable-libx264 --enable-shared\n",
      "  libavutil      56. 31.100 / 56. 31.100\n",
      "  libavcodec     58. 54.100 / 58. 54.100\n",
      "  libavformat    58. 29.100 / 58. 29.100\n",
      "  libavdevice    58.  8.100 / 58.  8.100\n",
      "  libavfilter     7. 57.100 /  7. 57.100\n",
      "  libavresample   4.  0.  0 /  4.  0.  0\n",
      "  libswscale      5.  5.100 /  5.  5.100\n",
      "  libswresample   3.  5.100 /  3.  5.100\n",
      "  libpostproc    55.  5.100 / 55.  5.100\n",
      "Input #0, mov,mp4,m4a,3gp,3g2,mj2, from 'unitCircle.mp4':\n",
      "  Metadata:\n",
      "    major_brand     : isom\n",
      "    minor_version   : 512\n",
      "    compatible_brands: isomiso2avc1mp41\n",
      "    encoder         : Lavf58.29.100\n",
      "  Duration: 00:00:06.00, start: 0.000000, bitrate: 276 kb/s\n",
      "    Stream #0:0(und): Video: h264 (High) (avc1 / 0x31637661), yuv420p, 720x720, 269 kb/s, 60 fps, 60 tbr, 15360 tbn, 120 tbc (default)\n",
      "    Metadata:\n",
      "      handler_name    : VideoHandler\n",
      "Stream mapping:\n",
      "  Stream #0:0 -> #0:0 (h264 (native) -> gif (native))\n",
      "Press [q] to stop, [?] for help\n",
      "[swscaler @ 0x55cecb32c900] No accelerated colorspace conversion found from yuv420p to bgr8.\n",
      "Output #0, gif, to 'unitCircle.gif':\n",
      "  Metadata:\n",
      "    major_brand     : isom\n",
      "    minor_version   : 512\n",
      "    compatible_brands: isomiso2avc1mp41\n",
      "    encoder         : Lavf58.29.100\n",
      "    Stream #0:0(und): Video: gif, bgr8, 720x720, q=2-31, 200 kb/s, 60 fps, 100 tbn, 60 tbc (default)\n",
      "    Metadata:\n",
      "      handler_name    : VideoHandler\n",
      "      encoder         : Lavc58.54.100 gif\n",
      "frame=  360 fps=308 q=-0.0 Lsize=    1379kB time=00:00:05.99 bitrate=1885.3kbits/s speed=5.12x    \n",
      "video:1379kB audio:0kB subtitle:0kB other streams:0kB global headers:0kB muxing overhead: 0.001417%\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "CompletedProcess(args=['ffmpeg', '-i', 'unitCircle.mp4', 'unitCircle.gif'], returncode=0)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import HTML \n",
    "import subprocess\n",
    "writervideo = animation.FFMpegWriter(fps=60)\n",
    "anim.save('unitCircle.mp4', writer=writervideo)\n",
    "\n",
    "subprocess.run([\"ffmpeg\", \"-i\", \"unitCircle.mp4\", \"unitCircle.gif\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6506ea77",
   "metadata": {},
   "source": [
    "![gif of output unit circle](unitCircle.gif)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3fb323e5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}