math/manim-walkthrough.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Manim Walkthrough\n",
    "\n",
    "_This is just a simple walk through on how to write you manim scenes_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup in Jupyter Notebook\n",
    "\n",
    "To be able to use the jupyter-manim `%%manim` cell magic, you must first `import jupyer_manim`.\n",
    "\n",
    "_**Note:** All code inside a cell with the `%%manim` cell magic will be run in it's own process, so you must include everything including applicable imports in that cell. The second paramater to `%%manim` is the class you wish to load. Said class should extend the manim Scene class from `manimlib.imports`._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "import jupyter_manim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create a Shape\n",
    "\n",
    "Create a blue circle, and Transform it into a yellow square:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <video\n",
       "      width=\"854\"\n",
       "      height=\"480\"\n",
       "      autoplay=\"autoplay\"\n",
       "      controls\n",
       "    >\n",
       "        <source src=\"data:video/mp4;base64,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\" type=\"video/mp4\">\n",
       "    </video>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%manim Shapes --base64\n",
    "from manimlib.imports import *\n",
    "\n",
    "class Shapes(Scene):\n",
    "    def construct(self):\n",
    "        circle = Circle(fill_color=BLUE, color=BLUE, fill_opacity=0.9)\n",
    "        square = Square(fill_color=YELLOW, color=YELLOW, fill_opacity=0.9)\n",
    "        self.play(Transform(circle, square))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create some Tex\n",
    "\n",
    "Now, create a TeX expression... ***todo***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Morph Shapes/Tex\n",
    "\n",
    "***todo***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simplify Complex Scenes\n",
    "\n",
    "As your scenes grow, the code can become a little messy. You might wish to move code into other functions or classes, or make complex shapes by extending the existing manim shapes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Complex Shape example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# todo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graph\n",
    "\n",
    "References: \n",
    "- <https://github.com/malhotra5/Manim-Tutorial/blob/master/code/graphing.py>\n",
    "- <https://mathieularose.com/function-composition-in-python/>\n",
    "\n",
    "_Something I noticed: When using `Transform(a, b)`, `a` needs to remain the original thing that was Transformed to begin with._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <video\n",
       "      width=\"854\"\n",
       "      height=\"480\"\n",
       "      autoplay=\"autoplay\"\n",
       "      controls\n",
       "    >\n",
       "        <source src=\"media/videos/tmp1v17ul_w/1440p60/Graph.mp4\" type=\"video/mp4\">\n",
       "    </video>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%manim Graph\n",
    "from manimlib.imports import *\n",
    "import functools\n",
    "\n",
    "# A helper function for recursive function composition\n",
    "# See: https://mathieularose.com/function-composition-in-python/\n",
    "def compose(*functions): \n",
    "    return functools.reduce(lambda f, g: lambda x: f(g(x)), functions, lambda x: x)\n",
    "\n",
    "def f(x): return x**2 # basic quadratic\n",
    "def g(x): return x**3 # basic cubic\n",
    "def h(x): return x**6 # Using this to show g(f(x)) = f(g(x))\n",
    "\n",
    "class Graph(GraphScene):\n",
    "    CONFIG = {\n",
    "        \"x_min\": -5,\n",
    "        \"x_max\": 5,\n",
    "        \"y_min\": -4,\n",
    "        \"y_max\": 4,\n",
    "        \"graph_origin\": ORIGIN,\n",
    "        \"function_color\": WHITE,\n",
    "        \"axes_color\": GRAY\n",
    "    }\n",
    "    \n",
    "    def construct(self):\n",
    "        self.setup_axes(animate=True)\n",
    "        self.play()\n",
    "        \n",
    "        # Draw f(x)\n",
    "        f_graph = self.get_graph(f,RED)\n",
    "        f_label = self.get_graph_label(f_graph, label = \"f(x) = x^{2}\")\n",
    "        self.play(ShowCreation(f_graph), Write(f_label))\n",
    "        self.wait()\n",
    "        \n",
    "        # Draw g(x)\n",
    "        g_graph = self.get_graph(g,GREEN)\n",
    "        g_label = self.get_graph_label(g_graph, label = \"g(x) = x^{3}\")\n",
    "        self.play(Transform(f_graph,g_graph), Transform(f_label, g_label))\n",
    "        self.wait()\n",
    "        \n",
    "        # Draw g(f(x)) or g o f\n",
    "        gof_graph = self.get_graph(compose(g, f),BLUE)\n",
    "        gof_label = self.get_graph_label(gof_graph, label = \"g \\circ f(x) = (x^{2})^{3} = x^{6}\")\n",
    "        self.play(Transform(f_graph, gof_graph), Transform(f_label,gof_label))\n",
    "        self.wait()\n",
    "        \n",
    "        # Draw f(g(x)) or f o g\n",
    "        fog_graph = self.get_graph(compose(f, g),YELLOW)\n",
    "        fog_label = self.get_graph_label(fog_graph, label = \"f \\circ g(x) = (x^{3})^{2} = x^{6}\")\n",
    "        self.play(Transform(f_graph,fog_graph), Transform(f_label,fog_label))\n",
    "        self.wait()\n",
    "        \n",
    "        # Draw h(x)\n",
    "        h_graph = self.get_graph(h,PINK)\n",
    "        h_label = self.get_graph_label(h_graph, label = \"h(x) = x^{6}\")\n",
    "        self.play(Transform(f_graph,h_graph), Transform(f_label,h_label))\n",
    "        self.wait()\n",
    "        \n",
    "\n",
    "        "
   ]
  },
  {
   "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": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}