Linear Mapping Animation

LinMapping.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ipywidgets import interact\n",
    "import ipywidgets as widgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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     "data": {
      "text/plain": [
       "(array([[2, 0],\n",
       "        [0, 0]]), 0.0)"
      ]
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     "execution_count": 3,
     "metadata": {},
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   "source": [
    "A = 1/5*np.array([\n",
    "    [3, 4],\n",
    "    [-4, 3]\n",
    "])\n",
    "A, np.linalg.det(A)\n",
    "B = lambda a: np.array([\n",
    "    [np.cos(a), -np.sin(a)],\n",
    "    [np.sin(a), np.cos(a)]\n",
    "])\n",
    "B(np.pi), np.linalg.det(B(np.pi))\n",
    "C = np.array([\n",
    "    [0, 1],\n",
    "    [1, 0]\n",
    "])\n",
    "C, np.linalg.det(C)\n",
    "D = np.array([\n",
    "    [2, 0],\n",
    "    [0, 0]\n",
    "])\n",
    "D, np.linalg.det(D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10+1\n",
    "a = -100\n",
    "b = 100\n",
    "space = np.linspace(a, b, N)\n",
    "x, y = np.meshgrid(space, space)\n",
    "color = np.linspace(0, 1, N*N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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     "data": {
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       "model_id": "42558b776e734919a7e70b5808edbb03",
       "version_major": 2,
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      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='w', max=1.0, step=0.01), Output()), _dom_classes=('w…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact(w=(0, 1, 0.01))\n",
    "def draw(w):\n",
    "    M = (1-w)*np.eye(2) + w*C\n",
    "    \n",
    "    x2, y2 = M.dot([x.flatten(), y.flatten()])\n",
    "    x2, y2 = x2.reshape((N,N)), y2.reshape((N,N))\n",
    "\n",
    "    plt.figure(figsize=(20, 10))\n",
    "    plt.ylim((3*a, 3*b))\n",
    "    plt.xlim((3*a, 3*b))\n",
    "    plt.gca().set_aspect('equal', adjustable='box')\n",
    "    plt.scatter(x, y, c=color, alpha=0.8)\n",
    "    plt.scatter(x2, y2, c=color, alpha=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "i = 0\n",
    "for w in np.linspace(0, 1, 100+1):\n",
    "    draw(w)\n",
    "    plt.savefig('data/anim_' + str(i) + '.png')\n",
    "    plt.close('all')\n",
    "    i+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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