class3-ex2-2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex. 2-2)  2D Transformations\n",
    "Let's learn geometric transformations by matrix multiplications. Implement a function that simulate the following code \n",
    "```\n",
    "img_rot = img.rotate(45)\n",
    "```\n",
    "\n",
    "| Original  | Rotated | \n",
    "| ---- | ---- | \n",
    "|<img src=\"fig/triangle.png\" style=\"width:200px\"> | <img src=\"fig/rotated.png\" style=\"width:200px\"> |\n",
    "\n",
    "Try to remove jaggy edges if possible.\n",
    "\n",
    "### Type your code below.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=320x200 at 0x10B557D60>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from PIL import Image\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "in_img_path = \"in/triangle.png\"\n",
    "img = Image.open(in_img_path)\n",
    "img.rotate(30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rotate_img(pix, angle):\n",
    "    mat = [[np.cos(angle*np.pi()/180), -np.sin(angle*np.pi()/180)], [np.sin(angle*np.pi()/180), np.cos(angle*np.pi()/180)]]\n",
    "    \n",
    "                                                                                                    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from PIL import Image\n",
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "in_img_path = \"in/triangle.png\"\n",
    "img = Image.open(in_img_path)\n",
    "img_rot = img.rotate(45)\n",
    "\n",
    "img_rot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pix = np.asarray(img)\n",
    "rotated = np.copy(pix)\n",
    "rotated.fill(0)\n",
    "\n",
    "tx = pix.shape[0]/2 # image center of the target image\n",
    "ty = pix.shape[1]/2\n",
    "\n",
    "cx = pix.shape[0]/2 # image center of the original image\n",
    "cy = pix.shape[1]/2\n",
    "\n",
    "angle = 45 # rorating angle\n",
    "angle = -math.radians(angle)\n",
    "r = [[round(math.cos(angle), 15), round(-math.sin(angle), 15)],\n",
    "     [round(math.sin(angle), 15), round(math.cos(angle), 15)]]\n",
    "\n",
    "for x in range(0,pix.shape[0]):\n",
    "    for y in range(0,pix.shape[1]):\n",
    "        v = [(x - tx),(y-ty)]\n",
    "        p = np.matmul(r, v)\n",
    "        x_ = p[0]+ cx\n",
    "        y_ = p[1]+ cy\n",
    "        if x_ > 0 and y_ > 0 and x_ < pix.shape[0] and y_ < pix.shape[1]: # if it is whithin the origina image size\n",
    "            rotated[x][y] = pix[int(x_)][int(y_)] # here you might want to replace it to bilinear or better interpolation\n",
    "       \n",
    "res = Image.fromarray(np.uint8(rotated))\n",
    "res.save(\"rotated.png\")\n",
    "plt.imshow(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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