3D Transformations.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "980d99c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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1bqGDev0C728hLMVjAo9rsfG4Fo95H9OCjlFLkubPoQ9JapxBLUmNG3pQJ7kmyY4kXxv2vhZSkhVJbktyb5KvJ7l01DUNQpKnJ/lKkn/rjusvR13ToCRZluTuJJ8adS2DkmRrks1J7kmyZB5ZmeSoJDcm+UaSLUleNOqa9leSk7r/p6nXY0ne3Ne6wx6jTnI2sBP4WFWdPNSdLaAkxwLHVtVdSY4ANgGr9/b418UgSYDDqmpnkoOBO4BLq+rOEZe235K8BRgHnllVF4y6nkFIshUYr6oldVNIko8CX6qqq7o7op9RVY+OuKyB6R4f/RCwqqpmujnwKYbeo66qLwI/HPZ+FlpVfbeq7urePw5sYYanCi421bOzmzy4ey36M85JjgdeCVw16lq0d0mOBM4GrgaoqieWUkh3zgW+3U9Ig2PUA5FkJXAasHHEpQxEN0RwD7AD+FxVLYXjuhJ4G/DkiOsYtAI+m2RTkrWjLmZAngNMAh/uhqquSnLYqIsasAuBDf02Nqj3U5LDgZuAN1fVY6OuZxCqaldVnUrvSYlnJFnUQ1ZJLgB2VNWmUdcyBC+uqtOB84E3dkONi91y4HTgg1V1GvAjYMl8BWA3lPMq4J/7Xceg3g/dGO5NwHVV9YlR1zNo3cfN24DzRlzK/joLeFU3nns9cE6Sa0db0mBU1UPdvzuAm+l9I9Nitx3YPu2T3I30gnupOB+4q6q+3+8KBvU+6k66XQ1sqar3jrqeQUkyluSo7v2h9L4r8xsjLWo/VdU7q+r4qlpJ7yPnF6rqohGXtd+SHNadyKYbGng5sOivrqqq7wHbkpzUzToXWNQn6fewhnkMe0DvI8ZQJdkAvAQ4Osl24LKqunrY+10AZwGvBTZ347kAf1pVnx5dSQNxLPDR7qz0QcANVbVkLmdbYo4Bbu71GVgOfLyqbh1tSQNzCXBdN0xwP3DxiOsZiO4P6suAN8xrPW8hl6S2OfQhSY0zqCWpcQa1JDXOoJakxhnUktQ4g1qSGmdQS1Lj/g+R5DS2YaJYLQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "# Define the 3D cube vertices\n",
    "cube_vertices = np.array([\n",
    "    [-1, -1, -1],\n",
    "    [1, -1, -1],\n",
    "    [1, 1, -1],\n",
    "    [-1, 1, -1],\n",
    "    [-1, -1, 1],\n",
    "    [1, -1, 1],\n",
    "    [1, 1, 1],\n",
    "    [-1, 1, 1]\n",
    "])\n",
    "\n",
    "\n",
    "# Define the transformation matrices\n",
    "scaling_matrix = np.array([\n",
    "    [2, 0, 0],\n",
    "    [0, 2, 0],\n",
    "    [0, 0, 2]\n",
    "])\n",
    "\n",
    "rotation_matrix = np.array([\n",
    "    [np.cos(np.pi/4), -np.sin(np.pi/4), 0],\n",
    "    [np.sin(np.pi/4), np.cos(np.pi/4), 0],\n",
    "    [0, 0, 1]\n",
    "])\n",
    "\n",
    "translation_matrix = np.array([\n",
    "    [1, 0, 0, 4],\n",
    "    [0, 1, 0, 3],\n",
    "    [0, 0, 1, 1],\n",
    "    [0, 0, 0, 1]\n",
    "])\n",
    "\n",
    "# Apply the transformations to the cube vertices\n",
    "transformed_cube_vertices = cube_vertices.dot(scaling_matrix).dot(rotation_matrix) + translation_matrix[:3,3]\n",
    "\n",
    "# Perform parallel projection\n",
    "parallel_projection_matrix = np.array([\n",
    "    [1, 0, 0],\n",
    "    [0, 1, 0]\n",
    "])\n",
    "projected_cube_vertices = transformed_cube_vertices[:, :2].dot(parallel_projection_matrix)\n",
    "\n",
    "# Perform perspective projection\n",
    "focal_length = 5\n",
    "perspective_projection_matrix = np.array([\n",
    "    [focal_length, 0, 0],\n",
    "    [0, focal_length, 0]\n",
    "])\n",
    "projected_cube_vertices_perspective = transformed_cube_vertices[:, :2].dot(perspective_projection_matrix) / transformed_cube_vertices[:, 2:]\n",
    "\n",
    "# Plot the original and transformed 3D cube\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "ax.scatter(cube_vertices[:, 0], cube_vertices[:, 1], cube_vertices[:, 2], color='blue')\n",
    "ax.scatter(transformed_cube_vertices[:, 0], transformed_cube_vertices[:, 1], transformed_cube_vertices[:, 2], color='red')\n",
    "plt.show()\n",
    "\n",
    "# Plot the parallel projection\n",
    "plt.scatter(projected_cube_vertices[:, 0], projected_cube_vertices[:, 1])\n",
    "plt.title('Parallel Projection')\n",
    "plt.show()\n",
    "\n",
    "# Plot the perspective projection\n",
    "plt.scatter(projected_cube_vertices_perspective[:, 0], projected_cube_vertices_perspective[:, 1])\n",
    "plt.title('Perspective Projection')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "df7b7010",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Perspective projection is a technique used \n",
    "#to create the illusion of depth and three-dimensionality in a two-dimensional image or screen.\n",
    "\n",
    "\n",
    "#Parallel projection is a type of projection in which all the projection lines are parallel to each other. \n",
    "#In this type of projection, the object is projected onto a plane that is parallel to the viewing plane."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "874ab76c",
   "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": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}